The electrical double layer: Problems and recent progress

Electroanalytical Chemistry and Interracial Electrochemistry, 41 (1973) 277-309. 277 © Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands

REVIEW

THE ELECTRICAL DOUBLE LAYER: PROBLEMS AND RECENT PROGRESS

RICHARD PAYNE

Air Force Cambridge Research Laboratories, L. G. Hanscom Field, Bedford, Mass. (U.S.A.)

(Received 8th May 1972)

CONTENTS

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 2. Experimental problems . . . . . . . . . . . . . . . . . . . . . . . 278 3. The diffuse layer . . . . . . . . . . . . . . . . . . . . . . . . . . 281 4. The inner layer . . . . . . . . . . . . . . . . . . . . . . . . . . 283 5. Specific adsorption of ions . . . . . . . . . . . . . . . . . . . . . 287 6. Adsorption of neutral molecules . . . . . . . . . . . . . . . . . . . 296 7. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 8. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304

1. INTRODUCTION

The problem of the electrical double layer is of fundamental importance in electrochemistry and has been studied extensively. However, progress has been slow in spite of the considerable activity, both experimental and theoretical, of recent years. The thermodynamic basis of the subject is firmly established and the theory of the diffuse region of the double layer appears to be basically correct. In contrast the nature of adsorption at the interface is poorly understood. This is especially true of specific adsorption of ions for which a considerable body of experimental data of a high quality exists much of which however cannot be satisfactorily interpreted. The principal object of the present article is to review this work with special emphasis on problems of interpretation.

The fundamentals of the subject have been reviewed a number of times 1-6 and in addition various reviews have treated special aspects such as nonaqueous solutions 7, role of the solvent 8, adsorption of organics 9, double layer effects in electrode kinetics 10, adsorption at solid electrodes 11, electrokinetic phenomena x 2, discreteness- of-charge effects13,14 theoretical considerations15,16, recent advances17, problem areasX8,19 and special viewpoints 2°. The present article is restricted in scope to the mercury-solution interface and will cover some aspects treated in earlier reviews although with a somewhat different emphasis.

A comprehensive summary of the available electrocapillary and capacity data up to 1968 is given by Parsons is. More recent work includes determination of ionic surface excesses in concentrated aqueous solutions of LiNO 3 and NH4NO321,

278 R. PAYNE

NaC104 z2, KF 23 and CsF 24, studies of specific adsorption of F- 25,26, C1 27, 1- 28 (dilute solutions), S C N - 2 9 S 2- 30,31, oxalate32, organic cations 33, aromatic cations 34, NO3 and phthalate 35, azide 36-39 and T1 + 4o in aqueous solutions containing a single electrolyte as well as F- 41 PF6 42 and Cs + 43,44 in mixed electrolyte solutions. Various measurements have been reported for aqueous solutions of LiC14s, concentrated LiC1, NaC10 4 and MgSO446, tetraalkylammonium cations 47'4s, decylammonium ions 49, NaC1045°, HNO3, HC104 and H2SO451, dilute MgSO4 and KC152, sodium maleate and fumarate 53, sodium decyl and dodecyl sulfates 54, KI, KC1 and KF 55, dilute NaF 25, halides 5v, dilute KC1 and K2SO45s, dilute HC10#, NaC104, NaOH, acetic acid and NH4OH 59, triethylphosphate 6°, octano154, methylethyl ketone and n-amyl alcohol 61, thiourea 62, various organic compounds 63'64, polyethoxy aliphatic, phenyl and naphthyl compounds 65, quinoline and methylquinolines 66, dibenzoate esters of tartaric acid 67, n-butyric acid 68, amino acids 69, maleic and succinic acids 7°, styrene and stearic acid vl and dioxane 72. Adsorption studies have been reported for aqueous solutions ofpolyhydric alcohols v 3, ethylene glycol 74, polyethylene glycol 75, diethylene and dipropylene glycols 76, aniline and derivatives 7v'78, coadsorbed isoamyl alcohol and cyclohexano179, pyridine s°'81 and derivatives s2, bipyridine s3, toluidines s4, e-acetyl-5-bromothiophene sS, cis and trans-l,2-dibromoethylenes 86, aliphatic acids 87, g-amJnocaproic acid ss, 5-chloro-1- pentano189, ~o-aminoenanthic acid 9°, benzodiazoles 91, cresols 92, camphor and related substances 93, butyric and isobutyric acids 94, ethyl bromide 95, methanol 96, diamines and dibasic acids 9 v, dodecyl ethers of polyethylene glycols 98, co-adsorbed valeric acid and amyl alcohol 99, hydroquinone, benzene, biphenyl and thiophene 1°° (also in methanol and DMF), propionic acid 1°1, 1-pentanol, 1-butanol and cyclohexanol 1°2, various alkyl alcohols 103, 3-pentanol, chloroform, cyclohexanol and cyclohexanone 104 furan derivatives and cyclopentanone 1°5. Nonaqueous solution studies include measurements in liquid ammonia 1°6, concentrated solutions of LiNO3 in methanol and ethanol 1°7, LiNO3-KNO 3 eutectic 1°8, ethylene glycol 1°9, acetonitrile 11°, dimethylformamide 111, various alcohols, ketones, amines and amides 112, propylene carbonate 113,114 and a range of aliphatic amide solvents 115. In dimethylformamide specific adsorption of I- and Cs + from CsI solutions 116, adsorption of various amines 117'118 aniline and c~-naphthylamine 119 (also in methanol), naphthalene and dipheny112° and thiourea 121 has been studied. Specific adsorption of C1- ions from LiC1 solutions in dimethylsulfoxide 122, the structure of the double layer for LiNO3 solutions in pyridine lz3 and specific adsorption of I- in ethylene glycol 124 have been investigated. Adsorption studies have been reported for C1- ions in aqueous mixtures with methanol 12 s and ethanol126 and also for the nonaqueous component in aqueous solutions of methanol, sulfolane and formic acid 127. Electrocapillary curves have also been reported for various organic compounds in aqueous solutions of ethanol1 z8 and acetic acid 129. A comprehensive review of nonaqueous solution work up to 1968 is given in ref. 7. The extensive Russian work on the adsorption of organic substances also up to 1968 was reviewed recently 13°.

2. EXPERIMENTAL PROBLEMS

Surface excesses of ions and molecules at the electrode surface can be determined from either electrocapillary or capacity measurements. Analysis of capacity

ELECTRICAL DOUBLE LAYER: PROBLEMS AND RECENT PROGRESS 279

data usually requires two independently determined integration constants, one of which is the potential of zero charge and the other a value of either the interfacial tension or the actual surface excess at a given value of the electrode potential (or charge). In their classic studies of ionic adsorption from aqueous solutions of in- organic salts, Grahame and Soderberg TM evaluated the second integration constant from diffuse layer theory with the aid of certain assumptions which, however, are not generally valid 132. In general, therefore, capacity measurements must be supplemented by electrocapillary data except in special cases, for example, where adsorption of a neutral substance from a fixed concentration of base electrolyte is being studied. The electrode charge and interfacial tension may then be reasonably assumed independent of the bulk concentration of the adsorbate in certain potential regions and a "back-integration" method applied in order to evaluate the constants of integration.

The electrocapillary measurements contain all the information required for evaluation of the surface excess, but it is frequently difficult to obtain the necessary accuracy. Furthermore, serious discrepancies between the electrocapillary curve,

4 2 0

4 1 0

¥ u ~ 400

~ 39C

380

' -0 !4 ' -018 ' -1!2 ' - I . 6

E / V vs. NCE

Fig. 1. Comparison of electrocapillary curve obtained by integration of the capacity (solid line) with direct electrocapillary measurements (points) for 0.01 M NaF (from Lawrence et a1.136). (1 dyne= 10 -5 N.)

obtained by the capillary electrometer method, and the doubly integrated capacity curve in some solutions have been reported 18'133-140. The discrepancies occur on the positive branch of the curve. Lawrence et al. 136 reported directly measured values of the interfacial tension lower than the doubly integrated capacity values by amounts of up to 1.6 dyn cm -1 in 0.1 M NaF and >20 dyn cm -1 in 0.01 M NaF (Fig. 1). The effect occurs generally in both aqueous and nonaqueous dilute solution of salts where specific adsorption of the anion is weak 1~ 5. Bockris and co-workers ~ 34 found similar discrepancies on both branches of the curve for dilute chloride solution. How- ever, the discrepancies on the cathodic side were evidently due to errors in the determination of the potential of zero charge ~3s. The real discrepancies on the anodic side result from low values of the measured interfacial tension apparently caused by a non-zero contact angle. Such errors should disappear if the interfacial tension is measured by a method which does not depend on the contact angle. This has been confirmed by Parsons and Trasatti 137 using the drop-time method for a 0.01 M NaF solution and also by Schiffrin 139 using the maximum bubble pressure

280 R. PAYNE

method for a 0.1 M KC1 solution. In both cases satisfactory agreement with the integrated capacity curves was demonstrated. It should be mentioned that none of these methods gives the absolute value of tb_e interfacial tension which is still based on the sessile drop measurements of Gouy TM. These measurements have been repeated and confirmed recently by Smolders and Duyvis 142 and Butler ~43. Results of an independent method devised by Parsons and Symons ~44 are also in agreement although the precision of this method is somewhat limited. On the other hand, recent careful measurements by Melik-Gaikazyan and co-workers ~45 using the pendant drop method gave an interfacial tension value of 431 dyn cm- 1 for a 0.5 M Na2SO4 solution at the electrocapillary maximum (temperature not. specified). This is ,,, 5 dyn cm-1 above Gouy's value. The source of this discrepancy is not clear.

Direct confirmation of the contact angle effect was reported recently by Doilido et al. ~ 6 for solutions of NaC104 in dimethytformamide where large discrepancies between directly measured electrocapillary curves and the integrated capacity were found. The meniscus in the capillary assumed a concave form when the mercury column was lowered indicating sticking of the mercury to the glass, a phenomenon which is common in nonaqueous solutions 115.

Penetration of electrolyte between the mercury thread and the glass wall inside the capillary is a serious experimental problem both in capillary electrometer and capacity measurements, especially in nonaqueous solutions. In the electrometer, the effect produces an unstable meniscus and in extreme cases the mercury thread may be broken at a point above the meniscus by occluded solution or gas bubbles 11~. Solution penetration at the dropping mercury electrode produces variations in the mercury flow rate and erratic drop formation. It is especially troublesome at extreme cathodic potentials and in nonaqueous solutions, presumably due to the lower interfacial tension under these conditions. However, it is rarely a problem for a positively polarized electrode, a fact which is probably related to the contact angle effect mentioned earlier. Solution penetration effects can usually be minimized by a silicone treatment of the capillary although the procedure is less satisfactory in nonaqueous solvents, which tend to remove the coating quickly.

Errors in the area of the drop in capacity measurements at the dropping mercury electrode due to non-uniform flow do not seem to be important provided that the same capillary and experimental conditions are used for a set of measurements. The important requirement is to obtain the same area for each concentration at a given constant electrode potential (or charge) since this is what controls the accuracy of the subsequent differentiation to find the surface excess. A systematic error of even a few percent in the capacity per unit area is relatively unimportant since the error involved in differentiation will usually be greater. The scatter of the data which often results from a change of capillary during the course of a series of measurements is much more troublesome. Elaborate corrections for the back pressure error have been made but they are not straightforward and involve some rather arbitrary assumptions concerning the dynamics of drop growth and breakaway ~46-149. The use of such correction procedures therefore hardly seems justified for most purposes.

