Ionic adsorption at the mercury-solution interface from solutions of lithium nitrate in dimethyl sulphoxide

Ionic adsorption at the mercury-solution interface from solutions of lithium nitrate in dimethyl sulphoxide

Electroanalytical Chemistry and InterJacial Electrochemistry, 41 (1973) 213-230 213 © Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands ...

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Electroanalytical Chemistry and InterJacial Electrochemistry, 41 (1973) 213-230

213

© Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands

IONIC A D S O R P T I O N AT THE M E R C U R Y - S O L U T I O N INTERFACE F R O M SOLUTIONS OF L I T H I U M NITRATE IN DIMETHYL SULPHOXIDE

G. J. HILLS

Department of Chemistry, The University, Southampton S09 5NH (England) R. M. REEVES

Chemistry Department, The University, Bristol BS8 l TH (England) (Received 9th February 1972; in revised form 12th June 1972)

INTRODUCTION

The solvent dimethylsulphoxide (DMSO) is a useful aprotic medium in which to study electrode and other charge-transfer processes. To do so invariably requires the presence of an excess of inert supporting electrolyte, the purpose of which is to reduce the ohmic resistance of the system and also to minimise the potential-dependence of the double layer capacitance. Such an arrangement, whilst instrumentally convenient, carries the penalty of an interface crowded with adsorbed species through which the electrode reaction must proceed. The distribution of solvent and solute species in the interface is then necessarily an important aspect of the description and understanding of the associated electrode process. In many non-aqueous systems it has been customary to use one of the tetraalkylammonium salts which are normally very soluble and frequently unassociated. These ha~,e the possible disadvantage that, as in aqueous solution, they may be strongly adsorbed. The use of simpler, inorganic salts might therefore be preferred, provided only that they do not form ion-associates too readily. In dimethylsulphoxide there are several soluble inorganic salts which are readily and cheaply available in' pure form and are good conductors, e.9. KPF6, LiCI and LiNO3. The adsorption and double layer characteristics of the first two have been the subjects of two recent and fairly detailed studies ~'z. The only information concerning nitrate systems in this solvent is of a cursory nature, notwithstanding the wide range of studies of nitrate adsorption that have been made on aqueous systems. Thus, Payne 3 has systematically studied the adsorption of nitrate ions from aqueous solutions o f K N O 3 and from mixtures of NH4NO 3 and NH4F at constant ionic strength. In the first case the adsorption was found to be closer in character to that of iodide rather than that of oxyanions 4'5. In the second case the results were found to fit either a Frumkin or a virial type isotherm : no approach to saturation was observed and a second virial coefficient of 4.4 (nm) 2 was noted. This behaviour has been found to be Presented at the meeting on The Electrical Double Layer held by the Society for Electrochemistry in Bristol 17th 19th April 1972.

214

G. J. HILLS, R. M. REEVES

typical of a number of ionic systems and it was thought interesting to study the adsorption of this ion from an aprotic solvent such as DMSO in which the anionic solvation energies are, in general, lower than those found in aqueous solutions. Damaskin et al. 6 recently proposed that the adsorption, at higher electrolyte concentrations, takes place against a partial ion-free layer of solvent molecules on the electrode surface. If this occurs in non-aqueous media, its effect may be manifest at lower electrolyte concentrations and might possibly be observed in these measurements if the relative degrees of interaction between DMSO and the electrode and between DMSO and the ion parallel the behaviour found in aqueous solutions. The absence of a "hump" in the capacity vs. potential function for both lithium halide and lithium nitrate solutions in DMSO was noted by Payne 1. The capacity was found to rise very rapidly at potentials anodic of the electrocapillary maximum (e.c.m.). However, it is known that some electrolytes, e.g. KPF6, do give maxima in this solvent 1, and from a comparison with other systems, e. 9. those in water, there might be expected to be some parallel between the appearance and disappearance of"humps" in the two systems. An obstacle to the wider study of electrocapillary phenomena, e.g. in nonaqueous solvents, is invariably the lack of supporting thermodynamic data. DMSO is no exception to this generalisation and part of the work recorded here was concerned with ancillary measurements of activity coefficients and transport numbers. EXPERIMENTAL

The differential double layer capacity at a dropping mercury electrode was measured with an a.c. series bridge as described elsewhere 7. The internal precision of the measurements varied from 0.05 ~ in the concentrated solutions to 1 ~o in the most dilute of the solutions. The potential of the working electrode was measured to + 1 mV with a high impedance digital voltmeter. The reference electrode was a separated silver/silver ion electrode constructed from a 0.2 cm o.d. silver rod ("spectroscopically pure"--Johnson-Matthey) in contact with a 10 -4 M solution of Ag ÷ prepared by anodising the silver into a 0.1 M lithium nitrate solution in DMSO. The electrode was then separated from the cell by three compartments, the liquid junctions between which were made through solution-sealed taps. Two compartments contained silverfree lithium nitrate solution (0.1 M) and the other a sample of the solution under study. It was possible in principle to use an unseparated (TI)Hg/T1C! electrode but this is sensitive to both oxygen and water, which would have been difficult to exclude continuously under the present experimental conditions. The potential of the e.c.m, was determined before, during, and after the capacity measurements at each concentration using a modified streaming mercury electrode v. The capacity was also checked for reproducibility. Both sets of measurements were subject to small drifts with time of the reference electrode potential and at the end of the complete series of measurements, the capacity at the e.c.m, and the potential of the e.c.m, were redetermined for the solutions in a cyclic manner until reproducible values were obtained. The original data were then corrected to this revised potential scale. The interfacial tension was measured as described elsewhere 7 using a Lippmann capillary electrometer. The mean of three or more separate determinations of the surface tension at the e.c.m, at each concentration was plotted as a function of elec-

