diffusion and charge transfer parameters for the ag∕agcl electrode

1364 J. Electrochem. Soc.: ELECTROCHEMI C A L

grounds, that the layer nearest the electrode is that of lowest oxidation state.

When the electrode is ful ly passivated, there is very li t t le dependence of the current on potential (between --0.5 to +0.60V). This can be explained in terms of both the increasing thickness of the layer (22) (Table III) and its progressive dehydrat ion; the oxide/ hy- droxide ratio shows a general ly increasing t rend as the potential is made more positive (Table II) . At still more positive potentials the thickness continues to in - crease but the current rises somewhat. This may be due to the onset of oxygen evolution or to imperfec- tions in the layer.

Acknowledgments A.F.P. would l ike to thank I.C.I. for the award of a

fellowship and R.O.A. would like to thank the Science Research Council for the award of a research associ- ateship.

Manuscript submit ted Jan. 21, 1977; revised m a n u - script received Apri l 28, 1977.

Any discussion of this paper will appear in a Discus- sion Section to be published in the June 1978 JOURNAL. All discussions for the June 1978 Discussion Section should be submit ted by Feb. 1, 1978.

REFERENCES 1. K. S. Kim, A. F. Gossman, and N. Winograd, Anal.

Chem., 46, 197 (1974). 2. G. C. Allen, P. M. Tucker, A. Capon, and R.

Parsons, J. Electroanal. Chem., 50, 335 (1974).

SCIENCE AND TECHNOLOGY September I977

3. A. F. Povey, Ph.D. Thesis, Univers i ty of Newcastle- upon-Tyne (1975).

,4. T. Dickinson, A. F. Povey, and P. M. A. Sherwood, J. Chem. Soc., Faraday Trans. 1, 71, 298 (1975).

5. T. Dickinson, A. F. Povey, and P. M. A. Sherwood, ibid., 73, 327 (1977).

6. R. O. Ansell, T. Dickinson, and A. F. Povey, Corros. Sci., In press.

7. T. Dickinson, A. F. Povey, and P. M. A. Sherwood, J. Chem. Soc. Faraday Trans. 1, 72, 686 (1976).

8. A. W. Hothersall, S. G. Clarke, and D. J. Mac- naughton, J. Electrodep. Tech. Soc., 9, 101 (1934).

9. F. F. Oplinger and C. J. Wernlund, U.S. Pat. 1,919,000 (1933).

10. R. Kerr, J. Soc. Chem. Ind., 57, 405 (1938). 11. H. Barbre, C. Bagger, and E. Maahn, Electrochim.

Acta, 16, 559 (1971). 12. D. Eurof Davies and S. N. Shah, ibid., 8, 663 (1963) ;

ibid., 8, 703 (1963). 13. N. A. Hampson and N. E. Spencer, Br. Corros. J.,

3, 1 (1968). 14. M. N. Anwar, U.A.R.J. Chem., 13, 109 (1970). 15. B. N. St i r rup and N. A. Hampson, J. Electroanal.

Chem., 67, 45 (1976). 16. B. N. Stirrup and N. A. Hampson, ibid., 67, 57

(1976). 17. D. R. Gabe and P. Sripatr, Trans. Inst. Met.

Finish., 51, 141 (1973). 18. T. Dickinson and S. Lotfi, In preparation. 19. A. F. Povey and P. M. A. Sherwood, J. Chem. Soc.,

Faraday Trans. 2, 70, 1240 (1974). 20. A. F. Povey, Submit ted to J. Electron Spectrosc.

Rlat. Phenom. 21. R. O. Ansell, T. Dickinson, A. F. Povey, and

P. M. A. Sherwood, ibid., 11, 301 (1977). 22. K. J. Vetter, Electrochim. Acta, 16, 1923 (1971).

Diffusion and Charge Transfer Parameters for the Ag/AgCI Electrode

Hiram Gu* and Douglas N. Bennion* Energy and Kinetics Department, School of Engineering and Applied Science,

University o] CaliSornia, Los Angeles, Cali]ornia 90024

ABSTRACT

Galvanostatic formation and potentiostatic reduction of silver chloride on silver have been studied. Experiments were conducted in 0.5, 1.0, 1.5, 2.0, and 3.0N KC1 solutions. The effective mass t ransfer coefficient, km o, for the t ransport of complex silver ions from AgC1 crystals to reaction sites on the si lver surface was found to depend on KC1 concentrations in the form

km~ 1.808 • 103 [exp (--1.519 • 103 Ce)] cm/sec

with Ce in mole per cubic centimeter. The apparent cathodic charge transfer coefficient, ac, was determined to be 0.30, and the exchange current density

io ---- 0.15 (cRsat/10.1 X 10-8) 0.70 A /cm 2

w i t h CR sat (mole per cubic centimeter) being the saturated concentrat ion of complexed silver ions in the KC1 solution.

