SYMPOSIUM ON INTERFACIAL PHENOMENA hydrogen adsorption or hydrogen evolution producing gas bubbles limits the optical technique. Thus only ions adsorbing in the region between the anodic and cathodic processes may be determined. Also, the method can only be applied to ions which have refractive indices significantly different from that of the solution. On the favorable side, the sensitivity of the method can probably still be improved somewhat, probably to a resolution of 0.OOlo. For ions such as iodide, which do not desorb before hydrogen evolution, measurements may be conducted at constant potential with a vari-
3577 ation of concentration to obtain the isotherms. Improvements in the calculation of e from changes in A can probably be made as more results on the submonolayer region in gas phase are obtained.24 A separation of the contributions of the diffuse and compact layers may result from the application of double-layer theory with double film computations. Acknowledgment. We wish to thank the National Aeronautics and Space Administration for their financial support of this work and Professor J. O'M. Bockris for the suggestion of the topic and encouragement in this work.
Adsorption Isotherms in Mixed Solvent Systemsla by John Lawrencelband Roger Parsons School of Chemistry, University of Bristol, Bristol 8, England
(Received February 81, 1969)
Previously published experimental results of the electrical double layer at a mercury electrode in contact with sulfolaneand water, methanol and water, and formic acid and water have been analyzed in terms of the adsorption of the nonaqueous component of the mixtures. Each of the three systems obeys a Flory-Huggins type of isotherm which has been modified to account for long-range particle-particle interactions. The isotherm best described the results if the parameter r was estimated assuming the solvent water t o exist on the electrode surface as monomer units rather than clusters. The standard free energy of adsorption has been calculated and for each of the systems it showed a quadratic dependence on electrode charge. The interaction parameter of the isotherms is discussed in terms of preferred orientation of the adsorbed species and its dependence on electrical charge.
Introduction Most of the early work on electrochemical adsorption of ions and neutral molecules was carried out in aqueous solutions, considering the solvent water as a continuum. More recently, however, adsorption from nonaqueous solvents has been receiving increasing attention2-* and it must be concluded from this work that the solvent plays an important role in interfacial adsorption processes. I n fact, adsorption should always be considered as a competitive process between the adsorbate and solvent since for an adsorbate molecule to move to a surface site, a certain number of solvent molecules must first be removed. In order to clarify this competitive effect of the solvent, the present study was undertaken of the adsorption of nonaqueous solvents from water over the entire composition range from pure nonaqueous solvent to pure water. The systems analyzed here are sulfolane-water at 30" formic acid-water at 25", and methanol-water a t 25", since experimental data are a ~ a i l a b l e . ~ The ~ 6 ~ results ~ for the first two systems were obtained using differential
capacity and electrocapillary measurements, while results for the third system were obtained by electrocapillary measurements alone. It is unfortunate that in these two experimental techniques it is necessary to have an electrolyte present because activity coefficients are not known for electrolytes in most solvent-water mixtures and consequently it is not possible to keep the electrolyte activity constant throughout the solvent (1) (a) For a recent tabulation of the numerous systems see R. Parsons, Rev. Pure Appl. Chem., 18, 91 (1968). (b) Address correspondence to this author at the Department of Chemistry, University of Ottawa, Ottawa 2, Ont., Canada. (2) R. Payne, J. Chem. Phys., 42,3371 (1965). (3) J. D. Garnish and R. Parsons, Trans. Faraday SOC.,63, 1754 (1967). (4) R. Payne, J. Amer. Chem. SOC.,89,489 (1967). (5) J. Lawrence and R. Parsons, Trans. Faraday SOC.,64, 751 (1968). (6) J. Lawrence and R. Parsons, ibid., 64, 1656 (1968). (7) B. B. Damaskin and R. V. Ivanova, Zh. Fiz. Khim., 38, 92 (1964). (8) R. Payne, Aduan. Electrochem. Electrochem. Eng., in press, (9) R. Parsons and M. A. V. Devanathan, Trans. Faraday SOC.,49, 673 (1953).
