J. Phys. Chem. 1985, 89, 3506-3512
3506
Mechanlsm of Ion Transfer through Ultrathin Films of Neutral Organic Species Adsorbed at the Electrode Surface M. Goledzinowski, J. Dojlido, Department of Chemistry, Warsaw University, 02-093 Warsaw, Pasteural, Poland
and J. Lipkowski* Guelph- Waterloo Centre for Graduate Work in Chemistry, Department of Chemistry and Biochemistry, University of Guelph, Guelph, Ontario, NIG ZWI Canada (Received: December 26, 1984)
The kinetics of Cd2+deposition and Cd(Hg) dissolutiop on the mercury electrode covered by monolayers of di- or trisubstituted alcohols was investigated. A relation between the rate of the ion transfer and the film pressure was derived. The cross-sectional area of the Cd2+ ion transported through the monolayers was determined. The effect of the local potential on the rate of CdZ+deposition and the magnitude of the lateral interactions between Cd2+and surfactant molecules were assessed. The permeability of the monolayers of the polyols was compared with the permeability of the films formed by normal aliphatic alcohols. It was found that the apparent area of an ion crossing a monolayer and its interactions with the monolayer are independent of the structure and thickness of these rather thin films.
Introduction Many phenomena of recent interest involve an ion transfer across a film of organic species. Semiconductor electrode surfaces are coated with an organic polymer to protect against photocorrosion.' Ion exchange between solution and the film takes place on the polyelectrolyte-coated electrodes.2 Conductive polymer films used for energy storage take in counterions to balance charge n e ~ t r a l i t y . ~Thus an investigation of the mechanism of the ion transfer across thin films on a well-defined model system could provide information valuable for many areas of research. The theory of ion transfer across monolayers of neutral ' has been tested organic species has been developed r e c e n t l ~ . ~ It on selected ion transfer reactions whereby the electrode surface was covered by films of normal aliphatic alcohols and acid^.^-'^ (1) R. Noufi, A. J. Frank, and A. J. Nozik, J. Am. Chem. Soc., 103,1849 (1981); R. Noufi, D. Tench, and L. F. Warren, J. Electrochem. Soc., 127, 2310 (1980); F. R. F. Fan, B. Wheeler, A. J. Bard, and R. Noufi, J. Electrochem. Soc., 128,2042 (1981); T.Stokheim, I. Lundstrom, and J. Prejza, J. Electrochem. Soc., 128, 1625 (1981). (2) I. R. Rubinstein and A. J. Bard, J. Am. Chem. Sa.,103,5007 (1981); N. Oyama and F. C. Anson, Anal. Chem., 52,1192 (1980); R. J. Nowak, F. A. Schultz, M. Umana, R. Lam, and R. W. Murray, Anal. Chem., 52,315 (1980); P. J. Peercc and A. J. Bard, J. Electroanal. Chem., 112,97 (1980); J. B. Ken, L. L. Miller, and M. R.J. Van De Mark, J. Am. Chem. Soc., 102, 3383 (1980); Yu-Min Tsou and F. C. Anson, J. Electrochem. Soc., 131, 595 (1984). (3) K. Kaneto, M. Maxfield, D. P. Nairns, A. G. MacDiarmid, and A. J. Heeget, J. Chem. SOC.,Forodoy Trons. I , 78,3417 (1982); J. H. Kaufman,
J. W. Kaufer, A. K. Heeger, R. Kaner, and A. G. MacDiarmid, Phys. Rev. B, 26,2327 (1982); J. H. Kaufman, E. J. Mele, A. J. Heeger, R. Kaner, and A. G. MacDiarmid, J. Electrochem. Soc.,130,571 (1983); G. C. Fanington, B. Scrosati, D. Frydrych, and J. De Nuzzio, J . Electrochem. SOC.,131, 7
