Ion clustering in aqueous solutions probedwith vibrational energy transferHongtao Biana, Xiewen Wena, Jiebo Lia, Hailong Chena, Suzee Hana, Xiuquan Sunb, Jian Songb,Wei Zhuangb, and Junrong Zhenga,1

a Department of Chemistry, Rice University, Houston, TX 77005; and bState Key Laboratory of Molecular Reaction Dynamics,Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, People’s Republic of China

Edited* by Robert F. Curl, Rice University, Houston, TX, and approved February 4, 2011 (received for review January 3, 2011)

Despite prolonged scientific efforts to unravel the hydration struc-tures of ions in water, many open questions remain, in particularconcerning the existences and structures of ion clusters in 1∶1strong electrolyte aqueous solutions. A combined ultrafast 2D IRand pump/probe study through vibrational energy transfersdirectly observes ion clustering in aqueous solutions of LiSCN,NaSCN, KSCN and CsSCN. In a near saturated KSCN aqueous solu-tion (water/KSCNmolar ratio ¼ 2.4∕1), 95% of the anions form ionclusters. Diluting the solution results in fewer, smaller, and tighterclusters. Cations have significant effects on cluster formation. Asmall cation results in smaller and fewer clusters. The vibrationalenergy transfer method holds promise for studying a wide varietyof other fast short-range molecular interactions.

The solution properties of ions in water are relevant to a widerange of systems, including electrochemistry, biological envir-

onments, and atmospheric aerosols (1, 2). For more than 100 yr,tremendous scientific efforts have been devoted to unravel thehydration structures of ions in water (1–11). However, manyfundamental questions remain open, in particular concerningthe existence, concentration, and structure of ion clusters in 1∶1strong electrolyte aqueous solutions. Whether strong 1∶1 electro-lytes (especially salts of Naþ and Kþ) form ion pairs or clusters inwater has been considered a key issue for understanding manyimportant problems, e.g., the excess ionic activity in 1∶1 electro-lytes (12), ion dependent conformational and binding equilibriaof nucleic acids (13), the concentration difference between Naþand Kþ in living cells, protein denaturation by salts (14, 15), andion concentration dependent properties of ion channels (16).

The properties of aqueous solutions of 1∶1 strong electrolytesdeviate from the ideal dilute solution at extremely low concentra-tions (<10−5 M). The deviations were generally believed to becaused by the attraction between ions of opposite charge andthe repulsion of ions of the same charge, leading to the develop-ment of the Debye-Hückel theory (17, 18). However, this theorybegins to fail at a very low concentration (∼10−3 M), as the as-sumptions upon which the theory was based become invalid. Theformation of ion pairs containing two ions of opposite charge hasbeen proposed to be primarily responsible for this failure (1, 2).Recently, calculations from molecular dynamics (MD) simula-tions, suggested that, clusters with more than one ion of the samecharge which are traditionally viewed as unlikely, could be a ma-jor factor contributing to the nonideality of solutions at mediumor high concentrations (12, 19). However, these predicted ionclusters cannot be investigated by the usual tools for probingmolecular structures and particle sizes in liquids, e.g., X-ray orneutron diffraction (20), or the dynamic light scattering (19, 21),because the contribution of ion-ion correlations to the total scat-tering pattern is too small compared to the contributions fromwater-water and water-ion interactions (19). In addition, the clus-ters are expected to be small, containing only a few ions whichexchange rapidly with ions in the water phase (12).

In this work, by monitoring intermolecular mode-specific reso-nant and nonresonant vibrational energy transfers (22–25) usingultrafast 2D IR and pump/probe techniques, we were able to di-

rectly probe ion clustering in a series of 1∶1 strong electrolyte(LiSCN, NaSCN, KSCN and CsSCN) aqueous solutions. Weobtained through these experiments clear evidence that a signif-icant portion of the ions form clusters in unsaturated solutions. Inhighly concentrated solutions, almost all anions (>90%) form ionclusters, suggesting water/ion microphase separations. In otherwords, in an apparent “homogeneous” SCN− aqueous solution,both clustered and water-solvated anions simultaneously exist, asillustrated in Fig.. 1A. Even at a medium concentration (1M) witha salt/water molar ratio only 1∶50, ∼27% of anions are clusteredunder the ambient condition. As expected, diluting the solutionshifts the dissolution equilibrium to fewer and smaller clusters,but, surprisingly, dilution makes the clusters tighter. The ionclustering is cation-size-dependent with smaller cations tendingto form smaller and fewer clusters.

Results and DiscussionAnions in a Cluster Can Exchange Vibrational Energy.We first describethe vibrational energy transfer method for studying ion clusteringin a concentrated KSCN solution, and then present the concen-tration and cation dependent results. Fig. 1B is the FTIR spec-trum of the CN and 13C15N− stretches of SCN− and S13C15N− in a1∶1 KSCN∕KS13C15N mixed aqueous (D2O) solution with asalt/water molar ratio 1∕2.4 (10M, which we name as solutionC). The isotope labeling shifts the CN stretch frequency from2;064 cm−1 (SCN−) down to 1;991 cm−1 (S13C15N−). Theoreticalpredictions for other concentrated or melt electrolyte solutions(26, 27), suggest that the probability of forming contact clustersof the general formula KnðSCNÞmðS13C15NÞp is statistically veryhigh in solution C. In these clusters, the anions SCN− andS13C15N− can be considered as “ligands” to the cation Kþ. Theanions thus held in close proximity can exchange vibrational en-ergy through their overlapped orbitals or via dipole-dipole inter-actions, in a manner similar to that observed for metal carbonylcompounds (28). Vibrational energy exchange between SCN− andS13C15N− in the clusters can be monitored with fast 2D IR meth-ods (Fig.. 1C, here the solution is C, i.e., 10M). From these 2D IRmeasurements, not only the vibrational energy exchange rates,but also the cluster concentration and the exchange dynamics be-tween clustered and separated anions can be obtained.

The intermolecular mode-specific vibrational energy transfer2D IR technique has been previously described in detail (22,23). Very briefly, energy exchange 2D IR measurements allowthe energy exchange between the CN and 13C15N stretches ofSCN− and S13C15N− to be followed in real time through the

Author contributions: J.Z. designed research; H.B., X.W., J.L., S.H., and J.Z. performedresearch; X.S., J.S., W.Z. did MD simulations; H.B., X.W., J.L., H.C., and J.Z. contributednew reagents/analytic tools; H.B., X.W., H.C., and J.Z. analyzed data; and J.Z. wrotethe paper.

The authors declare no conflict of interest.

*This Direct Submission article had a prearranged editor.1To whom correspondence should be addressed. E-mail: junrong@rice.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1019565108/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1019565108 PNAS ∣ March 22, 2011 ∣ vol. 108 ∣ no. 12 ∣ 4737–4742

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growth of the two cross peak pairs (Peaks 5 ∼ 8) as marked in the50-ps row of Fig.. 1C (for the 10M solution named C). The anionswhich have not exchanged their energy (including anions whichhave exchanged but received energy from reverse transfers andthe resonance acceptors of the same isotope) produce the twodiagonal peak pairs (Peaks 1 ∼ 4). Now we consider all six wait-ing-time (Tw) dependent 2D IR spectra of solution C at roomtemperature. The 200-fs row corresponds to a very short Tw,at which negligible vibrational energy exchange has occurred.During the Tw period, the initial and final energy carriers inthe sample are unchanged. Therefore, the ωpump (the excitationalfrequency) and ωprobe (the detected frequency) values of each redpeak (the 0–1 CN or 13C15N stretch transition) are identical, andthe peaks appear only on the diagonal. The two blue peaks 2 and4 are the 1-2 transitions, which shift to lower frequencies alongthe ωprobe axis because of vibrational anharmonicity. Peaks 1 and2 represent SCN− and Peaks 3 and 4 are for S13C15N−. With theincrease of probe delay time (Tw ¼ 200 fs ∼ 20 ps), vibrationalenergy begins to flow between the two anions. Cross peak pairsbegin to grow. After a long reaction period (Tw ¼ 50 ps), vibra-tional energy has exchanged to a substantial degree as shownby the additional peaks (Peaks 5 ∼ 8) that have appeared onthe off-diagonal. These new peaks arise from the vibrationalenergy exchange. The vibrational energy transfer from SCN−

to S13C15N− produces peaks 5 and 6 at positions with ωpump ¼2;064 cm−1 and ωprobe ¼ 1;991 cm−1 and 1;966 cm−1. ωpump ¼2;064 cm−1 is the 0–1 transition frequency of the CN stretch, re-presenting the vibrational energy is originally from SCN−.ωprobe ¼ 1;991 cm−1 and 1;966 cm−1 are the 0–1 and 1–2 transi-tion frequencies of the 13C15N− stretch, respectively, representingthat at the end of Tw the vibrational energy has transferred toS13C15N−. Likewise, peaks 7 and 8 are produced by energy trans-fer from S13C15N− to SCN−.

In contrast to the chemical exchange 2D IR methods (29–33),the cross peak intensities in the energy exchange method arenot equal. The ratio of the cross peaks’ growth rates is deter-mined by the Boltzmann distribution. The energy mismatch be-tween the CN and 13C15N stretches is 2;064-1;991 ¼ 73 cm−1,making the energy up-pumping rate constant from S13C15N−

to SCN− ∼70% of the down-flowing rate constant from SCN−

to S13C15N−. As in Fig.. 1C, Peaks 5 and 6 are always bigger thanPeaks 7 and 8 at the same Tws. In solution C, some anions areclustered and can transfer energy efficiently. Some anions arewell separated from each other and less able to exchange energywith other anions. These two types of anions are not frequencyresolvable. Both produce diagonal peak pairs in 2D IR spectra inFig.. 1C. Because the clustered anions can exchange energy muchmore efficiently, the cross peak pairs are mostly from the clus-tered anions. Therefore, simultaneous analysis of diagonal andcross peaks provides not only the rate constants for energy ex-change, but also the ratio of clustered to separated anions andthe rate constants for the exchange of anions from separatedto clustered.

In solution C, based on the liquid density, the nominal averageanion distance is calculated to be 5.5 Angstrom (Å). Can the en-ergy exchange observed in Fig. 1C be simply because of the shortaverage distance rather than ion clustering? The speculationcan be directly tested by diluting the solution. Previous experi-ments suggest that the intermolecular vibrational energy transfercan be described by the dipole-dipole interaction (25, 34–36):

k ∝�1

r

�6

; [1]

where k is the energy transfer rate constant and r is the donor/acceptor distance. According to [1], diluting solution C with awater/salt ratio from 2.4∕1 to 25∕1 will increase the average aniondistance for ∼1.9 times and therefore slow down the energy trans-

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Fig. 1. (A) A snapshot of a 1.8M KSCN aqueoussolution from a molecular dynamics simulation (De-tails are in SI Appendix). O (red), H (white), C (lightblue), N (deep blue), K (green), and S (yellow). Anion cluster is visible at the center of the picture.Some water molecules are removed from the origi-nal file to better display the cluster structure. (B) FT-IR absorption spectra of the CN and 13C15N stretchesof SCN− and S13C15N− of a 10M 1∶1 KSCN∕KS13C15Naqueous solution (solution C). (C) The time depen-dence of the 2D IR spectrum of solution C. As Tw

increases, the off-diagonal peaks grow in becauseof energy exchange between SCN− and S13C15N−.The vibrational coupling and the heat effect (22,23) (pump/probe data are in SI Appendix: Fig. S1)are too weak to show up in the spectra of the timerange.

4738 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1019565108 Bian et al.

fer rate for 51 times. However, from the concentration dependent2D IR measurements (Fig.. 2), in such a dilute solution (1.8M),the energy exchange cross peaks at 50 ps are still clearly visible,with a normalized intensity about 1

4of those of solution C at the

same waiting time (Fig.. 1C). This result indicates that the appar-ent energy transfer rate in the 1.8M solution is only about fourtimes slower than solution C, one order of magnitude smallerthan the predicted 51 times. The contradiction between experi-ments and the prediction based on the speculation suggests thatthe observed energy transfer is probably from some anionswith average distance much smaller than the nominal 5.5 Åand this distance is not affected by dilution significantly. The onlyplausible explanation of this dilution experiment is that the an-ions responsible for energy transfer are in clusters. In a controlexperiment, no energy exchange was observed between the SCNand S13C15N groups in a 1∶1 C2H5SCN and C2H5S13C15Nmixed liquid (Fig.. 3). In the control sample, the average mole-cular distance is 5.2 Å, and the energy mismatch (78 cm−1)between the two isotope-labeled CN stretches is very similarto that (73 cm−1) between the two anions in C. If anions inthe electrolyte solutions are not clustered, based on [1] withoutconsidering other factors, the energy transfer rates in the controlsample would be 67 times faster than those in the 1.8M solution,which has assuming no clustering an average anion distance of10.5 Å. However, at Tw ¼ 30 ps, the energy transfer cross peaksin the 2D IR spectrum of the 1.8M solution (Fig.. 2) are alreadyvisible, while no cross peaks are observed for the control sample,indicating that energy transfers faster in the 1.8M solution thanin the control sample. Ion clustering which holds anions within a

very close distance in the aqueous solutions is the most probablereason for this discrepancy. (More details and supporting experi-ments are in the control experiment part of the SI Appendix.)

The main reason for the smaller cross peaks in the spectraof a more dilute solution (Fig.. 2) is a lower concentration ofclustered ions instead of a slower energy transfer rate. Quanti-tative analysis based on the nonresonant energy transfer dataand the following kinetic model shows that only 35% of anions(Data and calculations are in SI Appendix) are clustered in the1.8M solution while 95% of the anions form clusters in solutionC. Surprisingly, diluting the solution in fact decreases ratherthan increases the average distance between two clustered an-ions, as observed from our energy transfer experiments pre-sented in following paragraphs.

95% of Anions Form Clusters with Average Anion Distance 3.7 Å in a10M KSCN Aqueous Solution. In solution C, some S13C15N− andSCN− form clustered anions (denoted as S13C15N−

clu andSCN−

clu), and the rest of the anions are separated (denoted asS13C15N−

iso and SCN−iso). These two types of anions are in dy-

namic equilibrium: they can exchange locations with rate con-stants kclu→iso and kiso→clu with a ratio equal to an equilibriumconstant K ¼ kiso→clu

kclu→iso. The S13C15N−

clu and SCN−clu anions can ex-

change vibrational energy with rate constants kS13C15N−→SCN− andkSCN−→S13C15N− with a ratio determined by detailed balance:

D ¼ kS13C15N−→SCN−

kSCN−→S13C15N−¼ e−

2;064−1;991205 ¼ 0.7 at experimental temperature

T ¼ 295 K. We assume that the energy transfer rate for the se-parated anions is negligibly small, i.e., a separated anion cannot

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Fig. 3. The time dependence of the 2D IRspectrum of a 1∶1 C2H5SCN∕C2H5S13C15Nmixed liquid. No cross peaks have grownin up to 30 ps, indicating negligible en-ergy has exchanged between the CNand 13C15N stretches of the two mole-cules.

Bian et al. PNAS ∣ March 22, 2011 ∣ vol. 108 ∣ no. 12 ∣ 4739

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transfer vibrational energy to another anion. The vibrational ex-citations of S13C15N− and SCN− decay with their own vibrationalrelaxation rate constants kS13C15N− and kSCN− (here we assume theclustered and separated ions have the same k. The assumptionwith different vibrational relaxation rate constants for clusteredand separated ions is also tested. See SI Appendix for moredetails). From these considerations, we construct a kinetic modelfor the observations as illustrated in the following scheme 1.

In these experiments, we obtained molecular-rotation-freedata (22). Therefore, the model doesn’t contain any orientationalcomponent. From the model, four differential equations are de-rived. By solving the equations (Details are in SI Appendix), theenergy transfer rate constants, the clustered/separated ion equi-librium constant, and the location exchange rate constantsare obtained. Because the ratio of the rate constants for locationexchange is the equilibrium constant and the ratio of the energytransfer rate constants are determined by the difference in theCN stretching energy of the isotopic species, there are only threeunknown parameters to be determined. The vibrational relaxa-tion rate constants, and the time dependent concentrationsof excited species are experimentally determined. Calculationssimultaneously fit the four experimental curves very well(Fig. 4 A and B) with the three parameters: 1∕kSCN−→S13C15N− ¼115� 15 ps, the equilibrium constant K ¼ 19� 3 (95� 1% ofanions are clustered), and the clustered and separated ionexchange time constant 1∕kclu→iso ¼ 12� 7 ps. Based on theenergy transfer rate constant, and the energy transfer equationfrom a previous publication (23), the experimentally determinedvibrational coupling constant, and the assumption of dipole-dipole interaction for vibrational energy transfer, the average dis-tance between the C≡N groups of two SCN− anions in a clusteris determined to be 3.7� 0.3 Å. The value is very close to theshortest C≡ N distance 3.8 ∼ 4.0 Å in KSCN crystals (37, 38).(More details are in SI Appendix.)

One Energy Donor has Seventeen Acceptors in a 10M KSCN Solution.In addition to the concentration of ion clusters revealed by thenonresonant energy transfer experiments, the cluster sizes canalso be evaluated by resonant energy transfer measurements.

In these experiments, the resonant energy transfer from onedonor to any acceptor, as well as molecular rotations, can causethe anisotropy of vibrational excitation to decay (25, 36). Duringresonant energy transfers, the energy can be transferred backfrom acceptors to the original donor. The probability of reversetransfer is inversely proportional to the number of acceptors:more acceptors resulting in statistically less likely reverse trans-

fers. When a reverse transfer occurs, the anisotropy is recovered.Therefore, fewer acceptors for one donor (corresponding to asmaller cluster) will result in slower energy-transfer-induced ani-sotropy decay. Based on the physical picture, we derive an equa-tion which can be used to extract the number of anions involvedin the effective energy transfer (Details are in SI Appendix):

RðtÞRð0Þ ¼ e−

tτor

��1 −

1

1þ ðntot − 1Þ × c

�e−½1þðntot−1Þ×c�tτ

þ 1

1þ ðntot − 1Þ × c

�; [2]

where τor is the molecular rotational time constant in a cluster,and c is the fraction of S13C15N− (the energy carrier) among theisotope-labeled anions in a cluster. Changing the ratio ofS13C15N−∕SCN− in a solution can change the number of resonantenergy acceptors for one donor and therefore the resonance-en-ergy-transfer-induced anisotropy decay rate, while the chemicalproperties of the cluster are unchanged. ntot is the number of an-ions (both S13C15N− and SCN−) within an effective energy trans-fer unit. τ is the resonant one-donor-to-one-acceptor energytransfer time constant. In Eq. 2, only two parameters (ntot andτ) are experimentally unknown. Calculations with the two adjus-table parameters simultaneously fit the experimental results ofsix different isotope ratios very well (Fig.. 5). The calculationsshow that τ ¼ 54� 8 ps and ntot ¼ 18� 3. The number 18 isthe same as the number of first shell SCN− anions surroundingone anion in the KSCN crystals (37, 38). (More details are inSI Appendix). At this point, we don’t have any solid evidenceto show that the energy acceptor number 18 − 1 ¼ 17� 3 ob-tained from our experiments represents the number of anionssurrounding one anion in the crystal. However, from the similar-ity of the anion distance and this acceptor number between theion clusters and the crystal, we believe that some structural as-pects of a big cluster in solution C is probably similar to thosein the crystal, e.g., the shortest anion distance and the number

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Fig. 5. The anisotropy decay data (dots) and calculations of Eq. 2 (lines) ofthe 13C15N stretch of S13C15N− in 10 M salt aqueous solutions with differentKS13C15N∕KSCN ratios. Adjusting the KS13C15N∕KSCN ratio changes thenumber of resonance energy acceptors for the excited S13C15N− donor.The calculations yield ntot ¼ 18� 3, τ ¼ 54� 8 ps.

4740 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1019565108 Bian et al.

of anions in the first solvation shell of an energy donor. In experi-ments, Kþ doesn’t produce any signal. Kþ

’s number in any clusterwas therefore not determined. In highly concentrated solutions,the clusters could be large and contain many energy transferunits. Thus ntot is not the same as the number of anions in a clus-ter. At lower concentrations, the numbers and sizes of clustersbecome smaller. ntot is expected to become closer to the numberof anions in a cluster.

Diluted Solutions Have Fewer, Smaller, and Tighter Clusters. Accord-ing to the thermodynamic principle (39), diluting solution C withwater shifts the dissolution equilibrium to fewer clusters. Dilutingsolution C with water shifts the dissolution equilibrium to fewerclusters, this can be revealed by simple inspection of the growthof cross peaks in 2D IR spectra of solutions with different saltconcentrations (Fig.. 2). At higher concentrations, the intensitiesof cross peaks are higher at the same Tws. As described above, thegrowth of cross peaks is from the energy exchange of clusteredanions, while the diagonal peak pairs are from both clusteredand separated anions. The cross/diagonal peak ratio representsnot only how fast the energy exchange is, but also how manyof the anions form clusters. A higher cross/diagonal peak ratioindicates a faster energy transfer and/or more clusters. Quantita-tive analyses based on the above methods show that fewer andsmaller clusters form in a lower concentration (Fig. 6A. Numer-ical values are listed in SI Appendix: Table S1). The fraction ofanions in clusters is unexpectedly large in all studied concentra-tions. In highly concentrated solutions (10 and 8.8M) almost allanions are in clusters (>90%). Even for a relatively dilute solution(1M) whose salt/water ratio is only ∼1∕50, there still ∼27% ofanions in clusters which contain three anions on average. The re-sults suggest microphase separation in these solutions.

SCN− is one of the strongest and most frequently used proteindenaturants. SCN− has been the subject of intense investigationsand debates for its “salt-in” effect for many years (40). The highclustering tendency of KSCN observed in these experimentssuggests another avenue for understanding SCN−

’s high effec-tiveness in denaturing proteins: it is conceivable that the interac-tion between SCN− and water is indeed not very strong so that

SCN− prefers to associate to amino acid residues of a proteinover water in a protein aqueous solution.

Another interesting result of the concentration dependentexperiments is that the one-donor-to-one-acceptor energy trans-fer rate is faster at a lower concentration (Fig.. 6B). Accordingto [1], this result suggests that a smaller cluster is tighter. Theexact molecular mechanism giving rise to this phenomenon is notclear at this point. Instead, we propose a qualitative explanation.In a bigger cluster, more anions are close to each cation so thatthe average radius of the anion shells could be larger because ofthe geometry constraint and electrostatic repulsion.

Salts with Bigger Cations Form More Clusters. It has long beenrecognized that the size and charge density of a cation haveprofound effects on the properties of electrolyte solutions andtheir biological activities (2). Theoretical calculations suggestthat cations may affect the formation of ion pairs and clustersin aqueous solutions (12, 41). To explore cation specific effects,we performed energy transfer measurements on 4M (salt∕water ratio ¼ 1∕10) aqueous solutions of LiSCN, NaSCN,KSCN, and CsSCN. These experiments show that in solution,smaller cations form smaller and fewer clusters (Fig.. 6 C and D.Numerical values are listed in SI Appendix: Table S1). In solutionwith the smallest cation Liþ (LiSCN), ∼50% of the anions formclusters which contain ∼4 anions on average. In solution withthe biggest cation Csþ (CsSCN), ∼70% of the anions form clus-ters containing ∼9 anions. This trend may be qualitatively under-stood with the theoretical description of “matching cation andanion sizes” for some electrolyte solutions (41, 42): small-smalland large-large easily associate, while small-large readily dissoci-ate. SCN− is large and polarizable, and therefore, more readilyassociates with the large and polarizable Csþ than the small Liþ.

The Energy Exchange Method Can Be General for Short-Range Mole-cular Interactions. The mode-specific vibrational energy exchangemethod can be used to study many molecular interactions if theinteractions are strong enough and the probe vibrational lifetimesare long enough. The energy exchange method may or may notneed isotope labeling, which in general does not perturb the

LiSCN NaSCN KSCN CsSCN0

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t

1 2 3 4 5 6 7 8 9 10 110

20

40

60

80

100

Clu

ster

ed io

n p

erce

nta

ge

Concentration of KSCN solution (M)

Clustered ion percentage

0

4

8

12

16

20 ntot

nto

t

Fig. 6. (A) The concentration depen-dences of clustered ion percentage andthe number (ntot) of anions in an energytransfer unit of KSCN aqueous solutions.(B) The concentration dependence ofthe one-donor-to-one-acceptor resonantenergy transfer time constant in ion clus-ters of KSCN aqueous solutions. (C) Thecation dependences of clustered ion per-centage and the number (ntot) of anionsin an energy transfer unit of 4M aqueoussolutions of LiSCN, NaSCN, KSCN, andCsSCN. (D) The cation dependence ofthe one-donor-to-one-acceptor resonantenergy transfer time constant in ion clus-ters of 4 M aqueous solutions of LiSCN,NaSCN, KSCN, and CsSCN.

Bian et al. PNAS ∣ March 22, 2011 ∣ vol. 108 ∣ no. 12 ∣ 4741

CHEM

ISTR

Y

molecular interactions. The only requirement is that the ions (ormolecules) have IR active modes and the vibrational lifetimes ofthe modes are comparable to the energy transfer time scales(which mostly range from a few ps to a few hundred ps). Manyimportant anions in biology or electrochemistry, e.g., CN−,SO4

2−, NO32−, PO4

3−, CO32−, BF4

−, SCN−, and ClO4−, have

strong IR active vibrational modes. These modes typically havelifetimes of a few to tens of ps, overlapping with the energy trans-fer time scales. In addition, high salt concentrations are notnecessarily required. The method can be applied to solutionsof any concentration if the percentage of the clustered ions ishigh enough to provide a sufficient signal/noise ratio. In principle,the requisite clustering percentage can be as low as ∼0.1%. Themethod is not limited to ions. The energy exchange method canbe also applied to the investigation of other short-range molecu-lar interactions, e.g., those of peptide/sugar, DNA/protein, anddrug/protein complexes, as long as the complexes have vibra-tional active modes fulfilling the requirements.

Concluding RemarksThe results presented here demonstrate that in the 1∶1 electro-lyte aqueous solutions with medium to high concentrations, a sig-nificant portion of the ions form clusters. Diluting the solutionresults in fewer, smaller, and tighter clusters. Cations have signif-icant effects on cluster formation. A small cation results in smal-ler and fewer clusters. The vibrational energy transfer methodholds promise for studying a wide variety of other fast short-rangemolecular interactions.

Materials and MethodsMaterials. Unless specified, chemicals were purchased from Sigma-Aldrichand used without further purification. KS13C15N and NaS13C15N were pur-chased from Cambridge Isotope Laboratory. D2O was from C/D/N ISOTOPESINC. LiS13C15N was synthesized by precipitating KClO4 out of the KS13C15Nand LiClO4 mixed aqueous solution. CsS13C15N was synthesized by precipitat-ing LiF out of the LiS13C15N and CsF mixed aqueous solution.

Methods. A ps amplifier and a fs amplifier are synchronized with the sameseed pulse. The ps amplifier pumps an optical parametric amplifier (OPA)to produce ∼1 ps mid-IR pulses with a bandwidth ∼21 cm−1 in a tunable fre-quency range from 900 cm−1 to 4;000 cm−1 with energy 10 ∼ 40 μJ∕pulse at1 KHz. The fs amplifier pumps another OPA to produce ∼140 fs mid-IR pulseswith a bandwidth ∼200 cm−1 in a tunable frequency range from 900 cm−1 to4;000 cm−1 with energy 10 ∼ 40 μJ∕pulse at 1 KHz. In 2D IR and pump/probeexperiments, the ps IR pulse is the pump beam (pump power is adjustedbased on need). The fs IR pulse is the probe beamwhich is frequency resolvedby a spectrograph yielding the probe axis of a 2D IR spectrum. Scanning thepump frequency yields the other axis of the spectrum. Two polarizers areadded into the probe beam path to selectively measure the parallel or per-pendicular polarized signal relative to the pump beam. Vibrational lifetimesare obtained from the rotation-free 1–2 transition signal Plife ¼ P∥ þ 2 × P⊥,where P∥;P⊥ are parallel and perpendicular data respectively. Rotational re-laxation times are acquired from τ ¼ P∥−P⊥

P∥þ2×P⊥.

ACKNOWLEDGMENTS.We thank Professors Anatoly Kolomeisky, Philip Brooks,Robert Curl, and James Kinsey at Rice, Xueming Yang at Dalian Institute ofChemical Physics (DICP) and Dr. Xin Chen at Harvard for insightful discussions.This work was supported by Rice University and the Welch foundation. W.Z.thanks DICP for the 100 Talents Support Grant and National Natural ScienceFoundation of China (NSFC) for the 2010 QingNian Grant.

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4742 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1019565108 Bian et al.

1

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Figure S1. Time dependent pump/probe spectra of a 10M 1:1 KSCN/KS13C15N mixed

aqueous solution. (A) and (B) are the time evolutions of Peak 7 and 8 (pumped at 1991

cm-1) in Fig. 1. (C) and (D) are the time evolutions of Peaks 5 and 6 (pumped at 2064 cm-

1). (B) and (D) are the early time portions of (A) and (C). The heat from vibrational

relaxations induced bleaching(1, 2) with a shift to a higher frequency at long waiting

(after 100ps), clearly visible in (A) and (C). The vibrational coupling peaks are also

visible in (B) and (D). Because their intensities are only ~1% of the Peaks 1 and 3 in fig.

1(C) in the main text, they don’t show up in fig. 1(C) which only displays features with

intensities at least 10% of the maximum intensity of the spectrum. In kinetic analyses, the

heat effect and the vibrational coupling are taken out with a method we developed

previously(1, 2).

2

Data descriptions

Data in Fig.3 in the main text are from the pump/probe experiments with the

pumping and probing frequencies corresponding to the peaks in Fig. 1C. The data are

rotation free, which are 2dataP P P⊥= + × , where ,P P⊥ are parallel and perpendicular

polarization configuration data respectively.

Data in Fig.4 in the main text are from the pump/probe experiments, which are the

real time anisotropy of the system, ( )2

P PR t

P P⊥

⊥

−=

+ ×

.

3

Experiments that support the argument that the observed energy transfer in the

MSCN aqueous solutions arises mostly from transfers in ion clusters and

calculations for the anion distance in the clusters

The control sample: C2H5SCN and C2H5S13C15N 1:1 mixed liquid. To compare

the energy transfer rates between the control sample and the MSCN aqueous solutions,

we use the equation from our previous work(1, 2):

12

2 2c

ij ijc ij

k τγ βτ ω

−

−=+

, Eq. (S1)

where 1

1 exp( )ij

ij

kT

γ ω=+ −

accounts for detailed balance. ijω is the energy mismatch.

β is the average coupling strength. cτ is the coupling correlation time, which is

replaced by the spectral diffusion time (1.9 ps for all systems we have studied including

the current ones: ~95% of the 2D IR diagonal linshape change from elongation to round

(fig. 1) is done within 1.9ps). Here, 2β is assumed to be equal to 2β . In Eq. S1, all

quantities (no fitting) were experimentally independently determined. This equation

successfully described an organic mixed system (CDCl3:C6H5SeCN)(1), an aqueous

solution (D2O:KSeCN), and the current MSCN/D2O systems with different coupling

strength, energy mismatches and different environments (in terms of dielectric constant).

D2O instead of H2O is used because deuteration can effectively remove the H2O

combination band at ~ 2000 cm-1 which overlaps in frequency with the nitrile stretches of

the anions. For solution C, the experimentally determined 113.6 2.0 cmβ −= ± , and

13 151/ 115 15SCN S C N

k ps− −→ = ± with an energy mismatch 73 cm-1. The vibrational coupling

4

strength 113.6 2.0 cmβ −= ± between the nitrile stretches of SCN- and S13C15N- in the

solution is determined based on the experimental off-diagonal and diagonal

anharmonicity values, according to the exciton model(3) and the matrix diagonalization

method(1, 2). This coupling strength is between one donor and nine acceptors (see the

resonant energy transfer part). The average coupling strength between one donor and one

acceptor is 113.69

4.5 cm−= .

The energy mismatch (78 cm-1) between the two isotope-labeled CN stretches of

the control sample is very similar to that (73 cm-1) between the two anions in the aqueous

MSCN solutions. Therefore, according to Eq.S1, β is the only factor determining

which system has a faster energy transfer rate. Because the dipole-dipole interaction

holds for intermolecular vibrational energy transfers(4, 5), β average over all angle

can be described(6) as

3 20

1 2 14 3

D A

r nβ

πε=

μ μ, Eq. S2

where r is the distance between the two oscillators. 0ε is the dielectric constant. iμ is

the transition dipole moment of donor or acceptor. n is the refractive index of the

solution at the transferred energy frequency. The spectral diffusion of the system is done

in about 2ps (the 2D IR lineshapes of the diagonal peaks in fig.1 in the main text become

round at about 2ps) and the rotational time constant (<11ps, dependent on the solution

concentration) of the anion is much smaller than the energy transfer times. Therefore, it is

reasonable to average the energy transfer over all angles. Eq. S2 and S1 are consistent

with eq.1 in the main text. The transition dipole moments of the nitrile stretches of SCN-

and S13C15N- in solution C are determined to be 0.33 0.2D± , based on their absorption

5

spectra in fig.1 in the main text and the well defined correlation between the transition

dipole moment and the absorption coefficient(6). 2 5

3 C H SCNSCNµ µ− = × . In the Mid-IR

range, the refractive index (real part) of solution C is 1.46 0.1Cn = ± , the same as that of

C2H5SCN 2 5

1.46 0.04C H SCNn = ± . The refractive index of the 1.8M KSCN/KS13C15N

aqueous solution is 1.36 0.03Cn = ± . In the 1.8M KSCN/KS13C15N aqueous solution, if

the ions don’t form clusters and therefore are well separated by water, the nominal energy

transfer distance 1.8 10.5Mr = Α

. In the C2H5SCN and C2H5S13C15N 1:1 mixture with a

nominal transfer distance 5.2controlr = Α

, the energy donor and acceptor directly contact

each other. In addition, DFT calculations show that two C2H5SCN/ C2H5S13C15N

molecules tend to orient with the SCN groups next to each other similar to the structure

of liquid acetonitrile(1). Based on eq. S1&2, the energy transfer rates in the control

samples are approximate the same as those in the 1.8M solution. However, experiments

(fig. 2&5 in the main text) show that energy transfers much faster in the 1.8M aqueous

solution than in the control sample. These results suggest that the observed energy

transfer must be from clustered anions.

From eq. S1&2 and the experimentally determined one-donor/one-acceptor

coupling strength 14.5 1.0 cmβ −= ± , the distance between two anions in solution C

based on the energy transfer distance is determined to be 3.7 0.3± Α

. The value is

significantly smaller than the nominal anion distance 5.5 Α

of solution C calculated

based on its density, but very close to the shortest C N≡ distance 3.8 ~ 4.0 Α

in KSCN

6

crystals(7, 12). This is another piece of evidence that the observed energy transfer is from

clustered anions.

In solution C, the effective refractive index (real part) for the energy transfer is

difficult to precisely determine in the Mid-IR range. However, its low limit must be that

of water, 1.33, and its up limit must be that of KSCN salt, 1.53(8). Based on eq. S2, the

low refractive index limit gives 3.8r = Α

, and the up limit gives 3.5r = Α

. In other

words, the uncertainty of the effective energy transfer refractive index only causes a very

small uncertainty of the energy transfer radius.

7

The location-energy- exchange model

To quantitatively analyze the energy transfer kinetics between the two CN

stretches, we created a location-energy-exchange kinetic model based on this molecular

picture of the solution (by Junrong Zheng and Xiewen Wen): in the solution, some

S13C15N- and SCN- form clusters (denoted as 13 15cluS C N − and cluSCN − ), and the rest of

the anions are separated from each other (denoted as 13 15isoS C N − and isoSCN − ). These

two types of anions (not FTIR resolvable) are in dynamic equilibrium: they can exchange

locations with rate constants clu isok → and iso cluk → the ratio of which is determined by the

equilibrium constant iso clu

clu iso

kKk

→

→

= (the correlation is determined by the principle of

microreversibility). The clustered 13 15cluS C N − and cluSCN − anions can exchange

vibrational energy with rate constants 13 15S C N SCNk − −→ and 13 15SCN S C N

k − −→ . The isolated

anions cannot transfer vibrational energy with other isolated anions or with the clustered

anions, as the energy transfer rate between the isolated anions must be much smaller than

the energy transfer rate inside the clusters. (The energy transfer rate is inversely

proportional to the sixth power of the donor/acceptor distance, eq.1 in the main text). The

vibrational excitations of S13C15N- and SCN- decay with each species having its own

vibrational relaxation rate constant 13 15S C Nk − and

SCNk − . We are forced to assume that for

each CN stretch, the vibrational lifetimes of clustered and isolated species are the same,

because experimentally these two species are not resolvable. In experiments, we can

8

manage to obtain rotation-free data ( 2I I⊥+ from polarization-selective measurements).

Therefore, the model doesn’t contain any rotational component. The model is described

in the following scheme,

.

(Scheme.1)

From the model, we derive four differential equations:

13 15 13 15

13 15

13 1513 15

13 15

* ( )( ) * ( )

* ( ) * ( )

cluclu iso cluS C N S C N SCN

iso clu iso cluSCN S C N

d S C N tk k k S C N t

dtk S C N t k SCN t

− − −

− −

−−

→ →

− −→ →

= − + +

+ +

Eq. S(3)

13 15

13 1513 15 13 15

* ( )( ) * ( ) * ( )iso

iso clu iso clu iso cluS C N

d S C N tk k S C N t k S C N t

dt −

−− −

→ →

= − + + Eq. S(4)

13 15

13 1513 15

* ( )( ) * ( )

* ( ) * ( )

cluclu iso cluSCN SCN S C N

iso clu iso cluS C N SCN

d SCN tk k k SCN t

dtk SCN t k S C N t

− − −

− −

−−

→ →

− −→ →

= − + +

+ +

Eq. S(5)

* ( )( ) * ( ) * ( )iso

iso clu iso clu iso cluSCN

d SCN tk k SCN t k SCN t

dt −

−− −

→ →

= − + + , Eq. S(6)

where * represents vibrational excitation. The equations are numerically solved with

initial conditions 13 15 * (0)1clu

KS C NK

− = +, 13 15 1* (0)

1isoS C NK

− = +,

* (0) * (0) 0clu isoSCN SCN− − = = if 13 15S C N − is initially excited.

13 15 13 15* ( ) * ( )clu isoS C N t S C N t− − + (Peak 3) and * ( ) * ( )clu isoSCN t SCN t− − +

(Peak 7) are experimentally determined. Similar expressions are applied if SCN − is

13 1513 15

13 15

13 15 13 15iso clu S C N SCN clu isoS C N SCN

clu iso iso cluSCN S C N

kk kk kiso clu clu isok k k

S C N S C N SCN SCN−→ −→ →− −

→ −→ − →

− − − −→ → →← →← ← ←

13 15S C Nk − SCN

k −

9

initially excited. Therefore, by matching calculations using Eq. S(3) ~ (6) with

experimental results, we obtain the energy transfer rate constants, the equilibrium

constant and the location exchange rate constants.

Both CN vibrational decays are experimentally observed to be bi-exponential.

Vibrational bi-exponential decay is frequently observed for modes in the range of

2000~2300 cm-1(1, 2, 9, 10). It has been attributed to the fast vibrational equilibrium

between the bright mode and one coupled dark mode(9). Here, we adopted the method

we developed for bi-exponential decays to analyze the kinetics(1, 2, 9). We separate each

CN stretch into two subgroups. The weighing factor of each subgroup is determined by

the prefactors of the bi-exponential. Each subgroup has a single-exponential-decay

lifetime time. Each subgroup can exchange energy with other CN stretches, but the

subgroups can’t exchange energy with each other (this follows the assumed physical

picture of bi-exponential: the sub-components can be considered as independent species).

In the model, the effects of dynamics: spectral diffusions, vibrational decays and

vibrational exchanges within each species are simply treated as apparent vibrational

decays as experimentally measured.

The experimentally determined vibrational decay rate constants include the effect

of energy transfer. Therefore, in calculations, they are allowed to vary by 10%. The other

parameters, specifically the exchange rate constants and the equilibrium constant are not

known beforehand. Because the ratio of the location exchange rate constants is the

equilibrium constant and the ratio of the energy transfer rate constants is determined by

the detailed balance, there are only three unknown parameters in the calculations. For the

system, the vibrational lifetimes, transition dipole moments, and quantities of the two

10

stretches are similar. Thus, the ratio of the normalized maximum energy transfer peak

intensities (Peaks 5 and 7 in Fig.1(C)) can be used to estimate the detailed balance. The

ratio is 7 0.04841 0.695 0.06972

PeakPeak

= = , which is very close to the ideal detailed balance

0.7D = determined by the 73 cm-1 energy mismatch between the two CN stretches. With

these constraints, calculations give 13 151/ 115 15SCN S C N

k ps− −→ = ± , the equilibrium

constant K is 19 3± , which corresponds to 95 1%± of anions in clusters, and the

clustered and isolated anions exchange time constant 1/ 12 7clu isok ps→ = ± . Calculations

with the three parameters simultaneously fit the four experimental curves very well,

shown in fig.3. The input parameters are

13 15 13 15

13 15

1 1 1 1

1 1

1/ 2.5 ( ); 1/ 44.6 ( ); 1/ 2.3 ( ); 1/ 51.4 ( );

1/ 7.6 ( ); K=18.9; 1/115 ( ); D=0.7SCN fast SCN slow S C N fast S C N slow

clu iso SCN S C N

k ps k ps k ps k ps

k ps k ps

− − − −

− −

− − − −

− −→ →

= = = =

= =

with pre-factors of the subgroups and offset of the bi-exponential

13 15 13 150.25; 0.75; 0.23; 0.77; 0slowSCN fast SCN slow S C N fast S C NA A A A offset− − − −= = = = = .

All experimental results and calculations with input and output parameters are

displayed in fig. S2~10.

In the above model, we assume that the nitrile stretch vibrational lifetimes of

separated and clustered anions are the same, which is different from the actual situation.

For example, in solution C, >95% of the anions form clusters. The vibrational lifetimes of

the anions are

13 15 13 151 1 1 11/ 2.5 ( ); 1/ 44.6 ( ); 1/ 2.3 ( ); 1/ 51.4 ( ).

SCN fast SCN slow S C N fast S C N slowk ps k ps k ps k ps− − − −

− − − −= = = =

In a 0.5M solution, more than 80% of the anions are separated by waters. Their

vibrational lifetimes are

11

13 15 13 151 1 1 11/1.8 ( ); 1/ 20 ( ); 1/1.7 ( ); 1/ 28 ( )

SCN fast SCN slow S C N fast S C N slowk ps k ps k ps k ps− − − −

− − − −= = = =

with similar prefactors. In general, these lifetimes determined from the two extreme

cases can’t be immediately applied into solutions of other concentrations, because the

liquid environments can be different at different concentrations. To test the uncertainty of

our kinetic analysis induced by the lifetime issue, we use the lifetimes from the two

extreme cases to fit the data for the 10M and 4M solutions, assuming the clustered anions

have lifetimes as those in Solution C, and the separated anions have lifetimes as those in

the 0.5M solution. The calculation results show that 13 151 1/115 ( )

SCN S C Nk ps− −

−→ = and

98% of anions form clusters for solution C, and 13 151 1/145 ( )

SCN S C Nk ps− −

−→ = and 63% of

anions form clusters for the 4M solution. Within experimental uncertainty, both results

are consistent with the results based on the assumption of same vibrational lifetimes for

both clustered and separated anions. The insensitivity of the kinetic results to the change

of vibrational lifetimes partially comes from the fact that the energy transfer rates and the

concentrations of clusters are mainly determined by the amplitudes of the cross peaks

rather than the diagonal peaks. Calculations and data are shown in fig. S2.