In addit ion to being used as reference electrodes, s i lver /s i lver chloride electrodes have found use as porous electrode plates in batteries such as the seawater battery. Previous studies on porous Ag/AgC1 electrodes (1, 2) have indicated that the electrode may be used successfully in secondary storage batteries.

The s i lver /s i lver chloride electrode is an electrode with a sparingly soluble reactant, AgC1. Numerous studies have been conducted on the thermodynamics of Ag/AgC1 electrodes (3) and the mechanism of AgC1 formation and reduction at silver electrodes (4-11). The studies of Kurtz (4) and Lal et al. (5) suggested

* Electrochemical Society Active Member. Key words: porous electrodes, batteries, exchange current.

that electrolytically formed AgC1 films are porous in nature. Briggs and Thirsk (6) studied the galvanostatic reduction of silver chloride films on silver at different current densities and KC1 concentrations. They found that an increase in the init ial AgC1 layer thickness reduces the number of reduction centers visible at a given percentage reduction. Jaenicke et al. (7) found that if a pore-free AgC1 layer is reduced by a cathodic current, pores soon appear. F le i shmann and Thirsk (8) studied the growth of AgC1 on Ag and concluded that the growth of AgCI is two dimensional. Giles (9), however, believed that the formation of AgC1 is by progressive nucleat ion and growth of th ree-d imen- sional centers and that the diffusion of AgCln+l - n may

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Vol. 124, No. 9 A g / A g C I ELECTRODE 1365

be rate determining. The value of n for the complex may be 0, 1, 2, or 3. Ka tan et al. (10) studied the reduction of silver ions from potassium chloride solutions saturated with AgC1. A rotat ing disk silver electrode was used. Their results also indicate that the formation and reduct ion of silver chloride involves the solution diffusion of AgCln+z -n. Aleskovskii et aL (11) studied the s tructure of silver deposits with respect to electrode potentials at which the reduction of AgC1 takes place. They also suggested that the reduct ion is via a solution diffusion path.

No informat ion regarding the charge t ransfer overvoltage of Ag/AgC1 electrodes was found in the l i tera- ture. The absence of charge t ransfer studies on Ag/ AgC1 electrodes is probably due to two reasons. First, the overvoltage in the case of solid silver electrodes consists main ly of crystal l ization and diffusion overvoltage with large exchange current densi ty according to Gerischer and Tischer (12, 13) and Bockris et aL (14, 15). Second, the coverage of silver surface by silver chloride adds complexity to the analysis of exper imenta l data.

The present s tudy was conducted with the in tent ion of de termining apparent diffusion and charge transfer parameters for the Ag/AgC1 system. These parameters are to be used in the mathemat ical model ing of Ag/AgC1 porous electrodes.

The potentiostatic reduct ion of porous silver chloride films on silver was analyzed. As the silver chloride is being converted to silver, the silver area available for charge t ransfer increases. The cathodic current in - creases to a m a x i m u m and decreases as the silver chloride is being depleted. The max imum current density reached dur ing potentiostatic reduction was used to construct the current -overpotent ia l curves. From the i--q curves, values of four parameters were deduced. They are: the cathodic charge transfer coefficient, ar the mass t ransfer coefficient of complexed silver ions, km o, for solution phase t ransport between Ag surface and AgCI surface; the exchange current density, io; and the order of dependence of io on silver ion concentration, ~.

Quali tat ive results observed on the galvanostatic formation of AgC1 are also presented.

E x p e r i m e n t a l The exper imenta l ar rangement is shown in Fig. 1.

The electrode studied was a c i rcular s i lver disk 1/8 in. in diameter embedded in Lucite. Another Lucite piece that consisted of the counterelectrode compartment, a 1/8 in. diam tunnel , and a small branch tunne l approximate ly 1/32 in. diam was spring pressed against the working electrode piece. The 1/8 in. tunne l was aligned with the silver disk al lowing uni form pr imary current d is t r ibut ion on the electrode surface. A th in film of electrolytic solution approximately 10 ~m thick existed between the two Lucite pieces which provided a solution connection between the ma in cell and the

Tube Pump

I

tem~rature

C ~ l l r bolh a g ~ el~roda

�9 I

Fig. |. Experimental arrangement

reference electrode compartment. The reference electrode was a Ag/AgC1 electrode. The same KC1 concentrat ion as the main cell was used in the reference electrode compartment. A tube pump was used to cir- culate the electrolyte so as to ma in ta in a constant electrolyte concentrat ion near the electrode surface. The electrolyte flow rate used during exper imental runs was 3.5 cm3/sec.

