On the mechanism of ion transfer across the monolayers of organic surfactants. The mechanism of Cu(II) deposition at Hg electrodes covered by monolayers of aliphatic alcohols

J. Electroanal. Chem., 123 (1981) 351--364

351

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

ON THE MECHANISM OF ION T R A N S F E R ACROSS THE M O N O L A Y E R S OF ORGANIC SURFACTANTS. THE MECHANISM OF Cu(II) DEPOSITION AT Hg ELECTRODES COVERED BY M O N O L A Y E R S OF ALIPHATIC ALCOHOLS

G R Z E G O R Z PYZIK and JACEK LIPKOWSKI

Department of Chemistry, Warsaw University, 02-093 Warsaw, Pasteura 1 (Poland) (Received 18th August 1980; in revised form 19th November 1980)

ABSTRACT The kinetics of deposition of Cu 2+ ion on the mercury electrode covered by monolayers of normal aliphatic alcohols containing from four to eight carbon atoms in the molecule were investigated. The relations between the film pressure or the bulk surfactant concentration and the rate of the electrode reaction were examined. The cross-sectional area of Cu 2+ ion transported through the monolayers was determined, and the magnitude of the lateral interactions between Cu 2+ ion and neighbouring water and alcohol molecules respectively, at the surfactant-free and surfactant-covered electrode surface, was estimated.

INTRODUCTION

Recently the problem of ion transfer across the monolayers of electroinactive neutral organic surfactants, formed at the electrode--solution interfaces, has been the subject of both theoretical and experimental investigations. The relations between the rate of the ion transfer reaction and the bulk surfactant concentration, or the film pressure have been derived [ 1--6 ] and verified [6--13 ]. Most of these investigations have been undertaken as an attempt to explain the inhibitive effect of organic surfactants on the rate of electrode reactions. However, as has been pointed o u t by Miller and Blank [ 1 ], investigation of the mechanism of an ion transfer across the monolayers can be used as a model to simulate processes taking place in biological membranes. This model can be especially useful for displaying the extent of dehydration of an ion penetrating inside the layer of oriented lipid-like surfactants, as well as providing information on the magnitude of lateral interactions between the ion submerged inside the film and contiguous segments of the organic molecules, as recently shown by Guidelli et al. [6]. This paper is one from the series [7,8,10] devoted to the mechanism and kinetics of an ion transfer across monolayers formed at the mercury electrode-solution interface by adsorbed aliphatic compounds. Here the results of the investigations of Cu 2+ deposition at the electrode covered by normal aliphatic alcohols are presented. 0022-0728/81/0000--0000/$02.50, © 1981, Elsevier Sequoia S.A.

352 EXPERIMENTAL Reagents, equipment, experimental pr o cedure and data t r e a t m e n t have been described in the preceding paper [14]. As supporting electrolyte 0.5 M H2SO4 was used. The c o n c e n t r a t i o n o f Cu 2+ was always equal to 10 -3 M. Concentrations of alcohols were always expressed with respect t o the c o n c e n t r a t i o n of the saturated solution Cs, given in Table 1. Electrode kinetics were investigated on the dropping m ercury electrode (DME) by c h r o n o c o u l o m e t r i c and polarographic techniques. The integration time was in the millisecond range in c h r o n o c o u l o m e t r i c experiments. The instantaneous currents at the end of the m e r c u r y drop lifetime were recorded in the case o f polarography. The drop lifetime was always equal to 4 s, and was controlled by an electronic timer coupled with a mechanical hammer. Diffusion coefficients were determined f r o m the limiting polarographic currents and the Ilkovic equation for solutions saturated with the alcohols are given in Table 1. All potentials were measured vs. the external saturated sulphate (Na2SO4) electr o d e (SSE) and were recalculated t o t he saturated calomel electrode (KC1) scale by subtracting - - 410 mV. The measurements were carried out at a temperature o f 25 + 5°C. The adsorption of alcohols has been described in ref. 10. It was f o u n d t hat for all the alcohols investigated here, the electrode surface is covered by a m onolayer (the degree of coverage 0 ~ 1) in the electrode potential range from ~ - - 0 . 4 V to ~ - - 0 . 8 V (vs. SCE), at bulk alcohol c o n c e n t r a t i o n c/cs >1 0.2. The surface pressure data for n-butanol were kindly provided by Dr. Dutkiewicz. The surface pressure data for n-pentanol were calculated from electrocapillary curves given by Hansen et al. [ 17 ]. The Ao points were read o u t from the enlarged p h o t o c o p y of Fig. 4 in ref. 17 with an accuracy o f ~ + 0 . 5 mN m -1, which is regarded as satisfactory in view of the purpose of this paper. The data f o r n-pentanol refer to 0.1 M KF and for n-pentanol to 0.1 M HC104 as supporting electrolytes; t h e y were used in this paper under the assumption t hat for a given reduced c o n c e n t r a t i o n c/cs, A o in 0.5 M H2SO4 and 0.1 M KF or 0.1 M HC104 solution is the same. The free energies of adsorption of n-butanol and n-pentanol were deter-

