SYMPOSIUMON INTERFACIAL PHENOMENA
3609
Entropy and Structural Effects in the Electrochemical Adsorption of Pyridine at Mercury by B. E. Conway and L. G. M. Gordon Department of Chemistry, University of Ottawa, Ottawa, Ontario, Canada
(Received February $6, 1969)
Previous studies on electrochemicaladsorption of pyridine at the mercury electrode-water interface have indicated the role of orientation and interaction effects. Work is reported on the evaluation of free energies, entropies, and heats of electrochemical adsorption of pyridine in 0.03 N aqueous NaC104 solutions from electrocapillary measurements over a range of temperatures. Comparative measurements were made with acetophenone. A new electrocapillary technique is described. The entropy effects are shown to be an important factor in determining the free energy of adsorption and depend appreciably on electrode surface charge. Substantial compensation between the heat and entropy of adsorption is shown to arise. The entropies of adsorption are examined in the light of calculations on the configurational and librational entropy of electrostatically adsorbed solvent molecules. The results of such calculations indicate that the experimental results are to be interpreted in terms of structure-breaking effects in the inner water layer adsorbed at the electrode The calculated thermodynamic results depend on the type of isotherm assumed; selected data have been treated in terms of a FloryHuggins type of equation for various ratios of the areas of the adsorbate and solvent molecules.
Introduction In previous papers,l-a we have studied the electrochemical adsorption of pyridine in neutral and ionic form in relation to orientation effects, the role of ionization, and the effect of the molecule on the components of charge in the double layer in aqueous KC1 solutions. Analogous work in regard to orientation of reactive functional groups was carried out with acetophenone in relation to the reduction kinetic^.^ I n the earlier work,' KC1 was used as the supporting electrolyte for neutral pyridine solutions but ionization studies showed2 the role of specific adsorption of the chloride ion in cornpariaon with that of Clod-. Here perchlorate supporting electrolytes were used to minimize coadsorption of anions. In the work reported at this symposium, we have studied the electrochemical adsorption of pyridine a t mercury over a range of temperatures in order to establish the relation between entropy of adsorption and the apparent'^^ interaction effects; the corresponding heats and standard free energies of adsorption were, of course, also evaluated. Few temperature studies exist in the literature: Anderson and Parsonss have studied K I solutions where the combined adsorption of the ion in the inner Helmholtz layer and in the diffuse layer adds complications in the thermodynamic interpretation of the data. The study of neutral molecules offers some advantages in this respect. Hills and Paynee have made a detailed study of the adsorption of several salts at mercury through capacity measurements over a range of temperatures and pressures and evaluated the excess volumes and entropies of the interphase as a function of surface charge; the potentials of zero charge at mercury in various solutions as a function of
temperature have also been measured.' The behavior of acetophenone was also examined both for direct comparative purposes and in relatibn to our previous work4 on the kinetics of reduction of this ketone. In the case of pyridine, the dipole is integrally within the whole molecule, while in acetophenone it is within a structurally independent functional group which is, however, involved in some conjugation with the ring.
Experimental Section 1. New Electrocapillary Technique. The evaluation of thermodynamic quantities for adsorption at the mercury electrode by electrocapillary measurements demands the execution of a large number of measurements both at closely spaced intervals of potentials and with a variety of solution concentrations if satisfactory accuracy in the derived thermodynamic quantities is to be attained. Previously,* we have published details of (a) a new (1) B. E. Conway and R. G. Barradas, Electrochim. Acta, 5, 319,349 (1961). (2) B. E.Conway, R. G. Barradas, P. G. Hamilton, and J. M. Parry, J. Electroanal. Chem., 10,485 (1965). (3) R. G. Barradas, P. G. Hamilton, and B. E. Conway, Collect. Czech. Chem. Commun., 32,1790 (1967). (4) B. E.Conway, L. G. M. Gordon, and E. Rudd, Discussions Faraday Soc., 45,84 (1968). (5) W.Anderson and R. Parsons, Second International Congress on Surface Activity, Vol. 111, J. H. Schulman, Ed., Butterworth and Co. Ltd., London, 1957,pp 45-52. (6) G. J. Hills and R. Payne, Trans. Faraday SOC.,61, 326 (1965); cf. D. C. Grahame, J. Amer. Chem. SOC.,79, 2093 (1957);J . Chem. Phys., 16,1117 (1948). (7) W.Paik, T.N. Andersen, and H. Eyring, J.Phys. Chem., 71, 1891 (1967). (8) B. E. Conway and L. G. M. Gordon, J . Electroanal. Chem., 15, 7 (1967). Volume 78, Number 11 November 1969
3610 electrical method for locating the meniscus in the fine capillary and (b) a new method for measurement of the excess pressure by means of an electrically indicating micrometer-manometer. Both of these modifications to the conventional technique give improved accuracy and diminish tedium in the measurements. In the present work, we have developed a further improvement in technique which again increases accuracy and greatly facilitates the measurements. The mercury capillary is strongly illuminated from the side and a television microscope is focussed on the capillary. The image from the television camera is fed to an 18411. screen television monitor and the end of the capillary can be seen directly at a high magnification. The fine end of the capillary appears as an image about 25 cm wide on the screen and the mercury can be seen as a dark (or bright, depending on the illumination) thread moving down the capillary and having a width on the screen of about 1 cm. A fiducial mark can be introduced on the outside of the capillary itself (e.g., by means of a fine wire8) or by marking the television screen with a transparent scale fixed at some point of reference with respect to the lower end of the capillary image. The capillary image was in fact projected horizontally by 90" rotation of the scanning system of the camera; this was found to give a sharper focus on the monitor screen. The microscope used was one side of the binocular