Low frequency bridge techniques in electrochemical impedance measurements have been used for many years but the grounding requirement continues to be a source of confusion. The problem is avoided in commercial transformer ratio-arm bridges where the impedance to ground of the unknown terminals is low and therefore


is not a source of error. However such instruments are seldom direct reading for a series RC network as encountered in double layer measurements, and it is usual therefore to build a bridge from components for this purpose. The simplest and most effective way to solve the grounding problem with such a bridge is to isolate both the source and the detector with electrostatically screened transformers of the General Radio 578 type 150. An alternative approach is to construct a virtual ground at one of the detector corners using either a screened and balanced transformer 151,~ 52 or a feedback amplifier ~ 53. In a recent paper 154 it was suggested that the only proper way to ground an a.c. bridge is the Wagner ground. This method will achieve the desired result but is unnecessarily cumbersome. An important advance in bridge techniques for double layer work in recent years is the application of phase-sensitive detection which greatly improves the sensitivity of capacitance measurements under conditions where the capacitive impedance is low compared with the series resistance, i.e., at high frequencies and low electrolyte concentrations 154,155.

3. THE DIFFUSE LAYER

The Gouy-Chapman theory of the diffuse layer 156"157 is based on a simple model of point charges in a structureless dielectric medium similar to the Debye- Hiickel theory of electrolytes. In the original treatment it was supposed that the diffuse layer would extend up to the physical interface but calculations based on this model were shown to be in conflict with experiment 158. In Stern's model of the double layer 159 the diffuse layer ions have a closer distance of approach as a result of their finite size, although there is no obvious correlation between ionic radii (crystallographic or solvated) and the double layer capacity 16°. Recent measurements in concentrated electrolyte solutions 161 however suggest that the approach of diffuse layer cations to the electrode is restricted by the solvation sheath of the ions. The principal usefulness of the Gouy-Chapman theory has been as a criterion of specific adsorption and as a way of calculating the amounts adsorbed rather than as a frame- work for studying the diffuse layer itself.

The Gouy-Chapman theory neglects the specific chemical properties of the ions, dielectric saturation and electrostriction in the solvent and the discrete nature of the ionic charge. It should therefore fail under most conditions. However, where an adequate test of the theory is possible (i.e., at low concentrations and low electrode charge) the agreement with experiment is excellent. There have been few experimental tests of the theory under conditions where deviations would be most likely to occur. In one such test Joshi and Parsons 162 investigated the ionic charge distribution for mixed solutions of HC1 and BaC12 in water, finding what they considered to be significant but small deviations from the theory which however were not found in subsequent coulometric measurements 163 and which were eventually traced to an error in calculation ~ 37. Parsons and Trasatti 13v recently repeated the experiment for mixed KC1 and MgC12 solutions finding satisfactory agreement of both these and the earlier results with the theory.

The distribution of the cation surface excess between K + and Mg 2+ ions shown in Fig. 2 is in good agreement with the diffuse layer theory but it is worth noting that the experimental points lie somewhat above the theoretical curves. The anion is correspondingly positively adsorbed whereas according to the theory it should be

282 g. PAYNE

repelled from the negatively charged electrode. This is not a peculiarity of mixed electrolytes. The same effect of increasing positive adsorption of anions as the electrode charge becomes more negative occurs in the data of Parsons and Trasatti for pure KC1 and pure MgCI2 solutions and has previously been reported164 in dilute aqueous solutions of NaOH, KNO3 and NazSO 4. All these results are based on capacity measurements but the effect is also present in Oldfield's electrocapillary data for LiOH, NaOH and KOH solutions 165. Similar deviations from diffuse layer behavior in some nonaqueous solutions 166-168 and in concentrated aqueous solutions 169 have been attributed to specific adsorption of cations. However, the effect is more pronounced in dilute solutions (Fig. 3) and evidently depends on the nature of the

u

r-t'

2o t' I~ °

o o I

• • a • * *

0 ° ° ° ° ° ° Cr- • i o

• • o

U

u

qluC cm -2

-I01-

0 -5 -I0 -15 G/~C cm -2

Fig. 2. Surface excesses of Mg z+, K + and C] - ions at a mercury electrode in 0.0208 M KC|+0.0555 M MgC12. Points are exptl. Lines calcd, from diffuse layer theory assuming no specific adsorption of ions. (from Parsons and Trasatti~37).

Fig. 3. Surface excesses of OH- ions in aq. NaOH solns, at 25 °. Points are exptl.: (C)) 0.01, ( I ) 1.0 M. Lines calcd, from diffuse layer theory (Payne, unpublished data).

anion. This does not seem consistent with specific adsorption of the cation. It has also been suggested 137 that the anomaly arises from slow relaxation of the diffuse layer in dilute solutions which would lead to frequency dependence of the capacity 17°. However, Paisons and Trasatti were unable to confirm this effect which in any case could not explain Oldfield's electrocapillary data.

Numerous attempts have been made to improve the Gouy-Chapman theory (see refs. 2 and 12). However, from the point of view of double layer measurements the simple equations seem adequate since improvements of the theory lead to rather cumbersome equations and result in only minor modifications. Under conditions where the Gouy-Chapman theory should be least reliable, i.e., at high electrolyte


concentrations and extreme electrode charges, it is not possible to devise an adequate test since the potential drop across the diffuse layer is small compared with the total potential difference across the double layer. Furthermore in solutions of 1 M concentration or greater, the thickness of the diffuse layer is comparable to the radius of a typical ion, and it may be justifiable therefore to neglect the diffuseness of charge in concentrated solutions as was done in a recent paper 22.

Two major problems arise in the calculation of amounts of specifically adsorbed ions using the Gouy-Chapman equations and the methods proposed by Grahamel. The first occurs in concentrated solutions and is not really concerned with the diffuse layer theory but rather the effect of exclusion of electrolyte from the inner layer. In the absence of specific adsorption this results in a surface deficiency of electrolyte at the interface, an effect known since Gouy's early work although its significance in adsorption calculations was recognized only comparatively recently46,1 s 3,171,172,2 2 3. In a unimolal aqueous electrolyte solution the mole fraction of the electrolyte is approximately 0.02. Consequently in the absence of specific adsorption of one or both ions there should be present within the inner layer approximately 2 ~ of a monolayer (assuming the ions and the solvent molecules are of equal size). In calculating amounts adsorbed from the surface excess this factor must be taken into account. This is quite difficult since it requires a knowledge of the surface concentration of the solvent. The second problem arises where specific adsorption is weak and again arises not so much from defects in the diffuse layer theory as from the form of the equations relating the cation and anion surface excesses in the diffuse layer 162. In studies of weak specific adsorption of anions for example the cation surface excess (F+) approaches the limiting repulsion value predicted by diffuse layer theory. The diffuse layer concentration of anions simultaneously approaches infinity and is consequently extremely sensitive to errors in the experimentally determined values of F+. It therefore becomes almost impossible to distinguish between specific and diffuse layer adsorption of anions under these conditions. For the same reason, direct detection of specific adsorption of cations in aqueous solutions is extremely difficult.

4. THE INNER LAYER

In the Stern model of the double layer the diffuse layer ions have a closest distance of approach which in Grahame's terminology is the outer Helmholtz plane (OHP). The region between the electrode and the OHP is the inner or compact region of the double layer consisting of a layer of solvent molecules which may include some specifically adsorbed ions. The Stern model implies a direct correlation between the capacity and the radius of diffuse layer ions which however is not found experimentally. This is hardly surprising in view of the simplicity of the model. Although the capacity is often discussed in terms of such macroscopic concepts as the thickness and the dielectric constant of the molecular condenser, a more realistic approach should take into account the microscopic structure of the inner layer as well as ionic solvation and other specific properties of the adsorbed ions and solvent molecules. Since short-range specific forces between adsorbed particles and between particles and electrode predominate over the ordinary coulombic interactions, the theoretical problem is much more complex than the diffuse layer problem where it seems permissible at least

284 R. PAYNE

to a first approximation to neglect short-range forces. The initial problem in discussion of the inner layer is a qualitative under-

standing of the potential-dependence of the capacity on which there is still considerable disagreement. In both aqueous and many nonaqueous solutions the capacity curve is dominated by a "hump" which in water occurs at a small positive electrode charge (Fig. 4). The hump is generally thought to be related to reorientation of solvent dipoles in the inner layer and the problem has been treated quantitatively by Watts- Tobinl 73, Macdonald and Barlow 174 and others. However two major objections have been raised to the dipole reorientation theory. Firstly the theory predicts a capacity curve symmetrical about the hump, whereas the capacity is generally higher on the anodic side. Secondly the hump in water occurs on the positive side of the pzc con-

tO

zo

V 5

0 .01 ~

0 - 0 5 -liO -I I I

Potential/V vs. O.INcal.

Fig. 4. Differential capacity curves for KNO a solutions in water at 25 ° (from Payne164).

sistent with a preferred positive (toward the electrode) orientation of the solvent dipole whereas other evidence supports the reverse orientation. In a recent paper Levine et al. 176 have shown how this anomaly can be resolved by assuming that the normal component of the dipole moment is different in the two orientations. However, this approach may not be able to explain the behavior of nonaqueous solvents such as formamide where the hump occurs far from the point of zero charge 7. In N- methylacetamide and related solvents two humps have been observed on opposite sides of the point of zero charge 7'115. This would seem inconsistent with dipole reorientation although the possibility of two reorientations cannot be ruled out. Bockris and co-workers 175 consider the hump in water to be due to specific adsorp-

ELECTRICAL D O U B L E LAYER : PROBLEMS AND RECENT PROGRESS 285

tion of anions. This can occur when the slope of the amount adsorbed against potential passes through a maximum value, but it has been shown repeatedly that the hump remains after the effects of the adsorption have been removed in the analysis16,,,171,177 - 181. There can also be little doubt that the formamide hump is a property of the solvent rather than the ions since anion adsorption is unlikely to be a factor at negative electrode charges 7. The general asymmetry of capacity curves suggests that anions move closer to the electrodes than cations. Since most anions are specifically adsorbed on a positively charged electrode this seems reasonable. However it has been suggested 21'22 that ions like NO3 and ClOg are specifically adsorbed with a layer of water molecules separating the ions from the metal which could account for the generally lower anodic capacity in solutions of these ions.

There is still no consensus of opinion on the nature of the high anodic capacity in fluoride solutions. Watts-Tobin 173 suggested that specific adsorption of OH- ions might be responsible but subsequent experimental work lvz'xs2 seemed to rule this out. However, Armstrong and co-workers 56 found evidence that mercury dissolves as Hg(OH)2 during the anodic reaction in fluoride solutions and hence concluded that specific adsorption of OH- ions causes the high capacity in the ideally polarized

35

E u

h_

z~

8 ~" g 3c [z

o.a ~ -o'2 -o.4' -o Potential / V vs. SCIE

Fig. 5. Differential capacity curves for solns, of x M K F + ( 1 - - x ) M K H F v x: (1) 0.94, (2) 0.68, (3) 0.35, (4) 0.14. (from Verkroost et al.411.

region. According to the diffuse layer criterion the F- ion is not specifically adsorbed to any significant degree but for the reasons mentioned earlier the test is inconclusive. In a recent paper, Verkroost e t al. 41 have avoided the diffuse layer problem by working with mixed solutions of KF and KHF 2 at constant ionic strength, finding evidence of substantial specific adsorption of F- ions. This conclusion is also supported by Schiffrin's measurements 26 for NaF solutions at 0 °. In view of the correlation of the capacity rise with the calculated reversible potential for discharge of F- ions noted earlier 172, the capacity rise is probably due to specific adsorption of F- ions. The addition of HF~ ions to a fluoride solution produces an unexpectedly large effect on the capacity (Fig. 5) which may help to explain the discrepancie,~ between the results of various workers 172.