12

0 50 100 150 200 250

0.0

0.2

0.4

0.6

0.8

1.0

Norm

alize

d Po

pula

tion

Waiting Time (ps)

KSCN KS13C15N

0 50 100 150 200 250-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Norm

alize

d Po

pula

tion

Waiting Time (ps)

Flowing down Pumping up

0 50 100 150 200 250

0.0

0.2

0.4

0.6

0.8

1.0

Norm

alize

d Po

pula

tion

Waiting Time (ps)

KSCN KS13C15N

0 50 100 150 200 250-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0.030

Norm

alize

d Po

pula

tion

Waiting Time (ps)

Flowing down Pumping up

10M 10M

4M 4M

(A) (B)

(C) (D)

0 50 100 150 200 250

0.0

0.2

0.4

0.6

0.8

1.0

Norm

alize

d Po

pula

tion

Waiting Time (ps)

KSCN KS13C15N

0 50 100 150 200 250-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Norm

alize

d Po

pula

tion

Waiting Time (ps)

Flowing down Pumping up

0 50 100 150 200 250

0.0

0.2

0.4

0.6

0.8

1.0

Norm

alize

d Po

pula

tion

Waiting Time (ps)

KSCN KS13C15N

0 50 100 150 200 250-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0.030

Norm

alize

d Po

pula

tion

Waiting Time (ps)

Flowing down Pumping up

10M 10M

4M 4M

(A) (B)

(C) (D)

Figure S2. Data and calculations of energy transfers for solution C [(A) and (B)] and the

4M solution [(C) and (D)] with different vibrational lifetimes for the clustered and

separated anions. Dots are data, and lines are calculations. Calculations for (A) and (B)

are with input parameters:

13 15 13 15

13 15

1 1 1 1

1 1 iso 1

1/ 2.5 ( ); 1/ 45.0 ( ); 1/ 2.3 ( ); 1/ 55.0 ( );

1/1.8 ( ); 1/ 20.0 ( ); 1/1.7 (SCN fast SCN slow S C N fast S C N slow

SCN fast SCN slow S C N fast

clu clu clu clu

iso iso

k ps k ps k ps k ps

k ps k ps k ps

− − − −

− − −

− − − −

− − −

= = = =

= = =13 15

13 15

1

1 1

); 1/ 28.0 ( );

1/10.0 ( ); K=40; 1/110 ( ); D=0.7S C N slow

iso

clu iso SCN S C N

k ps

k ps k ps

−

− −

−

− −→ →

=

= =

with pre-factors of the subgroups and offset of the bi-exponential

13 15 13 15 13 15 13 15

0.25; 0.75;

0.25; 0.75; 0SCN fast SCN fast SCN slow SCN slow

slow slowS C N fast S C N fast S C N S C N

clu iso clu iso

clu iso clu iso

A A A A

A A A A offset

− − − −

− − − −

= = = =

= = = = =

Calculations for (C) and (D) are with input parameters:

13

13 15 13 15

13 15

1 1 1 1

1 1 iso 1

1/ 2.5 ( ); 1/ 40.0 ( ); 1/ 2.3 ( ); 1/ 52.0 ( );

1/1.8 ( ); 1/17.0 ( ); 1/1.8 (SCN fast SCN slow S C N fast S C N slow

SCN fast SCN slow S C N fast

clu clu clu clu

iso iso

k ps k ps k ps k ps

k ps k ps k ps

− − − −

− − −

− − − −

− − −

= = = =

= = =13 15

13 15

1

1 1

); 1/ 23.0 ( );

1/10.0 ( ); K=1.7; 1/145 ( ); D=0.7S C N slow

iso

clu iso SCN S C N

k ps

k ps k ps

−

− −

−

− −→ →

=

= =

with pre-factors of the subgroups and offset of the bi-exponential

13 15 13 15 13 15 13 15

0.25; 0.75;

0.25; 0.75; 0SCN fast SCN fast SCN slow SCN slow

slow slowS C N fast S C N fast S C N S C N

clu iso clu iso

clu iso clu iso

A A A A

A A A A offset

− − − −

− − − −

= = = =

= = = = =

Correlation between anisotropy decay and resonance energy transfer 0.96anisotropy

energy

kk

=

The derivation follows how FRET changes the anisotropy of a molecule.

In a vibrational resonance energy transfer process, the orientational factor for the donor-acceptor pair is

2 2 2(3cos 1)cosκ θ ω= +

14

where θ being the angle between the donor transition moment and the direction joining donor and acceptor and ω being the angle between the electric field of the donor at the acceptor and the acceptor transition moment (as shown in the figure above). For simplicity, the molecules are assumed to be immobile and the excited state is assumed to remain localized on the originally excited molecule. Then neglecting the effects of rotational diffusion and only considering the situation at t = 0, the probability for transfer depends on θ and ω according to

2 2( , ) (3cos 1)cosW θ ω θ ω∝ + During the energy transfer, the donor transition moment is rotated by an angle ψ , so as to coincide with its own electric field at the acceptor. Then it is rotated from this new orientation by an angle ω so that it coincides finally with the acceptor transition moment. Assuming that the angular jump of ψ or ω is equally probable in all azimuths, the final anisotropy of acceptor emission for a given pair ( , )ψ ω is

2 2

2 22

2

1( , ) (3cos 1)(3cos 1)4

1 3(3cos 1)( , ) ( 1)(3cos 1)10 3cos 1

A D

A

r r

or

r

ψ ω ψ ω

θθ ω ωθ

= − −

−= − −

+

Here, Ar and Dr are the anisotropy of the acceptor and donor, respectively. We have

made use of the result 25Dr = and the fact that

2

2

3cos 1cos3cos 1

θψθ

−=

+ which can be

obtained from the form of the electric field of a static dipole. Thus, the anisotropy of a molecule can be obtained

0 0

0 02 2

2 2 220 0

2 2

0 0

( , ) ( , )sin sin

( , )sin sin

1 3(3cos 1)(3cos 1)cos ( 1)(3cos 1) sin sin10 3cos 1

(3cos 1)cos sin sin

4 81 5 15 0.016 4% 0.4210 4

3

AA

W r d dr

W d d

d d

d d

π π

π π

π π

π π

θ ω θ ω θ θ ω ω

θ ω θ θ ω ω

θθ ω ω θ θ ω ωθ

θ ω θ θ ω ω

=

−+ ⋅ − − ⋅

+=+

⋅= = = ×

⋅

∫ ∫∫ ∫

∫ ∫∫ ∫

15

Finally, it is shown that a single resonance energy transfer step can reduce the anisotropy to 4% of the initial value. In other words, the anisotropy decay rate constant is only 96% of the energy transfer rate constant. In practice, because 96% is very close to 100%, it is much simpler to use 100% instead of 96% in processing the data. Such an approximation only causes a very small uncertainty (~4%).

Calculations of the number of acceptors for an energy donor

In experiments, the resonant energy transfer from one donor to any acceptor, as

well as molecular rotations, can cause the anisotropy of vibrational excitation to decay(4,

5). During resonant energy transfers, the energy can be transferred back from acceptors to

the original donor. The probability of reverse transfer is inversely proportional to the

number of acceptors: more acceptors resulting in statistically less likely reverse transfers.

When a reverse transfer occurs, the anisotropy is recovered. Therefore, fewer acceptors

for one donor (corresponding to a smaller cluster) will result in slower energy-transfer-

induced anisotropy decay. In the physical picture, the anisotropy is directly proportional

to the time dependent number of excited donor molecules. A new kinetic equation can

therefore be derived as stated in the following (by Hailong Chen and Junrong Zheng). In

an energy transfer unit, there are n chromophores. Energy can exchange among them.

For an excited molecule i , the rate equation for its probability ( )ip t of being still excited

at time t is

16

( ) ( ) ( )iij j ij i

j i j i

dp t k p t k p tdt ≠ ≠

= −∑ ∑ . Eq. S(7)

kij is the transfer rate between molecules i and j. For resonant energy transfers,

ij jik k k= = . In Eq. S(7), we only consider the energy transfer processes which are

involved in changing anisotropy. The vibrational decay is thus not considered here. Then

we have

( ) ( ) ( ) [1 ( )] ( 1) ( ) [1 ( )]ij i i i i

j i j i

dp t k p t k p t k p t k n p t k np tdt ≠ ≠

= − = − − − = −∑ ∑ . Eq. S(8)

According to the experimental condition (less than 0.2% of the anions are excited), we

assume that only one molecule “1”, the donor, is excited in a cluster at time 0. We have

the initial conditions

1(0) 1, (0) 0 ( 1)mp p m= = ≠ . Eq. S(9)

Solving Eq. S(8), we obtain

1 11 1 1 1( ) (1 ) (1 ) , ( ) 1 ( ) ( 1)

ntknt

mp t e e p t p t mn n n n

τ−−= − + = − + = − ≠ . Eq. S(10)

Using the assumption that the anisotropy is directly proportional to the time dependent

number of excited donor molecules(11), we have the anisotropy decay rate equation

1

[1 ( 1) ]

( ) 1 1exp( ) ( ) [(1 ) ](0)

1 1[1 ]1 ( 1) 1 ( 1)

or

totor

t tn

ort tn c

tot tot

R t t p t e eR n n

e en c n c

τ τ

τ τ

τ

− −

− − + − ×

= − = − +

= − + + − × + − ×

, Eq. S(11)

where orτ is the rotational time constant of clustered S13C15N- which is experimentally

determined by removing the contribution of the isolated anions from the overall signal.

The concentration of the isolated ions is known from the non-resonant energy transfer

17

measurements. Their rotation time constants are assumed to be very close to the free

anions in dilute solutions (3.7 ~ 4.0 ps ). c is the fraction of S13C15N- (the energy carrier)

among the isotope-labeled anions in a cluster. Changing the ratio of S13C15N-/SCN- in a

solution can change the number of resonant energy acceptors for one donor and therefore

the resonance-energy-transfer-induced anisotropy decay rate, while the chemical

properties of the cluster are unchanged. ntot is the number of anions (both S13C15N- and

SCN-) in a cluster and 1k

τ = is the resonance one-donor-to-one-acceptor energy transfer

time constant. To obtain Eq. S(11), we use the equation,

1 ( 1)totn n c= + − × Eq. S(12)

The derivation of Eq. S(12)

Assuming sufficient A and B molecules, the concentration of A is c. [ ][ ] [ ]

Ac

A B=

+. Each

A contributes to the signal equally. They form N clusters of size totn (number of

molecules in a cluster). They can form 1totn + kinds of clusters. The number of each

cluster is:

(0) with totn A s in one cluster ( totnNc );

(1) totn -1 A s….; ( 1(1 )totntotNn c c− − )

…

(k) totn -k A s….; ( (1 )tot

tot

n kk knNC c c− − )

…

(n) 0 A in one cluster. ( (1 ) totnN c− )

18

We have 0

(1 ) [ (1 )]tot

tot tot

tot

nn k nk k

nk

NC c c N c c N−

=

− = + − =∑

The number of a cluster with m A s is (1 ) tot

tot

n mm mnNC c c −− . The total number of A in all

clusters ( totNn c= , by definition) is:

1 1

1

111

0

!(1 ) (1 )( )!( 1)!

( 1)! (1 )[( 1) ( 1)]!( 1)!

( 1)! (1 ) ( 1 )[( 1) ]! !

tot tottot tot

tot

tottot

tottot

n nn m n mm m mtot

nm m tot

nn mmtot

totm totn

n mmtottot

m tot

nmNC c c N c cn m m

nN n c cn m m

nN n c c m mn m m

Nn

− −

= =

−

=

−− −+

=

− = −− −

−= −

− − − −

−= − − →

− −

=

∑ ∑

∑

∑1

11

01

(1 )

[ (1 )]

tottot

tot

tot

nn mm m

tot nm

ntot tot

c C c c

Nn c c c Nn c

−− −

−=

−

−

= + − =

∑

The contribution of each cluster to the experimentally determined n (the number of A in a

cluster) is (1 ) tot

tot

n mm mn

tot

mNC c cm

Nn c

−−× . Therefore,

1

1

2

1 (1 )

1 [ ( 1) (1 ) (1 ) ]

!1 [ ( 1) (1 ) ]( )! !

!1 [ (1( )!( 2)!

tottot

tot

tottot tot

tot tot

tottot

nn mm m

nmtotn

n m n mm m m mn n

mtotn

n mmtottot

mtot tot

mtottot

tot tot

n m mC c cn c

m m C c c mC c cn c

nn c m m c cn c n m m

nn c cn c n m m

−

=

− −

=

−

=

= × −

= × − − + −

= + × − −−

= + −− −

∑

∑

∑

2

222

0

222

20

2

) ]

( 2)!1 [ ( 1) (1 ) ]( 2 )! !

1 [ ( 1) (1 ) ]

1 [ ( 1) ] 1 ( 1)

tottot

tottot

tottot

tot

nn m

m

nn mmtot

tot tot totmtot tot

nn mm m

tot tot tot nmtot

tot tot tot tottot

c

nn c n n c c cn c n m m

n c n n c C c cn c

n c n n c n cn c

−

=

−− −

=

−− −

−=

−= + − −

− −

= + − −

= + − = + −

∑

∑

∑

19

In the model, we consider the exchange between the anions inside an energy

transfer unit and anions outside this unit as a special type of molecular rotation. Its

contribution to the anisotropy decay is incorporated into Eq. (S11) as part of the effective

molecular rotational time constant orτ . This treatment is supported by experimental

results: 10or psτ = in the 10M solution, which is only about three times of the time for

free ions in a very dilute solution, while it contains at least nineteen anions. This

observation shows that the rotation time observed in the 10M solution is not for the

whole cluster. Instead, it is for the individual ion which is loosely bound to other ions.

The exchange event between clustered and separated position is part of the molecular

rotation mechanism. In fact, the independent measurements from the non-resonance

energy transfer experiments show that the clustered and separated ions exchange time is

also 7~20 ps (in the above location-energy-exchange model). This value is consistent

with 10or psτ = .

It is possible that the energy can transfer from one acceptor to another anion

which is far way from the original donor and so on, so that the energy will never transfer

back to the original donor. This effect is also included into the effective molecular

rotational time constant, because the anion is not symmetric (the atom S is a good

vibrational energy blocker(1, 2)). In order for an anion to transfer energy to another anion

which is not directly associated with the original donor, the anion probably has to rotate

to the right configuration before the energy can transfer away. Therefore, we consider the

anisotropy loss caused by this factor as already been included in the anisotropy loss

induced by the molecular rotation. Note, this effect only occurs in a very big cluster

which contains more than one effective energy transfer units.

20

Another assumption we make in the model is that the non-resonance energy

transfer from S13C15N- to SCN- is much slower than the resonance energy transfer among

S13C15N- so that the anisotropy decay induced by the non-resonance energy transfer is

negligible. This assumption is verified by experiments. In the non-resonance energy

exchange experiments, we found 13 1511/115 ( )

SCN S C Nk ps− −

−→ = which corresponds to

13 1511/165 ( )

S C N SCNk ps− −

−→ = (required by detailed balance). 13 15S C N SCN

k − −→ is the apparent

rate constant, which is the sum of 2totn one-donor-to-one-acceptor rate constants

13 151 1 S C N SCNk − −→− −

. In the 10M solution, 92totn

= . 13 151

1 1

1 ( )1485S C N SCN

k ps− −−

→− −= . The value

is more than one order of magnitude smaller than the resonance one-donor-to-one-

acceptor rate constant 11 1 ( )54

psτ

−= (Data are in fig. S2~10 and table S1.). Even in a

1:99 SCN-:S13C15N- mixed 10M solution, the total non-resonance energy transfer rate

from S13C15N- to SCN- is only 11 ( )87

ps− , still much slower than the molecular rotation

( 11 ( )10

ps− ). Another issue is important to point out. In our experiments, in any cluster, at

most one anion can be excited. In the non-resonance energy exchange experiments, for

each excited anion there are exactly 2totn acceptors (the other isotope-labeled anions). The

experimentally measured rate constant is the sum from all these acceptors. However, in

the resonance energy exchange experiments of a pure isotope solution, for each excited

anion there are exactly 1totn − acceptors. In processing the data, we obtain the one-donor-

21

to-one-acceptor rate constant 1τ

instead of the apparent rate constant (the sum for the

1totn − acceptors).

Based on the crystalline structures of KSCN(7, 12), the first anion shell

surrounding one anion has totally 26 anions (similar as simple cube): eight at the same

layer of the anion, nine at the top and another nine at the bottom. If we take away the

eight diagonal anions on the cube which are far away from the cube center, 18 are left. At

this point, we don’t have any solid evidence to show that the energy acceptor number

18 1 17 3− = ± obtained from our experiments represents the number of anions

surrounding one anion in the crystal. However, from the similarity of the anion distance

and this acceptor number between the ion clusters and the crystal, we believe that some

structural aspects of a big cluster in solution C is probably similar to those in the crystal,

e.g. the shortest anion distance and the number of anions in the 1st solvation shell.

To develop the above model, we used the linear average of isotope distribution in

a cluster which is simply determined by the experimentally set isotope ratio. However,

this is not perfectly precise, because the anisotropy decay induced by resonant energy

transfer is not linearly proportional to the isotope ratio in a cluster. A precise way to

count for the nonlinear dependence is to calculate the anisotropy for each cluster kind and

sum the signals from all clusters together. The following is the mathematical derivation

(suggested and derived by Prof. Robert Curl).

In anisotropy decay for a given (n, m) cluster where now let m = number of

S13C15N- in a cluster of n ( totn n= ) anions. Let the mole fraction of the normal species by

X2 and of 13C15NS be X1. The anisotropy decay upon excitation of S13C15N- is given by

22

[ ] ( ) [ ]/ 1 / 1(t) =e 1 R(0)ort mtm m

R m e mτ τ− − − − − + .

The probability that there will be a species excited in an (n, m) cluster is

proportional to m. Thus the signal from a given cluster is

[ ] ( ) [ ]/ 1 / 11

(t) =e 1 R(0)ort mtm

R m e m mτ τ− − − − − +

and the total signal summed over the clusters will be

( ) ( ) [ ]/ 1 / 11 2 1

1

!( ) e 1 R(0)! !

or

ntm n m mt

nm

nR t X X m m e mm n m

τ τ−− − − −

=

= − + −∑

This can be analyzed using the binomial moment generating function.

[ ] ( ) [ ] ( )/ // / /1 2 1 21 1

1 1( ) R(0) e 1 1 R(0) e 1or or

n nt tm n m mt m n m mt mt

nm m

R t X X m e X X me en nm m

τ ττ τ τ− −− − − − −

= =

= − + = − +

∑ ∑

The quantity inside the bracket equals zero when m = 0 because the first term

vanishes and the second and third term cancel each other. Thus we can change the sum

from starting with m = 1 to starting with m = 0.

[ ] ( )/ / /1 21

0( ) R(0) e 1or

nt m n m mt mt

nm

R t X X me enm

τ τ τ− − − −

=

= − +

∑

The last term after summing equals 1. The middle term after summing is the

binomial moment generating function and the first term is the first derivative of the

moment generating function with respect to t. Using the equations from Wolfram

Research (http://mathworld.wolfram.com/BinomialDistribution.html) and realizing that

the first term is the derivative of the second by the quantity -t/τ, we have

[ ] { }1/ / / /1 2 1 1 21

( ) R(0) e 1orn nt t t t

nR t n X e X X e X e Xτ τ τ τ−− − − − = + − + + .

23

When t = 0, we have

[ ] { } [ ]1 11 1(0) R(0) 1 1 R(0)nR nX nX= − + = .

Thus

{ }1/1 1 / / /1 1 2 1 1 2( ) / R(0) e 1or

n nt t t tn nR t n X n X e X X e X e Xτ τ τ τ−−− − − − − = + − + + .

The above equation is then converted into Eq. S13 with the same symbols as in eq. S11,

{ }1/1 1 / / /( ) / R(0) e 1 1 1tot totorn nt t t t

n n tot totR t n c n ce c ce ce cτ τ τ τ−−− − − − − = + − − + − + . Eq. S(13)

Eq. S13 is not exactly the same as Eq. S11. Numerical calculations for all

solutions in this work show that the difference between these two equations for

anisotropy values within the 10ps delay (data after 10ps are too small and therefore much

less reliable) is smaller than 10%. For solution C, the difference is smaller than 5%. The

difference is small enough that both approaches are suitable for the studied systems.

Generally speaking, Eq. S11 is from an assumption that the linear average doesn’t deviate

much from the actual situation, which holds for our experiments, but it is not necessarily

safe for other cases. Eq. S13 doesn’t have such an assumption and therefore is general for

all cases.

24

Data and calculations

(A) (B)

(C)

0 40 80 120 160 200 2400.0

0.2

0.4

0.6

0.8

1.0

Energy down-flowing Peaks 1 and 5

Energy up-pumping Peaks 3 and 7

Norm

alize

d Po

pula

tion

Waiting Time (ps)0 40 80 120 160 200 240

0.00

0.02

0.04

0.06

Norm

alize

d Po

pula

tion

Peak 7

Peak 5

Waiting Time (ps)

0 10 20 30 40 50 60 70-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1:99 2:98 10:90 20:80 50:50 100:0

Norm

alize

d An

isotro

py

Waiting Time (ps)

KS13C15N : KSCN

Figure S3. Data and calculations of nonresonance [(A) and (B)] and Resonance [(C)] for

a 10M KSCN aqueous solution. Dots are data, and lines are calculations. Calculations

for (A) and (B) are with input parameters:

13 15 13 15

13 15

1 1 1 1

1 1

1/ 2.5 ( ); 1/ 44.6 ( ); 1/ 2.3 ( ); 1/ 51.4 ( );

1/ 7.6 ( ); K=18.9; 1/115 ( ); D=0.7SCN fast SCN slow S C N fast S C N slow

clu iso SCN S C N

k ps k ps k ps k ps

k ps k ps

− − − −

− −

− − − −

− −→ →

= = = =

= =

with pre-factors of the subgroups and offset of the bi-exponential

25

13 15 13 150.25; 0.75; 0.23; 0.77; 0slowSCN fast SCN slow S C N fast S C NA A A A offset− − − −= = = = =

(C) 10or psτ = is experimentally determined, which is the rotation time of the clustered

ions. 18totn = , 54 psτ = .

0 50 100 150 200 250

0.0

0.2

0.4

0.6

0.8

1.0

Norm

alize

d Po

pula

tion

Waiting Time (ps)

KSCN KS13C15N

0 50 100 150 200 250-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.06

Norm

alize

d Po

pula

tion

Waiting Time (ps)

Flowing down Pumping up

(A) (B)

(C)

0 10 20 30 40 50-0.2

0.0

0.2

0.4

0.6

0.8

1.0

2:98 20:80 50:50 100:0

Norm

alize

d An

isotro

py

Waiting Time (ps)

Figure S4. Data and calculations of nonresonance [(A) and (B)] and Resonance [(C)] for

a 8.8M KSCN aqueous solution. Dots are data, and lines are calculations. Calculations

for (A) and (B) are with input parameters:

13 15 13 15

13 15

1 1 1 1

1 1

1/1.5 ( ); 1/ 33 ( ); 1/ 2.5 ( ); 1/ 35 ( );

1/10 ( ); K=11; 1/110 ( ); D=0.71SCN fast SCN slow S C N fast S C N slow

clu iso SCN S C N

k ps k ps k ps k ps

k ps k ps

− − − −

− −

− − − −

− −→ →

= = = =

= =

with pre-factors of the subgroups and offset of the bi-exponential

13 15 13 150.20; 0.80; 0.20; 0.80; 0slowSCN fast SCN slow S C N fast S C NA A A A offset− − − −= = = = = .

26

(C) 6.9or psτ = is experimentally determined, which is the rotation time of the clustered

ions. 13totn = , 40 psτ = .

(A) (B)

(C)

0 50 100 150 200 250 300

0.0

0.2

0.4

0.6

0.8

1.0

Norm

alize

d Po

pula

tion

Waiting Time (ps)

KSCN KS13C15N

0 50 100 150 200 250 300-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

Norm

alize

d Po

pula

tion

Waiting Time (ps)

Flowing down Pumping up

0 10 20 30 40 50-0.2

0.0

0.2

0.4

0.6

0.8

1.0

2:98 10:90 50:50 100:0

Norm

alize

d An

isotro

py

Waiting Time (ps)

Figure S5. Data and calculations of nonresonance [(A) and (B)] and Resonance [(C)] for

a 6.5M KSCN aqueous solution. Dots are data, and lines are calculations. Calculations

for (A) and (B) are with input parameters:

13 15 13 15

13 15

1 1 1 1

1 1

1/ 2.5 ( ); 1/ 32 ( ); 1/ 2.9 ( ); 1/ 34 ( );

1/10 ( ); K=2.3; 1/130 ( ); D=0.70SCN fast SCN slow S C N fast S C N slow

clu iso SCN S C N

k ps k ps k ps k ps

k ps k ps

− − − −

− −

− − − −

− −→ →

= = = =

= =

with pre-factors of the subgroups and offset of the bi-exponential

13 15 13 150.24; 0.76; 0.25; 0.75; 0slowSCN fast SCN slow S C N fast S C NA A A A offset− − − −= = = = = .

(C) 5.7or psτ = is experimentally determined, which is the rotation time of the clustered

ions. 9totn = , 32 psτ = .

27

0 50 100 150 200 250

0.0

0.2

0.4

0.6

0.8

1.0

Norm

alize

d Po

pula

tion

Waiting Time (ps)

KSCN KS13C15N

0 50 100 150 200 250-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0.030

Norm

alize

d Po

pula

tion

Waiting Time (ps)

Flowing down Pumping up

0 10 20 30 40 50-0.2

0.0

0.2

0.4

0.6

0.8

1.0

2:98 10:90 50:50 100:0

Norm

alize

d An

isotro

py

Waiting Time (ps)

(A) (B)

(C)

Figure S6. Data and calculations of nonresonance [(A) and (B)] and Resonance [(C)] for

a 4M KSCN aqueous solution. Dots are data, and lines are calculations. Calculations for

(A) and (B) are with input parameters:

13 15 13 15

13 15

1 1 1 1

1 1

1/1.3 ( ); 1/ 26 ( ); 1/ 2.2 ( ); 1/ 33 ( );

1/10 ( ); K=2.0; 1/140 ( ); D=0.70SCN fast SCN slow S C N fast S C N slow

clu iso SCN S C N

k ps k ps k ps k ps

k ps k ps

− − − −

− −

− − − −

− −→ →

= = = =

= =

with pre-factors of the subgroups and offset of the bi-exponential

13 15 13 150.25; 0.75; 0.225; 0.775; 0slowSCN fast SCN slow S C N fast S C NA A A A offset− − − −= = = = = .

(C) 4.3or psτ = is experimentally determined, which is the rotation time of the clustered

ions. 5totn = , 25psτ = .

28

(A) (B)

(C)

0 50 100 150 200

0.0

0.2

0.4

0.6

0.8

1.0

Norm

alize

d Po

pula

tion

Waiting Time (ps)

LiSCN LiS13C15N

0 50 100 150 200-0.005

0.000

0.005

0.010

0.015

0.020

0.025

Norm

alize

d Po

pula

tion

Waiting Time (ps)

Flowing down Pumping up

0 10 20 30 40 50-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

2:98 20:80 50:50 100:0

Norm

alize

d An

isotro

py

Waiting Time (ps)

Figure S7. Data and calculations of nonresonance [(A) and (B)] and Resonance [(C)] for

a 4M LiSCN aqueous solution. Dots are data, and lines are calculations. Calculations for

(A) and (B) are with input parameters:

13 15 13 15

13 15

1 1 1 1

1 1

1/1.55 ( ); 1/16.8 ( ); 1/1.58 ( ); 1/ 20.7 ( );

1/ 20 ( ); K=1.0; 1/ 80 ( ); D=0.70SCN fast SCN slow S C N fast S C N slow

clu iso SCN S C N

k ps k ps k ps k ps

k ps k ps

− − − −

− −

− − − −

− −→ →

= = = =

= =

with pre-factors of the subgroups and offset of the bi-exponential

13 15 13 150.31; 0.69; 0.24; 0.76; 0slowSCN fast SCN slow S C N fast S C NA A A A offset− − − −= = = = = .

(C) 10.2or psτ = is experimentally determined, which is the rotation time of the clustered

ions. 4totn = , 10 psτ = .

29

(A) (B)

(C)

0 50 100 150 200

0.0

0.2

0.4

0.6

0.8

1.0

Norm

alize

d Po

pula

tion

Waiting Time (ps)

NaSCN NaS13C15N

0 50 100 150 200-0.005

0.000

0.005

0.010

0.015

0.020

0.025

Norm

alize

d Po

pula

tion

Waiting Time (ps)

Flowing down Pumping up

0 10 20 30 40 50-0.2

0.0

0.2

0.4

0.6

0.8

1.0

2:98 20:80 50:50 80:20 100:0

Norm

alize

d An

isotro

py

Waiting Time (ps)

Figure S8. Data and calculations of nonresonance [(A) and (B)] and Resonance [(C)] for

a 4M NaSCN aqueous solution. Dots are data, and lines are calculations. Calculations for

(A) and (B) are with input parameters:

13 15 13 15

13 15

1 1 1 1

1 1

1/1.5 ( ); 1/ 23.5 ( ); 1/ 2.6 ( ); 1/ 31.6 ( );

1/ 20 ( ); K=1.5; 1/120 ( ); D=0.70SCN fast SCN slow S C N fast S C N slow

clu iso SCN S C N

k ps k ps k ps k ps

k ps k ps

− − − −

− −

− − − −

− −→ →

= = = =

= =

with pre-factors of the subgroups and offset of the bi-exponential

13 15 13 150.31; 0.69; 0.28; 0.72; 0slowSCN fast SCN slow S C N fast S C NA A A A offset− − − −= = = = = .

(C) 8.5or psτ = is experimentally determined, which is the rotation time of the clustered

ions. 5totn = , 18psτ = .

30

(A) (B)

(C)

0 50 100 150 200 250 300

0.0

0.2

0.4

0.6

0.8

1.0

Norm

alize

d Po

pula

tion

Waiting Time (ps)

CsSCN CsS13C15N

0 50 100 150 200 250 300-0.005

0.000

0.005

0.010

0.015

0.020

Norm

alize

d Po

pula

tion

Waiting Time (ps)

Flowing down Pumping up

0 10 20 30 40 50-0.2

0.0

0.2

0.4

0.6

0.8

1.0

2:98 50:50 100:0

Norm

alize

d An

isotro

py

Waiting Time (ps)

Figure S9. Data and calculations of nonresonance [(A) and (B)] and Resonance [(C)] for

a 4M CsSCN aqueous solution. Dots are data, and lines are calculations. Calculations for

(A) and (B) are with input parameters:

13 15 13 15

13 15

1 1 1 1

1 1

1/ 2.1 ( ); 1/ 26 ( ); 1/1.7 ( ); 1/ 27 ( );

1/10 ( ); K=2.3; 1/ 200 ( ); D=0.70SCN fast SCN slow S C N fast S C N slow

clu iso SCN S C N

k ps k ps k ps k ps

k ps k ps

− − − −

− −

− − − −

− −→ →

= = = =

= =

with pre-factors of the subgroups and offset of the bi-exponential

13 15 13 150.24; 0.76; 0.31; 0.69; 0slowSCN fast SCN slow S C N fast S C NA A A A offset− − − −= = = = = .

(C) 4.9or psτ = is experimentally determined, which is the rotation time of the clustered

ions. 9totn = , 45psτ = .

31

(A) (B)

(C)

0 50 100 150 200 250

0.0

0.2

0.4

0.6

0.8

1.0

Norm

alize

d Po

pula

tion

Waiting Time (ps)

KSCN KS13C15N

0 50 100 150 200 250

-0.002

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

Norm

alize

d Po

pula

tion

Waiting Time (ps)

Flowing down Pumping up

0 10 20 30 40 50-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

2:98 50:50 100:0

Norm

alize

d An

isotro

py

Waiting Time (ps)

Figure S10. Data and calculations of nonresonance [(A) and (B)] and Resonance [(C)] for

a 1.8M KSCN aqueous solution. Dots are data, and lines are calculations. Calculations

for (A) and (B) are with input parameters:

13 15 13 15

13 15

1 1 1 1

1 1

1/1.4 ( ); 1/ 22 ( ); 1/ 2.7 ( ); 1/ 29 ( );

1/10 ( ); K=0.55; 1/160 ( ); D=0.70SCN fast SCN slow S C N fast S C N slow

clu iso SCN S C N

k ps k ps k ps k ps

k ps k ps

− − − −

− −

− − − −

− −→ →

= = = =

= =

with pre-factors of the subgroups and offset of the bi-exponential

13 15 13 150.16; 0.84; 0.22; 0.78; 0slowSCN fast SCN slow S C N fast S C NA A A A offset− − − −= = = = = .

(C) 4.5or psτ = is experimentally determined, which is the rotation time of the clustered

ions. 4totn = , 18psτ = .

32

(A) (B)

(C)

0 50 100 150 200 250

0.0

0.2

0.4

0.6

0.8

1.0

Norm

alize

d Po

pula

tion

Waiting Time (ps)

KSCN KS13C15N

0 50 100 150 200 250-0.002

0.000

0.002

0.004

0.006

0.008

Norm

alize

d Po

pula

tion

Waiting Time (ps)

Flowing down Pumping up

0 10 20 30 40 50-0.2

0.0

0.2

0.4

0.6

0.8

1.0

10:90 50:50 100:0

Norm

alize

d An

isotro

py

Waiting Time (ps)

Figure S11. Data and calculations of nonresonance [(A) and (B)] and Resonance [(C)] for

a 1M KSCN aqueous solution. Dots are data, and lines are calculations. Calculations for

(A) and (B) are with input parameters:

13 15 13 15

13 15

1 1 1 1

1 1

1/1.7 ( ); 1/ 21 ( ); 1/1.6 ( ); 1/ 28 ( );

1/10 ( ); K=0.38; 1/180 ( ); D=0.70SCN fast SCN slow S C N fast S C N slow

clu iso SCN S C N

k ps k ps k ps k ps

k ps k ps

− − − −

− −

− − − −

− −→ →

= = = =

= =

with pre-factors of the subgroups and offset of the bi-exponential

13 15 13 150.25; 0.75; 0.21; 0.79; 0slowSCN fast SCN slow S C N fast S C NA A A A offset− − − −= = = = = .

(C) 4.3or psτ = is experimentally determined, which is the rotation time of the clustered

ions. 3totn = , 15psτ = .

33

1900 1950 2000 2050 2100

1920

1960

2000

2040

2080

2120

1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100

1900 1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100

1920

1960

2000

2040

2080

2120

ωpr

obe

(cm

-1)

ωpump (cm-1)

ωpr

obe

(cm

-1)

ωpump (cm-1)

100fs 0.5ps 1ps 2ps 5ps

10ps 20ps 30ps 50ps

1900 1950 2000 2050 2100

1920

1960

2000

2040

2080

2120

1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100

1900 1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100

1920

1960

2000

2040

2080

2120

ωpr

obe

(cm

-1)

ωpump (cm-1)

ωpr

obe

(cm

-1)

ωpump (cm-1)

100fs 0.5ps 1ps 2ps 5ps

10ps 20ps 30ps 50ps

Figure S12. The time dependence of the 2D IR spectrum of 1M 1:1 KSCN/KS13C15N

aqueous solutions. (water/salt molar ratio = 1:50)

34

1950 2000 2050 2100

1920

1960

2000

2040

2080

2120

100fs 0.5ps 1ps 2ps 5ps

10ps 20ps 30ps 50ps

1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100

1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100

1920

1960

2000

2040

2080

2120

ωpr

obe

(cm

-1)

ωpump (cm-1)

ωpr

obe

(cm

-1)

ωpump (cm-1)

1950 2000 2050 2100

1920

1960

2000

2040

2080

2120

1950 2000 2050 2100

1920

1960

2000

2040

2080

2120

100fs 0.5ps 1ps 2ps 5ps

10ps 20ps 30ps 50ps

1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100

1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100

1920

1960

2000

2040

2080

2120

ωpr

obe

(cm

-1)

ωpump (cm-1)

ωpr

obe

(cm

-1)

ωpump (cm-1)

Figure S13. The time dependence of the 2D IR spectrum of 4M 1:1 LiSCN/LiS13C15N

aqueous solutions. (water/salt molar ratio = 1:10)

35

1950 2000 2050 2100

1920

1960

2000

2040

2080

2120

100fs 0.5ps 1ps 2ps 5ps

10ps 20ps 30ps 50ps

1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100

1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100

1920

1960

2000

2040

2080

2120

ωpr

obe

(cm

-1)

ωpump (cm-1)

ωpr

obe

(cm

-1)

ωpump (cm-1)

1950 2000 2050 2100

1920

1960

2000

2040

2080

2120

100fs 0.5ps 1ps 2ps 5ps

10ps 20ps 30ps 50ps

1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100

1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100

1920

1960

2000

2040

2080

2120

ωpr

obe

(cm

-1)

ωpump (cm-1)

ωpr

obe

(cm

-1)

ωpump (cm-1)

Figure S14. The time dependence of the 2D IR spectrum of 4M 1:1 NaSCN/NaS13C15N

aqueous solutions. (water/salt molar ratio = 1:10)

36

1900 1950 2000 2050 2100

1920

1960

2000

2040

2080

2120

1900 1950 2000 2050 2100

1920

1960

2000

2040

2080

2120

1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100 1950 2000

1900 1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100 1950 2000 2050 2100

1920

1960

2000

2040

2080

2120

100fs 0.5ps 1ps 2ps 5ps

10ps 20ps 30ps 50ps

ωpr

obe

(cm

-1)

ωpump (cm-1)

ωpr

obe

(cm

-1)

ωpump (cm-1) Figure S15. The time dependence of the 2D IR spectrum of 4M 1:1 CsSCN/CsS13C15N

aqueous solutions. (water/salt molar ratio = 1:10)

37

Table S1. Experimental cluster concentrations, the number of anions ( totn ) in an energy

transfer unit, and the resonance one-donor-to-one-acceptor energy transfer time constant

(τ ).

Percentage of

clustered

ions

totn τ (ps)

KSCN (10M) 95 1%± 18 3± 54 8±

KSCN (8.8M) 92 1%± 13 2± 40 8±

KSCN (6.5M) 70 4%± 9 2± 32 6±

KSCN (4M) 67 4%± 5 2± 25 6±

KSCN (1.8M) 35 5%± 4 1± 18 5±

KSCN (1M) 27 6%± 3 1± 15 4±

LiSCN (4M) 50 4%± 4 1± 10 4±

NaSCN (4M) 60 4%± 5 1± 18 5±

CsSCN (4M) 70 4%± 9 2± 45 8±

38

MD simulations

The simulations were performed (by Xiuquan Sun, Jian Song, and Wei Zhuang) using the

AMBER11 package(13).

Models:

Water molecules were modeled using the TIP3P model, and SHAKE algorithm was

used to impose structure constraints on the water molecules. The Lennard-Jones (LJ)

parameters of potassium ions were taken from the all atom AMBER03 force field. The

force field parameters for SCN- ions were generated with the following procedure using

the ANTECHAMBER code in the AMBER11 package: the structure was optimized in

Gaussian03 at HF/6-31G* level and the ESP charges of the atoms were generated at

B3LYP/cc-pVTZ level(14, 15). The ESP charges were then input into ANTECHAMBER

and other force field parameters except the ones for S-C-N angle which were generated

based on the GAFF force field data base(16) in AMBER11. The S-C-N angle parameters

are not available in the GAFF database and thus we set the equilibrium value (

θ0) as 180

degrees (as the result in the previous optimization at HF/6-31G* level). To generate the

force constant, we carried out single point energy calculation at HF/6-31G* level for

several values of S-C-N angle

θ and fit them to the energy equation

Eα = Kθ (θ −θ0)2 .

The finally determined angle bending force constant is

Kθ = 92.72 kcal/mol/rad2. A cutoff

of 9 Å was used for both VdW and short-range electrostatic interactions. The particle

mesh Ewald summation technique was used to calculate the long range electrostatic

interactions.

MD simulation details:

39

In the 10 M solution, 233 KSCN molecules were evenly solvated in a water box

with 538 TIP3P waters. Periodic Boundary Condition is used to mimic the macroscopic

setting for the system. For the 10M solution, the water/salt ratio is 2.3 (the experimental

value is 2.4). For the 4M solution, the water/salt ratio is 10 (the experimental value is 10).

For the 1.8M solution, the water/salt ratio is 26 (the experimental value is 25). The

number of water molecules is 538 for all the systems.

The simulation system was first minimized using a steepest descent algorithm.

The minimized system was then equilibrated for 200 ps at a temperature of 300 K and a

pressure of 1 atm (an NPT simulation where temperature was set using Langevin

Dynamics thermostat). Finally, a 15 ns simulation in canonical ensemble (NVT) with 2 fs

time step was carried out and system configurations were stored every 0.2 ps for the last

10 ns for the later analysis. To improve the sampling, we repeated the calculation above

for 4 different sets of randomized starting coordinates and velocities.

Algorithm of calculating clusters:

When a cation and an anion are in the first solvation shell of each other, we define

them as “contacted ions”. The cations (anions) shared the same anion (cation) are defined

as “neighbor cations (anions)”. If two ions are “contacted” or “neighbor”, they are

considered to be “connected” to each other. Additionally, if ion A and B are both

connected to C, then A and B are considered to be connected. An ion cluster is a

collection of all the ions connected to each other. The first solvation shell is calculated

from the first minimum of the radial distribution function (RDF) between K+ and C atom

of SCN-. The calculated first minimum values are 4.83Α

(10M), 4.79 Α

(4M), and

4.73Α

(1.8M), respectively (fig. S15). The total percentage of ions in clusters (with at

40

least three ions) is calculated to be 99.7% (10M), 79.5% (4M), and 31.4% (1.8M),

respectively.

2 3 4 5 6 7 8 90

1

2

3

4

10M 4M 1.8M

G(r)

KC Distance (angstrom)

4.834.79

4.73

Figure S16. Radius distribution function between K+ and C atom of SCN- of KSCN

aqueous solutions at three different concentrations from MD calculations.