NITRATE ADSORPTION AT THE Hg/DMSO INTERFACE

215

trolyte activity and values from the smoothed curve were used in the succeeding analysis. On the anodic branch of the capillary curve, considerable sticking of the mercury meniscus was observed and although the electrometer electrode was siliconed, the silicone layer was rapidly attacked at high anodic or cathodic potentials and this eventually resulted in blockage of the capillary. Similar difficulties.were encountered during the operation of the dropping mercury electrode. The mercury and solvent were prepared by the usual procedures as described elsewhere v. The lithium nitrate was recrystallised twice from triply distilled water and dried at 60°C in vacuo. The salt was then recrystallised from redistilled absolute alcohol (AnalaR), the ethanol finally being removed at 70°C in vaeuo. Trials of this procedure using LiC1, inherently less hazardous, indicated that the salt had a purity > 99.9 ~o and that the content of residual water was negligible. The pure dry LiNO3 was stored in a sealed phial. Attempts to dry the salt using 2,2'-dimethoxypropane were discontinued after extensive discolouration of the salt had been observed. The influence of water on the capacity vs. potential function in DMSO has been discussed elsewhere 8. In order to interpret the capacity data, ancillary measurements of transport numbers and salt activities were required. The transport number of the Li + ion could not be determined using moving boundary methods even though attempts were made using a wide variety of electrode materials. The Hittorf method was finally used in conjunction with solid lithium electrodes, the whole apparatus being protected from atmospheric attack in a thermostatted dry box. The lithium electrodes were prepared from metal freshly cut with a glass knife under deoxygenated solutions in the dry box. Concentration changes were sensed conductimetrically because the standard analytical procedures were found to be insufficiently precise in solutions containing strong ligands. The activity coefficients were then derived from the e.m.f. of cells with transport in terms of the standard relationship: F

t_ d In a+

(1)

where AE is the observed e.m.f., t_ the anionic transference number, c the Concentration and a • the mean ionic activity. The construction of these cells and the amalgam cells are described elsewhere v'8. RESULTS

1. Transport and activity data

A salt concentration of --~0.1 M was used for the determination of the cation transport number of LiNO3. In order to avoid polymerisation of the solvent on the electrode, a current density of < 1 mA cm- 2 was employed. Three series of measurements on these solutions yielded values of tLi+= 0.226, 0.246 and 0.249. These are considerably lower than the comparable value of 0.35 for aqueous solution and which appears at first sight to be in conflict with the positive free energy of transfer of lithium salts from H20 to DMSO (see below). However, it must be remembered that relative ionic mobilities in any solvent are governed not only by ionic size but by the relative magnitudes of the dielectric drag, i.e. the retarding force resulting from the finite rate of dielectric relaxation which is sensitive to the charge density of the moving ion 9' xo. The Walden products of simple salts are far from constant in this and other solvents

216

G. J. HILLS, R. M. REEVES

and a major contribution to the effective viscosity as experienced by migrating ions is to be expected from the dielectric relaxation of this solvent. The activity data derived from the amalgam cells and from the mean transport number are shown in Fig. 1. These data could be fitted to an extended form of the Debye-Hfickel theory using an ao parameter of 0.3 nm which agrees well with the value found for LiC1 in this solvent by Dunnett and Gasser 1~ and which is close to the sum of the ionic radii. The minimum in the activity-concentration function occurs at ~0.5 M, i.e. in the same region as it occurs in aqueous solution 12.

~ F cma 4O

I

30 log

f_+

20I

0.1

0.2 0.3

C/'/mo~~ ,itrev2

o'.~

o!4

o'-~

o'.~

~'.o

i.~

10 I

0.5

1!0

I

1-5

E~

Fig. 1. Activity coefficientsof LiNO3 in DMSO as function of salt concn. Fig. 2. Differentialcapacity of electrical double layer at mercuryelectrode in contact with solns, of LiNO3 in DMSO: (1) 0.02, (2) 0.05, (3) 0.10, (4) 0.35, (5) 0.50, (6) 0.75, (7) 1.00 M. The activity data, illustrated in Fig. 1, whilst sufficiently precise for present purposes, should be treated with some reserve if only because the e.m.f, method used here relies on the knowledge of at least one absolute value off±. This is usually derived from measurements at very low concentrations where the limiting Debye-Hfickel law is valid but where the measurements are most difficult 12. The lowest concentration used here was 0.01 M and the corresponding value off+ =0.791 was obtained by an iterative procedure whereby the derived values off+- for the lowest concentrations were made to approach the Debye-Hfickel limiting slope. The general features of the activity data are close to those found 13 in comparable studies of LiC1.

2. Ionic adsorption from lithium nitrate solutions in DMSO The differential capacity of the electrical double layer, C, at the dropping mercury electrode, was measured as a function of potential for l l concentrations of LiNO3 (0.010-1.00 M) over the range of ideal polarisability as indicated by the absence of significant d.c. current. The peak-to-peak amplitude of the applied alternating