286 R. PAYNE

According to Deva'fiathan 183 the rise of the capacity on both sides of the minimum point is due to specific adsorption of ions, anions on the positive side and cations on the negative side. However the evidence for general specific adsorption of cations, in aqueous solutions at least, is sparse. In the alkali metal cation series only Cs ÷ has been shown to be specifically adsorbed by direct measurements, whereas K ÷, Na ÷ and Li ÷ behave like diffuse layer ions. However it is worth noting that these ions show specific effects in electrode kinetics studies 1° even though no specific adsorption is indicated by double laycr measurements. According to Macdonald 184 the minimum on the capacity curve and the rising capacity at more negative potentials results from the compensating effects of dielectric saturation and electrostatic com- pression of the solvent molecules in the inner layer. This implies that the inner layer is solid and impenetrable which is probably unrealistic although the idea seems basically correct. In addition to solvent molecules the inner layer probably contains solvated cations which eventually become desolvated on the side adjacent to the electrode at sufficiently negative potentials. This effect is apparently confirmed in some recent measurements ~61 for concentrated solutions of NaC104 in which the capacity curves coincide at extreme negative potentials indicating at least partial

15 I I ~ ,o ~ -,~ -2b -3o OIJJC c m -2

3 o

c~

Fig. 6. Differential capacity as function of electrode charge for solns, of NaCIO4: (1) 1, (2) 7.1, (3) 9.3 M (from Ivanov et a1.161).

dehydration of the cation (Fig. 6). In CaC10 4 solutions the curves converge but do not actually coincide (Fig. 7). The difference was attributed to stronger hydration of divalent Ca 2+ cation.

Various other explanations of the potential dependence of the inner layer capacity have been proposed. Grahame ls5 suggested that the hump in aqueous NaF solutions is due to the formation of an ice-like layer of water, which is equivalent to postulating a variation of the thickness rather than of the dielectric constant of the inner layer. Hills and Payne 186 reached a similar conclusion from the temperature and pressure dependence of the capacity in 0.1 M NaF solutions. From considerations of the dependence of the slope and size of the capacity hump in aqueous solutions Schwartz et al. l s v suggested that anions interact with the water molecules in the inner


E u 3C EL

o

-~ 20

layer affecting their reorientation which is responsible for the hump. In support of this idea Parsons is has compared the large hump found in solutions of ClOg a "structure-breaking" ion, with the much smaller hump in solutions of HEPO2 which is strongly hydrated. However, Damaskin and co-workers z1'22 have concluded from measurements in concentrated solutions that specifically adsorbed NO]- and ClOg

45

4(3

E u L ~ .a

o3C

o

~g z.'

2b 6 -6 -io -3b zc 6 -o'4 -o!8 qlJJC cm -2 Potential / Vvs.SCE

Fig. 7. Differential capacity as function of electrode charge for so]ns, of Ca(CIO4)2: (1) 1, (2) 5.8, (3) 6.6, (4) 8.1, (5) 9.3 N (from lvanov et al. lal) .

Fig. 8. Differential capacity curves for 1 M aq. solns, of (1) sodium fumarate, (2) sodium maleate (from Parsons and Reilly53).

ions are not in contact with the metal, in which case it is difficult to see how the ions can exert much influence on the adsorbed solvent molecules. A striking difference in the appearance of the capacity hump in solutions of the stereoisomeric maleate and fumarate anions was observed recently by Parsons and Reilly 53 (Fig. 8) who attributed the effect to modification of the water reorientation as proposed by Schwartz et al.

5. SPECIFIC ADSORPTION OF IONS

The fact that anions undergo some kind of specific adsorption superimposed on the ordinary electrostatic adsorption was realized by Gouy ls8, but detailed studies of the phenomenon began only after direct measurement of the double layer capacity became possible. Stern 159 introduced the adsorption isotherm approach relating the concentration of adsorbed ions to their concentration in the solution in terms of an assumed model of the adsorbed state. The first evaluation of amounts adsorbed from experimental data using the Stern model and the Gouy-Chapman theory of the diffuse layer is due to Grahame 1.

288 R. PAYNE

The nature of specific adsorption forces remains uncertain. Grahame considered specifically adsorbed anions to be covalently bonded to the metal, the strength of the bond increasing with the positive charge on the metal. This was expressed formally as an electrical dependence of the "specific adsorption potential" in the Stern theorv. However the idea of covalent bonding of variable strength and without formal electron transfer seems inconsistent with the usual concept of covalency. Various attempts have been made therefore to calculate the adsorption energy from electrostatic models. Using a modified form of Stern's adsorption isotherm and taking into account the effects of discreteness of the adsorbed charge, Levine and co-workers 189 were able to calculate the electrical dependence of Stern's "specific adsorption potential" for the chloride ion as determined by Grahame 1. Andersen and Bockris 19° went further and were able to calculate the entire free energy of adsorption for iodide ions from purely electrostatic considerations. However such calculations involve some arbitrary assumptions and approximations which cannot be adequately tested. Furthermore, there is strong evidence in favor of nonelectrostatic interaction of, for example, sulfur-containing species such as CNS-, S 2- and thiourea, and also halogen-substituted organic compounds which adhere more strongly to mercury than the corresponding unsubstituted compounds v. It seems probable therefore that some kind of chemical bonding occurs at least for some ions (and other species). Covalent bonding involving partial charge transfer from the adsorbed ion to the electrode has been proposed by Lorenz and co-workers 191'192. This work has been discussed by Parsons 193 who notes that the arguments invoked are essentially thermodynamic and therefore cannot be used to decide the question of partial charge transfer.

The question of whether or not an adsorbed ion interacts with the metal in a specific manner is still open but there can be little doubt of the important contribution of solvation, both at the interface and in the solution, to the adsorption energy. It now seems clear that for large "structure-breaking" anions such as C104 and PF6 in water, the "squeezing out" effect of the solvent is a major factor in the adsorption energy. This can be inferred from the behavior of these ions at the air-solution interface where they are also strongly adsorbed 194. In contrast the CI- ion, which is strongly adsorbed on mercury, is actually repelled from the air-water interface 194. Therefore the CI- ion must be stabilized on the electrode either by specific interaction with the metal or by interaction with adsorbed solvent molecules or both. Extensive measurements in nonaqueous solutions also confirm the importance of solvation. For example, the adsorption of polyatomic anions such as C104, PF6, NO~- and SCN- is much stronger in water than in dimethylformamide 115 a result which can be attributed to the "squeezing-out" effect in water which is absent in an unstructured solvent such as DMF.

The analysis of specific adsorption data worked out by Grahame 1,171,1 v 7,195 involves the formal separation of the inner layer potential difference (~b m- 2) into two parts, one contributed by the charge in the electrode surface and the other by the specifically adsorbed charge. Parsons 196 has formulated this in a rather more satisfactory way by writing ~m-2 as a function of q, the electrode charge and ql the specifically adsorbed charge;

c~,,,- 2 = f ( q , ql) (1)

leading to the following expression for C i the capacity of the inner layer:


1 dgb " -2 (O~m-2"~ (_~gb"-2~ dq'

C i ~ d ~ - - \ ~ / q , + ~ - q ~ / q dq (2)

The partial derivatives in the right-hand side of eqn. (2) are called qC i and q,C i respectively in Parsons' notation, qC ~ the component of the inner layer capacity measured at constant amount adsorbed is sometimes referred to as the "true" capacity especially in connection with the adsorption of neutral substances 9. It should be pointed out that neither qC i nor ~,C i is a directly measurable parameter under equilibrium conditions. However both can be calculated from experimental data wit h the aid of the diffuse layer theory. The value of this type of analysis is that the partial capacities can be related to a physical model of the inner layer whereas the total inner layer capacity cannot.

> Oil !

E

-q° l .uC crrf 2 Fig. 9. Potential difference across inner region of double layer as functiQn of specifically adsorbed charge (ql) and charge on the metal for solns, of KI in water. Charge on metal is indicated by numbers at the end of each line (from Grahamet77).

The first detailed analysis of this type was applied by Grahame 177 to his capacity measurements for aqueous solutions of KI. The plots of ~b"-2 vs. qX (sometimes referred to informally by Grahame as the "Christie plots") for this system were shown to be linear and almost parallel (Fig. 9). It follows that q,C i is therefore almost independent of q, and qC ~ the capacityat constant amount adsorbed is independent of the amount adsorbed. Furthermore qC ~ was shown to be identical within experimental error with the total inner layer capacity for KF solutions in which specific adsorption of anions was considered absent or minimal. The adsorbed anion therefore apparently behaves like a point charg e in a fixed plane having no effect on either the

290 R. PAYNE

thickness of the inner layer or its mean polarizability. In order to explain this un- expected result, Grahame suggested that accidental compensation of the dielectric constant and the thickness occur so that their ratio remains constant. This proposal unfortunately cannot be tested directly since the dielectric constant and thickness cannot be determined independently.

The idea of accidental compensation of dielectric constant and thickness effects over a wide range of coverage of the electrode with adsorbed anions (about 40% in the KI system) seems improbable and is not supported by more recent w o r k 133'144'164'171'178'197'198 in which parallel or nearly parallel Christie plots have been found generally in the adsorption of anions under conditions similar to those in Grahame's experiments, although the capacity at constant amount adsorbed is generally different from C i for KF solutions. In particular the _C i values for large anions such as NO~ are considerably lower than the K F values ~64. The adsorption of m-benzenedisulfonate anions from aqueous solutions of sodium m-benzenedisulfonate approaches saturation coverage but nevertheless also gives linear and parallel Christie plots ~78. Such a large anion cannot be represented even approximately as a point charge and, (assuming it is in contact with the electrode) must produce a large effect on the structure of the inner layer in the way that neutral substances do. The fact that it appatently does not has so far received no satisfactory interpretation.

In the isotherm approach to ionic adsorption first introduced by Stern in 1924, and subsequently developed mainly by Parsons and co-workers the equation of state of the adsorbed ions is investigated while the electrical conditions at the interface are kept constant. This is achieved in Parsons' approach by maintaining constant electrode charge. The original justification for controlling the electrode charge rather than the potential is the fact that the charge is a more precisely defined parameter; than the potential which is the sum of potential differences across several interfaces ~ 99.

This is a controversial.point especially in the case of adsorption of neutral substances. However ionic adsorption has invariably been studied at constant charge and since the indications are that no experimental distinction between the constant charge or constant potential approaches is possible in this type of system, a discussion of this point will be deferred.

The first objective of the isotherm approach is to see whether the adsorption can be represented by a single isotherm; that is, whether the individual isotherms for each value of the electrode charge (or potential) can be superimposed on a common curve. This has been called the congruency condition z°°. Isotherms for anion adsorption are generally congruent in the charge to a first approximation with few exceptions. Congruency tests have usually been made using the integrated form of the isotherm, i.e., the "surface-pressure" curve 199. This method avoids the errors involved in graphical differentiation of experimental data to obtain surface excesses through the Gibbs adsorption equation but at the expense of some loss of sensitivity. In the KNO3 system for example the constant charge surface pressure curves apparently superimpose perfectly on a common curve (Fig. 10). However, when the amounts adsorbed calculated from the Gibbs adsorption equation are compared with values calculated from the common surface-pressure curve small but systematic differences are found (Fig. 11). It appears therefore that the constant charge isotherms are only approximately congruent in the KNO3 system and this is also generally true in other anion adsorption systems.


,O,

o

to to

c~.

O3

40

'30

-20

- I 0

-0 -¢ -/ o I ,2 3, ? log Be_+ / .r,

_ 16 9 . . J Q" • 2 0 q / . . u C crn'~ ~

, f ; J ; J ' ~ ~2 . ° J "°"

o / o / o

/ , - Y o - / / ~ / ~ o / ? / ' "

- 2 o - ~.,5 - i .o - o p

Io9 a~ Fig. 10. Composite curve of surface pressure of nitrate ions specifically adsorbed from KNO3 solns. Range of q covered, 0-18 #C cm -2. Solid line calcd, from Frumkin isotherm (from Payne164).

Fig. 11. Comparison of charge due to specifically adsorbed nitrate ions in KNO 3 solns, calcd, directly from Gibbs adsorption equation and diffuse layer theory (O) with values calcd, from the isotherm (O) (from Payne164).