Volume 73, Number 11 November 1969
JOHN LAWRENCE AND ROGER PARSONS
3578 composition range. However, as Parsons and Devanathan showed for the aqueous methanol system19 by using a constant, dilute concentration of a nonadsorbed electrolyte, the effect on solvent adsorption can be minimized. The electrolytes chosen were 0.1 M potassium hexafluorophosphate for the sulfolane system, 0.01 M hydrogen chloride for the methanol system, and 0.1 M sodium formate for the formic acid system. The potentials were measured against electrodes reversible to one of the ions in the respective solutions and to eliminate liquid junction potentials the electrodes were prepared in the aqueous-solvent mixture. Potassium amalgam, hydrogen, and mercurymercurous formate electrodes were employed for the sulfolane, methanol, and formic acid systems, respectively. The activities of the nonaqueous components in the aqueous mixtures were calculated from vapor pressure measurements recorded in the literature. At this stage it had to be assumed that the presence of the low concentrations of electrolyte had no appreciable effecton the activity of the solvent components.
Calculation of Amounts Adsorbed and Analysis of the Adsorption Isotherm Surface excesses (ri)of the nonaqueous component in each mixture were calculated from the equation
+
(~tlW47, &sslt = - ri qE*, y is the interfacial tension, q is the
where f = y charge on the electrode, and A'+ the potential of the mercury electrode with respect to an electrode reversible to the cation (methanol and sulfolane mixtures) or anion (formic acid mixtures). dp is put equal t o RT d In a where a is the activity of the nonaqueous component in the mixture. The condition of constant salt chemical potential was shown previouslye to be approximately satisfied if a dilute solution of a nonspecifically adsorbed electrolyte is used. Adsorption was considered at constant charge rather than at constant potential throughout this work. There has been some controversy r e ~ e n t l y ' ~ - about '~ the vdidity of this condition in the consideration of nonelectrolyte adsorption. The arguments in favor of the constant potential condition have been applied to systems uf aqueous solutions which are dilute in the nonaqueous component. The application of such a condition to a system studied over the complete range of mixtures from one pure solvent to the other is difficult, if not impossible. In contrast, the constant charge condition can be applied exactly without any difficulties of principle. The surface excess of nonaqueous component with respect to water, defined as
could not be approximated to surface concentrations The Journal of Physical Chsmistrg
since it is only in dilute solutions of the adsorbing species that the second term can be safely neglected. At high nonaqueous concentrations, the second term actually exceeds the first. The true surface concentrations were calculated from the surface excesses using the following relationship,* which assumed adsorption in a monolayer
This can be rearranged to give
where N, represents the number of solvent sites on the surface and is equal to the reciprocal of the area of the solvent unit multiplied by a geometrical packing factor, r is the number of solvent molecule units desorbed when one adsorbed molecule moves on to a surface site, and Zi and xs are the bulk mole fractions of the adsorbing species and solvent, respectively. It has been suggested earlier18t19that water molecules are adsorbed at electrode interfaces in clusters of 5 or 6 with each cluster occupying an area of surface of 30-40 However, it will be shown here that these results do not support this suggestion and consequently the water molecules have been considered as monomer units in a close-packed hexagonal lattice. If the area occupied by each water molecule is 12.3 L2,the resulting number of adsorption sites is 0.813 X cm-*. The most likely isotherm to be obeyed by mixed systems such as these is the Flory-Huggins i ~ o t h e r m , ' ~ which was derived originally by Zhukovitskii.20 This is based on a model in which the adsorbed species form a monolayer at the electrode interface with each molecule replacing r solvent molecules. The basic isotherm can be written as
e r(1 - 6)'
= pa
but this has since been modified to allow for interactions between the adsorbed species by the addition of an exponential term in 8, l' i.e. (10) C . H. Langford, private communication, (11) A. N. Campbell and A. J. R. Campbell, Trans. Faraday Sac., 30, 1109 (1934). (12) J. A. V. Butler, D. W. Thornson, and W. H. Maclennan, J . Chem. Soc., 674 (1933). (13) R. Parsons, J . Electroanal. Chem., 7, 136 (1964). (14) R. Payne, J.Phys. Chem., 69,4113 (1965). (15) E. Dutkiewicz, J. D. Garnish, and R. Parsons, J . Electroanal. Chem.Interfac. Electrochem., 16,505 (1968). (16) A. N. Frumkin, Z. Phys., 35,792 (1926). (17) A. N. Frumkin, B. B. Damaskin, and A. A. Survita, J . Electroanal. Interfac. Electrochem., 16, 493 (1968). (18) J. M. Parry and R. Parsons, J . Electrochem. Soc., 113,992 (1966). (19) R. Parsons, J . Electroanal. Chem., 8,93 (1964). (20) A. A. Zhukovitskii, Acta Physicochim. U.R.S.S., 19, 176 (1944).
