electrochemical impedance of mercury electrodes with hematite particles adhered

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Journal of Adhesion Scienceand TechnologyPublication details including instructions forauthors and subscription informationhttpwwwtandfonlinecomloitast20

Electrochemical impedanceof mercury electrodes withhematite particles adheredEstela Mariacutea Andrade a amp Fernando Viacutector Molina ba INQUIMAE mdash Departamento de QuiacutemicaInorgaacutenica Analiacutetica y Quiacutemica Fiacutesica Facultadde Ciencias Exactas y Naturales UBA CiudadUniversitaria Pabelloacuten II C1428EHA Buenos AiresArgentinab INQUIMAE mdash Departamento de QuiacutemicaInorgaacutenica Analiacutetica y Quiacutemica Fiacutesica Facultadde Ciencias Exactas y Naturales UBA CiudadUniversitaria Pabelloacuten II C1428EHA Buenos AiresArgentinaPublished online 02 Apr 2012

To cite this article Estela Mariacutea Andrade amp Fernando Viacutector Molina (2001)Electrochemical impedance of mercury electrodes with hematite particlesadhered Journal of Adhesion Science and Technology 1512 1503-1510 DOI101163156856101753213330

To link to this article httpdxdoiorg101163156856101753213330

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or suitability for any purpose of the Content Any opinions and viewsexpressed in this publication are the opinions and views of the authors andare not the views of or endorsed by Taylor amp Francis The accuracy of theContent should not be relied upon and should be independently verifiedwith primary sources of information Taylor and Francis shall not be liablefor any losses actions claims proceedings demands costs expensesdamages and other liabilities whatsoever or howsoever caused arisingdirectly or indirectly in connection with in relation to or arising out of theuse of the Content

This article may be used for research teaching and private studypurposes Any substantial or systematic reproduction redistributionreselling loan sub-licensing systematic supply or distribution in any formto anyone is expressly forbidden Terms amp Conditions of access and use canbe found at httpwwwtandfonlinecompageterms-and-conditions

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J Adhesion Sci Technol Vol 15 No 12 pp 1503ndash1510 (2001)Oacute VSP 2001

Communication

Electrochemical impedance of mercury electrodes withhematite particles adhered

ESTELA MARIacuteA ANDRADE and FERNANDO VIacuteCTOR MOLINA curren

INQUIMAE mdash Departamento de Quiacutemica Inorgaacutenica Analiacutetica y Quiacutemica Fiacutesica Facultad deCiencias Exactas y Naturales UBA Ciudad Universitaria Pabelloacuten II C1428EHABuenos Aires Argentina

Received in nal form 30 May 2001

AbstractmdashThe effect of hematite particles adhesion on the electrochemical impedance of mercuryelectrodes was studied at different electrode potentials The impedance decreases as the number ofattached particles increases this impedance decrease is related to strong adhesion of particles Theimpedance diagrams show in the low frequency range the presence of a constant phase element(CPE) with an exponent of ca 05 The experimental results are analyzed in terms of an equivalentcircuit including the CPE The magnitude of this CPE is directly related to the coverage of theelectrode A qualitative interpretation for this behavior when an AC signal is applied is proposedin terms of a pore model for the metal hematite particles interphase

Keywords Particle adhesion electrochemical impedance hematite equivalent circuit pore model

1 INTRODUCTION

The adhesion of colloidal particles to metallic surfaces is relevant to many appli-cations such as corrosion protection sintering catalyst preparation drug manufac-turing biofouling and semiconductor technology However it has not receivedenough attention from a fundamental point of view [1]

In our group we have studied the adhesion of colloidal particles to metallicsurfaces under potentiostatic conditions [2ndash5] In this way the potential or chargeof both surfaces can be controlled independently the metallic surface potentialis externally controlled whereas the particle charge is xed through adjustmentof solution pH The number of attached particles as a function of the electrodepotential has a minimum near the metal zero charge potential Ez then it increasestowards anodic and cathodic potentials (implying that in some conditions the

currenTo whom correspondence should be addressed Fax +54-11 4576-3341 E-mail fmolinaq1fcenubaar