(1984). (4) J. Lipkowski and Z. Galus, J. Electroonal. Chem., 61, 11 (1975). (5) J. Lipkowski and Z. Galus, J. EkCt"aI. Chem., 98, 91 (1979). (6) R.Guidelli, M. L. Foresti, and M.R.Moncelli, J. EIectrwnuI. Chem., 113, 171 (1980). (7) G. Pyzik and J. Lipkowski, J . Electroanol. Chem., 123, 351 (1981). (8) J. Lipkowski, E. Kosinska, M. Goledzinowski, J. Nieniewska, and Z. Galus, J. Electrwnal. Chem., 59, 344 (1975). (9) M. Goledzinowski, J. Lipkowski, and Z. Galus, Elektrokhimiya, 13, 1099 (1977). (10) M. Goledzinowski, J. Kisova, J. Lipkowski, and Z . Galus, J . Elecrroanal. Chem., 95.43 (1979). (1 1) G. Pezzatini, P. Mariani, and R. Guidelli, J. ElectrmnaI. Chem., 185, 315 (1985). (12) G. Pezzatini, M. H. Foresti, and R. Guidelli, J . Electrwnal. Chem., 138, 139 (1982). (13) B. N. Afanasev, G. J. Avilova, and N. A. Borisova, Ukr. Khim. J., 44, 15, 370 (1978). (14) E. Mtiller and H-D. Dbrfler, J . Elecrroanal. Chem., 99, 111 (1979). (15) E. Miiller, H. Emons, and H-D. Wrfler, J . Elecrrwnal. Chem., 142, 39 (1982)
These results brought to attention that the film permeability to an ion depended critically on the size of the ion. Similarities were noted between the mechanism of ion transfer across the film a t the metalsolution interface and a transfer of a neutral molecule (such as water or a gas) at the solution-air interface.'^'^ To gain further information on how the ionic permeability depends on the size and orientation of the surfactant molecule, we performed investigations of the kinetics of Cd2+discharge at the mercury surface covered by a monolayer of the following dior trisubstituted alcohols; 2-butene-1,4-diol (BD), pinacol (P), hexane- 1,6-diol (HD), hexane- 1,2,6-triol (HT), octane- 1,&diol (OD). The poly01 molecules are adsorbed flat (parallel) to the surface forming ultrathin films."-" The adsorption of these surfactants contrasts that of normal aliphatic alcohols which adsorb perpendicular to the surface. Therefore we expected that differences in the magnitude of the lateral interactions between the ion and surfactant molecules could be observed on interfaces covered by the films of the two types of compounds. The results of this work are presented in this paper. Tbry There is a general consent that ion deposition reaction proceeds through an adsorbed intermediate called an adion. In the adion state the ion is partially desolvated and partially coordinated by atoms from the metal surface. The deposition of an ion MCt could be then represented
M'+(oHp)
+
M'+ad
+IC
M (Hg)
(1)
(16) I. Miller and M. Blank, J. Colloid Interfoce Sci., 26, 26, 34 (1968). (17) E. Dutkiewicz, J. T. Garnish, and R.Parsons, J. Electroonal. Chem., 16, 505 (1968). (18) S . Trasatti, J. Electroanol. Chem., 28, 257 (1970). (19) F. Pulidori, G. Borgeshani, R. Pedriali, A. Battisti, and S. Trasatti, J . Chem. Soc., Foradoy Trans. 1,74, 79 (1978). (20) V. M.Gerovich, B. B. Damaskin, and R.I. Kaganovich, Elektrokhimiya, 7, 1345 (1970). (21) M. Goledzinowski, J. Dojlido, and J. Lipkowski, J . Electroanal. Chem., 185, 131 (1985). (22) R. I. Kaganovich, B. B. Damaskin, and I. M. Ganzina, Elektrokhimiya, 4, 867 (1968). (23) R. I. Kaganovich, B. B. Damaskin, and M. M . Andrusev, Elektrokhimiya, 5, 745 (1969). (24) G. A. Dobrenkov and L. T. Guseva, Elektrokhimiya, 14,764 (1978). (25) B. E.Conway and J. 0.M. Bock&, Electrochim. Acta, 3,340 (1960). (26) A. S. Baranski and W. R. Fawcett, J . Chem. SOC.,Faraday Tram. I , 76, 1962 (1980). (27) A. S . Baranski and W. R. Fawcett, J. Chem. SOC.,Faraday Trans. 1 , 78, 1279 (1982). (28) W . R. Fawcett and J. S . Jaworski, J . Chem. Soc., Faraday Trans. I, 78, 1971 (1982).