TABLE 1 Selected experimental data of the system investigated Alcohol n-Butanol n-Pentanol n-Hexanol n-Heptanol n-Octanol

Cs/mol dcm -3 9.5 X 10 -1 1.5 × 10 -1 3.5 × 10 -2 ~7 × 10 -3 ~1 × 10 -3

r,/r A + 0.1

aA/nm 2 [15,16]

a,/nm 2

D / c m 2 s -1 X 1 0 6

1.38 1.51 1.53 1.57 1.65

0.32 0.34 0.36 0.37 0.39

0.44 0.51 0.55 0.58 0.64

4.9 5.2 4.5 4.5 4.5

In the absence of alcohol Dcu2+ = 5.7 × 10-6/cm2 s-l.

353

mined with the help of Aa vs. In cA plots and the relation: AGa°ds(E) = AG°(Ez) + R T A In c A where AG°(E~) is the free energy of adsorption at the potential of zero charge and A In cA is the amount by which the Ao = f(ln CA) curve at E ¢ Ez was shifted along the In CA axis to superimpose with the curve corresponding to Ez. Here, AG°(Ez) for n-butanol was equal to --15.7 kJ mol °1 and to --18.4 kJ m o l - ' for n-pentanol. These values were calculated from AG°(Ez) determined in 0.1 M HC104 [17--19], b y taking into account the correction for differences in the solubilities of the alcohols in 0.1 M HC104 and 0.5 M H2SO4 solutions. THEORY

When the film is formed by surfactants slightly soluble and weakly interacting with the reactant, and the ion transfer reaction proceeds through an activated complex created inside the film, the rate of this reaction is dependent on the film pressure r = --Ao according to the equation [1,4]:

ko _ N~o 7,,O=O exp{.---~a, --(z--c~n)F A~, } ko=o N~=o 7*,0 RT

(1)

where k o and ko=o, ~',.o and 7,.o=o, N~ and N~=o are the rate constants, activity coefficients of the ion in its activated State and number of molecules in the monolayer in the presence and absence of the surface active c o m p o u n d respectively; a, f is the cross-sectional area of the ion; A~, the difference between the inner potential at the reaction plane when the interface is covered and free from the surfactant; a and n are the cathodic charge transfer coefficient and the number of electrons in the rate-determining step; the other symbols have their usual meaning. 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 b y the monolayer of surfactant. The activity coefficient 7, can then be calculated from the excess function of these solutions with the help of the formula [4,20] :

R T l n 7, = GE -- ~ xi(~GE/~xi)

(2)

i¢4

where x i is the mole fraction of the i-component of the mixture, ¢ denotes the activated complex, A will be used to denote the surfactant and S the solvent (water). In the most general case when the film can be regarded as a nonathermal mixture of molecules of different size G E is given by [4,21]

GE = R T ~

xi In (0i/Xi) + R T ~

Cdij0i0 j

(3)

where 0i is the two-dimensional counterpart of the volume fraction, and ¢oij is the lateral interaction constant coupled with the lateral interaction energies wij by the expression: R T c o i j = ( w i j __ ~[wi 1 i+

w~j])c

(4)

354

where c is the coordination number of the two-dimensional lattice. From eqn. (2) in which G E given by eqn. (3) is used, the activity coefficients of the activated complex formed at the free electrode surface and covered by the alcohol can be calculated. In the particular case when x , -~ 0, XA -* 1 the ratio of the activity coefficients simplifies to the expression: V*.o=o/7*.o ~ exp{r,(co,,s -- W*.A) -- ( r , / r A ) ( r A

--

1)}

(5)

where ri is the number of solvent molecules replaced from the interface by one molecule of i. Taking into account relation (5), eqn. (1) can be written finally in the semilogarithmic form as In (ko/ko=o) = - - ( T r a , / R T )

--

(r,/rA)(r

A --

1) + r, (¢~,. s -- 6~,,A ) (6)

- - (z - - cm) F A L p , / R T

According to eqn. (6) a linear relationship between I n k and ~r should exist; from its slope the cross-sectional area of the ion transported through the monolayer can be determined, and from the intercept the difference in the lateral interactions between the ion and the neighbouring solvent molecules at the surfactant-free interface (co,, s) and the contiguous surfactant molecules when the surface is covered by the monolayer (co,, A ) can be estimated. The surface tension measurements are tedious, sometimes subject to systematic errors and n o t too numerous. However, eqn. (6) can be converted into a relation which allows us to correlate the reaction rate not with the surface pressure, but with the concentration of the surfactant in the bulk of the solution [2,6,22,23]. The most general form of this relation, given below, was recently derived by Guidelli et al. [ 6 ] *: ln(ko=l/ko=o) = - - ( r , / r A ) (ln(C A / 5 5 . 5 ) - - A G O d s / R T } + r~ (O)~:,s - - ~ s , n - - ~ # , h )

--

(Z

--

an)FA¢,/RT

(7)