NITRATE A D S O R P T I O N AT THE H g / D M S O INTERFACE

217

voltage was ~ 5 mV and there was negligible frequency dispersion of the observed resistance and capacitance. The computational procedures used to analyse these data are fully described elsewhere 7'14. Eventually, the results derived from the most dilute of the solutions were discarded, partly because of the restricted range of charge involved but principally because of the uncertainties in capacitance arising from the high values of the solution resistance. This type of difficulty has now been overcome by the use of an alternative bridge method in which the quadrature component of the impedance is recorded separately by means of phase-sensitive system and which will be described elsewhere 15. Representative data for the capacitance-potential function are shown in Fig. 2 for seven concentrations of LiNO 3, The curves are almost featureless, although the diffuse layer minimum can be detected at concentrations < 0.35 M. No sign of the large maxima observed with aqueous nitrate solutions is observed here and because those maxima are invariably associated with the onset of specific adsorption, it became a matter of prime importance to establish to what degree nitrate ions are specifically adsorbed from DMSO. Previously published evidence ~ is scanty and the more extensive data presented here were therefore investigated in the usual way, i.e. by first assuming that all of the adsorbed charge resides at or beyond the outer Helmholtz plane and that its associated capacity can be calculated from diffuse double layer theory. The inner layer capacity, Ci, can then be evaluated from the equation:

Ci- C

\

RT /

cosh \ 2 R T

(2)

where c is the electrolyte concentration, e the mean dielectric constant, 42 the outer Helmholtz plane potential and where the other terms have their usual significance 16. The resultant Ci values were found to be independent of concentration on the cathodic branch but markedly concentration dependent on the anodic branch, from which it may be concluded ~7 that the nitrate ion (but not the lithium ion) is specifically adsorbed. That one of the constituent ions is specifically adsorbed is also evident TABLE 1 C O O R D I N A T E S OF THE ELECTROCAPILLARY M A X I M U M FOR S O L U T I O N S OF LiNO 3 IN D M S O Conc./M

Potential o f zero charge vs. A g / A 9 + /- V

Capacity at the e.c.m, /l~F cm 2

Surface tension at the e.c.m. /mNm i

0.01 0.02 0.035 0.05 0.075 0.10 0.20 0.35 0.5 0.75 1.0

0.5868 0.5702 0.5577 0.5504 0.5415 0.5355 0.5217 0.5101 0.5022 0.4962 0.4856

11.50 12.53 14.67 16.31 18.03 19.21 21.98 24.24 25.62 27.28 28.12

370.4 370.3 370.0 369.8 369.3 368.9 368.1 366.7 366.3 364.9 363.2

218

G. J. HILLS, R. M. REEVES

from the marked concentration dependence of the interfacial tension at the electrocapillary maximum, c f Table 1. The capacity-potential data were integrated to give values of charge, q, and surface tension, 7, over the entire range of concentrations and potential. The observed potentials were converted to the E_ scale using the derived values of cationic transport number and mean ionic activity coefficient, and the Parsons' auxiliary function18, ~, was then evaluated from the equation: (3)

- = 7 + qE_

The surface excess of cations, F+, was then calculated from the relationship: -d~_ -

2RT

F+ d i n a+_ - E _ d q (4) F by computer differentiation of ~_ as a function of In a+_ at integral values of q. The surface excesses, expressed as q = zFF+, the charge due to excess of cations, are shown in Fig. 3. The minima which are seen to occur at all concentrations are similar to that found with aqueous solutions of strongly adsorbed species such as halide ions (and also with chloride solutions in DMSO2). Figure 3 also displays an apparent invariant point at q ~ - 7 # C cm-2 and further examples of such points may be found with aqueous nitrate systems 3 and also in the comparable study of LiC1 in DMSO 2. Whether these invariant points are realities or not is difficult to assess but it should be noted that observed values of the cationic charge at extremes of cathodic polarisation do not coincide with the predictions of the diffuse double layer theory. Using these values of cationic excesses, the surface excess of anions was calculated by difference from the equation: F_ -

q

F+

(5)

F Part of this excess is, of course, due to the anionic contribution, qD_, to the diffuse double layer which may be calculated from the values of q assuming that cations are not specifically adsorbed over the entire range of potential involved here. From qO_ and the total anionic excess, the charge due to specifically absorbed nitrate ions, qX, is obtained, again by difference, from the equation: q ~ = F F _ - qO

(6)

All these data and related functions, such as values of the potential drop across the inner layer and of dq~/dq, were derived from the computer programme and also, as a check, from manual calculations. The specifically adsorbed charge due to nitrate ions is shown in Fig. 4 as a function of electrode charge and LiNO3 concentration. The Figure is remarkable in that the concentration dependence of q l appears to increase as the electrode charge decreases whereas at q > 6 #C cm- 2 the lines become virtually parallel. The probable error in q 1 is 0.5 ~tC cm- 2 and certainly not large enough to account for the systematic deviations from the expected linearity. The limiting value of the slope at positive q values is 1.25, i.e. much larger than the value (1.0) found with aqueous nitrate solutions but similar to that for aqueous chloride solutions ~9. The logarithmic isotherms, ql vs. ( 2 R T / F ) In a_+, are also curved and similar in character to those obtained by Lawrence et al. 2° from aqueous bromide solutions.

219

NITRATE A D S O R P T I O N AT THE Hg/DMSO INTERFACE

zFP~p

C c m -2 15

10

,o

°

2 1 10 12

8

4

0

-4

-8

-12

~c cn~~

8

6

4

2

0

-2 Q

~ ~"'~

Fig. 3. Charge due to surface excess of cations as function of electrode charge and bulk concn, of LiNO 3 : (1) 0.02, (2) 0.036, (3) 0.05, (4) 0.075, (5) 0.10, (6) 0.20, (7) 0.35, (8) 0.50, (9) 0.75, (10) 1.00 M. Fig. 4. Charge due to specifically adsorbed nitrate ions as function of electrode charge and nitrate concns. Concns. as in Fig. 3.