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1504 E M Andrade and F V Molina

adhesion occurs even when both surface charges have the same sign) The electrodedifferential capacitance Ceq (considering an RC series circuit) shows a signi cantincrease upon particle attachment This suggests that both surfaces come into closecontact and the colloidal particles are polarized in the process These resultscannot be analyzed in terms of the DLVO theory alone [2] and it is necessaryto take into account other kinds of interactions as has been pointed out forparticle metal adhesion in air [6] In Ref [2] a linear relationship was foundbetween the surface coverage and Ceq The slope was found to be frequencydependent Thus it is interesting to investigate the electrochemical impedance ofthese interfaces Electrochemical impedance is a technique which has often beenemployed to characterize adhesion onto metallic surfaces of different deposits suchas protective coatings [7 8] scale deposits [9] deposits on heat exchangers [10]macromolecule deposits [11] porous electrodes [12] and blocking electrodes [13]Again relatively few papers deal with fundamental aspects

In order to analyze from a fundamental point of view the response to AC potentialperturbations of metallic surfaces with particles adhered we have investigatedin this work the electrochemical impedance of mercury electrodes with colloidalhematite particles adhered for different electrode potentials Mercury was chosenas the metallic surface because it is a liquid metal so that it is free of surface defectsand inhomogeneities On the other hand hematite particles were employed becauseit is a well known material and its adhesion to mercury has been already studied[2ndash5]

2 EXPERIMENTAL

Colloidal hematite was synthesized and characterized in our laboratory as describedelsewhere [2 14] Approximately-cubic particles of 1 sup1m3 were obtained Theirisoelectric point pH0 was 74 All the reagents used were analytical gradeand ultrapure water was obtained from a Millipore MilliQ apparatus A three-compartment cell was employed each having the working reference and auxiliaryelectrodes The working electrode was a silver disc of 05 mm diameter On ita mercury lm was electrodeposited as described in Ref [2] A saturated calomelelectrode (SCE)was used as reference and all the potentials in this work are referredto it The auxiliary electrode was a platinum foil A PAR 388 impedance systemwas employed in the measurements The impedance results were analyzed using theEQUIVCRT program [15] The deposits were observed using a Leika microscopemodel DM-RX having a video camera connected to a Pentium PC-compatiblecomputer which was equipped with a video frame grabber card

Hematite particles were allowed to deposit onto the mercury lm electrodes from80-mg l suspensions in 001 M NaClO4 at pH D 54 The depositions lasted 30 minat a constant electrode potential between iexcl03 and iexcl10 V At the end of this timeperiod the electrochemical impedance was measured with an AC amplitude of10 mV at frequencies ordm between 01 and 10 000 Hz (lack of long term stability

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Impedance of mercury with hematite adhered 1505

precluded measurements at lower frequencies) Finally the cell was turned upsidedown to change the electrode position from face up to face down to remove particleswhich were not adhered The electrode was then removed from the cell (withapplied potential) rinsed and dried Video images of the deposits were obtainedand processed using image analysis software obtaining the degree of coverage micro

3 RESULTS AND DISCUSSION

Figure 1 shows micro as a function of electrode potential These results are consistentwith the previous work [2] showing a maximum micro of 038 at iexcl09 V and a minimumof 015 at iexcl04 V Figure 2 shows the Nyquist and Bode diagrams correspondingto hematite deposits onto mercury lm at several potentials It can be observedthat the impedance values are lower as the number of attached particles is higher

Figure 1 Degree of coverage (micro ) of mercury electrodes by adhered hematite particles as a functionof electrode potential 80 mg l hematite in 001 M NaClO4 pH 54

(a) (b)

Figure 2 Nyquist diagrams (a) and Bode plots (b) of the impedance of hematite covered mercuryelectrodes at different potentials Same conditions as in Fig 1

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Figure 3 Calculated metal-particle capacitance (CMP continuous curve) as a function of electrodepotential (referred to Ez) for hematitemercury interphase The calculation was done for the sameconditions as of data in Fig 1 Magnitude of the constant phase element QY0 squares) as a functionof electrode potential (also referred to Ez) obtained by tting the data in Fig 2 to the equivalent circuitshown in the inset (see text for details)