From the plot of the rate constant of the electrode reaction in the function of the bulk surfactant concentration in logarithmic coordinates a linear relationship should be observed. From its slope the ratio r , / r A can be determined and from the intercept the lateral interactions can be estimated. It is worth noting that r , / r A is equal to the ratio of the cross-sectional a r e a s a , / a A and that tArOs,A is equivalent to the lateral interaction constant in the isotherm representing the adsorption of the surfactant molecules usually denoted as a, hence a , / a A = r , / r A and rACO~.A= a, see ref. 6 for details. It is essential to stress that eqns. (6) and (7) represent two forms of the same relationship which can be referred to as integral or as differential respectively, by analogy to the well-known forms of an adsorption isotherm [24,25]. In fact it can be easily shown that these two equations are related by the differential and integral forms of the generalized Frumkin isotherm used to describe the surfactant adsorption. In particular, when the reactant adsorption is negligible

* In ref. 6 the second t e r m of eqn. (7) is given explicitly in terms o f wij coupled with coij by eqn. (4).

355

so that 0¢ -~ 0, and 0 -- 0A one can write: flCA = ~A exp (--2a~A}/(1 -- ~A ) rA

(8)

or

7(

=

- - R T F m { a O ~ + (rA - - 1 ) 0 A + r A ln(1 --0A)}

(9)

where one must keep in mind that a = rAWs,A and moreover fl = e x p { - - A G ° A / R T } / 5 5 . 5

and

aA = 1/Fro

When 0A -~ 1, from eqn. (8) it follows that: rA ln(1 -- 0 A ) -- --2rA ~s. A -- ln(fiCA )

(10)

SO that eqn. (9) becomes = R T F m ( a + 1 -- rA + ln(~CA)}

(11)

Substitution of lr from eqn. (11) into eqn. (6) gives eqn. (7). The advantages of the data treatment according to eqns. (6) and (7) will be compared and discussed below. RESULTS

R e l a t i o n b e t w e e n the rate o f ion transfer and the film pressure

The polarographic curves of Cu 2÷ reduction in the presence of different concentrations of n-butanol are shown in Figs. 1 and 2. The values of the surface pressure of the film created by the alcohols are plotted for comparison in the same figures. These curves are representative for all the alcohols investigated here. It was always observed that, in the presence of alcohol, a characteristic minimum appears at potentials corresponding to the diffusion-limiting current in the absence of the surfactant. This minimum qualitatively reflects the bell shape of the surface pressure-potential plot. The depth and width of the minimum increases as the surface pressure expands in such a way that the upper and lower plots of Figs. 1 and 2 appear as mirror images. The decrease of the current below its diffusion-controlled limit indicates that in the minimum region the polarographic wave becomes irreversible. From these currents the apparent rate constants have been calculated, The rate constants, at a fixed electrode potential, are plotted in function of the surface pressure in semilogarithmic coordinates in Figs. 3 and 4. In agreement with eqn. (6) fairly good straight line relationships are observed with slopes independent of the electrode potential investigated. From the slopes the cross-sectional areas of the Cu 2+ ion transferred through the monolayers of n-butanol and n-pentanol were determined. These values are equal to 0.42 and 0.51 nm 2 for the two alcohols respectively. They are lower than the values of a. reported by Miller and Blank [1] as equal to 0.65 to 0.85 nm 2 from similar investigations of Cu 2+ transfer across the monolayer of d o d e c y l a m m o n i u m ions. However, this difference can be explained by the presence of repulsive interactions between Cu 2+ and positively charged surfactant molecules in the latter system. The dependence of the rate constants on the electrode potential, at constant

356 tmNm-1

~mNm -1

n-butanol

58

4o

,°// 30

1.o

20¸ 10¸ o'.s

/ia°

•

-E/V

10i/i. O,75

0.75

0,5

o.i~

%s

0.15 q25'

o,25

0.2 0.3

0

(~5V

1~) - E/V(SCE)

i

o.5

i.{)oEN(~E)

Fig. 1. T h e d e p e n d e n c e o f t h e surface pressure o f n - b u t a n o l film at t h e Hg e l e c t r o d e surface o n t h e f u n c t i o n o f t h e e l e c t r o d e p o t e n t i a l at c o n s t a n t c o n c e n t r a t i o n o f n - b u t a n o l in t h e b u l k o f s o l u t i o n ( u p p e r part), a n d t h e p o l a r o g r a p h i c curves o f Cu ~÷ r e d u c t i o n in 0.5 M H2SO4 ( l o w e r part). T h e r e d u c e d c o n c e n t r a t i o n s o f n - b u t a n o l - - c / c s are i n d i c a t e d at t h e corr e s p o n d i n g curves. T h e surface pressure curves were c o n s t r u c t e d f r o m t h e d a t a p r o v i d e d b y E. Dutkiewicz. Fig. 2. T h e d e p e n d e n c e o f t h e surface pressure o f n - p e n t a n o l film a t t h e Hg e l e c t r o d e surface o n t h e f u n c t i o n o f t h e e l e c t r o d e p o t e n t i a l at c o n s t a n t c o n c e n t r a t i o n o f n - p e n t a n o l in t h e b u l k o f s o l u t i o n ( u p p e r p a r t ) a n d t h e p o l a r o g r a p h i c curves o f Cu 2+ r e d u c t i o n in 0.5 M H2SO4 ( l o w e r part). T h e r e d u c e d c o n c e n t r a t i o n o f n - p e n t a n o l - - c / c s are i n d i c a t e d a t t h e c o r r e s p o n d i n g curves. T h e surface pressure curves were c o n s t r u c t e d f r o m t h e e l e c t r o c a p i l l a r y curves given in ref. 17.