The potential drop across the inner layer, q~M-2, generated by the specifically adsorbed charge was calculated by subtracting (RT/F) In a_+ and q52 from the E_ potential. Values of ~bM- 2 are shown in Fig. 5 as a function of ql at integral values of electrode charge, q. The observed relationship could reasonably be represented by a series of parallel straight lines, at least at values of q from 10 to 4 #C cm- 2, but at lower values of q it becomes increasingly difficult to force-fit the data in this way. Indeed, it is clear that the relationship of 4)u - 2 to ql varies systematically with electrode charge. This variation may, of course, simply be the result of systematic errors and certainly the evaluation of 4)2 at low values of F+ becomes increasingly sensitive zl to the errors in F+. The slopes of the lines in Fig. 5 are related to the variation with charge of the standard free energy of adsorption, AGad o s, according to the relationship 18 : d(bi - 2 dq 1 -

2RT (c~ In [:~] F

\ ~ q q ].T

(7)

where fi= - e x p (AG°ds/RT), and it is usual to assume that the relationship is linear and constant, especially with reference to non-aqueous solutions 22. This leads to simplifications in the subsequent analysis of the data but whether it is in fact the case will evidently require further investigation. The original capacity data were further analysed in terms of diffuse layer theory and the values of dq 1/dq obtained from the slopes of the lines in Fig. 4. Using values of q~2 and eqn. (1) to calculate CD, the capacity of the inner region of the double layer, Ci, was obtained from the relationship23 : C 1 = Ci- 1_~_(Co)- 1(1 +dql/dq)

(8)

220

G. J. HILLS, R. M. REEVES

¢ m'2,/v 40

0"5

""-,

30

o.,

20 o.,

0

6 10

2O

10

0

I

5

I

I

4

2

0

-2

-4

,,J_,-, t//,m.~ cm - 2

-6

-8

°)/~HCc n ; 2

Fig. 5. Potential difference across inner layer generated by specifically adsorbed ions, as function of specifically adsorbed charge due to anions and at integral values of electrode charge. Fig. 6. Differential capacity of inner region of electrical double layer as function of nitrate concn, and electrode charge. Concns. as for Fig. 3.

I

30

ore-'

I

I

I

I

~Nm-~

25

20

20

~

4

15

j

~ i.~+t(o,)

-.-,*-_. _.

I

10

I

8

6

[

4

I

2

I

0

.~

~ |

I -o.,

, o

,

)

o.,

~ , ' l l C cm -2

Fig. 7. Inner layer capacity megsured at constant amount adsorbed, qC~,as function of electrode charge and nitrate concns.: (1) 0.02, (2) 0.05, (3) 0.10, (4) 0.35, (5) 0.50, (6) 1.00 M. Fig. 8. Composite curve of surface pressure due to specifically adsorbed nitrate ions. Solid line is derived from virial isotherm with constants given in text.

NITRATE ADSORPTION AT THE Hg/DMSO INTERFACE

221

In Fig. 6, C i is plotted as a function of electrode charge and there is no evidence of any hump over the range of charge studied here. The resulting capacity is significantly concentration dependent, in contrast to the behaviour found in aqueous solutions. The values of dq 1/dq in the neighbourhood of q = 0 strongly influence the values of Ci and, in view of the preceding discussion, these values might be expected to display the largest errors• However, even allowing for this. no hump is observed. It is usual to separate Ci into two components, qCi, the capacity measured at constant amount adsorbed and qlC~, the capacity measured at constant charge on the metal. The parameters are defined and related 18 by the equations: qCi = (~?q/~dpU-2)q1 (9) Ci

aCi + ~

t

(10)

=

(11)

and by eqn. (8). Values of q,C~ can be obtained from the slopes of the lines in Fig. 5 and if it is assumed that the lines are essentially parallel, the integral capacity, qlKi, to which qiC i may now be equated, attains a value of 40.5/~F cm-2. The comparable value of q~K~for the adsorption of C1- from this solvent 2 was 35 #F cm- 2 which itself is significantly lower than the corresponding value in aqueous solution (96/~F cm-2) 3. The values of qCi are shown in Fig. 7 as a function of electrode charge ; as expected, they are also very concentration dependent. In the comparable aqueous system C~was concentration independent and even in the case of halide ion adsorption from non-aqueous solutions, the variation ofqC i is < 10 ~ whereas in the present case the variation is ~ 20 ~. This unusual behaviour might be assumed to be a consequence of the assumed parallel nature of the lines in Fig. 5 but if this were so, the concentration dependence of qCi might be expected to decrease when q~Ci assumes a more nearly constant value, i.e. at q > 6 pC cm-2 (cf Fig. 5). Such behaviour is not observed and this unusual concentration dependence seems to be a real characteristic of the system. The range of values of qCi observed agrees with the range of values of qK i recently found for the chloride system in DMSO 2, i.e. 10 < q~K i < 20/~F c m - 2. One reason why these results seem to be at variance with those from other non-aqueous studies might lie in the scheme of analysis. In recent papers, values of the various factors used in the analysis have been derived from the adsorption isotherm. This required the isotherm to be fitted to the experimental data at an early stage in the analysis in the hope of avoiding some of the cumulative errors resulting from repeated interpolations. This method relies on the degree of precision of the fit to the isotherm, and as data in most cases are generally not available in the range corresponding to Henry's law, the fit invariably involves some degree of approximation. Although Parsons has noted that the agreement between this procedure and that adopted here is not unsatisfactory, it seems to us better in principle to avoid introducing a model, i.e. a particular isotherm, at too earlier a stage in the analysis. In order to derive the isotherm for this system, the surface pressure ((b) due to specifically adsorbed nitrate ions was calculated according to the expression23 : (/)=~2-~1 -}-

FJ d#

F_D d p = •

1

(12)