0022-3654/85/2089-3506$01.50/0 0 1985 American Chemical Society
The Journal of Physical Chemistry, Vol. 89, No. 16, 1985 3507
Ion Transfer through Ultrathin Films It is a multistep reaction as only the transfer of z electrons takes place in z one-electron steps. Usually it is believed that the rate of the overall reaction is controlled by a charge-tmasfer step, but there are systems in which the rate of adion formation limits the rate of the overall reaction.2632 This step could be formally regarded as a transfer of the ion from the outer Heolmholtz plane and its energy of activation (oHp) to the adsorbed state M*+,,,, as equal to the energy spend on partial stripping of the ion from its solvation ~ h e l l . ~ ~ - ~ ' Assume that the overall rate of the reaction is controlled by the transfer of the ion from the oHp to the adsorbed state. According to activated complex theory, the rate of reaction can be expressed in terms of the concentration of the activated complex Ct:
u = (kT/h)ct
(2)
and the ratio of the reaction rate in the presence Ug, and absence Ug=o, of adsorbed surfactant can be given as the ratio of concentrations of the activated complex: ue/ue=o = Cte/c:,e-o
(3)
The theory assumes that the activated complex must be in equilibrium with the reactant so that Pt = P M ~ o H P )
(4)
where gzZ+(oHp)is the electrochemical potential of Mz+at the oHp: PMz+(oHp) = pMz+
+ zF42
(5)
and pt is the electrochemical potential of M* in the activated state
P t = P$ + ZF4t
(6)
42and $Jtare the inner potentials at the oHp and reaction plane, respectively, pM+ and pi are the corresponding chemical potentials. The reaction plane must be situated somewhere between the oHp and the electrode surface inside the inner part of the double layer. The inner layer may be regarded as a surface phase and hence the chemical potential pt should depend on the interfacial tension. Assume that the inner layer in the absence and in the presence of the surfactant could be described as a monolayer. In the monolayer approximation pi could be expressed as33-35 pt
=p t
+ R T In xh - yat
(7)
where xt is the mole fractioqft is the activity coefficient, p t is the standard chemical potential of the activated complex, ai is the partial molar area commonly taken as equal to the cross sectional area of the activated complex, and y is the interfacial tension. The chemical potential of the ion a t the oHp could be conisdered equal to pM* in the bulk of the solution. From eq 5-7 the mole fraction is given by
xt
=&-' exp
I
pMz*
- p t + Tat + zF(42 - @$) RT
)
(8)
In the particular case that surfactant is slightly soluble and interacts weakly with MI+,that the electrode reaction proceeds through this same activated complex at the surfactant-free and the surfactant-covered interface, the following conditions are satisfied pM'+,B=O 0
~t ,e-o
%
pMz+,B ~ t . 8
(9)
I. Dandoy and L. Gierst, J . Electroanal. Chem., 2, 116 (1961). N. S. Hush and I. W. Scarrot, J . Electroad. Chem., 7, 261 (1964). W. Gorski and J. Lipkowski, J. Elecfmnal. Chem., 123, 157 (1981). W. Gonki and J. Lipkowski, J . Electroaml. Chem., 133,253 (1982). R. Defay, J. Prigogine, and A. Bellemans, "Surface Tension and Adsorption", Longmans Green and Co., London, 1966. (34) J. C. Eriksson, Ark. Kem., 25, 331, 343 (1966). (35) J. E. B. Randles and B. Behr, J. Elecfroannl. Chem., 35, 389 (1972).