bulk alcohol concentration, is examined in Figs. 5a and 6a. For all the solutions investigated, these Tafel plots are non-linear, even in the region of full coverage of the electrode by the alcohols. To examine the nature of this non-linearity, eqn. (6) was used and the apparent rate constants were corrected for the term 7ra,/2.3R T. The corrected Tafel plots are placed below the apparent Tafel plots in Figs. 5b and 6b. In the full coverage region the experimental points corresponding to solutions of different concentrations of the alcohols fit one straight line. Keeping in mind that the correction amounted to a b o u t t w o orders of magnitude, the fit can be regarded as excellent. The linearity of the corrected Tafel plots points out that the non-linearity of the apparent Tafel plots reflects the potential dependent variation of the film pressure. The slope of the corrected Tafel plots is independent of the nature of the alcohol and corresponds to the factor an = 0.35.

357 T/mNm 4

.

.

n - butanol

/,0

20

_

_~

_',

-

_~

.

-

'~

.

-

_~ _,~ B/c= s-3

,n

Fig. 3. T h e d e p e n d e n c e o f t h e r a t e c o n s t a n t o f Cu 2+ r e d u c t i o n at c o n s t a n t e l e c t r o d e p o t e n tial o n t h e surface pressure o f t h e m o n o l a y e r o f n - b u t a n o l a d s o r b e d at a n Hg e l e c t r o d e . T h e values o f t h e p o t e n t i a l in volts, m e a s u r e d vs. SCE, are i n d i c a t e d a t t h e c o r r e s p o n d i n g plots.:

The Tafel plot determined from chronocoulometric experiments in the supporting electrolyte solution free from surface-active compounds is also included in Figs. 5b and 6b. The factor an determined from the slope of this plot is equal to 0.4 and is slightly higher than on the monolayer covered interface. The formal rate constant determined at the formal potential of the overall two-electron reaction (E ° = --10 mV vs. SCE)is equal to 2 × 10 -2 cm s -1. These values are in reasonable agreement with the recent literature data [26--28]. It is apparent that the correction for ra,/2.3RT did not take into account the whole effect of the film on the Cu 2÷ ion reduction. In solutions saturated with the alcohols the difference in the apparent rate constants on the surfactant-free and mono-

,rnNm -1 n-pentar~l

g

20

-0.5 -0.7

-06

-9

-8

-7

-6

-5

-0.8

-4

Fig. 4. T h e d e p e n d e n c e o f t h e rate c o n s t a n t o f Cd 2+ r e d u c t i o n at c o n s t a n t e l e c t r o d e p o t e n tial o n t h e surface pressure o f t h e m o n o l a y e r o f n - p e n t a n o l . T h e values o f t h e p o t e n t i a l in volts, m e a s u r e d vs. SCE, are i n d i c a t e d at t h e c o r r e s p o n d i n g plots.

358

log k ~p

n-pentanol

--I.0

log kap p

i.

n -abutoTnol

-1.0

0ti,

,

<

-2,0

-2.o -3,0

t\\\

-3,0

-/..0

6Z/

-Z,.O -5,0.

-/,,5

0

0.5

1,0

-E

log

/

,'A

2.0

-3.0

. z.l -3,0

\ a'2s

o.;

o)s

1.d -EIV(SCE)

19.

-E

t@

..,J

-1.0

-2.0 -

Oi5V

Og k c o r ] ®

i

,I/° -1.0

0 0

t

®

Y/ /-'1

,,t)I/

-/. D 0

0.25

0.5

0.75

1,0

- EIV(SCE)

Fig. 5. (a) The apparent Tafel plots of Cu 2÷ reduction at the Hg electrode in 0.5 M H2SO4 at constant concentration of n-butanol in the bulk of the solution expressed as C/Cs: (e) 1.0; (A) 0.5; (m) 0.3; (o) 0.2; (v) 0.1. (b) The apparent Tafel plot of Cu 2+ reduction in 0.5 M H2SO4 solution free from surface-active compounds (plot 1), the Tafel plots from Fig. 5a corrected for the term rra,/2.3RT (plot 2) and for the term (r$/rA){log(cA/55.5) -AG°/2.3RT} (plot 3). Fig. 6. (a) The apparentTafel plots of Cu 2+ reduction at the Hg electrode in 0.5 M H2SO4 at constant concentration of n-pentanol in the bulk of the solution expressed as C/Cs: ($) 1.0; (X) 0.75; (A) 0.5; (1) 0.4; ([]) 0.25; (o) 0.2; (v,) 0.1. (b) The apparent Tafel plot of Cu2+ reduction in 0.5 M H2SO4 solution free from surface-active compounds (plot 1), the Tafel plots from Fig. 6a corrected for the term ga,/2.3RT (plot 2) and for the term (r,/2.3rA){In(CA/55.5 ) -- AG°/RT} (plot 3).