zoom instrument used previous1y;'v2 the other optical path of the binocular eyepiece enabled the apparatus to be lined up and properly focussed by eye. The apparatus is shown in Figure 1. g. Cell. The cell was similar to that described previously* and was comprised of three compartments; the center one contained a detachable capillary endpieces for the Hg thread and was provided with an annular jacket for thermostating. The Hg reservoir and the reference electrode were also thermostated at the same temperature. A 0.03 N NaC1-calomel reference electrode was employed in a separate compartment; the NaCl solution used was chosen to give a minimum liquid junction potential with respect to 0.03 N Wac104 used as the supporting electrolyte. The reference electrode solution, together with Hg and Hg,C12, was contained in a separate tube closed with a small wetted 7-mm ground-glass joint and kept in the reference electrode compartment of the cell (see Figure 1); the latter compartment was filled with the experimental supporting electrolyte solution (0.03 N NaC104) and could be varied in temperature by circulation of controlled-temperature water through an annular jacket. In the experiments with acetophenone, a PtHz electrode was used in methanolic HzS04 solution and no liquid junction was present. 3. Xolutions. Solutions of redistilled pyridine were made up in aqueous 0.03 N NaC104. Acetophenone solutions were made up in purified methanol containing HzS04, these and other conditions being chosen to be The Journal of Physical Chemistry
13. E. CONWAY AND L. G. M. GORDON
Figure 1. Schematic drawing of television microscope and illurnination arrangement for electrocapillary measurements by the method of determining excess pressures.
similar to those employed in previous kinetic studies4on acetophenone reduction a t Hg carried out in this laboratory. A dilute perchlorate solution was used in the pyridine work as the supporting electrolyte in order to minimize complications due to specific anion adsorption (cf. ref 2 ) and to provide a basis for comparison with results obtained earlier in chloride solutions.1 4. XigniJicance of Measurements over a Range of Temperatures. Studies of adsorption over a range of temperatures normally lead to the evaluation of the heat and standard entropy of adsorption if constant, or "isosteric," conditions of coverage are specified. A number of types of heats and corresponding entropies of adsorption can in fact be specified depending on the condition^.^*^ Care must therefore be exercised, particularly in electrochemical adsorption studies carried out over a range of temperature, in defining the quantities evaluated. Under Langmuir conditions, it is convenient to take a standard state of half-coverage and this can be also taken as the isosteric condition enabling the standard heats of adsorption to be evaluated from the standard free energies of adsorption AGO. When interaction effects are involved and can be expressed in terms of a Frumkin type isotherm, the results may be examined in terms of the relation
e 1-
e.
C exp re = K
where K = exp - A G " / R T , C is the bulk adsorbate concentration, and r is an 'interaction parameter containing the factor 1/RT and determining the magnitude of an interaction term linear in e ; the question of evalu(9) D.H.Everett, Trans. Faraday Soc., 46,453,942,957 (1951).
SYMPOSIUM ON INTERFACIAL PHENOMENA
3611
ation of AGoadsis then more complex; exp re can be regarded as an activity coefficient termf so that
_-fe
= Cexp[-AGo/RT]
(2)
1-8
As in the electrolyte solution case, where unit activity is taken as the standard state, here it becomes convenient to evaluate AGoads for fe/(l - e) = 1, i.e., at 0 = 1/ (1 +f). Usuallyf is not directly known, so an apparent value of AGO is evaluated from eq 1 and extrapolated w.r.t. 8 to 0 = 0 thus eliminatingf. Evaluation of an apparent AGO a t a constant finite coverage, say 0 = 0.5, from eq 1 at various temperatures will include a varying interaction energy, since at 8 = 0.5 -AGO
= 0.5rRT
0
I Oil I
- R T In C0.6
(3)
where Co.5is the bulk concentration required to give 8 = 0.5 at the given temperature. In electrochemical measurements, the question of electrode potential E or surface charge q also becomes involved. For various reasons,'O it seems desirable to evaluate the thermodynamic quantities derived from surface tension or capacitance at constant q rather than a t constant E. I n the case of measurements at various temperatures, this has the added advantage that the changing absolute potential difference at the reference electrode interface does not directly complicate the evaluation of the thermodynamic quantities as it would with measurments at constant measured potential. However, even if AH" and AS" were derived at constant measured E , some correction could be made t o constant metal-solution potential difference at the reference electrode since only the temperature coeficients of emf are required (in this respect, allowing the reference electrode to vary with temperature may be preferable to maintaining it at room temperature and suffering the uncertainty of a thermal junction potential difference) and for the hydrogen electrode for example, this quantity can be calculated to *0.025 mV ("C)-l, i.e., to 10% since the single standard partial g ionic entropy 0.5 of H+ is known as - 5 eu to an accuracy of ca. eu. A procedure which enables these effects to be allowed for in a rigorous manner has been describedns I n the present, discussion, the results will be evaluated in terms of AGO, AH", and A#' derived for isosteric conditions at constant q (and constant supporting electrolyte activity) using the function employed in various publications of Parsonslo and others.2s6 The Gibbs equation also gives the excess entropy rs associated with the interphase from dy := - rsdT - ridpi - qdE (4)
*
for components i in the solution and in the interphase. It is evident (cf. ref 6) that -dy/dT does not simply give Ts unless the chemical potential@) of the components i in solution are kept constant a t constant E. In practice, this is difficult to achieve and implies, for
0
a
-3
- 4
c
\
I
I
I
I
I
t
I
I
I
0
01
0 2
03
04
05
06
07
08
COVERAGE
X:6
\ 09
I IO
e
Figure 2. Values of the difference of AGO for an adsorption process as calculated in terms of a Flory-Huggins and a Langmuir adsorption isotherm for a given value of coverage e of an adsorbate in equilibrium with the adsorbate in solution a t a fixed concentration.