From eq 3 and 8, taking into account condition 9, the ratio of the reaction rate can be given as ue/Ue=o
Ne ft,.~=o = -Ne=o 4.8
rat , + ; ;z
- 42)
1
(10)
where r = 7e-o - ye is the film pressure. The expression for the reaction rate controlled by electron transfer as the rate-determining step was given in our earlier works.5 It reads
where Ne and N8=0 are the tola1 numbers of the molecules in the surface phase in the presence and in the absence of the surfactant, respectively. With the exception being the term which contains the change in the inner potential at the reaction plane A4$, the two expressions are similar. In the absence of detectable adsorption of the reactant ion, the interfacial layer can be regarded as a two-dimensional infinitely dilute solution of the reactant in water in the absence of tensioactive additives, and in the organic solvent when the electrode is covered by the monolayer of a surfactant. The activity coefficient& can then be calculated from the excess function of these solutions with the formula'
RT In y t = GE - Z x I ( 8 C E / 8 x l ) i#
*
(12)
where x , is the mole fraction of the i component of the mixture, denotes the activated complex, A will be used to denote the surfactants, and S the solvent (water). In the most general case when the film can be regarded as a nonathermal mixture of molecules of different sizes, GE is given by3*
*
GE
+
R T Z X ,In ( 8 , / x l ) RTZwIJSl8,
(13)
where 8, is the two-dimensional counterpart of the volume fraction, and wl, is the lateral interaction constant coupled with the lateral interaction energies w,,by the expression RTwlJ
= (wlJ - l / z [ w l j + w l J l ) c
(14)
where c is the coordination number of the two-dimensional lattice. In the particular case when xA 1, which corresponds to the saturation of the electrode surface by the surfactant, and when the concentration of the activated complex is very small so that xt 0, from eq 10-12, with GE given by eq 13, the ratio of the reaction rates could be given in the semilogarithmic form as -+
-
In
(Ve/Ve=o)
=
- ( r t / r ~ ) (-r ~1) + ri(~:,s- w ~ , A )+ f(A$$ (15) wheref(h4J = zFA(& - ~ J ~ ) /orf(A4J RT = ( z - a)FA+JRT -(*at/RT)
when formation of the adion or electron transfer are the ratedetermining steps, respectively. Note that ut,&expresses the interactions between the discharged ion and the contiguous solvent molecules at the surfactant free interface, represents the interactions between the ion and the neighboring surfactant molecules when the surface is covered by the film, and r, = a,/a, is the number of solvent molecules replaced from the interface by one molecule of i. Actually, irrespective of the nature of the rate-determining step, a linear relationship between the logarithm of the rate ratio and the film pressure should be observed. From its slope the cross-sectional area of the ion can be determined. From the intercepts, the difference in the lateral interaction constants and f(A4*) can be estimated. The magnitude of the intercept depends on the nature of the rate-determining step. The character of the rate-determining step should be also reflected in the slope of the Tafel plot. When the reaction is controlled by the rate of adion formation, from eq 2 and 8 (see also ref 26-28) the slope depends on the apparent value of the coefficient: (36) L. Holleck, B. Kastening,.andR. D. Williams, 2.Elektrochem., 66, 396 (1962). (37) B. Kastening and L. Holleck, Talonta, 12, 1259 (1965). (38) E. A. Guggenheim, "Mixtures",Clarendon Press, Oxford, 1952.
Goledzinowski et al.
3508 The Journal of Physical Chemistry, Vol, 89, No. 14, 1985 -0.5
-1.0
-1.5
-2.0
For the electron transfer as the rate-determining step aapp is given by
The surface tension measurements are tedious, subject to systematic error, and not too numerous. Hence it is sometimes convenient to correlate the reaction rate not with the surface pressure but with the concentration of the surfactant in the bulk of the solution, .,c As we have already shown,7 eq 15 could be combined with the differential and integral forms of the generalized adsorption isotherm used to describe surfactant adsorption so that the following relation between the reaction rate and the bulk surfactant concentration is given by
where AGA is the free energy of the surfactant adsorption. An independent derivation of this equation was given earlier by Guidelli et a1.6 In an abbreviated form it was used by a number of authors.4,8-13,37,38 According to eq 18, in the logarithmic coordinates, the plot of the reaction rate against the bulk surfactant concentration should be linear. Its slope should allow the determination of the ratio a * / a Aand the intercept should provide information about the magnitude of the lateral interactions and f ( A 4 J . Below we shall use eq 15 and 18 to describe the transport of cadmium across films of polysubstituted alcohols. Note that for a first-order reaction ve/Ue=o = ks/ks=o,where k is the rate constant. Further in this paper we shall use eq 15 and 18 to describe the changes in the rate constants of the electrode reaction (first-order process).