layer c o v e r e d surface a m o u n t s ' t o a b o u t six orders o f m a g n i t u d e . T h e c o r r e c t i o n f o r 7ra,/2.3RT r e d u c e s this d i f f e r e n c e t o o n l y f o u r orders, so the r e m a i n i n g t e r m s o f eqn. (6) have t o be responsible f o r such a p r o n o u n c e d i n h i b i t i o n o f this ion t r a n s f e r reaction.

Relation between the rate of ion transfer and the bulk alcohol concentration T h e d e p e n d e n c e o f t h e rate c o n s t a n t o n t h e bulk s u r f a c t a n t c o n c e n t r a t i o n was investigated f o r all n o r m a l aliphatic alcohols f r o m n - b u t a n o l t o n - o c t a n o l .

359

The representative log k vs. log CA plots, at constant electrode potential are shown in Fig. 7. In agreement with eqn. (7) these relationships are linear with the slopes equal to the values of r, IrA given in Table 1. Within the region of the monolayer coverage of the electrode by the alcohols, these r , / r A values are independent of the potential. They agree well with the value of r , / r A = 1.5 -+ 0.1 found by Afanasev et al. [ 11 ], from similar investigations of Cu 2÷ transfer across the monolayer of n-butanol. As r , / r A is equal to the ratio of the cross-sectional areas a , / a A and the crosssectional areas of the alcohols are available in the literature, the cross-sectional area of the Cu 2. ion can be determined. The values of a, calculated in this way as well as the cross-sectional a A taken from the literature are inserted in Table 1. For two alcohols, n-butanol and n-pentanol, the apparent Tafel plots given in Figs. 5a and 6a were corrected with the help of eqn. (7) for the terms ( r , / r A ) {Iog(c A/Cw) - - G O d s / 2 . 3 R T } .

The corrected Tafel plots are placed in Figs. 5b and 6b, together with the Tafel plots corrected for the term ~ a , / 2 . 3 R T . Again the experimental points corresponding to solutions of different concentrations of the alcohols fit one straight line well, parallel to the plot constructed with the use of the surface pressure data. According to eqns. (6) and (7), at the constant electrode potential, the corrected Tafel plots represented by curves 2 and 3 in Figs. 5b and 6b should be separated by a distance A log k equal to: A log k = r, COs.A/2.3 -- ( r , / r A ) ( r A - - 1)/2.3

(12)

The values of A log k taken from Figs. 5b and 6b are equal to 0.65 -+ 0.1 and 0.95 + 0.1 for n-butanol and n-pentanol respectively. The adsorption of aliphatic alcohols is known to obey the Frumkin isotherm, hence rA = 1 and the parameter W,,A is estimated as 1.1 + 0.15 and 1.45 + 0.15 respectively, for the two alcohols. These data are in excellent agreement with the values of the lateral interac-

-3.0

-20

-1.0

[og(cA/mOI 1-1)

Fig. 7. Plots o f log k vs. log c A for Cu 2+ r e d u c t i o n in 0.5 M H2SO 4 a t E = - - 0 . 6 V vs. SCE in the presence o f normal aliphatic alcohols containing f r o m f o u r t o e i g h t c a r b o n atoms in the molecule.

360 tion parameter of the Frumkin adsorption isotherm generally reported in the literature; compare, for example, with the value 1.28 for n-butanol and 1.48 for n-pentanol determined by Damaskin et al. [15] at the potential of zero charge. The small potential variation of the interaction parameter reported in ref. 15 is below the accuracy of determination of ¢~s,A in the present experimental conditions. DISCUSSION The results presented above indicate unambiguously that eqns. (6) and (7) describe the process of an ion transfer across the monolayer of organic surfactants well. As has been pointed out by Miller and Blank [1], the rate of water evaporation at the air--solution interface covered by the monolayer of neutral organic molecules can be described by a relation essentially similar to eqn. 6 of this paper [29]. In fact, this relation is of more general character and can be used to describe the rate of both an ion and a neutral molecule transfer across the monolayers formed at various types of interface. The rate of such a process depends on two factors: (a) on the cross-sectional area of the transported species, and (b) on the magnitude of the lateral interactions of the transported species with the contiguous molecules within the monolayer. The value of a, determined here for the Cu 2÷ ion, in average equal to 0.55 -+ 0.1 nm 2, is comparable with the cross-sectional area of the octahedral aquocomplex estimated by Afanasev [11] as ~ 0.4 nm 2. This agreement suggests that cupric ions are transported across the monolayer together with their first hydration shell. The small t e n d e n c y of the cross-sectional area to increase as the length of the hydrocarbon chain of the alcohol increases can be observed. This tendency reflects either some deviations of the systems investigated here from the monolayer model on which derivation of eqns. (6) and (7) is based, or an increase of the effective van der Waals radius of the transported ion. The increase of the van der Waals radius can be understood as, by passing from n-butanol to n-octanol, the ions have to penetrate more deeply into the hydrocarbon, hydrophobic part of the monolayer. Hence, t h e y are more and more isolated from the bulk of the solution and their net interactions with the contiguous alcohol molecules become increasingly repulsive. The magnitude of the lateral interactions can be estimated with the help of Figs. 5b and 6b. According to eqn. (6), when rA = 1 at constant electrode potential, the Tafel plot determined in the absence of the surfactant (curve 1) should be separated from the corrected plot in the presence of surfactant (curve 2) by A log k', equal to: A log k ' = l o g ( k o / k o = o ) + ~ r a ~ / 2 . 3 R T = (r~/2.3) (~t,s -- ~*,A) + (Z - - c~n) F A ~ , / 2 . 3 R T