(at iexcl09 V) This agrees with the previous results where the series capacitance(interpreting the AC response in terms of a series RC circuit) rose with micro [2] Theseimpedance curves show an asymptotic behavior towards a straight line of unity slopeat low frequencies This type of behavior has been observed in the case of partiallyblocked [16] porous [12] or rough electrodes [13] It can be electrically representedusing a constant phase element (CPE) whose admittance Y is

Y D Y0jreg (1)

where Y0 is the magnitude of the CPE is the angular frequency j D iexcl11=2and reg is an exponent which has been related to surface characteristics [17] Aunity slope in the Nyquist diagrams means reg D 05 which can be related amongother interpretations to a porous electrode [18] or diffusional transport (Warburgimpedance [19])

The impedance measurements corresponding to the particles modi ed electrodeaqueous suspension interphase can be modeled by the circuit shown in the insetof Fig 3 Here RS represents the uncompensated suspension resistance C is thecapacitance corresponding to the metal double layer without particles attached Q

is the constant phase element associated with the deposited particles and RP is aseries resistance related to the current path between the particle solution interphaseand the solution bulk

The experimental data can be tted to the above mentioned circuit yielding C RP

and Y0 values which depend on the degree of coverage In this case at a givenelectrode potential Y0 is approximately proportional to micro whereas C is proportionalto 1 iexcl micro Thus the electrochemical impedance can be employed to evaluate thesurface coverage by colloidal particles

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On the other hand coverage independent values can be obtained by consideringthe total impedance as given by

Z D RS C1

1 iexcl microjCdl iexclmicro

RP C1Y

(2)

where Cdl is the double layer differential capacitance of the free mercury electrodeand RP C1=Y is the impedance of the fully covered electrode The tting procedureyields Cdl value of 16ndash20 sup1Fcm2 which is within the experimental uncertaintycoincident with the differential capacitance of the mercury electrode in the presenceof a non-speci cally adsorbing electrolyte The RP values show a slight potentialdependence ranging between 90 and 120 Auml cm2

Y0 on the other hand is found to be potential dependent as shown in Fig 3(squares) as a function of E iexcl Ez where E is the applied potential and Ez isthe metal zero charge potential For the present conditions Ez

raquoD iexcl06 V Itis observed also that Y0 has rather high values This is in agreement with thehigh capacitance values found when the AC response is interpreted in terms of anRC series circuit [2] This implies a close contact between the particle and themetal Otherwise the mercurywater inner layer capacitance would limit the totalimpedance causing slight or no decrease of the impedance Thus the impedancedecrease is indicative of strong adhesion

The CPE behavior extending to very low frequencies is the most striking featureof the experimental results A diffusional origin (Warburg impedance) should bediscarded as no net reaction is taking place so that the CPE behavior shouldbe attributed to surface effects such as roughness inhomogeneities porosity etcUsually a slope increase at low frequencies is observed the impedance becomingnearly capacitive because the mentioned surface effects have a range of spatialdimensions yielding high and low cut-off frequencies [16] A lower cut-offfrequency is not observed here at least up to the lowest frequency studied (01 Hz)However mercury being a liquid surface inhomogeneities and roughness can beneglected We will show now that the results can be interpreted in terms of a poremodel

As discussed above the impedance decrease upon particle adhesion implies arather close contact between the particle and the metal Thus the metal particlecapacitance should have a signi cant in uence on the results This capacitancecan be estimated as follows Recently [20] a model for the ionic equilibria atthe particle solution and metal particle interphases was proposed to explain thebehavior of this system The metal particle interphase can be regarded for smallpotential changes as having a differential capacitance given by

CMP Dfrac34M

AtildeD iexcl

frac34ef

Atilde (3)