41

Numerical Data of Kinetic Analysis Figure 4 Time Peak 1 Peak 5 Peak3 Peak7 Peak 1

fitting Peak 3 fitting

Peak 5 fitting

Peak 7 fitting

0 0.99999 0.00316 1.00001 0.00224 1 1 0 0 0.5 0.92215 0.00173 0.93461 5.59031E-4 0.94243 0.94488 0.00389 0.00272 1 0.87544 0.00245 0.89437 0.0038 0.89356 0.89888 0.00737 0.00516 1.1 0.86599 0.00231 0.88895 0.00646 0.88469 0.89061 0.00802 0.00561 1.2 0.8665 1.17235E-4 0.87087 0.00413 0.87609 0.88262 0.00866 0.00606 1.3 0.85335 0.00196 0.85157 0.00409 0.86776 0.8749 0.00929 0.0065 1.4 0.8418 0.00183 0.8579 0.00481 0.85967 0.86743 0.0099 0.00693 1.5 0.82973 9.95561E-4 0.86262 0.00617 0.85183 0.86022 0.01051 0.00735 1.6 0.8273 0.00322 0.85454 0.00714 0.84422 0.85323 0.0111 0.00777 1.7 0.83112 7.24472E-4 0.84488 0.00431 0.83683 0.84648 0.01168 0.00818 1.8 0.82252 0.00365 0.84583 0.00427 0.82966 0.83994 0.01225 0.00858 1.9 0.81747 0.0036 0.85103 0.00724 0.8227 0.8336 0.01281 0.00897 2 0.81297 0.00607 0.84112 0.00538 0.81594 0.82747 0.01336 0.00935 2.5 0.77887 0.00645 0.8082 0.00695 0.78484 0.79949 0.01599 0.01119 3 0.75261 0.00589 0.7853 0.009 0.75767 0.77535 0.01842 0.0129 3.5 0.72893 0.00881 0.76594 0.01173 0.73374 0.75432 0.02069 0.01448 4 0.71563 0.00992 0.7555 0.01308 0.71249 0.73581 0.02282 0.01598 4.5 0.70143 0.01558 0.73544 0.01603 0.69343 0.71933 0.02483 0.01738 5 0.67543 0.01592 0.71812 0.0158 0.6762 0.70452 0.02673 0.01871 5.5 0.66952 0.01637 0.69188 0.01588 0.66048 0.69105 0.02855 0.01998 6 0.65256 0.02131 0.6871 0.01906 0.64601 0.67869 0.03027 0.02119 6.5 0.63932 0.02003 0.67313 0.01782 0.63261 0.66723 0.03193 0.02235 7 0.62278 0.01937 0.66369 0.01898 0.62008 0.65652 0.03351 0.02346 7.5 0.6074 0.02251 0.65114 0.0216 0.6083 0.64643 0.03503 0.02452 8 0.59115 0.02673 0.63576 0.02349 0.59716 0.63685 0.03649 0.02555 8.5 0.58684 0.02659 0.63299 0.02328 0.58655 0.62771 0.0379 0.02653 9 0.57509 0.02978 0.61747 0.02503 0.5764 0.61894 0.03926 0.02748 9.5 0.56681 0.03327 0.61832 0.02829 0.56666 0.61048 0.04056 0.02839 10 0.55625 0.03204 0.5999 0.02967 0.55727 0.60228 0.04182 0.02928 11 0.54125 0.03755 0.58942 0.02708 0.53938 0.58657 0.04421 0.03094 12 0.5236 0.03967 0.57252 0.03157 0.52247 0.5716 0.04642 0.0325 13 0.50201 0.03956 0.56593 0.03166 0.50637 0.55723 0.04848 0.03394 14 0.48768 0.04292 0.54412 0.03284 0.49096 0.54336 0.05039 0.03527 15 0.47633 0.04393 0.52226 0.03399 0.47615 0.52994 0.05216 0.03651 16 0.45982 0.04786 0.52663 0.03403 0.46188 0.51692 0.05379 0.03765 17 0.44171 0.05025 0.50195 0.03803 0.44811 0.50427 0.0553 0.03871 18 0.4291 0.05103 0.48494 0.03941 0.4348 0.49197 0.05668 0.03968 19 0.41345 0.05418 0.47744 0.03996 0.42193 0.47999 0.05795 0.04056 20 0.40496 0.05359 0.46127 0.04083 0.40947 0.46834 0.05911 0.04138 22 0.37933 0.05814 0.43673 0.04028 0.38571 0.44592 0.06112 0.04278 25 0.34257 0.06262 0.41478 0.04532 0.35278 0.41441 0.06342 0.0444 28 0.31749 0.06681 0.38325 0.04415 0.32278 0.38524 0.06499 0.04549 30 0.29805 0.06415 0.3597 0.04646 0.30428 0.36699 0.06568 0.04598 33 0.26759 0.06783 0.33445 0.04801 0.27859 0.34131 0.06624 0.04637 35 0.25231 0.0657 0.32176 0.04692 0.26274 0.32524 0.06634 0.04644 38 0.23296 0.06972 0.29772 0.04841 0.24071 0.30261 0.06614 0.0463 40 0.21877 0.06857 0.28208 0.04777 0.2271 0.28845 0.06579 0.04605

42

43 0.2015 0.06644 0.26391 0.04642 0.2082 0.26849 0.06501 0.0455 45 0.18739 0.06679 0.2506 0.04764 0.19652 0.256 0.06433 0.04503 48 0.17706 0.06611 0.23458 0.04507 0.18027 0.23838 0.06312 0.04419 50 0.16556 0.06295 0.22296 0.04242 0.17023 0.22734 0.06221 0.04354 55 0.14816 0.06219 0.2 0.04324 0.14763 0.20202 0.05961 0.04173 60 0.13377 0.05865 0.17746 0.0419 0.12817 0.17964 0.05671 0.0397 65 0.10883 0.05582 0.15906 0.04055 0.1114 0.15982 0.05361 0.03753 70 0.10042 0.05174 0.14305 0.03357 0.09693 0.14227 0.05042 0.0353 75 0.08665 0.04892 0.12102 0.03261 0.08443 0.12672 0.04721 0.03305 80 0.07502 0.04736 0.10963 0.0303 0.07363 0.11293 0.04404 0.03083 85 0.064 0.04581 0.09877 0.03083 0.06428 0.10068 0.04094 0.02866 90 0.05494 0.04345 0.08556 0.02539 0.05619 0.08981 0.03795 0.02656 95 0.04462 0.03584 0.07879 0.02861 0.04916 0.08015 0.03508 0.02456 100 0.04124 0.03721 0.06835 0.02523 0.04306 0.07155 0.03236 0.02265 110 0.02748 0.02741 0.05571 0.01831 0.03315 0.05711 0.02738 0.01917 120 0.02458 0.02351 0.04378 0.01465 0.02563 0.04564 0.02301 0.01611 130 0.02236 0.02202 0.03405 0.01568 0.01989 0.03653 0.01925 0.01347 140 0.01516 0.01762 0.02644 0.00998 0.0155 0.02927 0.01602 0.01122 150 0.01502 0.01219 0.02206 0.00975 0.01213 0.02349 0.0133 0.00931 160 0.01088 0.01504 0.01954 0.00775 0.00952 0.01886 0.011 0.0077 170 0.0081 0.01045 0.01319 0.00405 0.0075 0.01516 0.00908 0.00636 180 0.00668 0.00972 0.01199 0.00514 0.00592 0.0122 0.00748 0.00523 190 0.00942 0.01022 0.00877 0.00503 0.00469 0.00982 0.00615 0.0043 200 0.00529 0.00441 0.00794 0.00223 0.00373 0.00792 0.00505 0.00353 210 0.00292 0.00537 0.00469 0.00358 0.00297 0.00638 0.00414 0.0029 220 0.00353 0.00541 0.00464 0.0026 0.00237 0.00515 0.00339 0.00237 230 -6.02379E-4 0.00174 0.00373 0.00195 0.00189 0.00416 0.00278 0.00194 240 0.00554 0.00335 0.00129 0.00257 0.00152 0.00336 0.00227 0.00159 250 0.00378 -0.00238 -6.96007E-4 0.00132 0.00122 0.00271 0.00186 0.0013 Figure 5 Time 1:99 Time 2:98 Time 10:90 Time 20:80 Time 50:50 Time 100:0 0 0.99999 0 0.9527 0 0.97513 0 0.98546 0.1 0.99611 0 1.00001 0.1 0.97407 0.1 1.00001 0.1 0.97144 0.1 1.00001 0.2 1 0.1 0.94902 0.2 0.98123 0.2 0.95442 0.2 0.99999 0.2 0.96219 0.3 0.91964 0.2 0.90021 0.3 0.95951 0.3 0.90438 0.3 0.95352 0.3 0.93384 0.4 0.88733 0.3 0.84415 0.4 0.94092 0.4 0.9359 0.4 0.94504 0.4 0.93588 0.5 0.87482 0.4 0.81678 0.5 0.96339 0.5 0.93219 0.5 0.89544 0.5 0.90028 0.6 0.83534 0.5 0.76929 0.6 0.9372 0.6 0.89919 0.6 0.88253 0.6 0.8649 0.7 0.84418 0.6 0.75481 0.7 0.91247 0.7 0.87687 0.7 0.90976 0.7 0.85358 0.8 0.80584 0.7 0.71845 0.8 0.91923 0.8 0.89362 0.8 0.85697 0.8 0.85151 0.9 0.7892 0.8 0.70777 0.9 0.92998 0.9 0.84496 0.9 0.88323 0.9 0.85574 1 0.74641 0.9 0.67173 1 0.87688 1 0.87462 1 0.81404 1 0.82726 1.1 0.72882 1 0.62571 1.1 0.89404 1.1 0.86387 1.1 0.84427 1.1 0.82152 1.2 0.70881 1.1 0.58438 1.2 0.85834 1.2 0.83714 1.2 0.82758 1.2 0.78801 1.3 0.6937 1.2 0.59333 1.3 0.8554 1.3 0.81324 1.3 0.8154 1.3 0.78119 1.4 0.67757 1.3 0.5538 1.4 0.83751 1.4 0.80075 1.4 0.81112 1.4 0.76536 1.5 0.67352 1.4 0.54681 1.5 0.83327 1.5 0.80341 1.5 0.82082 1.5 0.75568 1.6 0.66688 1.5 0.50056 1.6 0.79196 1.6 0.76688 1.6 0.76281 1.6 0.72937 1.7 0.62533 1.6 0.48211 1.7 0.80262 1.7 0.77074 1.7 0.77028 1.7 0.7339 1.8 0.62243 1.7 0.44717 1.8 0.81736 1.8 0.7382 1.8 0.75936 1.8 0.71984 1.9 0.6114 1.8 0.42812 1.9 0.78567 1.9 0.76649 2.3 0.69751 1.9 0.705 2 0.59514 1.9 0.41082 2 0.78504 2 0.79775 2.8 0.67048 2 0.72008 2.1 0.58037 2.4 0.35764 2.5 0.75882 2.5 0.70106 3.3 0.63807 2.5 0.66663 2.2 0.57055 2.9 0.30927 3 0.68383 3 0.6645 3.8 0.5898 3 0.61014 2.7 0.49038 3.4 0.24174

43

3.5 0.67627 3.5 0.65992 4.3 0.53834 3.5 0.55566 3.2 0.44383 3.9 0.19451 4 0.63011 4 0.59494 4.8 0.51259 4 0.5158 3.7 0.42421 4.4 0.1465 4.5 0.60236 4.5 0.59767 5.3 0.47832 4.5 0.49415 4.2 0.37365 4.9 0.14445 5 0.56631 5 0.54515 5.8 0.46723 5 0.46181 4.7 0.31 5.4 0.11026 5.5 0.54282 5.5 0.51828 6.3 0.39502 5.5 0.42557 5.2 0.27319 5.9 0.07962 6 0.49914 6 0.51164 6.8 0.39715 6 0.39226 5.7 0.26833 6.4 0.09118 6.5 0.4821 6.5 0.50559 7.3 0.3474 6.5 0.40174 6.2 0.25206 6.9 0.08544 7 0.46402 7 0.46677 7.8 0.36566 7 0.32408 6.7 0.23154 7.4 0.0733 7.5 0.43501 7.5 0.43518 8.3 0.33792 7.5 0.35241 7.7 0.1904 7.9 0.06278 8 0.44222 8 0.44152 8.8 0.33661 8 0.31117 8.7 0.14661 8.4 0.0668 9 0.40445 9 0.39272 9.3 0.31408 9 0.2786 9.7 0.10325 9.4 0.05222 10 0.32247 10 0.34251 9.8 0.30039 9.5 0.26453 10.2 0.08737 9.9 0.0279 11 0.2981 11 0.29112 10.8 0.21993 10 0.20805 11.2 0.06246 10.9 0.01687 12 0.29015 12 0.2771 11.8 0.23342 11 0.1895 12.2 0.02913 11.9 0.02928 13 0.27931 13 0.26181 12.8 0.22844 12 0.17552 13.2 0.0248 12.9 0.02728 14 0.25816 14 0.21956 13.8 0.18283 13 0.15242 14.2 0.04682 13.9 0.04272 15 0.21548 15 0.2512 14.8 0.16814 14 0.16876 15.2 0.03469 14.9 0.01638 16 0.19591 16 0.21063 15.8 0.16516 15 0.11441 16.2 0.02517 15.9 -0.01407 17 0.17205 17 0.19209 16.8 0.12431 16 0.11305 17.2 -0.00299 16.9 -0.00203 18 0.16476 18 0.17013 17.8 0.09163 17 0.11326 18.2 0.01663 17.9 0.01653 19 0.12687 19 0.1556 18.8 0.10702 18 0.11164 19.2 0.01796 18.9 0.01321 20 0.12858 20 0.11541 19.8 0.10546 19 0.10807 20.2 0.02224 19.9 -0.02588 22 0.10738 22 0.12327 21.8 0.08424 20 0.08814 22.2 0.00683 21.9 0.01044 25 0.07742 25 0.07818 24.8 0.03926 22 0.02829 25.2 -0.02874 24.9 -0.01957 28 0.09582 28 0.04966 27.8 0.02217 25 0.0893 28.2 -0.03126 27.9 0.0087 30 0.00516 30 0.04626 29.8 0.0212 28 0.01728 30.2 0.00218 29.9 0.00988 33 0.04468 33 0.03117 32.8 -0.00426 30 0.04161 33.2 -0.01594 32.9 0.03092 35 0.03283 35 0.03152 34.8 0.02226 33 0.02458 35.2 -0.01171 34.9 0.01381 38 -0.00328 38 0.01457 37.8 0.02012 38 -0.00343 38.2 -0.00215 37.9 -0.01367 40 0.02777 40 0.04001 39.8 0.00978 40 -0.01672 40.2 -0.00305 39.9 -0.00502 43 0.0208 43 0.05628 42.8 -0.01935 43 0.02129 43.2 -0.02496 42.9 -0.00438 45 0.00101 45 -0.03468 44.8 -0.02316 45 0.01262 45.2 -0.02101 44.9 -0.00822 48 -0.01734 48 0.0483 47.8 0.01145 48 -0.00246 48.2 -0.00429 47.9 0.01836 50 -0.01531 50 0.0206 49.8 0.03258 50 -0.016 50.2 -0.0064 49.9 0.0044 55 0.03214 55 -0.0226 54.8 0.01253 55 -0.02407 55.2 0.00828 54.9 -0.01368 60 -0.05865 60 0.01028 59.8 0.00496 60 0.03856 60.2 2.69095E-4 59.9 -0.02708 Time 1:99

fitting Time 2:98

fitting Time 10:90

fitting Time 20:80

fitting Time 50:50

fitting Time 100:0

fitting 0 1 0 1 0 1 0 1 0.1 0.97624 0 1 0.1 0.98983 0.1 0.98955 0.1 0.98732 0.1 0.98454 0.2 0.95307 0.1 0.96257 0.2 0.97976 0.2 0.97921 0.2 0.9748 0.2 0.96932 0.3 0.93047 0.2 0.92659 0.3 0.9698 0.3 0.96898 0.3 0.96245 0.3 0.95436 0.4 0.90843 0.3 0.89199 0.4 0.95993 0.4 0.95885 0.4 0.95026 0.4 0.93963 0.5 0.88694 0.4 0.85873 0.5 0.95017 0.5 0.94884 0.5 0.93823 0.5 0.92513 0.6 0.86597 0.5 0.82676 0.6 0.94051 0.6 0.93893 0.6 0.92635 0.6 0.91087 0.7 0.84552 0.6 0.79601 0.7 0.93095 0.7 0.92912 0.7 0.91463 0.7 0.89684 0.8 0.82558 0.7 0.76646 0.8 0.92148 0.8 0.91942 0.8 0.90306 0.8 0.88303 0.9 0.80612 0.8 0.73804 0.9 0.91211 0.9 0.90982 0.9 0.89165 0.9 0.86944 1 0.78715 0.9 0.71071 1 0.90284 1 0.90031 1 0.88038 1 0.85608 1.1 0.76864 1 0.68444 1.1 0.89366 1.1 0.89091 1.1 0.86925 1.1 0.84292 1.2 0.75059 1.1 0.65918 1.2 0.88458 1.2 0.88161 1.2 0.85827 1.2 0.82997 1.3 0.73298 1.2 0.63489 1.3 0.87558 1.3 0.87241 1.3 0.84744 1.3 0.81724 1.4 0.7158 1.3 0.61154 1.4 0.86668 1.4 0.8633 1.4 0.83674 1.4 0.8047 1.5 0.69905 1.4 0.58908 1.5 0.85787 1.5 0.85429 1.5 0.82619 1.5 0.79237 1.6 0.6827 1.5 0.56749 1.6 0.84915 1.6 0.84538 1.6 0.81577 1.6 0.78023 1.7 0.66676 1.6 0.54673 1.7 0.84052 1.7 0.83655 1.7 0.80549 1.7 0.76828 1.8 0.65121 1.7 0.52676 2 0.81516 2 0.81064 1.8 0.79534 1.8 0.75653 2 0.62124 1.8 0.50756 2.5 0.77457 2.5 0.76924 2.3 0.74653 2 0.73358 2.7 0.52731 2.4 0.40685

44

3 0.73602 3 0.72997 2.8 0.7008 2.5 0.67933 3.2 0.4695 2.9 0.33916 3.5 0.6994 3.5 0.69272 3.3 0.65795 3 0.62925 3.7 0.41837 3.4 0.28342 4 0.6646 4 0.65738 3.8 0.61779 3.5 0.58301 4.2 0.37315 3.9 0.23747 4.5 0.63154 4.5 0.62386 4.3 0.58016 4 0.54032 4.7 0.33313 4.4 0.19957 5 0.60014 5 0.59207 4.8 0.54488 4.5 0.50089 5.2 0.2977 4.9 0.16827 5.5 0.5703 5.5 0.5619 5.3 0.51181 5 0.46446 5.7 0.26631 5.4 0.14239 6 0.54195 6 0.53329 5.8 0.48081 5.5 0.43081 6.2 0.23849 5.9 0.12097 6.5 0.51501 6.5 0.50614 6.3 0.45175 6 0.3997 6.7 0.21381 6.4 0.10321 7 0.48942 7 0.48039 6.8 0.42449 6.5 0.37095 7.2 0.19192 6.9 0.08846 7.5 0.46511 7.5 0.45595 7.3 0.39892 7 0.34437 7.7 0.17248 7.4 0.07618 8 0.44201 8 0.43277 7.8 0.37495 7.5 0.31978 8.2 0.1552 7.9 0.06594 8.5 0.42006 8.5 0.41078 8.3 0.35245 8 0.29704 8.7 0.13984 8.4 0.05738 9 0.3992 9 0.38991 8.8 0.33135 8.5 0.276 9.2 0.12616 8.9 0.0502 9.5 0.37939 9.5 0.37011 9.3 0.31155 9 0.25653 9.7 0.11399 9.4 0.04417 10 0.36056 10 0.35132 9.8 0.29297 9.5 0.23851 10.2 0.10313 9.9 0.03908 11 0.32567 11 0.31658 10.8 0.25917 10 0.22182 11.2 0.08479 10.9 0.0311 12 0.29416 12 0.28529 11.8 0.22938 11 0.19204 12.2 0.07013 11.9 0.02528 13 0.26572 13 0.25712 12.8 0.20312 12 0.16648 13.2 0.05837 12.9 0.02096 14 0.24003 14 0.23175 13.8 0.17995 13 0.1445 14.2 0.04888 13.9 0.01768 15 0.21684 15 0.2089 14.8 0.15951 14 0.12559 15.2 0.04118 14.9 0.01513 16 0.19589 16 0.18832 15.8 0.14146 15 0.1093 16.2 0.03492 15.9 0.01312 17 0.17698 17 0.16977 16.8 0.12552 16 0.09525 17.2 0.02978 16.9 0.01148 18 0.1599 18 0.15307 17.8 0.11142 17 0.08311 18.2 0.02554 17.9 0.01013 19 0.14447 19 0.13802 18.8 0.09896 18 0.07262 19.2 0.02203 18.9 0.009 20 0.13053 20 0.12446 19.8 0.08794 19 0.06354 20.2 0.0191 19.9 0.00803 22 0.10657 22 0.10122 21.8 0.06954 20 0.05567 22.2 0.01455 21.9 0.00645 25 0.07865 25 0.07428 24.8 0.04907 22 0.0429 25.2 0.00997 24.9 0.00472 28 0.05805 28 0.05455 27.8 0.03477 25 0.0293 28.2 0.00702 27.9 0.00348 30 0.04742 30 0.04441 29.8 0.0277 28 0.02023 30.2 0.00561 29.9 0.00285 33 0.03502 33 0.03264 32.8 0.01976 30 0.01589 33.2 0.00406 32.9 0.00211 35 0.02862 35 0.02659 34.8 0.01581 33 0.01116 35.2 0.00329 34.9 0.00173 38 0.02114 38 0.01956 37.8 0.01134 38 0.0063 38.2 0.00241 37.9 0.00128 40 0.01728 40 0.01595 39.8 0.00911 40 0.00504 40.2 0.00196 39.9 0.00105 43 0.01277 43 0.01174 42.8 0.00657 43 0.00363 43.2 0.00145 42.9 7.81183E-4 45 0.01044 45 0.00958 44.8 0.00529 45 0.00292 45.2 0.00119 44.9 6.40319E-4 48 0.00772 48 0.00706 47.8 0.00384 48 0.00212 48.2 8.7758E-4 47.9 4.75191E-4 50 0.00631 50 0.00576 49.8 0.0031 50 0.00172 50.2 7.18527E-4 49.9 3.8951E-4 55 0.00382 55 0.00347 54.8 0.00183 55 0.00102 55.2 4.36359E-4 54.9 2.36945E-4 60 0.00231 60 0.00209 59.8 0.00108 60 6.08523E-4 60.2 2.65242E-4 59.9 1.44138E-4 S2.A Time KSCN (10M) KS13C15N (10M) KSCN (10M)

fitting KS13C15N (10M) fitting

0 0.99999 1.00001 1 1 0.5 0.92215 0.93461 0.94151 0.94041 1 0.87544 0.89437 0.89192 0.89086 1.1 0.86599 0.88895 0.88292 0.88198 1.2 0.8665 0.87087 0.87419 0.8734 1.3 0.85335 0.85157 0.86574 0.86512

45

1.4 0.8418 0.8579 0.85754 0.85712 1.5 0.82973 0.86262 0.84959 0.84939 1.6 0.8273 0.85454 0.84187 0.84192 1.7 0.83112 0.84488 0.83438 0.83469 1.8 0.82252 0.84583 0.82711 0.82771 1.9 0.81747 0.85103 0.82005 0.82095 2 0.81297 0.84112 0.81319 0.8144 2.5 0.77887 0.8082 0.78166 0.78464 3 0.75261 0.7853 0.75412 0.75908 3.5 0.72893 0.76594 0.72986 0.73691 4 0.71563 0.7555 0.70829 0.71748 4.5 0.70143 0.73544 0.68895 0.70026 5 0.67543 0.71812 0.67144 0.68485 5.5 0.66952 0.69188 0.65546 0.6709 6 0.65256 0.6871 0.64075 0.65814 6.5 0.63932 0.67313 0.62709 0.64636 7 0.62278 0.66369 0.61433 0.63538 7.5 0.6074 0.65114 0.60232 0.62507 8 0.59115 0.63576 0.59094 0.61531 8.5 0.58684 0.63299 0.58011 0.60602 9 0.57509 0.61747 0.56975 0.59712 9.5 0.56681 0.61832 0.5598 0.58855 10 0.55625 0.5999 0.5502 0.58027 11 0.54125 0.58942 0.53191 0.56442 12 0.5236 0.57252 0.51463 0.54936 13 0.50201 0.56593 0.49818 0.53492 14 0.48768 0.54412 0.48244 0.52102 15 0.47633 0.52226 0.46734 0.50758 16 0.45982 0.52663 0.4528 0.49457 17 0.44171 0.50195 0.43877 0.48194 18 0.4291 0.48494 0.42524 0.46968 19 0.41345 0.47744 0.41216 0.45776 20 0.40496 0.46127 0.39952 0.44617 22 0.37933 0.43673 0.37546 0.42392 25 0.34257 0.41478 0.3422 0.39273 28 0.31749 0.38325 0.31203 0.36395 30 0.29805 0.3597 0.29348 0.34601 33 0.26759 0.33445 0.2678 0.32083 35 0.25231 0.32176 0.252 0.30512 38 0.23296 0.29772 0.23011 0.28305 40 0.21877 0.28208 0.21664 0.26927 43 0.2015 0.26391 0.19797 0.24992 45 0.18739 0.2506 0.18647 0.23783 48 0.17706 0.23458 0.17052 0.22083 50 0.16556 0.22296 0.16069 0.21021 55 0.14816 0.2 0.13865 0.18594 60 0.13377 0.17746 0.11979 0.16458 65 0.10883 0.15906 0.10361 0.14577 70 0.10042 0.14305 0.08974 0.1292 75 0.08665 0.12102 0.07782 0.11457 80 0.07502 0.10963 0.06756 0.10166 85 0.064 0.09877 0.05873 0.09026 90 0.05494 0.08556 0.05112 0.08018 95 0.04462 0.07879 0.04455 0.07126 100 0.04124 0.06835 0.03887 0.06336 110 0.02748 0.05571 0.02969 0.05016 120 0.02458 0.04378 0.02279 0.03978 130 0.02236 0.03405 0.01757 0.03159 140 0.01516 0.02644 0.0136 0.02512 150 0.01502 0.02206 0.01057 0.02001 160 0.01088 0.01954 0.00824 0.01595 170 0.0081 0.01319 0.00645 0.01273

46

180 0.00668 0.01199 0.00507 0.01016 190 0.00942 0.00877 0.00399 0.00813 200 0.00529 0.00794 0.00315 0.0065 210 0.00292 0.00469 0.00249 0.0052 220 0.00353 0.00464 0.00198 0.00417 230 -6.02379E-4 0.00373 0.00157 0.00334 240 0.00554 0.00129 0.00125 0.00268 250 0.00378 -6.96007E-4 9.9998E-4 0.00215 S2.B Time Flowing down Pumping up Flowing down fitting Pumping up fitting 0 1.17235E-4 0.00224 0 0 0.5 7.24472E-4 5.59031E-4 0.00417 0.00292 1 0.0062 0.0038 0.00788 0.00551 1.1 0.0063 0.00646 0.00857 0.006 1.2 0.0064 0.00413 0.00925 0.00648 1.3 0.00645 0.00409 0.00992 0.00694 1.4 0.0065 0.00481 0.01057 0.0074 1.5 0.0067 0.00617 0.01121 0.00785 1.6 0.0065 0.00714 0.01184 0.00829 1.7 0.0066 0.00431 0.01245 0.00872 1.8 0.00645 0.00427 0.01306 0.00914 1.9 0.007 0.00724 0.01365 0.00955 2 0.0075 0.00538 0.01423 0.00996 2.5 0.00881 0.00695 0.017 0.0119 3 0.00992 0.009 0.01956 0.01369 3.5 0.01558 0.01173 0.02193 0.01535 4 0.01592 0.01308 0.02416 0.01691 4.5 0.01637 0.01603 0.02626 0.01838 5 0.02131 0.0158 0.02824 0.01977 5.5 0.02003 0.01588 0.03012 0.02109 6 0.01937 0.01906 0.03192 0.02234 6.5 0.02251 0.01782 0.03364 0.02355 7 0.02673 0.01898 0.03528 0.0247 7.5 0.02659 0.0216 0.03686 0.0258 8 0.02978 0.02349 0.03838 0.02686 8.5 0.03327 0.02328 0.03983 0.02788 9 0.03204 0.02503 0.04124 0.02887 9.5 0.03755 0.02829 0.04259 0.02981 10 0.0385 0.02967 0.04389 0.03072 11 0.03967 0.02708 0.04636 0.03245 12 0.03956 0.03157 0.04864 0.03405 13 0.04292 0.03166 0.05077 0.03554 14 0.04393 0.03284 0.05274 0.03691 15 0.04786 0.03399 0.05456 0.03819 16 0.05025 0.03403 0.05624 0.03936 17 0.05103 0.03803 0.05778 0.04045 18 0.05418 0.03941 0.0592 0.04144 19 0.05359 0.03996 0.0605 0.04235 20 0.05814 0.04083 0.06169 0.04318 22 0.06262 0.04028 0.06373 0.04461 25 0.06681 0.04532 0.06607 0.04625 28 0.06415 0.04415 0.06764 0.04735 30 0.06783 0.04646 0.06831 0.04782 33 0.0657 0.04801 0.06884 0.04819 35 0.06972 0.04692 0.06891 0.04824 38 0.06857 0.04841 0.06865 0.04806 40 0.06644 0.04777 0.06826 0.04778

47

43 0.06679 0.04642 0.06741 0.04718 45 0.06611 0.04764 0.06668 0.04668 48 0.06295 0.04507 0.06539 0.04577 50 0.06219 0.04242 0.06442 0.04509 55 0.05865 0.04324 0.06169 0.04318 60 0.05582 0.0419 0.05865 0.04105 65 0.05174 0.04055 0.05542 0.03879 70 0.04892 0.03357 0.0521 0.03647 75 0.04736 0.03261 0.04876 0.03413 80 0.04581 0.0303 0.04547 0.03183 85 0.04345 0.03083 0.04227 0.02959 90 0.03584 0.02539 0.03917 0.02742 95 0.03721 0.02861 0.03622 0.02535 100 0.02741 0.02523 0.03342 0.02339 110 0.02351 0.01831 0.02828 0.0198 120 0.02202 0.01465 0.02379 0.01666 130 0.01762 0.01568 0.01992 0.01394 140 0.01219 0.00998 0.01661 0.01162 150 0.01504 0.00975 0.0138 0.00966 160 0.01045 0.00775 0.01144 0.00801 170 0.00972 0.00405 0.00946 0.00662 180 0.01022 0.00514 0.00781 0.00547 190 0.00441 0.00503 0.00644 0.00451 200 0.00441 0.00223 0.0053 0.00371 210 0.00537 0.00358 0.00436 0.00305 220 0.00541 0.0026 0.00358 0.00251 230 0.00174 0.00195 0.00294 0.00206 240 0.00335 0.00257 0.00241 0.00169 250 -0.00238 0.00132 0.00198 0.00139 S2.C Time KSCN (4M) KS13C15N (4M) KSCN (4M)

fitting KS13C15N (4M) fitting

0 1.00001 0.99617 1 1 0.1 0.99011 1 0.98475 0.9857 0.2 0.97047 0.99253 0.97008 0.97196 0.3 0.94939 0.97416 0.95596 0.95877 0.4 0.93515 0.96113 0.94236 0.9461 0.5 0.91021 0.94601 0.92926 0.93392 0.6 0.89541 0.9342 0.91664 0.92222 0.7 0.88452 0.92073 0.90448 0.91096 0.8 0.86167 0.90856 0.89275 0.90012 0.9 0.84947 0.89898 0.88143 0.8897 1 0.83548 0.88809 0.8705 0.87966 1.1 0.82215 0.87986 0.85996 0.86998 1.2 0.81004 0.87314 0.84977 0.86066 1.3 0.79634 0.86098 0.83992 0.85168 1.4 0.79005 0.85386 0.83041 0.84301 1.5 0.78276 0.84592 0.82121 0.83465 1.6 0.7758 0.83963 0.8123 0.82658 1.7 0.7649 0.83116 0.80369 0.81878 1.8 0.76172 0.82537 0.79534 0.81125 1.9 0.74986 0.81968 0.78726 0.80397 2 0.7414 0.81518 0.77943 0.79693 2.1 0.73639 0.80918 0.77183 0.79012 2.2 0.73156 0.80465 0.76446 0.78353 2.3 0.72326 0.79426 0.75732 0.77715

48

2.4 0.71925 0.79177 0.75038 0.77096 2.5 0.70954 0.78365 0.74364 0.76497 2.6 0.70032 0.7809 0.73709 0.75915 2.7 0.70125 0.77415 0.73072 0.75351 2.8 0.69579 0.76996 0.72453 0.74804 2.9 0.68769 0.7665 0.71851 0.74272 3 0.6858 0.76059 0.71264 0.73755 3.1 0.68273 0.75593 0.70693 0.73253 3.2 0.67702 0.75209 0.70137 0.72764 3.3 0.67032 0.74587 0.69595 0.72288 3.4 0.66491 0.7425 0.69066 0.71825 3.5 0.66215 0.74031 0.6855 0.71374 3.6 0.65738 0.73428 0.68047 0.70935 3.7 0.64965 0.73117 0.67555 0.70506 3.8 0.64363 0.72824 0.67075 0.70088 3.9 0.64235 0.72334 0.66606 0.69679 4 0.63713 0.72136 0.66147 0.69281 4.1 0.6402 0.71689 0.65699 0.68891 4.2 0.63118 0.70892 0.6526 0.6851 4.3 0.62597 0.70617 0.6483 0.68138 4.4 0.62202 0.70327 0.64409 0.67774 4.5 0.62518 0.70214 0.63996 0.67417 4.6 0.61734 0.69766 0.63592 0.67068 4.7 0.6114 0.69233 0.63196 0.66725 4.8 0.6109 0.68958 0.62807 0.6639 4.9 0.60581 0.68671 0.62425 0.6606 5 0.60163 0.68566 0.62051 0.65737 5.1 0.60186 0.68253 0.61683 0.6542 5.2 0.59748 0.67628 0.61322 0.65109 5.3 0.58985 0.67378 0.60967 0.64803 5.4 0.59079 0.66986 0.60617 0.64502 5.5 0.58635 0.66752 0.60274 0.64207 5.6 0.5817 0.66484 0.59936 0.63916 5.7 0.57722 0.66084 0.59603 0.63629 5.8 0.57539 0.65784 0.59276 0.63347 5.9 0.57046 0.65583 0.58953 0.6307 6 0.56625 0.65338 0.58636 0.62796 6.1 0.56378 0.64983 0.58322 0.62527 6.2 0.56035 0.64483 0.58014 0.62261 6.3 0.55969 0.63982 0.57709 0.61998 6.4 0.55718 0.63782 0.57409 0.6174 6.9 0.54816 0.62581 0.55964 0.60493 7.4 0.52892 0.61099 0.54604 0.59317 7.9 0.51664 0.60077 0.53315 0.58198 8.4 0.49982 0.58777 0.52087 0.57129 8.9 0.49411 0.5764 0.50912 0.56101 9.4 0.48348 0.5661 0.49783 0.55109 9.9 0.46698 0.55173 0.48695 0.54149 10.4 0.45676 0.54374 0.47644 0.53216 11.4 0.4364 0.52555 0.45638 0.51423 12.4 0.41739 0.50414 0.43742 0.49712 13.4 0.40339 0.487 0.41942 0.48072 14.4 0.38636 0.46979 0.40227 0.46494 15.4 0.36891 0.45161 0.38589 0.44975 16.4 0.35534 0.43707 0.37023 0.43508 17.4 0.33835 0.42471 0.35524 0.42092 18.4 0.32436 0.40664 0.34088 0.40724 19.4 0.31044 0.3965 0.32712 0.39401 20.4 0.29525 0.38146 0.31392 0.38122 23.4 0.26524 0.35741 0.27748 0.34533 25.4 0.24391 0.3333 0.2556 0.32332 28.4 0.21921 0.30225 0.22599 0.29293

49

30.4 0.19664 0.27916 0.2082 0.27429 35.4 0.16339 0.23766 0.16966 0.23275 40.4 0.13104 0.20119 0.13831 0.19754 43.4 0.11481 0.18191 0.12238 0.17905 45.4 0.1021 0.17203 0.1128 0.1677 48.4 0.092 0.15533 0.09983 0.15202 50.4 0.08261 0.14495 0.09204 0.14239 55.4 0.07032 0.12469 0.07513 0.12092 60.4 0.05652 0.1055 0.06135 0.10271 65.4 0.04435 0.08937 0.05013 0.08726 70.4 0.0375 0.07609 0.04098 0.07415 75.4 0.02923 0.0641 0.03351 0.06301 80.4 0.02414 0.05535 0.02742 0.05356 85.4 0.02048 0.04709 0.02245 0.04553 90.4 0.01448 0.03894 0.01839 0.03871 95.4 0.01336 0.03407 0.01507 0.03291 100.4 0.0084 0.02982 0.01236 0.02799 110.4 0.0075 0.02071 0.00833 0.02025 120.4 0.00494 0.01504 0.00563 0.01466 130.4 9.26076E-5 0.01106 0.00381 0.01061 140.4 1E-3 0.00825 0.00259 0.00769 150.4 0.0012 0.00521 0.00176 0.00557 160.4 0.00369 0.00384 0.0012 0.00404 170.4 -8.47137E-5 0.0014 8.2429E-4 0.00293 180.4 9.268E-4 0.00214 5.6628E-4 0.00212 190.4 -6.67856E-4 -9.80186E-4 3.90154E-4 0.00154 200.4 -0.00117 0.00202 2.69581E-4 0.00112 210.4 -0.00193 5.38995E-4 1.86949E-4 8.11015E-4 220.4 -8.39232E-4 7.69612E-4 1.29921E-4 5.88691E-4 230.4 -0.00195 2.14259E-4 9.06284E-5 4.27369E-4 240.4 0.00283 -8.83906E-5 6.33492E-5 3.10284E-4 250.4 1.51583E-4 9.93781E-5 4.44474E-5 2.25358E-4 S2.D Time Flowing down Pumping up Flowing down fitting Pumping up fitting 0 3.20421E-4 6.79497E-5 0 0 0.1 0.00177 8.90059E-4 4.4393E-4 3.10751E-4 0.2 -2.24788E-4 0.00255 8.76541E-4 6.13579E-4 0.3 0.00113 5.82218E-4 0.0013 9.08785E-4 0.4 0.00222 0.00237 0.00171 0.0012 0.5 0.0016 0.00261 0.00211 0.00148 0.6 0.00453 0.00413 0.0025 0.00175 0.7 0.00271 0.00254 0.00288 0.00202 0.8 0.00433 0.00299 0.00326 0.00228 0.9 0.00351 0.00342 0.00362 0.00254 1 0.00308 0.00375 0.00398 0.00278 1.1 0.00508 0.00494 0.00433 0.00303 1.2 0.00439 0.00465 0.00467 0.00327 1.3 0.00373 0.00337 0.005 0.0035 1.4 0.00563 0.00554 0.00533 0.00373 1.5 0.00534 0.00421 0.00564 0.00395 1.6 0.00463 0.00488 0.00596 0.00417 1.7 0.00612 0.00521 0.00626 0.00438 1.8 0.00541 0.00402 0.00656 0.00459 1.9 0.00613 0.006 0.00686 0.0048 2 0.00658 0.00694 0.00714 0.005 2.1 0.00534 0.00495 0.00743 0.0052 2.2 0.0063 0.00706 0.0077 0.00539

50

2.3 0.00703 0.00526 0.00798 0.00558 2.4 0.007 0.00638 0.00824 0.00577 2.5 0.00743 0.00582 0.00851 0.00595 2.6 0.00753 0.00711 0.00876 0.00613 2.7 0.00734 0.00656 0.00902 0.00631 2.8 0.00876 0.00579 0.00927 0.00649 2.9 0.00762 0.00753 0.00951 0.00666 3 0.00818 0.00655 0.00975 0.00683 3.1 0.00882 0.00759 0.00999 0.00699 3.2 0.00904 0.00842 0.01022 0.00715 3.3 0.01113 0.00748 0.01045 0.00732 3.4 0.00913 0.00757 0.01068 0.00747 3.5 0.0096 0.00941 0.0109 0.00763 3.6 0.00998 0.00722 0.01112 0.00778 3.7 0.01051 0.00887 0.01133 0.00793 3.8 0.00996 0.00899 0.01155 0.00808 3.9 0.01086 0.00834 0.01176 0.00823 4 0.01108 0.00845 0.01196 0.00837 4.1 0.00991 0.00871 0.01217 0.00852 4.2 0.01169 0.00854 0.01237 0.00866 4.3 0.01181 0.00923 0.01256 0.0088 4.4 0.01185 0.01006 0.01276 0.00893 4.5 0.01206 0.00986 0.01295 0.00907 4.6 0.01226 0.00842 0.01314 0.0092 4.7 0.01234 0.00807 0.01333 0.00933 4.8 0.01239 0.01036 0.01352 0.00946 4.9 0.01243 0.0096 0.0137 0.00959 5 0.01258 0.01028 0.01388 0.00972 5.1 0.01268 0.00999 0.01406 0.00984 5.2 0.01285 0.00934 0.01423 0.00996 5.3 0.01351 0.00942 0.01441 0.01009 5.4 0.01455 0.01042 0.01458 0.01021 5.5 0.0146 0.0107 0.01475 0.01033 5.6 0.0147 0.01075 0.01492 0.01044 5.7 0.0148 0.01077 0.01509 0.01056 5.8 0.0149 0.01086 0.01525 0.01067 5.9 0.01501 0.01091 0.01541 0.01079 6 0.01505 0.01102 0.01557 0.0109 6.1 0.01506 0.01104 0.01573 0.01101 6.2 0.0151 0.01106 0.01589 0.01112 6.3 0.01512 0.01108 0.01604 0.01123 6.4 0.01513 0.00978 0.0162 0.01134 6.9 0.01474 0.01304 0.01694 0.01186 7.4 0.01804 0.01209 0.01764 0.01235 7.9 0.01763 0.01404 0.01831 0.01282 8.4 0.0179 0.01306 0.01894 0.01326 8.9 0.0184 0.01354 0.01954 0.01368 9.4 0.02069 0.0137 0.02011 0.01408 9.9 0.02 0.01386 0.02066 0.01446 10.4 0.01987 0.01412 0.02117 0.01482 11.4 0.02241 0.01625 0.02212 0.01548 12.4 0.0241 0.01589 0.02297 0.01608 13.4 0.02378 0.01674 0.02373 0.01661 14.4 0.0247 0.01617 0.0244 0.01708 15.4 0.02476 0.0166 0.02499 0.01749 16.4 0.02527 0.0169 0.02551 0.01785 17.4 0.02574 0.01822 0.02595 0.01817 18.4 0.0266 0.01635 0.02633 0.01843 19.4 0.02702 0.01912 0.02665 0.01866 20.4 0.0272 0.01897 0.02691 0.01884 23.4 0.02743 0.01893 0.02739 0.01917 25.4 0.02682 0.01863 0.02748 0.01923

51

28.4 0.02712 0.01947 0.02734 0.01914 30.4 0.02862 0.01842 0.02709 0.01896 35.4 0.02656 0.01767 0.02606 0.01824 40.4 0.02572 0.01614 0.02461 0.01723 43.4 0.02493 0.01614 0.02361 0.01653 45.4 0.02391 0.01609 0.02291 0.01604 48.4 0.02155 0.01538 0.02183 0.01528 50.4 0.02185 0.01432 0.0211 0.01477 55.4 0.01998 0.01231 0.01926 0.01348 60.4 0.02026 0.01156 0.01744 0.01221 65.4 0.01772 0.01016 0.0157 0.01099 70.4 0.0148 0.00972 0.01405 0.00984 75.4 0.01448 0.00738 0.01252 0.00877 80.4 0.01236 0.00811 0.01112 0.00778 85.4 0.01039 0.00621 0.00983 0.00688 90.4 0.00956 0.00547 0.00867 0.00607 95.4 0.00792 0.00502 0.00763 0.00534 100.4 0.00739 0.00589 0.00669 0.00468 110.4 0.00471 0.00422 0.00512 0.00358 120.4 0.00441 0.00309 0.00389 0.00272 130.4 0.00306 0.00212 0.00294 0.00206 140.4 0.00115 0.00121 0.00221 0.00154 150.4 0.00145 6.14085E-4 0.00165 0.00116 160.4 0.00113 0.00106 0.00123 8.62862E-4 170.4 6.39814E-4 -4.49872E-4 9.17091E-4 6.41963E-4 180.4 4.55911E-4 1.01079E-4 6.80548E-4 4.76347E-4 190.4 6.39106E-4 -1.38521E-4 5.04013E-4 3.52804E-4 200.4 0.00121 0.00124 3.72502E-4 2.6076E-4 210.4 4.08294E-4 9.33269E-4 2.74931E-4 1.92454E-4 220.4 3.91239E-4 3.3924E-4 2.02579E-4 1.41853E-4 230.4 -2.97471E-4 0.00127 1.49105E-4 1.04458E-4 240.4 5.92825E-4 -5.12917E-4 1.09652E-4 7.67682E-5 250.4 2.45445E-4 8.8445E-4 8.05445E-5 5.64608E-5 S3.A Time Peak 1 Peak 5 Peak3 Peak7 Peak 1

fitting Peak 3 fitting

Peak 5 fitting

Peak 7 fitting

0 0.99999 0.00316 1.00001 0.00224 1 1 0 0 0.5 0.92215 0.00173 0.93461 5.59031E-4 0.94243 0.94488 0.00389 0.00272 1 0.87544 0.00245 0.89437 0.0038 0.89356 0.89888 0.00737 0.00516 1.1 0.86599 0.00231 0.88895 0.00646 0.88469 0.89061 0.00802 0.00561 1.2 0.8665 1.17235E-4 0.87087 0.00413 0.87609 0.88262 0.00866 0.00606 1.3 0.85335 0.00196 0.85157 0.00409 0.86776 0.8749 0.00929 0.0065 1.4 0.8418 0.00183 0.8579 0.00481 0.85967 0.86743 0.0099 0.00693 1.5 0.82973 9.95561E-4 0.86262 0.00617 0.85183 0.86022 0.01051 0.00735 1.6 0.8273 0.00322 0.85454 0.00714 0.84422 0.85323 0.0111 0.00777 1.7 0.83112 7.24472E-4 0.84488 0.00431 0.83683 0.84648 0.01168 0.00818 1.8 0.82252 0.00365 0.84583 0.00427 0.82966 0.83994 0.01225 0.00858 1.9 0.81747 0.0036 0.85103 0.00724 0.8227 0.8336 0.01281 0.00897 2 0.81297 0.00607 0.84112 0.00538 0.81594 0.82747 0.01336 0.00935 2.5 0.77887 0.00645 0.8082 0.00695 0.78484 0.79949 0.01599 0.01119 3 0.75261 0.00589 0.7853 0.009 0.75767 0.77535 0.01842 0.0129 3.5 0.72893 0.00881 0.76594 0.01173 0.73374 0.75432 0.02069 0.01448 4 0.71563 0.00992 0.7555 0.01308 0.71249 0.73581 0.02282 0.01598 4.5 0.70143 0.01558 0.73544 0.01603 0.69343 0.71933 0.02483 0.01738 5 0.67543 0.01592 0.71812 0.0158 0.6762 0.70452 0.02673 0.01871 5.5 0.66952 0.01637 0.69188 0.01588 0.66048 0.69105 0.02855 0.01998