222

G. J. HILLS, R. M. REEVES

where ~2 is the Parsons' auxiliary function at concentration 2 and ~1 is the function at concentration 1, where concentration 1 < concentration 2. The surface pressure due to specifically adsorbed ions is shown in Fig. 8. This curve was constructed by displacing the separate curves of • vs. 2 R T / F In a+_ at constant q, parallel to the ordinate and abscissae. The superimposed data showed deviations from the common curve which are somewhat larger than those usually observed, i.e. ~ 0.5 mN m - 1 at the extremes of concentration, as compared to ~ 0.3 mN m - 1 for the comparable aqueous system. As it was possible to fit all the data to a common curve for all values of electrode charge studied, it is probable that the adsorption behaviour can be expressed by a unique isotherm with constants, in the equation of state, independent of the electrical variable, which in this case is the electrode charge. The displacements along the f (ln a +) axis involved in the construction of Fig. 8, give directly the change of free energy of adsorption with electrode charge. This variation, shown as the triangles (A) in Fig. 9, appears to be a linear one as has been found for all simple ionic systems. The slope of the plot, 0.204, is approximately the same as the value found for the comparable aqueous system. This is in contrast to the chloride system for which a higher value is found in DMSO than in aqueous solution 2. The linearity of A points in Fig. 9 implies a constant value of d In fl/dq over the whole range of surface charge densities, which is in conflict with the data in Fig. 5 where the plots of (aM-z vs. ql are strongly charge dependent at q < 6/~C cm -2. It may be that the surface pressure fitting procedure (A) or the virial data (+) (see below), which are based on differentials of ~b, are insufficiently sensitive. Certainly the corresponding data obtained from plots of in C( -1 vs. In a+, which appear in Fig. 9 as circles (and which are discussed later), could be regarded as non-linear and therefore partly in support of the data in Fig. 5. It is worth noting that both sets of data are closer to the "raw" results than the others. Even so, the balance of evidence from most of these systems is that for simple ionic systems In fl is close to a linear function of q. The changes of slope in Fig. 5 could be explained formally in terms of a variable thickness of the inner layer but this would only be significant in concentrated solutions. The discrepancy therefore remains. The isotherm for the adsorption of nitrate ions from DMSO was fitted using the methods described by Parsons 24. The theoretical isotherms were generated using a short computer programme. The simplest 1-constant isotherm that could be fitted over the entire range studied was the virial isotherm" In fl a_+ = In/-i + 2 B F i / R T

(13)

In fl = a + b q

(14)

where and where a is related to the standard free energy of adsorption and b = d In fl/dq. The solid line in Fig. 8 was drawn according to this isotherm with a = 17.2, b=0.204 and B = 5 (nm) 2 molecule- l. The constant a yields a value of - 98 kJ mol- 1 for the standard free energy of adsorption at the standard states of 1 mol- 1 in the bulk of solution and 1 ion cm -2 on the surface. This compares with a value of -84.5 kJ mol-1 calculated from Payne's data for the adsorption of nitrate from aqueous solutions 4. The significance of these values will be discussed further at a later stage.

223

NITRATE ADSORPTION AT THE Hg/DMSO INTERFACE

0.2

f(AG) -

o

o

0

L 8

I 15

I 4

0"1

I 10

I 2

I 0

I -2

I

I

I

15

10

5

q/~,c c.;' Fig. 9. Variation of standard free energy of adsorption with electrode charge. Values derived from : (A) composite surface pressure curve, (+) plots of the virial isotherm according to eqn. (15), (©) plots of log (-A(1/Ci)) vs. log a+. Fig. 10. Plot of virial isotherm according to eqn. (15).

The second virial coefficient and the variation of the standard free energy of adsorption with electrode charge may also be obtained from a plot of the data according t o 25'4"2 :

R T In ( - q 1/a+) - ~b2 F = - AG o (q) + 2Bq a

(15)

where (~2 = 0 for the "simple" virial isotherm. The term in ~b2 was included by de Levie 42 to allow for the work done in transporting the adsorbing ion from the bulk of the solution to the outer Helmholtz plane. The data plotted according to eqn. (15), in which the salt activity (a 2) replaces the mean ion activity (a+) and ~2=0, are shown in Fig. 10 at integral values of electrode charge. The lines are evidently non-parallel and B varies with electrode charge from 4.8 (nm) 2 molecule-1 at q = pC cm -2 to 3.8 (nm) 2 molecule-t at the e.c.m. 26. This systematic variation of B implies that the procedure of curve fitting to the surface pressure is insensitive to the precise charge dependence of B and that the dependence of the adsorption on the electric variable cannot be expressed entirely through the charge dependence of the standard free energy adsorption. The intercepts of the lines in Fig. 10 yield a further set of values off(In ae) = d In fl which are also included in Fig. 9. They evidently agree closely with the values derived from the superposition of surface pressure curves. These data were then replotted according to the virial isotherm, eqn. (15),

224

G. J. HILLS, R. M. REEVES

oIVnl O < o

12

i

0"25

0

lo

5[ *'1' .~

• •

/ 020

~

ff~

..~'..~ ,.l.. "':..'...