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where frac34 M is the metal charge Atilde is the metal potential and frac34 ef is the effective chargeon the hematite particle which originates from two contributions the total charge(determined by the acidndashbase constants of the oxide surface) and the charge of theadsorbed ions (given by the ionndashsurface association constants) Using the treatmentof Ref [20] it is possible to evaluate the metal particle interphase charge and thusthe capacitance as a function of electrode potential In Fig 3 (continuous line) thecalculated curve CMP vs E iexcl Ez at pH 54 is plotted It shows a minimum near theEz The capacitance at this minimum is of the same order as the mercury solutioncapacitance and it rises at both anodic and cathodic potentials This increase iscaused by the charge accumulation in the metal particle interphase due to thepolarization of the particle under the metal electric eld The Y0 values show abehavior roughly similar to CMP suggesting that the metal particle capacitance hasa signi cant in uence on the overall response

The above considerations mean that the metal particle interphase should bein some way connected to the solution bulk because when the metal potentialis varied the charge of the metal particle interphase should also change to re-establish the ionic equilibria in the interphase The ions must travel to or fromthe solution along the interphase between the plane surface of the liquid mercuryand the hematite particle Scanning tunneling microscopy [21] and atomic forcemicroscopy [22] studies have shown that hematite surfaces have periodicities ofabout 03ndash05 nm These irregularities (due to Fe vacancies on the surface) mayform channels allowing ions to travel along the interphase We will thus assumethat the metal particle interphase behaves as a set of pores parallel to the surfaceAccording to De Levie [18] the impedance Z0 of a pore of radius a length lresistance per unit length Rl and capacitance per unit length Cl is given by

Z0 D 1 iexcl j

sRl

2Cl

coth

sup31 C j l

rRlCl

2

acute (4)

which gives a CPE response with reg D 05 if the hyperbolic cotangent factorapproaches unity Here Rl and Cl can be expressed as

Rl D 1

middotfrac14plusmna

2

sup22 (5)

Cl D CMPa (6)

where CMP is the metal particle capacitance per unit area and middot the solutionconductivity within the pore It is very dif cult to estimate ion mobilities insubnanometer pores Recently several workers studied ion transport in Gramicidin-like channels of 04 nm diameter and found that the diffusion coef cients decreasedby about two orders of magnitude from the bulk water value [23] Thus we canroughly estimate for a 001 M solution with a single ion moving along the porethat middot raquoD 5 pound 10iexcl6 Scm and taking a D 02 nm and l D 1 sup1m it is found that for

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D 063 Hz (ordm D 01 Hz)

shyshyshyshycoth

sup31 C j l

rRlCl

2

acuteshyshyshyshyfrac14 098

Thus we can approximate the pore impedance as

Z0 frac14 1 iexcl j

sRl

2Cl

D

sRl

Cl

1j05

(7)

in the full range of frequencies employed here The magnitude Y0 in (1) can then beexpressed as

Y0 D1

Aef

sCl

Rl

D1

Aef

rCMPa3middotfrac14

4 (8)

where Aef is the effective surface area per pore It should be noted here that the poresare actually present along the particle perimeter so that Aef is not the actual poresurface area Using for Y0 and CMP the values presented in Fig 3 Aef is estimated as47pound10iexcl14 cm2 which is a reasonable value being greater than the model pore area(raquo4pound10iexcl16 cm2 ) but much smaller than the particle area (10iexcl8 cm2 ) Unfortunatelydue to lack of information mainly on ion migration within subnanometer channelsno further quantitative treatments can be done Based on the above considerationsthe AC electrical response of a mercuryhematite particles interphase can inprinciple be interpreted in terms of a porous structure parallel to the metal surface

4 CONCLUSIONS

The AC electrochemical impedance of mercury electrodes with hematite particlesadhered decreases as the degree of coverage increases This impedance decreaseindicates a close contact between the particles and the metal surface In the lowfrequency limit the impedance shows a behavior corresponding to a constant phaseelement This behavior is consistent with a pore model for the metal particleinterphase

Acknowledgements

Financial support from the University of Buenos Aires (project AX37) the AgenciaNacional de Promocioacuten Cientiacute ca y Tecnoloacutegica (project PICT98 06-04012) andthe Consejo Nacional de Investigaciones Cientiacute cas y Teacutecnicas (CONICET projectPIP 0449) is gratefully acknowledged F V M is a permanent staff member ofCONICET

