Langmuir 1990,6, 863-869
863
Universal Functional Group Activity Coefficient Model in Electrosorption. 2. Electrosorption of 1-Propanol at the Mercury-Solution Interface Marian Karolczak Universytet im. Adama Mickiewicza, Wydzial Chemii, Zakhad Chemii Fizycznej, ul. Grunwaldzka 6, 60-780 Poznah, Poland Received September 9, 1988. I n Final Form: September 27,1989 The electrosorption of 1-propanol on a mercury electrode from aqueous sodium sulfate solutions has been measured with a computer-controlled capillary electrometer. The data considered in the paper correspond to the temperature of 293.15 f 0.05 K. Experimental conditions meet the requirements of the thermodynamic theory of electrocapillarity: the activity of the supporting electrolyte has been kept constant, electrode potential has been measured with respect to a sulfate ion reversible electrode, and the activity of adsorbate instead of its concentration has been used in the determination of the relative surface excess. The results have been interpreted in terms of the universal functional group activity coefficient (UNIFAC) theory of electrosorption (Karolczak, M. J. Electroanal. Chem. 1989, 262, 263). The activities of 1-propanol and water as well as the excess electrochemicalGibbs energies of mixing in the surface solution have been calculated at various electrode potentials. The dependence of the interaction energy parameters of various functional groups of the adsorbed compounds on the electrode potential has also been presented. It has been shown that the deviations from ideality are bigger in the surface solution of 1-propanol than they are in the corresponding bulk solutions. This observation has been related to the structure-making, structure-breaking effects of 1-propanol influenced by the electrical field at the interface. The obtained results support the appliance of the UNIFAC model in the electrosorption studies.
I. Introduction In part 1 of this series,l a new approach to the theoretical description of electrosorption of organic compounds* has been put forward. This approach recognizes the contribution of an individual functional group of a compound and allows one to buildup a coherent theory founded on the structural properties of the adsorbed species theory of the electrosorption processes. It has been concluded in ref 1that the particular version of the proposed theory can be applied for the description of the electrosorption of 1-propanol at the mercury-olution interface. The purpose of this paper is twofold. First, the main purpose is a detailed and as comprenensive as possible description of the experimental conditions under which our data have been obtained. We recognize it as an important point because in subsequent publications we intend to answer some fundamental questions of adsorption modeling raised in 1977 by Mohilner et al.4 The way the experiments were done, their accuracy, significance, and consistency, mean very much in our proof and reasoning. They also provide a reliable and convenient reference point for these future investigations, brace them with the present findings, and support the developed theory.’ Our secondary purpose is the application of the UNIFAC theory to the extended collection of the experimental data and the presentation of its additional implications. In many respects, the presentation in this paper follows the standards established in initial publication^.^.^ However, a t one point there is a significant difference. (1)Karolczak, M. J. Electroanal. Chem. 1989,262,263. (2) Karolczak, M.; Mohilner, D. M. J. Phys. Chem. 1982,86, 2840. (3) Nakadomari, H.; Mohilner, D. M.; Mohilner, P. R. J. Phys. Chem. 1976.80., 1781. - -(4) Mohiiner, D. M.; Nakadomari, H.; Mohilner, P. R. J . Phys. Chem. 1977,81,244.
0743-7463/90/2406-0863$02.50/0
Mohilner et al.4 have chosen the polynomial expression for representing the dependence of excess electrochemical Gibbs energy of mixing of surface solutions, AGE, and the activity coefficients a t the interface on the surface mole fraction of adsorbate, xAads.Such a choice was submitted as the primary goal of their paper, which was to test, independently of a model, whether or not the inequality TIASEI 2 IMElis true, Le., whether “the solution properties are under entropy control”. Contrary to their choice, we have used in this paper the relations resulting from UNIFAC theory of electrosorption, i.e., eq 1315 of ref 1. Behind this alteration were the advantages resulting from a clearer (amendable to classification)physical interpretation offered by these relations as well as by their strong statistical foundations.
11. Experimental Section A. General. In order to obtain relative surface excess data consistent with the thermodynamical requirements of electrocapillarity, Nakadomari et al.8g3have developed an experimental procedure which meets these requirements. In this procedure, (1)the activity (the chemical potential)of the supporting electrolyte is held constant as the concentration of the organic substance is varied; (2) the activity, instead of the concentration, of the organic substance in the investigated mixture is used as the independent variable in the differentiation of the interfacial tension data; and (3) the potential of the working electrode is measured with respect to the proper (Le., reversible to one of the ions present in solution) indicator electrode. The two-phase lead amalgam-lead sulfate electrode has been used in these investigations. (5) Karolczak, M. J. Colloid Interface Sci. 1984,97, 284. (6) McMillian, W. G.; Mayer, J. E. J. Chem. Phys. 1945, 13, 276.