Experimental Section Reagents, equipment, experimental procedure, and data treatment were described in the preceding papers7 The supporting electrolyte 0.5 M N a 2 S 0 4acidified with H2S04to pH 2.7 was used. Solutions were deoxygenated by argon saturated with vapors of the investigated solution. The time and rate of deoxygenation were carefully controlled because prolonged or vigorous argon bubbling resulted in a decrease of the inhibitor concentration. Electrode kinetics were investigated on the dropping mercury electrode (DME) by chronocoulometric and polarographic techniques. Diffusion coefficients were determined from the limiting polarographic currents and Ilkovic equation. Equilibrium potentials were measured with the pool 5 X M Cd amalgam electrode and 2 X M solution of Cd2+ in a given electrolyte solution. All potentials have been measured vs. the external saturated sulfate (Na2S04) electrode. The measurements were carried out at the temperature 25 f 0.5 OC. Results Relation between the Rate of Ion Transfer and the Film Pressure. The dependence of the rate of ion transfer on the pressure of a film of surface-active species was investigated at a Hg surface covered by monolayer of 1,6-hexanediol (HD). The surface pressure of the H D film has been determined from interfacial tension measurements. The film pressure vs. electrode potential plots are shown in Figure la. The film pressure was differentiated with respect to the logarithm of the bulk concentration of H D a t a constant electrode potential, and the relative Gibbs excesses (r)of the hexanediol were determined. The r values are plotted against the electrode potential in Figure lb. The coverage of the electrode surface by the hexanediol exceeds 90% in the potential range -0.8 to -1.4 V for bulk H D concentration higher than 2.5 X lo-* M. In this range, at constant E , the film pressure could be easily increased by 20 m N m-', by to 0.5 M. increasing the bulk H D concentration from 2.5 X
r x iofo/ mol cm-* 2.0
1.o
Figure 1. (a, top) Film pressure against electrode potential plots at constant bulk H D concentration. (b, bottom) Relative Gibbs excesses of H D against the electrode potential at the following bulk concentrations M; 4, 5 X of the hexanediol: 1, 5 X lo-' M; 2, M; 3, 2.5 X M; 5, lo-' M; 6, 2 X lo-' M; 7, 5 X lo-' M. log k /cm f
,
I
-1 .o
-2.0
-3.0
-4.0
.,
F i p 2. The apparent Tafel plots for Cd2+/Cd(Hg) electrode in 0.5 M Na2! A, a
)4
solution at the following bulk concentrations of the hexanediol:' X, 0.1 M; 0 , 0.05 M; 0.025 M.
M; 0, 0.3 M; A, 0.2 M;
Under these experimental conditions, the kinetics of ion transport across the interface saturated with hexanediol should be well described by eq 15. Tafel plots for the discharge of CdZ+and the anodic dissolution of Cd(Hg) in solutions of different hexanediol compositions are shown in Figure 2. These plots correspond to the region of the mercury electrode that was totally covered by a monolayer of the hexanediol. Note that both the cathodic and anodic reactions display apparent dependence on the bulk H D concentration. The anodic and cathodic branches extrapolated to the equilibrium potential do not intersect. The cathodic branch is nonlinear and displays a characteristic upward bending. The film pressure at a fixed electrode potential is plotted as a function of the electrode potential in semilogarithmic coordinates in Figure 3. In agreement with eq 15, fairly good straight line relationships are observed. The slopes for the anodic and cathodic branches are different but are independent of patential for each of the electrode reactions. From the slopes the cross-sectionalareas of the species transferred across the monolayer of the hexanediol were determined. These values are equal to 0.73 nm2 for the cathodic deposition and to 0.52 nm2 for the anodic dissolution. Note that the values of the cross-sectional areas for the species transported across the monolayer in the cathodic and anodic direction differ. This points out that the species transported across the monolayer in the cathodic deposition is different from the
The Journal of Physical Chemistry, Vol. 89, No. 16, 1985 3509
Ion Transfer through Ultrathin Films
C / p F em'' 1
40
30 20
log k ImS'
- 4.0
- 3.0
-21)
-1 .o
Figure 3. Pressure of the monolayer of 1,6-hexanediol plotted against the rate constant of Cd2+ reduction (black points) and Cd(Hg) oxidation (open points). The values of the electrode potentials (volts) are given at the correspanding plots.
1.o 1.o
12
1.4
Figure 5. The apparent Tafel plots for Cd2+/Cd(Hg) electrode in 0.5 M Na2S04 solution and the following bulk concentrations of pinacol: 0, 0.5 M; A, 0.36 M; U, 0.25 M;A, 0.15 M; 0 , 0.1 M. Insert shows tensametric curves for the supporting electrolyte and different concentrations of the pinacol. The surfactant concentrations in mol dm" are given at the respective curve.