52

6 0.65256 0.02131 0.6871 0.01906 0.64601 0.67869 0.03027 0.02119 6.5 0.63932 0.02003 0.67313 0.01782 0.63261 0.66723 0.03193 0.02235 7 0.62278 0.01937 0.66369 0.01898 0.62008 0.65652 0.03351 0.02346 7.5 0.6074 0.02251 0.65114 0.0216 0.6083 0.64643 0.03503 0.02452 8 0.59115 0.02673 0.63576 0.02349 0.59716 0.63685 0.03649 0.02555 8.5 0.58684 0.02659 0.63299 0.02328 0.58655 0.62771 0.0379 0.02653 9 0.57509 0.02978 0.61747 0.02503 0.5764 0.61894 0.03926 0.02748 9.5 0.56681 0.03327 0.61832 0.02829 0.56666 0.61048 0.04056 0.02839 10 0.55625 0.03204 0.5999 0.02967 0.55727 0.60228 0.04182 0.02928 11 0.54125 0.03755 0.58942 0.02708 0.53938 0.58657 0.04421 0.03094 12 0.5236 0.03967 0.57252 0.03157 0.52247 0.5716 0.04642 0.0325 13 0.50201 0.03956 0.56593 0.03166 0.50637 0.55723 0.04848 0.03394 14 0.48768 0.04292 0.54412 0.03284 0.49096 0.54336 0.05039 0.03527 15 0.47633 0.04393 0.52226 0.03399 0.47615 0.52994 0.05216 0.03651 16 0.45982 0.04786 0.52663 0.03403 0.46188 0.51692 0.05379 0.03765 17 0.44171 0.05025 0.50195 0.03803 0.44811 0.50427 0.0553 0.03871 18 0.4291 0.05103 0.48494 0.03941 0.4348 0.49197 0.05668 0.03968 19 0.41345 0.05418 0.47744 0.03996 0.42193 0.47999 0.05795 0.04056 20 0.40496 0.05359 0.46127 0.04083 0.40947 0.46834 0.05911 0.04138 22 0.37933 0.05814 0.43673 0.04028 0.38571 0.44592 0.06112 0.04278 25 0.34257 0.06262 0.41478 0.04532 0.35278 0.41441 0.06342 0.0444 28 0.31749 0.06681 0.38325 0.04415 0.32278 0.38524 0.06499 0.04549 30 0.29805 0.06415 0.3597 0.04646 0.30428 0.36699 0.06568 0.04598 33 0.26759 0.06783 0.33445 0.04801 0.27859 0.34131 0.06624 0.04637 35 0.25231 0.0657 0.32176 0.04692 0.26274 0.32524 0.06634 0.04644 38 0.23296 0.06972 0.29772 0.04841 0.24071 0.30261 0.06614 0.0463 40 0.21877 0.06857 0.28208 0.04777 0.2271 0.28845 0.06579 0.04605 43 0.2015 0.06644 0.26391 0.04642 0.2082 0.26849 0.06501 0.0455 45 0.18739 0.06679 0.2506 0.04764 0.19652 0.256 0.06433 0.04503 48 0.17706 0.06611 0.23458 0.04507 0.18027 0.23838 0.06312 0.04419 50 0.16556 0.06295 0.22296 0.04242 0.17023 0.22734 0.06221 0.04354 55 0.14816 0.06219 0.2 0.04324 0.14763 0.20202 0.05961 0.04173 60 0.13377 0.05865 0.17746 0.0419 0.12817 0.17964 0.05671 0.0397 65 0.10883 0.05582 0.15906 0.04055 0.1114 0.15982 0.05361 0.03753 70 0.10042 0.05174 0.14305 0.03357 0.09693 0.14227 0.05042 0.0353 75 0.08665 0.04892 0.12102 0.03261 0.08443 0.12672 0.04721 0.03305 80 0.07502 0.04736 0.10963 0.0303 0.07363 0.11293 0.04404 0.03083 85 0.064 0.04581 0.09877 0.03083 0.06428 0.10068 0.04094 0.02866 90 0.05494 0.04345 0.08556 0.02539 0.05619 0.08981 0.03795 0.02656 95 0.04462 0.03584 0.07879 0.02861 0.04916 0.08015 0.03508 0.02456 100 0.04124 0.03721 0.06835 0.02523 0.04306 0.07155 0.03236 0.02265 110 0.02748 0.02741 0.05571 0.01831 0.03315 0.05711 0.02738 0.01917 120 0.02458 0.02351 0.04378 0.01465 0.02563 0.04564 0.02301 0.01611 130 0.02236 0.02202 0.03405 0.01568 0.01989 0.03653 0.01925 0.01347 140 0.01516 0.01762 0.02644 0.00998 0.0155 0.02927 0.01602 0.01122 150 0.01502 0.01219 0.02206 0.00975 0.01213 0.02349 0.0133 0.00931 160 0.01088 0.01504 0.01954 0.00775 0.00952 0.01886 0.011 0.0077 170 0.0081 0.01045 0.01319 0.00405 0.0075 0.01516 0.00908 0.00636 180 0.00668 0.00972 0.01199 0.00514 0.00592 0.0122 0.00748 0.00523 190 0.00942 0.01022 0.00877 0.00503 0.00469 0.00982 0.00615 0.0043 200 0.00529 0.00441 0.00794 0.00223 0.00373 0.00792 0.00505 0.00353 210 0.00292 0.00537 0.00469 0.00358 0.00297 0.00638 0.00414 0.0029 220 0.00353 0.00541 0.00464 0.0026 0.00237 0.00515 0.00339 0.00237 230 -6.02379E-4 0.00174 0.00373 0.00195 0.00189 0.00416 0.00278 0.00194 240 0.00554 0.00335 0.00129 0.00257 0.00152 0.00336 0.00227 0.00159 250 0.00378 -0.00238 -6.96007E-4 0.00132 0.00122 0.00271 0.00186 0.0013

53

S3.B Time Peak 5 Peak7 Peak 5

fitting Peak 7 fitting

0 0.00316 0.00224 0 0 0.5 0.00173 5.59031E-4 0.00389 0.00272 1 0.00245 0.0038 0.00737 0.00516 1.1 0.00231 0.00646 0.00802 0.00561 1.2 1.17235E-4 0.00413 0.00866 0.00606 1.3 0.00196 0.00409 0.00929 0.0065 1.4 0.00183 0.00481 0.0099 0.00693 1.5 9.95561E-4 0.00617 0.01051 0.00735 1.6 0.00322 0.00714 0.0111 0.00777 1.7 7.24472E-4 0.00431 0.01168 0.00818 1.8 0.00365 0.00427 0.01225 0.00858 1.9 0.0036 0.00724 0.01281 0.00897 2 0.00607 0.00538 0.01336 0.00935 2.5 0.00645 0.00695 0.01599 0.01119 3 0.00589 0.009 0.01842 0.0129 3.5 0.00881 0.01173 0.02069 0.01448 4 0.00992 0.01308 0.02282 0.01598 4.5 0.01558 0.01603 0.02483 0.01738 5 0.01592 0.0158 0.02673 0.01871 5.5 0.01637 0.01588 0.02855 0.01998 6 0.02131 0.01906 0.03027 0.02119 6.5 0.02003 0.01782 0.03193 0.02235 7 0.01937 0.01898 0.03351 0.02346 7.5 0.02251 0.0216 0.03503 0.02452 8 0.02673 0.02349 0.03649 0.02555 8.5 0.02659 0.02328 0.0379 0.02653 9 0.02978 0.02503 0.03926 0.02748 9.5 0.03327 0.02829 0.04056 0.02839 10 0.03204 0.02967 0.04182 0.02928 11 0.03755 0.02708 0.04421 0.03094 12 0.03967 0.03157 0.04642 0.0325 13 0.03956 0.03166 0.04848 0.03394 14 0.04292 0.03284 0.05039 0.03527 15 0.04393 0.03399 0.05216 0.03651 16 0.04786 0.03403 0.05379 0.03765 17 0.05025 0.03803 0.0553 0.03871 18 0.05103 0.03941 0.05668 0.03968 19 0.05418 0.03996 0.05795 0.04056 20 0.05359 0.04083 0.05911 0.04138 22 0.05814 0.04028 0.06112 0.04278 25 0.06262 0.04532 0.06342 0.0444 28 0.06681 0.04415 0.06499 0.04549 30 0.06415 0.04646 0.06568 0.04598 33 0.06783 0.04801 0.06624 0.04637 35 0.0657 0.04692 0.06634 0.04644 38 0.06972 0.04841 0.06614 0.0463 40 0.06857 0.04777 0.06579 0.04605 43 0.06644 0.04642 0.06501 0.0455 45 0.06679 0.04764 0.06433 0.04503 48 0.06611 0.04507 0.06312 0.04419 50 0.06295 0.04242 0.06221 0.04354 55 0.06219 0.04324 0.05961 0.04173 60 0.05865 0.0419 0.05671 0.0397 65 0.05582 0.04055 0.05361 0.03753

54

70 0.05174 0.03357 0.05042 0.0353 75 0.04892 0.03261 0.04721 0.03305 80 0.04736 0.0303 0.04404 0.03083 85 0.04581 0.03083 0.04094 0.02866 90 0.04345 0.02539 0.03795 0.02656 95 0.03584 0.02861 0.03508 0.02456 100 0.03721 0.02523 0.03236 0.02265 110 0.02741 0.01831 0.02738 0.01917 120 0.02351 0.01465 0.02301 0.01611 130 0.02202 0.01568 0.01925 0.01347 140 0.01762 0.00998 0.01602 0.01122 150 0.01219 0.00975 0.0133 0.00931 160 0.01504 0.00775 0.011 0.0077 170 0.01045 0.00405 0.00908 0.00636 180 0.00972 0.00514 0.00748 0.00523 190 0.01022 0.00503 0.00615 0.0043 200 0.00441 0.00223 0.00505 0.00353 210 0.00537 0.00358 0.00414 0.0029 220 0.00541 0.0026 0.00339 0.00237 230 0.00174 0.00195 0.00278 0.00194 240 0.00335 0.00257 0.00227 0.00159 250 -0.00238 0.00132 0.00186 0.0013 S3.C Time 1:99 Time 2:98 Time 10:90 Time 20:80 Time 50:50 Time 100:0 0 0.99999 0 0.9527 0 0.97513 0 0.98546 0.1 0.99611 0 1.00001 0.1 0.97407 0.1 1.00001 0.1 0.97144 0.1 1.00001 0.2 1 0.1 0.94902 0.2 0.98123 0.2 0.95442 0.2 0.99999 0.2 0.96219 0.3 0.91964 0.2 0.90021 0.3 0.95951 0.3 0.90438 0.3 0.95352 0.3 0.93384 0.4 0.88733 0.3 0.84415 0.4 0.94092 0.4 0.9359 0.4 0.94504 0.4 0.93588 0.5 0.87482 0.4 0.81678 0.5 0.96339 0.5 0.93219 0.5 0.89544 0.5 0.90028 0.6 0.83534 0.5 0.76929 0.6 0.9372 0.6 0.89919 0.6 0.88253 0.6 0.8649 0.7 0.84418 0.6 0.75481 0.7 0.91247 0.7 0.87687 0.7 0.90976 0.7 0.85358 0.8 0.80584 0.7 0.71845 0.8 0.91923 0.8 0.89362 0.8 0.85697 0.8 0.85151 0.9 0.7892 0.8 0.70777 0.9 0.92998 0.9 0.84496 0.9 0.88323 0.9 0.85574 1 0.74641 0.9 0.67173 1 0.87688 1 0.87462 1 0.81404 1 0.82726 1.1 0.72882 1 0.62571 1.1 0.89404 1.1 0.86387 1.1 0.84427 1.1 0.82152 1.2 0.70881 1.1 0.58438 1.2 0.85834 1.2 0.83714 1.2 0.82758 1.2 0.78801 1.3 0.6937 1.2 0.59333 1.3 0.8554 1.3 0.81324 1.3 0.8154 1.3 0.78119 1.4 0.67757 1.3 0.5538 1.4 0.83751 1.4 0.80075 1.4 0.81112 1.4 0.76536 1.5 0.67352 1.4 0.54681 1.5 0.83327 1.5 0.80341 1.5 0.82082 1.5 0.75568 1.6 0.66688 1.5 0.50056 1.6 0.79196 1.6 0.76688 1.6 0.76281 1.6 0.72937 1.7 0.62533 1.6 0.48211 1.7 0.80262 1.7 0.77074 1.7 0.77028 1.7 0.7339 1.8 0.62243 1.7 0.44717 1.8 0.81736 1.8 0.7382 1.8 0.75936 1.8 0.71984 1.9 0.6114 1.8 0.42812 1.9 0.78567 1.9 0.76649 2.3 0.69751 1.9 0.705 2 0.59514 1.9 0.41082 2 0.78504 2 0.79775 2.8 0.67048 2 0.72008 2.1 0.58037 2.4 0.35764 2.5 0.75882 2.5 0.70106 3.3 0.63807 2.5 0.66663 2.2 0.57055 2.9 0.30927 3 0.68383 3 0.6645 3.8 0.5898 3 0.61014 2.7 0.49038 3.4 0.24174 3.5 0.67627 3.5 0.65992 4.3 0.53834 3.5 0.55566 3.2 0.44383 3.9 0.19451 4 0.63011 4 0.59494 4.8 0.51259 4 0.5158 3.7 0.42421 4.4 0.1465 4.5 0.60236 4.5 0.59767 5.3 0.47832 4.5 0.49415 4.2 0.37365 4.9 0.14445 5 0.56631 5 0.54515 5.8 0.46723 5 0.46181 4.7 0.31 5.4 0.11026 5.5 0.54282 5.5 0.51828 6.3 0.39502 5.5 0.42557 5.2 0.27319 5.9 0.07962 6 0.49914 6 0.51164 6.8 0.39715 6 0.39226 5.7 0.26833 6.4 0.09118 6.5 0.4821 6.5 0.50559 7.3 0.3474 6.5 0.40174 6.2 0.25206 6.9 0.08544 7 0.46402 7 0.46677 7.8 0.36566 7 0.32408 6.7 0.23154 7.4 0.0733 7.5 0.43501 7.5 0.43518 8.3 0.33792 7.5 0.35241 7.7 0.1904 7.9 0.06278 8 0.44222 8 0.44152 8.8 0.33661 8 0.31117 8.7 0.14661 8.4 0.0668

55

9 0.40445 9 0.39272 9.3 0.31408 9 0.2786 9.7 0.10325 9.4 0.05222 10 0.32247 10 0.34251 9.8 0.30039 9.5 0.26453 10.2 0.08737 9.9 0.0279 11 0.2981 11 0.29112 10.8 0.21993 10 0.20805 11.2 0.06246 10.9 0.01687 12 0.29015 12 0.2771 11.8 0.23342 11 0.1895 12.2 0.02913 11.9 0.02928 13 0.27931 13 0.26181 12.8 0.22844 12 0.17552 13.2 0.0248 12.9 0.02728 14 0.25816 14 0.21956 13.8 0.18283 13 0.15242 14.2 0.04682 13.9 0.04272 15 0.21548 15 0.2512 14.8 0.16814 14 0.16876 15.2 0.03469 14.9 0.01638 16 0.19591 16 0.21063 15.8 0.16516 15 0.11441 16.2 0.02517 15.9 -0.01407 17 0.17205 17 0.19209 16.8 0.12431 16 0.11305 17.2 -0.00299 16.9 -0.00203 18 0.16476 18 0.17013 17.8 0.09163 17 0.11326 18.2 0.01663 17.9 0.01653 19 0.12687 19 0.1556 18.8 0.10702 18 0.11164 19.2 0.01796 18.9 0.01321 20 0.12858 20 0.11541 19.8 0.10546 19 0.10807 20.2 0.02224 19.9 -0.02588 22 0.10738 22 0.12327 21.8 0.08424 20 0.08814 22.2 0.00683 21.9 0.01044 25 0.07742 25 0.07818 24.8 0.03926 22 0.02829 25.2 -0.02874 24.9 -0.01957 28 0.09582 28 0.04966 27.8 0.02217 25 0.0893 28.2 -0.03126 27.9 0.0087 30 0.00516 30 0.04626 29.8 0.0212 28 0.01728 30.2 0.00218 29.9 0.00988 33 0.04468 33 0.03117 32.8 -0.00426 30 0.04161 33.2 -0.01594 32.9 0.03092 35 0.03283 35 0.03152 34.8 0.02226 33 0.02458 35.2 -0.01171 34.9 0.01381 38 -0.00328 38 0.01457 37.8 0.02012 38 -0.00343 38.2 -0.00215 37.9 -0.01367 40 0.02777 40 0.04001 39.8 0.00978 40 -0.01672 40.2 -0.00305 39.9 -0.00502 43 0.0208 43 0.05628 42.8 -0.01935 43 0.02129 43.2 -0.02496 42.9 -0.00438 45 0.00101 45 -0.03468 44.8 -0.02316 45 0.01262 45.2 -0.02101 44.9 -0.00822 48 -0.01734 48 0.0483 47.8 0.01145 48 -0.00246 48.2 -0.00429 47.9 0.01836 50 -0.01531 50 0.0206 49.8 0.03258 50 -0.016 50.2 -0.0064 49.9 0.0044 55 0.03214 55 -0.0226 54.8 0.01253 55 -0.02407 55.2 0.00828 54.9 -0.01368 60 -0.05865 60 0.01028 59.8 0.00496 60 0.03856 60.2 2.69095E-4 59.9 -0.02708 Time 1:99

fitting Time 2:98

fitting Time 10:90

fitting Time 20:80

fitting Time 50:50

fitting Time 100:0

fitting 0 1 0 1 0 1 0 1 0.1 0.97624 0 1 0.1 0.98983 0.1 0.98955 0.1 0.98732 0.1 0.98454 0.2 0.95307 0.1 0.96257 0.2 0.97976 0.2 0.97921 0.2 0.9748 0.2 0.96932 0.3 0.93047 0.2 0.92659 0.3 0.9698 0.3 0.96898 0.3 0.96245 0.3 0.95436 0.4 0.90843 0.3 0.89199 0.4 0.95993 0.4 0.95885 0.4 0.95026 0.4 0.93963 0.5 0.88694 0.4 0.85873 0.5 0.95017 0.5 0.94884 0.5 0.93823 0.5 0.92513 0.6 0.86597 0.5 0.82676 0.6 0.94051 0.6 0.93893 0.6 0.92635 0.6 0.91087 0.7 0.84552 0.6 0.79601 0.7 0.93095 0.7 0.92912 0.7 0.91463 0.7 0.89684 0.8 0.82558 0.7 0.76646 0.8 0.92148 0.8 0.91942 0.8 0.90306 0.8 0.88303 0.9 0.80612 0.8 0.73804 0.9 0.91211 0.9 0.90982 0.9 0.89165 0.9 0.86944 1 0.78715 0.9 0.71071 1 0.90284 1 0.90031 1 0.88038 1 0.85608 1.1 0.76864 1 0.68444 1.1 0.89366 1.1 0.89091 1.1 0.86925 1.1 0.84292 1.2 0.75059 1.1 0.65918 1.2 0.88458 1.2 0.88161 1.2 0.85827 1.2 0.82997 1.3 0.73298 1.2 0.63489 1.3 0.87558 1.3 0.87241 1.3 0.84744 1.3 0.81724 1.4 0.7158 1.3 0.61154 1.4 0.86668 1.4 0.8633 1.4 0.83674 1.4 0.8047 1.5 0.69905 1.4 0.58908 1.5 0.85787 1.5 0.85429 1.5 0.82619 1.5 0.79237 1.6 0.6827 1.5 0.56749 1.6 0.84915 1.6 0.84538 1.6 0.81577 1.6 0.78023 1.7 0.66676 1.6 0.54673 1.7 0.84052 1.7 0.83655 1.7 0.80549 1.7 0.76828 1.8 0.65121 1.7 0.52676 2 0.81516 2 0.81064 1.8 0.79534 1.8 0.75653 2 0.62124 1.8 0.50756 2.5 0.77457 2.5 0.76924 2.3 0.74653 2 0.73358 2.7 0.52731 2.4 0.40685 3 0.73602 3 0.72997 2.8 0.7008 2.5 0.67933 3.2 0.4695 2.9 0.33916 3.5 0.6994 3.5 0.69272 3.3 0.65795 3 0.62925 3.7 0.41837 3.4 0.28342 4 0.6646 4 0.65738 3.8 0.61779 3.5 0.58301 4.2 0.37315 3.9 0.23747 4.5 0.63154 4.5 0.62386 4.3 0.58016 4 0.54032 4.7 0.33313 4.4 0.19957 5 0.60014 5 0.59207 4.8 0.54488 4.5 0.50089 5.2 0.2977 4.9 0.16827 5.5 0.5703 5.5 0.5619 5.3 0.51181 5 0.46446 5.7 0.26631 5.4 0.14239 6 0.54195 6 0.53329 5.8 0.48081 5.5 0.43081 6.2 0.23849 5.9 0.12097 6.5 0.51501 6.5 0.50614 6.3 0.45175 6 0.3997 6.7 0.21381 6.4 0.10321 7 0.48942 7 0.48039 6.8 0.42449 6.5 0.37095 7.2 0.19192 6.9 0.08846 7.5 0.46511 7.5 0.45595 7.3 0.39892 7 0.34437 7.7 0.17248 7.4 0.07618

56

8 0.44201 8 0.43277 7.8 0.37495 7.5 0.31978 8.2 0.1552 7.9 0.06594 8.5 0.42006 8.5 0.41078 8.3 0.35245 8 0.29704 8.7 0.13984 8.4 0.05738 9 0.3992 9 0.38991 8.8 0.33135 8.5 0.276 9.2 0.12616 8.9 0.0502 9.5 0.37939 9.5 0.37011 9.3 0.31155 9 0.25653 9.7 0.11399 9.4 0.04417 10 0.36056 10 0.35132 9.8 0.29297 9.5 0.23851 10.2 0.10313 9.9 0.03908 11 0.32567 11 0.31658 10.8 0.25917 10 0.22182 11.2 0.08479 10.9 0.0311 12 0.29416 12 0.28529 11.8 0.22938 11 0.19204 12.2 0.07013 11.9 0.02528 13 0.26572 13 0.25712 12.8 0.20312 12 0.16648 13.2 0.05837 12.9 0.02096 14 0.24003 14 0.23175 13.8 0.17995 13 0.1445 14.2 0.04888 13.9 0.01768 15 0.21684 15 0.2089 14.8 0.15951 14 0.12559 15.2 0.04118 14.9 0.01513 16 0.19589 16 0.18832 15.8 0.14146 15 0.1093 16.2 0.03492 15.9 0.01312 17 0.17698 17 0.16977 16.8 0.12552 16 0.09525 17.2 0.02978 16.9 0.01148 18 0.1599 18 0.15307 17.8 0.11142 17 0.08311 18.2 0.02554 17.9 0.01013 19 0.14447 19 0.13802 18.8 0.09896 18 0.07262 19.2 0.02203 18.9 0.009 20 0.13053 20 0.12446 19.8 0.08794 19 0.06354 20.2 0.0191 19.9 0.00803 22 0.10657 22 0.10122 21.8 0.06954 20 0.05567 22.2 0.01455 21.9 0.00645 25 0.07865 25 0.07428 24.8 0.04907 22 0.0429 25.2 0.00997 24.9 0.00472 28 0.05805 28 0.05455 27.8 0.03477 25 0.0293 28.2 0.00702 27.9 0.00348 30 0.04742 30 0.04441 29.8 0.0277 28 0.02023 30.2 0.00561 29.9 0.00285 33 0.03502 33 0.03264 32.8 0.01976 30 0.01589 33.2 0.00406 32.9 0.00211 35 0.02862 35 0.02659 34.8 0.01581 33 0.01116 35.2 0.00329 34.9 0.00173 38 0.02114 38 0.01956 37.8 0.01134 38 0.0063 38.2 0.00241 37.9 0.00128 40 0.01728 40 0.01595 39.8 0.00911 40 0.00504 40.2 0.00196 39.9 0.00105 43 0.01277 43 0.01174 42.8 0.00657 43 0.00363 43.2 0.00145 42.9 7.81183E-4 45 0.01044 45 0.00958 44.8 0.00529 45 0.00292 45.2 0.00119 44.9 6.40319E-4 48 0.00772 48 0.00706 47.8 0.00384 48 0.00212 48.2 8.7758E-4 47.9 4.75191E-4 50 0.00631 50 0.00576 49.8 0.0031 50 0.00172 50.2 7.18527E-4 49.9 3.8951E-4 55 0.00382 55 0.00347 54.8 0.00183 55 0.00102 55.2 4.36359E-4 54.9 2.36945E-4 60 0.00231 60 0.00209 59.8 0.00108 60 6.08523E-4 60.2 2.65242E-4 59.9 1.44138E-4 S4.A Time KSCN (8.8M) KS13C15N (8.8M) KSCN (8.8M)

fitting KS13C15N (8.8M) fitting

-1.22E-6 1.00001 0.9995 1 1 0.1 0.99361 1 0.98574 0.9893 0.2 0.97032 0.9916 0.97205 0.97892 0.3 0.96399 0.97751 0.95892 0.96886 0.4 0.95277 0.96218 0.9463 0.9591 0.5 0.93349 0.95506 0.93418 0.94963 0.6 0.9309 0.94725 0.92254 0.94044 0.7 0.91424 0.9377 0.91134 0.93152 0.8 0.89454 0.91671 0.90057 0.92285 0.9 0.88618 0.91363 0.8902 0.91443 1 0.87377 0.9085 0.88023 0.90625 1.1 0.86675 0.90064 0.87062 0.8983 1.2 0.86283 0.89653 0.86136 0.89057 1.3 0.85368 0.88601 0.85243 0.88305 1.4 0.84815 0.86956 0.84382 0.87574 1.5 0.8341 0.86278 0.83552 0.86862 1.6 0.81597 0.85645 0.8275 0.86169 1.7 0.81454 0.84744 0.81976 0.85494 1.8 0.81692 0.84794 0.81227 0.84836 1.9 0.80978 0.84048 0.80504 0.84196

57

2 0.79709 0.83439 0.79804 0.83571 2.1 0.78732 0.82879 0.79127 0.82962 2.2 0.78044 0.82253 0.78471 0.82368 2.3 0.77979 0.81662 0.77836 0.81789 2.4 0.76963 0.81319 0.7722 0.81223 2.5 0.76541 0.8069 0.76622 0.8067 2.6 0.77197 0.80186 0.76042 0.80131 2.7 0.75803 0.80593 0.7548 0.79603 2.8 0.75215 0.79622 0.74933 0.79088 2.9 0.74974 0.79168 0.74401 0.78584 3 0.7442 0.78813 0.73884 0.78091 3.1 0.73683 0.78036 0.73381 0.77609 3.2 0.74502 0.78044 0.72892 0.77137 3.3 0.73371 0.77182 0.72414 0.76675 3.4 0.72694 0.76728 0.71949 0.76222 3.5 0.71764 0.75732 0.71496 0.75779 3.6 0.71397 0.75258 0.71053 0.75344 3.7 0.71185 0.75115 0.70621 0.74918 3.8 0.70788 0.74854 0.70199 0.745 3.9 0.70937 0.75354 0.69787 0.7409 4 0.69931 0.74359 0.69384 0.73687 4.1 0.69257 0.74314 0.68989 0.73292 4.2 0.70261 0.73526 0.68603 0.72904 4.3 0.6893 0.73341 0.68224 0.72523 4.4 0.6888 0.72898 0.67854 0.72148 4.5 0.6811 0.72543 0.6749 0.7178 4.6 0.67597 0.72476 0.67134 0.71418 4.7 0.6777 0.71694 0.66784 0.71062 4.8 0.67446 0.70886 0.6644 0.70711 4.9 0.66645 0.70555 0.66103 0.70366 5 0.66352 0.70891 0.65772 0.70026 5.1 0.65426 0.70565 0.65446 0.69692 5.2 0.65276 0.69808 0.65125 0.69362 5.3 0.6514 0.69405 0.64809 0.69038 5.4 0.65691 0.69313 0.64499 0.68717 5.5 0.64645 0.693 0.64193 0.68402 5.6 0.64598 0.69455 0.63891 0.6809 5.7 0.64285 0.6874 0.63594 0.67783 5.8 0.63513 0.68149 0.63302 0.6748 6.3 0.62576 0.67108 0.61894 0.66021 6.8 0.61037 0.65501 0.60568 0.64645 7.3 0.60266 0.63681 0.59311 0.63341 7.8 0.58597 0.62524 0.58111 0.62098 8.3 0.5782 0.61658 0.56959 0.60908 8.8 0.56635 0.60415 0.55849 0.59765 9.3 0.54588 0.58605 0.54775 0.58663 9.8 0.54065 0.5748 0.53734 0.57597 10.8 0.51707 0.55653 0.51735 0.55559 11.8 0.49574 0.53886 0.49834 0.53629 12.8 0.47643 0.51609 0.48017 0.5179 13.8 0.46375 0.50007 0.46275 0.50031 14.8 0.44203 0.47846 0.44603 0.48344 15.8 0.42733 0.46259 0.42996 0.46721 16.8 0.41231 0.44669 0.4145 0.45159 17.8 0.397 0.42939 0.39962 0.43654 18.8 0.37859 0.41576 0.3853 0.42203 19.8 0.36817 0.39905 0.37151 0.40802 22.8 0.3326 0.36166 0.33311 0.36885 24.8 0.30708 0.33846 0.30982 0.34492 27.8 0.277 0.30821 0.27797 0.312 29.8 0.25991 0.28721 0.25864 0.29186 34.8 0.21624 0.24265 0.21614 0.24718

58

39.8 0.18415 0.20545 0.1808 0.2095 42.8 0.1652 0.18867 0.16252 0.18979 44.8 0.15409 0.17438 0.1514 0.17771 47.8 0.13907 0.15955 0.13617 0.16106 49.8 0.12929 0.15084 0.12691 0.15086 54.8 0.1118 0.12907 0.10649 0.12817 59.8 0.09514 0.11024 0.08944 0.10896 64.8 0.08174 0.0933 0.0752 0.0927 69.8 0.06933 0.08014 0.06329 0.07892 74.8 0.05792 0.06899 0.05332 0.06724 79.8 0.0518 0.05836 0.04497 0.05732 84.8 0.04216 0.05141 0.03796 0.04889 89.8 0.03838 0.0431 0.03207 0.04173 94.8 0.02996 0.03729 0.02712 0.03564 99.8 0.02583 0.03106 0.02296 0.03045 109.8 0.01855 0.02433 0.01649 0.02227 119.8 0.01199 0.0202 0.01189 0.01632 129.8 0.00944 0.01334 0.0086 0.01198 139.8 0.00885 0.01038 0.00624 0.00881 149.8 0.00304 0.00838 0.00454 0.00649 159.8 0.00313 0.00551 0.00331 0.00479 169.8 0.00213 0.00361 0.00242 0.00353 179.8 -6.94343E-5 0.00292 0.00177 0.00261 189.8 0.0019 4.46018E-4 0.0013 0.00193 199.8 0.00105 0.00257 9.59587E-4 0.00143 209.8 0.00104 0.00167 7.07591E-4 0.00106 219.8 -0.00226 4.92567E-4 5.22638E-4 7.89349E-4 229.8 8.67446E-4 4.96339E-5 3.86613E-4 5.86423E-4 239.8 -0.00202 0.0026 2.86382E-4 4.35988E-4 249.8 -0.00117 -1.55725E-4 2.12406E-4 3.24348E-4 S4.B Time Flowing down Pumping up Flowing down fitting Pumping up fitting -1.22E-6 -4.22526E-4 8.73596E-4 -1.01667E-8 -7.11666E-9 0.1 -8.4208E-4 0.00109 8.22839E-4 5.75987E-4 0.2 4.90249E-4 0.00119 0.00163 0.00114 0.3 3.06712E-4 5.18956E-4 0.00241 0.00169 0.4 2.53406E-4 0.00182 0.00317 0.00222 0.5 0.00257 0.00205 0.00392 0.00274 0.6 0.0029 0.00374 0.00465 0.00325 0.7 0.00284 0.00422 0.00536 0.00375 0.8 0.00296 0.00527 0.00606 0.00424 0.9 0.00438 0.00575 0.00674 0.00472 1 0.0044 0.00461 0.00741 0.00518 1.1 0.00392 0.00586 0.00806 0.00564 1.2 0.0043 0.00771 0.0087 0.00609 1.3 0.00603 0.00594 0.00933 0.00653 1.4 0.00548 0.00635 0.00994 0.00696 1.5 0.0059 0.00723 0.01054 0.00738 1.6 0.00713 0.00813 0.01113 0.00779 1.7 0.00775 0.01015 0.01171 0.0082 1.8 0.00675 0.0104 0.01228 0.0086 1.9 0.00854 0.00824 0.01284 0.00899 2 0.00852 0.0082 0.01339 0.00937 2.1 0.01153 0.01037 0.01393 0.00975 2.2 0.00889 0.01005 0.01446 0.01012 2.3 0.01022 0.01007 0.01498 0.01049

59

2.4 0.00967 0.01332 0.0155 0.01085 2.5 0.01127 0.01152 0.016 0.0112 2.6 0.01179 0.01038 0.0165 0.01155 2.7 0.0133 0.01187 0.01699 0.01189 2.8 0.01369 0.01151 0.01747 0.01223 2.9 0.01381 0.01341 0.01794 0.01256 3 0.01257 0.01376 0.01841 0.01289 3.1 0.01323 0.01415 0.01887 0.01321 3.2 0.01412 0.0144 0.01932 0.01353 3.3 0.01635 0.01429 0.01977 0.01384 3.4 0.01594 0.01499 0.02021 0.01415 3.5 0.01436 0.01453 0.02064 0.01445 3.6 0.01513 0.0152 0.02107 0.01475 3.7 0.01659 0.01523 0.0215 0.01505 3.8 0.01667 0.01527 0.02191 0.01534 3.9 0.01528 0.01522 0.02233 0.01563 4 0.0163 0.01695 0.02273 0.01591 4.1 0.01857 0.01712 0.02314 0.01619 4.2 0.01943 0.01648 0.02353 0.01647 4.3 0.01904 0.01576 0.02392 0.01675 4.4 0.01938 0.01688 0.02431 0.01702 4.5 0.01845 0.0162 0.02469 0.01729 4.6 0.01923 0.0167 0.02507 0.01755 4.7 0.02113 0.01667 0.02544 0.01781 4.8 0.01943 0.01851 0.02581 0.01807 4.9 0.02215 0.01784 0.02618 0.01833 5 0.02028 0.02127 0.02654 0.01858 5.1 0.02262 0.01926 0.0269 0.01883 5.2 0.02272 0.01946 0.02725 0.01907 5.3 0.02296 0.02041 0.0276 0.01932 5.4 0.02305 0.02066 0.02794 0.01956 5.5 0.02351 0.02078 0.02828 0.0198 5.6 0.02385 0.021 0.02862 0.02003 5.7 0.02419 0.0213 0.02895 0.02027 5.8 0.02463 0.02037 0.02928 0.0205 6.3 0.0258 0.02159 0.03088 0.02162 6.8 0.02837 0.02239 0.0324 0.02268 7.3 0.02876 0.02507 0.03385 0.02369 7.8 0.03231 0.02498 0.03522 0.02466 8.3 0.03606 0.026 0.03653 0.02557 8.8 0.03357 0.02672 0.03778 0.02644 9.3 0.03516 0.02865 0.03896 0.02727 9.8 0.03736 0.03007 0.04009 0.02806 10.8 0.04005 0.03244 0.04219 0.02953 11.8 0.04123 0.0326 0.04409 0.03086 12.8 0.0438 0.03449 0.0458 0.03206 13.8 0.0446 0.03543 0.04733 0.03313 14.8 0.05039 0.03623 0.0487 0.03409 15.8 0.05088 0.03543 0.04992 0.03494 16.8 0.05068 0.03641 0.05099 0.0357 17.8 0.0482 0.03756 0.05193 0.03635 18.8 0.04873 0.03815 0.05274 0.03692 19.8 0.0509 0.03903 0.05344 0.0374 22.8 0.05287 0.0387 0.05487 0.03841 24.8 0.05579 0.03998 0.05536 0.03875 27.8 0.05648 0.03877 0.0555 0.03885 29.8 0.05445 0.03979 0.05527 0.03869 34.8 0.05489 0.03707 0.05378 0.03764 39.8 0.05178 0.03682 0.05135 0.03594 42.8 0.05101 0.03545 0.04958 0.03471 44.8 0.04841 0.03446 0.04832 0.03382 47.8 0.04905 0.03408 0.04632 0.03243

60

49.8 0.047 0.02984 0.04495 0.03147 54.8 0.04359 0.02918 0.04144 0.02901 59.8 0.03884 0.02648 0.03791 0.02654 64.8 0.03672 0.02378 0.03446 0.02412 69.8 0.03463 0.02346 0.03116 0.02182 74.8 0.02935 0.01972 0.02805 0.01964 79.8 0.02862 0.01836 0.02515 0.01761 84.8 0.02308 0.01636 0.02248 0.01573 89.8 0.02388 0.01434 0.02003 0.01402 94.8 0.01944 0.01344 0.01779 0.01246 99.8 0.01847 0.01306 0.01578 0.01104 109.8 0.01513 0.01043 0.01232 0.00863 119.8 0.0086 0.00856 0.00956 0.0067 129.8 0.00862 0.00732 0.00738 0.00517 139.8 0.00784 0.00508 0.00567 0.00397 149.8 0.00422 0.00538 0.00434 0.00304 159.8 0.00471 0.00405 0.00332 0.00232 169.8 0.00335 8.56797E-4 0.00253 0.00177 179.8 7.47645E-4 0.00198 0.00192 0.00134 189.8 5.3227E-4 1.38413E-4 0.00146 0.00102 199.8 0.00281 0.00141 0.0011 7.71822E-4 209.8 0.00275 0.00237 8.33978E-4 5.83777E-4 219.8 0.00153 5.52012E-4 6.30095E-4 4.41066E-4 229.8 0.0024 -3.4671E-4 4.75604E-4 3.32924E-4 239.8 2.41125E-4 0.00149 3.58704E-4 2.51085E-4 249.8 5.12221E-4 -3.39447E-4 2.70345E-4 1.89242E-4 S4.C Time 100:0 Time 50:50 Time 20:80 Time 2:98 -1.65E-6 0.98574 -1.22E-6 1.00001 0 0.95708 0 1 0.1 1.00233 0.1 0.96114 0.1 1.00232 0.1 0.93436 0.2 0.93232 0.2 0.94205 0.2 0.96603 0.2 0.99508 0.3 0.89324 0.3 0.9074 0.3 0.92875 0.3 0.94588 0.4 0.80952 0.4 0.87455 0.4 0.88649 0.4 0.90822 0.5 0.80263 0.5 0.85768 0.5 0.87851 0.5 0.90935 0.6 0.77197 0.6 0.83072 0.6 0.8896 0.6 0.91742 0.7 0.72318 0.7 0.81939 0.7 0.85418 0.7 0.91805 0.8 0.70171 0.8 0.77971 0.8 0.83747 0.8 0.86917 0.9 0.66055 0.9 0.76536 0.9 0.83512 0.9 0.83675 1 0.62387 1 0.73595 1 0.80425 1 0.83105 1.1 0.60889 1.1 0.72662 1.1 0.7634 1.1 0.81929 1.2 0.5804 1.2 0.71221 1.2 0.76502 1.2 0.83246 1.3 0.56277 1.3 0.69374 1.3 0.77307 1.3 0.78038 1.4 0.54943 1.4 0.65673 1.4 0.75885 1.4 0.82003 1.5 0.51179 1.5 0.64286 1.5 0.73843 1.5 0.83852 1.6 0.4872 1.6 0.62964 1.6 0.73786 1.6 0.76915 1.7 0.48954 1.7 0.6132 1.7 0.67758 1.7 0.7417 1.8 0.5053 1.8 0.60736 1.8 0.65191 1.8 0.71287 1.9 0.43637 1.9 0.56552 1.9 0.66486 1.9 0.71057 2.4 0.41124 2.4 0.50171 2 0.63867 2 0.67598 2.9 0.33252 2.5 0.50608 2.5 0.57338 2.5 0.64551 3.4 0.24904 3 0.46385 3 0.52479 3 0.56604 3.9 0.21584 3.5 0.37991 3.5 0.48001 3.5 0.55046 4.4 0.18936 4 0.33595 4 0.4378 4 0.52348 4.9 0.13261 4.5 0.31753 4.5 0.40738 4.5 0.4939 5.4 0.12552 5 0.26955 5 0.34241 5 0.41892 5.9 0.08984 5.5 0.21587 5.5 0.28749 5.5 0.42068 6.4 0.07646 5.6 0.22471 6 0.32521 6 0.42121

61

6.9 0.05191 5.8 0.2305 7 0.26366 7 0.33595 7.4 0.05964 6.3 0.18958 7.5 0.22616 7.5 0.31329 7.9 0.05832 6.8 0.16789 8 0.20715 8 0.29066 8.4 0.06005 7.3 0.16788 8.5 0.1812 8.5 0.30114 8.9 0.04216 7.8 0.14585 9 0.16149 9 0.27036 9.4 0.03852 8.3 0.11451 9.5 0.1562 9.5 0.25916 9.9 0.0231 8.8 0.10867 10 0.11338 10 0.24795 10.9 0.01178 9.3 0.10193 11 0.12901 11 0.21883 11.9 0.03248 9.8 0.07867 12 0.09961 12 0.2198 12.9 -0.00818 10.8 0.06703 13 0.0637 13 0.16713 13.9 0.03183 11.8 0.05077 14 0.10389 14 0.12967 14.9 -0.012 12.8 0.03907 15 0.05797 15 0.08378 15.9 0.02982 13.8 0.03732 16 0.04897 16 0.08754 16.9 0.0028 14.8 0.02303 17 0.04471 17 0.11175 17.9 -1.61673E-4 15.8 0.0297 18 -0.00743 18 0.05613 18.9 0.0214 16.8 0.01001 19 0.00116 19 0.07623 19.9 -0.01985 17.8 0.00275 20 -5.3354E-4 20 0.06803 21.9 0.00591 18.8 0.00237 22 0.00325 22 0.0465 24.9 0.00197 19.8 0.00377 25 0.01327 25 0.05515 27.9 -0.00736 22.8 -0.00879 28 -0.02475 28 0.04013 29.9 0.01233 24.8 -0.00528 30 -0.00239 30 0.01159 32.9 0.00497 27.8 -0.00295 33 0.02205 33 0.02304 34.9 0.00988 29.8 -0.00428 35 0.0271 35 0.00615 37.9 0.01615 34.8 -0.01426 38 -0.02442 38 0.0199 39.9 -0.00324 39.8 -0.00292 40 -0.00508 40 0.01368 42.9 -0.00324 42.8 -0.00208 43 0.01071 43 -0.01004 44.9 8.966E-4 44.8 0.00842 45 -0.0011 45 -0.0038 47.9 0.00483 47.8 -0.00964 48 0.00957 48 -0.01311 49.9 0.00249 49.8 -4.78689E-4 50 -0.00854 50 -0.00789 Time 100:0

fitting Time 50:50

fitting Time 20:80

fitting Time 2:98

fitting -1.65E-6 1 -1.22E-6 1 0 1 0 1 0.1 0.9573 0.1 0.97145 0.1 0.98004 0.1 0.98523 0.2 0.91648 0.2 0.94375 0.2 0.96049 0.2 0.97068 0.3 0.87747 0.3 0.91687 0.3 0.94135 0.3 0.95635 0.4 0.84019 0.4 0.89078 0.4 0.9226 0.4 0.94223 0.5 0.80455 0.5 0.86548 0.5 0.90423 0.5 0.92832 0.6 0.77049 0.6 0.84092 0.6 0.88625 0.6 0.91461 0.7 0.73793 0.7 0.81709 0.7 0.86863 0.7 0.90111 0.8 0.7068 0.8 0.79397 0.8 0.85138 0.8 0.88782 0.9 0.67705 0.9 0.77153 0.9 0.83448 0.9 0.87471 1 0.64861 1 0.74975 1 0.81793 1 0.86181 1.1 0.62142 1.1 0.72862 1.1 0.80172 1.1 0.84909 1.2 0.59542 1.2 0.70811 1.2 0.78584 1.2 0.83656 1.3 0.57057 1.3 0.68821 1.3 0.77029 1.3 0.82422 1.4 0.54681 1.4 0.66889 1.4 0.75506 1.4 0.81206 1.5 0.52409 1.5 0.65014 1.5 0.74013 1.5 0.80009 1.6 0.50237 1.6 0.63195 1.6 0.72552 1.6 0.78829 1.7 0.4816 1.7 0.61429 1.7 0.7112 1.7 0.77666 1.8 0.46174 1.8 0.59715 1.8 0.69718 1.8 0.76521 1.9 0.44274 1.9 0.58051 2 0.66998 2 0.74281 2.4 0.35951 2 0.56436 2.5 0.60671 2.5 0.68966 2.9 0.29285 2.5 0.49044 3 0.54962 3 0.64033 3.4 0.23941 3 0.4267 3.5 0.4981 3.5 0.59456 3.9 0.1965 3.5 0.3717 4 0.45158 4 0.55207 4.4 0.16197 4 0.32421 4.5 0.40957 4.5 0.51263 4.9 0.13415 4.5 0.28317 5 0.37162 5 0.47603 5.4 0.11166 5 0.24767 5.5 0.33731 5.5 0.44206 5.9 0.09346 5.5 0.21694 6 0.3063 6 0.41052 6.4 0.07867 5.6 0.2113 6.5 0.27826 6.5 0.38125