SYMPOSIUM ON INTERFACIAL PHENOMENA
3579 log /? = 1.39
The adsorbed species are considered as a thermally disordered, two-dimensional gas or liquid and A can be related to a two-dimensional second virial coefficient a t low values of 8, a is the activity of the adsorbing species in the bulk, and RT In p = - AGO is the standard free energy of adsorption. The standard states are unit mole fraction activity of pure nonaqueous component in the bulk and @*on the surface where @*= r(1 B*)re-AB*,while the reference states are infinite dilution for both the bulk and surface phases. The isotherm can be rearranged to give a(:[ -
log----
e
elr
A - 2.303 X e ~
- log pr
and consequently plots of log (a(1 - @)?/e) against 0 at constant charge should yield a series of straight lines of slope A/2.303 and intercepts -log pr. These plots are shown for the sulfolane and water system in Figure 1. The projected area occupied by a sulfolane molecule was estimated from both “Courtmlds” atomic models and van der Waals crystal radii calculations as 28.6 A2. This leads to a value of r of 2.27. It was found that variations in the values of r and N , of up to 15% had only a small effect on the overall shape of the curves, It is unfortunate that there is no independent method for calculating a reliable value for r. It has been shown’g that b@/3In p for this isotherm has a maximum when @ = (1 G ) - I but for systems such as these where the standard free energy of adsorption is normally a quadratic function of electrode charge there is no direct way of relating b@/bIn ,B to experimental results. However, if r was taken as unity or less, which is necessary for the cluster theory to apply, then the points became just a scattered array. The figure sliows that, assuming monomer solvent units, good linearity is obtained for 0 less than 0.9. For 0 greater than 0.9, marked deviations occur due probably to the approximate nature of the isotherm. Even on the imperfect gas model higher terms in 0 would be expected in the exponential term corresponding to interaction between more than two particles. The vertical scale of this graph has been compressed to allow all the lines to be shown. However, this does not conceal any curvature since with a tenfold magnification of this scale, the lines remain linear. The lines are all parallel with a slope of -0.94 corresponding to a small attractive force between the molecuIes. The values of log p obtained from the intercepts follow, within the limits of error, a quadratic dependence on the electrode charge with a maximum value (log Pmax) of 1.39 occurring at a charge qmax of -5.4 p C cm+. The total dependence of log p on qM can be expressed as
- 0.007262
where 6 = (qmax - q). Figure 2 shows the corresponding isotherm plots for the aqueous methanol system. The same value of N , was used as for the previous system and the total area occupied by a methanol molecule was taken This leads to a value of r of 1.51. Again as 18.6 iz. it was found that if r was made less than or equal to unity corresponding to the existence of solvent clusters, then the points became scattered. This figure shows a similar behavior to the sulfolane system except that the slopes are not independent of electrode charge. The slight increase in scatter of the points is mainly a consequence of the increase in error in the original values of I?. The lines all have a negative slope with A varying from -2.42 at qM = 0 to -0.30 at q M = -5 to -1.89 a t yM = -8 pC corresponding t o an attraction between the molecules which is a minimum at yM = -5pC emv2. The values of log /? from the intercepts again show a quadratic dependence on qM with ymax occurring at the same charge as the minimum particle-particle attraction. Log pmsx for this system is equal to 0.886 and the charge dependence can be written as log p = 0.886 - 0.039962 Figure 3 shows the isotherms for the aqueous formic acid system with the total area occupied by a formic
+
- Id
?
/’
--& -1
/
0’
0-0 5
0 0
*4? 3 -2
-
qM=*4
0 I
I
M
0
“9
= o
o-o.oA-
0’
FRACTIONAL COVERAGE (01
Figure 1. Modified Flory-Huggins isotherm for adsorption of sulfolane from sulfolane-water mixtures a t constant electrode charge, q’. Volume 73, Number 11
November 1959
3580
JOHNLAWRENCE AND ROGER PARSONS
.3r
-2 -I
qM = - 7
c
/
CaP
0 -0-
0-
0
00
0
L
:
u
/D
0
a
0 -I
01
0
I
0.1
1
I
I
0.2 0.3 0.4
1
0.5
I
I
0.6
0.7
FRACTIONAL COVERAGE
(e)
1
0.8
1
0.9
I
1.0
Figure 3. Modified Flory-Huggins isotherm for adsorption of formic acid from formic acid-wat'er mixtures a t constant electrode charge, qaf.
