Hyperfine InteractDOI 10.1007/s10751-012-0670-z

Electrical conductivity, DSC, XRD, and 7Li NMRstudies of rotator crystals n-C21H43COOLixK(1−x)

(0.33 ≤ x ≤ 0.50), n-CmH(2m+1)COOLi,and n-CmH(2m+1)COOK (m = 13, 15, 17, 19, and 21)

Tomoyuki Hayasaki · Hisashi Honda ·Satoru Hirakawa

© Springer Science+Business Media Dordrecht 2012

Abstract Differential scanning calorimetry (DSC) thermograms, X-ray diffraction(XRD) analysis, electrical conductivity (σ ), and 7Li NMR spectroscopy characteriza-tion of n-CmH(2m+1)COOM solids (M = Li, Na, K; m = 13, 15, 17, 19, 21) and mixedcrystals n-C21H43COOLixK(1−x) (0.25 ≤ x ≤ 0.75) was performed as a function oftemperature. DSC thermograms of n-CmH(2m+1)COOM revealed several solid-solidphase transitions with large entropy changes. Electrical conductivity studies estab-lished that n-CmH(2m+1)COOLi crystals are poor electrical conductors. In contrast,n-CmH(2m+1)COOK salts were found to have σ values of 10−7–10−8 S·cm−1. Since thecrystal structures and phase-transition temperatures of both n-CmH(2m+1)COOLi andn-CmH(2m+1)COOK crystals were similar, they were able to form mixed crystals withthe structure n-CxH(2m+1)COOLixK(1−x). DSC thermograms of the mixed crystalsshowed a small entropy change at the melting point (�Smp < 13 J K−1 mol−1), inaddition, large �S values at the solid-solid phase transition temperature. The σ

values obtained for mixed crystals were roughly one order of magnitude greaterthan those determined for n-C21H43COOK crystals. 7Li NMR spectra of the mixedcrystals recorded at various temperatures suggested that the self-diffusion of Li+ ionswas excited in the highest-temperature solid phase. Based on these results, we haveclassified these mixed crystals as rotator crystals.

Keywords Rotator phase · Ion conductor · 7Li NMR · Mixed crystal

T. Hayasaki · H. Honda (B)Graduate School of Nanobioscience, Yokohama City University,Kanazawa-ku, Yokohama, 236-0027, Japane-mail: hhonda@yokohama-cu.ac.jp

T. Hayasaki · H. Honda · S. HirakawaInternational College of Arts and Sciences, Yokohama City University,Kanazawa-ku, Yokohama, 236-0027, Japan

T. Hayasaki et al.

1 Introduction

Li ion cells are recently used for compact and high-energy density batteries of mobilecomputers and phones, etc. To further improve their safety and performance, mucheffort has been put into the development of new solid electrolytes to replace theorganic and polymer solvents currently employed in Li ion cells. One promisingcandidate arising from these investigations is ionic plastic crystals [1], in which ionicself-diffusion has been detected. In plastic-crystal phases, the molecular orientationis fused, meaning that small entropy changes are observed at each melting point(<20 J K−1 mol−1) [2] and large changes are detected at the phase transitiontemperature from low-temperature solid-phase to the plastic phase. MNO2 (whereM = K, Rb, Cs, Tl, or NH4) salts have been shown to form ionic plastic crystalswith high electrical conductivity [3–16]; in contrast, Li and Na salts exhibit no plasticphases [3, 17–24]. This difference is because the former contains a planer ion similarin size to the counter-ion that can undergo low-energy isotropic rotations in crystals.This structural requirement makes it difficult to prepare simple ionic plastic crystalsof LiX where X is an anion.