(7)Ralston, A. A First Course in Numerical Analysis; McGraw-Hill: New York 1965; Chapter 6. (8)Nakadomari, H.; Mohilner, D. M. J. Electroanal. Chem. 1976, 65, 843.
0 1990 American Chemical Society
864 Langmuir, Vol. 6, No. 4, 1990
Table I. Solution Composition I-propanol water mole mole molarity molarity" fraction activityb fraction activity of Na,SO," 0.9982 0.9957 0.0000 0.000 000 O.oo00 0.100 00 0.0370 0.000 662 0.0070 0.9976 0.9950 0.09846 0.0460 0.000 824 0.0088 0.9974 0.9949 0.098 09 0.0580 0.001 031 0.0110 0.9972 0.9947 0.097 59 0.0700 0.001 255 0.0134 0.9970 0.9944 0.097 09 0.0860 0.001544 0.0164 0.9967 0.9941 0.09643 0.1050 0.001887 0.0201 0.9964 0.9938 0.09564 0.1250 0.002248 0.0239 0.9960 0.9934 0.094 81 0.1470 0.002 647 0.0282 0.9957 0.9931 0.093 90 0.092 74 0.1750 0.003 157 0.0336 0.9952 0.9925 0.2100 0.003795 0.0404 0.9945 0.9919 0.091 28 0.2550 0.004 620 0.0492 0.9938 0.9910 0.08942 0.3000 0.005 449 0.0580 0.9930 0.9902 0.087 55 0.4200 0.007 680 0.0817 0.9908 0.9880 0.08257 0.5000 0.009 187 0.0977 0.9893 0.9864 0.079 25 0.075 10 0.6000 0.011 084 0.1179 0.9875 0.9844 0.7000 0.013006 0.1384 0.9857 0.9827 0.07095 0.8400 0.015733 0.1674 0.9830 0.9800 0.065 14 0.05850 Loo00 0.018905 0.2011 0.9800 0.9769 0.052 90 1.2000 0.022 949 0.2442 0.9760 0.9729 1.5000 0.029178 0.2981 0.9700 0.9666 0.045 20 0.04200 1.7000 0.033 507 0.3371 0.9657 0.9623 0.033 60 2.0000 0.040152 0.3803 0.9592 0.9557 a 25 O C . 20 O C . The original interfacial tension data a t the mercury-solution interface of 1-propanol in aqueous sodium sulfate of constant activity (aa = 0.070 87) a t 293.15 f 0.05 K, which are reported in this paper, have been obtained by rigorously following the recommended procedure. They were collected in the laboratory of D. M. Mohilner by using a computer-controlled capillary e l e c t r ~ m e t e r . ~ J ~ B. Reagents and Solutions. Fisher (Scientific Certified Reagent) 1-propanol was twice destilled in small portions prior to use. An occasional test of its purity and eventual water content had been performed by GC. Fisher (Scientific Certified Reagent) sodium sulfate was used without further purification, relying on findings in ref 3; it was only dried in the oven a t 383 K for a long time. Water was triply distilled-in the first stage from alkaline permanganate in order to eliminate traces of adsorb able organic impurities. Mercury was purified according to a standard method followed by triple distillation under vacuum. The 23 solutions containing 0.0370-2.0 M of 1-propanol (c.f. Table I) and an appropriate amount of Na,SO,, necessary to hold constant the activity of this salt in the mixture, were prepared by weighing the required amounts and transferring them to a 1-L volumetric flask, which was then filled with water, equilibrated a t 298.15 f 0.05 K (usually overnight) in the water bath, and refilled to the mark. The procedure used to determine the recipe for preparing the solution has been described in ref 8. The data corresponding to 1-propanol were prepared on the basis of experiments carried out previously." C. EMF Measurements. The indicator two-phase lead amalgam-lead sulfate electrode was prepared before the measurements of each electrocapillary curve. The preparation of the new indicator electrode prior to the measurements of each electrocapillary curve was unavoidable because the investigated mixture had different electrolyte concentration (to keep its chemical potential constant). The method of preparation was as follows: T h e measuring cell and electrode compartment were evacuated and subsequently filled with argon (in turns, 4 consequtive times). Next, the amount of two-phase lead amalgam, necessary to cover the bottom, has been dosed under vacuum to the electrode compartment. Subsequently, also under the vacuum, a deaerated, stirred slurry of the mixture of PbSO, with the investigated solution has been dosed to the same com(9)Lawrence, J.; Mohilner, D. M. J.Electrochem. SOC.1971,118,1596. (IO) Mohilner, D. M.; Kakiuchi, T. J. Electrochem. Soc. 1981,128, 350. (11) Mohilner, D. M.; Kakiuchi, T.; Taraszewska, J. Can. J. Chem.