62

6.9 0.06661 5.8 0.2005 7 0.25289 7 0.35407 7.4 0.05675 6.3 0.17606 7.5 0.22992 7.5 0.32884 7.9 0.04866 6.8 0.15484 8 0.20913 8 0.30542 8.4 0.04198 7.3 0.1364 8.5 0.1903 8.5 0.28367 8.9 0.03645 7.8 0.12036 9 0.17324 9 0.26348 9.4 0.03184 8.3 0.10639 9.5 0.15778 9.5 0.24474 9.9 0.02798 8.8 0.0942 10 0.14376 10 0.22733 10.9 0.02198 9.3 0.08356 11 0.11949 11 0.19617 11.9 0.01761 9.8 0.07426 12 0.09949 12 0.16929 12.9 0.01436 10.8 0.05897 13 0.08298 13 0.14612 13.9 0.01187 11.8 0.04716 14 0.06933 14 0.12613 14.9 0.00993 12.8 0.038 15 0.05802 15 0.10888 15.9 0.00838 13.8 0.03083 16 0.04864 16 0.09401 16.9 0.00712 14.8 0.02518 17 0.04084 17 0.08117 17.9 0.00608 15.8 0.0207 18 0.03434 18 0.07009 18.9 0.00522 16.8 0.01712 19 0.02893 19 0.06054 19.9 0.00448 17.8 0.01424 20 0.0244 20 0.05228 21.9 0.00334 18.8 0.01191 22 0.01744 22 0.03902 24.9 0.00216 19.8 0.01 25 0.01065 25 0.02517 27.9 0.0014 22.8 0.00606 28 0.00658 28 0.01624 29.9 0.00105 24.8 0.00441 30 0.0048 30 0.01214 32.9 6.84805E-4 27.8 0.00278 33 0.00301 33 0.00784 34.9 5.14467E-4 29.8 0.00206 35 0.00221 35 0.00587 37.9 3.35044E-4 34.8 9.85908E-4 38 0.0014 38 0.00379 39.9 2.51738E-4 39.8 4.78126E-4 40 0.00104 40 0.00284 42.9 1.63958E-4 42.8 3.10567E-4 43 6.64235E-4 43 0.00184 44.9 1.23195E-4 44.8 2.33081E-4 45 4.94125E-4 45 0.00138 47.9 8.02389E-5 47.8 1.51634E-4 48 3.17878E-4 48 8.91594E-4 49.9 6.02902E-5 49.8 1.13878E-4 50 2.3724E-4 50 6.67784E-4 S5.A Time KSCN (6.5M) KS13C15N (6.5M) KSCN (6.5M)

fitting KS13C15N (6.5M) fitting

0 0.99873 1.00001 1 1 0.1 1.00001 0.98787 0.98816 0.98821 0.2 0.98407 0.97282 0.97674 0.97682 0.3 0.97417 0.96294 0.96571 0.9658 0.4 0.9643 0.94901 0.95506 0.95515 0.5 0.94805 0.93579 0.94477 0.94485 0.6 0.93177 0.9256 0.93482 0.93488 0.7 0.91698 0.9165 0.92521 0.92524 0.8 0.91374 0.91067 0.91591 0.9159 0.9 0.89699 0.89882 0.90692 0.90686 1 0.89668 0.89107 0.89822 0.89811 1.1 0.89064 0.87742 0.88979 0.88963 1.2 0.87609 0.86712 0.88163 0.8814 1.3 0.86904 0.85862 0.87372 0.87343 1.4 0.86519 0.8546 0.86605 0.8657 1.5 0.85254 0.84549 0.85861 0.85819 1.6 0.85169 0.84191 0.8514 0.85091 1.7 0.84776 0.83724 0.8444 0.84384 1.8 0.84021 0.83289 0.8376 0.83697 1.9 0.82941 0.82837 0.831 0.8303 2 0.8218 0.82178 0.82458 0.82382 2.1 0.81666 0.81455 0.81834 0.81751 2.2 0.81445 0.81265 0.81227 0.81138 2.3 0.81101 0.80873 0.80636 0.80541 2.4 0.80472 0.80411 0.80061 0.7996 2.5 0.80224 0.79754 0.79501 0.79395

63

2.6 0.79999 0.78634 0.78956 0.78844 2.7 0.79007 0.7864 0.78424 0.78307 2.8 0.78857 0.77856 0.77905 0.77784 2.9 0.78029 0.77753 0.77399 0.77273 3 0.77341 0.76643 0.76905 0.76775 3.1 0.76457 0.77067 0.76422 0.76289 3.2 0.76695 0.76318 0.75951 0.75814 3.3 0.76386 0.7547 0.7549 0.75351 3.4 0.75148 0.75664 0.7504 0.74898 3.5 0.74827 0.74699 0.74599 0.74455 3.6 0.75048 0.74096 0.74167 0.74022 3.7 0.74492 0.74547 0.73745 0.73599 3.8 0.73299 0.73858 0.73331 0.73184 3.9 0.73442 0.73507 0.72925 0.72778 4 0.72936 0.73319 0.72528 0.7238 4.1 0.72957 0.73077 0.72137 0.71991 4.2 0.72211 0.72176 0.71755 0.71609 4.3 0.71769 0.71906 0.71379 0.71235 4.4 0.7096 0.71793 0.7101 0.70867 4.5 0.71398 0.7127 0.70648 0.70507 4.6 0.70893 0.71211 0.70291 0.70153 4.7 0.70369 0.70638 0.69941 0.69806 4.8 0.70332 0.70119 0.69596 0.69464 4.9 0.69811 0.69866 0.69257 0.69129 5 0.70002 0.69376 0.68924 0.68799 5.1 0.6907 0.68827 0.68595 0.68475 5.2 0.69125 0.68417 0.68271 0.68156 5.7 0.67603 0.66945 0.6672 0.66633 6.2 0.65494 0.65946 0.65268 0.65215 6.7 0.64329 0.64425 0.63897 0.63886 7.2 0.63022 0.62954 0.62595 0.62632 7.7 0.6158 0.61926 0.61352 0.6144 8.2 0.60213 0.60068 0.6016 0.60302 8.7 0.59067 0.58931 0.59011 0.5921 9.2 0.57861 0.58107 0.579 0.58158 10.2 0.5522 0.55096 0.55777 0.56156 11.2 0.53476 0.53142 0.53765 0.54267 12.2 0.51251 0.50904 0.51847 0.52469 13.2 0.49327 0.49381 0.5001 0.50749 14.2 0.47738 0.48167 0.48248 0.49098 15.2 0.45954 0.46247 0.46553 0.47509 16.2 0.44551 0.44623 0.44922 0.45977 17.2 0.42425 0.43202 0.43351 0.44498 18.2 0.40781 0.41294 0.41836 0.43069 19.2 0.39673 0.40342 0.40376 0.41689 22.2 0.35459 0.36528 0.36299 0.37813 24.2 0.33066 0.34083 0.33815 0.35435 27.2 0.29782 0.3111 0.30408 0.32149 29.2 0.27457 0.29441 0.28332 0.30131 34.2 0.22657 0.24798 0.23745 0.25629 39.2 0.1916 0.21402 0.19908 0.21806 42.2 0.1732 0.19466 0.17914 0.19794 44.2 0.1571 0.18286 0.16697 0.18558 47.2 0.14325 0.16658 0.15027 0.16849 49.2 0.13606 0.15698 0.14009 0.15799 54.2 0.11533 0.13656 0.11757 0.13453 59.2 0.09755 0.11602 0.09871 0.11459 64.2 0.08458 0.09872 0.08291 0.09762 69.2 0.07246 0.08458 0.06966 0.0832 74.2 0.0589 0.07462 0.05855 0.07092 79.2 0.05312 0.06304 0.04922 0.06046 84.2 0.04437 0.0538 0.0414 0.05156

64

89.2 0.03983 0.04613 0.03484 0.04398 94.2 0.03125 0.03843 0.02932 0.03753 99.2 0.02626 0.03398 0.02469 0.03202 109.2 0.02157 0.02596 0.01753 0.02334 119.2 0.01558 0.01818 0.01246 0.01702 129.2 0.01122 0.01289 0.00887 0.01242 139.2 0.00836 0.01093 0.00632 0.00908 149.2 0.00907 0.00812 0.00452 0.00663 159.2 0.00617 0.00545 0.00323 0.00485 169.2 0.00412 0.00286 0.00231 0.00355 179.2 0.00379 0.00322 0.00166 0.0026 189.2 0.00209 0.0042 0.00119 0.00191 199.2 0.00301 0.00219 8.56748E-4 0.0014 209.2 0.00423 0.00152 6.17026E-4 0.00103 219.2 0.002 6.48443E-4 4.44969E-4 7.52304E-4 229.2 0.00254 -1.81632E-4 3.21315E-4 5.52366E-4 239.2 5.82006E-4 0.00101 2.32303E-4 4.05754E-4 249.2 0.00108 0.00156 1.68153E-4 2.98177E-4 259.2 0.00375 0.00154 1.21883E-4 2.19202E-4 269.2 2.62824E-4 0.00104 8.84448E-5 1.61212E-4 279.2 0.00187 2.09873E-4 6.42465E-5 1.18607E-4 289.2 0.00156 3.53553E-5 4.67226E-5 8.72869E-5 299.2 3.51054E-4 -7.15441E-4 3.4006E-5 6.42467E-5 S5.B Time Flowing down Pumping up Flowing down fitting Pumping up fitting 0 -0.00131 5.1039E-4 0 0 0.1 4.02662E-4 0.00171 4.7804E-4 3.34628E-4 0.2 4.94641E-4 0.00156 9.44733E-4 6.61313E-4 0.3 0.00108 0.00197 0.0014 9.80377E-4 0.4 8.749E-4 0.00152 0.00185 0.00129 0.5 -0.0015 0.00219 0.00228 0.0016 0.6 3.64111E-4 0.00153 0.00271 0.00189 0.7 0.00305 0.00121 0.00312 0.00219 0.8 0.00151 5.3479E-4 0.00353 0.00247 0.9 0.00238 9.66755E-4 0.00393 0.00275 1 0.00122 0.00168 0.00432 0.00302 1.1 0.00245 0.00338 0.0047 0.00329 1.2 0.00566 0.00411 0.00508 0.00355 1.3 0.00249 0.00235 0.00545 0.00381 1.4 0.00266 0.00684 0.00581 0.00407 1.5 0.00426 0.00376 0.00616 0.00431 1.6 0.00754 0.00402 0.00651 0.00456 1.7 0.00499 0.00348 0.00685 0.00479 1.8 0.00747 0.00381 0.00718 0.00503 1.9 0.00823 0.00671 0.00751 0.00526 2 0.0059 0.00554 0.00784 0.00549 2.1 0.00731 0.0049 0.00816 0.00571 2.2 0.00706 0.00499 0.00847 0.00593 2.3 0.00911 0.00552 0.00878 0.00614 2.4 0.0053 0.00477 0.00908 0.00635 2.5 0.00828 0.00532 0.00938 0.00656 2.6 0.00743 0.00553 0.00967 0.00677 2.7 0.00707 0.00781 0.00996 0.00697 2.8 0.00821 0.0073 0.01024 0.00717 2.9 0.00874 0.00684 0.01052 0.00737 3 0.00805 0.00907 0.0108 0.00756 3.1 0.01026 0.00839 0.01107 0.00775

65

3.2 0.01136 0.0076 0.01134 0.00794 3.3 0.0102 0.00757 0.0116 0.00812 3.4 0.01148 0.00915 0.01187 0.00831 3.5 0.00997 0.00827 0.01212 0.00849 3.6 0.00762 0.00774 0.01238 0.00866 3.7 0.0076 0.00958 0.01263 0.00884 3.8 0.01387 0.00856 0.01287 0.00901 3.9 0.01353 0.00627 0.01312 0.00918 4 0.01104 0.00716 0.01336 0.00935 4.1 0.01381 0.00875 0.0136 0.00952 4.2 0.01193 0.01161 0.01383 0.00968 4.3 0.01412 0.00903 0.01407 0.00985 4.4 0.0095 0.01128 0.0143 0.01001 4.5 0.01257 0.01021 0.01452 0.01017 4.6 0.0128 0.01027 0.01475 0.01032 4.7 0.0132 0.00977 0.01497 0.01048 4.8 0.0138 0.0113 0.01519 0.01063 4.9 0.0142 0.01138 0.01541 0.01078 5 0.01479 0.01045 0.01562 0.01093 5.1 0.0149 0.01058 0.01583 0.01108 5.2 0.015 0.0109 0.01604 0.01123 5.7 0.0151 0.0139 0.01706 0.01194 6.2 0.0159 0.01369 0.01802 0.01261 6.7 0.0172 0.01495 0.01894 0.01326 7.2 0.0189 0.01225 0.01981 0.01387 7.7 0.02 0.01304 0.02064 0.01445 8.2 0.02091 0.01423 0.02143 0.015 8.7 0.02276 0.01384 0.02219 0.01553 9.2 0.02252 0.01809 0.02291 0.01604 10.2 0.02378 0.01773 0.02426 0.01698 11.2 0.02623 0.01684 0.02548 0.01784 12.2 0.02724 0.02077 0.02659 0.01861 13.2 0.02723 0.01966 0.0276 0.01932 14.2 0.03002 0.01957 0.02851 0.01995 15.2 0.03034 0.01923 0.02932 0.02053 16.2 0.02873 0.02046 0.03005 0.02104 17.2 0.0294 0.02202 0.0307 0.02149 18.2 0.03175 0.02118 0.03127 0.02189 19.2 0.0321 0.02129 0.03176 0.02223 22.2 0.03289 0.02353 0.03286 0.023 24.2 0.03085 0.02356 0.0333 0.02331 27.2 0.03449 0.02279 0.03359 0.02351 29.2 0.03322 0.02332 0.03357 0.0235 34.2 0.03004 0.0231 0.03295 0.02307 39.2 0.03055 0.02169 0.03171 0.02219 42.2 0.0291 0.02021 0.03075 0.02152 44.2 0.02718 0.01876 0.03005 0.02103 47.2 0.02683 0.01825 0.02892 0.02025 49.2 0.02825 0.01942 0.02814 0.0197 54.2 0.02708 0.0186 0.0261 0.01827 59.2 0.02205 0.01595 0.02401 0.01681 64.2 0.02497 0.01543 0.02194 0.01536 69.2 0.02178 0.01409 0.01994 0.01396 74.2 0.01736 0.01404 0.01803 0.01262 79.2 0.01864 0.01266 0.01624 0.01136 84.2 0.01855 0.01138 0.01457 0.0102 89.2 0.01544 0.00953 0.01302 0.00912 94.2 0.01304 0.00689 0.01161 0.00813 99.2 0.01092 0.00844 0.01033 0.00723 109.2 0.01091 0.00726 0.00811 0.00568 119.2 0.00793 0.00408 0.00632 0.00443 129.2 0.0053 0.00379 0.0049 0.00343

66

139.2 0.00523 0.00461 0.00377 0.00264 149.2 0.00544 0.00255 0.00289 0.00203 159.2 0.00326 0.00233 0.00221 0.00155 169.2 0.00172 0.00122 0.00168 0.00118 179.2 0.00259 0.00279 0.00128 8.9536E-4 189.2 0.00166 0.00302 9.6881E-4 6.78154E-4 199.2 0.00255 3.88455E-4 7.32161E-4 5.12509E-4 209.2 0.0016 0.00228 5.52239E-4 3.86563E-4 219.2 7.87254E-4 -3.04833E-4 4.15814E-4 2.91063E-4 229.2 0.00109 -0.0013 3.126E-4 2.18829E-4 239.2 -6.831E-5 -1.37719E-4 2.34696E-4 1.6428E-4 249.2 -4.63594E-4 5.93392E-4 1.75996E-4 1.23178E-4 259.2 0.00267 6.94041E-4 1.31813E-4 9.22631E-5 269.2 5.96833E-4 7.69418E-4 9.86241E-5 6.90292E-5 279.2 -3.24312E-4 -4.18438E-4 7.37299E-5 5.15954E-5 289.2 1.79335E-4 7.106E-5 5.50707E-5 3.85379E-5 299.2 -2.32699E-4 -8.4734E-4 4.11139E-5 2.87753E-5 S5.C Time 100:0 Time 50:50 Time 10:90 Time 2:98 0 1 -7E-7 0.99999 0 1 0 1 0.1 0.93935 0.1 0.96313 0.1 1.00624 0.1 0.94109 0.2 0.92284 0.2 0.91476 0.2 0.95157 0.2 0.93463 0.3 0.92119 0.3 0.87057 0.3 0.95062 0.3 0.89981 0.4 0.90928 0.4 0.82893 0.4 0.91976 0.4 0.86156 0.5 0.82003 0.5 0.79394 0.5 0.92368 0.5 0.82443 0.6 0.76201 0.6 0.77499 0.6 0.88429 0.6 0.82232 0.7 0.71944 0.7 0.78804 0.7 0.89412 0.7 0.81771 0.8 0.69154 0.8 0.76247 0.8 0.85478 0.8 0.7754 0.9 0.65134 0.9 0.74293 0.9 0.78432 0.9 0.7684 1 0.63181 1 0.71462 1 0.78694 1 0.78394 1.1 0.62916 1.1 0.70618 1.1 0.79959 1.1 0.7216 1.2 0.56394 1.2 0.70404 1.2 0.71419 1.2 0.69601 1.3 0.4954 1.3 0.65213 1.3 0.75079 1.3 0.73926 1.4 0.5056 1.4 0.62756 1.4 0.70134 1.4 0.71285 1.5 0.49668 1.5 0.64925 1.5 0.7006 1.5 0.68087 1.6 0.47241 1.6 0.64435 1.6 0.74303 1.6 0.66497 1.7 0.46434 1.7 0.63487 1.7 0.703 1.7 0.68371 1.8 0.43966 1.8 0.62146 1.8 0.67947 1.8 0.67706 1.9 0.41035 1.9 0.58469 1.9 0.68099 1.9 0.67862 2 0.37434 2 0.55553 2 0.59537 2 0.64871 2.5 0.32354 2.5 0.50213 2.5 0.53113 2.5 0.55947 3 0.27122 3 0.44482 3 0.48601 3 0.43959 3.5 0.2076 3.5 0.40171 3.5 0.46549 3.5 0.44244 4 0.15276 4 0.36401 4 0.36256 4 0.44953 4.5 0.1505 4.5 0.31503 4.5 0.3494 4.5 0.35276 5 0.09616 4.8 0.28935 5 0.35443 5 0.32062 5.5 0.12759 4.9 0.25347 5.5 0.31584 5.5 0.35582 6 0.05915 5 0.28453 6 0.26101 6 0.28737 6.5 0.05181 5.1 0.27246 6.5 0.24622 6.5 0.302 7 0.05912 5.2 0.25175 7 0.21957 7 0.22347 7.5 0.01831 5.7 0.23263 7.5 0.16904 7.5 0.28801 8 0.00834 6.2 0.20251 8 0.1546 8 0.17618 8.5 0.0211 6.7 0.17409 8.5 0.14963 8.5 0.16246 9 0.05157 7.2 0.17056 9 0.15316 9 0.18844 9.5 0.00784 7.7 0.13344 9.5 0.14968 9.5 0.13882 10 0.01587 8.2 0.12509 10 0.12675 10 0.16975 11 -0.00337 8.7 0.10178 11 0.0929 11 0.1786

67

12 0.0094 9.2 0.08778 12 0.08976 12 0.10984 13 0.01682 10.2 0.08529 13 0.07594 13 0.10899 14 7.49796E-4 11.2 0.04434 14 0.07391 14 0.09896 15 0.0101 12.2 0.03387 15 0.02838 15 0.05541 16 -0.01307 13.2 0.03637 16 0.05466 16 0.07116 17 0.01899 14.2 0.04928 17 0.03256 17 0.07597 18 -0.00874 15.2 0.02429 18 0.03834 18 0.07856 19 -0.00896 16.2 0.03121 19 0.01887 19 0.03743 20 -0.00947 17.2 0.04453 20 0.00856 20 0.05604 22 -0.00594 18.2 0.02754 22 -0.02676 22 0.02837 25 -0.01291 19.2 0.02457 25 0.01603 25 0.03325 28 0.03722 22.2 0.01835 28 -0.01074 28 0.02394 30 -0.01594 24.2 0.01657 30 0.009 30 0.00818 33 0.01457 27.2 0.03184 33 -0.02378 33 -1.967E-4 35 -0.01353 29.2 0.01281 35 0.0186 35 -0.031 38 -0.02884 34.2 -8.80031E-4 38 -0.00102 38 -0.02106 40 -0.00684 39.2 0.00165 40 0.00859 40 0.01684 43 -0.00707 42.2 -0.00166 43 0.00346 43 -0.01534 45 -0.00128 44.2 0.00568 45 -0.00746 45 0.01385 48 -0.03747 47.2 0.01003 48 -0.00931 48 -0.01678 50 -0.00832 49.2 -0.01929 50 0.01063 50 4.27359E-4 Time 100:0

fitting Time 50:50

fitting Time 10:90

fitting Time 2:98

fitting 0 1 -7E-7 1 0 1 0 1 0.1 0.95853 0.1 0.97048 0.1 0.98014 0.1 0.98209 0.2 0.91886 0.2 0.94187 0.2 0.96069 0.2 0.9645 0.3 0.8809 0.3 0.91413 0.3 0.94163 0.3 0.94722 0.4 0.84457 0.4 0.88725 0.4 0.92295 0.4 0.93026 0.5 0.80981 0.5 0.86119 0.5 0.90465 0.5 0.9136 0.6 0.77654 0.6 0.83593 0.6 0.88672 0.6 0.89725 0.7 0.74471 0.7 0.81145 0.7 0.86915 0.7 0.88118 0.8 0.71424 0.8 0.78771 0.8 0.85194 0.8 0.86541 0.9 0.68508 0.9 0.7647 0.9 0.83508 0.9 0.84992 1 0.65717 1 0.74239 1 0.81855 1 0.83471 1.1 0.63046 1.1 0.72076 1.1 0.80236 1.1 0.81977 1.2 0.60489 1.2 0.69979 1.2 0.78649 1.2 0.8051 1.3 0.58042 1.3 0.67946 1.3 0.77094 1.3 0.79069 1.4 0.55699 1.4 0.65975 1.4 0.75571 1.4 0.77654 1.5 0.53456 1.5 0.64064 1.5 0.74078 1.5 0.76265 1.6 0.51309 1.6 0.62211 1.6 0.72616 1.6 0.749 1.7 0.49253 1.7 0.60414 1.7 0.71182 1.7 0.7356 1.8 0.47284 1.8 0.58672 1.8 0.69778 1.8 0.72245 1.9 0.45399 1.9 0.56982 1.9 0.68402 1.9 0.70953 2 0.43594 2 0.55343 2 0.67053 2 0.69684 2.5 0.35653 2.5 0.47864 2.5 0.60705 2.5 0.63673 3 0.29248 3 0.41443 3 0.54969 3 0.58182 3.5 0.24075 3.5 0.35927 3.5 0.49783 3.5 0.53167 4 0.19888 4 0.31185 4 0.45096 4 0.48586 4.5 0.16492 4.5 0.27103 4.5 0.40857 4.5 0.44401 5 0.13733 4.8 0.24931 5 0.37023 5 0.40578 5.5 0.11484 4.9 0.24249 5.5 0.33555 5.5 0.37085 6 0.09647 5 0.23587 6 0.30417 6 0.33894 6.5 0.08141 5.1 0.22944 6.5 0.27578 6.5 0.30979 7 0.06903 5.2 0.2232 7 0.25008 7 0.28315 7.5 0.05882 5.7 0.19461 7.5 0.22682 7.5 0.25882 8 0.05036 6.2 0.16992 8 0.20575 8 0.23658 8.5 0.04333 6.7 0.14858 8.5 0.18668 8.5 0.21626 9 0.03746 7.2 0.1301 9 0.1694 9 0.19769 9.5 0.03253 7.7 0.11409 9.5 0.15375 9.5 0.18072 10 0.02838 8.2 0.1002 10 0.13956 10 0.16521

68

11 0.02187 8.7 0.08813 11 0.11506 11 0.13808 12 0.01712 9.2 0.07763 12 0.09492 12 0.11542 13 0.01359 10.2 0.0605 13 0.07836 13 0.09649 14 0.0109 11.2 0.04743 14 0.06472 14 0.08067 15 0.00883 12.2 0.0374 15 0.05349 15 0.06746 16 0.00721 13.2 0.02966 16 0.04424 16 0.05641 17 0.00592 14.2 0.02365 17 0.03661 17 0.04718 18 0.00489 15.2 0.01895 18 0.03031 18 0.03946 19 0.00405 16.2 0.01526 19 0.02511 19 0.03301 20 0.00336 17.2 0.01235 20 0.02081 20 0.02761 22 0.00234 18.2 0.01003 22 0.01432 22 0.01933 25 0.00136 19.2 0.00818 25 0.0082 25 0.01133 28 8.01968E-4 22.2 0.00452 28 0.00471 28 0.00664 30 5.63449E-4 24.2 0.00308 30 0.00326 30 0.00466 33 3.32165E-4 27.2 0.00176 33 0.00189 33 0.00273 35 2.33621E-4 29.2 0.00122 35 0.00131 35 0.00192 38 1.37836E-4 34.2 4.94308E-4 38 7.61848E-4 38 0.00113 40 9.69694E-5 39.2 2.03027E-4 40 5.30961E-4 40 7.89934E-4 43 5.72231E-5 42.2 1.19401E-4 43 3.09449E-4 43 4.64407E-4 45 4.02599E-5 44.2 8.38755E-5 45 2.16129E-4 45 3.25983E-4 48 2.37592E-5 47.2 4.94197E-5 48 1.26322E-4 48 1.91763E-4 50 1.67163E-5 49.2 3.47452E-5 50 8.83759E-5 50 1.34655E-4 S6.A Time KSCN (4.0M) KS13C15N (4.0M) KSCN (4.0M)

fitting KS13C15N (4.0M) fitting

0 1.00001 0.99617 1 1 0.1 0.99011 1 0.97813 0.98732 0.2 0.97047 0.99253 0.95767 0.9751 0.3 0.94939 0.97416 0.93849 0.96331 0.4 0.93515 0.96113 0.92053 0.95195 0.5 0.91021 0.94601 0.90368 0.94099 0.6 0.89541 0.9342 0.88786 0.93042 0.7 0.88452 0.92073 0.873 0.92021 0.8 0.86167 0.90856 0.85902 0.91035 0.9 0.84947 0.89898 0.84587 0.90083 1 0.83548 0.88809 0.83347 0.89163 1.1 0.82215 0.87986 0.82178 0.88274 1.2 0.81004 0.87314 0.81074 0.87415 1.3 0.79634 0.86098 0.80031 0.86583 1.4 0.79005 0.85386 0.79044 0.85778 1.5 0.78276 0.84592 0.78109 0.84999 1.6 0.7758 0.83963 0.77222 0.84245 1.7 0.7649 0.83116 0.7638 0.83514 1.8 0.76172 0.82537 0.7558 0.82806 1.9 0.74986 0.81968 0.74818 0.82119 2 0.7414 0.81518 0.74092 0.81453 2.1 0.73639 0.80918 0.73399 0.80806 2.2 0.73156 0.80465 0.72737 0.80179 2.3 0.72326 0.79426 0.72103 0.79569 2.4 0.71925 0.79177 0.71496 0.78977 2.5 0.70954 0.78365 0.70914 0.78401 2.6 0.70032 0.7809 0.70355 0.77841 2.7 0.70125 0.77415 0.69817 0.77297 2.8 0.69579 0.76996 0.69299 0.76766 2.9 0.68769 0.7665 0.68799 0.7625 3 0.6858 0.76059 0.68316 0.75747 3.1 0.68273 0.75593 0.67849 0.75257 3.2 0.67702 0.75209 0.67397 0.74779

69

3.3 0.67032 0.74587 0.66959 0.74313 3.4 0.66491 0.7425 0.66534 0.73858 3.5 0.66215 0.74031 0.66121 0.73414 3.6 0.65738 0.73428 0.65719 0.7298 3.7 0.64965 0.73117 0.65327 0.72555 3.8 0.64363 0.72824 0.64945 0.72141 3.9 0.64235 0.72334 0.64573 0.71735 4 0.63713 0.72136 0.64209 0.71338 4.1 0.6402 0.71689 0.63852 0.7095 4.2 0.63118 0.70892 0.63504 0.70569 4.3 0.62597 0.70617 0.63162 0.70196 4.4 0.62202 0.70327 0.62827 0.6983 4.5 0.62518 0.70214 0.62498 0.69472 4.6 0.61734 0.69766 0.62174 0.6912 4.7 0.6114 0.69233 0.61857 0.68775 4.8 0.6109 0.68958 0.61544 0.68436 4.9 0.60581 0.68671 0.61236 0.68103 5 0.60163 0.68566 0.60932 0.67776 5.1 0.60186 0.68253 0.60633 0.67454 5.2 0.59748 0.67628 0.60338 0.67138 5.3 0.58985 0.67378 0.60047 0.66826 5.4 0.59079 0.66986 0.59759 0.6652 5.5 0.58635 0.66752 0.59475 0.66218 5.6 0.5817 0.66484 0.59194 0.65921 5.7 0.57722 0.66084 0.58916 0.65629 5.8 0.57539 0.65784 0.58641 0.6534 5.9 0.57046 0.65583 0.58368 0.65055 6 0.56625 0.65338 0.58099 0.64775 6.1 0.56378 0.64983 0.57832 0.64498 6.2 0.56035 0.64483 0.57567 0.64225 6.3 0.55969 0.63982 0.57305 0.63955 6.4 0.55718 0.63782 0.57044 0.63689 6.9 0.54816 0.62581 0.55774 0.62403 7.4 0.52892 0.61099 0.54548 0.61185 7.9 0.51664 0.60077 0.5336 0.60024 8.4 0.49982 0.58777 0.52205 0.58912 8.9 0.49411 0.5764 0.5108 0.57842 9.4 0.48348 0.5661 0.49984 0.56808 9.9 0.46698 0.55173 0.48913 0.55806 10.4 0.45676 0.54374 0.47867 0.54833 11.4 0.4364 0.52555 0.45845 0.52962 12.4 0.41739 0.50414 0.43911 0.51176 13.4 0.40339 0.487 0.42061 0.49465 14.4 0.38636 0.46979 0.40289 0.4782 15.4 0.36891 0.45161 0.38593 0.46235 16.4 0.35534 0.43707 0.36968 0.44707 17.4 0.33835 0.42471 0.35413 0.43233 18.4 0.32436 0.40664 0.33924 0.41808 19.4 0.31044 0.3965 0.32498 0.40432 20.4 0.29525 0.38146 0.31132 0.39103 23.4 0.26524 0.35741 0.27372 0.35373 25.4 0.24391 0.3333 0.25123 0.33089 28.4 0.21921 0.30225 0.22094 0.29939 30.4 0.19664 0.27916 0.20282 0.28008 35.4 0.16339 0.23766 0.16381 0.23713 40.4 0.13104 0.20119 0.13235 0.2008 43.4 0.11481 0.18191 0.11648 0.18175 45.4 0.1021 0.17203 0.10698 0.17007 48.4 0.092 0.15533 0.09418 0.15396 50.4 0.08261 0.14495 0.08652 0.14408 55.4 0.07032 0.12469 0.07 0.12207 60.4 0.05652 0.1055 0.05667 0.10345

70

65.4 0.04435 0.08937 0.04589 0.08768 70.4 0.0375 0.07609 0.03719 0.07433 75.4 0.02923 0.0641 0.03015 0.06302 80.4 0.02414 0.05535 0.02446 0.05343 85.4 0.02048 0.04709 0.01986 0.04531 90.4 0.01448 0.03894 0.01613 0.03843 95.4 0.01336 0.03407 0.01311 0.0326 100.4 0.0084 0.02982 0.01066 0.02766 110.4 0.0075 0.02071 0.00707 0.01991 120.4 0.00494 0.01504 0.0047 0.01434 130.4 9.26076E-5 0.01106 0.00313 0.01033 140.4 1E-3 0.00825 0.0021 0.00745 150.4 0.0012 0.00521 0.00141 0.00537 160.4 0.00369 0.00384 9.47387E-4 0.00387 170.4 -8.47137E-5 0.0014 6.4025E-4 0.00279 180.4 9.268E-4 0.00214 4.34332E-4 0.00201 190.4 -6.67856E-4 -9.80186E-4 2.95638E-4 0.00145 200.4 -0.00117 0.00202 2.01961E-4 0.00105 210.4 -0.00193 5.38995E-4 1.38458E-4 7.56723E-4 220.4 -8.39232E-4 7.69612E-4 9.52574E-5 5.46252E-4 230.4 -0.00195 2.14259E-4 6.58058E-5 3.94372E-4 240.4 0.00283 -8.83906E-5 4.55872E-5 2.84752E-4 250.4 1.51583E-4 9.93781E-5 3.16891E-5 2.0563E-4 S6.B Time Flowing down Pumping up Flowing down fitting Pumping up fitting 0 3.20421E-4 6.79497E-5 0 0 0.1 0.00177 8.90059E-4 4.77957E-4 3.34571E-4 0.2 -2.24788E-4 0.00255 9.39567E-4 6.57696E-4 0.3 0.00113 5.82218E-4 0.00139 9.70081E-4 0.4 0.00222 0.00237 0.00182 0.00127 0.5 0.0016 0.00261 0.00224 0.00157 0.6 0.00453 0.00413 0.00264 0.00185 0.7 0.00271 0.00254 0.00304 0.00212 0.8 0.00433 0.00299 0.00342 0.00239 0.9 0.00351 0.00342 0.00379 0.00265 1 0.00308 0.00375 0.00415 0.00291 1.1 0.00508 0.00494 0.0045 0.00315 1.2 0.00439 0.00465 0.00485 0.00339 1.3 0.00373 0.00337 0.00518 0.00363 1.4 0.00563 0.00554 0.00551 0.00386 1.5 0.00534 0.00421 0.00583 0.00408 1.6 0.00463 0.00488 0.00614 0.0043 1.7 0.00612 0.00521 0.00645 0.00451 1.8 0.00541 0.00402 0.00674 0.00472 1.9 0.00613 0.006 0.00704 0.00493 2 0.00658 0.00694 0.00732 0.00513 2.1 0.00534 0.00495 0.0076 0.00532 2.2 0.0063 0.00706 0.00788 0.00552 2.3 0.00703 0.00526 0.00815 0.00571 2.4 0.007 0.00638 0.00842 0.00589 2.5 0.00743 0.00582 0.00868 0.00608 2.6 0.00753 0.00711 0.00894 0.00626 2.7 0.00734 0.00656 0.00919 0.00643 2.8 0.00876 0.00579 0.00944 0.00661 2.9 0.00762 0.00753 0.00968 0.00678 3 0.00818 0.00655 0.00992 0.00695

71

3.1 0.00882 0.00759 0.01016 0.00711 3.2 0.00904 0.00842 0.01039 0.00728 3.3 0.01113 0.00748 0.01062 0.00744 3.4 0.00913 0.00757 0.01085 0.0076 3.5 0.0096 0.00941 0.01108 0.00775 3.6 0.00998 0.00722 0.0113 0.00791 3.7 0.01051 0.00887 0.01151 0.00806 3.8 0.00996 0.00899 0.01173 0.00821 3.9 0.01086 0.00834 0.01194 0.00836 4 0.01108 0.00845 0.01215 0.00851 4.1 0.00991 0.00871 0.01236 0.00865 4.2 0.01169 0.00854 0.01256 0.00879 4.3 0.01181 0.00923 0.01277 0.00894 4.4 0.01185 0.01006 0.01296 0.00908 4.5 0.01206 0.00986 0.01316 0.00921 4.6 0.01226 0.00842 0.01336 0.00935 4.7 0.01234 0.00807 0.01355 0.00948 4.8 0.01239 0.01036 0.01374 0.00962 4.9 0.01243 0.0096 0.01393 0.00975 5 0.01258 0.01028 0.01411 0.00988 5.1 0.01268 0.00999 0.0143 0.01001 5.2 0.01285 0.00934 0.01448 0.01014 5.3 0.01351 0.00942 0.01466 0.01026 5.4 0.01455 0.01042 0.01484 0.01039 5.5 0.0146 0.0107 0.01501 0.01051 5.6 0.0147 0.01075 0.01519 0.01063 5.7 0.0148 0.01077 0.01536 0.01075 5.8 0.0149 0.01086 0.01553 0.01087 5.9 0.01501 0.01091 0.0157 0.01099 6 0.01505 0.01102 0.01587 0.01111 6.1 0.01506 0.01104 0.01603 0.01122 6.2 0.0151 0.01106 0.0162 0.01134 6.3 0.01512 0.01108 0.01636 0.01145 6.4 0.01513 0.00978 0.01652 0.01156 6.9 0.01474 0.01304 0.01729 0.01211 7.4 0.01804 0.01209 0.01803 0.01262 7.9 0.01763 0.01404 0.01873 0.01311 8.4 0.0179 0.01306 0.0194 0.01358 8.9 0.0184 0.01354 0.02003 0.01402 9.4 0.02069 0.0137 0.02063 0.01444 9.9 0.02 0.01386 0.0212 0.01484 10.4 0.01987 0.01412 0.02173 0.01521 11.4 0.02241 0.01625 0.02273 0.01591 12.4 0.0241 0.01589 0.02362 0.01653 13.4 0.02378 0.01674 0.0244 0.01708 14.4 0.0247 0.01617 0.0251 0.01757 15.4 0.02476 0.0166 0.02571 0.018 16.4 0.02527 0.0169 0.02624 0.01837 17.4 0.02574 0.01822 0.02669 0.01868 18.4 0.0266 0.01635 0.02707 0.01895 19.4 0.02702 0.01912 0.02738 0.01917 20.4 0.0272 0.01897 0.02764 0.01935 23.4 0.02743 0.01893 0.02807 0.01965 25.4 0.02682 0.01863 0.02813 0.01969 28.4 0.02712 0.01947 0.02792 0.01954 30.4 0.02862 0.01842 0.02762 0.01934 35.4 0.02656 0.01767 0.02645 0.01852 40.4 0.02572 0.01614 0.02487 0.01741 43.4 0.02493 0.01614 0.02379 0.01666 45.4 0.02391 0.01609 0.02305 0.01613 48.4 0.02155 0.01538 0.0219 0.01533 50.4 0.02185 0.01432 0.02112 0.01478

72

55.4 0.01998 0.01231 0.01918 0.01343 60.4 0.02026 0.01156 0.01729 0.0121 65.4 0.01772 0.01016 0.01548 0.01084 70.4 0.0148 0.00972 0.01379 0.00965 75.4 0.01448 0.00738 0.01223 0.00856 80.4 0.01236 0.00811 0.0108 0.00756 85.4 0.01039 0.00621 0.00951 0.00666 90.4 0.00956 0.00547 0.00835 0.00584 95.4 0.00792 0.00502 0.0073 0.00511 100.4 0.00739 0.00589 0.00638 0.00446 110.4 0.00471 0.00422 0.00483 0.00338 120.4 0.00441 0.00309 0.00364 0.00255 130.4 0.00306 0.00212 0.00272 0.0019 140.4 0.00115 0.00121 0.00203 0.00142 150.4 0.00145 6.14085E-4 0.0015 0.00105 160.4 0.00113 0.00106 0.00111 7.78637E-4 170.4 6.39814E-4 -4.49872E-4 8.20388E-4 5.74272E-4 180.4 4.55911E-4 1.01079E-4 6.03649E-4 4.22555E-4 190.4 6.39106E-4 -1.38521E-4 4.43279E-4 3.1029E-4 200.4 0.00121 0.00124 3.24946E-4 2.27468E-4 210.4 4.08294E-4 9.33269E-4 2.37858E-4 1.66507E-4 220.4 3.91239E-4 3.3924E-4 1.73887E-4 1.21719E-4 230.4 -2.97471E-4 0.00127 1.26978E-4 8.88831E-5 240.4 5.92825E-4 -5.12917E-4 9.26289E-5 6.48479E-5 250.4 2.45445E-4 8.8445E-4 6.75157E-5 4.72736E-5 S6.C Time 100:0 Time 50:50 Time 10:90 Time 2:98 0 1 -8.7E-7 1 0 0.99999 0 0.99999 0.1 0.95966 0.1 0.97284 0.1 1.00084 0.1 0.89015 0.2 0.93176 0.2 0.9681 0.2 0.98625 0.2 0.83939 0.3 0.89093 0.3 0.94881 0.3 0.94006 0.3 0.901 0.4 0.83315 0.4 0.92687 0.4 0.89148 0.4 0.78903 0.5 0.7899 0.5 0.87978 0.5 0.88807 0.5 0.73191 0.6 0.74421 0.6 0.86227 0.6 0.84434 0.6 0.8317 0.7 0.69507 0.7 0.85273 0.7 0.81281 0.7 0.85878 0.8 0.67848 0.8 0.80601 0.8 0.7806 0.8 0.70996 0.9 0.66004 0.9 0.78446 0.9 0.75242 0.9 0.82175 1 0.61373 1 0.73733 1 0.72516 1 0.84685 1.1 0.59049 1.1 0.73161 1.1 0.73843 1.1 0.70519 1.2 0.57648 1.2 0.71152 1.2 0.67615 1.2 0.69779 1.3 0.53494 1.3 0.70188 1.3 0.67507 1.3 0.71549 1.4 0.52536 1.4 0.67439 1.4 0.62379 1.4 0.69625 1.5 0.48404 1.5 0.64567 1.5 0.62422 1.5 0.66475 1.6 0.48651 1.6 0.6269 1.6 0.63318 1.6 0.78096 1.7 0.48801 1.7 0.61384 1.7 0.61284 1.7 0.61315 1.8 0.43919 1.8 0.59527 1.8 0.60236 1.8 0.61081 1.9 0.47742 1.9 0.58978 1.9 0.56261 1.9 0.61288 2.4 0.38139 2 0.53604 2.4 0.52285 2.4 0.49609 2.9 0.2983 2.1 0.50933 2.9 0.45725 2.9 0.41263 3.4 0.2443 2.2 0.53894 3.4 0.41945 3.4 0.41219 3.9 0.20249 2.3 0.48255 3.9 0.35699 3.9 0.2971 4.4 0.14882 2.4 0.49257 4.4 0.30648 4.4 0.3314 4.9 0.12961 2.5 0.46772 4.9 0.28382 4.9 0.21172 5.4 0.11013 2.6 0.45376 5.4 0.26343 5.4 0.26451 5.9 0.0953 2.7 0.44915 5.9 0.22664 5.9 0.26579 6.4 0.08301 2.8 0.43366 6.4 0.20599 6.4 0.21821 6.9 0.0636 2.9 0.39637 6.9 0.15504 6.9 0.18616

73

7.4 0.06797 3 0.40242 7.4 0.20273 7.4 0.1553 7.9 0.04721 3.1 0.38319 7.9 0.14324 7.9 0.18272 8.4 0.05418 3.2 0.35561 8.4 0.12304 8.4 0.14057 8.9 0.04445 3.3 0.33267 8.9 0.12651 8.9 0.14799 9.4 0.02364 3.4 0.32188 9.4 0.10855 9.4 0.09499 9.9 0.02179 3.5 0.32896 9.9 0.12082 9.9 0.11713 10.9 0.00675 3.6 0.3216 10.9 0.08876 10.9 0.05594 11.9 0.00873 3.7 0.32991 11.9 0.04836 11.9 0.01721 12.9 0.01649 3.8 0.30645 12.9 0.05128 12.9 0.03621 13.9 -0.00769 3.9 0.30824 13.9 0.01918 13.9 0.02406 14.9 -0.01484 4 0.3191 14.9 0.0096 14.9 0.00915 15.9 -0.014 4.1 0.31179 15.9 0.01413 15.9 0.01587 16.9 -0.00419 4.2 0.30833 16.9 0.02242 16.9 -0.0091 17.9 0.00542 4.3 0.26675 17.9 -0.00425 17.9 0.02472 18.9 -0.00799 4.4 0.26185 18.9 0.03884 18.9 -0.00297 19.9 0.00185 4.5 0.24664 19.9 0.00191 19.9 -0.01834 21.9 -0.00303 4.6 0.23993 21.9 0.00849 21.9 0.01324 24.9 -0.00109 4.7 0.23834 24.9 0.05172 24.9 0.0026 27.9 0.00624 4.8 0.24712 27.9 -0.01524 27.9 -0.00728 29.9 -0.01443 4.9 0.23651 29.9 0.01106 29.9 0.01291 32.9 -0.00161 5 0.22606 32.9 -0.03658 32.9 0.01381 34.9 0.01861 5.1 0.2283 34.9 0.00452 34.9 0.00221 37.9 -0.0116 5.2 0.19175 37.9 -0.01621 37.9 -0.02199 39.9 0.01981 5.3 0.18599 39.9 -0.0597 39.9 -0.01539 42.9 -0.02428 5.4 0.18809 42.9 0.01748 42.9 0.00597 44.9 -0.02264 5.5 0.20381 44.9 -0.00413 44.9 0.00858 47.9 0.01588 5.6 0.188 47.9 0.03434 47.9 -0.01513 49.9 -0.00958 5.7 0.16982 49.9 -0.01113 49.9 -0.02288 5.8 0.17545 5.9 0.18257 6 0.17276 6.1 0.19446 6.2 0.17179 6.7 0.13375 7.2 0.12819 7.7 0.10863 8.2 0.07391 8.7 0.06299 9.2 0.06012 9.7 0.06055 10.2 0.05215 11.2 0.03199 12.2 0.02367 13.2 0.04146 14.2 0.01879 15.2 0.02603 16.2 0.00722 17.2 0.00743 18.2 0.01349 19.2 -0.01415 20.2 -0.00876 23.2 -0.0076 25.2 -0.01822 28.2 -0.00478 30.2 -0.00666 35.2 0.00224 40.2 -0.01039 43.2 0.00351 45.2 -0.00821 48.2 -1.81284E-4 50.2 -0.00367