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REFERENCES

1 E M Andrade and F V Molina in Encyclopediaof Surfaceand Colloid Science A T Hubbard(Ed) Marcel Dekker New York (in press)

2 E M Andrade F V Molina and D Posadas J Colloid Interface Sci 165 450ndash458 (1994)3 E M Andrade F V Molina G J Gordillo and D Posadas J Colloid Interface Sci 165

459ndash466 (1994)4 E M Andrade F V Molina G J Gordillo and D Posadas J Colloid Interface Sci 173

231ndash235 (1995)5 E M Andrade F V Molina and D Posadas J Colloid Interface Sci 176 495ndash497 (1995)6 R A Bowling in Particles on Surfaces 1 Detection Adhesion and Removal K L Mittal

(Ed) pp 129ndash142 Plenum Press New York (1988)7 F De orian and L Fedrizzi J Adhesion Sci Technol 13 629ndash645 (1999)8 J E G Gonzalez and J C Mirza Rosca J Adhesion Sci Technol 13 379ndash391 (1999)9 C Deslouis C Gabrielli M Keddam A Khalil R Rosset B Tribollet and M Zidoune

Electrochim Acta 42 1219ndash1233 (1997)10 J Abellaacute J Barceloacute and L Victori Corrosion Sci 40 1561ndash1574 (1998)11 S Omanovic and S G Roscoe J Colloid Interface Sci 227 452ndash460 (2000)12 L M Gassa J M Vilche M Ebert K Juumlttner and W J Lorenz J Appl Electrochem 20

677ndash685 (1990)13 E Chassaing and B Sapoval J Electrochem Soc 141 2711ndash2715 (1994)14 E M Andrade PhD Thesis University of Buenos Aires Buenos Aires (1992)15 B A Boukamp Equivalent Circuit Users Manual University of Twente Twente (1989)16 T Pajkossy and L Nyikos Electrochim Acta 34 171ndash179 (1989)17 T Pajkossy and L Nyikos Phys Rev B 42 709ndash719 (1990)18 R De Levie in Advances in Electrochemistryand ElectrochemicalEngineering P Delahay and

C W Tobias (Eds) pp 329ndash 397 Wiley New York (1967)19 C H Hamann A Hamnett and W Vielstich Electrochemistry Wiley-VCH Weinheim (1998)20 E M Andrade F V Molina and D Posadas J Colloid Interface Sci 215 370ndash380 (1999)21 C Eggleston Am Mineral 84 1061ndash 1070 (1999)22 P A Johnsson C M Eggleston and M F Hochella Am Mineral 76 1442ndash1445 (1991)23 B Roux and M Karplus J Phys Chem 95 4856ndash 4868 (1991)

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or suitability for any purpose of the Content Any opinions and viewsexpressed in this publication are the opinions and views of the authors andare not the views of or endorsed by Taylor amp Francis The accuracy of theContent should not be relied upon and should be independently verifiedwith primary sources of information Taylor and Francis shall not be liablefor any losses actions claims proceedings demands costs expensesdamages and other liabilities whatsoever or howsoever caused arisingdirectly or indirectly in connection with in relation to or arising out of theuse of the Content

This article may be used for research teaching and private studypurposes Any substantial or systematic reproduction redistributionreselling loan sub-licensing systematic supply or distribution in any formto anyone is expressly forbidden Terms amp Conditions of access and use canbe found at httpwwwtandfonlinecompageterms-and-conditions

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Communication







1 INTRODUCTION




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2 EXPERIMENTAL



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(a) (b)


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Y D Y0jreg (1)






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Z D RS C1


RP C1Y

(2)






CMP Dfrac34M

AtildeD iexcl

frac34ef

Atilde (3)

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Z0 D 1 iexcl j

sRl

2Cl

coth

sup31 C j l

rRlCl

2

acute (4)


Rl D 1

middotfrac14plusmna

2

sup22 (5)

Cl D CMPa (6)


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shyshyshyshycoth

sup31 C j l

rRlCl

2



Z0 frac14 1 iexcl j

sRl

2Cl

D

sRl

Cl

1j05

(7)