1981,59,1672. (12)Taraszewska,J.; Mohilner, D. M. J . Phys. Chem. 1981,85,902.
Karolczak partment. The PbSO, has been allowed to precipitate and cover the lead amalgam. In the next step, the nitrogen, presaturated in the investigated solution (two I-m-long, half-filled thermostated columns), was allowed to fly over the measuring cell and indicator electrode compartment. Removing the oxygen from the indicator electrode compartment prior to its preparation and the work under vacuum were the necessary steps in the view of Kakiuchi e t a1.,l1 who indicated that the time necessary to reach the equilibrium potential by this electrode can be much reduced (especially a t lower than room temperatures) when the above procedure is followed. The sophisticated system of glass valves necessary in the procedure described above has been designed by Kakiuchi. The two-phase lead amalgam was prepared by cathodic deposition of lead from lead nitrate into pure (triple vacuum destilled) mercury. The lead sulfate was prepared from reagent grade chemicals according to the method of Harned and Hecker.13 The potential difference between the working electrode and the indicator electrode has been set from computer through potentiostat in 20-mV increments. I t has been additionally monitored and measured, within *lo-pV accuracy, on a Fluka Model 8300 A digital voltmeter. The temperature in the measuring cell, in the indicator electrode compartment, and in the two deaerating columns has been controlled by pumping water from the thermostat through their glass jackets. This enabled one to control the temperature within the cell with a precision of f0.05 OC a t 25 "C; it was slightly worse, ca. 0.5 "C, a t 5 "C. The working electrode was a U-bended glass ~ a p i l l a r y . ~ .The ' ~ method of preparation of a reliable working electrode, which could be used in the maximum bubble pressure technique of electrocapillary measurements, differed in some details', from those previously described in the literature. D. Electrocapillary Measurements. The electrocapillary curves for 23 solutions containing 1-propanol, sodium sulfate, and water (Table I) were measured by using an improved version" of the computer-controlled capillary ele~trometer.~ The improvements seemed necessary due to the not very well marked dependence of the interfacial tension on temperature. As a result of the improvements, the precision of the interfacial tension measurements, f0.02 mN m-l, has been achieved.1° Standard deviations of the interfacial tension data have been confirmed to be independent of the electrode potential." Each electrocapillary curve has been measured in triplicate a t 60 different electrode potentials. The potential interval was 20 mV. The potential range was -0.6 to +0.6 V vs a lead amalgam-lead sulfate indicator electrode. The sodium sulfate (the supporting electrolyte) activity was kept constant: a, = 0.070 87 (Le., a t the activity corresponding to 0.1 M (or 0.10045 m) aqueous sodium sulfate without the organic species). The experimental points at each electrode potential were arithmetically averaged, and at each point the standard deviation was calculated. The demanding rejection routine3 enabled one to collect a statistically uniform set of data. The time required to collect one set of measurements for one electrocapillary curve was ca. 6-8 h; this includes one so-called raw run, used as a guide, and three subsequent measurements of the whole electrocapillary curve a t each electrode potential as well as the possible repetitions. Before the main experiment, the measuring system was always calibrated by using 0.1 M NaCl solutions as the standard.16 This calibration procedure enabled one to update the electrometer capillary constant, to monitor the capillary radius in time, and to perform the internal test of the behavior of the measuring system. The necessity of daily calibration of the working electrode in the computer-controlled capillary electrometer results from the enhanced precision of the electrocapillary measurements evolved in this technique. The time required for the calibration amounts to ca. 1.5-2 h prior to the run of the main experiment. (13)Harned, H. S.;Hecker, J. C. J.Am. Chem. SOC.1934,56,650. (14)Karolczak, M. Wybrane zagadnienia z fizykochemii ukladow homo-i heterogennych; University of A. Mickiewicz,Seria Chemia, 1985; Vol. 45,p 27 (in Polish with English abstract). (15)Karolczak, M. Wybrane zagadnienia z /izykochemii ukladow homo4 heterogennych; University of A. Mickiewicz, Seia Chemia, 1985; Vol. 45,p 33 (in Polish with English abstract). (16) Kakiuchi, T.; Mohilner, D. M. J. Electrochem. SOC.1981, 128, 2599.