The KC1 solutions used were prepared from doubly distilled water and reagent grade KC1. The ini t ial silver surface was mechanical ly finished with 4/0 emery polishing paper purchased from Buehler Limited.

The experiments were conducted at 25 ~ ___ 1~ in 0.5, 1.0, 1.5, 2.0, and 3.0N KC1 solutions. The electrode was galvanostatically charged at 5 m A / c m 2 and subse- quent ly reduced potentiostatically. A PAR Model 173 potent iosta t /galvanostat was used to impose the exper imental current or voltage.

The overpotential, ~, reported in this communicat ion is the potential measured or imposed between the working electrode and the Ag/AgC1 reference electrode.

Results Galvanostatic lormation of AgCl.--Typical ~l-t (over-

potent ia l - t ime) curves for the galvanostatic charging (passage of constant anodic current) of silver elec-, trodes in KC1 solutions are shown in Fig. 2. Curve a was obtained when silver chloride was formed on an electrode with a freshly polished silver surface. The curve shows a close to l inear rise in potential with time. After the electrolytically formed silver chloride was totally reduced back to silver (either galvanostatically or potentiostat ically), galvanostatic recharg- ing of the electrode exhibited a different ~]-t curve (curve b). The ~-t curve has a ra ther flat portion a t the beginning followed by a rapid rise. Addit ional cycling (charged and discharged) did not seem to have fur ther effect on the ~-t curves for galvanostatic charging nor was there any observable dependence (based on scanning electron microscope observation) of the electrode surface roughness on the number of cycles. However, it was observed that the flat port ion of the ~]-t curve was usual ly lower and the rapid rise in potential was usual ly earlier (shorter tp as defined in Fig. 2) when higher concentrations of KC1 solutions were used. Figure 3 shows the equivalent amount of charge, Q* (equal to itp), at tp with respect to KC1 concentrations. The time tp is t ime at which rapid rise in potential begins as defined in Fig. 2. Galvanostatic charging in 1N KC1 with current densities from 2.5 to 100 mA/cm 2 indicated that the value of Q* is inde- pendent of the charging current in the range studied.

Scanning electron microscope pictures of the electrode surfaces at positions 1, 2, and 3 as indicated in

0.1

A I--

_1

0.05

w

O

a

2 3

: tp !

3 0 6 0 9 0 T I M E ( s e c )

120

Fig. 2. Overpotential vs. time curves for the galvanostatic formation of silver chloride at 5 mA/cm 2 in 1.5N KCI solution. Curve a, initial freshly polished silver surface; curve b, cycled silver surface.




1366 J. Electrochem. Soc.: E L E C T R O C H E M I C A L S C I E N C E A N D T E C H N O L O G Y September I977

i.o

_ 0.81 %

0.6

b o~

0 . 2 ds ,'o ,'.5 2'.o 2:~ 3:o

KQ CONCENTRATION ,Ce= tO 5 ~motes/crn 5 )

Fig. 3. Dependence of Q* on KCI concentrations. Anodic charging current was 5 mA/cm 2.

Fig. 2 are s h o w n in Fig. 4. F i g u r e s 4a and 4b g ive com- par i son of the sur faces ( f resh and cycled) at the same s ta te of cha rge wh i l e Fig. 4b and 4c g ive com pa r i son of the sur faces at the s a m e e l ec t rode potent ia l . The sma l l par t ic les b e t w e e n the AgC1 crys ta l l i t es in Fig. 4c a re s i lver .

Potentiostatic reduction of AgCl.--The cu r r en t f low d u r i n g the r e d u c t i o n of AgC1 depends on the ra te of diffusion of c o m p l e x e d s i lve r ions f r o m the s i lve r ch lor ide sur face to the s i lve r surface. As an a p p r o x i - mat ion , one can say t h a t t h e s i lve r a r e a is eA and the s i lve r ch lor ide a rea is (1 -- e)A. H e r e A is the total e l ec t rode a rea and e is the f r ac t ion of s i lve r a r ea e x - posed. By a s suming a l i n e a r concen t r a t i on prof i le b e - t w e e n the AgC1 a r e a and A g area, t he r eac t ion rate, based on the a rea A, cau ~e w r i t t e n as (16)

i ---- nFkm o (0) 1/2 (1 -- 0) 1/2 (cR s -- cR sat) [1]

w h e r e Ca s is the concen t r a t i on of c o m p l e x e d s i lve r ions at the s i lve r su r face w h e r e charge t r ans fe r r eac t ion takes p lace and cR sat is the s a tu ra t i on concen t r a t i on of c o m p l e x e d s i lve r ions wh ich p reva i l s at the AgC1 su r - face. F is the F a r a d a y cons tan t and n is the n u m b e r of e lec t rons i n v o l v e d in t he cha rge t r a n s f e r react ion . T h e mass t r ans fe r coefficient, km~ is equa l to D/5 w h e r e D is the c o m p l e x e d ions diffusion coefficient and 5 is t he a v e r a g e diffusion length . One can also define an o v e r - all mass t r ans f e r coefficient, kin, such tha t

k m = km~ 1/2 (1 -- 0)I/2 [2]

The o v e r - a l l mass t r ans f e r coefficient thus var ies w i t h the a m o u n t of su r face c o v e r a g e by AgC1.