example, that for a neutral adsorbate such as pyridine, the partial vapor pressure at various temperatures must be kept constant by adjustments of the concentration or by appropriate interpolations. Alternatively, if dpi/dT is known (it is the partial molar entropy of the adsorbate in solution), rs can be evaluated.s In fact rSwill be a complex quantity related to the temperature dependence of the free energy of solute and solvent species, and their interactions, in the interphase. It is for this reason that the entropy (and heat) of the substitutional adsorption process directly evaluated from AGO, calculated for various temperatures, is the quantity to which preferred attention is given in the present paper.
Results and Discussion 1. Isotherms and the Free Energies of Adsorption. As in previous it is convenient to evaluate the quantity AGO, the apparent standard free energy of adsorption in an isotherm P ( r ) where
In P ( r ) =
AGO -+ In c RT
(10) R.Parsons, Trans. Faraday Soc., 51,1518 (1955). (11) E. Blomgren and J. O'M. Bockria, J . Phys. Chem., 6 3 , 1475 (1959). Volume 78, Number 11
November 1060
B. E. CONWAY AND L. G. M. GORDON
3612
C
I
lpi0.5
Figure 3. Evaluation of apparent A G O values as a function of Pafor pyridine adsorption at mercury a t various values of q or E - , and a t several temperatures: (a) 280.5"K; (b) 313OK; (c) 353°K. [In (b), the A G O data were evaluated for two values of the saturation coverage
rm.l
and I' is the surface excess evaluated preferably for constant charge q and for various values of concentration C. When interaction effects are significant, the apparentla standard free energy value AGO varies with I' but a value A G O 0 referring to the adsorption process in the absence of interactions or equivalent structural effects may be obtainedll by extrapolation to I' = 0. Generally such values and corresponding ASoo and AHooquantities will not be so accurate as the actual values evaluated a t finite I'. Following the procedures adopted in earlier publications, e.g.,llll we assume
-I
-
k n N \
-2 4
where I', is the saturation surface coverage (e = I), and obtain AG" as a function of r which may be plotted, e.g., with respect to I"/' or Os/' if dipole repulsion effects dominate the nonideality of the surface layer.' "Langmuir" substitutional adsorption'3 will give AGO values independent of 8, a result rarely found in adsorption at mercury. In cases where the ratio of areas of adsorbate and solvent molecules is appreciable, the relative area factor may be as significant as the interaction effect and F ( r ) will then be (cf. ref 4) of the Flory-Huggins form (r/r,)/z(l - F/r'rn)z as examined in the paper by Lawrence and Parsons presented at this symposium. However, for a given value of z applicable to the substitutional adsorption, variation of the apparent AGO, calculated from eq 7, with I' will still properly characterize the interaction or other equivalent effects (see below). In the above case, it is of interest to compare the results for AGO or K which would be derived from the Langmuir (1,) and Flory-Huggins (FH) type isotherms for a given determined coverage in equilibThe Journal of Physical Chemistry
0
0.2 0.40.6 0 8 10 1.2 1.4 1.6 1.8 2.0 2 2 2.4 $4 (mole cm-q3'2 x 1015
Figure 4. Evaluation of apparent A G O values for acetophenone adsorption a t mercury from methanolic 1 N HzSOd solutions a t 293'K.
rium with adsorbate a t a fixed bulk concentration C in the solution. Writing the FH isotherm as a function of 0 in the form
(7) (12) E. Gileadi and B. E. Conway, "Modern Aspects of Electrochemistry," Vol. 111,J. O'M. Bockris and B. E. Conway, Ed., Butterworth and Co. Ltd., London, 1964,Chapter V. (13) R.Parsons, J . Electroand. Chem., 7 , 136 (1964); cf. A. N, Frumkin, ibid., 7, 162 (1964).
3613
SYMPOSIUM ON INTERFACIAL PHENOMENA
x
- 4
A-025V
a/A
0
2
1
3
I
I
1
I
.