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Electrosorption of Organic Compounds
111. Data Analysis T h e relative surface excess of the adsorbed 1propanol, r A W , the excess charge density, and the smoothed values of the interfacial tension have been calculated by means of fitting of a moving least-squares patch on the electrocapillary surface y = y ( K , In a,) followed by twodimensional differentiation. Individual patches on this surface were fitted by least-squares polynomials in two independent variables which included terms up to fourth degree in the E variable (the electrode potential) and second degree in In aA (the activity of 1-propanol). The most effective size found experimentally for the fitting patch appears to be 9 X 4 for this collection of data. Details on the computer programs used in such calculations were published in ref 17. The programs actually used contained some minor modifications as described by Nakadomari."" The relative surface excess data have been derelativized by using
derived in ref 3, with n = 4 and SA = 31.8 A2 (r, = 5.41 X lo-'' mol cmP2) found from the precise molecular modes.lg In eq 1, X , and xw denote bulk mole fraction of alcohol and water, respectively. Next, the surface mole fractions of the adsorbed 1-propanol, xAnda, have been ~ a l c u l a t e dfrom ~ * ~ the relation = rA/(rA+ rw) or directly from the equation
(2)
xAad
xAab
=
nlo"
L-'XA + S A r A W ( 1 - XA - x,)
n W L-'(1- x,) + (n - 1 ) S A r A W ( 1 - XA - x,) where x , is the mole fraction of the electrolyte in bulk (variable in this experiment). At this stage, the first 16 concentrations from Table I have been considered. The other concentrations have not been accounted for in this paper since they correspond to slightly higher values of the surface concentrations than the assumed maximal value in the monolayer. (This may indicate a partial reorientation or breaking of the monolayer concept at higher concentrations). In the next step, the natural logarithms of the activity of the adsorbed water, In aWads, have been calculated by means of eq 4 of ref 20:
Thus, calculated values have been converted to natural logarithms of the activity coefficients, In yads,and fitted to the theoretical equations resulting from the UNIFAC model of electrosorption:' In yWad*= -In [A,x~'&+ (1- XAad")] 2xA'& kA'& A$A'~' + (1- X A " ~ ) A ~ X A ' ~(1- X A ' ~ )
+
+
(17) Mohilner, P. R.; Mohilner, D. M. In Computers in Chemistry and Instrumentation; Mattson, J. S., Mark, H.B., Jr., MacDonald, H. C., Jr., Eds.; Marcel Dekker: New York, 1972; Vol. 2, Chapter 1. (18) Nakadomari, H.P b D . Dissertation, Colorado State University, 1974. (19) W i n g Catalog 1978, Vol. 79, p 11. (20) Karolczak, M. J . Phys. Chem. 1985,89, 1556.
A t this stage of data analysis, it appeared necessary to develop a new computer program to facilitate the nonlinear fitting procedure. The new program incorporates the Marquardt-Levenberg21 strategy of optimalizing a nonlinear least-squares fitting. The options for introducing the weighting factors of both the independent and the dependent variables have been included. To assure the numerical stability during the intermediate calculations, the Banachiewicz-Crout methodz2has been adopted for solving the resultant simultaneous equations. Additionally, the fitting procedure has been equipped with the statistical package which contains the evaluation of the residual values of the fitting, calculation of the x2 value, calculation of the standard deviations of the estimated fitting parameters, and evaluation of the condition number. The last quantity makes it possible to judge the obtained results in the light of possible inaccuracies resulting from numerical transformations and instability of used algorithms as well as those inherent from the natural limitations in the original sets of data. A compact, numerically stable and fast-exchange algorithm2' has been used for matrix inversion in the statistical package. A new fitting procedure leaves a wide margin of free experimentation in the electrosorption modeling, within a model, and makes it possible to select statistically the most significant model.