Rotator crystals are classified in the family of plastic crystals. Rotator phases arefrequently detected in salts that contain several long-chain molecular ions and amonoatomic counter ion [25–42]. In this phase, two-dimensional rotation about themolecular chain is found as well as two-dimensional translational self-diffusion. Inplastic-crystal phases, there is three-dimensional rotation of molecules; therefore,rotator crystals are called two-dimensional plastic-crystal. Thermodynamic prop-erties of rotator crystals is similar to plastic crystals, e.g. small and large entropychanges are detected at melting point and the phase transition temperature fromlow-temperature solid-phase to the rotator phase, respectively. In the example of n-CmH(2m+1)COOLi (where m = 7–18; hereafter abbreviated to CmLi), it is reportedthat some of the potential structures (12 < m ≤ 18) have rotator phases [43–45].Reported differential scanning calorimetry (DSC) measurements indicate that theentropy change at the melting point (�Smp) is smaller than the total entropy-change (�Stotal) detected at solid-solid phase transition temperatures above roomtemperature (�Smp = 28.43 < �Stotal = 38.37 J K−1 mol−1 for C15Li and �Smp =33.14 < �Stotal = 49.48 J K−1 mol−1 for C17Li). For C13Li, however, the oppositerelationship (�Smp = 27.67 > �Stotal = 17.9 J K−1 mol−1) has been reported [45].X-ray diffraction (XRD) spectra obtained at ambient temperature have revealedthat these crystals belong to the triclinic crystal system in the P1 space group,and that the n-alkyl chains are uniformly in the trans-conformation with the Li+ions forming a layer perpendicular to direction of long chains [44]. Infrared (IR)and 13C NMR spectra recorded at room temperature have provided informationabout the interactions among the longer n-alkyl chains of CmLi (m ≤ 18) [45].In contrast to CmLi, other rotator crystals of the form n-CyH(2y+1)NH3Cl (wherey ≥ 4) exhibit the relationship of �Smp < �Stotal and �Smp < 20 J K−1 mol−1

[42]. These n-alkylammonium halides salts have tetragonal crystal structures inthe rotator phase in which ionic self-diffusion has been detected using electricalconductivity and solid-state NMR characterization. These salts and CmLi compoundshave similar molecular structures, i.e., both compounds comprise an n-alkyl groupand a monoatomic ion, therefore, the CmLi crystals are also expected to exhibitionic conductivity. However, no data relating to the electrical conductivity of CmLi

DSC, XRD, and 7Li NMR studies of rotator crystals

crystals have yet been reported, prompting us to carry out in this study. In addition,because arachidic acid (n-C19H39COOH) and behenic acid (n-C21H41COOH) areeasily obtained commercially, we were able to synthesize and characterize C19Li andC21Li crystals as well. We considered CmLi species where 11 ≤ m ≤ 21 and m wasan odd number, as n-alkyl compounds frequently display even-odd effects [46–48].In addition, impurities in plastic crystals have often been found to increase electricalconductivity [1], and therefore, we also considered mixed crystals containing K saltsin this study. Hereafter, the mixed crystals of the form n-CmH(2m+1)COOLixK(1−x)

will be abbreviated to CmLixK(1−x) (0 < x < 1). In order to determine the ionicdynamics of Li+ ions, 7Li NMR measurements were also carried out. Since the7Li nucleus has a quadrupole moment, 7Li NMR spectroscopy is often employedto characterize Li+ dynamics in solid samples [17]. Additionally, DSC and XRDwere also employed to characterize the n-CmH(2m+1)COOK crystals, which arecomponents of the mixed crystals.

2 Experimental

CmLi (where m is an odd number from 11 to 21, inclusive) crystals were prepared us-ing the following protocol: n-CmH(2m+1)COOH and LiOH were separately dissolvedin ethanol at 70 ◦C and then mixed. The solution was maintained at this temperaturewith stirring overnight, followed by cooling to produce white CmLi crystals. Thecrude products were redissolved in ethanol at 70 ◦C and recrystallized to improve thepurity, then dried at 80 ◦C overnight. CmNa and CmK crystals were prepared usingthe same process, beginning with NaOH and KOH, respectively, instead of LiOH.

Mixed crystals of CmLixK(1−x) (0< x < 1) were prepared by combining CmLi andCmK in ethanol at 70 ◦C with stirring for 30 min. The solution was cooled slowlyto 10 ◦C to yield crystals, which were then dried in an oven at 80 ◦C for one day.The same preparation was attempted for CmLi and CmNa mixed crystals, but did notobtain usable product; XRD spectra of the product reveals peaks only for the startingmaterials, CmLi and CmNa.