J

i

/

0"15

15

10

5

10'~(C=)~_. 2 -,

15

10

": "'"

5 ~/,~C crn"2

Fig. 11. Plot of virial isotherm accordingto eqn. (i 5) and including the ~b2 term. Fig. 12. Change of inner layercapacityresultingfromspecificadsorption of nitrate ions from LiNO3 solns. as function of concn, and charge on the metal. including the ~b2 term, in Fig. 11. The linearity of these plots is good at 2 < q < 10 pC cm 2 but at the extremes there is a significant tendency towards curvature. The slopes are not constant and the B coefficient is evidently still not independent of the electrical variable. The extended isotherm including q~2 does not seem to represent a better fit to this system. At low concentrations the plots in both Figs. 10 and 11 are significantly curved. A similar trend had been observed in aqueous systems 43, the maximum in the plots occurring at values of ql slightly greater than the point of zero charge in the diffuse layer. This seems to be a feature of many simple ionic systems and may be the result of systematic errors at low electrolyte concentrations. As the virial isotherm may be expressed as a reduction of the Frumkin isotherm when B is large 2s, it is necessary to show that indeed the Frumkin isotherm is no better an approximation with which to describe the observed adsorption behaviour. An analysis based on the capacity is the most sensitive method of discriminating between the two isotherms. The change in the inner layer capacity, in the presence of the adsorbing species compared with the value in the absence of specific adsorption, may be expressed 25 by the relationship: -

A (ljCi) = k T b 2 ( f - 1 + 2B)-1

(16)

which has a limiting value given by:

A < lim-

2B \ c~q /

(17)

225

NITRATE A D S O R P T I O N AT THE H g / D M S O INTERFACE

This function is plotted in Fig. 12 and if the data were to be better described by a Frumkin isotherm, the plots should pass through a maximum 27. In fact the limiting value, described by eqn. (18) and predicted by eqn. (17) for a virial isotherm, is observed. From the estimated limiting value, B is calculated to be 4.0 (nm) 2 and bearing in mind that the plot is still some distance from the actual limiting asymptote, this value is in reasonable agreement with that derived earlier from the surface pressure data. It is also possible to derive directly from the capacity the value of b in eqn. (14), provided the form of the isotherm is known. At low coverages, the isotherm approximates to Henry's law and it follows that in this region the plots in Fig. 13 should be linear with a slope equal to a/2.3. Because of the non-asymptotic nature of the lines in Fig. 4 and their influence on the calculation of dqt/dq at lower coverages and therefore on the calculation of Ci, significant values of A(1/Ci) could not be obtained in the low coverage region. The lines in Fig. 13 do show a tendency to approach a limiting value at higher coverages although very large positive electrode charges would be required to demonstrate convincingly the convergence. Evidently the process of fitting the isotherm directly to the capacity data is not more discriminating than the fit to the surface pressure curves in determining the variation of B with electrode charge. It is possible to determine the value of a in eqn. (14), directly from the capacity data. The curves of log (--A (1/Ci)) VS. log a_+ should be superimposable in this system if B is independent of charge, cf the surface pressure curves 24. These curves are shown in Fig. 14 and it should be noted that the composite curve, for a 1-constant isotherm, has a universal shape independent of the isotherm constants. The change of the free energy of adsorption with electrode charge derived from this plot is also included in Fig. 9; the l~ossibility that it may be a curved relationship, especially in the region q < 6/~C cm- 2, was discussed above. It is evident that the capacity data correspond to a virial type isotherm as no maximum values characteristic of isotherms based on the Langmuir model are observed. This may simply be a result of 0 < ½ under which conditions it is difficult to distinguish between many of the simpler isotherms. No further information concerning the adsorption process can be obtained by using more complex isotherms. It is interesting to reconsider in relation to the adsorption isotherm one of the anomalies in this analysis, namely the apparent non-parallelism of the lines in Fig. 5. The use of the simple expression relating b to q (eqn. 14)) inevitably results in a nonlinear dependence of AGOon electrode charge. Use of the fuller relationship, derived

log~,/~ ~

!

0.5 2RT a~VV

"--F" In

0 110 ~

~

4I

2I

0I

-2I

--0.2

-0,1

0

Fig. 13. Change in inner layer capacity, as in (a), as function of concn, and charge on electrode. Fig. 14. Change in inner layer capacity, as in (a), as function of charge on electrode and electrolyte activity.

226

G.J.

HILLS,

R. M . R E E V E S

by Parry and Parsons z3, does not entirely eliminate the non-parallelism and thus confirm the relationship of Fig. 9. The capacity analysis involving eqns. (9) and (10) is clearly influenced by this discrepancy but it is not clear how to improve the agreement. It is usual als9 to investigate the degree of specific adsorption in terms of the Esin-Markov coefficients, defined18 as:

~,~]q= - (~q).

(18)

\ ~?#}q

(19)

or

F [_~,~q-q).+ k~}J

In the absence of specific adsorption these coefficients take values of - 1 (as q ~ o0), -½ (at q=0) and 0 (as q ~ - o0). The coefficients observed for this system are listed in Table 2 and on the cathodic branch, at q < 8 pC era- 2, they agree well with the predicted values. At higher values of q there is increasing evidence of specific adsorption of the anion and the deviations of the coefficients from the values predicted for nonspecific adsorption are well outside experimental error. The specific adsorption of nitrate ions is thus further confirmed and is similar to that found for chloride ions in the same solvent 2. The Esin and Markov effect is also related to the isotherm through the relationship2V :

0E+I

~y-yJq=

L ~?q' I

L 01n fll

t~n/U.