IV. Results and Discussion A. Activity Coefficients of Adsorbed 1-Propanol and Adsorbed Water and Their Dependence on Electrode Potential. The fitting coefficients and their standard deviations have been determined just as described above. Their statistical and numerical significance were carefully examined a t each electrode potential. The accepted values of the fitting coefficients have been substituted into eq 4 and into the corresponding eq 5 In ?Aads = -2 In [xAnds+ (1- XA")/&] - 2 In [ x A + ~ (1-
(5) (which also results from eq 4 and a common thermodynamical relation) to calculate the smoothed activity coefficients of the adsorbed water and adsorbed 1-propanol, respectively-the values defined on the basis of the s y m metrical choice of standard states. Fi ure 1 illustrates the behavior of In yAadaand In ywa'at selected electrode potentials. No significant departure from the activity coefficients at the potential of the maximum adsorption (assumed here equal to +0.0142 V vs indicator electrode), drawn as the continuous line in Figure 1, can be detected at other considered potentials, T = +0.3137 V. Such results could except perhaps for I be interpreted in the terms of c ~ n g r u e n c eas : ~a~perfect or strict congruence. However, the former is theoretically i m p ~ s s i b l ewhich , ~ ~ means that the plots, as those presented in Figure 1, are not sensitive enough to show the potential dependence of molecular interaction energies (to which the congruence problem has been shown (21) Marquardt, D. W. J. SOC.Ind. Appl. Math. 1963,11,431. (22) Bsrck, A.; Dahlquist,G. Numerical Methods, Prentice Hall: -lewood Cliffs, NJ, 1974; Chapter 5. (23) Henrici, P. Essentials of Numerical Analysis; Wiley: New York, 1982; Chapter 4. (24) Mohilner, D. M.; Karolczak, M. J . Phys. Chem. 1982,86,3838.
Langmuir, Vol. 6, No. 4 , 1990
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16
14
12
10
8 6
b
2
I 00
I
I
02
,
I
04
1
OK
I
I
08
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Figure 1. Activity Coefficientsof the adsorbed 1-propanol (curves running down from left to right) and the adsorbed water (curves running up from left to right) on the basis of the symmetrical choice of standard states at various electrode potentials. E values in volts: 0, +0.3137; V, +0.1137; 0, +0.0142; X, -0.0859; O , -0.2860. Continuous lines represent the data at the maximum adsorption potential. related24). In fact, the molecular interaction energies have to depend on the electrode potential, and it is rather the matter of the analysis whether or not one can detect such a dependence. Evidently, the activity coefficients as well as the surface pressure II (to which they are directly relatedM,'.') are not suitable in this respect. One may note that the variations of the activity coefficients of the adsorbed 1-propanol and the adsorbed water with the potential are much smaller in magnitude than the corresponding variations in the 2-butanol-water system as well as in the 2-methylpropanol-water system.' B. Excess Electrochemical Gibbs Energy of Mixing of the Surface Solution. The excess electrochemical Gibbs energy of mixing of the surface solution has been calculated from the set of estimated least-squares fitting parameters and the experimental surface mole fraction by means of the relation corresponding to the UNIFAC model
A c * / R T = - ~ X A ' ~ ' In [ X A " ~ + ' (1 - XA"')/AZ] 2XAadS In [xAads+ (1- XA"~')/A~] - (1- xAadS)In [A,x~"*+ (1 - X*ldS)] + ~ X A " ~In' [(I + 3X~"~')/4](6) which results from the definition of the excess mixing function, AGE/RT = xAadsIn yAad'+ zw In ywads,as well as from eq 4 and 5. The results of the calculations are illustrated in Figure 2. The value of the electrode potentials chosen for the excess electrochemical Gibbs energy of mixing curves displayed in Figure 2 are the same as those chosen for the activity coefficients curves, shown in Figure 1. The points on the curves indicate the experimental values of xAEdS which were actually used, a t the specified E-, to determine the set of least-squares fitting parameters A,, A,, and A,. The curves in Figure 2 show some scattering with respect to the curve corresponding to the potential of maximum of adsorption (this is a tentative indication of the noncongruent electrosorption). However, the scattering is less pronounced than the corresponding change in the case of 2-butanol. Moreover, no monotonic change can be noted. All curves are highly symmetrical-this fact allowed elimination of some of the electrosorption models considered a t the preliminary stage of the UNIFAC