(13)

In fact, plots 1 and 2 in Figs. 5b and 6b are not exactly parallel, but the value of A log k' can be estimated at E = --0.25 V as equal to --3.9 and --4.2 for n-butanol and n-pentanol respectively. The term (z - - c~n) F , ~ , / 2 . 3 R T can be estimated only roughly with the help of Payne's [30] data on SO~- adsorption from neutral solutions. In 0.5 M Na2SO4 at E = --0.2 V the electrode charge

361

density qM is equal to +8.6 pQ cm -'2 and the charge of adsorbed SO42 ion ql is equal to --14.5 pQ cm -2 and hence the outer Helmholtz plane potential ~2 is equal to --25 mV. When the electrode is covered by the monolayer of n-butanol or n-pentanol the electrode charge density is close to zero, and under these circumstances ~2 is also negligibly small. Piccardi and Guidelli [27] have shown recently that the effect of C1OZ ion adsorption on the rate of Cu 2÷ deposition can be well described by the simple Frumkin formula represented b y the second term of eqn. (9) with A~, taken as equal to A~:. Assuming that adsorbed SO~ions have no electrocatalytic effect on Cu 2÷ reduction and that there is no appreciable ion pairing between Cu 2÷ and SO~- in the interface, the term (2 - - a n ) F A~2/2.3RT can be estimated as equal to 0.7. However, the adsorption of the sulphate depends on pH due to equilibrium H ÷ + S O ~ - ~ HSO~ and simultaneous adsorption of the HSO~ ion. Hence, in 0.5 M H2SO4 the a m o u n t of adsorbed charge probably differs from the value determined in 0.5 M Na2SO4 solution. However, even in the case of stronger adsorption of HSO~ than SO~ions, as the valency of the adsorbed ion decreases, one can hardly expect that the negative values of ~02 will increase. Hence, one can estimate that the second term of eqn. (13) should n o t appreciably exceed 1.0 and the term r,(eo,.s -¢0,.A)/2.3 should be of the order of --3.0. Finally w,.s -- ¢O,.A can be estimated as equal to --4.5. For further discussion of the physical meaning of the interaction constants estimated above the kinetics of Cu 2÷ transport across the monolayers of n-butanol and n-pentanol were compared with the rate of the transfer of the Cd 2+ ion. The rate constants of Cd 2÷ deposition in the presence of different concentrations of n-butanol and n-pentanol had been taken from refs. 10 and 31 and were corrected for:

~ra,/2.3RT

(curve 2)

or

(r,/rA){log(cA/55.5)- AG°ads/2.3RT~ (curve 3) terms with the help of eqns. (6) and (7) respectively. The corrected Tafel plots are presented in Figs. 8 and 9 where they are compared with the plot determined in the supporting electrolyte solution free from the surface-active compounds b y Gerischer and Krause [ 32] (curve 1). At constant electrode potential the distance between plots 2 and 3 gives the Frumkin interaction constant which was found to be equal to ~ 1.2 for n-butanol and ~ 1.5 for n-pentanol, in good agreement with the literature values. The distance between curves 1 and 2 is equal to --0.25 -+ 0.05, irrespective of the nature of the alcohol. At the electrode potentials more negative £han --0.6 V the sulphate ions are no longer adsorbed [30], and in the vicinity of E = --0.6 V the electrode charge density in the absence and presence of the alcohols is of comparable magnitude. Hence, in the first approximation A~2 can be taken as zero, and with r, = 2.4 taken from ref. 10, co,. s -- ¢o,. A can be estimated as equal to - 0 . 2 5 . On the contrary, with the phenomena observed in the case of Cu 2÷ transfer in similar circumstances the lateral interactions of the Cd 2÷ ion are negligible. Large negative values of co,, s -- W,.A can be expected if either (a) strong repulsive interactions between the activated complex and contiguous alcohol

362 10- log ~ / c m s-~Cd 2÷

n-butQno[ v'

log~/cm s-1~Cd2+

-1,0-

~- ~.~=-

- 1,0

o.