DSC analysis was performed using a Shimadzu DSC-60 calorimeter with areference sample of Al2O3. The heating rate was maintained at 10 ◦C·min−1 forexperiments above room temperature. For those at low temperature, liquid nitrogenwas used to cool samples. From these results, we determined melting points (Tmp)

and some transition temperatures in solid phase as well as entropy changes at thesetransition temperatures.

Electrical conductivity measurements at 1 kHz were carried out from roomtemperature to just below Tmp employing a two-terminal method using an AndouAG-4303 LCR meter equipped with silver electrodes. The powdered sample waspressed into a disc 1 cm in diameter and ∼1 mm thick. XRD spectra of the powderedsamples at and above room temperature were obtained using a Rigaku RINT-2100 and Bruker D8 ADVANCE equipped with a Cu anticathode, respectively.Spectra were recorded using a scan range of 5∼50◦ with a step size of 0.02◦ at roomtemperature and at 0.01◦ in high temperature ranges.

7Li (I = 3/2) NMR spectra were recorded at 233.23 MHz using a Bruker Avance600 spectrometer (14.10 T). For 7Li MAS NMR measurements, a spinning rate of1 kHz was maintained throughout the free-induction-decay (FID) acquisition. The

T. Hayasaki et al.

10 20 30 40 50

2 / degree

C11Li

C13Li

C15Li

C17Li

C19Li

C21Li

10 20 30 40 50

2 / degree

C11K

C13K

C

C17K

C19K

C21K

15K

Fig. 1 XRD spectra of n-CmH(2m+1)COOLi (CmLi) and n-CmH(2m+1)COOK (CmK) observed atroom temperature

powdered samples were packed in a ZrO rotor with an outer diameter of 4.0 mm.Pulse sequences of 7Li were designed without a 1H decoupling pulse, and a recycletime of 5 s was employed. 7Li MAS NMR spectra were obtained through Fouriertransformation of FID signals recorded after a single pulse. Chemical shifts werecalibrated using an external reference of LiCl powder (δ = 0 ppm). 7Li NMR spectrain high temperature ranges were recorded using a JEOL CMX300 spectrometer(7.01 T). Samples were sealed in Pylex glass tubes with an outer diameter of 5.0 mm.

3 Results and discussion

XRD spectra of CmLi and CmK recorded at room temperature are shown inFig. 1. The spectra obtained for CmLi (where m = 11, 13, 15, 17) are in agreement

DSC, XRD, and 7Li NMR studies of rotator crystals

300 400 500

C11Li

C13Li

C15Li

C17Li

C19Li

C21Li

300 400 500

C13Na

C15Na

C17Na

300 400 500

T / KT / KT / K

C13K

C15K

C17K

C19K

C21K

Endothermic

200 300

(a) (b) (c) (d)

Fig. 2 DSC thermograms of n-CmH(2m+1)COOLi (CmLi), n-CmH(2m+1)COONa (CmNa), andn-CmH(2m+1)COOK (CmK) with heat process. a CmLi (below RT), b CmLi (above RT), c CmNa,d CmK

with previous reports [43], and the C19Li, C21Li, and C21K crystals yielded similarpatterns. These results suggest that CmLi (m = 11∼21) and C21K crystals have similarmolecular arrangements.

DSC thermograms of CmLi, CmNa, and CmK recorded above room temperatureand thermograms of CmLi recorded below the ambient temperature with heatprocess are shown in Fig. 2. The largest peak in each line, except that for C15Na, hasbeen set to unity. The variation appearing around 300 K in Fig. 2b–d and 200 K inFig. 2a is due to instrument noise. The symbols Ttr1, Ttr2, etc., are used to indicate thetransition temperatures in solid phases moving from higher to lower temperatures;Phase I, Phase II, etc., are used to designate the solid phases moving from higherto lower temperatures. Thermograms of CmLi (m = 11∼17) recorded above ambi-ent temperature show transition temperatures similar to those previously reported[43–45] as listed in Table 1.