74

Time 100:0

fitting Time 50:50

fitting Time 10:90

fitting Time 2:98

fitting 0 1 -8.7E-7 1 0 1 0 1 0.50404 0.80634 0.50707 0.84512 0.50404 0.87907 0.50404 0.88585 1.00808 0.6515 1.01414 0.71492 1.00808 0.77291 1.00808 0.78476 1.51212 0.52754 1.52121 0.60539 1.51212 0.6797 1.51212 0.69523 2.01616 0.42816 2.02828 0.51317 2.01616 0.59783 2.01616 0.61594 2.5202 0.34837 2.53535 0.43545 2.5202 0.52593 2.5202 0.5457 3.02424 0.28419 3.04242 0.3699 3.02424 0.46275 3.02424 0.4835 3.52828 0.23248 3.54949 0.31456 3.52828 0.40723 3.52828 0.4284 4.03232 0.19072 4.05656 0.2678 4.03232 0.35844 4.03232 0.37959 4.53636 0.15694 4.56364 0.22825 4.53636 0.31554 4.53636 0.33635 5.0404 0.12955 5.07071 0.19476 5.0404 0.27783 5.0404 0.29805 5.54444 0.10729 5.57778 0.16637 5.54444 0.24467 5.54444 0.26412 6.04848 0.08914 6.08485 0.14229 6.04848 0.2155 6.04848 0.23406 6.55253 0.07431 6.59192 0.12183 6.55253 0.18984 6.55253 0.20742 7.05657 0.06216 7.09899 0.10444 7.05657 0.16726 7.05657 0.18382 7.56061 0.05217 7.60606 0.08963 7.56061 0.14739 7.56061 0.16292 8.06465 0.04393 8.11313 0.07701 8.06465 0.1299 8.06465 0.14439 8.56869 0.03712 8.6202 0.06625 8.56869 0.1145 8.56869 0.12797 9.07273 0.03146 9.12727 0.05705 9.07273 0.10094 9.07273 0.11343 9.57677 0.02676 9.63434 0.04919 9.57677 0.08901 9.57677 0.10054 10.08081 0.02282 10.14141 0.04246 10.08081 0.07849 10.08081 0.08911 10.58485 0.01953 10.64848 0.03669 10.58485 0.06923 10.58485 0.07899 11.08889 0.01676 11.15555 0.03174 11.08889 0.06107 11.08889 0.07002 11.59293 0.01442 11.66263 0.02749 11.59293 0.05388 11.59293 0.06207 12.09697 0.01244 12.1697 0.02383 12.09697 0.04754 12.09697 0.05502 12.60101 0.01075 12.67677 0.02068 12.60101 0.04195 12.60101 0.04878 13.10505 0.00932 13.18384 0.01796 13.10505 0.03703 13.10505 0.04324 13.60909 0.00809 13.69091 0.01562 13.60909 0.03269 13.60909 0.03834 14.11313 0.00704 14.19798 0.01359 14.11313 0.02886 14.11313 0.03399 14.61717 0.00614 14.70505 0.01184 14.61717 0.02548 14.61717 0.03013 15.12121 0.00536 15.21212 0.01032 15.12121 0.0225 15.12121 0.02671 15.62525 0.00469 15.71919 0.00901 15.62525 0.01987 15.62525 0.02369 16.12929 0.00411 16.22626 0.00787 16.12929 0.01755 16.12929 0.021 16.63333 0.0036 16.73333 0.00688 16.63333 0.0155 16.63333 0.01862 17.13737 0.00316 17.2404 0.00602 17.13737 0.0137 17.13737 0.01651 17.64141 0.00278 17.74747 0.00527 17.64141 0.0121 17.64141 0.01464 18.14545 0.00245 18.25454 0.00461 18.14545 0.01069 18.14545 0.01298 18.64949 0.00215 18.76162 0.00404 18.64949 0.00945 18.64949 0.01151 19.15354 0.0019 19.26869 0.00355 19.15354 0.00835 19.15354 0.01021 19.65758 0.00168 19.77576 0.00311 19.65758 0.00738 19.65758 0.00905 20.16162 0.00148 20.28283 0.00273 20.16162 0.00653 20.16162 0.00803 20.66566 0.00131 20.7899 0.0024 20.66566 0.00577 20.66566 0.00712 21.1697 0.00115 21.29697 0.00211 21.1697 0.0051 21.1697 0.00631 21.67374 0.00102 21.80404 0.00186 21.67374 0.00451 21.67374 0.0056 22.17778 9.01968E-4 22.31111 0.00164 22.17778 0.00399 22.17778 0.00496 22.68182 7.97988E-4 22.81818 0.00144 22.68182 0.00353 22.68182 0.0044 23.18586 7.06237E-4 23.32525 0.00127 23.18586 0.00312 23.18586 0.0039 23.6899 6.25227E-4 23.83232 0.00112 23.6899 0.00276 23.6899 0.00346 24.19394 5.53661E-4 24.33939 9.85065E-4 24.19394 0.00244 24.19394 0.00307 24.69798 4.90407E-4 24.84646 8.68697E-4 24.69798 0.00216 24.69798 0.00272 25.20202 4.34475E-4 25.35353 7.66342E-4 25.20202 0.00191 25.20202 0.00242 25.70606 3.84997E-4 25.86061 6.76268E-4 25.70606 0.00169 25.70606 0.00214 26.2101 3.41214E-4 26.36768 5.96966E-4 26.2101 0.0015 26.2101 0.0019 26.71414 3.02457E-4 26.87475 5.27117E-4 26.71414 0.00133 26.71414 0.00169 27.21818 2.6814E-4 27.38182 4.65569E-4 27.21818 0.00117 27.21818 0.00149 27.72222 2.37746E-4 27.88889 4.11313E-4 27.72222 0.00104 27.72222 0.00133

75

28.22626 2.10821E-4 28.39596 3.63469E-4 28.22626 9.19208E-4 28.22626 0.00118 28.7303 1.86963E-4 28.90303 3.21264E-4 28.7303 8.13755E-4 28.7303 0.00104 29.23434 1.6582E-4 29.4101 2.8402E-4 29.23434 7.20449E-4 29.23434 9.25292E-4 29.73838 1.47079E-4 29.91717 2.51145E-4 29.73838 6.37883E-4 29.73838 8.20756E-4 30.24242 1.30466E-4 30.42424 2.22118E-4 30.24242 5.64816E-4 30.24242 7.28039E-4 30.74646 1.15736E-4 30.93131 1.9648E-4 30.74646 5.0015E-4 30.74646 6.45804E-4 31.25051 1.02676E-4 31.43838 1.73831E-4 31.25051 4.42914E-4 31.25051 5.72864E-4 31.75455 9.10932E-5 31.94545 1.53817E-4 31.75455 3.92251E-4 31.75455 5.08168E-4 32.25859 8.08209E-5 32.45252 1.36128E-4 32.25859 3.47404E-4 32.25859 4.50784E-4 32.76263 7.17098E-5 32.9596 1.20489E-4 32.76263 3.07702E-4 32.76263 3.99884E-4 33.26667 6.3628E-5 33.46667 1.06661E-4 33.26667 2.72552E-4 33.26667 3.54735E-4 33.77071 5.64588E-5 33.97374 9.44318E-5 33.77071 2.4143E-4 33.77071 3.14687E-4 34.27475 5.00988E-5 34.48081 8.3614E-5 34.27475 2.13873E-4 34.27475 2.79163E-4 34.77879 4.44564E-5 34.98788 7.40434E-5 34.77879 1.89471E-4 34.77879 2.47652E-4 35.28283 3.94503E-5 35.49495 6.55749E-5 35.28283 1.67862E-4 35.28283 2.197E-4 35.78687 3.50086E-5 36.00202 5.80804E-5 35.78687 1.48725E-4 35.78687 1.94905E-4 36.29091 3.10675E-5 36.50909 5.14469E-5 36.29091 1.31775E-4 36.29091 1.7291E-4 36.79495 2.75706E-5 37.01616 4.55749E-5 36.79495 1.16763E-4 36.79495 1.53398E-4 37.29899 2.44676E-5 37.52323 4.03761E-5 37.29899 1.03465E-4 37.29899 1.36089E-4 37.80303 2.17141E-5 38.0303 3.5773E-5 37.80303 9.16862E-5 37.80303 1.20735E-4 38.30707 1.92706E-5 38.53737 3.16968E-5 38.30707 8.12516E-5 38.30707 1.07114E-4 38.81111 1.71023E-5 39.04444 2.80869E-5 38.81111 7.20076E-5 38.81111 9.50301E-5 39.31515 1.51781E-5 39.55151 2.48895E-5 39.31515 6.38178E-5 39.31515 8.43104E-5 39.81919 1.34705E-5 40.05859 2.20574E-5 39.81919 5.65618E-5 39.81919 7.48005E-5 40.32323 1.19551E-5 40.56566 1.95485E-5 40.32323 5.01327E-5 40.32323 6.63638E-5 40.82727 1.06103E-5 41.07273 1.73259E-5 40.82727 4.4436E-5 40.82727 5.88792E-5 41.33131 9.41676E-6 41.5798 1.53566E-5 41.33131 3.93881E-5 41.33131 5.22391E-5 41.83535 8.35753E-6 42.08687 1.36118E-5 41.83535 3.49148E-5 41.83535 4.63482E-5 42.33939 7.41748E-6 42.59394 1.20657E-5 42.33939 3.09507E-5 42.33939 4.11219E-5 42.84343 6.5832E-6 43.10101 1.06956E-5 42.84343 2.74376E-5 42.84343 3.64852E-5 43.34747 5.84277E-6 43.60808 9.48137E-6 43.34747 2.4324E-5 43.34747 3.23715E-5 43.85152 5.18563E-6 44.11515 8.40529E-6 43.85152 2.15644E-5 43.85152 2.87219E-5 44.35556 4.60242E-6 44.62222 7.45157E-6 44.35556 1.91185E-5 44.35556 2.54839E-5 44.8596 4.0848E-6 45.12929 6.60624E-6 44.8596 1.69506E-5 44.8596 2.26111E-5 45.36364 3.62541E-6 45.63636 5.85697E-6 45.36364 1.50289E-5 45.36364 2.00623E-5 45.86768 3.21769E-6 46.14343 5.19281E-6 45.86768 1.33255E-5 45.86768 1.78009E-5 46.37172 2.85583E-6 46.6505 4.60407E-6 46.37172 1.18154E-5 46.37172 1.57945E-5 46.87576 2.53467E-6 47.15758 4.08217E-6 46.87576 1.04768E-5 46.87576 1.40143E-5 47.3798 2.24962E-6 47.66465 3.6195E-6 47.3798 9.29009E-6 47.3798 1.24349E-5 47.88384 1.99664E-6 48.17172 3.20933E-6 47.88384 8.238E-6 47.88384 1.10335E-5 48.38788 1.77211E-6 48.67879 2.84569E-6 48.38788 7.30525E-6 48.38788 9.79013E-6 48.89192 1.57282E-6 49.18586 2.52329E-6 48.89192 6.47826E-6 48.89192 8.68691E-6 49.39596 1.39595E-6 49.69293 2.23746E-6 49.39596 5.74503E-6 49.39596 7.70806E-6 49.9 1.23897E-6 50.2 1.98403E-6 49.9 5.0949E-6 49.9 6.83954E-6 S7.A Time LiSCN (4.0M) LiS13C15N (4.0M) LiSCN (4.0M)

fitting LiS13C15N (4.0M) fitting

-8.7E-7 0.99672 1.00001 1 1 0.1 1.00001 0.98788 0.97579 0.98109 0.2 0.97611 0.97148 0.95285 0.96312 0.3 0.94956 0.94862 0.9311 0.94604 0.4 0.92749 0.93137 0.91047 0.92979 0.5 0.90069 0.91212 0.8909 0.91432 0.6 0.87513 0.89831 0.87231 0.89958 0.7 0.85229 0.88192 0.85465 0.88554

76

0.8 0.83472 0.87003 0.83786 0.87215 0.9 0.81566 0.85385 0.82188 0.85936 1 0.79686 0.84153 0.80667 0.84715 1.1 0.78115 0.83018 0.79217 0.83547 1.2 0.76965 0.8181 0.77835 0.8243 1.3 0.75836 0.81002 0.76517 0.81361 1.4 0.74868 0.79723 0.75258 0.80337 1.5 0.73863 0.78742 0.74055 0.79355 1.6 0.73217 0.7784 0.72905 0.78412 1.7 0.71267 0.77103 0.71804 0.77507 1.8 0.70246 0.76721 0.7075 0.76637 1.9 0.69858 0.75601 0.69739 0.758 2 0.69004 0.74788 0.6877 0.74995 2.1 0.67639 0.73975 0.67839 0.74218 2.2 0.66961 0.73232 0.66944 0.7347 2.3 0.65844 0.72655 0.66084 0.72747 2.4 0.65464 0.7178 0.65256 0.72049 2.5 0.6439 0.71312 0.64458 0.71374 2.6 0.63759 0.70748 0.63689 0.70721 2.7 0.63644 0.69805 0.62946 0.70088 2.8 0.62643 0.69501 0.62229 0.69475 2.9 0.62075 0.69103 0.61536 0.6888 3 0.61115 0.68055 0.60866 0.68303 3.1 0.60278 0.67951 0.60217 0.67741 3.2 0.60266 0.67267 0.59587 0.67196 3.3 0.58824 0.66566 0.58977 0.66665 3.4 0.59401 0.66462 0.58385 0.66147 3.5 0.58583 0.65531 0.57809 0.65643 3.6 0.58495 0.65194 0.57249 0.65151 3.7 0.5736 0.64615 0.56705 0.64671 3.8 0.57042 0.64607 0.56175 0.64201 3.9 0.55813 0.64015 0.55658 0.63742 4 0.55368 0.63597 0.55154 0.63294 4.1 0.55537 0.62889 0.54663 0.62854 4.2 0.54767 0.62467 0.54182 0.62424 4.3 0.54418 0.6214 0.53713 0.62002 4.4 0.54205 0.61477 0.53254 0.61588 4.5 0.54724 0.61619 0.52805 0.61181 4.6 0.53009 0.6089 0.52365 0.60782 4.7 0.52741 0.60503 0.51934 0.6039 4.8 0.52209 0.6006 0.51512 0.60005 4.9 0.5183 0.59372 0.51097 0.59626 5 0.51424 0.5943 0.50691 0.59253 5.1 0.51498 0.58848 0.50291 0.58885 5.2 0.50609 0.58158 0.49899 0.58523 5.3 0.50352 0.58061 0.49513 0.58166 5.4 0.4982 0.576 0.49133 0.57814 5.5 0.49315 0.57404 0.4876 0.57467 5.6 0.49843 0.57089 0.48392 0.57125 5.7 0.48808 0.5637 0.4803 0.56787 5.8 0.48377 0.55937 0.47673 0.56453 5.9 0.48714 0.55785 0.47322 0.56123 6 0.47987 0.5563 0.46975 0.55797 6.1 0.47302 0.5524 0.46633 0.55475 6.2 0.46617 0.54827 0.46296 0.55156 6.7 0.45761 0.53153 0.44671 0.53612 7.2 0.42798 0.51541 0.43137 0.52141 7.7 0.41539 0.5006 0.41682 0.50731 8.2 0.396 0.48589 0.40295 0.49376 8.7 0.38135 0.474 0.38967 0.48069 9.2 0.36734 0.46167 0.37694 0.46805 9.7 0.3544 0.44759 0.3647 0.45582

77

10.2 0.32923 0.43669 0.35292 0.44395 11.2 0.32924 0.41503 0.33062 0.42125 12.2 0.31164 0.39397 0.30983 0.3998 13.2 0.29154 0.37645 0.29042 0.3795 14.2 0.27434 0.35503 0.27228 0.36028 15.2 0.25681 0.33475 0.25531 0.34206 16.2 0.23528 0.31816 0.23943 0.32478 17.2 0.22502 0.30482 0.22455 0.30839 18.2 0.20838 0.28727 0.21062 0.29285 19.2 0.19617 0.27416 0.19757 0.2781 20.2 0.18568 0.26027 0.18535 0.26411 23.2 0.14871 0.22309 0.15308 0.22625 25.2 0.13716 0.20588 0.13479 0.20411 28.2 0.11135 0.17664 0.11142 0.17493 30.2 0.09471 0.15965 0.09815 0.15784 35.2 0.07243 0.12806 0.07153 0.12211 40.2 0.05477 0.09986 0.05218 0.0945 43.2 0.04445 0.0871 0.04319 0.08104 45.2 0.03951 0.07758 0.03808 0.07315 48.2 0.03377 0.06748 0.03153 0.06274 50.2 0.02585 0.0626 0.02781 0.05663 55.2 0.02693 0.05032 0.02032 0.04385 60.2 0.01894 0.03769 0.01485 0.03396 65.2 0.01243 0.03091 0.01086 0.0263 70.2 0.00741 0.02329 0.00795 0.02037 75.2 0.00609 0.01959 0.00582 0.01578 80.2 0.0041 0.01486 0.00426 0.01223 85.2 0.00272 0.01191 0.00313 0.00947 90.2 0.00641 0.00827 0.00229 0.00734 95.2 0.00677 0.00974 0.00168 0.00569 100.2 0.00186 0.00588 0.00124 0.00441 110.2 -9.09791E-4 0.00173 6.68273E-4 0.00265 120.2 0.00338 0.00154 3.62372E-4 0.00159 130.2 8.26094E-4 0.00142 1.97237E-4 9.55531E-4 140.2 0.00135 6.93118E-4 1.07746E-4 5.74283E-4 150.2 6.69943E-5 -1.92173E-5 5.89876E-5 3.45122E-4 160.2 -0.00192 -4.96655E-4 3.24821E-5 2.07512E-4 170.2 0.00115 3.99046E-4 1.79208E-5 1.24715E-4 180.2 0.00211 -2.09716E-4 9.99349E-6 7.49704E-5 190.2 -0.00151 4.81516E-4 5.55269E-6 4.51373E-5 200.2 -0.0018 4.94826E-4 3.21608E-6 2.71117E-5 S7.B Time Flowing down Pumping up Flowing down fitting Pumping up fitting -8.7E-7 0.00197 4.69538E-5 -6.6923E-9 -4.6846E-9 0.1 0.00282 0.0016 7.50925E-4 5.25647E-4 0.2 0.00115 7.13746E-4 0.00147 0.00103 0.3 0.00136 0.00262 0.00215 0.0015 0.4 0.00204 0.00357 0.0028 0.00196 0.5 0.00102 0.00334 0.00343 0.0024 0.6 0.00106 0.00359 0.00402 0.00281 0.7 0.00173 0.0046 0.00459 0.00321 0.8 9.74916E-4 0.00467 0.00514 0.0036 0.9 0.00101 0.0045 0.00566 0.00396 1 0.00362 0.00546 0.00616 0.00432 1.1 0.0037 0.00681 0.00665 0.00465 1.2 0.003 0.00623 0.00711 0.00498 1.3 0.00326 0.00724 0.00756 0.00529

78

1.4 0.00391 0.00656 0.00799 0.00559 1.5 0.00528 0.0078 0.0084 0.00588 1.6 0.00477 0.00785 0.0088 0.00616 1.7 0.005 0.0079 0.00918 0.00643 1.8 0.00639 0.00825 0.00955 0.00669 1.9 0.00542 0.00796 0.00991 0.00694 2 0.00616 0.00861 0.01025 0.00718 2.1 0.00652 0.0101 0.01059 0.00741 2.2 0.00746 0.00937 0.01091 0.00764 2.3 0.00658 0.00908 0.01122 0.00786 2.4 0.00652 0.00834 0.01153 0.00807 2.5 0.00682 0.01003 0.01182 0.00827 2.6 0.00929 0.0096 0.01211 0.00847 2.7 0.00882 0.01012 0.01238 0.00867 2.8 0.00964 0.01013 0.01265 0.00885 2.9 0.00912 0.00868 0.01291 0.00904 3 0.00874 0.00908 0.01316 0.00921 3.1 0.00913 0.01098 0.01341 0.00938 3.2 0.00818 0.01171 0.01364 0.00955 3.3 0.00985 0.01055 0.01388 0.00971 3.4 0.00971 0.01088 0.0141 0.00987 3.5 0.01132 0.01225 0.01432 0.01002 3.6 0.01075 0.01082 0.01453 0.01017 3.7 0.00979 0.01209 0.01474 0.01032 3.8 0.01103 0.01131 0.01494 0.01046 3.9 0.01159 0.0114 0.01514 0.0106 4 0.0106 0.01324 0.01533 0.01073 4.1 0.01194 0.01122 0.01552 0.01086 4.2 0.01112 0.01243 0.0157 0.01099 4.3 0.01195 0.01156 0.01588 0.01112 4.4 0.01338 0.01169 0.01605 0.01124 4.5 0.01325 0.01299 0.01622 0.01135 4.6 0.01329 0.01197 0.01639 0.01147 4.7 0.01376 0.01095 0.01655 0.01158 4.8 0.01339 0.01191 0.0167 0.01169 4.9 0.01335 0.01229 0.01685 0.0118 5 0.01338 0.01235 0.017 0.0119 5.1 0.01386 0.01222 0.01715 0.012 5.2 0.01395 0.01334 0.01729 0.0121 5.3 0.01433 0.01276 0.01743 0.0122 5.4 0.01471 0.01231 0.01756 0.01229 5.5 0.01515 0.01317 0.01769 0.01239 5.6 0.0153 0.0128 0.01782 0.01248 5.7 0.0154 0.01419 0.01795 0.01256 5.8 0.0158 0.01321 0.01807 0.01265 5.9 0.016 0.01264 0.01819 0.01273 6 0.01625 0.01382 0.0183 0.01281 6.1 0.0163 0.01346 0.01842 0.01289 6.2 0.0164 0.01321 0.01853 0.01297 6.7 0.0164 0.01341 0.01904 0.01332 7.2 0.01757 0.01341 0.01948 0.01364 7.7 0.01741 0.01307 0.01987 0.01391 8.2 0.01793 0.01498 0.02021 0.01415 8.7 0.02002 0.0137 0.0205 0.01435 9.2 0.02008 0.01439 0.02074 0.01452 9.7 0.02043 0.01407 0.02094 0.01466 10.2 0.02043 0.01524 0.02111 0.01477 11.2 0.02159 0.01531 0.02133 0.01493 12.2 0.02168 0.01416 0.02144 0.01501 13.2 0.02173 0.01514 0.02144 0.01501 14.2 0.02244 0.01457 0.02136 0.01495 15.2 0.02115 0.01454 0.02119 0.01484

79

16.2 0.02033 0.01473 0.02097 0.01468 17.2 0.02054 0.01477 0.02069 0.01448 18.2 0.02034 0.01424 0.02037 0.01426 19.2 0.01998 0.01322 0.02001 0.01401 20.2 0.01961 0.01404 0.01962 0.01373 23.2 0.0188 0.01305 0.01831 0.01282 25.2 0.01697 0.01252 0.01738 0.01216 28.2 0.01669 0.01145 0.01594 0.01116 30.2 0.01427 0.01083 0.01498 0.01049 35.2 0.01286 0.0098 0.01269 0.00888 40.2 0.00999 0.00726 0.0106 0.00742 43.2 0.00908 0.00778 0.00947 0.00663 45.2 0.0075 0.007 0.00877 0.00614 48.2 0.00623 0.00578 0.0078 0.00546 50.2 0.00529 0.00467 0.0072 0.00504 55.2 0.00389 0.00488 0.00588 0.00411 60.2 0.00391 0.00213 0.00477 0.00334 65.2 0.00219 0.00304 0.00385 0.0027 70.2 0.00171 0.00176 0.0031 0.00217 75.2 0.00164 0.00207 0.00248 0.00174 80.2 8.99787E-4 7.17123E-4 0.00199 0.00139 85.2 3.76282E-4 0.00108 0.00158 0.00111 90.2 0.00102 1.23907E-4 0.00126 8.82362E-4 95.2 6.91354E-4 3.94976E-4 0.001 7.0059E-4 100.2 -4.90169E-5 -6.61067E-5 7.9339E-4 5.55313E-4 110.2 -7.49589E-4 2.13642E-5 4.96172E-4 3.47287E-4 120.2 -4.81504E-4 1.16637E-4 3.08564E-4 2.16068E-4 130.2 -0.00122 -3.60023E-4 1.9105E-4 1.33746E-4 140.2 -3.28505E-4 -8.19223E-4 1.17906E-4 8.25009E-5 150.2 4.47647E-4 -4.63678E-4 7.25632E-5 5.07053E-5 160.2 2.96846E-4 -1.65158E-4 4.44639E-5 3.11481E-5 170.2 -5.40495E-5 9.76171E-5 2.72586E-5 1.91751E-5 180.2 7.48241E-4 -3.82882E-4 1.66778E-5 1.16503E-5 190.2 -5.40495E-5 3.89353E-5 1.01521E-5 7.06881E-6 200.2 7.48241E-4 1.3028E-4 6.18467E-6 4.27655E-6 S7.C Time 100:0 Time 50:50 Time 20:80 Time 2:98 0 1 0 1 0 1 0 0.98866 0.1 0.9967 0.1 1.00224 0.1 0.97332 0.1 1.02468 0.2 1.00486 0.2 0.97574 0.2 0.948 0.2 0.9848 0.3 0.91806 0.3 0.96384 0.3 0.95834 0.3 0.98514 0.4 0.86598 0.4 0.94294 0.4 0.93082 0.4 0.9783 0.5 0.88844 0.5 0.91538 0.5 0.92644 0.5 0.97304 0.6 0.82474 0.6 0.8895 0.6 0.8848 0.6 0.95338 0.7 0.80884 0.7 0.88338 0.7 0.89138 0.7 0.95102 0.8 0.7527 0.8 0.86844 0.8 0.88138 0.8 0.93352 0.9 0.73724 0.9 0.8412 0.9 0.85258 0.9 0.89212 1 0.71968 1 0.82494 1 0.85726 1 0.91588 1.1 0.71472 1.1 0.80754 1.1 0.85892 1.1 0.86316 1.2 0.67336 1.2 0.77548 1.2 0.83362 1.2 0.85814 1.3 0.64944 1.3 0.76672 1.3 0.80632 1.3 0.8615 1.4 0.6725 1.4 0.7671 1.4 0.75758 1.4 0.85768 1.5 0.65208 1.5 0.74888 1.5 0.79046 1.5 0.78702 1.6 0.56756 1.6 0.75106 1.6 0.7387 1.6 0.805 1.7 0.54624 1.7 0.72504 1.7 0.7274 1.7 0.8064 1.8 0.54174 1.8 0.69608 1.8 0.78324 1.8 0.81792 1.9 0.56828 1.9 0.67204 1.9 0.7243 1.9 0.78486 2 0.5507 2 0.66684 2 0.7282 2 0.78786

80

2.5 0.49424 2.5 0.60346 2.5 0.66512 2.5 0.74634 3 0.37522 3 0.5697 3 0.62676 3 0.75338 3.5 0.38158 3.5 0.51738 3.5 0.59514 3.5 0.66366 4 0.28958 4 0.49198 4 0.60432 4 0.65716 4.5 0.25046 4.5 0.45052 4.5 0.5246 4.5 0.63944 5 0.21396 5 0.42784 5 0.57868 5 0.65888 5.5 0.23892 5.5 0.37794 5.5 0.52684 5.5 0.58726 6 0.17164 5.9 0.34194 5.9 0.4498 5.9 0.61924 6.5 0.1858 6.4 0.31812 6 0.49608 6.4 0.54456 7 0.1878 6.9 0.29618 6.6 0.47424 6.9 0.57768 7.5 0.15558 7.4 0.28864 7.6 0.38856 7.4 0.48638 8 0.12484 7.9 0.2579 8.1 0.3645 7.9 0.49076 8.5 0.12902 8.4 0.236 8.6 0.33108 8.4 0.40658 9 0.08454 8.9 0.23452 9.1 0.29862 8.9 0.39288 9.5 0.13594 9.4 0.21032 9.6 0.3099 9.4 0.39722 10 0.12398 9.9 0.17008 10.1 0.32354 9.9 0.4135 11 0.0735 10.9 0.1503 11.1 0.2453 10.9 0.30144 12 0.09402 11.9 0.13982 12.1 0.22358 11.9 0.3296 13 0.06306 12.9 0.11522 13.1 0.21878 12.9 0.26528 14 0.04742 13.9 0.09692 14.1 0.15842 13.9 0.23962 15 0.03572 14.9 0.07892 15.1 0.14942 14.9 0.24812 16 0.04542 15.9 0.0666 16.1 0.11952 15.9 0.22542 17 0.05406 16.9 0.05914 17.1 0.03806 16.9 0.13226 18 0.02592 17.9 0.04574 18.1 0.06346 17.9 0.1239 19 0.01616 18.9 0.02632 19.1 0.02066 18.9 0.13046 20 -0.00176 19.9 0.02464 20.1 0.04184 19.9 0.08958 23 -0.01666 22.9 0.01226 23.1 -0.00704 22.9 0.0372 25 -0.00598 24.9 -0.00153 25.1 0.0021 24.9 0.00412 28 0.00896 27.9 -0.02298 28.1 0.02928 27.9 -9.34966E-4 30 -0.00474 29.9 -0.00484 30.1 -0.00554 29.9 0.00388 35 0.0081 34.9 0.0058 35.1 0.00177 34.9 -7.92724E-4 40 -2.01802E-5 39.9 -0.00336 40.1 8.04048E-4 39.9 -0.00438 43 -0.02628 42.9 -0.01588 43.1 0.01238 42.9 -0.02728 45 -5.22444E-6 44.9 0.00844 45.1 -1.26862E-5 44.9 -0.03338 48 -2.32226E-6 47.9 -0.00414 48.1 0.00292 47.9 0.00101 50 0.01198 49.9 0.0064 50.1 -3.63464E-6 49.9 -0.0164 Time 100:0

Fitting Time 50:50

Fitting Time 20:80

Fitting Time 2:98

Fitting 0 1 0 1 0 1 0 1 0.1 0.96187 0.1 0.97588 0.1 0.98438 0.1 0.98952 0.2 0.92546 0.2 0.95247 0.2 0.96906 0.2 0.97915 0.3 0.89069 0.3 0.92976 0.3 0.95403 0.3 0.96889 0.4 0.85748 0.4 0.90772 0.4 0.93928 0.4 0.95875 0.5 0.82576 0.5 0.88633 0.5 0.92482 0.5 0.94872 0.6 0.79545 0.6 0.86556 0.6 0.91062 0.6 0.9388 0.7 0.7665 0.7 0.84541 0.7 0.8967 0.7 0.92899 0.8 0.73884 0.8 0.82584 0.8 0.88303 0.8 0.91929 0.9 0.7124 0.9 0.80684 0.9 0.86962 0.9 0.90969 1 0.68714 1 0.7884 1 0.85647 1 0.9002 1.1 0.66299 1.1 0.77049 1.1 0.84355 1.1 0.89081 1.2 0.6399 1.2 0.75309 1.2 0.83088 1.2 0.88152 1.3 0.61783 1.3 0.7362 1.3 0.81843 1.3 0.87233 1.4 0.59673 1.4 0.71979 1.4 0.80622 1.4 0.86325 1.5 0.57654 1.5 0.70385 1.5 0.79423 1.5 0.85426 1.6 0.55724 1.6 0.68836 1.6 0.78247 1.6 0.84537 1.7 0.53877 1.7 0.67331 1.7 0.77091 1.7 0.83658 1.8 0.5211 1.8 0.65869 1.8 0.75957 1.8 0.82788 1.9 0.50419 1.9 0.64448 1.9 0.74843 1.9 0.81928 2 0.48801 2 0.63067 2 0.73749 2 0.81077

81

2.1 0.47252 2.1 0.61724 2.1 0.72675 2.1 0.80235 2.2 0.45769 2.2 0.60419 2.2 0.7162 2.2 0.79403 2.3 0.44349 2.3 0.5915 2.3 0.70584 2.3 0.78579 2.4 0.42989 2.4 0.57916 2.4 0.69567 2.4 0.77764 2.5 0.41686 2.5 0.56716 2.5 0.68568 2.5 0.76958 2.6 0.40437 2.6 0.5555 2.6 0.67586 2.6 0.76161 2.7 0.39241 2.7 0.54415 2.7 0.66621 2.7 0.75372 2.8 0.38095 2.8 0.5331 2.8 0.65674 2.8 0.74592 2.9 0.36996 2.9 0.52236 2.9 0.64743 2.9 0.73821 3 0.35942 3 0.51191 3 0.63829 3 0.73057 3.1 0.34931 3.1 0.50174 3.1 0.6293 3.1 0.72302 3.2 0.33961 3.2 0.49184 3.2 0.62047 3.2 0.71555 3.3 0.33031 3.3 0.4822 3.3 0.61179 3.3 0.70816 3.4 0.32138 3.4 0.47282 3.4 0.60326 3.4 0.70084 3.5 0.3128 3.5 0.46369 3.5 0.59488 3.5 0.69361 3.6 0.30457 3.6 0.4548 3.6 0.58665 3.6 0.68645 3.7 0.29666 3.7 0.44614 3.7 0.57855 3.7 0.67937 3.8 0.28907 3.8 0.4377 3.8 0.57059 3.8 0.67237 3.9 0.28177 3.9 0.42949 3.9 0.56276 3.9 0.66544 4 0.27475 4 0.42148 4 0.55507 4 0.65858 4.1 0.26801 4.1 0.41368 4.1 0.54751 4.1 0.6518 4.2 0.26152 4.2 0.40608 4.2 0.54007 4.2 0.64509 4.3 0.25528 4.3 0.39867 4.3 0.53276 4.3 0.63845 4.4 0.24928 4.4 0.39145 4.4 0.52557 4.4 0.63189 4.5 0.24349 4.5 0.38441 4.5 0.51849 4.5 0.62539 4.6 0.23793 4.6 0.37755 4.6 0.51154 4.6 0.61896 4.7 0.23257 4.7 0.37086 4.7 0.5047 4.7 0.6126 4.8 0.2274 4.8 0.36433 4.8 0.49797 4.8 0.60631 4.9 0.22242 4.9 0.35796 4.9 0.49135 4.9 0.60008 5 0.21762 5 0.35175 5 0.48485 5 0.59392 5.1 0.213 5.1 0.34569 5.1 0.47844 5.1 0.58783 5.2 0.20853 5.2 0.33978 5.2 0.47214 5.2 0.5818 5.3 0.20422 5.3 0.33401 5.3 0.46594 5.3 0.57583 5.4 0.20006 5.4 0.32838 5.4 0.45984 5.4 0.56993 5.5 0.19605 5.5 0.32288 5.5 0.45384 5.5 0.56409 5.6 0.19216 5.6 0.31751 5.6 0.44794 5.6 0.55831 5.7 0.18841 5.7 0.31226 5.7 0.44212 5.7 0.55259 5.8 0.18479 5.8 0.30714 5.8 0.4364 5.8 0.54693 6 0.17789 5.9 0.30214 5.9 0.43077 5.9 0.54134 6.5 0.16249 6.4 0.27879 6 0.42523 6.4 0.51422 7 0.14929 6.9 0.25794 6.6 0.39376 6.9 0.4885 7.5 0.13788 7.4 0.23925 7.6 0.34735 7.4 0.4641 8 0.12793 7.9 0.22244 8.1 0.32663 7.9 0.44095 8.5 0.11916 8.4 0.20726 8.6 0.30738 8.4 0.41898 9 0.11137 8.9 0.1935 9.1 0.28946 8.9 0.39813 9.5 0.10439 9.4 0.18099 9.6 0.27278 9.4 0.37835 10 0.09809 9.9 0.16958 10.1 0.25722 9.9 0.35956 11 0.08712 10.9 0.14954 11.1 0.22911 10.9 0.3248 12 0.07783 11.9 0.13254 12.1 0.2045 11.9 0.29346 13 0.06982 12.9 0.11798 13.1 0.18287 12.9 0.26519 14 0.06281 13.9 0.10537 14.1 0.1638 13.9 0.23968 15 0.05662 14.9 0.09437 15.1 0.14693 14.9 0.21665 16 0.0511 15.9 0.08471 16.1 0.13195 15.9 0.19587 17 0.04617 16.9 0.07617 17.1 0.11863 16.9 0.1771 18 0.04174 17.9 0.06858 18.1 0.10676 17.9 0.16015 19 0.03775 18.9 0.06182 19.1 0.09615 18.9 0.14483 20 0.03415 19.9 0.05578 20.1 0.08666 19.9 0.13099 23 0.0253 22.9 0.04112 23.1 0.06366 22.9 0.09696 25 0.02073 24.9 0.03361 25.1 0.05193 24.9 0.07936 28 0.01537 27.9 0.02489 28.1 0.03834 27.9 0.05879 30 0.0126 29.9 0.02038 30.1 0.03135 29.9 0.04814 35 0.00765 34.9 0.01237 35.1 0.019 34.9 0.02922

82

40 0.00465 39.9 0.00752 40.1 0.01153 39.9 0.01775 43 0.00345 42.9 0.00558 43.1 0.00855 42.9 0.01316 45 0.00283 44.9 0.00457 45.1 0.007 44.9 0.01078 48 0.0021 47.9 0.00339 48.1 0.00519 47.9 0.008 50 0.00172 49.9 0.00278 50.1 0.00425 49.9 0.00655 S8.A Time NaSCN (4.0M) NaS13C15N (4.0M) NaSCN (4.0M)

fitting NaS13C15N (4.0M) fitting

0 1.00001 1 1 1 0.1 0.98554 0.99893 0.97659 0.98681 0.2 0.96293 0.9934 0.9545 0.97404 0.3 0.93493 0.98246 0.93365 0.96167 0.4 0.91197 0.9727 0.91396 0.94969 0.5 0.88698 0.9552 0.89535 0.93807 0.6 0.87036 0.93097 0.87777 0.92681 0.7 0.84668 0.91463 0.86113 0.91589 0.8 0.83463 0.9067 0.84539 0.90531 0.9 0.82272 0.8893 0.83048 0.89504 1 0.80632 0.87933 0.81634 0.88508 1.1 0.79349 0.87022 0.80294 0.87542 1.2 0.78207 0.85794 0.79022 0.86604 1.3 0.76922 0.84519 0.77814 0.85693 1.4 0.76018 0.83282 0.76666 0.84809 1.5 0.75226 0.82864 0.75574 0.8395 1.6 0.7401 0.81752 0.74534 0.83115 1.7 0.73405 0.81659 0.73544 0.82304 1.8 0.72304 0.81005 0.726 0.81516 1.9 0.71941 0.80031 0.71699 0.80749 2 0.70916 0.78731 0.70839 0.80004 2.1 0.70032 0.78213 0.70017 0.79279 2.2 0.69437 0.77858 0.6923 0.78573 2.3 0.68754 0.76789 0.68477 0.77886 2.4 0.68346 0.76156 0.67755 0.77217 2.5 0.67453 0.75996 0.67062 0.76566 2.6 0.66693 0.75357 0.66397 0.75932 2.7 0.66136 0.74613 0.65757 0.75314 2.8 0.65756 0.74069 0.65142 0.74711 2.9 0.65226 0.73246 0.64549 0.74123 3 0.64616 0.73222 0.63978 0.7355 3.1 0.64157 0.72839 0.63427 0.72991 3.2 0.63594 0.72417 0.62895 0.72446 3.3 0.62948 0.71561 0.6238 0.71913 3.4 0.62527 0.71338 0.61882 0.71393 3.5 0.62024 0.70403 0.61399 0.70885 3.6 0.61299 0.70249 0.60931 0.70388 3.7 0.61051 0.69278 0.60477 0.69903 3.8 0.60868 0.69431 0.60036 0.69429 3.9 0.60264 0.68855 0.59608 0.68965 4 0.59717 0.68416 0.5919 0.68511 4.1 0.59273 0.68124 0.58784 0.68067 4.2 0.5889 0.67887 0.58387 0.67633 4.3 0.58421 0.67182 0.58001 0.67207 4.4 0.57925 0.67536 0.57623 0.6679 4.5 0.57606 0.67066 0.57254 0.66381 4.6 0.57289 0.66292 0.56893 0.65981 4.7 0.5708 0.65891 0.5654 0.65588 4.8 0.5674 0.65765 0.56194 0.65203

83

4.9 0.56094 0.65342 0.55855 0.64826 5 0.55954 0.64982 0.55522 0.64455 5.1 0.5544 0.64659 0.55195 0.64091 5.2 0.55181 0.64126 0.54874 0.63734 5.3 0.54809 0.63535 0.54559 0.63383 5.4 0.54601 0.63986 0.54249 0.63039 5.5 0.54261 0.63294 0.53943 0.627 5.6 0.53874 0.63275 0.53643 0.62367 5.7 0.53804 0.62776 0.53347 0.62039 5.8 0.53305 0.62571 0.53055 0.61717 5.9 0.5277 0.62814 0.52767 0.614 6 0.52445 0.62586 0.52483 0.61088 6.1 0.52171 0.62314 0.52202 0.60781 6.2 0.51626 0.60879 0.51926 0.60478 6.3 0.51248 0.61015 0.51652 0.6018 6.8 0.49964 0.59194 0.5033 0.58754 7.3 0.48658 0.57225 0.49073 0.5742 7.8 0.47397 0.55934 0.47869 0.56166 8.3 0.45869 0.54794 0.46712 0.5498 8.8 0.44682 0.54021 0.45594 0.53852 9.3 0.43526 0.52389 0.44511 0.52776 9.8 0.42256 0.51554 0.4346 0.51745 10.3 0.41502 0.50967 0.42439 0.50753 11.3 0.39402 0.48601 0.40476 0.4887 12.3 0.37381 0.4649 0.38612 0.471 13.3 0.35627 0.44779 0.36837 0.45424 14.3 0.33907 0.43205 0.35147 0.43827 15.3 0.32309 0.41597 0.33536 0.42301 16.3 0.31014 0.40136 0.32 0.40837 17.3 0.29332 0.38416 0.30536 0.39431 18.3 0.28093 0.3733 0.29139 0.38078 19.3 0.27011 0.36008 0.27807 0.36774 20.3 0.25609 0.34647 0.26536 0.35518 23.3 0.23083 0.31323 0.23066 0.32009 25.3 0.20772 0.29383 0.2101 0.29868 28.3 0.18288 0.26793 0.18268 0.26925 30.3 0.16721 0.24844 0.16643 0.25128 35.3 0.13516 0.21152 0.13189 0.21145 40.3 0.10696 0.17488 0.10457 0.17797 43.3 0.09463 0.15744 0.09099 0.1605 45.3 0.08543 0.15031 0.08294 0.14982 48.3 0.07674 0.13358 0.07219 0.13512 50.3 0.07119 0.12846 0.06582 0.12613 55.3 0.05733 0.10881 0.05225 0.1062 60.3 0.04507 0.09261 0.0415 0.08944 65.3 0.03528 0.07963 0.03298 0.07532 70.3 0.02949 0.06562 0.02622 0.06344 75.3 0.02281 0.05597 0.02086 0.05344 80.3 0.01773 0.04628 0.0166 0.04502 85.3 0.01507 0.03885 0.01322 0.03793 90.3 0.01045 0.03452 0.01053 0.03196 95.3 0.01004 0.02748 0.0084 0.02693 100.3 0.00644 0.02397 0.0067 0.0227 110.3 0.00117 0.01816 0.00428 0.01612 120.3 9.64739E-4 0.01063 0.00274 0.01145 130.3 -0.002 0.0086 0.00176 0.00814 140.3 -0.00427 0.00517 0.00113 0.00578 150.3 -0.00123 0.00518 7.33016E-4 0.00411 160.3 -0.00372 0.00489 4.76309E-4 0.00292 170.3 -0.00413 0.0012 3.1065E-4 0.00208 180.3 -0.00391 0.00104 2.03641E-4 0.00148 190.3 -0.00413 9.45587E-4 1.34029E-4 0.00105