The m a x i m u m cu r r en t dens i ty r eached du r ing po - t en t ios ta t ic r educ t ion was found to d e p e n d on the in i - t ia l cove rage of s i lve r su r face by AgC1. If the in i t i a l coverage , 1 -- ~, was above 0.5 and be low abou t 0.8 (s tate of cha rge in the fiat po r t i on of cu rve b in Pig. 2), the m a x i m u m cu r ren t r e m a i n e d the s a m e o v e r a

20C - o

E 15C -

=0.5

IOC-

F-

~ 5C- ~ =L c

C- -- 0 ~ ' ~

L

TIME (sec)

Fig. 5. Current-time curves for the potentiostotic reduction of AgCI at - -100 mV in 1N KCI solution. Curve a, initial porous coverage of AgCI; curve b, heavy initial coverage of AgCI; and curve c, nonporous initial coverage of AgCI with few reduction centers.

wide r ange of in i t ia l charge. H o w e v e r , i f the e l ec t rode was in i t i a l ly heav i l y cove red by AgC1 (s ta te of cha rge co r respond ing to r is ing po r t i on of cu rve b in Fig. 2), l o w e r m a x i m u m cur ren t s w e r e obta ined. Typ i ca l i - t curves are shown in ~ig. 5. C u r v e a was ob ta ined w i t h an in i t i a l ly porous s i l ve r ch lo r ine film. Curves b and c w e r e ob ta ined f r o m in i t i a l ly h e a v i l y cha rged e lec - trodes. C u r v e c had a m o r e dense c o v e r a g e of AgC1 c o m p a r e d to c u r v e b.

Sur face m o r p h o l o g y of the e lec t rode at the ca thodic cu r r en t m a x i m u m for the cases co r respond ing to cu rves a and c in Fig. 5 a re s h o w n in ~ig. 6. F o r t he case w i t h in i t i a l h e a v y coverage , t he r e w e r e f e w re - duc t ion centers , and the boundar i e s of the centers e x - p a n d e d in a c i r cu la r m a n n e r as AgC1 was be ing r e - duced (Fig. 6 d and e) . For t he case w h e r e the in i t ia l AgCt fi lm was qu i t e porous , t h e r e w e r e m a n y m o r e ~educt ion centers d i spersed among the s i lve r ch lor ide c rys ta l l i t es (~ig. 6 a, b, and c). F i g u r e 6c shows the s t ruc tu re of r educed s i lve r a f te r the r e m a i n i n g s i lve r ch lor ide had been r e m o v e d by sod ium th iosul fa te . S imi l a r su r face m o r p h o l o g y was also r e p o r t e d by Br iggs and Th i r sk (6).

Ca thod ic i -n cu rves ob ta ined for KC1 concen t ra t ions of 0.5, 1.0, 1.5, 2.0, and 3.0N are shown in Fig. 7. Ex- periments were performed on a cycled electrode with the surface undisturbed between runs. Before each potentiostatic reduction run, the electrode was charged galvanostatically at 5 mA/cm 2 to approximately 85% of t~ (see Fig. 2). This assured that the AgCl film was porous and the surface coverage was approximately the same for each run. Data points in ~-ig. 7 correspond to maximum currents reached during potentiostatic re- ductions. At the maximum current, the fraction of ex-

Fig. 4. Scanning electron microscope pictures of the electrode surface during galvanostatic formation of AgCI. Pic- tures a, b, and c correspond to positions 2, 1, and 3 in Fig. 2, respectively.




Vol. I24, No. 9 A g / A g C 1 E L E C T R O D E 1367

Fig. 6. Pictures showing electrode morphology at the maximum cathodic current, a, b, and c correspond to curve a in Fig. 5. a, Optical microscope picture of the surface; b, SEM picture of the surface; c, SEM picture of the surface after the remain- ing AgCI has been removed by sodium thiosulfate; d, e, correspond to curve c in Fig. 5 with d, optical microscope picture showing large reduction centers, and e, SEM picture showing cir- cular growth of the reduction center,

posed si lver area, ~, was 0.5 as de te rmined f rom microscope pictures.

