The penetration of ions into charged films

THE PENETRATION OF IONS INTO CHARGED FILMS J. T. Davies and Sir Eric Rideal, F.R.S.

Department of Physical Chemistry, University of London, King's College, London, England ABSTRACT It has been shown that the Gouy equations for charged monolayers rest on assumptions which are not valid under certain conditions. These include high charge densities and the presence of large counter-ions. By means of studies of surface viscosities, potentials, pressures, reaction kinetics, desorption rates, dipole moment variations, and zeta potentials, a coherent qualitative explanation of deviations from the Gouy equations has been given. The conditions under which the Gouy equations hold satisfactorily have been stated.

INTRODUCTION The question has often been raised whether a monolayer at an interface can be represented mathematically as a plane. Some authors have been successful in regarding it as such, but others have preferred to treat it as a bulk phase, although a very thin and highly oriented one. This question concerning the use of the third dimension in interpreting surface phenomena is thrown into relief when we come to consider electrically charged films, as of the long-chain quarternary ions, CIsH37N(CH3)~ +, which we can treat either by the G o u y theory or by the Donnan equations. The distribution of the counter-ions is calculated, according to the former theory, on the assumptions that the counter-ions are themselves of negligible dimensions and that the charged surface is a mathematical plane, impenetrable and uniformly charged. The Donnan equations, on the other hand, assume the existence of a "surface phase" of small but by no means negligible thickness. While allowing, in consequence of the latter assumption, for the fact that the counter-ions, as well as the tong-chain ions constituting the monolayer, may not be infinitesimally small, the arbitrary use of a definite thickness of the "surface phase" introduces an additional assumption, even though i t may be shown that the Debye-Hiicket value 1/K for this term leads to reasonable results in certain cases (1). A point in favor of the Gouy theory is that it allows for the intense electric effects due to the interface being unsymmetric electrically; nearly all the lines of force must enter the phase of higher dielectric constant, usually water. In doing this they tend to become parallel (Fig. 1), so that 1

2. T. DAVIES AND SIR ERI(~ RIDEAL AIr

Water surface

D

Lines of force Wa~r

FIG. 1. Lines of force radiating from an array of long-chain ions held in a monolayer. At a short distance below the surface they become almost parallel, leading to intense electric effects. To minimize the number of lines of force entering the nonpolar air or oil, the long-chain ion is pulled below the upper limit of the aqueous phase (represented by the broken line). A, B, C, D represent typical positionswhich can be. taken up by the oppositely charged counter-ions. the electric effects will operate more strongly than if the lines of force radiate spherically symmetrically from each long-chain ion, as in bulk phases and as it is tacitly assumed, in the use of the Donnan equations. In this paper it is pointed out that the Gouy theory, already shown to. account satisfactorily for potential effects in charged interracial films, breaks down under certain conditions, owing to the fact that in practice the surface is neither uniformly charged nor impenetrable. Electric potential measurements per se are rather insensitive to these effects, and here attention has been concentrated on other interracial properties, such as reaction kinetics in charged films, surface viscosity changes, film pressures (i.e., free energies), changes in surface dipole moments, the relation between the potentials and desorption rates in charged films, and the zeta potential. It is suggested that there is a pronounced increase in the penetration .by the counter-ions into and above the plane of the charged groups, especially at relatively high salt concentrations, with counter-ions of low hydration, and in films of high charge density. This is shown in Fig. 1~ where penetration into positions A and B may occur. EXPERIMENTAL ~/[ETHODS

Films of octadecyltrimethylammonium ions, CIsH3~N(CH~)2, were spread following the methods described elsewhere (2). All solvents were redistilled in all-glass apparatus. Salts were of A.R. quality. Potentials were measured using the vibrating plate apparatus, which was suitable for either the air-water interface or that between petrolether and water. Surface viscosities were measured using the canal apparatus described by Joly (3), for which purpose facilities were kindly provided for one of u~ (J.T.D.) by Dr. D. G. Dervichian at the Institut Pasteur, Paris. The accuracy of the results was estimated at 2.5 %--a figure not easily improved