84

200.3 -0.0038 -7.25743E-4 8.87474E-5 7.47521E-4 S8.B Time Flowing down Pumping up Flowing down fitting Pumping up fitting 0 -0.00119 3.96875E-4 0 0 0.1 -0.00121 -2.5016E-4 4.90589E-4 3.43413E-4 0.2 0.00169 0.00173 9.63063E-4 6.74144E-4 0.3 -2.06709E-4 0.00164 0.00142 9.929E-4 0.4 -0.00146 0.00343 0.00186 0.0013 0.5 -5.14906E-4 0.00438 0.00228 0.0016 0.6 0.00162 0.00237 0.00269 0.00188 0.7 0.00255 0.00221 0.00309 0.00216 0.8 0.00125 0.00312 0.00347 0.00243 0.9 0.00257 0.00377 0.00384 0.00269 1 0.00112 0.00488 0.0042 0.00294 1.1 0.00216 0.00533 0.00455 0.00318 1.2 0.00418 0.00461 0.00489 0.00342 1.3 0.00247 0.00567 0.00521 0.00365 1.4 0.00523 0.0057 0.00553 0.00387 1.5 0.00325 0.00578 0.00584 0.00409 1.6 0.00318 0.00538 0.00614 0.0043 1.7 0.00544 0.00458 0.00644 0.0045 1.8 0.0036 0.00651 0.00672 0.0047 1.9 0.00531 0.00663 0.007 0.0049 2 0.00538 0.00458 0.00727 0.00509 2.1 0.00716 0.00636 0.00753 0.00527 2.2 0.00704 0.00739 0.00779 0.00545 2.3 0.00644 0.00725 0.00804 0.00563 2.4 0.00713 0.00617 0.00829 0.0058 2.5 0.00737 0.00593 0.00853 0.00597 2.6 0.00946 0.00559 0.00877 0.00614 2.7 0.00708 0.00652 0.009 0.0063 2.8 0.00697 0.00723 0.00922 0.00646 2.9 0.00813 0.00831 0.00944 0.00661 3 0.00881 0.00733 0.00966 0.00676 3.1 0.00713 0.00761 0.00987 0.00691 3.2 0.00795 0.00674 0.01008 0.00706 3.3 0.00651 0.00891 0.01028 0.0072 3.4 0.00948 0.00746 0.01048 0.00734 3.5 0.00891 0.00666 0.01068 0.00748 3.6 0.00923 0.00994 0.01087 0.00761 3.7 0.00875 0.00573 0.01106 0.00774 3.8 0.00897 0.0091 0.01125 0.00787 3.9 0.00983 0.00934 0.01143 0.008 4 0.01117 0.00935 0.01161 0.00813 4.1 0.00952 0.00848 0.01179 0.00825 4.2 0.00996 0.00893 0.01196 0.00837 4.3 0.00974 0.00725 0.01213 0.00849 4.4 0.01179 0.01035 0.0123 0.00861 4.5 0.01035 0.00961 0.01247 0.00873 4.6 0.01008 0.00918 0.01263 0.00884 4.7 0.00919 0.01072 0.01279 0.00895 4.8 0.0098 0.00991 0.01295 0.00906 4.9 0.01095 0.00955 0.01311 0.00917 5 0.01426 0.00979 0.01326 0.00928 5.1 0.01035 0.00941 0.01341 0.00939 5.2 0.01046 0.00889 0.01356 0.00949 5.3 0.01036 0.00861 0.01371 0.00959 5.4 0.01289 0.00913 0.01385 0.0097

85

5.5 0.01274 0.01024 0.01399 0.0098 5.6 0.01299 0.00888 0.01413 0.00989 5.7 0.01315 0.00996 0.01427 0.00999 5.8 0.01315 0.01101 0.01441 0.01009 5.9 0.01346 0.00936 0.01455 0.01018 6 0.01368 0.01004 0.01468 0.01028 6.1 0.0144 0.01128 0.01481 0.01037 6.2 0.01503 0.00841 0.01494 0.01046 6.3 0.01565 0.01037 0.01507 0.01055 6.8 0.01628 0.01067 0.01568 0.01098 7.3 0.01722 0.01107 0.01626 0.01138 7.8 0.01785 0.01258 0.0168 0.01176 8.3 0.01816 0.01204 0.0173 0.01211 8.8 0.01843 0.01174 0.01778 0.01245 9.3 0.01953 0.01212 0.01822 0.01276 9.8 0.01941 0.01215 0.01864 0.01305 10.3 0.01931 0.01409 0.01903 0.01332 11.3 0.01932 0.01283 0.01973 0.01381 12.3 0.0215 0.01353 0.02034 0.01424 13.3 0.02272 0.01369 0.02087 0.01461 14.3 0.02045 0.01397 0.02132 0.01492 15.3 0.02272 0.01585 0.02169 0.01519 16.3 0.02128 0.01593 0.022 0.0154 17.3 0.023 0.01528 0.02225 0.01558 18.3 0.02381 0.01611 0.02244 0.01571 19.3 0.02272 0.01556 0.02258 0.01581 20.3 0.022 0.01576 0.02268 0.01587 23.3 0.0227 0.01532 0.0227 0.01589 25.3 0.02185 0.01518 0.02254 0.01578 28.3 0.0211 0.01607 0.0221 0.01547 30.3 0.02135 0.01554 0.02169 0.01518 35.3 0.02008 0.01531 0.02039 0.01427 40.3 0.01872 0.01435 0.01885 0.01319 43.3 0.01609 0.01337 0.01786 0.0125 45.3 0.01601 0.01215 0.01719 0.01203 48.3 0.01577 0.01132 0.01618 0.01133 50.3 0.01309 0.01121 0.01552 0.01086 55.3 0.01278 0.01059 0.01389 0.00972 60.3 0.0108 0.00993 0.01234 0.00864 65.3 0.00909 0.00794 0.0109 0.00763 70.3 0.00892 0.00744 0.00959 0.00671 75.3 0.00626 0.00701 0.00839 0.00587 80.3 0.00639 0.00628 0.00732 0.00512 85.3 0.00577 0.00394 0.00636 0.00445 90.3 0.0049 0.00602 0.00552 0.00386 95.3 0.00583 0.00289 0.00477 0.00334 100.3 0.00231 0.00456 0.00412 0.00288 110.3 0.00242 0.00292 0.00305 0.00213 120.3 0.0012 9.43396E-4 0.00224 0.00157 130.3 -2.41683E-4 0.00174 0.00164 0.00115 140.3 4.13763E-4 3.41116E-4 0.0012 8.38285E-4 150.3 5.30206E-4 0.0014 8.70159E-4 6.09109E-4 160.3 -0.00107 0.00146 6.30497E-4 4.41333E-4 170.3 6.89695E-4 -7.43493E-4 4.55735E-4 3.19029E-4 180.3 -5.74321E-4 -9.87085E-5 3.28782E-4 2.30132E-4 190.3 1.67093E-4 7.16573E-4 2.36759E-4 1.65743E-4 200.3 -2.67683E-4 -0.00142 1.70307E-4 1.19199E-4 S8.C

86

Time 100:0 Time 80:20 Time 50:50 Time 20:80 Time 2:98 0 1.00002 0 0.99998 0 1.00002 -1.73E-6 1.00002 0 1 0.1 1.01348 0.1 0.99707 0.1 1.00708 0.1 0.99987 0.1 0.9693 0.2 1.0016 0.2 0.94705 0.2 1.00733 0.2 0.96827 0.2 0.95362 0.3 0.96418 0.3 0.8734 0.3 0.9998 0.3 0.94493 0.3 0.94935 0.4 0.96727 0.4 0.88558 0.4 0.99788 0.4 0.93978 0.4 0.91442 0.5 0.94312 0.5 0.85877 0.5 0.98125 0.5 0.93605 0.5 0.93592 0.6 0.894 0.6 0.80275 0.6 0.97373 0.6 0.95427 0.6 0.91723 0.7 0.85857 0.7 0.80742 0.7 0.93518 0.7 0.86473 0.7 0.87567 0.8 0.82832 0.8 0.79267 0.8 0.9406 0.8 0.86848 0.8 0.89065 0.9 0.79998 0.9 0.70962 0.9 0.88463 0.9 0.85447 0.9 0.89583 1 0.77863 1 0.70902 1 0.85688 1 0.87317 1 0.78427 1.1 0.74978 1.1 0.72538 1.1 0.84033 1.1 0.82677 1.1 0.84525 1.2 0.71427 1.2 0.69203 1.2 0.8034 1.2 0.82317 1.2 0.87738 1.3 0.6602 1.3 0.67948 1.3 0.7776 1.3 0.80138 1.3 0.82678 1.4 0.64823 1.4 0.67893 1.4 0.77952 1.4 0.74585 1.4 0.86325 1.5 0.608 1.5 0.62293 1.5 0.7504 1.5 0.78232 1.5 0.77648 1.6 0.60265 1.6 0.64657 1.6 0.71358 1.6 0.74437 1.6 0.8669 1.7 0.5916 1.7 0.57048 1.7 0.66432 1.7 0.7259 1.7 0.83763 1.8 0.5919 1.8 0.60465 1.8 0.6514 1.8 0.77972 1.8 0.77617 1.9 0.55343 1.9 0.58708 1.9 0.64023 1.9 0.74285 1.9 0.71922 2 0.53363 2 0.5684 2 0.63512 2 0.68405 2 0.74307 2.5 0.47962 2.5 0.47595 2.5 0.56957 2.5 0.65312 2.5 0.72325 3 0.41707 3 0.43227 3 0.53948 3 0.57923 3 0.70082 3.5 0.37525 3.5 0.38618 3.5 0.49692 3.5 0.57987 3.5 0.64945 4 0.27583 4 0.33345 4 0.43955 4 0.48213 4 0.68662 4.5 0.2733 4.5 0.24675 4.5 0.3964 4.5 0.46008 4.5 0.58085 5 0.23575 5 0.2773 5 0.33882 5 0.45957 5 0.5194 5.5 0.15788 5.4 0.25717 5.5 0.3381 5.5 0.40375 5.5 0.50542 6 0.1893 5.5 0.20907 6 0.2824 6 0.3296 5.6 0.46202 6.5 0.13778 5.6 0.19232 6.5 0.27055 6.3 0.34677 5.9 0.51282 7 0.1524 5.7 0.2236 6.6 0.27138 6.4 0.33313 6 0.57358 7.5 0.09822 6.2 0.21158 7.1 0.237 6.9 0.32877 6.5 0.48062 8 0.10533 6.7 0.1791 7.6 0.25595 7.4 0.29167 7 0.4118 8.5 0.09622 7.2 0.14158 8.1 0.2327 7.9 0.28267 7.5 0.48378 9 0.1035 7.7 0.1453 8.6 0.21152 8.4 0.28467 8 0.39017 9.5 0.08823 8.2 0.13498 9.1 0.19295 8.9 0.2411 8.5 0.3611 10 0.07395 8.7 0.12503 9.6 0.17248 9.4 0.18202 9 0.36933 11 0.05473 9.2 0.12018 10.1 0.14262 9.9 0.21402 9.5 0.31685 12 0.02063 9.7 0.09597 10.6 0.14948 10.4 0.15037 10 0.2738 13 0.04865 10.7 0.04753 11.6 0.16383 11.4 0.12797 11 0.32302 14 0.0344 11.7 0.06075 12.6 0.12447 12.4 0.1263 12 0.25285 15 0.01918 12.7 0.02295 13.6 0.09592 13.4 0.11437 13 0.21072 16 0.0146 13.7 0.01705 14.6 0.07452 14.4 0.06967 14 0.21415 17 0.00642 14.7 -0.00373 15.6 0.06035 15.4 0.08215 15 0.21715 18 0.01623 15.7 -0.00912 16.6 0.06413 16.4 0.04638 16 0.18422 19 0.02343 16.7 0.02647 17.6 0.04763 17.4 0.0326 17 0.15673 20 2.3892E-4 17.7 0.01747 18.6 0.04048 18.4 0.03993 18 0.19343 22 -0.00868 18.7 -0.01632 19.6 0.05035 19.4 0.03377 19 0.12772 25 -0.00935 19.7 -0.00106 20.6 0.05032 20.4 0.01508 20 0.09118 28 7.31133E-4 22.7 0.02402 23.6 0.0129 23.4 0.0132 23 0.0871 30 0.00288 24.7 0.02088 25.6 -0.0101 25.4 0.00565 25 0.06762 33 9.20437E-4 27.7 0.00403 28.6 -0.03957 28.4 0.00217 28 0.07675 35 0.0025 29.7 -0.01262 30.6 -0.0379 30.4 0.00312 30 0.0374 38 -0.00902 34.7 -0.00795 35.6 -0.03522 35.4 -0.0175 35 0.00562 40 -0.02298 39.7 -0.01492 40.6 -0.01692 40.4 -0.0081 40 0.01418 43 -0.00408 42.7 -0.021 43.6 -0.02257 43.4 -0.02405 43 -0.01472 45 -0.01775 44.7 -0.01127 45.6 -0.01457 45.4 -0.01733 45 -8.67153E-6 48 -0.01597 47.7 -0.02502 48.6 -0.03808 48.4 -0.02437 48 -0.03928 50 -0.0066 49.7 0.0041 50.6 -0.03855 50.4 -0.03323 50 -2.48443E-6

87

Time 100:0

Fitting Time 80:20

Fitting Time 50:50

Fitting Time 20:80

Fitting Time 2:98

Fitting 0 1 0 1 0 1 -1.73E-6 1 0 1 0.1 0.96506 0.1 0.96968 0.1 0.97665 0.1 0.98368 0.1 0.98792 0.2 0.93147 0.2 0.94039 0.2 0.95392 0.2 0.96765 0.2 0.97598 0.3 0.89918 0.3 0.91208 0.3 0.93178 0.3 0.95191 0.3 0.96419 0.4 0.86814 0.4 0.88473 0.4 0.91022 0.4 0.93645 0.4 0.95255 0.5 0.8383 0.5 0.85831 0.5 0.88922 0.5 0.92127 0.5 0.94105 0.6 0.80961 0.6 0.83277 0.6 0.86877 0.6 0.90636 0.6 0.92969 0.7 0.78202 0.7 0.80809 0.7 0.84886 0.7 0.89171 0.7 0.91847 0.8 0.75549 0.8 0.78424 0.8 0.82946 0.8 0.87733 0.8 0.90739 0.9 0.72998 0.9 0.76119 0.9 0.81056 0.9 0.8632 0.9 0.89645 1 0.70545 1 0.7389 1 0.79215 1 0.84933 1 0.88564 1.1 0.68185 1.1 0.71736 1.1 0.77422 1.1 0.8357 1.1 0.87496 1.2 0.65916 1.2 0.69654 1.2 0.75675 1.2 0.82231 1.2 0.86441 1.3 0.63733 1.3 0.67641 1.3 0.73973 1.3 0.80916 1.3 0.85399 1.4 0.61633 1.4 0.65695 1.4 0.72315 1.4 0.79624 1.4 0.8437 1.5 0.59612 1.5 0.63814 1.5 0.70699 1.5 0.78355 1.5 0.83354 1.6 0.57669 1.6 0.61994 1.6 0.69124 1.6 0.77108 1.6 0.8235 1.7 0.55798 1.7 0.60235 1.7 0.6759 1.7 0.75883 1.7 0.81359 1.8 0.53998 1.8 0.58533 1.8 0.66095 1.8 0.7468 1.8 0.80379 1.9 0.52266 1.9 0.56887 1.9 0.64638 1.9 0.73498 1.9 0.79412 2 0.50599 2 0.55296 2 0.63218 2 0.72336 2 0.78456 2.5 0.43153 2.5 0.48082 2.5 0.56638 2.5 0.66825 2.5 0.73851 3 0.36987 3 0.41962 3 0.50842 3 0.61776 3 0.6952 3.5 0.31867 3.5 0.36758 3.5 0.45729 3.5 0.57146 3.5 0.65447 4 0.27604 4 0.32323 4 0.41213 4 0.52898 4 0.61616 4.5 0.24044 4.5 0.28534 4.5 0.37217 4.5 0.48997 4.5 0.58013 5 0.21059 5 0.25287 5 0.33675 5 0.45412 5 0.54623 5.5 0.18547 5.4 0.23023 5.5 0.3053 5.5 0.42116 5.5 0.51434 6 0.16425 5.5 0.22498 6 0.27733 6 0.39083 5.6 0.50819 6.5 0.14623 5.6 0.21989 6.5 0.25241 6.3 0.3738 5.9 0.4902 7 0.13087 5.7 0.21494 6.6 0.24776 6.4 0.36831 6 0.48434 7.5 0.11771 6.2 0.19227 7.1 0.22601 6.9 0.34215 6.5 0.45611 8 0.10636 6.7 0.17265 7.6 0.20655 7.4 0.31803 7 0.42955 8.5 0.09654 7.2 0.1556 8.1 0.18911 7.9 0.29578 7.5 0.40456 9 0.08798 7.7 0.14073 8.6 0.17344 8.4 0.27524 8 0.38103 9.5 0.08049 8.2 0.12772 9.1 0.15934 8.9 0.25626 8.5 0.35889 10 0.07389 8.7 0.11629 9.6 0.14662 9.4 0.23871 9 0.33805 11 0.06284 9.2 0.10621 10.1 0.13513 9.9 0.22248 9.5 0.31844 12 0.054 9.7 0.09729 10.6 0.12473 10.4 0.20745 10 0.29997 13 0.04678 10.7 0.08229 11.6 0.10671 11.4 0.18062 11 0.26623 14 0.04079 11.7 0.07025 12.6 0.09178 12.4 0.15755 12 0.23631 15 0.03574 12.7 0.06045 13.6 0.0793 13.4 0.13765 13 0.20979 16 0.03144 13.7 0.05236 14.6 0.0688 14.4 0.12045 14 0.18627 17 0.02773 14.7 0.04561 15.6 0.05991 15.4 0.10555 15 0.1654 18 0.02452 15.7 0.0399 16.6 0.05233 16.4 0.09262 16 0.14689 19 0.02171 16.7 0.03503 17.6 0.04583 17.4 0.08138 17 0.13047 20 0.01925 17.7 0.03084 18.6 0.04024 18.4 0.07158 18 0.1159 22 0.01517 18.7 0.02721 19.6 0.0354 19.4 0.06303 19 0.10296 25 0.01065 19.7 0.02405 20.6 0.0312 20.4 0.05555 20 0.09148 28 0.00749 22.7 0.01674 23.6 0.02153 23.4 0.03822 23 0.06419 30 0.00593 24.7 0.01319 25.6 0.0169 25.4 0.02989 25 0.0507 33 0.00417 27.7 0.00926 28.6 0.0118 28.4 0.02076 28 0.03561 35 0.0033 29.7 0.00732 30.6 0.00931 30.4 0.01632 30 0.02815 38 0.00233 34.7 0.00408 35.6 0.00516 35.4 0.00898 35 0.01565 40 0.00184 39.7 0.00227 40.6 0.00287 40.4 0.00497 40 0.00871

88

43 0.0013 42.7 0.0016 43.6 0.00202 43.4 0.00349 43 0.00613 45 0.00103 44.7 0.00127 45.6 0.0016 45.4 0.00276 45 0.00485 48 7.23766E-4 47.7 8.9302E-4 48.6 0.00113 48.4 0.00194 48 0.00341 50 5.72995E-4 49.7 7.06985E-4 50.6 8.92855E-4 50.4 0.00154 50 0.0027 S9.A Time CsSCN (4.0M) CsS13C15N (4.0M) CsSCN (4.0M)

fitting CsS13C15N (4.0M) fitting

-1.73E-6 0.99061 1 1 1 0.1 0.99999 0.992 0.98557 0.97949 0.2 0.99393 0.96642 0.97168 0.96002 0.3 0.99503 0.94391 0.9583 0.94152 0.4 0.97751 0.92139 0.94542 0.92393 0.5 0.96711 0.8933 0.933 0.90721 0.6 0.94539 0.87093 0.92104 0.8913 0.7 0.92892 0.85626 0.9095 0.87617 0.8 0.90829 0.84428 0.89837 0.86176 0.9 0.89162 0.83036 0.88763 0.84804 1 0.87939 0.81756 0.87726 0.83497 1.1 0.866 0.80141 0.86725 0.82251 1.2 0.85863 0.79542 0.85758 0.81062 1.3 0.8373 0.78194 0.84823 0.79927 1.4 0.83012 0.77465 0.83919 0.78843 1.5 0.82525 0.76498 0.83044 0.77808 1.6 0.80797 0.75949 0.82198 0.76819 1.7 0.80653 0.7525 0.81378 0.75873 1.8 0.7975 0.74291 0.80585 0.74967 1.9 0.78616 0.73513 0.79815 0.741 2 0.78283 0.72778 0.7907 0.73269 2.1 0.77469 0.71902 0.78347 0.72472 2.2 0.76905 0.71611 0.77645 0.71707 2.3 0.76493 0.70963 0.76963 0.70973 2.4 0.75428 0.70259 0.76302 0.70268 2.5 0.75453 0.69853 0.75658 0.6959 2.6 0.74646 0.6944 0.75033 0.68938 2.7 0.74086 0.69264 0.74425 0.6831 2.8 0.73247 0.67796 0.73833 0.67705 2.9 0.72461 0.67559 0.73257 0.67121 3 0.72134 0.67111 0.72696 0.66558 3.1 0.7133 0.66387 0.72149 0.66015 3.2 0.71224 0.66088 0.71616 0.65489 3.3 0.70882 0.65099 0.71095 0.64981 3.4 0.69822 0.64901 0.70588 0.6449 3.5 0.70176 0.64556 0.70092 0.64014 3.6 0.69361 0.6434 0.69608 0.63552 3.7 0.69045 0.63611 0.69135 0.63104 3.8 0.68644 0.63248 0.68672 0.6267 3.9 0.68725 0.62883 0.68219 0.62248 4 0.67437 0.6251 0.67776 0.61837 4.1 0.67287 0.62438 0.67343 0.61438 4.2 0.66603 0.61952 0.66918 0.61049 4.3 0.66444 0.61975 0.66501 0.6067 4.4 0.6624 0.61187 0.66093 0.60301 4.5 0.6626 0.61113 0.65693 0.5994 4.6 0.65825 0.60249 0.653 0.59588 4.7 0.6549 0.59779 0.64914 0.59244 4.8 0.64727 0.59574 0.64535 0.58908

89

4.9 0.64367 0.59388 0.64163 0.58579 5 0.63876 0.58704 0.63797 0.58257 5.1 0.63094 0.58498 0.63438 0.57942 5.2 0.6297 0.58582 0.63084 0.57632 5.3 0.62668 0.5789 0.62736 0.57329 5.4 0.62626 0.57576 0.62393 0.57031 5.5 0.62244 0.57241 0.62055 0.56738 5.6 0.61795 0.56918 0.61723 0.56451 5.7 0.6153 0.56575 0.61395 0.56168 5.8 0.61155 0.56468 0.61072 0.5589 5.9 0.60908 0.55802 0.60754 0.55616 6 0.60358 0.55389 0.60439 0.55347 6.1 0.60131 0.54518 0.60129 0.55081 6.2 0.59854 0.54086 0.59823 0.54819 6.3 0.59455 0.53869 0.59521 0.54561 6.4 0.59019 0.53757 0.59222 0.54307 6.9 0.57528 0.52666 0.57781 0.5308 7.4 0.56041 0.51082 0.56416 0.51921 7.9 0.54802 0.49863 0.55115 0.50816 8.4 0.53859 0.48983 0.5387 0.49756 8.9 0.52363 0.47642 0.52673 0.48735 9.4 0.51481 0.46666 0.51518 0.47746 9.9 0.50043 0.45602 0.50401 0.46787 10.4 0.4871 0.44783 0.49318 0.45855 11.4 0.47077 0.43269 0.47244 0.44058 12.4 0.44779 0.42079 0.45275 0.42343 13.4 0.42761 0.40312 0.43401 0.40702 14.4 0.41093 0.38612 0.41613 0.39128 15.4 0.39091 0.37277 0.39902 0.37616 16.4 0.37798 0.35789 0.38266 0.36165 17.4 0.35898 0.34297 0.36698 0.3477 18.4 0.344 0.32862 0.35196 0.3343 19.4 0.32975 0.31567 0.33756 0.32142 20.4 0.3201 0.30427 0.32376 0.30904 23.4 0.28177 0.26779 0.28567 0.27469 25.4 0.25945 0.24708 0.26282 0.25395 28.4 0.22887 0.22256 0.23193 0.22575 30.4 0.21446 0.20437 0.21338 0.20872 35.4 0.17332 0.1691 0.17328 0.17157 40.4 0.14117 0.13858 0.14073 0.14105 43.4 0.12585 0.12241 0.12422 0.12541 45.4 0.11371 0.11477 0.11431 0.11597 48.4 0.10015 0.10402 0.10091 0.10313 50.4 0.09411 0.0965 0.09287 0.09537 55.4 0.07822 0.08154 0.07546 0.07843 60.4 0.06345 0.0687 0.06132 0.06451 65.4 0.0517 0.05512 0.04984 0.05307 70.4 0.04349 0.04398 0.04052 0.04367 75.4 0.03468 0.03758 0.03294 0.03593 80.4 0.02755 0.03067 0.02679 0.02957 85.4 0.02359 0.02483 0.02179 0.02434 90.4 0.0177 0.02181 0.01772 0.02003 95.4 0.01773 0.01735 0.01442 0.01649 100.4 0.01186 0.01581 0.01173 0.01358 110.4 0.00892 0.00954 0.00777 0.00921 120.4 0.00486 0.00717 0.00515 0.00625 130.4 0.0032 0.00424 0.00342 0.00424 140.4 0.00231 0.00319 0.00227 0.00288 150.4 0.0021 0.00198 0.00151 0.00196 160.4 0.002 0.00251 0.001 0.00133 170.4 2.66458E-5 0.00101 6.66238E-4 9.03071E-4 180.4 3.49317E-4 -1.32575E-4 4.43377E-4 6.13949E-4

90

190.4 8.86396E-5 0.00106 2.95461E-4 4.17716E-4 200.4 -0.00101 1.50992E-4 1.96849E-4 2.84117E-4 210.4 -2.17789E-4 -2.73453E-5 1.3142E-4 1.93507E-4 220.4 5.62622E-4 6.03644E-4 8.76534E-5 1.31644E-4 230.4 3.08E-4 -9.02703E-4 5.8579E-5 8.9727E-5 240.4 4.41828E-4 0.00187 3.92135E-5 6.1098E-5 250.4 -5.90912E-4 7.61252E-4 2.61383E-5 4.15737E-5 260.4 -0.00126 5.39724E-4 1.75621E-5 2.84455E-5 270.4 -9.76211E-4 6.39296E-4 1.18258E-5 1.93968E-5 280.4 -3.79586E-5 -2.42889E-4 7.92657E-6 1.32358E-5 290.4 9.57296E-4 -2.56858E-5 5.30815E-6 9.03338E-6 300.4 1.72827E-4 3.17378E-4 3.57504E-6 6.14259E-6 S9.B Time Flowing down Pumping up Flowing down fitting Pumping up fitting -1.73E-6 2.20678E-4 -2.3E-4 -6.21021E-9 -4.34715E-9 0.1 -5.12791E-4 7.5835E-4 3.52483E-4 2.46738E-4 0.2 -0.00113 5.16516E-4 6.92448E-4 4.84713E-4 0.3 6.03542E-4 -6.34643E-5 0.00102 7.14406E-4 0.4 7.96585E-4 8.67241E-4 0.00134 9.36253E-4 0.5 4.61469E-4 4.86271E-4 0.00164 0.00115 0.6 0.00278 0.00214 0.00194 0.00136 0.7 0.00194 0.0045 0.00223 0.00156 0.8 0.00149 0.0026 0.0025 0.00175 0.9 0.0018 9.28908E-4 0.00277 0.00194 1 0.0026 9.94552E-4 0.00303 0.00212 1.1 0.00351 0.00355 0.00329 0.0023 1.2 0.00293 0.0025 0.00353 0.00247 1.3 0.00322 0.00314 0.00377 0.00264 1.4 0.00351 0.00295 0.004 0.0028 1.5 0.004 0.00475 0.00423 0.00296 1.6 0.00383 0.00424 0.00445 0.00312 1.7 0.00393 0.00421 0.00466 0.00327 1.8 0.00401 0.00476 0.00487 0.00341 1.9 0.00494 0.00389 0.00508 0.00355 2 0.00566 0.00518 0.00528 0.00369 2.1 0.00527 0.00578 0.00547 0.00383 2.2 0.00606 0.00423 0.00566 0.00396 2.3 0.00582 0.00497 0.00584 0.00409 2.4 0.00596 0.00505 0.00603 0.00422 2.5 0.00703 0.00596 0.0062 0.00434 2.6 0.00459 0.00421 0.00638 0.00446 2.7 0.00597 0.00568 0.00655 0.00458 2.8 0.00656 0.00516 0.00671 0.0047 2.9 0.00602 0.00675 0.00688 0.00481 3 0.00584 0.00913 0.00704 0.00492 3.1 0.00753 0.00497 0.00719 0.00503 3.2 0.00685 0.00704 0.00735 0.00514 3.3 0.00725 0.00594 0.0075 0.00525 3.4 0.0066 0.00556 0.00765 0.00535 3.5 0.00713 0.00583 0.00779 0.00545 3.6 0.00709 0.00555 0.00793 0.00555 3.7 0.00656 0.00606 0.00807 0.00565 3.8 0.00958 0.00676 0.00821 0.00575 3.9 0.00794 0.00578 0.00835 0.00584 4 0.0084 0.00632 0.00848 0.00594 4.1 0.00869 0.00744 0.00861 0.00603 4.2 0.00815 0.00739 0.00874 0.00612

91

4.3 0.00704 0.00926 0.00887 0.00621 4.4 0.00937 0.00791 0.009 0.0063 4.5 0.01089 0.00728 0.00912 0.00639 4.6 0.00965 0.00996 0.00924 0.00647 4.7 0.00856 0.00646 0.00936 0.00656 4.8 0.01014 0.00663 0.00948 0.00664 4.9 0.0078 0.00791 0.0096 0.00672 5 0.00952 0.00641 0.00972 0.0068 5.1 0.00913 0.00872 0.00983 0.00688 5.2 0.00969 0.01064 0.00994 0.00696 5.3 0.00984 0.00869 0.01005 0.00704 5.4 0.01038 0.00849 0.01016 0.00711 5.5 0.0105 0.00797 0.01027 0.00719 5.6 0.0106 0.0073 0.01038 0.00726 5.7 0.0108 0.00821 0.01048 0.00734 5.8 0.011 0.00789 0.01058 0.00741 5.9 0.011 0.01046 0.01069 0.00748 6 0.0112 0.00997 0.01079 0.00755 6.1 0.011 0.00972 0.01089 0.00762 6.2 0.0113 0.0088 0.01099 0.00769 6.3 0.0112 0.00926 0.01108 0.00776 6.4 0.01123 0.00819 0.01118 0.00783 6.9 0.01116 0.0094 0.01164 0.00815 7.4 0.01187 0.01001 0.01208 0.00845 7.9 0.01215 0.00979 0.01249 0.00874 8.4 0.01297 0.00922 0.01287 0.00901 8.9 0.01347 0.01126 0.01324 0.00927 9.4 0.01328 0.01153 0.01358 0.00951 9.9 0.0138 0.01117 0.0139 0.00973 10.4 0.0143 0.01117 0.01421 0.00994 11.4 0.01531 0.01012 0.01476 0.01033 12.4 0.01459 0.0101 0.01524 0.01067 13.4 0.01555 0.011 0.01566 0.01096 14.4 0.01569 0.01149 0.01602 0.01121 15.4 0.01689 0.01169 0.01633 0.01143 16.4 0.01743 0.01034 0.01658 0.01161 17.4 0.01576 0.01148 0.01679 0.01175 18.4 0.01823 0.01124 0.01696 0.01187 19.4 0.01744 0.01157 0.01708 0.01196 20.4 0.01741 0.01204 0.01717 0.01202 23.4 0.01739 0.01227 0.01725 0.01207 25.4 0.01662 0.01085 0.01716 0.01201 28.4 0.01739 0.01204 0.01686 0.0118 30.4 0.01666 0.01145 0.01657 0.0116 35.4 0.0163 0.01014 0.01562 0.01093 40.4 0.01428 0.00949 0.01446 0.01012 43.4 0.01329 0.00941 0.01371 0.0096 45.4 0.01417 0.00859 0.0132 0.00924 48.4 0.01303 0.00744 0.01244 0.0087 50.4 0.01238 0.00842 0.01192 0.00835 55.4 0.01138 0.00816 0.01067 0.00747 60.4 0.01085 0.00701 0.00948 0.00663 65.4 0.00967 0.00484 0.00836 0.00586 70.4 0.0076 0.00428 0.00734 0.00514 75.4 0.00743 0.00401 0.00641 0.00449 80.4 0.00573 0.00339 0.00558 0.00391 85.4 0.00591 0.00223 0.00484 0.00339 90.4 0.00417 0.00184 0.00418 0.00293 95.4 0.00412 0.00212 0.0036 0.00252 100.4 0.00317 0.00222 0.0031 0.00217 110.4 0.0035 0.00141 0.00227 0.00159 120.4 0.00245 9.3125E-4 0.00165 0.00116

92

130.4 4.86459E-4 3.75376E-4 0.0012 8.38018E-4 140.4 -2.69312E-4 -5.23368E-4 8.61541E-4 6.03078E-4 150.4 2.11112E-4 4.27663E-4 6.17142E-4 4.32003E-4 160.4 4.34838E-4 0.00102 4.40298E-4 3.08206E-4 170.4 -2.87387E-4 -4.711E-4 3.13036E-4 2.19132E-4 180.4 -8.42026E-4 -5.83669E-4 2.21856E-4 1.553E-4 190.4 -5.44902E-4 7.26113E-4 1.56833E-4 1.09788E-4 200.4 2.02766E-4 -1.15401E-4 1.10573E-4 7.74067E-5 210.4 1.11215E-4 -0.00103 7.78274E-5 5.44659E-5 220.4 -0.00115 1.31992E-4 5.46301E-5 3.82397E-5 230.4 4.35418E-4 2.12927E-4 3.83068E-5 2.68129E-5 240.4 -7.73923E-4 2.247E-4 2.68249E-5 1.87753E-5 250.4 -0.0012 -5.19215E-4 1.87249E-5 1.31128E-5 260.4 -4.05543E-4 6.95981E-4 1.30739E-5 9.15566E-6 270.4 -6.85267E-4 -4.09765E-4 9.13881E-6 6.40062E-6 280.4 1.19284E-4 -6.81693E-4 6.37076E-6 4.45808E-6 290.4 8.54916E-4 -1.9474E-4 4.43691E-6 3.09574E-6 300.4 4.05706E-4 0.00115 3.07511E-6 2.1719E-6 S9.C Time 100:0 Time 50:50 Time 2:98 -1.22E-6 1.00001 -1.29E-6 1.00001 -1.22E-6 1.00003 0.1 0.93366 0.1 0.97467 0.1 0.97346 0.2 0.93587 0.2 0.92493 0.2 0.95004 0.3 0.89079 0.3 0.9119 0.3 0.94077 0.4 0.84481 0.4 0.88137 0.4 0.93326 0.5 0.80297 0.5 0.86481 0.5 0.9005 0.6 0.78439 0.6 0.83023 0.6 0.88307 0.7 0.76643 0.7 0.80494 0.7 0.84077 0.8 0.725 0.8 0.77021 0.8 0.83059 0.9 0.69917 0.9 0.75031 0.9 0.81453 1 0.65636 1 0.74206 1 0.7832 1.1 0.63621 1.1 0.72481 1.1 0.78387 1.2 0.5893 1.2 0.68493 1.2 0.76877 1.3 0.58539 1.3 0.67654 1.3 0.76757 1.4 0.55751 1.4 0.64357 1.4 0.75227 1.5 0.55754 1.5 0.64829 1.5 0.72379 1.6 0.526 1.6 0.60497 1.6 0.7044 1.7 0.50866 1.7 0.61717 1.7 0.68473 1.8 0.49099 1.8 0.58509 1.8 0.68254 1.9 0.4609 1.9 0.55367 1.9 0.6687 2 0.45209 2 0.55109 2 0.66503 2.1 0.41866 2.1 0.54521 2.1 0.65187 2.2 0.42124 2.2 0.51426 2.2 0.6368 2.3 0.37847 2.3 0.51603 2.3 0.61439 2.4 0.38084 2.4 0.49109 2.4 0.6095 2.5 0.362 2.5 0.48847 2.5 0.6 2.6 0.33597 2.6 0.4701 2.6 0.59161 2.7 0.34083 2.7 0.44723 2.7 0.57909 2.8 0.36103 2.8 0.4456 2.8 0.57003 2.9 0.32684 2.9 0.42941 2.9 0.56561 3 0.32563 3 0.44257 3 0.52766 3.1 0.31426 3.1 0.41657 3.1 0.52067 3.2 0.28744 3.2 0.39744 3.2 0.51687 3.3 0.31897 3.3 0.41309 3.3 0.51604 3.4 0.25131 3.4 0.37686 3.4 0.49801 3.5 0.24041 3.5 0.36694 3.5 0.50714 3.6 0.21157 3.6 0.35536 3.6 0.48144

93

3.7 0.22844 3.7 0.35916 3.7 0.48363 3.8 0.22524 3.8 0.33496 3.8 0.45894 3.9 0.21476 3.9 0.3513 3.9 0.45539 4 0.25836 4 0.3317 4 0.4548 4.1 0.21664 4.1 0.32754 4.1 0.44576 4.2 0.23061 4.2 0.31011 4.2 0.44266 4.3 0.16773 4.3 0.2983 4.3 0.42621 4.4 0.19821 4.4 0.28091 4.4 0.40634 4.5 0.16269 4.5 0.2746 4.5 0.39091 4.6 0.18384 4.6 0.26513 4.6 0.3965 4.7 0.17977 4.7 0.2653 4.7 0.39769 4.8 0.14893 4.8 0.25576 4.8 0.38486 4.9 0.12494 4.9 0.24909 4.9 0.37933 5 0.1532 5 0.26081 5 0.3779 5.1 0.15109 5.1 0.24709 5.1 0.37097 5.2 0.12991 5.2 0.23569 5.2 0.37646 5.3 0.14817 5.3 0.2118 5.3 0.36597 5.4 0.11726 5.4 0.22133 5.4 0.34259 5.5 0.1042 5.5 0.22217 5.5 0.33806 5.6 0.10946 5.6 0.20011 5.6 0.338 5.7 0.0948 5.9 0.1809 5.7 0.32689 5.8 0.12234 6 0.19936 5.8 0.3382 6.3 0.09086 6.8 0.16427 6.3 0.26941 6.8 0.0971 7.3 0.1485 6.8 0.26173 7.3 0.05509 7.8 0.12174 7.3 0.23556 7.8 0.06123 8.3 0.11476 7.8 0.21453 8.3 0.04314 8.8 0.09027 8.3 0.19897 8.8 0.04034 9.3 0.08049 8.8 0.17473 9.3 0.03017 9.8 0.07081 9.3 0.17251 9.8 0.01859 10.3 0.0668 9.8 0.16211 10.8 0.03037 11.3 0.03367 10.8 0.12019 11.8 0.02417 12.3 0.02997 11.8 0.10907 12.8 -0.00226 13.3 0.01543 12.8 0.09134 13.8 -0.01609 14.3 0.00779 13.8 0.07479 14.8 -0.01603 15.3 0.01089 14.8 0.05403 15.8 -1.76883E-4 16.3 -8.20367E-5 15.8 0.05251 16.8 -0.01431 17.3 -1.37113E-4 16.8 0.04143 17.8 -0.00624 18.3 -8.29697E-4 17.8 0.04601 18.8 7.11557E-6 19.3 0.00167 18.8 0.03681 19.8 -0.01139 20.3 -5.78117E-4 19.8 0.01329 22.8 -0.01804 23.3 -0.0032 22.8 0.01031 24.8 8.89263E-4 25.3 -0.00976 24.8 0.01504 27.8 0.00557 28.3 -0.01446 27.8 7.576E-4 29.8 0.01086 30.3 0.00193 29.8 -0.00501 34.8 0.00726 35.3 -0.0111 34.8 -0.02907 39.8 -0.00119 40.3 -0.00304 39.8 -0.01997 42.8 -0.00977 43.3 0.0149 42.8 -0.01691 44.8 0.01499 45.3 0.00491 44.8 -0.02514 47.8 -1.39556E-7 48.3 -0.00273 47.8 -0.01527 49.8 0.00854 50.3 0.00639 49.8 -0.04293 Time 100:0

Fitting Time 50:50

Fitting Time 2:98

Fitting -1.22E-6 1 -1.29E-6 1 -1.22E-6 1 0.1 0.96388 0.1 0.97181 0.1 0.97948 0.2 0.9291 0.2 0.94443 0.2 0.95938 0.3 0.89561 0.3 0.91783 0.3 0.93969 0.4 0.86335 0.4 0.892 0.4 0.92041 0.5 0.83228 0.5 0.86691 0.5 0.90152 0.6 0.80236 0.6 0.84254 0.6 0.88302 0.7 0.77354 0.7 0.81887 0.7 0.8649

94

0.8 0.74579 0.8 0.79588 0.8 0.84716 0.9 0.71905 0.9 0.77355 0.9 0.82978 1 0.69331 1 0.75186 1 0.81275 1.1 0.66851 1.1 0.73079 1.1 0.79608 1.2 0.64462 1.2 0.71032 1.2 0.77975 1.3 0.62161 1.3 0.69044 1.3 0.76375 1.4 0.59944 1.4 0.67112 1.4 0.74808 1.5 0.57809 1.5 0.65236 1.5 0.73274 1.6 0.55752 1.6 0.63414 1.6 0.71771 1.7 0.53771 1.7 0.61643 1.7 0.70299 1.8 0.51862 1.8 0.59923 1.8 0.68857 1.9 0.50023 1.9 0.58252 1.9 0.67444 2 0.48251 2 0.56629 2 0.66061 2.1 0.46544 2.1 0.55052 2.1 0.64706 2.2 0.449 2.2 0.5352 2.2 0.63379 2.3 0.43315 2.3 0.52031 2.3 0.62079 2.4 0.41789 2.4 0.50585 2.4 0.60806 2.5 0.40318 2.5 0.4918 2.5 0.59559 2.6 0.389 2.6 0.47815 2.6 0.58338 2.7 0.37534 2.7 0.46489 2.7 0.57142 2.8 0.36218 2.8 0.452 2.8 0.5597 2.9 0.3495 2.9 0.43948 2.9 0.54822 3 0.33728 3 0.42731 3 0.53698 3.1 0.3255 3.1 0.41549 3.1 0.52597 3.2 0.31414 3.2 0.40401 3.2 0.51519 3.3 0.3032 3.3 0.39285 3.3 0.50463 3.4 0.29266 3.4 0.382 3.4 0.49428 3.5 0.2825 3.5 0.37147 3.5 0.48415 3.6 0.2727 3.6 0.36123 3.6 0.47422 3.7 0.26326 3.7 0.35128 3.7 0.4645 3.8 0.25415 3.8 0.34161 3.8 0.45498 3.9 0.24538 3.9 0.33221 3.9 0.44565 4 0.23692 4 0.32308 4 0.43652 4.1 0.22877 4.1 0.31421 4.1 0.42757 4.2 0.22091 4.2 0.30558 4.2 0.41881 4.3 0.21333 4.3 0.2972 4.3 0.41022 4.4 0.20602 4.4 0.28906 4.4 0.40182 4.5 0.19898 4.5 0.28114 4.5 0.39358 4.6 0.19218 4.6 0.27345 4.6 0.38552 4.7 0.18563 4.7 0.26597 4.7 0.37761 4.8 0.17932 4.8 0.25871 4.8 0.36988 4.9 0.17322 4.9 0.25164 4.9 0.3623 5 0.16735 5 0.24478 5 0.35487 5.1 0.16169 5.1 0.2381 5.1 0.3476 5.2 0.15622 5.2 0.23162 5.2 0.34048 5.3 0.15095 5.3 0.22531 5.3 0.3335 5.4 0.14587 5.4 0.21919 5.4 0.32667 5.5 0.14097 5.5 0.21323 5.5 0.31998 5.6 0.13624 5.6 0.20744 5.6 0.31342 5.7 0.13168 5.9 0.19102 5.7 0.307 5.8 0.12728 6 0.18585 5.8 0.30071 6.3 0.10749 6.8 0.14934 6.3 0.27115 6.8 0.09094 7.3 0.13036 6.8 0.24449 7.3 0.07707 7.8 0.11386 7.3 0.22046 7.8 0.06544 8.3 0.0995 7.8 0.1988 8.3 0.05567 8.8 0.08701 8.3 0.17926 8.8 0.04745 9.3 0.07613 8.8 0.16165 9.3 0.04053 9.8 0.06666 9.3 0.14577 9.8 0.03468 10.3 0.0584 9.8 0.13145 10.8 0.02556 11.3 0.04491 10.8 0.1069 11.8 0.019 12.3 0.03462 11.8 0.08694 12.8 0.01424 13.3 0.02676 12.8 0.07071