~q--q )

(20)

An isotherm based on the Langmuir model, e.9.the Frumkin isotherm, would require a maximum value in the coefficient (dql/d In fl)u which is evidently not found in this system, assuming that we can neglect the influence of diffuse layer contributions in TABLE ESIN

2 AND

MARKOV

COEFFICIENTS

q/#C cm -2

-F(c~E+/OlOq

_ (~ql /Oq) (0.095M)

- 12

-0.04

--

- 10

- 0.03

--

-

8

0.00

--

-

6 4 2

0.11 0.24 0.37

---

0

0.57

0.62

1 2 3

0.87 1.03 L10

0.77 0.96 1.04

4 5 6 7

1.18 1,18 1.18 1.18

1.17 1.17 1.17 1.17

NITRATE ADSORPTION AT THE Hg/DMSO INTERFACE

227

eqn. (19). The appearance of a positive slope at q ~ - 10 pC cm-2 closely parallels the behaviour of the corresponding aqueous system 4, but the significance of this effect depends on the absence of systematic errors and on the precision of the activity coefficients. DISCUSSION

In this section the general nature of the results and their implications in the field of double layer studies are discussed. The raw capacitance data closely overlap on the cathodic branch and reflect the absence of cationic specific adsorption and this is in keeping with the strong ligand properties of DMSO for cations. Moreover, the values of cationic charge calculated from diffuse layer theory agreed well with the observed values. At all salt concentrations studied, the capacitance vs. potential function displayed a broad minimum. Electrostrictive compression of the first solvent layer should occur at potentials cathodic of the capacity minimum resulting in a rise in capacity, but over a potential range of more than 1.5 V no significant capacity rise was detected. In terms of electrode charge as the electrical variable, the range of invariant capacity is perhaps not as great and even at the most cathodic potentials studied, q attained a value of only ~ - 14 #C cm-2. There is evidence that at higher cathodic potentials, i.e. at q ~ - 18 pC c m - 2 the capacity may rise, as is observed in aqueous systems, but the rise tends to be overshadowed by the onset of the faradaic reaction. These data therefore offer little evidence for the Barlow-Macdonald theory of the capacity 29. On the anodic branch, the range of capacitance measurements is also limited by the onset of the faradaic reaction, which occurs at potentials which relative to the e.c.m, are more cathodic than those, for example, noted for aqueous systems 3°. This reflects the influence of solvation energy on the relative reactivity of dissolved ions and, compared with aqueous systems, cations in D M S O are more strongly solvated and anions more weakly solvated 31 -33. The capacity minimum which results from the diffuse layer capacity contribution to the total capacity is less pronounced than in the corresponding aqueous system and is a direct result of the rapid anodic rise in the capacity. The potentials of zero charge are similar for both cloride- and nitrate-containing systems when they are compared on the same potential scale 7. However, the actual capacities for the two systems are quite different. For example, in 0.1 M LiCI, Cq = o = 47.7/~F cm- 2 whereas in 0.1 M LiNO 3, Cq= o = 19.2 pF cm- 2. These differences reflect not only the differing degrees of ionic adsorption but also the proximity of the faradaic process in the two systems. However, it should be noted that the steep rise in capacity was not frequency dependent. The series resistance was also independent of frequency and no direct current was detected in this potential region. It seems unlikely that the rise is caused by adatom 35 or phase formation 36'3v but is rather a normal adsorption capacitance. The anodic rise in nitrate solutions is less steep than that in chloride solutions but larger than would be expected from the studies of the corresponding aqueous system t'7'3. In terms of absolute values of adsorbed charge, the results are similar, over the charge range shown in Fig. 4. However, if in terms of the Esin-Markov coefficients we extrapolate the values of adsorbed charge to the maximum values studied

228

G. J. HILLS,R. M. REEVES

by Payne 3, then the differences between 0.1 M aqueous and non-aqueous nitrate solutions are very evident, i.e. in the values of ql at q = 20/aC cm-z, which were 30.5 /aCcm -2 for DMSO and only 18.5 ktC cm -2 for H20. This difference results from a combination of two factors, the different degrees of anionic solvation and the different solvent/mercury interactions. The free energy of transfer for LiCI from H20 to DMS O is reported 32 to be 20.8 kJ tool- 1 at 25°C and it is supposed that most of this change is associated with the Li + ion 3s. If the ionic solvation factor was overriding, the degree of specific adsorption might be expected to be higher at all electrode charges, the value of dqr/dq being the same. This is not observed and the metal surface-solvent interaction must also be important. Support for this may be adduced from the fact that dql/dq in water (1.08-1.1) is lower than the corresponding values in DMSO (cf Table 2). Kim et al. z suggested that only ionic solvation was important although they overlooked the fact of the rise of specific adsorption with electrode charge which was higher in their system than in the corresponding aqueous system (up to 1.3 for DMSO 2, cf 1.22 for water2S). An alternative approach is to compare the parameters of the isotherm for the two solvent systems, although this method introduces the problem of describing the isotherm in terms of a real molecular model. The virial isotherm used in this study and also fitted to the aqueous nitrate system3 has been discussed by Parsons 2s'39. It involves consideration of the second virial coefficient in terms of electrostatic interactions which in turn involve the dielectric constants of regions of the inner layer and equates the ion size to the crystallographic radius. It therefore neglects the solvent contributions and oversimplifies an essentially complex molecular problem. All calculations based On this model, yield values for the "inner layer dielectric constant" of 2-10 irrespective of the solvent which do notexplain why the specific adsorption is different in the two solvents and for different ions in the same solvent. Also neglected in these calculations are the real charge distributions at the interface. Some comparison of derived functions is also possible. Thus the distance ratios for both nitrate and chloride ions are larger than they are in aqueous media and this is in accord with the geherally higher values found in non-aqueous media. The data for the present systems are shown in Fig. 15. As with aqueous nitrate systems, the value increases slightly with decreasing electrode charge. Assuming a monomolecular layer

0"5

X2"~1 X2

0"4 o-------

0"3

0.2

0.1 I 10

I 8

I 6

I 4

] 2

I 0 ~pC

c m -2

Fig. i 5. Variationof distanceratio. (x2-xl)/x2, as functionof charge on electrode.