The adsorption equilibrium can be written as:

f(o) - # (3) a

where f(0) and a represent the activity of the adsorbing species at the inter(~ee and in the solution respectively, 0 is the fractional coverage of the electrode with adsorbed material and fl is the adsorption equilibrium constant which is related to the standard free energy of adsorption AG O according to

fl = exp [ -AG°/kT] (4)

In a congruent system f(O) contains no electrically dependent parameters. The electrical dependence of the adsorption is expressed solely through the equilibrium constant fl and therefore in view of eqn. (4) represents the electrical dependence of the free energy of the adsorbed ion in the standard state. The slope of the Christie plots is approximately related to the charge dependence of fl according to 196

e o (~bm-2~ _ d in fl (5)

kT ~ q l / q dq

The diffuse layer is neglected in the derivation of eqn. (5). An exact relationship is given by Parry and Parsons 178.

Since d In fl/dq is a total differential, (assuming that the congruency condition holds,) the linearity of the Christie plots confirms the correctness of charge congruen-

292 R PAYNE

cy. If they are also parallel the standard free energy of adsorption is linearly dependent on the charge according to eqn. (5). The experimental Christie plots therefore generally indicate charge congruency but as in the case of superimposed surface-pressure curves a more careful inspection of the data reveals small but systematic deviations from congruency in most cases.

Frumkin 2°1 has shown that the correct form off(0) for adsorption from solution where the solute and solvent particles are of equal size and non-interacting is the Langmuir expression,

f(O) = 0/(1 - 0) (6)

Lateral interaction is taken into account in Frumkin's empirical extension z° /o f the Langmuir isotherm,

0(1 - 0)- 1 exp AO = fla (7)

More recently the effect of different size of solvent and solute particles has been considered by Levine et al. 189 using Flory-Huggins 2°3 volume fraction statistics. Frumkin's isotherm then becomes 18,

(O/p)(1 -O) -p exp (AO)= fla (8)

where on solute particle displaces p solvent particles on the electrode. The validity of volume fraction statistics for two-dimensional mixing has been questioned by Macdonald and Barlow 2°4. More important, as a practical matter the use of a three- parameter isotherm like eqn. (8) is rarely justified by the accuracy of experimental data which usually can be fitted with two parameters and often with one. The usefulness of eqn. (8) is therefore limited in practice.

Although the Langmuir form of isotherm with allowance for lateral interaction is appropriate from a theoretical standpoint, experimental data for ionic adsorption can often be described by a much simpler isotherm. Grahame's KI results for example were shown by him to fit a logarithmic form of isotherm at not too low values of the electrode charge and the amount adsorbed (Fig. 12). A more complete fit of the same data to a virial form of isotherm was obtained by Parsons (Fig. 13). Neither the logarithmic nor the virial isotherm can be considered realistic for this kind of system and it now appears that this behavior is the result of strong lateral repulsion in the adsorbed layer 18'19~. Equation (8) can be expanded to give

In [ta= In O/p + (A + p) 0 + p02/2 + p03/3 + . . . (9)

When A is large and positive (strong lateral repulsion) the first term and terms in 02 and higher can be neglected and the isotherm reduces to the logarithmic form

(A+p)O = In fla (10)

If the first term is retained the resulting equation has the form of the virial isotherm in which the second virial coefficient B is given by

B = (A+p)/2 I~ (11)

where F~ is the amount adsorbed at saturation. For non-interacting hard spheres, the second virial coefficient would be equal to twice the particle area or about 34 A 2 for the I- ion based on the crystallographic radius of 2.2 A. Experimental values of the composite parameter B for aqueous KI solutions vary with the electrode charge


44

4O

36

52

~ 28

~ 24

16

8

4

0

., , , , , J : :

" 8

.

0.025 0.05 0.1 0.::='5 0.5 ID

i ! i

. / ' 164 4C . ~ . /

-" /

I J ~ • ~ ~ . ~ ~ ;~ | / . ~ ~ ~ . ~ ~ . ~ ,ot-~ . ~ ~ ~ . ~ ~ -

I ~ . ~ / ~ ~ I / : ~ f ~

i I I -4 -3 -2

log (-a+Elq ~ )

Fig. 12. Test of logarithmic is6therm for adsorption of iodide ions from KI solns.in water (from Grahamel 77).

Fig. 13. Test of virial isotherm for adsorption of iodide ions from KI solns, in water (Data of Grahame 177, from Parsonsa96).

from 310-390 •2/ion 196 giving some indication of the magnitude of lateral repulsion. Similar "virial" behavior was found for KI solutions in formamide 197 where the value of B is about 620 AZ/ion, alme~t independent of the electrode charge. This value is for an isotherm based on the salt activity whereas the value given in the original paper is based on the mean ionic activity. Much larger values varying with the electrode charge from 900-1500 AZ/ion were reported for mixed solutions of KI and KF in methanol z° 5. The nature of this strong lateral interaction and its dependence on the solvent is not understood. The electrical dependence of B of course indicates departure of the isotherm from congruency.

The behavior of other anions is generally more complex. The adsorption of C1- ions from KCI solutions in water for example cannot be represented by constant charge isotherms of the general form of eqn. (8), or any of its limiting forms 18,171,1sl. The Br- ion in KBr solutions behaves similarly a36. The isotherms in these systems flatten off to an unexpectedly high value of the amount adsorbed at low concentrations. This effect is also clearly present in the KNO3 data of Fig. 11 where the charge due to specifically adsorbed anions seems to approach a value numerically equal to the electrode charge at low electrolyte concentrations. There is some residual uncertainty in the measured amounts adsorbed in this concentration region because of the uncertainty of the diffuse layer calculation mentioned earlier. However, the trend is systematic, and in the KC1 system Grahame's original measurements have recently been confirmed by Trasatti 137. This effect therefore seems to be real.

tn a recent review de Levie 2°6 has pointed out that the general shape of these isotherms can be reproduced if the Frumkin isotherm is modified by the inclusion of a Boltzmann term in ~b z (the diffuse layer potential difference) in the adsorption energy,

0(1-0)- 1 exp [AO+ze°4)2/kT] = ~a (12)

294 R. PAYNE

De Levie noted that the use of isotherms of this form in the interpretation of specific adsorption of anions is not new. However, the relationship of the ~b 2 t e rm to the flatten- ing of the isotherms at low concentrations of the electrolyte had not been realized. It seems clear that isotherms of the form of eqn. 12 cannot be congruent in the electrode charge since the q~z term introduces a concentration-dependent electrical dependence into the adsorption energy. In a recent study of specific adsorption of azide ions from aqueous solutions ofNaN3, d'Alkaine et al. 39 were able to fit their data to the low-coverage approximation, ( 1 - 0 ~ 1 ) of eqn. (12) at constant electrode charge. However, the approach has been less successful with other simple anions and remains tentative.

The adsorption of anions from mixed electrolyte solutions in which the ionic strength is kept constant by the addition of inert electrolyte usually differs in important respects from the adsorption of the same ion from solutions of a single electrolyte. The advantage of working with mixed electrolytes is that the diffuse layer correction is eliminated from the calculation of the specifically adsorbed charge 2°°'2°v.

The appropriate form of the Gibbs adsorption equation for a solution containing two 1:1 electrolytes, CA at x M concentration and CB at ( b - x ) M concentration (where b is a constant) is,

- d~ = - d (7 + qE) = k T [ F ~ - - x (b - x)-X F~-] d In x - Edq (13)

F 1_ and F~- are surface concentrations (strictly surface excesses) of specifically adsorbed A - and B- anions respectively and 7 is the interracial tension. The activity coefficients of both electrolytes are assumed constant. If specific adsorption of B- can be neglected (or in any case when x,~ b) the second term in braces vanishes and F~- is given directly by

F~- = - ( k r ) - 1 ( ~ / 0 In x)q (14)

This method therefore offers a particularly direct route to the specifically adsorbed charge and avoids the ambiguity of the diffuse layer calculation at low concentrations. On the other hand, it introduces the complication of the second electrolyte which may itself be specifically adsorbed. This would not affect the validity of eqn. (14), providing x is kept small but would of course modify the conditions for the adsorption of A- .

Several systems of this type have been studied .1'42'44'179"18°'181,200 using a fluoride as the inert electrolyte, usually at a total ionic strength of ! M. The adsorption of I - from KI + KF mixtures 2°° was shown to be similar to its behavior in KI solutions. However the NO3 ion behaves quite differently in N H a N O 3 + N H 4 F solutions 179 than in KNO 3 solutions 164. In terms of the adsorption isotherm the basic difference is that the standard free energy of adsorption is linearly dependent on the charge in KNO 3 (and other single electrolyte systems) whereas in NH4NO 3 + NH4F the dependence is approximately quadratic. This is reflected in the Christie plots which are no longer parallel but decrease in slope with increasing positive electrode charge (Fig. 14). The slope passes through zero at q ~ 10 #C cm -2 which corresponds to a maximum in In fl according to eqn. (5). At more positive charges the tendency is to desorb the anion in spite of its negative charge. This effect is shown clearly in the effect on the capacity (Fig. 15). These curves are remarkably similar to the corresponding curves for adsorption of aliphatic organic compounds with the


-0.4

-0.2

0 >

i

0.2

0.4

y q = - 8

- 6

~ . . ~ . . . . * .~..- - 4

~.......~ - 2

~ o

~ 4

-. _- : ., ; -. = • IO

12

6 -zb -3'o ql / t ic cm -2

-5

~-o

"-5

"- I0

° f ° ~ , ,

° ~.° " ,

, ---..~---.~\" ',,

/;///171 o.o5"--.I/111i

\ ~ / / / / ' / xMNH4N%+ (,-xJMNH4F o.~ \x_.iZl I o.z .. I I /

,

\ J io q -iQ -2,o

Surface c h a r g e density q / p C crrf 2

Fig. 14. Potential difference across inner region of double layer as function of specifically adsorbed charge qa for solns, of xM NH4NO 3 + (1 - x)M NH4F in water. Charge on metal (in #C cm-2) is indicated by each line (from PaynelVg).

Fig. 15. Change of reciprocal of inner layer capacity as function of electrode charge for solns, of xM NH4NO 3 + (1- x)M NH4F in water (from PaynelV9).

difference that the NO~ adsorption is shifted toward positive charges as would be expected for a negatively charged ion.

The behavior of the NO3 ion (and also C10~ 180 and PF6 42 ions) in mixed electrolyte solutions is consistent with competitive adsorption of the anion and another species, probably the solvent. It is not clear however why similar effects are not apparent in single electrolyte solutions. The important difference in the adsorption environment seems to be not the presence of the fluoride in the mixed solutions so much as the wide variation of the ionic strength in single salt solutions, which affects the electrostatic contribution to the adsorption energy. De Levie's calculations 2°6 seem to confirm the importance of variations of the diffuse layer potential in single electrolyte solutions. Important differences in the composition of the diffuse layer in mixed electrolytes as compared to single electrolyte solutions have also been noted 181.

The decreasing slope of the lines in Fig. 14 can be interpreted physically in terms of decreasing dielectric constant or increasing thickness, or both, accompanying the adsorption of nitrate ions. The simple picture of point charges at a fixed location in a structureless medium of the Stern-Grahame model of specific adsorption clearly cannot apply to this kind of system because the component of the capacity measured at constant charge becomes negative at extreme anodic values of the electrode charge. In order to explain this in terms of the Stern-Grahame model either the dielectric constant or the thickness would have to be negative, neither of which seem to have any physical significance.

296 R. PAYNE

Damaskin and co-workers 21'22 have suggested that ions like NO 3 and C102 are adsorbed with a layer of water separating the ions from the electrode. The principal contribution to the adsorption energy in this scheme is the "squeezing out" effect of the solvent. There seems little doubt that the "squeezing-out" effect is important for large ions, but it is difficult to explain results like those in Figs. 14 and 15 if the ions are outside the region of high field strength. Furthermore there is strong evidence that these ions undergo specific interaction with mercury in unstructured solvents like dimethyisulfoxide and dimethylformamide indicating contact With the metal 7. It seems reasonable to assume that the same forces are involved in aqueous solutions and that the ions are in fact in contact with the electrode.