No l imi t ing current p la teau was observed in the 0.5N KC1 solution. F rom the l imi t ing cur ren t p la teaus in 1.0, 1.5, 2.0, and 3.0N KC1 solutions, the over -a l l mass t ransfer coefficients for the t r anspor t of AgCln+l - n (at 0 ---- 0.5) were calcula ted using the fol lowing equat ion

--ilim ~m - - - [3]

FCI~ sat

Values of CR sat were obtained f rom exper imenta l r e - sults (17). The mass t ransfe r coefficient, km o, was then calcula ted f rom Eq. [2] where km o is 2kin at 0 = 0.5.

The mass t ransfe r coefficient was found to depend on KC1 concentrat ions (Fig. 8). Examina t ion of Fig. 8 shows tha t the dependence follows the re la t ionship

km o = B exp (Ece) [4]

wi th B : - 1.808 X 103 cm/sec and E ~ --1.519 X 10~ cm3/mole.

The kinetic ra te express ion appl ied to the present system can be wr i t t en as

i~-6io [ ( CR---~s ) ~ - a ~ e x p ( ~ ) CR sat

( CRS ~ "-c~c

where ~/ is the order of dependence of io on the com- p lexed si lver ion concentrat ion; C~a and ~c are the anodic and cathodic charge t ransfer coefficients, re - spect ively; R is the gas constant; and T is the absolute tempera ture . The exchange cur ren t dens i ty io can be

I ' ' 2.0 wr i t t en as

% -3.0 1.5 IO.C

^ 8.C- -" -2o~ 30. Kc, ,o . ~ i l 0.5 ~ 6s

0 ]10 I I O[ 02 03 04 05 06 0 8 9 0 1.0 2.0 3.0 ,

OVERPOTENTIAL , 17 (VOLT) KCI CONCENTRATION , Ce x IO 5 (moles/era 3 )

Fig. 7. Current-overpotenHo] curves for the reduction of silver Fig. 8, Dependence o/{ the mass transfer coefficient on KCI chloride. The current is the maximum current from the i - t curves, concentrations. ecsdl.org/site/terms_use address. Redistribution subject to ECS license or copyright; see 129.97.180.147Downloaded on 2013-12-13 to IP



1368 J. Electrochem. Soc.: E L E C T R O C H E M I C A L S C I E N C E A N D T E C H N O L O G Y S e p t e m b e r I977

CR sat ~'/ io = ioO ~ c - -~- - / [6]

where ioo is the exchange cur ren t densi ty corresponding to the concentrat ion of complexed si lver ions, CR*. In the present investigation, cR* was selected as the saturated concentrat ion of AgCln+l -n in 1N KC1 solution, i.e., cR* = C R s a t in 1N KC1.

It is bel ieved that the si lver dissolution and deposition involves a one-e lec t ron t ransfer e lementa ry step. Therefore, Eq. [5] can be rearranged, with 7 = aa and aa -}- ac ---- 1.0, tO read

In -- In Fn [ ( ]

( oR__= ) CR*

CRSa t

\ CR*

Using the results f rom Fig. 7 and 8, values of cR s were first calculated f rom Eq. [1]. The le f t -hand side of Eq. [7] was then plotted against the terms in the bracket on the r igh t -hand side as shown in Fig. 9. The slope of the plot al lowed the deteminat ion of ac and the intercept gives the value of #/o ~ with e ---- 0.5 (since the peak current was used). The values of -c and %o were determined to be 0.3 and 0.15 A / c m 2, respectively.

The current density, i, can be calculated with respect to e at a fixed ~q by solving Eq. [1] and [7] s imul tane- ously. Calculations of i vs. 6 for several different ~ indicate that the m a x i m u m currents occur at 0 around 0.75 instead of 0.5 as was exper imenta l ly observed. The solubil i ty of AgC1 is quite low and thus the distance f rom si lver chloride sites where AgCln+l -n ions are reduced is probably quite small. It is possible that the effective charge t ransfer si lver area for the reduct ion of AgCln+, -n was actually less than the total exposed si lver area when the electrode surface was less than 50% covered by AgC1.