0
-1 .o
-2.0
E/ V
-3.0 -1.0
-1.2
-1.4
Figure 4. The Tafel plots from Figure 2 corrected for term m , / 2 . 3 R T (plot 1) and the apparent plot of Cd2+reduction at the Hg electrode in 0.5 M NalSO4 solution free from surface-active compounds (plot 2).
species transported during anodic dissolution reaction. Next, the Tafel plots were corrected by adding the term ?ra,/2.3RT to each value of the logarithm of the apparent rate constant displayed in Figure 2. The corrected Tafel plots are given in Figure 4. Now the experimental points corresponding to solutions of different concentrations of the alcohol fit one straight line. Keeping in mind that the correction amounted to about two orders of magnitude, one can regard the fit as excellent. The linearity of the corrected Tafel plots points out that the nonlinearity of the apparent Tafel plots reflects the potential-dependent variation of the film pressure. Incidentally, the corrected anodic and cathodic tiranches of the Tafel plots extrapolated to the reversible half-wave potential do intersect at the same point. The slope of these plots corresponds to the factor aaW= 0.23 for the cathodic branch arid to pa, = 1.36 for the anodic branch, respectively (/3 is the anodic charge-transfer coefficient). The sum of aapp and Bappis equal to 1.6. For a reaction controlled by this same rate-determining step in both the cathodic and the anodic direction, the sum should be equal to the total number of electrons transferred which is two. Apparently aapp pa, # z and this reflects that the anodic and cathodic reactions proceed through different rate-limiting steps. This conclusion is consistent with an earlier observation that the cross-sectional area for the activated complex determined from the kinetics of the cathodic and anodic reaction differ. Curve 2 in Figure 4 is the Tafel plot determined in the supporting electrolyte free from surface-active compounds.3g The
+
(39) H.Gerischer and M . Krause, Z . Phys. Chem. (Frankfurt am Main), 10, 264 (1957).
factor aapp determined from the slope of this plot is equal to 0.25 and is equal to the value found from the corrected Tafel plot (curve 1) on the monolayer covered interface. The vertical distance between curve 2 and 1 in Figure 4 amounts to A log k = -0.7 and reflects the contribution from the second, third, and fourth terms of eq 15 to the overall effect of the monolayer on the rate of Cd2+ discharge. To estimate the magnitude of the second term r,&,= aA/asmust be determined. It is not obvious what value of a, should be used in this calculation, since water is believed to be associated into clusters at the interfaceeW2 Should we take a, corresponding to the monomer or to a cluster? To solve this dilemma we assumed the following. Normal aliphatic alcohols are known to conform well to the Frumkin adsorption is0therm.4~ For these compounds rA is equal to 1 and aA is equal to a,. Therefore to determine r A for the hexanediol we took for a, the value of the area occupied a t the surface by one molecule of 1-butanol, which is equal to 0.32 nm2. With this value the term (i*/iA)(rA - 1)/2.3 is determined as equal to 0.35. Therefore r * ( ~- w,,)/2.3 , ~ +f(A$,) can be estimated as equal to -0.3. This indicates that both r t ( w t s - w , , ~ )and f(A$,) are probably small. Relation between the Rate of the Ion Transfer Reaction and the Bulk Alcohol Concentration. The dependence of the rate of the ion transfer reaction on the bulk surfactant concentration was investigated for five different polyols. For four of these surfactants tensametric curves were recorded to determine the concentration and potential range at which the saturation of the electrode surface by a monolayer of the surfactant was attained. Tafel plots for the Cd2+/Cd(Hg) system in the presence of different concentrations of pinacol and 2-butenediol- 1,'I as representative polyols are given in Figures 5 and 6, respectively. In the insets to these Figures the tensametric curves are included. With these tensametric curves and the Frumkin equation
it was possible to estimate the degree of coverage of the electrode (40) R. Parsons, J. Electroanal. Chem., 8, 93 (1964). (41) A. Frumkin, B. Damaskin, N. Grigoriev, and J. Bagotskaya, Elecrrochim. Acta, 19, 69 (1974). (42) R. Parsons, Electrochim. Acta, 21, 681 (1976). (43) B. B. Damaskin, A. A. Survila, and L. E. Rybalka, Elecrrokhimiya, 3, 146, 937 (1967).