There has been some discussion on the question of which concentration variable is appropriate for the adsorption isotherm, the salt activity or the single ion activity approximated by the mean ionic activity 164'181'197'2°°. This choice affects the value of the assigned interaction parameter in the isotherm and is consequently of some importance. From a consideration of the adsorption equilibrium it appears that the single ion activity is the correct parameter in spite of the fact that it cannot be defined in a satisfactory way. Dutkiewicz and Parsons 2°° have reached the opposite conclusion from a comparison of iodide adsorption from single and mixed electrolyte solutions. Similar comparisons made for chloride Is' and nitrate 164 solutions however lead to the opposite conclusion. According to de Levie 2°6 the isotherms in the KI and K I + KF systems can be reconciled without invoking salt activities if the (~2 term is included in the isotherm (eqn. (12)).

6. ADSORPTION OF NEUTRAL MOLECULES

Much of the published work on the adsorption of non-ionic substances on mercury is based on Frumkin's 1926 analysis 2°8 which assumes (i) the validity of the Frumkin isotherm and (ii) that the double layer can be treated as two condensers in parallel; one containing the adsorbed material and the other the solvent. At any given potential E, the model predicts that the charge on the electrode is the sum of the charges on the covered and uncovered parts of the electrode;

q = qo(1 -O)+q'O (15)

In eqn. (15) qo is the charge corresponding to zero adsorption (0=0) and q' corresponds to saturation coverage (0= 1). Values of the fractional coverage 0 can be calculated directly from eqn. (15) if the experimental dependence of q, qo and q' has been determined, e.g., from electrocapillary or capacity measurements. Differentiation of eqn. (15) gives the following expression for the capacity:

C = Co (1 - 0) + C'O + (q'- qo) dO~dE (16)

in which C O and C' are the differential capacities of the bare and fully covered electrode respectively. The first two terms in eqn. (16) represent the capacity at constant amount adsorbed;

Co = C0(1-O)+C'O (17)

known as the "true capacity" in Frumkin's terminology. C, Co and C' are measurable parameters and eqn. (17) has been used to calculate 0 directly. This is justified however


only when the last term in eqn. (16) can be neglected. Breiter and Delahay 2°9 com- par.ed values of 0 calculated from eqn. (17) with the thermodynamic surface excesses for adsorption of n-amyl alcohol, finding satisfactory agreement over a narrow range of potentials close to the potential of zero charge where the adsorption passes through a maximum and the approximation in eqn. (16) is met.

The use of eqn. (17) was criticized by Parsons 196 on the grounds that the linear dependence of the capacity on 0 is not predicted by any theoretical adsorption isotherm with the exception of the simple Henry's Law or Freundlich isotherms, but this was disputed by Frumkin and Damaskin 9 in view of the results of Breiter and Delahay. However, Parsons' analysis showed only that eqn. (17) is generally invalid which is obvious since it was obtained from eqn. (16) by neglecting the differential term. More importantly, Parsons showed that Frumkin's parallel-plate condenser model and the equations deriving from it have a firm thermodynamic basis provided only that the isotherm is congruent in the potential; that is when the isotherm is of the form

f(O) = fie (18)

in which f(0) depends only on 0 (at constant potential) and the adsorption equilibrium constant fl is a function only of the potential E. Equation (18) and the thermodynamic equations then lead directly to Frumkin's equation for the charge (eqn. (15)) and to the following general expression for the capacity,

C - C o = k T F s [(00/O In fl)(d In/J/dE)Z+ 0(d 2 In/J/dE2)] (19)

The linear dependence of the capacity on 0 follows from eqn. (19) at the adsorption maximum (d In/J/dE = 0). The resulting equation

C - C o = kTFs 0 d 2 In ~J/dE 2 (20)

gives for 0 = 1 (C = C')

C ' - C o = k TF~ d 2 In/J/dE 2 (21)

which when recombined with eqn. (20) gives Frumkin's equation for the capacity (eqn. 17).

Since the isotherm dependence in eqn. (19) is in the coefficient ~0/0 In fl this also vanishes when d In t iME = 0. Equation (20) (and hence eqn. (17)) are therefore independent of the type of isotherm and can be used to determine the form and constants of the isotherm, but only at the adsorption maximum and only if the isotherm can be assumed to be congruent in the potential.

The question of whether adsorption isotherms for neutral organic molecules on mercury are congruent in the electrode potential or in the charge is controversial 18'130'210-215. Since, as shown by Parsons 196, Frumkin's model is equivalent to the a priori assumption of potential congruency the Russian work is largely based on the constant potential approach whereas Parsons and co-workers have taken the opposite view. For a charge-congruent isotherm the analog of eqn. (15) is

E = E 0 (1 - 0) + E' 0 (22)

where E o and E' are the potentials corresponding to 0 = 0 and 0 = 1 respectively at constant charge. The corresponding capacity at constant amount adsorbed is given by

298 g. PAYNE

(8E/Oq)o = 1~Co = (1 - O)/C o + O/C' (23)

Thus, while Frumkin's model and the constant potential approach corresponds to condensers connected in parallel, the constant charge approach corresponds to condensers connected in series which according to Frumkin et al.211,2t2 is physically unrealistic. However, both models can be rationalized in terms of the dependence of the dielectric constant (e) and thickness (x) on the amount adsorbed 18. The parallel condenser formula can be derived from the assumption that e/x depends linearly on 0 whereas the series condenser formula follows if x/e is assumed linear in 0. Both assumptions are physically reasonable although they obviously represent special cases which would not be generally expected for real systems. The choice of one approach or the other therefore must depend on how well a specific system conforms experimentally to the predictions of the two models.

A rigorous experimental distinction between the constant potential and the constant charge approach appears possible through eqns. (15) and (22). According to eqn. (15), q should be linearly dependent on 0 at constant potential for an isotherm congruent in the potential, whereas according to eqn. (22) E should depend linearly on 0 at constant charge for an isotherm congruent in the charge. This test was applied by Dutkiewicz et al. 213 to their measurements for n-butanol, 1,4-butanediol and 1,4- but-2-ynediol. The two diols were found to fit both eqn. (15) and eqn. (22) equally well (Fig. 16). The n-butanol data on the other hand gave curved plots in both cases (Fig. 17). It was suggested therefore on the basis of these results that if an isotherm is congruent in one electrical variable it is congruent in both and vice versa. Frumkin et al. 212 contend that the n-butanol system is congruent in the constant potential case but not in the constant charge case, and that the deviation of the plots of q vs. 0 from linearity in Fig. 17 is within experimental error. However this seems improbable 2t3. It should be noted that Dutkiewicz et al. obtained values of 0 by the thermo-

0

o -

5

0

0 0 2 0.4 0.6 0.8

- I 0 ; " ~ ' . ~ . ~ , ~ . . . . . ~ . ~ m - 2

L . . . . - - - - . . . . |

" ' r . . . . . . . . . 1 I - - " - - 2 ~ - /

,_q.. _ . . . . . . .

.oA~..-

r " / , / , . . . . . . - •

• ° /

I0

1010 I"1 / m o l c m -2

O

0 0 2 0 4 0.6 0.0

- 0 6 . ~ q = - I I

-~ i , - ~ _ ~ . . . . . . . - ; - ~" _- ;-'-', - - . ' _ - : ~ ' - - _ _ : . . . . ~ ' _ - ; : .--.z

: , - . '~ . . ' :~ . ' ~ : . = . '-'~2 02 L=~'~5"_.~--~-" . . . . . . . .

B 0.4

~) f i i i 1 2

1010 ~ ' / too l crn "2

o b Fig. 16, Dependence on amount adsorbed of(a) electrode charge at constant potential difference across the inner region, (b) potential difference across inner region at constant charge for 1,4-but-2-ynediol adsorbed from aq. 0.095 M NH4F (from Dutkiewicz et alflL3).

E L E C T R I C A L D O U B L E LAYER: P R O B L E M S A N D R E C E N T P R O G R E S S 299

dynamic method whereas Frumkin et al. used eqns. (15) and (22) which, as pointed out by Parsons ~8, are invalid if the isotherms are not congruent. The effect of the initial assumption of congruency on values of 0 calculated from eqns. (15) and (22) is not clear.

- I 0

E u (..)

¢

5

e 0.2 0.4 0.6 0.8

~ . 6 2

•

. . . . ~ " .-:-:~q £ o ~ 2 . ~ . . . . . . . .

oo. ~ . ~ " :.D~--';~

/ 0 . ~ 8

101° P I too l c m "2

e o 0.2 0.4 9,e o. 9

- 1 2 / ' ! ' t '

-o.d..,: ,~/ / " ,." } t .'/~." -8/" .." I, I ~. - 6 / " ,

-o4 / / > t " . j J

-0.2 '~..._. !

E t

- 2

0 . . . .

: .... ~ " ~ o ° , 2 "x. :,,

~'% ,~4 "~. ,~ 0,4 " 6

o

101° I-' I t oo l c m "2

a b

Fig. 17. Dependence on amount adsorbed of (a) electrode charge at constant potential difference across inner layer, (b) potential difference across inner layer at constant electrode charge for n-butanol adsorbed from aq. 0.1 M KF (from Dutkiewicz et al.213).

The ambiguity found in the diols was attributed by Frumkin et al. 212 to the fact that these compounds do not produce much lowering of the capacity. The constant-charge model predicts a linear dependence of E on 0 according to eqn. (22) whereas the constant-potential model predicts a non-linear dependence. This can be shown by rewriting eqn. (15) in the form

q = C o E ( 1 - O ) + C ' ( E - E N ) O (24)

in which the E values are referred to the potential of zero charge for 0-- 0, and E N is the shift of the pzc as 0 changes from 0 to 1. Rearrangement of eqn. (24) now gives

E = (q + C' ENO)/(C' [Co/C'(1 - O) + 0]) (25)

The dependence of E on 0 at constant q therefore is generally non-linear. However if C o ~ C', eqn. (25) reduces to

E = q/C' + E N 0 (26)

which gives the same linear dependence of E on 0 ~u, q = 0 (and generally for all q if C' is assumed constant) as the constant charge model. Frumkin et al. 211,212 have plotted E vs. 0 in a number of systems for the special case q = 0, finding generally curved plots as predicted by eqn. (25) and the constant-potential model. A typical example is shown in Fig. 18. Linear plots however were found at the air-solution interface and also occur in special cases like the butanediols and butynediols 213 where Co/C' is

300 R. PAYNE

small (Frumkin et al. 212 have suggested that the constant-charge behavior observed in ionic adsorption is also due to approximate equality of Co and C' in these systems).

Frumkin's treatment has been generalized in several recent papers 216-2~8 to cover the entire range of behavior between the extreme cases of Frumkin's model

> • t o o

.~ol O. 2 l / 0

~= , ,,e

I 0 I 2 3 4 5 6

IOm£ ' / m o l e c m -2

Fig. 18. Dependence of potential of zero charge on amount of adsorbed n-propanol at (]) solution-air interface, (2) mercury-solution interface. Data obtained from (©) e]ectrocapillary measurements, (0 ) minimum on the differential capacity curves in dilute solns. (from Frumkin et al.212).

(linear 0 dependence of e/x) and Parsons' model (linear 0 dependence of x/E). The electrode charge is written,

q = { [Co(l -O)+n C'O]E-nC'EN[k(1-0) +0] 0}/(1 +nO-O) (27)

where n and k are adjustable parameters which determine the adsorption model. Thus when n = k = l , eqn. (27) reduces to Frumkin's model (eqn. (15)). For k = l , n= Co/C' the equation becomes

q = ( E - ENO)/[ [(I - O)/Co] + O/C'} (28)

which corresponds to Parson's model, whereas n = 1, k = Co/C' gives

q = [Co (1 - 0) + C' 0] ( E - EN 0) (29)

corresponding to a model proposed by Hansen and co-workers 219 in which parallel layers of water molecules and organic molecules are sandwiched between an ideal conductor and a dielectric rather than two conductors as in Frumkin's model. The analysis of experimental data through the generalized surface layer model proceeds in the usual way by the assumption of the validity of Frumkin's isotherm, eqn. (7) which then allows O-E curves to be calculated for each concentration in terms of experimentally determined parameters. However, whereas previously deviations of experimental results from the Frumkin model were interpreted formally in terms of a potential dependence of the lateral interaction parameter (A) in the isotherm 9"13°, the new treatment assumes that A is constant and considers departures from the constant- potential model, tending in the limit to either the Parsons model or the Hansen model as indicated by the values of n and k.