=&v~

.

o

n-pentonol

v

@

-20

-

-3.0-

2,0-

" -3.0.

04

a

o9'

ld

1; -E/V SCE

0,7

O.g

0.9

1.0

1,1

- E/V (SCE)

Fig. 8. The apparent Tafel plot of Cd 2+ reduction at the Hg electrode in 0.5 M Na2SO4 solution free from surface-active compounds (plot 1), the Tafel plots corrected for the term ~a,/2.3RT (plot 2) and for the term (r,/2.3rA){ln(CA/55.5) -- AG°~/RT} (plot 3) in 0.5 M Na2SO4, 10 -3 M H2SO4 and various concentrations of n-butanol expressed as C/Cs: (e) 1.0; (o) 0.85; (X) 0.75; (~) 0.5; (El) 0.4; (") 0.3; (A) 0.2. Fig. 9. The apparent Tafel plot of Cd 2÷ reduction at the Hg electrode in 0.5 M Na2SO4 solution free from surface-active compounds (plot 1), and the Tafel plots corrected for the term ~a,/2.3RT (plot 2) and for the term (r,/2.3rA)(ln(CA/55.5) --AG°ds/RT} (plot 3) in 0.5 M Na2SO 4 + 10 -3 M H2SO4 and various concentrations of n-propanol expressed as c/cs: (¢) 1.0; (©) 0.85; (X) 0.75; (~) 0.5; (m) 0.3; (A) 0.2.

molecules at the m o n o l a y e r covered surface (positive values of ~*.A) are dominant over co,,s, or (b) attractive interactions between activated com pl ex and contiguous water molecules at the surfactant-free interface (negative value of co,.s) are stronger than co,. A. In the first case one can e x p e c t t hat ion--dipole interactions should c o n t r i b u t e mainly to the ~*,A observed. These interactions are inversely proportional to the square of the ion--dipole distance, so a rough measure o f the relative magnitude of the ion--dipole interactions can be the ratio o f the cross- sectional areas of Cd 2+ and Cu 2÷. The ratio ac~2*/acd2+ is equal to 0.6 which is a b o u t an order of magnitude less than the ratio of the interaction constants. Hence co,,~ must be the leading term, and the energy spent to overcome attractive ion--water interactions when the activated c o m p l e x is transferred f r o m the surfactant-free to the monolayer-covered surface c o n tributes mainly to the co,,~ -- ~*,A values observed. This conclusion is exactly the same as tha t reached by Guidelli et al. [6], but our estimations of the magnitude o f the lateral interactions, especially for Cd 2÷, differ from the values presented in ref. 6. An open question as to, w hy ¢o,,~ for Cu 2÷ and Cd 2÷ ions differ so m uch remains. The difference in ~,,~ is paralleled by a noticeable difference in the cross-sectional areas ~ 0 . 5 nm 2 f or Cu 2÷ and ~ 0 . 8 nm 2 for Cd 2÷. This indicates that Cu 2+ ions penetrating inside the film are less h y d r a t e d than Cd 2+ ions. However, the conventional free energy of h y d r a t i o n of Cu 2÷ is higher t han t he free energy o f h y d r a t i o n of the Cd 2+ ion [33], so the opposite t e n d e n c y to dehydration could be expected. However, while the Cd 2÷ aquo ion has a m ore or less ideal octahedral structure, the octahedral configuration of Cu 2÷ is markedly dis-

363

torted due to the Jahn--Teller effect, and this aquo ion readily undergoes structural changes, as for example octahedral--tetragonal transition [34,35]. Maybe it is merely a change of the configuration which is responsible for the decrease of the cross-sectional area, and the energy spent to force this transition is contributing to an appreciable a),,s value. However, more broad comparative material is needed to make a more definite conclusion in this regard. In conclusion, investigations of ion transfer reactions across monolayers of organic surfactant can provide information about the ion size and magnitude of interactions of the ion with its environment at the interface. If possible the rate of the process investigated should be correlated with the surface pressure exerted by adsorbed surfactant molecules, as then direct information about the cross-sectional area of the ion investigated and about the difference of lateral interactions of the ion, both at free interfaces and those covered by surfactants, can be determined. If surface pressure data are lacking the rate can be correlated with the bulk surfactant concentrations. Then however, only the ratio of the cross-sectional areas of the ion in respect to the surfactant molecule can be determined, and moreover the lateral interaction term contains the constant of lateral interactions between adsorbed surfactant molecules. ACKNOWLEDGEMENT

The authors express their gratitude to Prf. Z. Galus for m a n y helpful discussions, to Prof. E. Dutkiewicz for making the surface data for n-butanol adsorption available and to Prof. R. Guidelli for helpful criticism of the first version of this paper and for sending the manuscript of his work prior to p u b l i c a t i o n . This work was sponsored by the Polish Academy of Sciences through contract No. 03.10. REFERENCES