I
I
3
4
5
6’b
2
4
(mole crrizfi
x
1015
r”? (mole
- 0.1v
k
crn+)s/~ xi015
Figure 5. Calculations of AGO from the experimental results on the basis of the Flory-Huggins isotherm with various z values(eq 7).
we see immediately that
x ~ / K = ~~ ( ~i ey-1
(8)
or 1 -(AGOBH
RT
- AGOL) = In 2 + (x - 1) In (1 - 0)
(9)
where z is the molecular size ratio of adsorbate and adsorbed solvent. (AGOFH - A G o ~ ) / 2 . 3 0 3 R Tis shown as a function of 0 in Figure 2 for various values of z from 1 (Langmuir case) to 6, ;.e., over the range applicable to pyridine in water (z = 3-4). It is evident that at appreciable coverages (0 > 0.5-0.7) the relative area factor can introduce changes in the evaluated AGO quantity which are comparable with the magnitudes of AGO commonly obtained (ca. - 2 to - 6 kcal mol-’) for substitutional molecular adsorption a t Hg. However, a t 0 = 0.25 the AGO values derived from both isotherms are almost identical. Also, the choice of the correct value for rmis critical. Plots of AGO on the basis of eq 6 (used for evaluation purposes only) are shown in Figure 3a-c for various temperatures and a t various y values. At T = 280.5”K for example, AGO initially becomes more negative with but eventually becomes less coverage (plotted as r *Iz) negative, the effect increasing as y becomes more positive. Similar effects are maintained, for example, a t 353°K but the variation of AGO to less negative values with increasing I’is more marked and the minima occur correspondingly at lower r. That this behavior is not peculiar to pyridine is shown in Figure 4 where typical
results are shown for methanolic solutions of acetophenone (in which the essential dipole is in an orientable functional group [ ~ C O= 2.9 D] rather than in the “whole molecule” as it is in pyridine). The results obtained in dilute (0.03 N ) NaC104 may be assumed to refer to pyridine molecule adsorption (hydrolysis effects are negligible14)in the absence of significant specific adsorption of anions. It is for this reason that they probably differ from the previous results’ obtained for pyridine adsorption at 298°K which were based on experiments in 1 N KCI. The results in that supporting electrolyte were interpretedl-a in terms of relatively sudden orientation of pyridine at a critical I’ dependent on electrode potential, and the behavior was shown2to be dependent on the C1- adsorption. It is evident that the present results in the presence of Clod- anions are rather different although formally, over much of the AGO - curves, AGO is numerically decreasing, corresponding to repulsion or other nonideality effects, but the apparent repulsion effectsare evidently least at the most negative q values. The extent to which the variations of AGO calculated from the experimental observations depend on the choice of z in eq 7 is shown in Figure 5 for x = 1 , 2 , and 4. Space-filling models indicate x will be between 2 and 4, depending on the rotational freedom. Increasing z has the effect of lowering the AGO values calculated for the larger coverages. A variation of AGO with I’ need not, of course, be (14)
B. E. Conway and R. G. Barradas, J. Electroanal. Chem., 6 , 314
(1963).
3614
B. E. CONWAY AND L. G.
IVI. GORDON
r x 1 0 ' ~ mcm2 ~1~
7 2.4t-t
24
2o
7
I .6
--
6
i
V e,
Y
-
I
I
I
1
IO
8
6 4 2 0 -2 -4 -6 -8 q pcoul cm-2
I
,
,
I
,
,
Figure 6. Variation of AGO calculated for various a function of surface charge p (for 5 = 1).
,
r values as
ascribed only to repulsion effects, although this was112 and is a reasonable interpretation of the results obtained previouslylJ in chloride solutions. The role of solvent structural effects in relation to the adsorbate(so1ute)solvent interaction in the ad-layer, similar to those which occur in aqueous solutions of soluble organic molecules,1611emust be considered. It is in regard to such effects that the studies over a range of temperatures are particularly informative insofar as entropies of substitutional adsorption can be evaluated for appropriate isosteric and constant charge conditions. Before referring to such results, however, it is of interest to illustrate how A G O evaluated for various constant r values is dependent on q (Figure 6 ) . Basically, AGO has maximum values of ca. -4.5 kcal mol-I for various I' and these maxima occur at q values which become more negative with increasing I'. AGO for neutral molecules usually17has a parabolic form with respect to q (except a t high fq where orientation saturation polarization becomes dominant). There is evidently (Figure 6) a shift of the AGO-q relationship toward higher q values as I' increases so that at given q values, AGO tends to become less negative with increasing I' except where the curves cross over toward the more negative q values. Over most of the curves, a higher negative value of q is required for AGO to attain a given value as I' increases; we suggest this reflects (a) the competition arising from orientation polarization of water dipoles and pyridine molecules in the interphase, and the resulting hydrogen bonding which can arise at the N-center when it is oriented away from the electrode at more negative q; (b) the change in two-dimensional structure breaking in the water adT h e Journal of Physical Chemistry
1.0
4
Figure 7. Isosteric heats of adsorption of pyridine plotted as a function of charge p for various coverages.