Adsorption data have been analyzed for a large number ofaliphatic compounds ineluding alcohols, carboxylic acids and amines 118. The resulting values of n and k are summarized in Fig. 19 from which the experimental data are seen to "conform


fairly closely to the Frumkin model (n= 1, k = 1). Deviations toward Hansen's model (n= 1; 1 < k< Co/C') found in the adsorption of aliphatic alcohols could be due, according to Damaskin et al., to the discrete nature of the organic dipoles whereas deviations toward Parsons' model (k= 1, 1 < n< Co/C') observed in the adsorption of n-valeric acid and other carboxylic acids could be attributed to increase of the double layer thickness. However this difference in behaviour of similar molecules is not explained. Values of n and k less than unity in Fig. 19 also cannot be explained in this simple way.

Co ..... .~,3

!

? - ' f ~ _ I_ 2 I i

o / i , 1 I 2 c._~o

c ~ ,k-

Fig. 19. Values of n and k for adsorption models of Frumkin (I), Hansen (2) and Parsons (3) compared with exptl, points for a large number of alJphatic compounds adsorbed on mercury and bismuth electrodes. The exptl, points fall within the shaded area (from Damaskin et al.21s).

In a further extension of this approach 218 it was suggested that the Frumkin model of the surface layer consisting of separate areas containing either organic molecules or solvent molecules is only rigorous if two-dimensional condensation occurs, i.e., when strong lateral attraction is present. For a more general model of organic dipoles uniformly distributed in the solvent layer the potential (measured with respect to the pzc) can be written as the sum of two terms, one due to the charge on the metal and the other due to oriented dipoles of the adsorbed organic molecules,

E = 4nq x/e + (4nfi/e) FsO (30)

where fi is the normal component of the dipole moment of the adsorbed organic molecule. Rearrangement of the equation gives the following expression for the charge :

q = (e/4nx)E-( f i /x)F~O (31)

However substitution in eqn. (31) of the relationship

e/x = (eo/Xo)(1 - 0) + (E'/x')O (32)

where % and e' are the dielectric constants for 0 =0 and 0 = 1 respectively and x o and x' are the corresponding thicknesses, leads directly to eqn. (15) for Frumkin's model if

EN = fiFs/C' x (33)

302 R. PAYNE

Similarly substitution of

x /e = (Xo/eo)(1 - O) + (x'/~')O (34)

leads to eqn. (22) and Parsons model for

eN = 4~rs /~ (35) The validity of these simple models therefore does not depend on the assumption of two-dimensional condensation but only on the assumed linear dependence of either e/x or x/e on 0 in eqns. (32) and (34). Two-dimensional condensation in any case seems inconsistent with the statistical basis of Langmuir's isotherm. By comparing eqns. (27) and (31) Damaskin et al. arrived at expressions for the ratios of dielectric constant to thickness and normal component of the dipole moment to thickness:

e _ e k l _ p - ( p - n ) O x(4rtC') x 1 + ( n - 1)0 (36)

F s _ [t k2 _ n k - n ( k - 1 ) O (37) x C ' E N x 1 + ( n - 1)0

where p = C o / C ' and k t and k z are constants. Frumkin's model ( n = k = 1) therefore predicts a linear decrease of e/x with 0 and constant ~ / x whereas Parsons' model (k= 1, n = p ) predicts the same inverse 0 dependence of both ratios;

k , e /x = k 2 f~/x = p / [1 + ( p - 1)0] (38)

Comparison of a range of experimen.tal data with these ratios calculated through eqns. (36) and (37) again shows generally better agreement with the Frumkin model than with either the Hansen or Parsons models (Fig. 20). The ~/x values for aliphatic

7,.

4

ii o~-Z z - z z ~ ' ; o o ; ,o o oI~ ,.;

0 0

(a) (b) Fig. 20. Dependence of the ratios ~/x and ~/x on the relative adsorption calcd, from eqns. (36) and (37) for (1) Frumkin's model, (2) Hansen's model, (3) Parsons' model. Shaded areas cover dependence of e/x and ~/x for a large number of exptl, systems (from Damaskin et al.218).

alcohols from n-propyl to n-hexyl spread over a small range whereas a much wider spread occurs for carboxylic acids from propionic to n-valeric (Fig. 21). This is explained in terms of specific interaction of the - C O O H group with the mercury surface at small values of 0, an effect which produces a pronounced reorientation change with increasing 0. This effect would be expected to diminish with increasing chain length as found.


In a different approach to the problem Bockris and co-workers 214 have also attributed the apparent complex potential dependence of the lateral interaction parameter in the Frumkin isotherm to deviations from constant-potential behavior. However, whereas Damaskin et al. conclude that the deviations are small, Bockris et al. take the opposite viewpoint and assume the correctness of the constant charge approach giving a number of justifications, some of which however are open to criti- cism. They use an extended form of the Langmuir isotherm expression based on mole fraction statistics :

f (O) = 0(1 - 0)-" [0 + n(1 - 0)]"- i /n" (39)

where n is the number of solvent molecules replaced by each adsorbed solute molecule. An important difference between this approach and that of Frumkin is that Bockris et al. take into account lateral interactions of adsorbed solvent molecules explicitly in terms of molecular properties and neglect lateral interaction of the ad-

1.5

1.0 z

i~ ' lx 0.5

0 0!5 1.0

0

0 .4

0 ,3

O,Z

O,

~0 I0 0 - I 0

q/pC crn -2

Fig. 21. Dependence of ratio f~/x on relative adsorption on mercury of various aliphatic acids calcd, by means of eqn. (37): (1) propionic, (2) n-butyric, (3) n-valeric, (4) n-hexanoic. (5) n-heptanoic. Shaded area covers dependence of fi/x on 0 for adsorption of aliphatic alcohols from n-propanol (lower boundary) to n-hexanol (from Damaskin et al.218).

Fig. 22. Adsorption curves for n-butanol adsorbed on mercury from 0.1 N HC1 in methanol ( . . . . . ) compared with theoretical curves ( ) (from Bockris et al.214).

sorbed solute molecules. Lateral interactions of adsorbed solvent molecules are assumed independent both of the coverage of the electrode by the solute molecules and the electrical variable but field reorientation of both solvent and solute dipoles is considered.

Bockris et al. compare their theoretical predictions with experimental results for adsorption of n-butanol and phenol from solutions in water and methanol, ob- taining fair agreement. Asymmetric adsorption curves for n-butanol in methanol (Fig. 22) were attributed to reorientation of the butanol molecule from a normal orientation of the hydrocarbon chain on the cathodic side to a fiat orientation on the anodic side. Invariant normal orientation was assumed in water owing to the "squeezing-out" of the hydrocarbon group resulting in symmetrical adsorption curves (Fig. 23). The adsorption maximum at a small negative charge which occurs for many aliphatic compounds in water was attributed to the effect of replacing solvent dipoles which are least strongly held in this region of charge: the polar functional

304 R. PAYNE

0.8

0.6

0.4 .~ ~-

0,2

0

15 . . . . 5 0 - 5 - l O - 15

q/ .uC cm -2

Fig. 23. Adsorption curves for n-butanol adsorbed on mercury from 0.1 N HCI in water ( - - - ) compared with theoretical curves ( ) (from Bockris et al.214).

group of the solute molecule is outside the double layer and does not contribute significantly to the potential difference. The theory correctly predicts adsorption maxima on the positive side of the pzc for phenol in both water and methanol without the need to assume n-electron interaction of the aromatic nucleus with the electrode. However, the calculation does seem to depend on the assumption of a flat orientation of the phenol molecule for reasons that are not clear.

The theoretical calculation of Bockris et al. has been strongly criticized on two levels. From'a theoretical viewpoint, according to Damaskin z2°'221, the treatment neglects the change in energy of the molecular condenser in the process of adsorption and consequently is inconsistent with thermodynamics. However this is disputed by Gileadi z2a. Comparison with experiment shows that the predicted dependence of the adsorption energy on the size of the adsorbing molecule is absent suggesting that an important factor has been omitted from the theory. Parsons 18 has remarked that the model assumes charge-congruent isotherms and hence a linear dependence of potential on the amount adsorbed at constant charge which is not generally found. Damas- kin 22° has also pointed out the fact that the experimentally observed dependence of the shape of the adsorption isotherm on the length of the hydrocarbon chain for homologs cannot be explained if direct lateral interaction of adsorbed solute particles is neglected. However, the approach of Bockris et al. remains the only treatment of the problem based on a molecular model. New experimental results may suggest ways of improving the model in order to remove the present anomalies of the treatment.

7. SUMMARY

The current status of the electrical double layer at the electrode-solution interface is reviewed with emphasis on recent progress and residual problem areas.

8. REFERENCES

1 D. C. Grahame, Chem. Rev., 41 (1947) 441. 2 R. Parsons in J. O'M. Bockris (Ed.), Modern Aspects of Electrochemistry, Vol. l, Butterworths, London,

1954, p. 103.

ELECTRICAL DOUBLE LAYER : PROBLEMS AND RECENT PROGRESS 305

3 J. Th. G. Overbeek in H. R. Kruyt (Ed.), Colloid Science, Fol. 1, Elsevier, Amsterdam, 1952, p. 115. 4 B. B. Damaskin, Usp. Khim., 30 (1961) 220. 5 P. Delahay, Double Layer and Electrode Kinetics, Interscience, New York, 1965. 6 D. M. Mohilner in A. J. Bard (Ed.), Electroanalytical Chemistry, Fol. l, Marcel Dekker, New York,

1966, p. 241. 7 R. Payne in P. Delahay and C. W. Tobias (Eds.), Advances in Electrochemistry and Electrochemical

Engineering, Fol. 7, Interscience, New York, 1970, p. 1. 8 K. Mtiller in E. Gileadi (Ed.), Electrosorption, Plenum Press, New York, 1967, p. ll7. 9 A. N. Frumkin and B. B. Damaskin in J. O'M. Bockris and B. E. Conway (Eds.), Modern Aspects of

Electrochemistry, Vol. 3, Butterworths, London, 1964, p. 149. 10 R. Parsons in P. Delahay and C. W. Tobias (Eds.), Advances in Electrochemistry and Electrochemical

Engineering, Vol. I, Interscience, New York, 1961, p. 1. 11 B. J. Piersma in E. Gileadi (Ed.), Electrosorption, Plenum Press, New York, 1967, p. 19. 12 D. A. Haydon in J. F. Danielli, K. G. A. Pankhurst and A. C. Riddiford (Eds.), Recent Progress in

Surface Science, Vol. 1, Academic Press, New York, 1964, p. 94. 13 S. Levine, J. Mingins and G. M. Bell, J. Electroanal. Chem., 13 (1967) 280. 14 C.A. Barlow and J. R. Macdonald in P. Delahay and C. W. Tobias (Eds.), Advances in Electrochemistry

and Electrochemical Engineering, Vol. 6, Interscience, New York, 1967, p. 1. 15 H. D. Hurwitz in E. Gileadi (Ed.), Electrosorption, Plenum Press, New York, 1967, p. 147. 16 C. A. Barlow, Phys. Chem., 9A (1970) 167. 17 B. B. Damaskin, Elektrokhirniya, 5 (1969) 771. 18 R. Parsons, Rev. Pure Appl. Chem., 18 (1968) 91. 19 R. Parsons, Croat. Chem. Acta, 42 (1970) 390. 20 M. A. V. Devanathan and B. V. K. S. R. A. Tilak, Chem. Rev., 65 (1965) 635. 21 B. B. Damaskin, V. F. Ivanov, N. I. Melekhova and L. F. Maiorova, Elektrokhirniya, 4 (1968) 1342. 22 B. B. Damaskin, A. N. Frumkin, V. F. Ivanov, N. I. Melekhova and V. F. Khonina, Elektrokhimiya, 4