Y0 D1

Aef

sCl

Rl

D1

Aef

rCMPa3middotfrac14

4 (8)


4 CONCLUSIONS


Acknowledgements


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REFERENCES









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Communication







1 INTRODUCTION




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2 EXPERIMENTAL



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(a) (b)


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Y D Y0jreg (1)






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Z D RS C1


RP C1Y

(2)






CMP Dfrac34M

AtildeD iexcl

frac34ef

Atilde (3)

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Z0 D 1 iexcl j

sRl

2Cl

coth

sup31 C j l

rRlCl

2

acute (4)


Rl D 1

middotfrac14plusmna

2

sup22 (5)

Cl D CMPa (6)


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shyshyshyshycoth

sup31 C j l

rRlCl

2



Z0 frac14 1 iexcl j

sRl

2Cl

D

sRl

Cl

1j05

(7)


Y0 D1

Aef

sCl

Rl

D1

Aef

rCMPa3middotfrac14

4 (8)


4 CONCLUSIONS


Acknowledgements


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REFERENCES









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2 EXPERIMENTAL



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(a) (b)


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Y D Y0jreg (1)






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Z D RS C1


RP C1Y

(2)






CMP Dfrac34M

AtildeD iexcl

frac34ef

Atilde (3)

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Z0 D 1 iexcl j

sRl

2Cl

coth

sup31 C j l

rRlCl

2

acute (4)


Rl D 1

middotfrac14plusmna

2

sup22 (5)

Cl D CMPa (6)


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shyshyshyshycoth

sup31 C j l

rRlCl

2



Z0 frac14 1 iexcl j

sRl

2Cl

D

sRl

Cl

1j05

(7)


Y0 D1

Aef

sCl

Rl

D1

Aef

rCMPa3middotfrac14

4 (8)


4 CONCLUSIONS


Acknowledgements


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REFERENCES









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(a) (b)


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negi

e M

ello

n U

nive

rsity

] at

04

31 1

5 O

ctob

er 2

014




Y D Y0jreg (1)






Dow

nloa

ded

by [

Car

negi

e M

ello

n U

nive

rsity

] at

04

31 1

5 O

ctob

er 2

014



Z D RS C1


RP C1Y

(2)






CMP Dfrac34M

AtildeD iexcl

frac34ef

Atilde (3)

Dow

nloa

ded

by [

Car

negi

e M

ello

n U

nive

rsity

] at

04

31 1

5 O

ctob

er 2

014




Z0 D 1 iexcl j

sRl

2Cl

coth

sup31 C j l

rRlCl

2

acute (4)


Rl D 1

middotfrac14plusmna

2

sup22 (5)

Cl D CMPa (6)


Dow

nloa

ded

by [

Car

negi

e M

ello

n U

nive

rsity

] at

04

31 1

5 O

ctob

er 2

014



shyshyshyshycoth

sup31 C j l

rRlCl

2



Z0 frac14 1 iexcl j

sRl

2Cl

D

sRl

Cl

1j05

(7)


Y0 D1

Aef

sCl

Rl

D1

Aef

rCMPa3middotfrac14

4 (8)


4 CONCLUSIONS


Acknowledgements


Dow

nloa

ded

by [

Car

negi

e M

ello

n U

nive

rsity

] at

04

31 1

5 O

ctob

er 2

014


REFERENCES









Dow

nloa

ded

by [

Car

negi

e M

ello

n U

nive

rsity

] at

04

31 1

5 O

ctob

er 2

014




Y D Y0jreg (1)






Dow

nloa

ded

by [

Car

negi

e M

ello

n U

nive

rsity

] at

04

31 1

5 O

ctob

er 2

014



Z D RS C1


RP C1Y

(2)






CMP Dfrac34M

AtildeD iexcl

frac34ef

Atilde (3)

Dow

nloa

ded

by [

Car

negi

e M

ello

n U

nive

rsity

] at

04

31 1

5 O

ctob

er 2

014




Z0 D 1 iexcl j

sRl

2Cl

coth

sup31 C j l

rRlCl

2

acute (4)