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

J. Millet a n d M. Blank, J. Colloid I n t e r f a c e Sci., 26 ( 1 9 6 8 ) 26, 34. J. L i p k o w s k i a n d Z. Galus, J. Electroanal. Chem,, 61 ( 1 9 7 5 ) 11. B.B. D a m a s k i n a n d B.N. Afanasev, E l e k t r o k h i m i y a , 13 ( 1 9 7 7 ) 1 0 9 9 . J. L i p k o w s k i a n d Z. Galus, J. E l e c t r o a n a l . Chem,, 98 ( 1 9 7 9 ) 91. R. Guidelli a n d M.L. Foresti, J. E l e c t r o a n a l . Chem., 77 ( 1 9 7 7 ) 73. R. GuidelU, M.L. Foresti a n d M.R. MonceUi, J. E l e c t r o a n a l . Chem., 1 1 3 ( 1 9 8 0 ) 171. J. L i p k o w s k i , E. Kosifiska, M. G o l e d z i n o w s k i , J. Nieniewska a n d Z. Galus, J. E l e c t r o a n a l . Chem., 59 ( 1 9 7 5 ) 344. M. G o l e d z i n o w s k i , J. L i p k o w s k i a n d Z. Galus, E l e k t r o k h i m i y a , 13 ( 1 9 7 7 ) 646. G.J. Avilova a n d B.N. Afanasev, E l e k t r o k h i m i y a , 13 ( 1 9 7 7 ) 1 0 9 9 . M. G o l e d z i n o w s k i , L. Kisova, J. L i p k o w s k i a n d Z. Galus, J. E l e c t r o a n a l . Chem., 95 ( 1 9 7 9 ) 43. B.N. Afanasev, G,J. Avilova a n d N.A. Borisova, Ukr. Khim. J., 4 4 ( 1 9 7 8 ) 15, 370. E. MUllet a n d H-D. D6rfler, J. E l e c t r o a n a l . Chem., 99 ( 1 9 7 9 ) 1 1 1 . L.D. K u c h a r e n k o , A.V. Lisogut a n d B.N. Afanasev, E l e k t r o k h i m i y a , 16 ( 1 9 8 0 ) 291. L. Kisova, M. G o l e d z i n o w s k i a n d J. L i p k o w s k i , J. E l e c t r o a n a l . Chem., 9 5 ( 1 9 7 9 ) 29. B.B. D a m a s k i n , A.A. Survllla a n d L.E. R y b a l k a , E l e k t r o k h i m i y a , 3 ( 1 9 6 7 ) 146. R. Bennes, J. E l e c t r o a n a l . Chem., 1 0 5 ( 1 9 7 9 ) 85. R.S. Hansen, D.J. Kelsh a n d D.H. G r a n t h a n , J. Phys. Chem., 67 ( 1 9 6 3 ) 2 3 1 6 . K.G. Baikerikar a n d R.S. Hansen, J. Colloid I n t e r f a c e Sci., 52 ( 1 9 7 5 ) 2 7 7 . R.S. Hansen, R.E. M i n t u r n a n d D.A. H i c k s o n , J. Phys. Chem., 6 0 ( 1 9 5 6 ) 1 1 8 5 . J.W. R o w l i n s o n , L i q u i d s a n d Liquid Mixtures, Butterworths, London, 1 9 5 9 . E.A. G u g g e n h e i m , Mixtures, C l a r e n d o n Press, O x f o r d , 1 9 5 2 . L. Holleck, B. K a s t e n i n g a n d R.D. Williams, Z. E l e k t r o c h e m . , 66 ( 1 9 6 2 ) 3 9 6 . B. K a s t e n i n g a n d L. Holleck, Talanta, 12 ( 1 9 6 5 ) 1 2 5 9 .

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R. Parsons, Trans. Faraday Soc., 51 (1955) 1518. R. Parsons, J. Electroanal. Chem., 7 (1964) 136. J.R. Burrows, K.L. Dick and J.A. Harrison, Electrochim. Acta, 21 (1976) 81. G. Piccardi and R. GuideUi, J. Electroanal. Chem., 90 (1978) 173. T. Hurlen, A. Staurset and E. Eriksrud, J. Electroanal. Chem., 83 (1977) 263. R.J. Archer and V.K. La Met in V.K. La Mer (Ed.), R e t a r d a t i o n of Evaporation by Monolayers, Academic Press, New York, 1962. R. Payne, J. Electroanal. Chem., 60 (1975) 183. M. Goledzinowski, Ph.D. Thesis, University of Warsaw, Warsaw, 1977. H. Gerischer and M. Krause, Z. Phys. Chem. N.F., 10 (1957) 264. R.M. Noyes, J. Am. Chem. Soc., 84 (1962) 513. T.J. Swift and R.E. Connick, J. Chem. Phys., 37 (1962) 307. T.J. Swift, Inorg. Chem., 3 (1964) 523.