3510 The Journal of Physical Chemistry, Vol. 89, No. 16, 1985
11
Goledzinowski et al.
log k Icms-'
C/pFcm-*
BD
-2 .o
,,OH\ c 'v)
E Y Y
-8
-3.0
0 -1 .o
- 4.0 -2.0
-3 .O
-5.0 I
II
I
I
I
I
1.o 1.2 1.4 Figure 6. The apparent Tafel plots for Cdzt/Cd(Hg) electrode in 0.5 M Na2S04solution and the following bulk concentration of 2-butene-1,4diol: 0, 1.4 M; A, 1.0 M;X, 0.75 M; V, 0.5 M; U, 0.4 M; m, 0.3 M; 0 , 0.2 M. Insert shows tensimetric curves for the supporting electrolyte and different concentrations of BD. The butendiol concentrations in mol dm" are given at the respective curves.
I
I
I
't
I
-3.0 -2.0 -1 .o 0 Figure 7. The dependence of the cathodic rate constant on the bulk surfactant concentration at E = -1.04 V for OD (octane-l,l-diol), HD (hexane-1,6-diol),P (pinacol), HT (hexane-1,2,6-triol),BD (2-butene1,4-diol).
TABLE I: Kinetic Parameted for the Cd*'/Cd(Hg) System in the Presence of Polysubstituted Alcohols
surfactant concn, M aPpp j3, 0.26 1.39 2-butene-1,4-diol 1.4 1.0 0.24 0.90 pinacol 0.3 0.19 1.15 1,6-hexanediol 0.32 1.20 1,2,6-hexanetriol 1.0 0.26 1.36 1,I-octanediol 0.01
k,,,/cm s-' 6.9 X IO4 5.7 X 10"
k,,/cm s-I 4.9 X IO-' 4.2 X lo4 6.0 X
1.4 X lo4
1.0 X
3.2
1.6 X IO4
8.1 X
X
.\B
" k , , and k , , are the rate constants extrapolated to the standard electrode potential E, = -1.008 V from the cathodic and anodic branch of the Tafel plot respectively, ann = -(RT/F)(B In k J X ) and fin,, = (RT/F)(BIn k,/BE), k, and k, are the rate constants for the cathodic
and anodic reaction, respectively. surface by the surfactant. It was found that 0 was higher than 0.8 for -1.3 V < E < -0.7 V for pinacol, and -1.4 V < E < -0.8 V for 2-butenediol-1,4 at the bulk surfactant concentrations for which the electrode kinetics was investigated. The Tafel plots are linear in the potential range -1.2 V < E < -0.8 V. The values of aaPp and sa,, and the rate constants extrapolated from the anodic and cathodic regions to the standard potential, for the most concentrated solutions of the polyols investigated, are given in Table I. Within the limits of the experimental error the, ,@, and &,,values are independent of the nature of the surfactant (with exception of Bappfor pinacol) and are equal to the value found for the Tafel plot corrected for a (Figure 4). The standard rate constant extrapolated from the anodic and cathodic regions are never equal. Representative log k against log C, plots, at constant electrode potential, are shown in Figures 7 and 8 for the cathodic and anodic reaction, respectively. In agreement with eq 18 these relationships are linear with slopes equal to u,/u, given in Table 11. From the a,/aA ratio the cross-sectional area of the species transported through the monolayer ( a , ) could be determined provided aA is known. The values of aA were determined from the dependence of E, on the bulk surfactant concentration. E , is the potential of the cathodic desorption peak observed on the tensametric curves. The surfactant concentrations investigated were high enough that the condition ,C >> ( B is the equilibrium constant for the adsorption isotherm) was satisfied and the following equation holds:M In cA = b(E,,, - E,)2 constant (20)
+
Figure 8. The dependence of the anodic rate constant on the bulk surfactant concentration at E = 0.94 V for OD (octane-1,8-diol), HD
(hexane-1,6-diol),P (pinacol), HT (hexane-1,2,6-triol),BD (2-butene1,4-diol). TABLE 11: Cross-Sectional Areas ~~
surfactant 2-butene-1,4-diol pinacol 1,6-hexanediol 1,2,6-hexanetriol 1,8-octanediol
~
anodic cathodic aA/nm2 a,/aA a,/nm2 at/aA a r / n m 2 0.41
1.1
0.5
1.3
0.5
0.45 0.51 0.50 0.62
1.5
0.7
1.6
0.7
0.9 0.9
0.5
1.3 1.2
0.7
0.8
0.5 0.5
1.1
0.6 0.7
where b = uA(C,,, - CO=I)/ZRT.The plots of In CA against (Emx - E,)2 were linear and from their slopes U, was calculated. The aA values are also given in Table 11. These surface areas vary approximately by 0.1 nm2 when the number of the carbon atoms (44) R.