In the previously reports, however, thermograms for C19Li, C21Li, and for CmLiat low temperatures have not been shown. In addition, no exothermic processeswere observed at temperatures just below Ttr1 as displayed in Fig. 2. Melting pointsdetermined for CmLi crystals (m = 11, 13, 15, 17, 19, 21) linearly decreased withincreasing carbon chain length, and the pre-melting transition temperatures (Ttr1)

of CmLi (m ≥ 13) also decreased (Fig. 2b). Based on this trend, we expected thatthe highest-temperature solid phase (Phase I), which is reported to be the rotatorphase [44], can be formed using CmLi (m ≥ 23). In contrast, the temperatures forTtr2 detected around 360 K showed the opposite dependence on Ttr1 and Tmp.Therefore, CmLi crystals (m ≥ 23) are interesting samples, but unfortunately, wecould not obtain n-CmH(2m+1)COOH (m ≥ 23) commercially. For C11Li, we found

T. Hayasaki et al.

Table 1 Melting andphasetransition temperaturesand entropy changes ofn-CmH(2m+1)COOLi

m This study Literature [45]

tr2 tr1 mp tr2 tr1 mp

Temperatures (K)13 354.3 490.9 499.8 363.10 484.90 502.1015 368.5 469.6 496.4 378.50 470.90 500.0017 375.9 458.9 493.5 387.70 463.30 499.7019 375.6 451.6 486.821 380.1 444.6 482.6

Entropy changes (J K−1 mol−1)13 4.8 1.2 26.7 5.30 12.60 27.6715 9.8 5.8 22.7 20.16 18.21 28.4317 10.7 8.8 23.2 21.45 28.03 33.1419 13.0 9.0 25.121 31.8 14.1 21.1

that Ttr1 accorded with Tmp, and Phase I disappeared, and therefore, we usedsamples of CmNa and CmK with m ≥ 13 in this study. Some phase transitions ofCmK crystals were recorded until melting points, as shown in Fig. 2d. The meltingtemperature of CmK exhibited a trend similar to that observed for CmLi but atslightly lower temperature. This fact suggests that attractive interactions between K+and n-alkylcarbonate ions are weaker and/or repulsion energies among the ions arelarger than those in the highest-temperature solid-phase of the CmLi crystals. Thispoint will be discussed in detail in a later section. Three phase transitions in solids forCmK (m ≤ 17) above room temperature were recorded in addition to one transitiondetected for CmK (m ≥ 19). The largest enthalpy change in CmK was observed atTtr3, which increased with the length of the carbon chain. The temperature rangearound 350 K corresponds to Ttr2 of CmLi. Based on these results, including that largeheat changes were detected at similar temperatures for Li and K compounds andthat their transition temperatures exhibited similar dependence on carbon length,we hypothesized that CmK crystals have similar thermodynamic properties as CmLicrystals. For CmNa, however, a more complex dependence on chain length wasobserved, especially for C15Na crystals, which decomposed at around 500 K withthe exothermic peak as shown in Fig. 2c. In addition, XRD analysis revealed thatCmNa formed no mixed crystals with CmLi. Therefore, we did not pursue any furthercharacterization of CmNa crystals in this study. The entropy changes associatedwith each phase transition for CmLi and CmK (13 ≤ m ≤ 21) are listed in Tables 1and 2, respectively. Some of the �S values for CmLi that we determined disagreewith those previously reported [45]. This difference may arise from the fact thatthe reported DSC thermograms have exothermic peaks just below Ttr1 with heatprocess [44, 45], while no such irregular signals were found in our thermograms ofCmLi. The experimentally obtained �Smp values of 21–27 J K−1 mol−1 are similarto those of previously reported rotator crystals [42]. However, the values for totalentropy changes in solid phase (�Str1 + �Str2) are smaller than �Smp except forC21Li; the results obtained for C21Li crystals satisfied the requirements of rotatorcrystals. If another transition associated with a large entropy change was detectedbelow room temperature, other CmLi compounds could also classified as rotatorcrystals. Therefore, DSC measurements from ∼200 K to ambient temperature werecarried out. However, as shown in Fig. 2a, the resulting thermograms revealed only