A model was developed to calculate the effective silver react ing area. The model assumes that the effective si lver area per si lver chloride center is a ring extending a fixed distance f rom the per imeter of the si lver chlor ide-s i lver interface. The effective width of the ring is calculated by assuming that all the exposed Ag is effective at ~ equals 0.5. At 0 --~ 0.5

0eff .~- 0 [8a] and at 6 --~ 0.5

0elf ---- (1 -- ~/0.5) [ 2 ~ ( 1 -- 0) + (1 -- ~/0.5)] [Sb]

An effective silver chloride area was also assumed for the supply of complexed si lver ions at 0 < 0.5. S imi lar to the t rea tment in obtaining effective silver area at 0 < 0.5, the effective silver chloride area per center at 0 < 0.5 was also assumed to be a r ing extending a fixed distance f rom the si lver chlor ide-s i lver interface;

�9 0

E , , , , t

-is -i~ -12 -i0 -8 -5

Fig. 9. Plot corresponding to Eq. [7]

O 0.5N KCI AI.0

[] 1.5

�9 2.0 �9 3.0

I I

-4 -2

the distance being calculated by assuming that all the si lver chloride area is effective at e ---- 0.5. Therefore, at 0 ~ 0 . 5

(1 - - o)eff ---- 2~/I -- o~/b-~ -- 0.5 [9a]

and at 0 ~ 0.5 (i -- O)eff : 1 -- 0 [9b]

According to the model, 0 and (i -- e) in Eq. [I], [2], [5], and [7] should now be replaced by 0elf, and (i -- e)em respectively. The km in Eq. [2] is thus in the form, at 0 ---~ 0.5

km ---- km~ [2~1 -- 0 ~/0.5 -- 0.5]'/,[#] Y2 [10a]

and at # ~ 0.5

k m = kmo [1 - 0]'/2 [2x/1 - ~ (1 - ~/0.-~)

+ (1 - -v/0.5)2] 1/2 [10b]

Applying this revised form of the model, a max i - m u m in current was obtained mathemat ica l ly at 0 = 0.5.

To obtain the var ia t ion of 0 wi th respect to Q (accumulated charge) for application in porous bat tery electrode modeling, the i-o profiles were first calculated at various ~ using revised Eq. [1] and [5] for KC1 concentrat ion of 1.0N. F rom the exper imenta l potentiostatic i - t curves at the corresponding o, a se t of i-Q curves were then obtained approximate ly by graphical integration. Comparison of the calculated i-o curves wi th the corresponding i-Q curves gave the variat ion of 0 wi th respect to Q. It was found that the best fitted relat ionship is of the form

o : (0.25) Q/a* [11]

Discussion The two differently shaped ~-t curves obtained on

two different s i lver surfaces have Mso been observed separately by previous investigators. Briggs and Thirsk (6) obtained curves similar to curve a in Fig. 2 on their freshly polished silver surface while Katan et al (I0) obtained curves similar to curve b on their cycled silver surface. The exchange current densities on a freshly polished silver surface and a cycled silver surface are probably different. The growth of AgCI on the two different surfaces is also different as can be seen from Fig. 4. On a freshly polished silver surface, there are a large number of AgCI nucleation centers formed at the beginning. As more charge is passed, the porous AgCl film thickens with a slow decrease in porosity. On a cycled surface, there are less nucleation centers and more crystal growth of silver chloride (Fig. 4 b and c). In addition, the true silver surface area of a cycled electrode is larger, as has been reported by Giles (9), and can be seen from Fig. 4 b and e. As a result, there is more silver surface available for charge transfer to occur for a longer duration and the overpoten- tim is smaller. Finally, as anodic charging continues on the cycled Ag electrode, the AgCl crystallites begin to grow together, blocking off the silver surfaces, and the rapid rise in overpotential results. These observations support the fact that the formation of AgCI is mainly via solution phase diffusion of AgCln+1 -n followed by crystal growth from a supersaturated solution.

For cycled surfaces, higher KC1 concentrat ions pro- duced lower overpotentials. This is a t t r ibuted to h igher AgCln+~ -n solubil i ty and result ing smaller concentration overpotentials. The shorter t ime to surface coverage, tp, at h igher KC1 concentrations seems to indicate ear l ier coverage of the si lver surface by AgCI in solutions of higher C1- content. The earl ier coverage can be due to the increase in nucleat ion sites. Briggs and Thirsk (6) have also observed the earl ier surface coverage in higher KCI concentrations. From their ~-t curves (which are similar to curve a of Fig. 2), one




Vol. 124, No. 9 Ag/AgC1 ELECTRODE 1369

can see that the slopes of the curves are steeper in higher KC1 concentrations.

The init ial higher overpotential of the galvanostatic ~]-$ curves of Fig. 2 are probably due to slow nuclea- t ion. leading to a "nucleat ion overpotential" (18).

An electrolyte flow rate of 3.5 cm2/see was used to keep the KC1 concentrat ion near the electrode surface constant. No dependence of current densities on the flow rate was observed dur ing potentiostatic reduction wi thin the flow rate range of 2.0-7.4 cmS/sec. With no circulation of the electrolyte, the measured current densities were higher as a result of the increase in KC1 concentrations near the electrode surface as the AgC1 was being converted to silver, the increase in KC1 concentrations increases the solubil i ty of the silver chloride.