layer comprising the interphase as the surface excess of pyridine is increased; and (c) the displacement of anions as q is made more negative, an effect which we have shown previously to depend on the pyridine adsorption2 insofar as at higher pyridine coverage the anion specific adsorption (Cl- in that case) is enhanced at a given potential. 8. T h e Heats and Entvopies of Adsorption. Here isosteric entropies of adsorption were evaluated at constant charge from plots of AGO vs. T and AH" was obtained from AGO with the derived values of AS". Previously, for ions,6 isotensile thermodynamic functions for adsorption were evaluated but the isosteric quantities will reflect better any effects of changing interaction effects with charge at given degrees of coverage. The standard heats and entropies of adsorption are shown in Figures 7 and 8 as a function of q. The striking feature of these results is that AS" for give I' values increases toward a maximum positive value (cf. ref 14) as q varies from 48 t o ca. -pC cm-2 and then tends to decrease while AH" has a corresponding variation with q. Similarly, the isotensile entropy of adsorption of I- is largest near q = 0.6 Behavior related to these effects is more difficult to discern in the AGO plots and indeed there is a substantial compensation between AH" and AS" or TAS" tending to make AGO a function rather less sensitive t o
+
(15) B. E. Conway and L. Lalibertb, "Hydrogen Bonded Solvent Systems" (Proceedings of the Symposium on Equilibria and Kinetics in Hydrogen Bonded Systems, Newcastle, 1958),Taylor and Francis, London, 1968,p 139; see also J . Phys. Chem., 72,4317 (1968). (16) R.M.Diamond, ibid., 67,2513 (1963);W.Y.Wen and S.Saito, {bid., 69, 3589 (1965);H. S. Frank, 2. Phya. Chern. (Leipzig), 228, 364 (1965). (17) R.Parsons, J . Electroanat. Chem., 5,397 (1963);cf. A.N.Frumkin, 2.Phys., 35, 792 (1926),and I. Zhukovitskii, Acta Physicochim., U.R.S.S., 19, 176 (1944),for relative area effects.
SYMPOSIUM ON INTERFACIAL PHENOMENA
3615
-2
-
I-
- 12 -
\ 2.4 I
I
I
1
I
1
I
I
p (cf. the analogous case of ionization constants in relation to structure of organic acids and bases). This type of compensation is familiar in ionic solution^^^^^^ and has recently bleen demonstratedz0in the thermodynamics of binding of acetylcholine competitors at the enzyme acetylcholinesterase. The compensation plot relating AH" arid ASo for pyridine adsorption a t Hg is shown in Figure 9 and covers a wide range of ASo values (for various r and p values) with B slope of ca. 300°K close to the value obtained for binding of various competitors at the enzyme mentioned above2O and for hydration of ions.19 At high values of r and for the more positive values of p, the degree of compensation is less (Figure 8) and the relation has a slope of ca. 200°K. This is probably connected with the reversal of orientation of pyridine together with the presence of c104ions in the ad-layer which enhance structure-breaking effects in the interphase. In general, as is shown below, the best compensation between entropy and energy terms is achieved when interaction-dependent librations are involved. Configurational entropy changes are usually insufficientz1 to account for the large changes of entropy often associated with substantial energies of interaction (cf. the case of ionic ~ o l u t i o n s ~ ~ ) . Although pyridine is more strongly adsorbed at a given concentration of the negative branch of the
\o \I
*
4
electrocapillary curve so that AGO values are relatively more negative at the negative p values, AH" in fact tends to become less negative as - p increases except at higher r values where it tends to remain more constant (Figure 7). The unfavorable trend in AH" is compensated by an opposite trend in -TASo. At low coverage, the positive AS" reflects, we believe, release of structured, low-entropy water at the surface with a consequent net positive entropy change in the adsorption process, an effect which we have observed previou~ly'~ a t solid electrodes. This implies that the water layer at Hg tends to be most structured in the region of p = - 3 to -6 p C cm-z (Figure 8). This may not seem consistent with the maximum observed6 in the derived excess entropy rSof the interphase in NaF solution at ca. p = -8 pC cm-z, but rais a complex quantity involving both the electrostatically adsorbed ions, their hydration shells, and the water itself in the interphase, and cannot be directly related to the entropy of the water layer or to the entropies of adsorption calculated here.z4 That the water in the interphase may be maximally structured near the potential of zero charge might be inferred by analogy with the effect of large organic hydrophobic groups in promoting structure in water solutions. z 2 Mercury probably has little specific interaction with water moleculesz3(except perhaps residually (18) K. J. Laidler, Trans. Faraday SOC., 5 5 , 1725 (1959); cf, P. Ruetschi, 2.Phys. Chem., 14,277 (1958). 34, 1093 (19) D. D. Eley and M. G. Evans, Trans. Faraday SOC., (1938). (20) B. Belleau and J. L. Lavoie, Can. J . Biochem., 46, 1397 (1968). (21) T. L. Hill, "Introduction to Statistical Thermodynamics," Addison-Wesley Publ. Co., Reading, Mass., 1960, pp 380, 381. (22) G. Nemethy and H. A. Scheraga, J. Chem. Phys., 36, 3401 (1962) ; cf. A. Ben Naim, J. Phys. Chem., 69, 1922 (1966). Roy. Soc., A261,79 (1961). (23) R. Parsons, PTOC. (24) R. Parsons, Can. J . Chem., 37,308 (1959),
Volume 7.9, Number 11 November 1969
3616
B. E. CONWAY AND L. G. M. GORDON
R
B
i
0.5
1
1,&,
I
16
20
22
24
26
2.6
4 pcoui cm:2
I
longer leads to anomalous positive entropy changes, and (b) orientation of the pyridine itself (et. ref 1, 2) at high fields. At positive q values, the tendency for Clod- ions increasingly to enter the interphase may assist the structure-breaking effect of the electrode field itself and enhance the tendency for AS” to become more negative. 3. Components of the Entropy of the Water Layer. It is of interest to examine to what extent the electrostatic and configurational entropy of water in the interphase could vary with electrode surface charge and then to examine if such solvent adsorption effects could account for part of the substitutional entropy changes found in the present thermodynamic study of pyridine adsorption. ( a ) Configumtional Effects. Solvent dipole orientation can be considered in terms of the model of Bockris, Devanathan, and J4uller26in which dipoles are regarded direction with as being in an up (f) and down respect to the surface. This will give rise to a molar configurational entropy of mixing Soof the two orientational states
(4)
S,
0
02
04
06
08
I O
r (mole
I2 14 l6 I S C ~ ~ . ~ X I O ~ ~ I
20
Figure 10. (a) Dependence of AS” on coverage dependence of AH’ on coverage r.