DSC, XRD, and 7Li NMR studies of rotator crystals

Table 2 Melting and phasetransition temperatures andentropy changes ofn-CmH(2m+1)COOK

m Temperatures (K) Entropy changes(J K −1mol−1)

Ttr3 Ttr2 Ttr1 Tmp �Str3 �Str2 �Str1 �Smp

13 334.5 405.6 414.7 481.6 49.7 3.0 3.515 338.0 405.1 417.6 467.2 50.8 3.6 6.3 19.817 344.6 404.2 422.2 459.9 54.9 4.1 7.0 25.419 345.6 404.2 423.8 456.7 60.1 4.4 7.0 30.421 357.5 402.1 424.3 445.2 48.3 4.1 6.6 30.8

Fig. 3 Electrical conductivitiesof n-C15H31COOKi(C15K)(�), n-C17H35COOKi(C17K) (�) andn-C21H42COOK (C21K) (�)as a function of temperature

2.3 2.4 2.5 2.6

10-8

10-7

103T -1 / K-1

/ S

cm-1

390430 410T / K

C21K

C17K

C15K

minor heat changes. In contrast, large total entropy changes (�Str1 + �Str2 + �Str3)

as compared to �Smp were observed for CmK crystals, as shown in Fig. 2d andTable 2. These results suggest that ionic motions with a large degree of freedomwere excited in solid phases above 360 K.

In order to detect ionic diffusion in solid phases of CmLi and CmK, electricalconductivity measurements were performed. For CmLi (13 ≤ m ≤ 21), our LCRmeter measured large resistances greater than 10 M� over the whole temperaturerange except at each melting point. In contrast, the CmK crystals exhibited smallresistances above room temperature. The experimentally-determined σ values forC17K and C21K crystals as a function of temperature are shown in Fig. 3. Uponheating, the σ values measured for C15K, C17K and C21K reached ∼1 × 10−8, 3 × 10−8

and 2 × 10−7 S cm−1, respectively. In a case of C19K, large resistances were obtained.The results of DSC analysis of C21Li crystals provided the needed information toclassify them as rotator crystals, but the very small σ values measured over the wholetemperature range except for the melting points were unexpected.

In order to investigate the cationic motions in the C21Li crystals, 7Li NMR analysiswas carried out. Line shapes characteristic of quadrupole interactions were observedat room temperature, as shown in Fig. 4a. Since 7Li nuclei have a spin of 3/2,the central peak observed at 0 ppm and the satellite lines around ±40 ppm areassignable to the transitions between spins of 1/2 and −1/2 and between ±3/2 and±1/2, respectively. The central transition signal was fitted using a Lorentzian function

T. Hayasaki et al.

Fig. 4 7Li NMR spectra ofn-C21H43COOLi observed atroom temperature andsimulated curves. a The staticspectrum obtained without a1H-decouplingpulse-sequence. b Theoreticalcurves convoluted using aLorentzian function with ahalf-height width of 1.2 kHz.This line shape gives e2Qqh−1

of 60.6 kHz and η of 0.38.c MAS speed of 1 kHz with1H-decoupling pulses. d MASrate of 1 kHz without1H-decoupling pulses

-1000100Chemical Shift / ppm

Static

MAS : 1 KHz

MAS : 1 KHz

Theoretical Curves

with 1H Decoupling

without 1H Decoupling

(a)

(b)

(c)

(d)

with 1.2 kHz of full line-width at a half-height of the peak. This value enabled thesimulation of the line shape of the satellites peaks by theoretical curves convolutedby Lorentzian broadening. The theoretical curves yielded a quadrupole couplingconstant (e2Qqh−1) of 60.6 kHz and an asymmetry parameter (η) of 0.33, as shownin Fig. 4b. The spectrum was modified using a magic-angle-spinning (MAS) ratio of1 kHz with a 1H decoupling pulse-sequence, as shown in Fig. 4c. In contrast, when nodecoupling pulses were employed, line shapes similar to those observed in the staticspectrum (Fig. 4a) were obtained as displayed in Fig. 4d. This result suggests thatthe line-width of 1.2 kHz was largely caused by 1H–7Li dipole-dipole coupling. Thisinteraction can be described by the following equation.