NITRATE ADSORPTION AT THE Hg/DMSO INTERFACE

229

of DMSO molecules (0.48 nm) 4° and a crystallographic radius for the lithium ion of 0.068 nm 41, the thickness of the inner Helmholtz plane varies from 0.324-0.327 nm using a simple parallel capacitor model. As pointed out by Payne 3, this simple calculation neglects the influence of replaced solvent dipoles on the potential drop across the inrier layer. Further calculations have not been made, using the model proposed by Parry and Parsons 23, due to the probability of cumulative errors in the analysis, to the unusual concentration dependence of qCi and the difficulty of defining q~Ki. ACKNOWLEDGEMENTS

R.M.R. acknowledges the receipt of an S.R.C. Studentship during the tenure of which this work was carried out, SUMMARY

The specific adsorption of nitrate ions at the mercury/dimethylsulphoxide interface has been determined from measurements of interfacial capacitance and corresponding activity coefficients in the system Hg/LiNO3 in DMSO. The standard free energy of adsorption was found to be a linear function of electrode charge. The data were fitted to a virial isotherm and charge saturation was not approached. The second virial coefficient (B) was found to be larger than that for the comparable aqueous value and to be significantly charge dependent. The Esin and Markov coefficients were larger than the corresponding aqueous values and suggest that nitrate ions are more strongly adsorbed from this solvent than from water. No evidence for the specific adsorption of the cation was found. REFERENCES R. Payne, J. Amer. Chem. Soc., 89 (1967) 489. S. H. Kim, T. N. Anderson and H. Eyring, J. Phys. Chem., 74 (1970) 4555. R. Payne, J. Electrochem. Soc., 113 (1966) 999. R. Payne, J. Phys. Chem., 69 (1965) 4113. D. C. Grahame and B. Sodenberg, J. Chem. Phys., 22 (19541 449. B. B. Damaskin, A. N. Frumkin, V. F. Ivanov, N, I. Melkova and V. F. Kohina, Elektrokhimiya, 4 (1968) 1336. 7 R. M. Reeves, Thesis, University of Southampton~ 1969. 8 G. J. Hills and R. M. Reeves, J. Eleetroanal. Chem., 38 (1972) 1. 9 R. H. Boyd, J. Chem. Phys., 35 (1961) 1281. 10 R. Zwanzig, J. Chem. Phys., 38 (1963) 1603. 11 J. S. Dunnett and R. P. H. Gasser, Trans. Faraday Soc., 61 (1965) 922. 12 R.A. Robinson and R. H. Stokes, Electrolyte Solutions, Butterworths, London, 2nd ed., 1959. 13 W. H. Smyrl and C. W. Tobias, J. Electrochem. Soc., 113 (1966) 754. 14 G. J. Hills and R. M. Reeves, J. Electroanal. Chem., 31 (1971) 269. 15 G. J. Hills, D. J. Schiffrin and T. Solomon, in preparation. 16 D. M. Mohilner in A. J. Bard (Ed.), Electroanalytical Chemistry, Vol. 1, Marcel Dekker, New York, 1966, p. 241. 17 D. C. Grahame, J. Amer. Chem. Soe., 76 (1954) 4819. 18 R. Parsons, Trans. Faraday Soc., 55 (1959) 999. 19 R. Payne, Trans. Faraday Soc., 64 (1968) 1638. 20 J. Lawrence, R. Parsons and R. Payne, J. Electroanal. Chem., 16 (1968) 193. 1 2 3 4 5 6

230 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

G. J. HILLS. R. M. REEVES

K. M. Joshi and R. Parsons, Electrochim. Acta, 4 (1961) 129. J. Lawrence and R. Parsons, Trans. Faraday Soc., 64 (1968) 751. J. M. Parry and R. Parsons, Trans. Faraday Soc., 59 (1963) 241. R. Parsons, Proc. R. Soe. Lond., A51 (1961) 79. R. Payne, J. Chem. Phys., 42 (1965) 3371. R. Parsons, Rev. Pure Appl. Chem., 18 (1968) 91. R. Parsons, J. Electroanal. Chem., 7 (1964) 136. R. Parsons, Proceedings of the Second International Congress on Surface Activity, Vol. 2, Butterworths, London, 1957, pp. 38, 45. C.A. Barlow and J. R. MacDonald in P. Delahay (Ed.), Advances in Electrochemistry and Electrochemical Engineering, Vol. 6, Interscience, New York, 1968, p. 1. J. L. Jones and H. A. Hritsche, J. Electroanal. Chem. 12 (1966) 334. D. Martin, A. Weise and H. J. Niclas, Angew. Chem. lnt. ed. Engl., 6 (1967) 318. M. Salomon, J. Eleetrochem. Soc., 116 (1969) 1392. A. J. Parker, Quart. Rev. (Lond.), 16 (1962) 163. A. J. Parker, Chem. Rev., 69 (1969) 1. N. F. Mott and R. J. Watts-Tobin, Electrochim. Acta, 4 (1961) 79. R. D. Armstrong, W. P. Race and H. R. Thirsk, J. Electroanal. Chem., 16 (1968) 517. P. Delahay, Double Layer and Electrode Kinetics, Interscience, New York, 1966. M. Salomon, J. Eleetroanal. Chem., 117 (1970) 325. R. Parsons in P. Delahay (Ed.), Advances in Electrochemistry and Electrochemical Engineering, Vol. 1, Interscience, New York, 1961, p. 1. R. Thomas, C. R. Shoemaker and K. Eriks, Aeta Crystallogr., 21 (1966) 12. R.C. West (Ed.),'Handbook of Chemistry and Physics, The Chemical Rubber Publishing Co., Cleveland, Ohio, 50th ed., 1969. R. de Levie, J. Eleetroehem. Soc., 118 (1971) 184C. G. J. Hills and R. M. Reeves, J. Electroanal. Chem., in press.