Figure 2. Excess electrochemical Gibbs energy of mixing of the surface solution at various values of the eletrode potentials. E+ values are same for correspondingsymbols as in Figure 1. theory of electrosorption (cf. ref 1). The excess electrochemical Gibbs energy values are positive through the entire concentration range, i.e., 0 < xAadS< 1, approaching the origin linearly with a positive slope > 1 (Henry's law). Consequently, the corresponding surface solution will exhibit positive deviations from Raoult's law. The extent of nonideality of the surface solution (the inner layer) measured in the terms of the magnitude of ACE is close to that of 2-butanol. However, if one characterizes the departure from ideality by means of the deviation from Raoult's law, it is similar for both compounds a t the potential of maximum adsorption and much higher in the case of 1-propanol at the extreme potentials of the adsorption range. The dependence on the electrode potential of these deviations for both considered compounds is different too. To examine this more deeply, we have calculated the fugacity ratio in the adsorbed state, and this will be discussed in the following section. It is interesting to compare the extent of the deviation from Raoult's law in the surface solution with the corresponding deviations in the bulk solutions. Mohilner et al. have found in the case of the electrosorption of 2-butanol that the surface solutions are far more ideal than the corresponding bulk solutions. In the case of l-propanol, the deviations from ideality are higher in the surface solution than they are in the bulk solution, although they are the same order of magnitude. This, in turn, confirms the findings of Mazhar et al.,25who noted the same effect for 2-methyl-2-propanol adsorbed from 0.1 M KCl aqueousz6 solutions. In this respect, the l-propanolwater-sodium sulfate-mercury system, considered in this paper, confirms the exception to the rule of thumb: "the presence of an interface decreases (smoothes out) the nonidealities of the bulk solutions". The significance of the AGE function as well as other excess functions in the electrosorption studies results from the fact that they do not contain any standard quantities. Therefore, they have been chosen to test thermodynamical implications of some popular adsorption modelsn4 The study of temperature dependence of the AGE function tends to achieve this aim. Preliminary studies20 have show2 that ASE # 0 and AHE # 0 as well as that 51AsEI > IAHEl. More extensive investigations in this direction are now pending. If the temperature dependence of the fitting parametersjn eq 4 is established, the determination, of ASEand AHE (25) Mazhar, A.; Bennes, R.; Vanel, P.; Schuhmann J . Electroanal. Chem. 1979,100,395.
(26) Karolczak, M. J.Electroanal. Chem. 1984, 121, 21.
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I \
.,4
19
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'
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I
03
02
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01
0
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ELECTRODE POTENTIAL in VOLTS
Figure 3. Standard electrochemicalfugacity ratio for adsorbed 1-propanolas a function of electrode potential.
is possible on the basis of eq 4 in a simple and direct manner. C. Electrochemical Fugacity Ratio f b e / f A o . Mohilner et al.4 expressed the view that the ratio of the electrochemical fugacity of the adsorbed species in each of its two alternative standard states "... is a direct measure of the inter-molecular interactions in the surface solution between the adsorbed orgnic compound and the adsorbed water under the condition that there are no complications from any organic-organic intermolecular interactions". They further suggested that the way the f A e / f A o ratio depends on the electrical variable provides indication of how the water structure in the inner layer changes with the same variable. In our present view, the above statement requires an additional clarification and some specifications; it is shown that the ratio f A e / f A o contains contributions from various functional group interactions; nevertheless, the suggestion of Mohilner et al. stimulated a strong interest to examine the dependence of the f A e / f A o ratio on the electrode potential. Within the applied version of the UNIFAC theory, the electrochemical fugacity ratio is given by the relation
resulting from eq 5; it has been used for the calculation of the electrochemical fugacity ratio at different electrode potentials. The results of the calculations are presented in Figure 3. The significance of the results in Figure 3 consist in the fact that they can be indirectly compared with the corresponding results of ref 4. The dependence on the electrical variable of the electrochemical fugacity ratio is different for 1-propanol and 2-butanol. In the latter case, the charge dependence is roughly a bell-shaped function with the maximum in the point which coincides with the potential of the adsorption maximum. For 1-propanol, it is a more complicated form; the potential dependence is less pronounced, and it has two extrema (a maximum and a minimum). If f A g / f A o > 1, the surface solution exhibits positive deviations from Raoult's law; if f A g / f A o < 1, the surface solution exhibits negative deviations from Raoult's law. If the bulk solutions are compared, the deviations from Raoult's law are smaller in the case of lpropanol than they are in the case of 2-butanol; that is quite opposite what we observe in the corresponding surface solution. The experimental value of the fugacity ratio for the binary mixture 1-propanol-water calculated on