�ν = γ7Liγ1H

πr3 �

Here, �ν, γ , and r are the full line-width at half-height of the peak, the gyromagneticratio of each nucleus, and the average distance between Li+ ions and H atoms in acrystal, respectively. Substituting 1.2 kHz for �ν in the equation yields r = 498 pm.This length is similar to the distance between Li+ cations and H atoms bonded to theα-carbon of n-alkyl carbonate in the crystal. Therefore, we concluded that the Li+ions are localized in the solid phase at room temperature.

In general, impurities in a sample increase electrical conductivity. Since the C21Kcrystals exhibited the highest σ value measured in this study, and DSC analysis

DSC, XRD, and 7Li NMR studies of rotator crystals

Fig. 5 XRD spectra ofn-C21H43COOLixK(1−x)

(C21LixK(1−x))

10 20 30 40 50

2 / degree

C21Li

C21Li0.67K0.33

C21Li0.6K0.4

C21Li0.5K0.5

C21Li0.4K0.6

C21Li0.33K0.67

C21K

indicated that the n-alkyl carbonate ions move with a large degree of freedom inboth C21K and C21Li crystals, we anticipated even higher electrical conductivity inmixed crystals of C21Li and C21K. In addition, XRD spectra of both samples revealedsimilar crystal structures, as shown in Fig. 1. Therefore, mixed crystals of C21LixK(1−x)

were prepared. XRD spectra obtained for the mixed crystals are shown in Fig. 5,where the highest count in each graph has been scaled to unity. Some of thesediffraction patterns recorded in the 20∼25◦ range revealed that the mixed crystalswere produced in molar ratios such that 0.25 ≤ x ≤ 0.60 in C21LixK(1−x).

Results of DSC analysis are shown in Fig. 6, where the most strength peak ineach thermogram has been normalized; variation observed around 300 K is due toinstrument noise. Based on the fact that new phase transitions were detected in themixed crystals, it can be concluded that mixed crystals of the C21LixK(1−x) structureare successfully obtained. In samples where x = 0.60 and 0.67, exothermic peaks wereobserved at ∼430 K with heat process. This temperature is just above the meltingtemperatures observed for the other mixed crystals characterized, suggesting thatthe endothermic peak observed just below this exothermic signal in C21Li0.60K0.40

and C21Li0.67K0.36 crystals could not be identified as either a melting point or solid-solid transition. Large enthalpy changes observed at ∼380 K in C21LixK(1−x) where0.25 ≤ x ≤ 0.50 suggested that mixed crystals of this composition were successfullyproduced, as no phase transition at this temperature was detected for the starting

T. Hayasaki et al.

Fig. 6 DSC thermograms ofn-C21H43COOLixK(1−x)

(C21LixK(1−x)) with heatprocess

300 350 400 450 500T / K

C21Li

C21Li0.25K0.75

C21Li0.33K0.67

C21Li0.40K0.60

C21Li0.50K0.50

C21K

C21Li0.67K0.33

C21Li0.60K0.40

Table 3 Melting andphasetransition temperaturesand entropy changes ofn-C21H43COOLixK(1−x)

x Temperatures (K) Entropies (J K−1mol−1)

Ttr3 Ttr2 Ttr1 Tmp �Str3 �Str2 �Str1 �Smp

0.25 369.2 380.2 403.8 413.8 3.6 32.4 13.6 4.60.33 369.6 381.0 401.5 423.5 5.0 39.2 24.9 5.50.40 369.1 380.4 402.7 423.2 3.2 33.0 28.0 5.00.50 368.9 381.0 404.0 426.8 2.9 27.8 35.5 9.70.60 365.5 398.6 404.0 426.6 13.0 13.7 34.0 12.20.67 365.7 398.9 404.4 427.2 15.4 24.6 14.1 7.7