3

PENETRATION OF IONS INTO CHARGED FILMS

on owing to instability of the films at low salt concentrations and because of a tendency for the quarternary salts to wet the threads of the apparatus. Reaction rates were measured by following the rate of change of surface potential. Acid hydrolysis of cholesterol formate monolayers with various amounts of C2~H4~S0~~ incorporated in the film was studied (4). RESULTS

In Figure 2 are compared the surface viscosity, surface dipole moment slope (~/~A), and the film pressure deviation from that forecast from the Gouy equations. In all cases results are for fihns of C~sH37N(CH3)3+ c..) ,.~

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Normal slope

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due to penetration of CI'

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log C F l a . 2. Comparison of v a r i a t i o n s of surface viscosity, slope of ~-A curve, a n d surface pressure increases w i t h increasing c o n c e n t r a t i o n s of NaC1. Results are for the air-water i n t e r f a c e a t room t e m p e r a t u r e . T h e size of t h e chloride ions is compared w i t h t h e Debye-Hiickel t e r m 1/~, t h e l a t t e r r e p r e s e n t i n g a p p r o x i m a t e l y t h e m e a n thickness of t h e diffuse ionic a t m o s p h e r e . T h e surface pressure i n c r e m e n t s are relative to t h e v a l u e on N/100 NaC1. The/2 values are calculated using t h e simple Helmholtz equation, AV = 4vn# (2).

4

J. T. DA¥IES AND SIR ERIC RIDEAL

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FIG. 3. Surface viscosities of films of C~HarN(CHa)a + a t the air-water interface p l o t t e d against I/c } at areas of 85 A.2 and 170 A. 2 per long-chain ion. On the more conc e n t r a t e d NaC1 solutions there is a steep rise in the viscosity of the film of higher charge density, not shown by the more expanded monolayer.

at 85 A.= at the interface between air and aqueous NaC1 solutions. A marked rise in all the curves is evident between 10-* N and 2N NaC1. The decrease in the (~/6A) values between 10-2 N and 0.4 N is in good accord with the Gouy theory. At 180 A.~ the viscosity plot (Fig. 3) does not show any rise; only a continued decrease is observed at higher salt concentrations. Fluoride and iodide ions (added as the sodium salts) show, at 85 A?, effects different from that of CI'. With iodide ions the surface viscosity increases at concentrations above 3 X 10-2 N, with fluoride only above 0.5 N (Fig. 4). Figure 5 shows the relation between ~" and the electrical potential in the plane of the surface at the upper aqueous limits, i.e., along the broken line in Fig. 1. (Here 6 has been calculated from AV by an extrapolation method (5) and is in agreement with the Gouy equations.) The electrokinetic potential ~ has been calculated from the mobilities of oil drops in detergent solutions (6, 7). The relation ~ = 0.55 6 holds quite satisfactorily. The relative differences between ~ and 60 (the potential at the center of each quarternary ion) is shown in Fig. 6. The latter potentials have been calculated (2) from desorption rates, which vary as exp(e6o/taT). The potential 60 has here been equated with 6 at the lowest ionic strength used, i.e., 10-= N.

PENETRATION OF ZO~NS INTO CHARGED FILMS

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FIe. 4. Surface viscosities at the air-water surface for films of C,sH~TN(CH~)a+ spread on solutions of NaF, NaC1, and NaI, of concentration c. The plots (against 1/c ~) show minima, corresponding to higher concentrations, for the more highly hydrated ions. +200

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FIG. 5. Relation between ¢ and f for positively charged films. These include in~ soluble films of serum albumin and hemoglobin (at different pH values) and adsorbed films of cetyltrimethylammonium ions, The potentials ~ and ~"were both measured at the oil-water interface. The ionic strengths were 0.01 for the protein determinations and 0.05 M for the CTA data (6, 7).