the basis of data from Butler et al.,' is 12.94; it is 10.64 in mixtures with sodium sulfate a t 20 "C, as follows from Table I. This value is lower than the minimum value in Figure 3. Positive deviations from Raoult's law imply that there is a tendency for "structure-making" in the surface mixture. In the investigated potential range, this "structuremaking" property of 1-propanol evidently overcomes the "structure-breaking" effects of the electrical field. Moreover, the presence of the interface itself increases the "structure-making" effects. The balance of two opposite effects seems to be very delicate in the case of 1-propanol. Comparison with 2-butanol suggests that it depends on the physicochemical properties of the adsorbate, particulary on the number of functional groups in the molecule. It would be difficult to explain the observed effects only in terms of order-disorder properties of the adsorbed watethe interpretation favored so far in the majority of theoretical and experimental studies on adsorption. In other words, the water-related structural effects, while still predominant, are not the only factors that should be considered in the interpretation of the electrosorption data and the structure of the interface. D. Potential Dependence of the Functional Group Interaction Energy Parameters. According to the proposed UNIFAC theory,' the fitting parameters A,, A,, and A, in eq 4-6 are related to the functional group interaction energies as follows:
A, = 2(1+ exp[-(u21- ull)l/RT)/(ex~[-(u32- u11)1/RT) (9)
A3 = 2 0 + exp[-(ulz - u22)l/RT)/(ex~[-(u3~ - ~22)1/RT) (10) In these relations, uij denotes the interaction energy between different functional groups i and j : 1 stands for CH, and CH, groups; 2 stands for the CH,OH group; 3 stands for water treated as an individual group. Since the parameters A,, A,, and A, make the principal components of the fugacity ratio, it was interesting to examine their individual dependence on the electrode potential. The results of these studies are illustrated in Figure 4. They reveal, contrary to what one could merely deduce from Figure 1, that the numerical values of these parameters in fact change with the electrode potential. The observed variations confirm that the electrosorption of 1-propanol is noncongruent. This has been anticipated in light of the discussion in ref 24, but the results of Figure 1 raised a question in this respect. It is again evident that such plots as in Figure 1are, in general, not sensitive enough for testing or demonstrating the congruence. The same can be stated about the plots of AGE presented in Figure 2, especially when they are only examined near the origin. As it results from ref 24, the problem of congruence occurs temporarily less important from the practical point of view (especially in the context of problems for which it was originally introduced), although it is still interesting from a theoretical point of view. In an attempt to interpret the course of the curves in Figure 4, one could postulate additional relations concerning the dependence of the functional group interaction energies on the electrode potential. For instance, a quadratic dependence is plausible. Moreover, such a dependence could be easily justified when one considers (27) Butler, J. A. V.; Thomaon, D. W.; Maclennan, W. H. J . Chem. SOC.1933, 135, 674.
868 Langmuir, Vol. 6, No. 4, 1990
Karolczak
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Expressed in Terms of Surface Coverage. With the general from of the electrosorption isotherm^^*^'^^
10 5
250r 2 10 2701 04
.
together with n = 4 and the explicit form of the AGE function corresponding to the UNIFAC model of electrosorption, i.e., eq 6, and introducing the following relations between the surface mole fractions and the surface
coverage^^'^
1
,
,
02
00
, -02
-0L
4(1- 8) = ___ 4-36 we have obtained the following equation for the electrosorption isotherm of 1-propanol expressed in terms of surface coverage: xwads
P ’ ~ / ( ~ W ) ~=
0(l
+ C,8)4
4(1- ~9)~(1 + C28)2(l+ C38)2 2C38 4(1+ C,)C18] (12) 1 + C36 1 + C16 +
u
04
02
00
-02
-04
ELECTRODE POTENTIAL in VOLTS
Figure 4. Variation of functional combined group interactions energy parameters A,, A,, and A , in eq 2 with electrode potential. Vertical bars represent standard deviations determined from the correlation matrixes of the nonlinear leastsquares fitting.