material (CmLi and CmK crystals). Hereafter, Ttr1 and Ttr2 will be used to indicate thephase transition temperatures around 405 and 380 K, respectively. Since additionalendothermic peaks observed just below Ttr1 of C21Li0.25K0.75, C21Li0.33K0.67, andC21Li0.40K0.60 crystals were very small, we did not characterize them further. Anadditional transition for C21Li0.33K0.67 was observed at 415.2 K with an associatedentropy change of �S = 20.4 J K−1mol−1. Entropy changes estimated for Ttr1, Ttr2,and melting temperatures are listed in Table 3. That �Str2 was greater than �Smp

suggests that some motions with large degrees of freedom were excited in Phases Iand II. Based on the facts that �Smp < 20 J mol−1K−1 and �Smp < (�Str1 + �Str2),we can conclude that Phase I and/or Phase II are rotator phases.

DSC, XRD, and 7Li NMR studies of rotator crystals

Fig. 7 Electrical conductivityof n-C21H43COOLixK(1−x)

(C21LixK(1−x)) as function oftemperature: x = 0.50 (�),0.40 (�), 0.33 (�), 0.25 (�),and n-C21H42COOK(C21K) (×)

2.3 2.4 2.5 2.6 2.7 2.8

10-8

10-7

10-6

103T -1 / K-1

/ S

cm-1

420 400 380 360

T / K

C21Li0.50K0.50 C21Li0.40K0.60 C21Li0.33K0.67 C21Li0.25K0.75 C21K

In order to detect ionic diffusion, the temperature dependence of electricalconductivity was characterized. The results obtained are plotted in Fig. 7, whichreveals higher σ values for the mixed crystals as compared with C21K; as anticipated,C21Li exhibited a large resistance over 10 M�. The C21Li0.33K0.67 crystals particularlyelectrifies 1 order comparing with C21K. The discontinuity of σ values recordedaround 380 and 402 K corresponds with the phase-transition temperatures of Ttr2

and Ttr1. By plotting ln(σ T) versus T−1, activation energies of 25.3, 93.4, 41.4, and30.8 kJ mol−1 were determined for C21LixK(1−x) where x = 0.25, 0.33, 0.40, and 0.50,respectively. These are similar to reported activation energy values for rotator andisotropic plastic crystals [42].

In order to obtain information about the molecular dynamics in the crystals, 7LiNMR measurements were carried out. A MAS rate of 1 kHz was used even thoughthe use of high speed spinning is known to reduce the first order interaction ofquadrupole coupling. Our apparatus, unfortunately, requires that a non-zero MASrate be used in order to allow control over sample temperature. The 7Li MAS NMRspectrum of the C21Li crystals obtained using a spinning rate of 1 kHz without 1Hdecoupling pulse exhibited the same line shapes as the static spectrum demonstratedin Fig. 4, and so we applied this method to the mixed crystals. 7Li NMR spectra ofthe mixed crystals obtained at room temperature show characteristic indications ofquadrupole interactions (Fig. 8).

The line width of the central transition was independent of temperature belowTtr2 except for C21Li0.25K0.75 crystals, although the peak difference between thesatellite signals (�ν) decreased with increasing temperature. This result suggeststhat the dipole-dipole interactions between 7Li and 1H nucleus occurred in PhaseIII of the C21LixK(1−x) crystals where 0.33 ≤ x ≤ 0.50. The half-height line-widthwas estimated as 1.2 kHz from the central transition signal. Employing this value,the line simulation of satellite signals using a Lorentzian function gave the e2Qqh−1

and η values listed in Table 4. The trend of decreasing e2Qqh−1 and η values withincreasing temperature may arise from thermal vibrations by which the EFG valuesat the 7Li nucleus in mixed crystals are averaged. Above Ttr2, at which the largest

T. Hayasaki et al.

-1000100

C21Li 0.40K0.60 C21Li 0.50K0.50C21Li 0.25K0.75 C21Li 0.33K0.67

-1000100-1000100

Chemical Shift / ppm

-1000100

298 K

378 K

393 K

Fig. 8 7Li MAS NMR spectra of n-C21H43COO LixK(1−x) (C21LixK(1−x)) observed at 233.23 MHzwith MAS speed of 1 kHz