(1968) 1336. 23 N. I. Melekhova, V. F. Ivanov and B. B. Damaskin, Elektrokhirniya, 5 (1969) 613. 24 B. B. Damaskin, V. F. Ivanov and N. I. Melekhova, Elektrokhirniya, 6 (1970) 385. 25 E. T. Verdier and G. Berge, J. Chim. Phys. Physieoehirn. Biol., 67 (1970) 1671. 26 D. J. Schiffrin, Trans. Faraday Soe., 67 (1971) 3318. 27 J. Jastrzebska, Rocz. Chem., 44 (1970) 1779. 28 P. Delahay and D. J. Kelsh, J. Electroanal. Chem., 16 (1968) 116. 29 B. Behr, J. Dojlido and J. Stroka, Collect. Czech. Chem. Cornmun., 36 (1971) 1317. 30 R. D. Armstrong, J. Electroanal. Chem., 26 (1970) 387. 31 R. D. Armstrong, W. P. Race and H. R. Thirsk, J. Electroanal. Chem., 27 (1970) 21. 32 W. P. Race, J. Electroanal. Chem., 24 (1970) 315. 33 B. B. Damaskin, R. I. Kaganovich, V. M. Gerovicb and S. L. Diatkina, Elektrokhimiya, 5 (1969) 507. 34 B. B. Damaskin and S. L. Diatkina, Elektrokhimiya, 5 (1969) 124. 35 B. V. K. S. R. A. Tilak and M. A. V. Devanathan, J. Phys. Chem., 73 (1969) 3582. 36 A. A. Moussa, M. M. Abou Romia and M. A. Razik, Chem. Commun., 18 (1965) 429. 37 A. A. Moussa and M. M. Abou Romia, Electrochirn. Acta, 15 (1970) 1373; 15 (1970) 1381. 38 A. A. Moussa, M. M. Abou Romia and F. E1 Taib Heaka~, Electrochirn. Acta, 15 (1970) 1391. 39 C. V. D'Alkaine, E. R. Gonzalez and R. Parsons, J. Eleetroanal. Chem., 32 (1971) 57. 40 N. S. Polianovskaya, A. N. Frumkin and B. B. Damaskin, Elektrokhirniya, 7 (1971) 578. 41 A. W. M. Verkroost, M. Sluyters-Rehbach and J. H. Sluyters, J. Electroanal. Chem., 24 (1970) 1. 42 G. J. Hills and R. M. Reeves, J. Electroanal. Chem., 31 (1971) 269. 43 R. Parsons and A. Stockton, J. Electroanal. Chern,, 25 (1970) App. 10. 44 R. V. Ivanova, B. B. Damaskin and I. Mazurek, Elektrokhirniya, 6 (1970) 1041 ; B. B. Damaskin and

R. V. Ivanova, Divinoi Sloi Adsorbtsiya Tverd. Elektrodakh, Mater. Sirnp., 2nd, (1970) 139. 45 R. G. Barradas and E. W. Hermann, J. Phys. Chem., 73 (1969) 3619. 46 J. A. Harrison, J. E. B. Randles and D. J. Schiffrin, J. Electroanal. Chem., 25 (1970) 197. 47 R. J. Meakins, M. G. Stevens and R. J. Hunter, J. Phys. Chem., 73 (1969) 112. 48 T. Yoshida, S. Nomoto and N. Kimizuka, Mere. Sch. Sci. Eng., Waseda Univ., Tokyo, Jap., 31 (1967) 81. 49 I. R. Miller, Electrochirn. Aeta, 15 (1970) 1143. 50 P. Champion, C. R., 269 (1969) 1159. 51 R. D. Armstrong, W. P. Race and H. R. Thirsk, J. Electroanal. Chem., 22 (1969) 207.

306 R. PAYNE

52 C. Cachet, I. Epelboin and ,I. C. Lest.'ade, Bull. Soc. Chhn. Ft'., (19691 1452. 53 R. Parsons and J. T. Reilly. S. Electroanal. Chem., 24 (1970) App. 23. 54 K. Eda. K. Takahashi and 13. Tamamushi ill J. Th. G. Overbeck (Ed.). Proc. 4th Int. Can.qr. Chem.

Phys. Appl. Sur/?we Actire Subst. 1964. Gordon and Breach. New York. 1967. p. 2289. 55 E. T. Verdier and P. Vant, el, d. Chhn. Phys. Physicochinl. Biol., 67 (1970) i412. 56 R. D. Armstrong, W. P. Race and H. R. Thirsk..I. Electroanal. Chem., 14 (19671 143. 57 W. F. Condon, Diss. Abstr. Int., 30 (B1970) 5396. 58 L. I. Antropov. M. A. Gerasimenko and Yu. S. Gerasimenko. Ukr. Khh11. Zh.. 36 (1970) 1218. 59 K. Takahashi and R. Tamamushi, Electrochhn. Acta. 16 (1971) 875. 60 H. Sohr and K. Lobs. J. Electroaltal. Chem., 20 (1969) 449. 61 L. K. Partridge, A. C. Tansley and A. S. Porter. Electrochim. Acta, 13 (1968) 2029. 62 R. Narayan and N. Hackerman. ,I. Electrochem. Soc., 118 (1971) 1426. 63 M. A. Loshkarev, I--'. I. Danilov and L. I. Zasova, Khim. Technol. 8 (1967) 41. 64 T. Smith. J. Colloid Inte~f, ce Sci.,'28 (1968) 531:30 (1969) 183:31 (1969) 270. 65 $r-G. Meibuhr, Electrochim. Acta, 14 (1969) 169. 66 S. Bordi and G. Papeschi, J. Electroanal. Chem.. 20 (1969) 297. 67 A. Inesi. F. Rallo and L. Rampazzo, Trans. Faraday Soc.. 64 (1968) 3340. 68 A. V. Chizhov and B. B. Da,naskin, Elektrokhimiya, 5 (1969) 1012. 69 D. B. Matthews, .I. Biomed. Mater. Res., 3 (1969)475. 70 L. Pospisil and J. Kuta, Collect. Czech. Chem. Commun., 34 (1969) 3047. 71 W. H. Grant, Diss. Abstr.. 29 (B1969) 4126. 72 S. Ueda. A. Watanabe and I-'. Tsuji, Mere. Coll. A~.lric. Kyoto Univ. Chem. Set'.. 32 [1967) 49. 73 R. I. Kaganovich. B. B. Damaskin and I. M. Ganzhim,. Elektroldtimiya. 4 (1968) 867. 74 S. Trasatti, J. Electroa~lal. Chem.. 28 (19701 257. 75 G. A. Dobren'kov and L. T. Guseva, Elektrokhimiya. 7 (19711 563. 76 V. M. Gerovich, B. B. Damaskin and R. I. Kaganovich. Elektrokhimiya, 7 (1971) 1345. 77 S. L. Diatkina and B. B. Damaskin, Elektrokhimiya. 4 (I968) 1000. 78 L. A. Korshikov. V. B. Titova, N. V. Krupskaya and V. D. Bezuglyi. Elektrokhimiya. 5 (1969) 726. 79 G. A. Dobren'kov and G. D. Shilotkach, Elektrokhimiy,, 6 (1970) 1416. 80 B. E. Conway and L. G. M. Gordon..1. Phys. Chem., 73 (1969) 3609. 81 R. D. Armstrong, .I. Electroamd. Chem., 20 (19691 168. 82 R. I. Kaganovich, B. B. Damaskin and M. A. Suranova, Elektrokhhniya, 6 (1970) 1158. 83 H. Sawamoto, Bull Chem. Soc. tap., 43 (19701 2096. 84 B. B. Damaskin, S. L. Diatkina and V. K. Venkatesan, Elektrokhimiya, 5 (1969) 524. 85 A. B. Ershle.', I. M. Levinson, S. G. Mairanovskii, G. A. Tedoradze and Yu. 13. Volkenshtein. Elek-

trokhioliya, 5 (19691 880. 86 I. G. Markova and L. G. l:'eoktistov. Elektrokhimiya, 5 (1969) 1095. 87 A. V. Chizhov and B. B. Damaskin, Elektrokhimiya. 5 (1969) 1012. 88 B. B. Damaskin. S. L. Diatkina and N. A. Borovaya, Elektrokhimiya. 6 (1970) 712. 89 J. Law.'ence and D. M. Mohilner, .I. Phys. Chem., 75 (1971) 1699. 90 N.A. Borovaya and B. B. Da.n;tskin, Elektrokhimiya, 7 (1971) 571. 91 V. Sh. Tsveniashvili, S. I. Zhdanov and Z. V. Todres, Elektrohimiya, 7 (1971) 28. 92 G. Manohar and S. Sathyanarayana, d. EIcctroaltal. Chem.. 30 (1971) 301. 93 K. G. Baike.'ikar and S. Sathyanarayana, d. Electroanal. Chem., 24 (1971) 333. 94 K. M. Joshi, M. R. Bapat and S. W. Dhawale. Electrochim. Acta, 15 (1970) 1519. 95 S. Trasatti and G. Olivieri, ,I. Electroanal. Chem., 27 (1970) App. 7. 96 M. Matsumoto. Nil~pon Kae.laktt Zasshi, 91 (1970) 708. 97 R. I. Kay,anovich, B. B. Damaskin and M. M. Andrusov. Elektrokhhniya. 5 (1969) 745. 98 S. Ueda, A. Watanabe and F. Tsuji, Mere. Coll. Ayric. Kyoto Univ. Chem. Set'.. 32 (19671 65. 99 R.A.Arake~yan` G.A. Ted~radze and E. D. B e ~ k ~ s ~ E~ektr~khim. P~.~tsessy Uchestiem ~re`t. Veschestt`.~

(1970) 24. 100 U. Gaunitz and W. Lorenz, Collect. Czech. Chem. Commml., 36 (1971) 796. I0I K. M. Joshi. M. R. Bapat and S. W. Dhawale. d. hldian Chem. Soc.. 47 (1970) 949. 102 A. K. Shallal. H. H. Bauer and D. Britz, Collect. Czech. Chem. Colnmlm.. 36 (197I) 767. 103 A. K. Shallal and H. H. Bailer. Atlal. Lett.. 4 (1971) 371. 104 D. E. Broadhcad, R. S. Hanson and G. W. Potter, ,I. Collohl hirer(ace So; ~,1 (1969) 61. 105 R. G. Barradas and J. M. Sedlak, Electrochhtt. Acta, 16 (197I) 2091.