the physics of dipolar interactions. Although preliminary attempts with the fitting of such semitheoretical relationships proved successful (Le., we could effectively fit the sum of two Gaussian-type functions, c.f. eq 8, to represent the dependence of A, on the electrode potential), it is premature to recommend such an approach. Still more experimental evidence is necessary in order to establish sufficient basis for postulating any potential dependence of the functional group interaction energies, although, on the other side, some speculations on the terms of “effective”quantities such as “effective dipole moment”, “effective dielectric constant”, or “effective polarizability“, along the lines admitted in other electrosorption theories, could be easily advanced and look even attractive. However, the terms effective dipole moment, effective dielectric constant, effective polarizability, etc., while changing the language of the interpretation are not extending our knowledge on the true molecular relations at the interface. In fact, they only apparently shift the discussion to the molecular level, thus providing no desirable solution. It seems necessary to point out explicitly the difference between the analysis of the electrosorption data in this treatment and the treatment of Mazar et ~ l . , ’which ~ a t the first glance may give an impression of being very similar. The key difference is the interpretation of the interaction energy parameters; they are related to molecular energies of interactions in the Mazhar et al. approach, whereas in the present treatment they are related to various functional group interaction energies in a surface mixture. E. Electrosorption Isotherm of 1-Propanol
The parameters C,,C,, and C, in this equation are related to the parameters defined above, A,, A,, and A, as follows: c1 =
(A1/4) - 1
C, = (A,/4) - 1 C, = (A,/4)
-1
8 is the electrosorption equilibrium constant related to the standard Gibbs electrosorption energy, AGahe, defined on the basis of the unsymmetrical choice of standard state for the adsorbed specie^,^ viz. In pe = -AG,~;/RT The electrosorption isotherms of 1-propanol, a t different electrode potentials, plotted according to eq 12 and in 8, uA/(a,J4 coordinates, are illustrated in Figure 5. Equation 1 2 fits the experimental data below the experimental errors. Its parameters have a definitive physical meaning which is more comprehensivethan those which appear in isotherms previously used. It is also more rigorous from the thermodynamical point of view. The complicated mathematical form of this equation results, on the one side, from the contributions due to the different molecular size of 1-propanol and water (so-called configurational contributions’) and on the other side from the distinction between the functional groups in the molecule, in particular, from their mutual interactions (the residual contributions’). At the end, we will note that the results obtained in this paper are consistent (to the extent in which such a comparison is permissible) with those reported by previous investigators.% Thus, we have obtained the value of the apparent mutual interaction energy parameter, Frumkin’s “ao”, as reported by Damaskin et al. (i.e., a. = 1.0). For this purpose, we expanded a properly rearranged form of eq 12 in the Taylor series in 8 (around 8 = 0.5, the value which corresponds to the application of Damaskin’s method used in ref. 28) considering only the linear term of the expansion. In the
Electrosorption of Organic Compounds
n./ f a 2 Figure 5. Electrosorption isotherms for 1-propanol in terms of the fractional surface coverage at various values of the electrode potentials as a function of the bulk activity ratio aAl (a,)”. e values in volts 0 , +0.3137; v, +0.1137; 0, +0.0142; +, -0.1859 0,-0.2860.
same way, Damaskin’s value of the parameter /3 (=0.47;
0 in their interpretation expresses the dependence of the a parameter on the electrode potential (they assumed a
linear dependence)) has been obtained as well. Besides, the method yielded an adsorption Gibbs energy value (as defined by the Soviet School) of AGA = -2.6 kcal mol-’ and a differential capacitance at full coverage of C’ = 5 r F cm-*. In view of the approximations used in the calculations and different experimentalconditions, the agreement between the estimated values and those of ref 28 must be considered satisfactory.
V. Conclusions The electrosorption of 1-propanol on mercury electrode from aqueous sodium sulfate has been measured with a computer-controlled capillary electrometer. The (28) Damaekin, B. B.; Survila, A. A.; Rybalka, R. E. Elektrokhimiya 1967, 3, 114.
Langmuir, Vol. 6, No. 4, 1990 869
measurements and the following data elaboration respect the rigorous conditions implicated by the thermodynamic theory of electrocapillarity. The obtained results confirm the application of the UNIFAC model in the studies of electrosorption. By means of this model, one obtains the electrosorption isotherm parameters whose physical meaning is more comprehensive than those of previously used isotherms. The electrosorption of 1-propanol is noncongruent with respect to the electrode potential. However, the noncongruence is only weakly marked in both pltos: the logs of activities in the adsorbed state versus the surface mole fractions and AGE versus the surface mole fractions, corroboratingthus the view that such plots are not very helpful in this type of analysis. In the investigated potential range, the surface solution exhibits positive deviations from Raoult’s law. These deviations depend on the electrode potential. They have a minimum in the vinicity of the maximum adsorption potential, and they increase on both positive and negative sides of this potential. Contrary to the respective findings for the adsorbed 2-butanol, the deviations from ideality are bigger in magnitude in the surface solution then they are in the corresponding bulk solution. The balance between the structure-making and the structure-breaking effects of the electrical field depends on the molecular structure of the adsorbate, not only on the properties of the adsorbed water, as it has been assumed in many previous studies on the electrosorption. This balance is very delicate in the case of the adsorbed 1-propanol. The electrosorption isotherm of 1-propanol expressed in terms of the surface coverage has a more complicated mathematical form than any other electrosorption isotherm used so far in the adsorption studies. This results from the fact that it takes into account the contributions from various functional groups of the molecules present in the surface solution. However, the advantage of this approach is a more coherent, predictable description of the interfacial behavior than the one offered by the traditional isotherms, which have not been so closely related to the structural and physicochemical properties of the adsorbates. Registry No. 1-Propanol,71-23-8;mercury, 7439-97-6;water, 7732-18-5.