95

13.8 0.01076 14.3 0.02074 13.8 0.05751 14.8 0.0082 15.3 0.01612 14.8 0.04678 15.8 0.0063 16.3 0.01256 15.8 0.03805 16.8 0.00487 17.3 0.00981 16.8 0.03096 17.8 0.00379 18.3 0.00768 17.8 0.02518 18.8 0.00297 19.3 0.00603 18.8 0.02049 19.8 0.00234 20.3 0.00474 19.8 0.01667 22.8 0.00117 23.3 0.00234 22.8 0.00898 24.8 7.54782E-4 25.3 0.00148 24.8 0.00595 27.8 3.9571E-4 28.3 7.52149E-4 27.8 0.00321 29.8 2.59352E-4 30.3 4.83122E-4 29.8 0.00212 34.8 9.16589E-5 35.3 1.63356E-4 34.8 7.59256E-4 39.8 3.27765E-5 40.3 5.65494E-5 39.8 2.71647E-4 42.8 1.77293E-5 43.3 3.01568E-5 42.8 1.46669E-4 44.8 1.17766E-5 45.3 1.98789E-5 44.8 9.72652E-5 47.8 6.37878E-6 48.3 1.06688E-5 47.8 5.25385E-5 49.8 4.23947E-6 50.3 7.05628E-6 49.8 3.4851E-5 S10.A Time KSCN (1.8M) KS13C15N (1.8M) KSCN (1.8M)

fitting KS13C15N (1.8M) fitting

0 0.99763 1 1 1 0.1 1.00002 0.9915 0.98494 0.98916 0.2 0.99023 0.98621 0.97067 0.97863 0.3 0.97814 0.97082 0.95712 0.96839 0.4 0.95952 0.95491 0.94426 0.95843 0.5 0.94484 0.94479 0.93204 0.94874 0.6 0.92391 0.93388 0.9204 0.93931 0.7 0.90706 0.92064 0.90933 0.93014 0.8 0.89446 0.90919 0.89877 0.92122 0.9 0.88532 0.89854 0.88869 0.91253 1 0.87592 0.88933 0.87906 0.90406 1.1 0.86869 0.8748 0.86984 0.89582 1.2 0.85949 0.86794 0.86102 0.88779 1.3 0.85092 0.86421 0.85257 0.87997 1.4 0.84349 0.85536 0.84446 0.87234 1.5 0.83801 0.85309 0.83667 0.8649 1.6 0.82328 0.84218 0.82917 0.85765 1.7 0.82292 0.83028 0.82196 0.85057 1.8 0.81346 0.82325 0.815 0.84367 1.9 0.80492 0.81971 0.80829 0.83693 2 0.79692 0.81635 0.80181 0.83035 2.1 0.79256 0.8186 0.79554 0.82392 2.2 0.7858 0.80914 0.78947 0.81764 2.3 0.78365 0.80339 0.78359 0.81151 2.4 0.7818 0.7981 0.77789 0.80551 2.5 0.78017 0.79493 0.77234 0.79965 2.6 0.77708 0.78814 0.76696 0.79392 2.7 0.76449 0.7816 0.76171 0.78832 2.8 0.75942 0.78048 0.7566 0.78283 2.9 0.75094 0.77213 0.75162 0.77746 3 0.7442 0.7719 0.74676 0.7722 3.1 0.74062 0.77359 0.74201 0.76706 3.2 0.74289 0.76255 0.73737 0.76201 3.3 0.73447 0.75559 0.73283 0.75707 3.4 0.72857 0.75339 0.72838 0.75223 3.5 0.7231 0.74983 0.72401 0.74748 3.6 0.71755 0.73785 0.71974 0.74283 3.7 0.71516 0.74744 0.71554 0.73826

96

3.8 0.70969 0.74248 0.71141 0.73378 3.9 0.70786 0.73631 0.70735 0.72938 4 0.7031 0.73069 0.70336 0.72506 4.1 0.69582 0.72663 0.69944 0.72082 4.2 0.69572 0.72195 0.69557 0.71666 4.3 0.69214 0.71617 0.69175 0.71256 4.4 0.68931 0.71279 0.688 0.70854 4.5 0.67929 0.70719 0.68429 0.70458 4.6 0.68427 0.7048 0.68063 0.70069 4.7 0.67342 0.70176 0.67701 0.69687 4.8 0.67052 0.69331 0.67344 0.6931 4.9 0.66923 0.68916 0.66991 0.6894 5.1 0.64535 0.68802 0.66297 0.68216 5.6 0.63309 0.67102 0.64623 0.66499 6.4 0.62032 0.64802 0.62093 0.63984 6.9 0.5983 0.63518 0.60588 0.62534 7.4 0.58333 0.61842 0.59131 0.61163 7.9 0.56692 0.60812 0.57719 0.5986 8.4 0.55644 0.59898 0.56346 0.58616 8.9 0.54425 0.5861 0.55011 0.57424 9.4 0.52823 0.57111 0.5371 0.56279 9.9 0.51678 0.55906 0.52443 0.55175 10.9 0.49365 0.53985 0.5 0.53073 11.9 0.47336 0.51453 0.47675 0.51094 12.9 0.44131 0.50189 0.45459 0.49217 13.9 0.42687 0.48499 0.43347 0.47429 14.9 0.40231 0.46498 0.41334 0.4572 15.9 0.38561 0.44721 0.39415 0.44083 16.9 0.37459 0.43324 0.37585 0.4251 17.9 0.34905 0.41508 0.3584 0.40998 18.9 0.33717 0.39944 0.34176 0.39543 19.9 0.32291 0.38877 0.3259 0.38143 22.9 0.27723 0.34904 0.2826 0.34238 24.9 0.2559 0.32145 0.25698 0.31862 27.9 0.22197 0.28989 0.22285 0.28607 29.9 0.2039 0.26896 0.20266 0.26624 34.9 0.16001 0.22478 0.15983 0.22249 39.9 0.12611 0.18618 0.12606 0.18594 42.9 0.11266 0.16977 0.10934 0.16696 44.9 0.1035 0.1551 0.09944 0.15539 47.9 0.08833 0.14035 0.08625 0.13954 49.9 0.08256 0.13119 0.07845 0.12988 54.9 0.07024 0.11325 0.0619 0.10855 59.9 0.05244 0.09301 0.04884 0.09073 64.9 0.04099 0.08015 0.03855 0.07584 69.9 0.03138 0.06424 0.03042 0.06339 74.9 0.02765 0.05541 0.02402 0.05299 79.9 0.02178 0.04635 0.01896 0.0443 84.9 0.01707 0.03697 0.01497 0.03703 89.9 0.01166 0.02894 0.01182 0.03096 94.9 0.00752 0.02835 0.00934 0.02588 99.9 0.007 0.02076 0.00738 0.02164 109.9 0.00743 0.01666 0.00461 0.01512 119.9 0.00111 0.0117 0.00288 0.01057 129.9 0.00212 0.00548 0.0018 0.00739 139.9 0.00133 0.00546 0.00113 0.00517 149.9 -8.12127E-5 8.60769E-4 7.07547E-4 0.00361 159.9 -4.75198E-5 0.00304 4.44326E-4 0.00253 169.9 0.00182 -8.88804E-4 2.79208E-4 0.00177 179.9 8.08465E-4 -0.00103 1.75919E-4 0.00123 189.9 -7.1744E-4 -0.00235 1.10835E-4 8.63454E-4 199.9 -0.00262 -0.00137 7.01606E-5 6.03827E-4

97

209.9 3.69921E-4 8.65404E-4 4.42967E-5 4.22203E-4 219.9 -1.46705E-4 0.00102 2.82059E-5 2.95333E-4 229.9 0.00165 -2.55693E-4 1.79009E-5 2.06411E-4 239.9 -7.06388E-4 -0.00337 1.13613E-5 1.44491E-4 249.9 3.57425E-4 -8.20876E-4 7.36867E-6 1.01048E-4 S10.B Time Flowing down Pumping up Flowing down fitting Pumping up fitting 0 -1.13E-4 1.57884E-4 0 0 0.1 5.20033E-4 3.87406E-4 2.18814E-4 1.53172E-4 0.2 -1.29E-4 0.00161 4.31899E-4 3.0234E-4 0.3 0.00127 8.08382E-4 6.39536E-4 4.47687E-4 0.4 -5.48279E-4 0.0019 8.41978E-4 5.89394E-4 0.5 0.00123 0.0014 0.00104 7.27634E-4 0.6 3.80467E-4 0.00149 0.00123 8.62563E-4 0.7 0.00127 0.00259 0.00142 9.94333E-4 0.8 -1.64792E-4 0.00246 0.0016 0.00112 0.9 -3.76821E-4 0.00266 0.00178 0.00125 1 -8.60494E-4 0.00442 0.00196 0.00137 1.1 0.00245 0.00368 0.00213 0.00149 1.2 4.64708E-4 0.00346 0.0023 0.00161 1.3 0.00158 0.00361 0.00247 0.00173 1.4 0.00408 0.00435 0.00263 0.00184 1.5 0.00259 0.00371 0.00279 0.00195 1.6 0.00434 0.0032 0.00294 0.00206 1.7 0.00102 0.00443 0.00309 0.00217 1.8 6.20315E-4 0.00426 0.00324 0.00227 1.9 8.2264E-4 0.00466 0.00339 0.00237 2 5.36347E-4 0.00413 0.00353 0.00247 2.1 0.00153 0.00476 0.00368 0.00257 2.2 0.0035 0.00542 0.00382 0.00267 2.3 0.0011 0.00567 0.00395 0.00277 2.4 0.00253 0.0053 0.00409 0.00286 2.5 0.00159 0.00538 0.00422 0.00295 2.6 0.00314 0.00495 0.00435 0.00304 2.7 0.00401 0.00592 0.00448 0.00313 2.8 0.00248 0.00522 0.0046 0.00322 2.9 0.00178 0.00526 0.00473 0.00331 3 0.00418 0.00603 0.00485 0.00339 3.1 0.00445 0.00461 0.00497 0.00348 3.2 0.00542 0.00358 0.00509 0.00356 3.3 0.00471 0.00531 0.0052 0.00364 3.4 0.0071 0.00605 0.00532 0.00372 3.5 0.00425 0.00478 0.00543 0.0038 3.6 0.0045 0.00665 0.00554 0.00388 3.7 0.00346 0.00553 0.00565 0.00396 3.8 0.00406 0.00619 0.00576 0.00403 3.9 0.00555 0.00539 0.00587 0.00411 4 0.0061 0.00569 0.00598 0.00418 4.1 0.00334 0.00657 0.00608 0.00426 4.2 0.0044 0.00691 0.00618 0.00433 4.3 0.00615 0.00647 0.00628 0.0044 4.4 0.00581 0.00685 0.00638 0.00447 4.5 0.00287 0.00619 0.00648 0.00454 4.6 0.0066 0.00643 0.00658 0.00461 4.7 0.00688 0.00542 0.00668 0.00467 4.8 0.00702 0.00569 0.00677 0.00474 4.9 0.00612 0.0063 0.00686 0.00481

98

5.1 0.00776 0.0075 0.00705 0.00493 5.6 0.00507 0.00787 0.00749 0.00524 6.4 0.00793 0.00701 0.00814 0.0057 6.9 0.00756 0.0077 0.00851 0.00596 7.4 0.00823 0.00816 0.00886 0.0062 7.9 0.0074 0.00893 0.0092 0.00644 8.4 0.00908 0.00788 0.00951 0.00666 8.9 0.01111 0.00868 0.0098 0.00686 9.4 0.01076 0.00802 0.01008 0.00705 9.9 0.01037 0.00849 0.01034 0.00724 10.9 0.01136 0.00837 0.01081 0.00757 11.9 0.01019 0.00834 0.01122 0.00785 12.9 0.01178 0.00845 0.01158 0.00811 13.9 0.01208 0.00924 0.01189 0.00832 14.9 0.01139 0.00866 0.01215 0.00851 15.9 0.01289 0.00954 0.01238 0.00866 16.9 0.01295 0.00799 0.01256 0.00879 17.9 0.01181 0.0087 0.01271 0.0089 18.9 0.01182 0.00875 0.01282 0.00898 19.9 0.01182 0.00932 0.01291 0.00904 22.9 0.01173 0.00942 0.013 0.0091 24.9 0.01314 0.00869 0.01295 0.00907 27.9 0.01281 0.00872 0.01274 0.00892 29.9 0.01343 0.00845 0.01253 0.00877 34.9 0.01219 0.00839 0.01181 0.00827 39.9 0.0115 0.00629 0.01093 0.00765 42.9 0.01047 0.00719 0.01036 0.00725 44.9 0.01042 0.00677 0.00997 0.00698 47.9 0.00913 0.00585 0.00938 0.00657 49.9 0.00927 0.00675 0.00899 0.00629 54.9 0.00846 0.00583 0.00803 0.00562 59.9 0.00639 0.00421 0.00712 0.00498 64.9 0.00556 0.00413 0.00627 0.00439 69.9 0.00507 0.00344 0.0055 0.00385 74.9 0.00512 0.0036 0.0048 0.00336 79.9 0.00481 0.00191 0.00417 0.00292 84.9 0.00388 0.00207 0.00361 0.00252 89.9 0.00307 0.0023 0.00311 0.00218 94.9 0.00247 0.00258 0.00268 0.00188 99.9 0.00209 0.00163 0.0023 0.00161 109.9 0.00169 0.00135 0.00169 0.00118 119.9 -7.57099E-6 9.40166E-4 0.00123 8.58705E-4 129.9 7.28106E-4 0.00119 8.87582E-4 6.21285E-4 139.9 8.56983E-4 0.00105 6.39154E-4 4.47403E-4 149.9 -4.94226E-5 8.94217E-4 4.58443E-4 3.20912E-4 159.9 2.13404E-4 9.77246E-4 3.27743E-4 2.29419E-4 169.9 0.00123 2.02979E-4 2.33626E-4 1.63542E-4 179.9 4.70494E-4 -3.12061E-4 1.66153E-4 1.16308E-4 189.9 -5.791E-4 2.33428E-4 1.17906E-4 8.25387E-5 199.9 2.44488E-4 5.07285E-4 8.35428E-5 5.8473E-5 209.9 5.75289E-4 -3.82052E-4 5.9066E-5 4.13548E-5 219.9 8.80234E-4 5.54893E-4 4.17456E-5 2.92215E-5 229.9 1.54658E-4 8.51775E-4 2.94428E-5 2.0611E-5 239.9 3.52846E-4 -2.86148E-4 2.07314E-5 1.45299E-5 249.9 7.0935E-4 7.9703E-5 1.46329E-5 1.02435E-5 S10.C Time 100:0 Time 50:50 Time 2:98

99

0 1 0 1 0 0.99997 0.1 0.95006 0.1 1.02589 0.1 0.93606 0.2 0.88114 0.2 1.06234 0.2 0.81626 0.3 0.89409 0.3 0.99163 0.3 0.86663 0.4 0.7502 0.4 0.93449 0.4 0.8654 0.5 0.75326 0.5 0.90197 0.5 0.83309 0.6 0.74391 0.6 0.91911 0.6 0.7654 0.7 0.68986 0.7 0.87109 0.7 0.74406 0.8 0.69291 0.8 0.79834 0.8 0.80051 0.9 0.6106 0.9 0.81537 0.9 0.77111 1 0.6234 1 0.75674 1 0.71411 1.1 0.59446 1.1 0.76689 1.1 0.77086 1.2 0.53409 1.2 0.75257 1.2 0.78714 1.3 0.50851 1.3 0.68829 1.3 0.71249 1.4 0.50443 1.4 0.66471 1.4 0.74394 1.5 0.49211 1.5 0.6902 1.5 0.73483 1.6 0.46463 1.6 0.64894 1.6 0.61966 1.7 0.42703 1.7 0.63534 1.7 0.71866 1.8 0.39197 1.8 0.62749 1.8 0.68354 1.9 0.41294 1.9 0.58546 1.9 0.71031 2 0.412 2 0.62446 2 0.66263 2.5 0.31557 2.5 0.51746 2.5 0.67023 3 0.27451 3 0.49646 3 0.63377 3.5 0.13554 3.5 0.40257 3.5 0.472 4 0.20446 4 0.34306 4 0.4752 4.5 0.13854 4.5 0.32249 4.5 0.38711 5 0.08754 4.8 0.304 5 0.34743 5.5 0.07531 4.9 0.30317 5.5 0.30797 6 0.0566 5 0.31086 6 0.2628 6.5 0.05397 5.5 0.25611 6.5 0.23843 7 0.08897 6 0.26163 7 0.26663 7.5 0.05397 6.5 0.22514 7.5 0.24329 8 0.01523 7 0.16311 8 0.13709 8.5 0.01083 7.5 0.13794 8.5 0.14697 9 0.05303 8 0.15929 9 0.16286 9.5 0.05374 8.5 0.13209 9.5 0.13966 10 0.04617 9 0.0806 10 0.13154 11 0.05694 9.5 0.10966 11 0.06371 12 0.01746 10 0.0984 12 0.11171 13 -0.01234 11 0.08229 13 0.08486 14 0.00394 12 0.09186 14 0.06806 15 -0.00411 13 0.02214 15 0.07269 16 0.03434 14 2.51827E-4 16 0.07411 17 0.00937 15 0.01851 17 0.1074 18 -0.00491 16 0.01946 18 0.07811 19 0.0234 17 -0.00583 19 0.05106 20 -0.01117 18 0.00171 20 0.06283 22 -0.03374 19 -0.00631 22 0.00989 25 -0.00577 20 0.01477 25 0.03571 28 0.03737 23 -0.00277 28 0.02831 30 0.01506 25 -0.00248 30 -0.01954 33 -0.00247 28 0.01377 33 -0.03009 35 0.02003 30 0.01551 35 0.01611 38 -0.00363 35 0.00414 38 0.00757 40 -0.00631 40 0.00669 40 -0.03074 43 0.00303 43 0.00631 43 -0.0316 45 0.02531 45 0.02306 45 -0.0218 48 0.02374 48 9.05863E-4 48 5.01969E-5 50 0.04211 50 -0.00213 50 -0.02429 Time 100:0

Fitting Time 50:50

Fitting Time 2:98

Fitting

100

0 1 0 1 0 1 0.1 0.96246 0.1 0.97021 0.1 0.97771 0.2 0.92642 0.2 0.94136 0.2 0.95592 0.3 0.89181 0.3 0.9134 0.3 0.93461 0.4 0.85858 0.4 0.88631 0.4 0.91378 0.5 0.82665 0.5 0.86006 0.5 0.89342 0.6 0.796 0.6 0.83464 0.6 0.87351 0.7 0.76655 0.7 0.80999 0.7 0.85405 0.8 0.73826 0.8 0.78612 0.8 0.83502 0.9 0.71108 0.9 0.76298 0.9 0.81642 1 0.68498 1 0.74055 1 0.79824 1.1 0.65989 1.1 0.71882 1.1 0.78046 1.2 0.63579 1.2 0.69776 1.2 0.76307 1.3 0.61263 1.3 0.67735 1.3 0.74608 1.4 0.59038 1.4 0.65756 1.4 0.72947 1.5 0.56899 1.5 0.63838 1.5 0.71322 1.6 0.54843 1.6 0.61979 1.6 0.69734 1.7 0.52867 1.7 0.60177 1.7 0.68182 1.8 0.50968 1.8 0.5843 1.8 0.66664 1.9 0.49142 1.9 0.56736 1.9 0.6518 2 0.47386 2 0.55094 2 0.63729 2.5 0.3957 2.5 0.47603 2.5 0.56947 3 0.33133 3 0.41179 3 0.50888 3.5 0.27822 3.5 0.35663 3.5 0.45476 4 0.2343 4 0.30921 4 0.4064 4.5 0.19788 4.5 0.26841 4.5 0.36321 5 0.16762 4.8 0.2467 5 0.32461 5.5 0.1424 4.9 0.23988 5.5 0.29013 6 0.12133 5 0.23326 6 0.25932 6.5 0.10368 5.5 0.20294 6.5 0.23178 7 0.08885 6 0.17677 7 0.20718 7.5 0.07635 6.5 0.15413 7.5 0.1852 8 0.06579 7 0.13455 8 0.16555 8.5 0.05684 7.5 0.11757 8.5 0.14799 9 0.04923 8 0.10285 9 0.1323 9.5 0.04274 8.5 0.09006 9.5 0.11827 10 0.03719 9 0.07894 10 0.10574 11 0.02835 9.5 0.06926 11 0.08452 12 0.02177 10 0.06082 12 0.06756 13 0.01684 11 0.04704 13 0.05402 14 0.0131 12 0.0365 14 0.04319 15 0.01024 13 0.02841 15 0.03453 16 0.00804 14 0.02218 16 0.02762 17 0.00634 15 0.01737 17 0.02209 18 0.00501 16 0.01363 18 0.01766 19 0.00397 17 0.01072 19 0.01413 20 0.00315 18 0.00845 20 0.0113 22 0.00199 19 0.00667 22 0.00723 25 0.00101 20 0.00527 25 0.0037 28 5.16221E-4 23 0.00263 28 0.0019 30 3.30224E-4 25 0.00166 30 0.00122 33 1.69196E-4 28 8.40711E-4 33 6.22941E-4 35 1.084E-4 30 5.3512E-4 35 3.99058E-4 38 5.56157E-5 35 1.7412E-4 38 2.04644E-4 40 3.56502E-5 40 5.69798E-5 40 1.31126E-4 43 1.82991E-5 43 2.91946E-5 43 6.72636E-5 45 1.1732E-5 45 1.87009E-5 45 4.31065E-5 48 6.02292E-6 48 9.59142E-6 48 2.21173E-5 50 3.86166E-6 50 6.14682E-6 50 1.41759E-5

101

S11.A Time KSCN (1.0M) KS13C15N (1.0M) KSCN (1.0M)

fitting KS13C15N (1.0M) fitting

0 0.99027 1 1 1 0.1 0.99999 0.99017 0.98201 0.98435 0.2 0.99783 0.98207 0.96485 0.96949 0.3 0.99049 0.9618 0.94848 0.95537 0.4 0.95141 0.94055 0.93286 0.94194 0.5 0.93526 0.92325 0.91794 0.92916 0.6 0.92957 0.91304 0.9037 0.91699 0.7 0.89894 0.89959 0.89008 0.9054 0.8 0.88014 0.88597 0.87705 0.89435 0.9 0.86089 0.88337 0.86459 0.88382 1 0.84951 0.86606 0.85265 0.87376 1.1 0.8385 0.85856 0.84121 0.86415 1.2 0.82282 0.84768 0.83024 0.85496 1.3 0.81626 0.8435 0.81972 0.84617 1.4 0.80261 0.8353 0.80962 0.83776 1.5 0.79766 0.82428 0.79992 0.8297 1.6 0.78082 0.81677 0.79059 0.82198 1.7 0.77914 0.81227 0.78163 0.81456 1.8 0.76287 0.807 0.77299 0.80744 1.9 0.76593 0.80425 0.76467 0.8006 2 0.74886 0.79249 0.75666 0.79402 2.1 0.73563 0.78531 0.74892 0.78768 2.2 0.73188 0.78724 0.74146 0.78157 2.3 0.72714 0.77735 0.73425 0.77568 2.4 0.7221 0.77667 0.72728 0.77 2.5 0.7207 0.76835 0.72054 0.76451 2.6 0.71638 0.76277 0.71401 0.7592 2.7 0.7035 0.76273 0.70768 0.75406 2.8 0.69617 0.75473 0.70155 0.74909 2.9 0.69747 0.74906 0.6956 0.74426 3 0.68552 0.74326 0.68983 0.73958 3.1 0.69312 0.73975 0.68422 0.73504 3.2 0.6992 0.7305 0.67876 0.73062 3.3 0.68483 0.72475 0.67345 0.72633 3.4 0.67881 0.7218 0.66828 0.72215 3.5 0.67806 0.71975 0.66324 0.71807 3.6 0.67345 0.71721 0.65833 0.7141 3.7 0.65879 0.70849 0.65354 0.71022 3.8 0.66079 0.70206 0.64886 0.70643 3.9 0.65051 0.70019 0.64429 0.70273 4 0.6532 0.7003 0.63982 0.69911 4.5 0.61036 0.68044 0.61884 0.68208 5 0.60454 0.66101 0.59976 0.66651 5.5 0.58538 0.63905 0.58219 0.65208 6 0.56637 0.62806 0.56582 0.63852 6.5 0.56134 0.6146 0.55042 0.62567 7 0.53736 0.6027 0.53582 0.61338 7.5 0.52174 0.58672 0.5219 0.60155 8 0.50222 0.57361 0.50855 0.59012 8.5 0.49121 0.56154 0.4957 0.57903 9 0.47235 0.54919 0.4833 0.56823 9.5 0.47073 0.53851 0.4713 0.5577 10 0.45738 0.53 0.45966 0.54741 11 0.43643 0.52186 0.43737 0.52749 12 0.40713 0.5026 0.41627 0.50837

102

13 0.39213 0.4855 0.39625 0.48999 14 0.37553 0.4681 0.37723 0.47229 15 0.35936 0.44997 0.35914 0.45524 16 0.33738 0.4328 0.34193 0.43882 17 0.32392 0.41702 0.32555 0.42299 18 0.30641 0.4011 0.30996 0.40773 19 0.29449 0.386 0.29512 0.39303 20 0.27298 0.37356 0.28099 0.37886 23 0.23876 0.33418 0.24254 0.33934 25 0.21834 0.30966 0.21988 0.31531 28 0.18602 0.27925 0.18979 0.28242 30 0.16979 0.26215 0.17206 0.26243 35 0.13221 0.21654 0.13465 0.21842 40 0.10371 0.18224 0.10538 0.1818 43 0.09059 0.16415 0.09097 0.16284 45 0.07964 0.15246 0.08248 0.15132 48 0.07152 0.13646 0.0712 0.13554 50 0.06352 0.1276 0.06456 0.12595 55 0.05374 0.11186 0.05053 0.10483 60 0.04191 0.09073 0.03956 0.08726 65 0.03467 0.07688 0.03096 0.07263 70 0.02487 0.06445 0.02424 0.06046 75 0.01818 0.05364 0.01898 0.05033 80 0.01459 0.04585 0.01486 0.04189 85 0.01201 0.03859 0.01164 0.03487 90 0.00999 0.03263 0.00911 0.02903 95 0.00735 0.02688 0.00714 0.02417 100 0.00517 0.0222 0.00559 0.02012 110 0.00355 0.01633 0.00343 0.01394 120 0.00376 0.01174 0.00211 0.00966 130 0.00214 0.0082 0.00129 0.0067 140 2.82076E-4 0.00501 7.95392E-4 0.00464 150 3.93942E-4 0.00411 4.89212E-4 0.00322 160 -3.2635E-6 0.00243 3.00999E-4 0.00223 170 5.57667E-5 0.0026 1.85514E-4 0.00154 180 4.59095E-4 0.00109 1.14273E-4 0.00107 190 5.28503E-4 6.70033E-4 7.06092E-5 7.42078E-4 200 -3.51326E-4 0.00108 4.35326E-5 5.14225E-4 210 -4.07957E-4 1.5807E-4 2.70345E-5 3.56529E-4 220 -2.29471E-4 2.34261E-4 1.66546E-5 2.46996E-4 230 -2.0012E-4 1.22817E-4 1.03659E-5 1.71303E-4 240 6.62507E-4 -2.50353E-4 6.48759E-6 1.18669E-4 250 -2.04122E-4 -2.02352E-4 3.95996E-6 8.22421E-5 S11.B Time Flowing down Pumping up Flowing down fitting Pumping up fitting 0 4.80041E-4 -8.32068E-4 0 0 0.1 -6.99436E-4 5.09048E-4 1.50342E-4 1.05241E-4 0.2 2.37165E-4 4.49636E-4 2.95613E-4 2.06944E-4 0.3 3.38726E-4 1.99578E-4 4.36098E-4 3.05301E-4 0.4 3.23359E-4 2.99164E-4 5.72059E-4 4.00489E-4 0.5 7.52293E-4 -3.26594E-4 7.03745E-4 4.92677E-4 0.6 5.68838E-4 3.77775E-4 8.31385E-4 5.82026E-4 0.7 -6.08961E-5 4.45195E-4 9.55202E-4 6.68691E-4 0.8 8.33584E-4 0.00122 0.00108 7.52818E-4 0.9 5.00952E-4 0.0019 0.00119 8.3455E-4 1 -5.77613E-4 0.00217 0.00131 9.14019E-4 1.1 0.00122 0.00124 0.00142 9.91349E-4 1.2 0.00154 0.00234 0.00152 0.00107

103

1.3 0.00195 0.00274 0.00163 0.00114 1.4 0.00188 0.00305 0.00173 0.00121 1.5 0.00316 0.00218 0.00183 0.00128 1.6 0.00159 0.00199 0.00193 0.00135 1.7 0.00169 0.00295 0.00202 0.00142 1.8 0.00127 0.00199 0.00212 0.00148 1.9 0.00221 0.00184 0.00221 0.00154 2 0.00296 0.00223 0.0023 0.00161 2.1 0.00194 0.00389 0.00238 0.00167 2.2 0.00203 0.00288 0.00247 0.00173 2.3 0.00207 0.00294 0.00255 0.00179 2.4 0.00188 0.00338 0.00263 0.00184 2.5 0.00156 0.00276 0.00271 0.0019 2.6 0.00324 0.00239 0.00279 0.00195 2.7 0.00241 0.00197 0.00287 0.00201 2.8 0.00257 0.00211 0.00295 0.00206 2.9 0.00284 0.0018 0.00302 0.00211 3 0.00289 0.00232 0.00309 0.00217 3.1 0.00239 0.00285 0.00317 0.00222 3.2 0.00368 0.00252 0.00324 0.00227 3.3 0.0021 0.0029 0.00331 0.00232 3.4 0.00363 0.00278 0.00338 0.00236 3.5 0.00312 0.00313 0.00344 0.00241 3.6 0.00403 0.00338 0.00351 0.00246 3.7 0.00277 0.00436 0.00358 0.0025 3.8 0.00448 0.00251 0.00364 0.00255 3.9 0.00323 0.00395 0.0037 0.00259 4 0.00417 0.00197 0.00377 0.00264 4.5 0.00512 0.00335 0.00407 0.00285 5 0.00398 0.00309 0.00435 0.00305 5.5 0.00599 0.00378 0.00461 0.00323 6 0.00464 0.00361 0.00486 0.0034 6.5 0.0059 0.00343 0.0051 0.00357 7 0.00544 0.00446 0.00532 0.00372 7.5 0.00589 0.00371 0.00552 0.00387 8 0.00585 0.0043 0.00572 0.004 8.5 0.0067 0.00515 0.0059 0.00413 9 0.00544 0.00498 0.00608 0.00425 9.5 0.00589 0.0045 0.00624 0.00437 10 0.00688 0.005 0.00639 0.00447 11 0.00714 0.00525 0.00667 0.00467 12 0.0077 0.00543 0.00691 0.00484 13 0.00716 0.00511 0.00712 0.00498 14 0.00791 0.0052 0.0073 0.00511 15 0.00795 0.00496 0.00745 0.00522 16 0.00804 0.0053 0.00758 0.00531 17 0.00748 0.00524 0.00768 0.00538 18 0.00807 0.0055 0.00776 0.00543 19 0.00748 0.0049 0.00782 0.00548 20 0.008 0.00494 0.00786 0.0055 23 0.00768 0.00549 0.00789 0.00552 25 0.00759 0.00489 0.00784 0.00549 28 0.00722 0.00515 0.00769 0.00538 30 0.00722 0.00499 0.00754 0.00528 35 0.0067 0.00452 0.00707 0.00495 40 0.0059 0.0045 0.0065 0.00455 43 0.00573 0.00393 0.00614 0.0043 45 0.00498 0.00349 0.0059 0.00413 48 0.00553 0.00415 0.00553 0.00387 50 0.00524 0.00325 0.00529 0.0037 55 0.00494 0.003 0.0047 0.00329 60 0.00401 0.00248 0.00414 0.0029

104

65 0.00381 0.00221 0.00363 0.00254 70 0.00273 0.00305 0.00316 0.00221 75 0.00223 0.00125 0.00275 0.00192 80 0.00183 0.00223 0.00237 0.00166 85 0.00127 0.00205 0.00204 0.00143 90 0.00115 0.00153 0.00175 0.00123 95 0.0013 0.00199 0.0015 0.00105 100 0.00141 9.99525E-4 0.00128 8.97764E-4 110 0.00107 6.13151E-4 9.30029E-4 6.50998E-4 120 8.10535E-4 7.42626E-4 6.6976E-4 4.68825E-4 130 3.83717E-4 2.94303E-4 4.79627E-4 3.35733E-4 140 -1.41823E-4 -3.29591E-4 3.41871E-4 2.39307E-4 150 -1.31815E-4 -2.86301E-5 2.42738E-4 1.69913E-4 160 6.25934E-4 7.58403E-4 1.71788E-4 1.20246E-4 170 5.17412E-4 -4.09829E-6 1.21244E-4 8.48714E-5 180 -3.65208E-7 -2.25435E-4 8.53616E-5 5.97606E-5 190 5.12629E-4 8.65237E-4 5.99887E-5 4.19979E-5 200 4.22378E-4 4.96664E-4 4.20724E-5 2.94524E-5 210 3.19677E-4 -3.63577E-4 2.94795E-5 2.06308E-5 220 -6.09744E-4 2.74745E-4 2.06089E-5 1.44311E-5 230 -1.08255E-4 8.30175E-4 1.44106E-5 1.0093E-5 240 3.81195E-4 -1.24638E-4 1.00626E-5 7.0388E-6 250 -9.52953E-5 -8.30005E-5 6.99815E-6 4.90849E-6 S11.C Time 100:0 Time 50:50 Time 10:90 -1.65E-6 1 0 1 0 0.99996 0.1 0.92774 0.1 0.97937 0.1 1.03893 0.2 0.84344 0.2 0.94974 0.2 0.85615 0.3 0.84952 0.3 0.91593 0.3 0.70767 0.4 0.85874 0.4 0.86452 0.4 0.72085 0.5 0.727 0.5 0.91581 0.5 0.75411 0.6 0.74496 0.6 0.83737 0.6 0.78193 0.7 0.73656 0.7 0.80993 0.7 0.75174 0.8 0.65719 0.8 0.77256 0.8 0.66515 0.9 0.68326 0.9 0.72896 0.9 0.65881 1 0.65807 1 0.73819 1 0.53985 1.1 0.54415 1.1 0.75804 1.1 0.52156 1.2 0.56811 1.2 0.72048 1.2 0.72944 1.3 0.621 1.3 0.64056 1.3 0.61589 1.4 0.6537 1.4 0.67148 1.4 0.65485 1.5 0.51593 1.5 0.71574 1.5 0.56178 1.6 0.47548 1.6 0.66293 1.6 0.5693 1.7 0.46863 1.7 0.58419 1.7 0.70956 1.8 0.54996 1.8 0.68081 1.8 0.51222 1.9 0.37441 1.9 0.56167 1.9 0.45456 2.4 0.40011 2 0.5987 2.4 0.39267 2.9 0.45107 2.1 0.61885 2.9 0.4663 3.4 0.34774 2.2 0.54659 3.4 0.39274 3.9 0.31756 2.3 0.56452 3.9 0.3297 4.4 0.2677 2.4 0.52856 4.4 0.27511 4.9 0.2147 2.5 0.55474 4.9 0.3643 5.4 0.13504 2.6 0.46981 5.4 0.36104 5.9 0.13119 2.7 0.45752 5.9 0.21259 6.4 0.15989 2.8 0.46259 6.4 0.18963 6.9 0.14778 2.9 0.42067 6.9 0.21107 7.4 0.08107 3 0.42074 7.4 0.15544 7.9 0.13004 3.1 0.41904 7.9 0.18096 8.4 0.08807 3.2 0.48052 8.4 0.20693

105

8.9 0.05978 3.3 0.40474 8.9 0.15963 9.4 0.03485 3.4 0.41526 9.4 0.15374 9.9 0.10744 3.5 0.38189 9.9 0.0687 10.9 0.01819 3.6 0.43404 10.9 0.10159 11.9 -0.05863 3.7 0.34748 11.9 0.02552 12.9 0.01048 3.8 0.45378 12.9 -0.00589 13.9 -0.01722 3.9 0.43107 13.9 0.06093 14.9 0.0057 4 0.40804 14.9 0.04267 15.9 0.008 4.1 0.38041 15.9 0.04037 16.9 -0.02163 4.2 0.44078 16.9 -0.02356 17.9 -0.0147 4.3 0.33519 17.9 6.50444E-4 18.9 -0.033 4.4 0.33893 18.9 -0.07219 19.9 -0.03104 4.5 0.31556 19.9 0.01096 21.9 -0.00519 4.6 0.28522 21.9 0.01311 24.9 -0.04359 4.7 0.255 24.9 0.03933 27.9 -0.01589 4.8 0.26744 27.9 -0.036 29.9 0.01567 4.9 0.22622 29.9 0.06626 32.9 0.02781 5 0.33644 32.9 0.04385 34.9 -0.01756 5.1 0.30037 34.9 0.07111 37.9 0.00674 5.2 0.31889 37.9 0.07922 39.9 -0.07844 5.3 0.25604 39.9 -3.02693E-5 42.9 0.00793 5.8 0.27285 42.9 0.02222 44.9 -0.00108 6.3 0.24004 44.9 0.02559 47.9 0.03307 6.8 0.18781 47.9 -0.1033 49.9 -0.00118 7.3 0.14204 49.9 0.03137 7.8 0.17267 8.3 0.15763 8.8 0.11756 9.3 0.1047 10.3 0.13656 11.3 0.04119 12.3 0.04244 13.3 0.03463 14.3 0.06393 15.3 0.08522 16.3 0.02193 17.3 0.00822 18.3 0.03778 19.3 0.0263 22.3 0.02611 24.3 0.01963 27.3 0.03319 29.3 -0.01881 34.3 0.03993 39.3 0.02719 42.3 0.02296 44.3 0.02519 47.3 -0.0103 49.3 0.05822 Time 100:0

Fitting Time 50:50

Fitting Time 10:90

Fitting -1.65E-6 1 0 1 0 1 0.50404 0.8365 0.49798 0.86436 0.50404 0.8845 1.00808 0.70115 0.99596 0.74783 1.00808 0.78249 1.51212 0.58895 1.49394 0.64764 1.51212 0.69237 2.01616 0.49575 1.99192 0.56142 2.01616 0.61275 2.5202 0.41822 2.4899 0.48713 2.5202 0.54238 3.02424 0.35359 2.98788 0.42308 3.02424 0.48018 3.52828 0.29961 3.48586 0.36779 3.52828 0.42518

106

4.03232 0.25444 3.98384 0.32002 4.03232 0.37654 4.53636 0.21656 4.48182 0.27871 4.53636 0.33352 5.0404 0.18473 4.9798 0.24295 5.0404 0.29546 5.54444 0.15793 5.47778 0.21197 5.54444 0.26178 6.04848 0.13531 5.97576 0.1851 6.04848 0.23198 6.55252 0.11617 6.47374 0.16177 6.55253 0.2056 7.05656 0.09995 6.97172 0.14149 7.05657 0.18224 7.5606 0.08617 7.4697 0.12386 7.56061 0.16156 8.06465 0.07443 7.96768 0.10851 8.06465 0.14325 8.56869 0.06442 8.46566 0.09514 8.56869 0.12702 9.07273 0.05585 8.96364 0.08347 9.07273 0.11265 9.57677 0.04851 9.46162 0.07329 9.57677 0.09992 10.08081 0.0422 9.9596 0.06439 10.08081 0.08864 10.58485 0.03677 10.45758 0.05662 10.58485 0.07863 11.08889 0.03209 10.95556 0.04981 11.08889 0.06977 11.59293 0.02805 11.45354 0.04385 11.59293 0.06191 12.09697 0.02454 11.95152 0.03863 12.09697 0.05494 12.60101 0.02151 12.44949 0.03405 12.60101 0.04876 13.10505 0.01887 12.94747 0.03002 13.10505 0.04328 13.60909 0.01657 13.44545 0.02649 13.60909 0.03842 14.11313 0.01457 13.94343 0.02339 14.11313 0.03411 14.61717 0.01282 14.44141 0.02066 14.61717 0.03029 15.12121 0.01129 14.93939 0.01825 15.12121 0.02689 15.62525 0.00996 15.43737 0.01614 15.62525 0.02388 16.12929 0.00878 15.93535 0.01427 16.12929 0.02121 16.63333 0.00775 16.43333 0.01263 16.63333 0.01883 17.13737 0.00685 16.93131 0.01118 17.13737 0.01673 17.64141 0.00606 17.42929 0.0099 17.64141 0.01486 18.14545 0.00536 17.92727 0.00877 18.14545 0.0132 18.64949 0.00474 18.42525 0.00777 18.64949 0.01173 19.15353 0.0042 18.92323 0.00689 19.15354 0.01042 19.65757 0.00372 19.42121 0.0061 19.65758 0.00926 20.16162 0.0033 19.91919 0.00541 20.16162 0.00823 20.66566 0.00292 20.41717 0.0048 20.66566 0.00731 21.1697 0.00259 20.91515 0.00426 21.1697 0.0065 21.67374 0.0023 21.41313 0.00378 21.67374 0.00577 22.17778 0.00204 21.91111 0.00336 22.17778 0.00513 22.68182 0.00181 22.40909 0.00298 22.68182 0.00456 23.18586 0.00161 22.90707 0.00265 23.18586 0.00405 23.6899 0.00143 23.40505 0.00235 23.6899 0.0036 24.19394 0.00127 23.90303 0.00209 24.19394 0.0032 24.69798 0.00113 24.40101 0.00186 24.69798 0.00285 25.20202 0.001 24.89899 0.00165 25.20202 0.00253 25.70606 8.88674E-4 25.39697 0.00147 25.70606 0.00225 26.2101 7.89788E-4 25.89495 0.00131 26.2101 0.002 26.71414 7.01995E-4 26.39293 0.00116 26.71414 0.00178 27.21818 6.24034E-4 26.89091 0.00103 27.21818 0.00158 27.72222 5.54789E-4 27.38889 9.18001E-4 27.72222 0.00141 28.22626 4.93276E-4 27.88687 8.16609E-4 28.22626 0.00125 28.7303 4.38622E-4 28.38485 7.26496E-4 28.7303 0.00111 29.23434 3.90055E-4 28.88283 6.46396E-4 29.23434 9.88675E-4 29.73838 3.4689E-4 29.38081 5.75184E-4 29.73838 8.79208E-4 30.24242 3.08523E-4 29.87879 5.11865E-4 30.24242 7.81885E-4 30.74646 2.74417E-4 30.37677 4.55557E-4 30.74646 6.95355E-4 31.2505 2.44094E-4 30.87475 4.05477E-4 31.25051 6.18418E-4 31.75454 2.17133E-4 31.37273 3.60931E-4 31.75455 5.50008E-4 32.25859 1.93158E-4 31.87071 3.21302E-4 32.25859 4.89178E-4 32.76263 1.71838E-4 32.36869 2.86044E-4 32.76263 4.35087E-4 33.26667 1.52877E-4 32.86667 2.54672E-4 33.26667 3.86985E-4 33.77071 1.36013E-4 33.36465 2.26755E-4 33.77071 3.4421E-4 34.27475 1.21013E-4 33.86263 2.01909E-4 34.27475 3.06169E-4 34.77879 1.0767E-4 34.36061 1.79796E-4 34.77879 2.72339E-4

107

35.28283 9.58012E-5 34.85859 1.60113E-4 35.28283 2.42251E-4 35.78687 8.52427E-5 35.35657 1.42592E-4 35.78687 2.15492E-4 36.29091 7.58494E-5 35.85455 1.26993E-4 36.29091 1.91692E-4 36.79495 6.74926E-5 36.35253 1.13106E-4 36.79495 1.70524E-4 37.29899 6.00575E-5 36.85051 1.00742E-4 37.29899 1.51696E-4 37.80303 5.34424E-5 37.34848 8.97325E-5 37.80303 1.34949E-4 38.30707 4.75567E-5 37.84646 7.99291E-5 38.30707 1.20053E-4 38.81111 4.23197E-5 38.34444 7.11991E-5 38.81111 1.06803E-4 39.31515 3.76599E-5 38.84242 6.34247E-5 39.31515 9.5017E-5 39.81919 3.35135E-5 39.3404 5.65008E-5 39.81919 8.45327E-5 40.32323 2.9824E-5 39.83838 5.03342E-5 40.32323 7.52063E-5 40.82727 2.65409E-5 40.33636 4.48418E-5 40.82727 6.69098E-5 41.33131 2.36194E-5 40.83434 3.99497E-5 41.33131 5.95293E-5 41.83535 2.10196E-5 41.33232 3.55922E-5 41.83535 5.29635E-5 42.33939 1.87062E-5 41.8303 3.17106E-5 42.33939 4.71226E-5 42.84343 1.66474E-5 42.32828 2.8253E-5 42.84343 4.19262E-5 43.34747 1.48154E-5 42.82626 2.51728E-5 43.34747 3.73033E-5 43.85151 1.3185E-5 43.32424 2.24289E-5 43.85152 3.31905E-5 44.35556 1.17341E-5 43.82222 1.99844E-5 44.35556 2.95315E-5 44.8596 1.04429E-5 44.3202 1.78066E-5 44.8596 2.62761E-5 45.36364 9.29381E-6 44.81818 1.58663E-5 45.36364 2.33798E-5 45.86768 8.2712E-6 45.31616 1.41377E-5 45.86768 2.08029E-5 46.37172 7.36113E-6 45.81414 1.25976E-5 46.37172 1.85102E-5 46.87576 6.55121E-6 46.31212 1.12254E-5 46.87576 1.64704E-5 47.3798 5.83042E-6 46.8101 1.00028E-5 47.3798 1.46554E-5 47.88384 5.18895E-6 47.30808 8.91342E-6 47.88384 1.30406E-5 48.38788 4.61807E-6 47.80606 7.94278E-6 48.38788 1.16038E-5 48.89192 4.11E-6 48.30404 7.07791E-6 48.89192 1.03254E-5 49.39596 3.65783E-6 48.80202 6.30727E-6 49.39596 9.18784E-6 49.9 3.25542E-6 49.3 5.62059E-6 49.9 8.1757E-6

108

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