The fact that no l imit ing current was observed dur - ing potentiostatic reduction in 0.5N KC1 solution can be explained by nonuni form secondary current dis t r ibutions and nonuni fo rm concentrat ion distr ibutions of complexed silver ions at the silver surface. The exper imenta l a r rangement was designed for uni form macroscopic p r imary current distr ibution. However, due to the roughness of the electrode surface and because the reactants are supplied from the silver chloride crystallites, the secondary current dis t r ibut ion and the reactant concentrat ion on a micro scale on the order of 1 ~m at the silver surface are not uniform with respect to distance from AgC1 crystals. This is espe- cially t rue in 0.5N KCI, where the solubil i ty of AgCt is lower and the microscale nonuni formi ty becomes more pronounced. As a result, the diffusion l imit ing current of silver deposition was not separable from the onset of another reaction (possibly hydrogen evolu- t ion) for the 0.5N KC1 run.

An increase in si lver chloride coverage reduces the n u m b e r of reduct ion centers. The lesser number of reduction centers resulted in larger area per reduction center at e = 0.5 dur ing discharging. For the case with heavy ini t ial coverage of silver chloride, i-~ curves similar to those reported by Ka tan et al. [Fig. 7 of Ref. (10)] were obtained. As can be expected, no l imit ing currents were observed due to the large area per reduction center at ~ ---- 0.5 (see Fig. 6 d and e), which resulted in very nonuni form microscale dis- t r ibut ion of complexed silver ions and secondary reaction current across the exposed silver surface. The total effective silver area (boundaries of reduction centers) for the reduction of complexed silver ions was very small as compared to the total exposed silver area. Again, the l imit ing diffusion current was obscured by the onset of another reaction. The total effective area for the case with a large area per reduction center is also smaller than that for the case with a large number of reduct ion centers, and resulted in lower currents at # = 0.5 during potentiostatic reduction (Fig. 5, curve c).

The almost order of magni tude difference in maxi- m u m currents between curve a and curve c in Fig. 5 supports the solution diffusion mechanism in the electrochemical formation and reduct ion of silver chloride. If significant solid phase t ranspor t had occurred, there should have been less differences in the magni tude of the max imum currents.

The decrease in km o at higher concentrations of KC1 is due to the increased portion of AgC14 -3 present as can be shown from calculations using stabil i ty con- stants (19). The complexed AgC14 -3 has a larger ionic radius and thus a smaller diffusion coefficient than the other complexes. The measured km o which includes all AgCI~+I -~, is therfore smaller at higher concentrations of KCI. Katan e t al. (10), from their rotat ing disk experiments, also obtained a smaller effective diffusion coefficient for complexed silver ions in 4N KC1 compared to that obtained in the 2N KC1 solution.

The overpotential n, as measured, includes concen- t rat ion overpotential, ~o as well as the charge t ransfer

overpotential, ~]~. At high overpotentials, ~]c becomes important. The terms involving cRs/CR sat w e r e in t ro- duced in Eq. [5] to correct for the concentrat ion overpotential. At low overpotentials (less than --60 mV), surface diffusion of adions may become rate determining as was indicated by Bockris et al. (14, 15) in their studies of the dissolution and deposition of silver from solutions of silver perchlorate in aqueous per- chloride acid. The effect of adion surface diffusion was not included in Eq. [5]. Therefore, in obtaining the slopes and intercepts according to Eq. [7], only data points above cathodic overpotential of 100 mV were used. In addition, since kinetic parameters were to be determined, data in the range where reaction rates might be predominant ly solution phase mass t ransfer l imit ing were also excluded when constructing Fig. 9. The data excluded were I~]1 > 0.4V in 0.5, 1.0, and 1.5N KC1, ]0] > 0.3V in 2.0N KC1, and Inl > 0.25V in 3.0N KC1.

It might be emphasized that the data in Fig. 7 and 9 are the same with the exceptions noted. The combina- tion of Eq. [1] and [5] correlate the data as shown in Fig. 9. Since Fig. 7 presents the same data, it follows that these same equations yield approximately the curves shown in Fig. 7. The curves in Fig. 7 can be seen to be S shaped, the lower portions being near the inflection point of the S. The data at low ,I are in the region of exponential dependence of i on ~ shown in Eq. [5]. However, at larger ~] the curve in Fig. 7 bends downward due to a decrease in CR s as described by Eq. [1].