6

J . T . DAVIES AND SIR ERIC RIDEAL

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100

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log C 17ze. 6. Difference between ~band ~b0.The form~ (represented -A-) is the potential along the broken line in fig. 1, i.e., at the upper limit of the aqueous phase, and has been obtained, by extrapolation, from electric measurements (2). The latter (represented -(i)-) is obtained from the kinetics of the desorption process (2) and is the potential at the centers of the charged groups in Fig. 1. The difference between these two potentials at high salt concentrations arises from penetration of counter-ions (Cl') into position A (Fig. I). The film in both eases was ClsH37N(CH~)3+ at the air-water interface, and the salt was NaC1.

14 12

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Fro. 7. Catalysis of hydrolysis of films of cholesterol formate by ions of C~H~SOZ included in the film (4). The negative charge due to the latter attracts H + to the surface, thus accelerating the reaction. The effect is greater than predicted by the Gouy equations, probably owing to the fact ~.hat the hydrogen ions can enter the film in positions A and B (Fig. 1).

PENETRATION OF IONS I1NTO CHARGED FILMS

7

Figure 7 shows the results of the superficial acid hydrolysis experiments: catalysis by relatively small amounts of the long-chain sulfate is clearly marked. DISCUSSION

The results show that above a certain salt concentration, which depends on the size of the counter-ions, the basic assumptions of all mathematical treatments (e.g. 8), namely that a charged surface may be treated as a uniformly charged impenetrable plane, break down. Although the Gouy equations for ¢ continue, even at high salt concentrations, to hold approx.imately (2, 5), this must be due to the fact that the effect of ionic size (preventing a close approach of the ions in position C, Fig. i) is roughly compensated by the effect of penetration between the charged heads and above them, in positions B and A. The first will tend to increase ~b, the second, to reduce it. The film behaves as a uniformly charged plane at high areas and at low salt concentrations. It is at smaller areas and with higher concentrations that deviations occur, i.e., for larger ratios of the size of the counter-ions to the distance of separation of the charged "heads" and to the mean thickness of the ionic atmosphere of the counter-ions. The latter is given by the term I/K of the Debye-Hiiekel treatment, in which similar, semiempirical corrections must be introduced at even moderate ionic strengths. Fluoride ion, large because of hydration, is evidently less effective Jn actually penetrating and linking up the charged heads and so increasing the surface viscosity, than are the smaller, less hydrated ions of chlorine and bromine. The relationship between $ and ~"suggests that an important part of the potential drop (in 0.01-0.05 M solutions) occurs in the immobile ionic layers, either in positions A and B, or C (Fig. 1). The difference between and ~0 indicates penetration of CI' at higher concentrations of NaC1, reducing 6 relative to ~0. The kinetic data in Fig. 7 show that the rate of hydrolysis by H + of cholesterol formate films increases at high negative surface charges more steeply than predicted by the Gouy equations or by the Donnan equations (1, 4). This means that either the H + held electrostatically in the surface is more catalytically active than that in the bulk immediately below or that the long-chain sulfate ions are able to attract more H + into the surface than is allowed for in the Gouy equations, owing to penetration into and above the plane of the film. We favor the latter explanation, though further research on this point is required to confirm it. I~EFERENCES i. DAVIES, J. T., riNDRID~AL, E. K., J. Colloid Sci. 3,313 (1948). 2. DnvI~s, J. T., Proc. Roy. Soc. (London) ~-08A,224 (1951).

8

J. T. DAVIS AND SIR :ERIC RIDEAL

3. JoLY, M., Kolloid Z. 89, 26 (1939). 4. LLo~,IS, J., AND DAVIES, J. T., Anales real soc. espa~, fis. y qu~m. (Madrid) B49, 671 (1953), DAvis, J. T., Adv. Catalysis 6 (1954). 5. DAvIEs, J. T., Trans. Faraday Soc. 48, 1052 (1952). 6. DAVIES, J. T., AND CZECZOWlCZKA,N., to be published. 7. ALEXANDER, A. E., AND McM~LLEN, A. I., Surface Chemistry, p. 309. Butterworths, London, 1949. 8. HOSKIN, N. E., Trans. Faraday Soc. 49, 1471 (1953).