EI.FCTRICAL DOUBLE LAYER : PROBLEMS AND RECENT PROGRESS 307

106 S. Minc and S. Muszalska, Rocz. Chem., 43 (1969) 1569. 107 V. F. Ivanov, B. B. Damaskin and N. I. Melekhova, Elektrokhimiya, 6 (1970) 382. 108 D. R. Flinn, Diss. Abstr., 29 (B1969) 3700. 109 D. I. Dzhaparidze, G. A. Tedoradze and Sh. S. Dzhaparidze, Elektrokhimiya, 5 (1969) 955. 110 P. Champion, C. R., 272 (1971) 987; 272 (1971) 1090. 111 R. G. Wedel, Diss. Abstr. Int., 31 (B1970) 1848. 112 R. R. Salem, Zh. Fiz. Khim., 43 (1969) 1839, 2876; 45 (1971) 1264. 113 T. Biegler and R. Parsons, J. Electroanal. Chem., 21 (1969)App. 4. 114 V. A. Kuznetsov, N. G. Vasil'kevich and B. B. Damaskin, Elektrokhimiya, 6 (1970) 1339. 115 R. Payne, J. Phys. Chem., 73 (1969) 3598. 116 Ya. Doilido, R. V. Ivanova and B. B. Damaskin, Elektrokhimiya, 6 (1970) 3. 117 1. M. Ganzhina, B, B. Damaskin and R. V. Ivanova, Elektrokhimiya, 6 (1970) 709; 7 (1971) 362. 118 B. B. Damaskin, I. M. Ganzhina and R. V. lvanova, Elektrokhimiya, 6 (1970) 1540. 119 V. D. Bezuglyi, L. A. Korshikov and V. B. Titova, Elektrokhimiya, 6 (1970) 1150. 120 R. I. Kaganovich, B. B. Damaskin and M. K. Kaisheva, Elektrokhimiya, 6 (1970) 1359. 121 I. M. Ganzhina and B. B. Damaskin, Elektrokhimiya, 6 (1970) 1715. 122 S. lrI. Kim, T. N. Andersen and H. Eyring, a r. Phys. Chem., 74 (1970) 4555. 123 B. B. Damaskin, V. F. Ivanov and V. F. Balashov, Elektrokhimiya, 7 (1971) 127. 124 D. I. Dzhaparidze, Sh. S. Dzhaparidze and B. B. Damaskin, Elektrokhimiya, 7 (1971) 1305. 125 S. Minc, J. Jastrzebska and J. Andrzejczak, Electrochim. Acta, 14 (1969) 821. 126 S. Minc, M. Jurkiewicz and J. Jastrzebska, Rocz. Chem., 44 (1970) 837. 127 J. Lawrence and R. Parsons, J. Phys. Chem., 73 (1969) 3577. 128 R. M. Kulikova and V. D. Ryzhov, Tr. Tomsk. Gos. Univ., 192 (1968) 150. 129 R. M. Kulikova, V. D. Ryzhov and L. Beresneva, Tr. Tomsk. Gos. Univ., 192 (1968) 139. 130 B. B. Damaskin, Adsorption of Organic Compounds on Electrodes, Part I, Plenum Press, New York,

1971, p. 3. 131 D. C. Grahame and B. Soderberg, J. Chem. Phys., 22 (1954) 449. 132 A. N. Frumkin, R. V. Ivanova and B. B. Damaskin, Dokl. Akad. Nauk SSSR, 157 (1964) 1202. 133 R. Parsons and F. G. R. Zobel, J. Electroanal. Chem., 9 (1965) 333. 134 J. O'M. Bockris, K. Miiller, H. Wroblowa and Z. Kovac, J. Electroanal. Chem., 10 (1965) 416. 135 R. Payne, J. Electroanal. Chem., 15 (1967) 95. 136 J. Lawrence, R. Parsons and R. Payne, J. Electroanal. Chem., 16 (1968) 193. 137 R. Parsons and S. Trasatti, Trans. Faraday Soc., 65 (1969) 3314. 138 S. Trasatti, J. ElectroanaL Chem., 31 (1971) 17. 139 D. J. Schiffrin, J. Electroanal. Chem., 23 (1969) 168. 140 J. Lawrence and D. M. Mohilner, J. Electrochem. Soc., 118 (1971) 259. 141 G. Gouy, Ann. Phys., 6 (1916) 5. 142 C. A. Smolders and E. M. Duyvis, Recl. Tray. Chim., 80 (1961) 635. 143 J. N. Butler, J. Phys. Chem., 69 (1965) 3817. 144 R. Parsons and P. C. Symons, Trans. Faraday Soc., 64 (1968) 1077. 145 V. I. Melik-Gaikazyan, V. V. Voronchikhina and E. A. Zakharova, Elektrokhimiya, 4 (1968) 1420. 146 D. C. Grahame, J. Phys. Chem., 61 (•957) 701. 147 G. C. Barker and A. W. Gardner in I, S. Longmuir (Ed.), Advances in Polarography, Vol. 1, Pergamon

Press, London, 1960, p. 330. 148 J. M. Los and D. W. Murray in I. S. Longmuir (Ed.), Advances in Polarography, Vol. 2, Pergamon

Press, London, 1960, p. 425. 149 G. H. Nancollas and C. A. Vincent, Electrochim. Acta, 10 (1965) 97. 150 R. Payne, J. Amer. Chem. Soc., 89 (1967) 489. 151 F. E. Terman and J. M. Pettit, Electronic Measurements, McGraw-Hill, New York, 1952. 152 G. J. Hills and R. Payne, Trans. Faraday Soc., 61 (1965) 316. 153 Wireless WorM, Nov. 1961, p. 595. 154 R. D. Armstrong, W. P. Race and H. R. Thirsk, Electrochim. Acta, 13 (1968) 215. 155 R. de Levie and A. A. Husovsky, J. Electroanal. Chem., 20 (1969) 181. 156 G. Gouy, J. Phys., 9 (1910) 457. 157 D. L. Chapman, Philos. Mag., 25 (1913) 475. 158 A. N. Frumkin, Philos. Mag., 40 (1920) 384. 159 O. Stern, Z. Elektrochem., 30 (1924) 508.

308 R. PAYNE

160 D. C. Grahame, J. Electrochem. Soc., 98 (1951) 343. 161 V.F. Ivanov, B. B. Damaskin, A. N. Frumkin, A. A, Ivaskchenko and N. I. Peshkova, Elektrokhimiya,

1 (1965) 279. 162 K. M. Joshi and R. Parsons, Electrochim. Acta, 4 (1961) 129. 163 F. C. Anson, R. F. Martin and C. Yarnitzky, J. Phys. Chem., 73 (1969) 1835. 164 R. Payne, J. Electrochem. Soc., 113 (1966)999. 165 L. F. Oldfield, Thesis, University of London, 1951. 166 B. B. Damaskin, R. V. Ivanova and A. A. Survila, Elektrokhimiya, 1 (1965) 767. 167 G. H. Nancollas, D. S. Reid and C. A. Vincent, J. Phys. Chem., 70 (1966) 3300. 168 B. B. Damaskin and R. V. Ivanova, Zh. Fiz. Khim., 38 (1964) 176. 169 A. N. Frumkin, R. V. Ivanova and B. B. Damaskin, Dokl. Akad. Nauk SSSR, 157 (1964) 1202. 170 G. C. Barker, d. Electroanal. Chem., 12 (1966) 495. 171 D. C. Grahame and R. Parsons, d. Amer. Chem. Soc., 83 (1961) 1291. 172 R. Payne, J. Electroanal. Chem., 7 (1964) 343. 173 R. J. Watts-Tobin, Philos. Mag., 6 (1961) 133. 174 J. R. Macdonald and C. A. Barlow, J. Chem. Phys., 36 (1962) 3062. 175 J. O'M. Bockris, M. A. V. Devanathan and K. Miiller, Proc. R. Soc. Lond., A274 (1963) 55. 176 S. Levine, G. M. Bell and A. L. Smith, J, Phys. Chem., 73 (1969) 3534. 177 D. C. Grahame, J. Amer. Chem. Soc., 80 (1958) 4201. 178 J. M. Parry and R. Parsons, Trans. Faraday Soc., 59 (1963) 241. 179 R. Payne, J. Phys. Chem., 69 (1965) 4113. 180 R. Payne, J. Phys. Chem., 70 (1966) 204. 181 R. Payne, Trans. Faraday Soc., 64 (1968) 1638. 182 M. J. Austin and R. Parsons, Proc. Chem. Soc, (1961) 239. 183 M. A, V. Devanathan, Trans. Faraday Soc., 50 (1954) 373. 184 J. R. Macdonald, J. Chem. Phys., 22 (1954) 1857. 185 D. C. Grahame, J. Amer. Chem. Soc., 79 (1957) 2093. 186 G. J. Hills and R. Payne, Trans. Faraday Soc., 61 (1965) 326. 187 E. Schwartz, B. B. Damaskin and A. N. Frumkin, Zh. Fiz. Khim., 36 (1962) 2419. 188 G. Gouy, C. R., 146 (1908) 1374. 189 S. Levine, G. M. Bell and D. Calvert, Can. J. Chem., 40 (1962) 518. 190 T. N. Andersen and J. O'M. Bockris, Electrochim. Acta, 9 (1964) 347. 191 W. Lorenz and G. Krtiger, Z. Phys. Chem. Leipz., 221 (1962) 231. 192 W. Lorenz, Z. Phys. Chem. Leipz., 224 (1963) 145. 193 R. Parsons in P. Delahay and C. W. Tobias (Eds.), Advances in Electrochemistry and Electrochemical

En#ineering, Vol. 7, Interscience, New York, 1970, p. 177. 194 J. E. B. Randles in P. Delahay and C. W. Tobias (Eds.), Advances in Electrochemistry and Electro-

chemical Engineering, Vol. 3, Interscience, New York, 1963, p. 1. 195 D. C. Grahame, Z. Elektrochem., 62 (1958) 264. 196 R. Parsons, Trans. Faraday Soc., 55 (1959) 999. 197 R. Payne, J. Chem. Phys., 42 (1965) 3371. 198 J. Lawrence and R. Parsons, Trans. Faraday Soc., 64 (1968) 751. 199 R. Parsons, Trans. Faraday Soc., 51 {1955) 1518. 200 E. Dutkiewicz and R. Parsons, J. Electroanal. Chem., I1 (I966) i00. 201 A. N. Frumkin, d. Electroanal. Chem., 7 (1964) 152. 202 A. N. Frumkin, Z. Phys. Chem., 116 (1925) 466. 203 P. J. Flory, J. Chem. Phys., 10 (1942) 51; M. L. Huggins, J. Phys. Chem., 46 (1942) 131. 204 J, R. Macdonald and C. A. Barlow, Electrochemistry, Proceedings of the 1st Australian Conference,

Sydney, 1963, Pergamon Press, London, 1964, p. 199. 205 J. D. Garnish and R. Parsons, Trans. Faraday Soc., 63 (1967) 1~/54. 206 R. de Levie, J. Electrochem. Soc., 118 (1971) 185C. 207 H. D. Hurwitz, J. Electroanal. Chem., 10 (1965) 35. 208 A. N. Frumkin, Z. Phys., 35 (1926) 792. 209 M. W. Breiter and P. Delahay, J. Amer. Chem, Soc., 81 (195~9) 2938. 210 B. B. Damaskin, J. Electroanal. Chem., 7 (1964) 155, 211 A. N. Frumkin, B. B. Damaskin, V. M. Gerovich and R. I. Kaganovich, Dokl. Akad. Nauk SSSR, 158

(1964) 706.


212 A. N. Frumkin, B. B. Damaskin and A. A. Survila, J. Electroanal. Chem., 16 (1968) 493. 213 E, Dutkiewicz, J. D. Garnish and R. Parsons, J. Electroanal. Chem., 16 (1968) 505. 214 J. O'M. Bockris, E. Gileadi and K. MiiUer, Electrochim. Acta, 12 (1967) 1301. 215 R. Parsons, J. Electroanal. Chem., 8 (1964) 93; 7 (1964) 136. 216 B. 217 B. 218 B. 219 R. 220 B. 221 B. 222 E. 223 S.

B. Damaskin, Elektrokhimiya, 6 (1970) 1135. B. Damaskin and A. V. Chizhov, Elektrokhimiya, 6 (1970) 1140. B. Damaskin, A. N. Frumkin and A. Chizhov, J. Electroanal. Chem., 28 (1970) 93. S. Hansen, D. J. Kelsh and D. H. Grantham, J. Phys. Chem., 67 (1963) 2316. B. Damaskin, J. Electroanal. Chem., 23 (1969) 431. B. Darnaskin, J. Electroanat. Chem., 30 (1971) 129. Gileadi, J. Electroanal. Chem., 30 (1971) 123. Jofa and A. N. Frumkin, Acta Physicochim. U.R.S.S., 10 (1939) 473.

The electrical double layer: Problems and recent progress

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