The overpotential as measured by the reference electrode also contained a small IR or ohmic resistance contr ibut ion which was considered negligible. The KC1 solutions served as support ing electrolytes with high conductivity. Calculations showed, for example, at a current density of 2.0 A/cm 2, in 1N KC1, the ma x imum I R drop was about 20 mV, approximately 3% of the total observed overpotential, ,1.

Current densities as reported in this communicat ion are based on the apparent electrode area. As ment ioned earlier, the true surface area increases after the electrode has been cycled in KC1 solutions. To account for the surface roughness based only on scanning elec- t ron microscope observations would not be very ac- curate. It was decided, therefore, that the results should be reported based on the apparent electrode area, keeping in mind that the exper iment was performed on cycled electrode surfaces.

The true surface area also v a r i e d slightly between runs. Random checks showed that the current densities reported are reproducible to wi thin •

It must also be pointed out that the var iat ion of with accumulated charge shown in Eq. [11] is quite approximate. The var iat ion of o is actually potent ial dependent. This is because the growth of silver deposits is potential dependent as has been indicated by Ales- kovskii et al. (11). The result also varied somewhat with the KC1 concentration. However, the results shown in Eq. [11] appear to be suitable for purposes of mathematical modeling of porous Ag/AgC1 bat tery electrodes.

Conclusions The electrochemical behavior of a Ag/AgC1 electrode

is highly dependent on the surface coverage by AgC1 during gaIvanostatic charging. The ~-t (overpotential- t ime) curves differ widely in shape depending on whether the silver surface is freshly polished or pre- viously cycled.

The number of silver chloride nucleat ion centers increases with increasing KC1 concentrations dur ing galvanostatic charging.

Exper imental observations support previous conclusions that the formation and dissolution of AgC1 on silver is via solution diffusion of complexed silver ions, AgCln+l -n, with n = 0, 1, 2, or 3.




1370 J. Electrochem. Soc.: ELECTROCHEMICAL SCIENCE AND TECHNOLOGY September 1977

The max imum current density dur ing potentioststic discharge depends highly on the number of reduction centers. The number of reduction centers in tu rn depends on the degree of init ial coverage by silver chloride. A heavier ini t ial coverage gives lesser number of reduction centers during discharge. A larger number of small reaction sites leads to lower overpotentials at comparable current densities.

The mass t ransfer coefficient, krn o, for the diffusion of AgCln+l -n was found to depend on KC1 concentrations in the form

km~ ---- B exp (Ece)

with 13 _-- 1.808 • 103 cm/sec and E = --1.519 X 103 cm3/mole.

The exchange current density was determined to be

eRsat )0.70 A/cm ~ io = 0.15 10.1 • 10 - s

The units of CR sat a r e mole per cubic centimeter. The cathodic charge t ransfer coefficient, ~c was de-

termined to be 0.30.

Acknowledgment This work was supported by the Office of Naval Re-

search under Contract no. N0014-75-C-0794 and the Univers i ty of California, Los Angeles, California.

Manuscript submit ted Oct. 18, 1976; revised ma nu- script received April 23, 1977.

Any discussion of this paper will appear in a Discus- sion Section to be published in the June 1978 JOURNAL. All discussions for the June 1978 Discussion Section should be submit ted by Feb. 1, 1978.

Publication costs o~ this article were assisted by the University oS Cali]ornia.

LIST OF SYMBOLS A electrode surface area, cm 2 Ce electrolyte concentration, mole/cm3 CR s complexed silver ions concentrat ion at the silver

surface m o l e / c m 3 CR sat saturated concentrat ion of complexed silver ions

in the KC1 solution mole /cm s ca* saturated concentrat ion of co mplexed ions in 1N

KC1 solution, mole /cm z D effective diffusion coefficient of complexed silver

ions, cm2/sec F Faraday constant, 96,487 C/equiv. i current density, A/cm 2 io exchange current density, A/cm 2 ioo exchange current density based on saturated

concentrations of complexed ions in 1N KC1 solution, A/cm 2

km surface coverage dependent mass t ransfer coefficient, cm/sec

km o

n

Q Q* RT

C~a~ ce c ,,/

8

tie ~ls 0

effective mass t ransfer coefficient of complexed silver ions (equal to 2kin at 0 ----- 0.5), cm/sec number of electrons t ransferred in electrode reaction; or n u m b e r of charge on complexed silver ions charge, C/cm 2 charge parameter, equal to itp, C/cm 2 gas constant mult ipl ied by absolute tempera- ture, J /mole anodic and cathodic charge t ransfer coefficients exponent in composition dependence of the exchange current density effective diffusion path, cm overpotential, ~1 ----- ~lc q- ~s, V concentrat ion overpotential, V charge t ransfer overpotential, V fraction of silver surface not covered by silver chloride

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diffusion and charge transfer parameters for the ag∕agcl electrode

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