studied and since this is approaching the limits of the error no attempt has been made to determine the dependence. Log /? at qM = 0 is 1.67. 01 0
I
0.1
1
I
I
0.2 0.3 0.4
I
I
0.5
0.6
I
0.7
I
I
0.8
0.9
I
I O
FRACTIONAL COVERAGE (0) Figure 2. Modified Flory-Huggins isotherm for adsorption of methanol from methanol-water mixtures a t constant electrode charge, qM.
acid molecule taken as 18.85 iz.This gives 7" a value of 1.53. As a further test of the cluster theory, a value of approximately 0.5 was substituted for r (asand suming the area of a water unit t o be 35-40 i2), a corresponding change made in the value of N,. However, the curve obtained had zero slope at 0 = 0 and l and a positive slope of up to 9.7 a t intermediate coverages. Hence it must be concluded that this and the two previous systems support the argument that the solvent water exists as monomer units and not as clusters. The linearity is again satisfactory for coverages of less than about 0.7 but marked deviations occur above 0.7 probably again because higher terms in e have been omitted from the exponential. The positive slopes correspond t o intermolecular repulsion and there is a slight increase a t negative charges, A a t qM = 0 is +2.97. The variation of log 0 with electrode charge is less than 4% over the charge range The Journal of Physical Chemistry
Discussion It is evident from the preceding section that the Flory-Huggins isotherm modified t o a first approximation to account for long-range interparticle interactions closely describes the adsorption behavior of the three systems. Since the isotherm is an approximate form which does not allow for interactions between more than two particles, it is not surprking that deviations occur at high coverages. It has been suggested in a previous publication6 that sulfolane is preferentially adsorbed at the mercury interface with the hydrocarbon ring in contact with the metal and the polar
\ No S
/\
0
group directed toward the solution. This suggestion is further substantiated by the fact that log pmax occurs at qM = -5.4 p C cm-2 corresponding to AGO, the standard free energy of adsorption having a maximum negative value at that charge. The negative value of A is also consistent with this preferred orientation since the repulsion between the oriented dipolar
SYMPOSIUM ON INTERFACIAL PHENOMENA groups, which must be at least 4.5 from the surface and consequently in a region of relatively high dielectric constant, is likely to be more than compensated for by the attraction between the hydrocarbon rings which are close to the electrode surface and therefore in a region of relatively low dielectric constant. The observed dependence of A on the electrode charge for the aqueous methanol system tends to suggest that the molecules have only a small preferential orientation with the -OH group directed toward the solution. It is then reasonable to suppose that the main interacticn would be attractive with only a small repulsive contribution from the oriented dipoles. This repulsive term would increase to a maximum a t qM = gmax as a result of an increase in orientation leading to an overall minimum in the attraction at that charge. The repulsion between the adsorbed formic acid molecules, which increases slightly a t negative charges, can be attributed to the interaction of the partially oriented, polar carboxyl groups. Previously published results on the preferred orientation of formic acid at the mercury interfacea suggested that the negative end of the dipole was directed toward the metal and consequently a repulsive interaction is only to be expected. The relatively large value of log pmax
3581 for this system undoubtedly arises from the strong interaction of the lone pairs of electrons on the two carboxyl oxygen atoms with the mercury. I n the other two systems, the preferred orientation is such that any lone pairs of electrons are directed toward the solution phase and hence log pmaxis relatively smaller. It should be noted that the interpretation of the A values given above is only qualitative. This parameter can be interpreted for the adsorption of a simple species a t low densities as a two-dimensional second virial coefficient and under these circumstances it gives direct information about the forces between the adsorbed particles. However, in mixed solvent system its significance is less clear-cut since its value must depend not only on the solute-solute interactions but also on solute-solvent and solvent-solvent interactions. Nevertheless the interpretation of the sign of A given above in terms of net attraction or repulsion seems likely to be meaningful.
Acknowledgment. We are grateful to General Electric Company (Schenectady) and Texas Instruments Incorporated (Dallas) for maintenance awards to J. L. during 1965-1966 and 1966-1967, respectively.
Volume 75, Number 11
November 1969