22
r;
24
(b)
a t positive q with the lone pair electrons on oxygen; cf. the weak €Ig(II) complex with dioxane), but its metallic nature will allow an effective continuation of the dipole (hydrogen bond) interactions among the water molecules “through” the interface on account of the dipole images and their interactions with the parent charge distributions on the solution side. As in the AGO plots (Figure 3), Ah‘” depends appreciably on the coverage, becoming less positive for AS” values calculated for higher I’ values (Figure loa). This suggests that at the higher I’ values in Figure 10, the water layer is already disorganized so that less entropy is released per mole of pyridine adsorbed under such conditions and the apparent standard entropy of adsorption, like the corresponding AG” , varies with the equilibrium l7 value from which the A G O , and hence the AS” value, has been calculated. The dependence of A H o on coverage is shown in Figure lob. At higher negative or positive q values, the AXo values decrease presumably due to (a) the field effect on water orientation leading to structure-breaking effects analogous to those associated with electrostriction which arise at small ions, so that substitutional adsorption no The Journal of Physical Chemistry
=
- R[eJI In e+
+ of
In
of]
(10)
where the 0 terms are the surface fractions (and hence relative coverages) of dipoles oriented in t or JI directions. In eq 10, interaction effects (see below) have not been considered. The orientation of dipoles will be determined by their interaction with the electrode field E and by their mutual interaction^.^^ The resulting distribution functionz6for interacting dipoles is given26by
(11) where U is the interaction energy per pair of dipoles in a configuration with coordination number z and N f , N $ are the numbers of dipoles in f and orientaN + . In terms tions, respectively, and N r = N f of the relative coverages e
+
(24,) - 1 = tanh
(2ef
-
1)
4
”1
4- IcT
(12)
which is evaluated below for various values of the interaction factor f i = Uz/lcT and the electrostatic fielddipole interaction term pE/lcT. The configurational entropy of the layer of molecules with mixed orientat and 0 4 may be tions then follows from eq 10. O related to q through2’ E given by E -47rq/e where (25) J. O’M.Bockris, M. A. V. Devanathan, and K, Muller, Proc. Roy.Soc., A274,55 (1963), (26) B. E. Conway, “Theory and Principles of Electrode Processes,” Ronald Press Go., New York, N. Y., 1964. (27) R. Parsons, “Modern Aspects of Electrochemistry,” Vol. I., J. O’M. Bockris and B. E. Conway, Ed., Butterworth and Co., Ltd., London, 1954, Chapter 3.
SYMPOSIUM ON INTERFACIAL PHENOMENA
.L
f
S
3617 L
I
mixing. For Of = 0 4 near q = 0, the maximum value of this entropy correction amounts to only -0.5 eu for 2U/kT = 5 say. (b) Librational Entropy. In an electric field, a dipole tends to become oriented but this orientation is rarely complete and the degree of orientation is determined by the field-dipole interaction energy factor pE/kT. The dipole executes librative motion in the field and the partition function for the libration mode isl9,30 fL
I
I
1,154
1.731
I
2.308
I
=
8 lrz (81r31Jz13k3T 3 )’’*sinh [ U,/kT] ah3 Ue/kT
(14)
2 085
pE/kT
where U , is the electrostatic field-dipole interaction energy and 1’s are the principal moments of inertia of the water dipole. The entropy associated with the librational energy states in the field is then
3 R
=:
In
8n2(8n8111213k3T3) ’/’ - In U,/kT ah3
+
In sinh [U,/kT] -
tqipcoulornb
cm-2!
Figure 11. Configurational and librational entropy of oriented water molecules in the electrode interphase in relation to the Orientation distribution function (lower figure) plotted in terms of the orienting field E and corresponding charge =kq.