Parsons, Trans. Faraday SOC.,55, 999 (1959).
'
Ion Transfer through Ultrathin Films
The Journal of Physical Chemistry, Vol. 89, No. 16, 1985 3511
in the molecule changes by two. This is consistent with Trasatti's estimation that one CH, group contributes to aA by 0.05 nm2 l9 and points out that the polyol molecules adsorb flat on the surface. Finally, the cross-section areas a , were determined. They are included in Table I1 as well. The average a , value for the cathodic reaction is equal to 0.7 f 0.05/nm2 (the slightly lower value of a, found in presence of the butenediol is probably due to a random error). The average value of a , for the anodic reaction is equal to 0.5 f 0.05/nm2 (again the slightly higher value found in the presence of pinacol is probably affected by a random error).
Discussion Comparison of Theory with Experiment. The results presented above indicate that the experimental data conform perfectly to the predictions of the theory. As foreseen by eq 15 and 18 plots of the logarithm of the rate constant against ?r or log C, are linear. The Tafel plots determined in solutions of different surfactant concentration, when corrected for the film pressure, superimposed to give one linear relationship. The results show that the rate at which the ion is transported across the monolayer critically depends on the ion size or strictly on its cross-sectional area. Thus in a 0.5 M 1,6-hexanediol solution about 80% of the film effect on the rate of Cd2+discharge could be taken into account by the ?ra,/RT term. The cross-sectional area found in this work corresponds to 0.7 nm2. Estimations, with the help of a space-filling model, show that an octahedral Cd(H20),Z+ complex should have a cross-sectional area equal to 0.65 nm2. The experimental data conform well to this value. Therefore we can conclude that the ion transported across a monolayer of a neutral organic species enters into the film together with its first solvation shell. The cross-sectional areas of the species transported across the film in the anodic reaction correspond to about 0.5 nmz and are slightly smaller than the values found for the cathodic process. Presumably, the species going from H g to water is partially solvated by both H g atoms and water molecules. On the other hand, the species going from water to Hg is more strongly solvated by water than by Hg. This confirms earlier observations that the anodic and the cathodic reactions proceed, at least partially, through different rate-determining steps. Comparison of C&+ Permeability through Monolayers of Polyols and Normal Aliphatic Alcohols. It is interesting to compare the present results on the permeability of the polyol films to Cd2+with our earlier investigations on the kinetics of transfer of this ion through the monolayers of normal aliphatic alcohol^.^*^^ Adsorption of the polyols contrasts that of the normal aliphatic alcohols. The di- and trifunctional molecules are adsorbed flat at the i n t e r f a ~ e . ' ~Thus - ~ ~ any change in the hydrocarbon chain length of these molecules affects only the area which they occupy a t the surface. The thickness of the film is roughly the same for all the polyols investigated and should not exceed 0.5 nm. Normal aliphatic alcohols adsorb perpendicular to the surface. In this case changes in the hydrocarbon chain length influence the thickness of the film (for 1-hexanol and I-octanol the thickness is approximately equal to 0.9 and 1.2 nm, r e s p e ~ t i v e l y ~ ~ ) . However, the surface which a given molecule occupies at the interface depends on the chain length only slightly. Thus the two classes of surfactants provide the possibility to look a t how ion permeability through the monolayer depends on the orientation of the surfactant molecule and on the film thickness. The shape of the Tafel plots determined in the presence of the polyols and the normal aliphatic alcohols is similar. The charge transfer coefficients are equal within the limit of experimental error and independent of the nature of the surface active compound (mono- or polysubstituted). Apparently, no differences are observed in the mechanism of the ion transfer through the films of the various surfactants. Recently, Pezzatini et al." reported new data on Cd2+ and a number of other ions discharge across monolayers of normal aliphatic alcohols. They observed a small but with the length of the alcohol molecule. systematic increase of aapp However, the a values reported in ref 11 were not corrected for (45) V. V. Eletsky and Yu. V. Pleskov, Electrokhimiya, 10, 179 (1974).