Rl D 1

middotfrac14plusmna

2

sup22 (5)

Cl D CMPa (6)


Dow

nloa

ded

by [

Car

negi

e M

ello

n U

nive

rsity

] at

04

31 1

5 O

ctob

er 2

014



shyshyshyshycoth

sup31 C j l

rRlCl

2



Z0 frac14 1 iexcl j

sRl

2Cl

D

sRl

Cl

1j05

(7)


Y0 D1

Aef

sCl

Rl

D1

Aef

rCMPa3middotfrac14

4 (8)


4 CONCLUSIONS


Acknowledgements


Dow

nloa

ded

by [

Car

negi

e M

ello

n U

nive

rsity

] at

04

31 1

5 O

ctob

er 2

014


REFERENCES









Dow

nloa

ded

by [

Car

negi

e M

ello

n U

nive

rsity

] at

04

31 1

5 O

ctob

er 2

014



Z D RS C1


RP C1Y

(2)






CMP Dfrac34M

AtildeD iexcl

frac34ef

Atilde (3)

Dow

nloa

ded

by [

Car

negi

e M

ello

n U

nive

rsity

] at

04

31 1

5 O

ctob

er 2

014




Z0 D 1 iexcl j

sRl

2Cl

coth

sup31 C j l

rRlCl

2

acute (4)


Rl D 1

middotfrac14plusmna

2

sup22 (5)

Cl D CMPa (6)


Dow

nloa

ded

by [

Car

negi

e M

ello

n U

nive

rsity

] at

04

31 1

5 O

ctob

er 2

014



shyshyshyshycoth

sup31 C j l

rRlCl

2



Z0 frac14 1 iexcl j

sRl

2Cl

D

sRl

Cl

1j05

(7)


Y0 D1

Aef

sCl

Rl

D1

Aef

rCMPa3middotfrac14

4 (8)


4 CONCLUSIONS


Acknowledgements


Dow

nloa

ded

by [

Car

negi

e M

ello

n U

nive

rsity

] at

04

31 1

5 O

ctob

er 2

014


REFERENCES









Dow

nloa

ded

by [

Car

negi

e M

ello

n U

nive

rsity

] at

04

31 1

5 O

ctob

er 2

014




Z0 D 1 iexcl j

sRl

2Cl

coth

sup31 C j l

rRlCl

2

acute (4)


Rl D 1

middotfrac14plusmna

2

sup22 (5)

Cl D CMPa (6)


Dow

nloa

ded

by [

Car

negi

e M

ello

n U

nive

rsity

] at

04

31 1

5 O

ctob

er 2

014



shyshyshyshycoth

sup31 C j l

rRlCl

2



Z0 frac14 1 iexcl j

sRl

2Cl

D

sRl

Cl

1j05

(7)


Y0 D1

Aef

sCl

Rl

D1

Aef

rCMPa3middotfrac14

4 (8)


4 CONCLUSIONS


Acknowledgements


Dow

nloa

ded

by [

Car

negi

e M

ello

n U

nive

rsity

] at

04

31 1

5 O

ctob

er 2

014


REFERENCES









Dow

nloa

ded

by [

Car

negi

e M

ello

n U

nive

rsity

] at

04

31 1

5 O

ctob

er 2

014



shyshyshyshycoth

sup31 C j l

rRlCl

2



Z0 frac14 1 iexcl j

sRl

2Cl

D

sRl

Cl

1j05

(7)


Y0 D1

Aef

sCl

Rl

D1

Aef

rCMPa3middotfrac14

4 (8)


4 CONCLUSIONS


Acknowledgements


Dow

nloa

ded

by [

Car

negi

e M

ello

n U

nive

rsity

] at

04

31 1

5 O

ctob

er 2

014


REFERENCES









Dow

nloa

ded

by [

Car

negi

e M

ello

n U

nive

rsity

] at

04

31 1

5 O

ctob

er 2

014


REFERENCES









Dow

nloa

ded

by [

Car

negi

e M

ello

n U

nive

rsity

] at

04

31 1

5 O

ctob

er 2

014

electrochemical impedance of mercury electrodes with hematite particles adhered

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