Table 4 Quadrupole couplingconstants (e2Qqh−1) andasymmetry parameters (η)

obtained from 7Li MAS NMRspectra ofn-C21H43COOLixK(1−x)

T (K) e2Qqh−1 η T (K) e2Qqh−1 η

(kHz) (kHz)

x = 0.25 x = 0.33298 51.3 0.38 298 53.6 0.50378 37.3 0.33 378 39.6 0.36393 – – 393 32.6 0.33

x = 0.40 x = 0.50298 56.0 0.47 298 46.6 0.50378 42.0 0.45 378 37.3 0.40393 30.3 0.33 393 32.6 0.33

entropy change is detected for each mixed crystal, a component giving rise to anarrow line width appeared on the central signal of each 7Li MAS NMR spectrum.Because this component did not produce any satellite peaks, we propose that theEFG anisotropy of the Li+ ion was averaged by ionic motions (in other words, thatthe quadrupole interaction was dynamically averaged out), and/or the Li+ ions werelocated at a site that gave statistically equivalent EFG values as the xx, yy, and zzcomponents. In order to better understand the crystal structure in Phase II, XRDanalysis at some temperatures was carried out. The resulting spectra revealed thatonly minor changes in crystal structures occurred after the phase transition at Ttr2,as shown in Fig. 9. Based on this result, we concluded that the component givingthe sharp signal is assignable to diffusing Li+ ions, consistent with our conductivityresults showing that σ values increased from Phase II (Fig. 7).

DSC, XRD, and 7Li NMR studies of rotator crystals

0 10 20 30 40 50 60

300 K

390 K

410 K

C21Li0.33K0.67

0 10 20 30 40 50 60

300 K

390 K

410 K

C21Li0.40K0.60

0 10 20 30 40 50 60

300 K

390 K

410 K

C21Li0.50K0.50

0 10 20 30 40 50 602 / degree

300 K

390 K

400 K

410 K

C21Li0.67K0.33

0 10 20 30 40 50 60

300 K

390 K

410 K

C21Li0.60K0.40

2 / degree 2 / degree

2 / degree 2 / degree

Fig. 9 Temperature dependence of XRD spectra of n-C21H43COOLixK(1−x) (C21LixK(1−x))

T. Hayasaki et al.

4 Conclusion

Using DSC, XRD, electrical conductivity, and 7Li NMR, we characterized mixedcrystals with the structure C21LixK(1−x) (0 < x < 1) and CmLi and CmK crystals wherem = 13, 15, 17, 19, 21. CmLi (m = 13, 15, 17) crystals exhibited similar transitiontemperatures and crystal structures, as assessed using DSC and XRD, as thosepublished in the literature [43–45]; however, our DSC thermograms did not exhibitany exothermic error peaks with heat process. The entropy changes �Smp observedat the melting points were larger than the total entropy changes �Stotal betweensolid phases, except in C21Li crystals. Electrical conductivity measurements revealedthat CmLi crystals were poor conductors, while the analysis of C21K crystals yieldedσ values of ∼2 × 10−7 S·cm−1. Crystal structures and phase transition patterns ofCmK and CmLi were similar to one another but dissimilar enough from CmNa suchthat CmLi/CmK mixed crystals could be obtained but neither compound would formmixed crystals with CmNa. DSC thermograms of C21LixK(1−x) crystals revealed someendothermic peaks. A small entropy change (�Smp < 20 J K−1 mol−1) at the meltingtemperatures and large �S values were obtained at the solid-solid phase transition.In addition, self-diffusion of Li+ ions was detected using electrical conductivity and7Li NMR spectral analysis. These results suggest that the C21LixK(1−x) mixed crystalsare rotator crystals.

Acknowledgements The authors are grateful to Prof. M. Tadokoro of Tokyo University of Sciencefor the use of the CMX300 spectrometer. This work was partly supported by a Grant-in-Aid forScientific Research (23550230) from the Japan Society for the Promotion of Science.

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