‘
E, the effective dielectric constant of the surface layer, may be taken as ca. 628J9(actually E will bef(q) at low values of p but we take the reasonable value of 6 discussed previousIy). The results are shown in Figure 11. The problem considered here is seen to be closely related to that involved in the calculation of magnetization in a lattice of magnetic dipoles. While interaction effects have been included here in the orientation distribution function, we have followed the usual BraggWilliams approximation in assuming that the interactions do not appreciably influence the configurational entropy. This is not an entirely satisfactory assumption in any problem in lattice statistics (except in the quasi-ideal case of regular solutions) but corrections for nonrandom mixingz3when interaction effects are significant are in fact relatively small and to a first-order approximation, are of the order
i.e., the nonrandomness introduced by interaction contributes, as expected, a negative term in the entropy of
SLwas evaluated for various values of the inner Helmholtz field E = -4nq/e with PH,O taken as 1.87 D (a larger value could be taken corresponding to the water molecule associated in the water structure; this would result in given S L values arising at somewhat lower values of field E or charge a). SLas a function of j=q is shown in Figure 11 for one librational mode. The variation of entropy with q is appreciable and larger than that of X, with p. It is also approximately linear with U , thus providing a basis for compensation between energy and entropy terms. (c) Vibrations. It can generally be assumed that the internal vibrations of HzO molecules are little affected by the field except indirectly by hydrogen bond bending or breaking effects. I n any case, the internal vibrational entropy will be small a t room temperatures since the bend and stretch vibrational quanta are between 8 and 16kT. However, near the electrode surface, water dipoles will tend to execute vibrations normal to the surface, as a t ions.Ig This effect is difficult to evaluate in terms of the associated entropy 0 cm-2) the magnitude of but for appreciable q ( ~ 2 pC S Y i b may be assumed to be similar to that at an ion where the field is of similar magnitude to that a t the interface. E.g., for the F- ion (4 coordinated) S v i b of water in the hydration shell is ca. 2.05 cal mol-’ (“C)-l, while for the I- ion (6 coordinated) S Y i b is ca. 3.0 cal mol-’ (“C)-’.’9 (28) B. E. Conway, J. O’M.Bockris,.and I. A. Ammar, Trans. FaradaySoc., 47,756 (1951). (29) R. W.Rampolla, R. C. Miller, and C. P. Smyth, J. Chem. Phys,,. 30, 566 (1959); (cf. ref 25). (30) E. A. Moelwyn-Hughes, “Physical Chemistry,” Pergamon Pres&, Ltd., London, 1957; see also R. H. Fowler, “Statistical Mechanics,’’ Cambridge University Press, 1936,and ref 19.
Volume 73, Number 11
November 1969
B. E. CONWAY AND L. G. M. GORDON
3618 (d) Translational E$ects and Entropy of Water in the Bulk. According to the calculations of Eley and Evans,lg the components of the entropy of water a t 25" in the bulk are Svib
=
5.3;
#lib
=
6.7;
S,,,,,= 12.8 cal mol-1 ("C)-l
per pair of water molecules. We can assume that the translational entropy of water in the interphase is ca. of the value in the bulk and will be almost independent of field except insofar as the free area in the interphase may diminish due to electrostriction (cf. ref 6). 4. Relation to Pyridine Adsorption. The curves of Figure 8 indicate appreciable positive entropy changes for low coverages and the lower q values. At higher coverages, the entropy changes are negative but exhibit a reproducible maximum around q = - 3 to -6 pC The magnitudes of AS" for various conditions reflect (i) the entropy of adsorption of pyridine itself and (ii) the entropy associated with displacements of x water molecules (cf. eq 7) previously adsorbed where x will be between 2 and 4 based on inspection of spacefilling models. The entropies of adsorption and their variation with q or r are seen to be quite large in comparison with the calculated librational entropy of water in the interphase or in relation to the known entropy of fusion of water (ca. 6 eu). If allowance is made, however, for the fact that substitutional adsorption will involve displacement of several water molecules (x = 2 to 4) per pyridine molecule, the observed values of AX" seem plausible. They can be accounted for qualitatively in terms of structural effects to be discussed below. We have seen above that electrostatic effects in the interphase would tend to give rise to both diminishing configurational and librational entropy contributions as =kq increases. I n point of fact, the librational freedom of solvent water may be less on the negative branch than on the positive, by analogy with the lower entropy of hydrate water a t anions in comparison with that a t cations. It is now seen (cf. Figure loa) that the observed entropy change for low coverage conditions (I' = 0.4 and 1.0 X 10-10 mol cm-2) is the opposite of what might be expected in terms of the electrostatic entropy of water in the interphase as a function of q (Figure 11). It is for this reason that it becomes necessary to suppose that the Hg interface has a structure-promoting effect which minimizes the entropy of water in the interphase near the potential of zero charge. This effect may be enhanced by the dipole image interaction which in effect preserves the local structure "across" the interface and indeed the surface excess volume rVtends toward a maximum value near the potential of zero charge.6 At positive q the AS" values tend to be more negative than at corresponding negative charges. It seems likely that this could be due to the different orientation which pyridine can take up in the interphase, since on T h e Journal of Physical Chemistry
the positive branch the N center will be oriented away from the solvent with which it tends to hydrogen bond, and thus tend to be more specifically associated with the electron-deficient metal surface. I n this connection, it is interesting to note that the excess partial molal entropy of pyridine31 in aqueous solution calculated limitingly for infinite dilution is - 12 cal ("C) -l mol-1, an unusually low value reflecting presumably strong association with water molecules (cf. the case of ionic solution^^^). Loss of some of this associated water upon adsorption would cause release of positive entropy. The observation that entropies of adsorption a t positive q are in fact the most negative (at low r) seems to indicate retention of some of the hydrogen bonding to water so that a "flat" orientation (rather than one in which the pyridine dipole is oriented toward the metal surface) may be preferred in order to minimize "dehydration." At higher coverages, structure-breaking by the pyridine itself15 may become significant, so that the entropy of displacement of water is a less positive quantity and the librational effects calculated above may become more representative of the experimental Corresituation, e.g., for r = 2.4 X 10-lo mol sponding variations of enthalpy can arise in a similar way: at appreciable coverage, water in the interphase will be less hydrogen bonded and more easily displaced, so that the process of displacement can become relatively more exothermic; this effect will be enhanced by increasing pyridine-pyridine interactions which can contribute approximately 1.47 kcal mol-' per pair as may be estimated from the known beat of vaporization of pure pyridine (8.8 kcal mol-l) assuming 12coordination in a close-packed liquid lattice. Analogously, with regard to the variation of the heats of adsorption a t low F with charge, AH tends to become (Figure 7) appreciably less negative with decreasing q; this effect could also be interpreted in terms of increasing difficulty of substitutional adsorption requiring H-bond breaking in the structured and H-bonded water layer as q decreases since the electrostatic energy difference of pyridine and water dipoles, due to field-dipole interactions, can only amount to ea. 1 kcal over this range of q (see below). At higher 'I values, an opposite trend is seen and AH" becomes more exothermic with decreasing q; with a sufficient population of the ad-layer with pyridine, the structural effects associated with the water layer will be less important so that the pyridine reorientation effect can become dominant; Le., the tendency for the adsorption energy of the N center to be smaller a t positive than at negative q owing to the diminution of H bonding which the N center would suffer if oriented away from the solvent must be considered. Contrary to earlier expectations,' the AH" is quite negative at the most positive q values (31) R. J. L. Andon, J. D. Cox, and E. F. G. Herington, Trans. F a r e dagSoc., 53,410 (1957); J . Chem. Soc., 3188 (1954).
SYMPOSIUM ON INTERFACIAL PHENOMENA where the N center of pyridine is presumably oriented more toward Ihe mercury and is thus less H bonded. The disadvantage with respect to H bonding which the molecule would experience when in this orientation may be compensated by electron overlap (specific adsorption) with the positive Hg surface under these conditions (cf. the stability of thiourea a t Hg,23the existence of ammonia, amine, and amide complexes with Hg(I1) and the n-orbikal interaction of pyridine with positive surfaces’). 011 the other hand, a t appreciable q values (4 and 6 p C ~ r n - ~ AHo ) ) changes relatively little with I’; this may indicate that pyridine is oriented in a “flat” manner a t the electrode and carries with it locally a t least one HzO molecule which at the same time is able to interact with the charged metal surface. This is consistent with the argument made above regarding AS” and “dehydration” effects. Electrostatic calculations (cf. ref 1) of the energy of polarization of pyridine (dipole-field and electronic
3619 polarization energy) a t various fields in comparison with that of 2 or 3 water molecules which it would replace indicate that water would tend to remain prefAgain, a erentially adsorbed even up to high * q . purely electrostatic treatment of the problem seems qualitatively inadequate so that structural effects involving hydrogen bonding may be as important in the enthalpies of adsorption as in the entropies. The close compensation between the entropy and enthalpy terms lends confirmation to the supposition that the adsorption characteristics of pyridine a t mercury are closely and specifically connected with the behavior of water adsorbed in the interphase. Acknowledgments. We are indebted to the National Research Council, Canada, for support of this work. L. G. 1%.G. acknowledges the award of a fellowship from the Sprague Electric Company, which also provided some financial assistance with the research project.
Electrocapillary Studies in Aqueous Lithium Chloride Solutions’ by R. G. Barradas and E. W. Hermann Department of Chemistry, Carleton Uniaersity, Ottawa 1, Ontario, Canada
(Received February $2, 1969)
A modified Lippmann electrocapillarometerfor the direct determination of interfacial tension as a function of variation in applied electrode potential, aqueous lithium chloride solution activity, and temperature is described. Measurements of electrocapillary curves for Licl from to 3.19 m were investigated over a temperature range of 1-45”, Derived results comprised of total charge on the electrode, ionic components of charge in the inner and diffuse double layer, Esin and Markov coefficientsat constant charge are presented and discussed. All calculations were carried out by digital computer methods. The significance of certain peculiar charge effects is explained in terms of ion-water interactions, and the importance of the role of adsorbed water in the double layer is emphasized. Some preliminary data on entropies of adsorption are presented,
Introduction Adsorption on mercury from lithium chloride solutions has been determined by the electrocapillary method2 and by capacity measurements3 a t 25”. In general there is a relative scarcity of temperature dependent double-layer studies, but a few noteworthy papers have been reported in the l i t e r a t ~ r e . ~ -There ~ are two apparent shortcomings in most of the work cited, namely the small number of temperature intervals studied and/or the lack of simultaneous variation of solution activities in the bulk phase.
Experimental Section Lippmann Capillary Electrometer. Improvement in electrometer design has been stated as one of several
possible ways of overcoming some of the experimental problems associated with double-layer studies’o and (1) Presented as an invited paper at the Symposium on Interfacial Phenomena at Electrodes, 156th National Meeting of the American Chemical Society, Atlantic City, N. J., Sept 1968. (2) H. Wroblowa, 2. Kovac, and J. O’M. Bookris, Trans, Faraday SOC.,61,1523 (1965). (3) D. C. Grahame, E. M. Coffin, J. I. Cummings, and M.A. Poth, J . Amer. Chem. Soc., 74,1207 (1952); D. C. Grahame, J.Electrochem. SOC.,98, 343 (1951). (4) J. E. B. Randles and K. S. Whiteley, Tr&ns. Faraday SOC.,52, 1509 (1956). (5) W. Anderson and R. Parsons, Proceedings of the 2nd International Congress of Surface Activity, Butterworth and Co., Ltd., London, p 45. (6) G. J. Hills and R. Payne, Trans. Faraday SOC.,61,326 (1965). (7) J . M. Parry and R. Parsons, J . Electrochem. SOC.,113, 992 (1966). (8) J. N . Butler, J.Phys. Chem., 70,2312, (1966).
Volume 73, Number 11 November 1969
