Effects of counterion specificity on the interactions between quaternary

J. Phys. Chem. 1986, 90, 2145-2150

2145

Effects of Counterion Specificity on the Interactions between Quaternary Ammonium Surfactants in Monolayers and Bilayers Johan Marra Department of Applied Mathematics, Research School of Physical Sciences, Australian National University, Canberra, ACT, Australia (Received: September 19, 1985; In Final Form: December 12, 1985)

Results are presented of the effects of counterion specificity on the measured forces between bilayers of dioctadecyldimethylammonium (DOA) salt surfactants deposited on mica, and on the contraction of DOA monolayers at the air/water interface. The anions investigated are F, AcO-, OH-, C1-, Br-, Sod2-, and CO:-. The binding affinity of these anions follows a lyotropic series where the least hydrated ions bind strongest. The same is true for the ability of the anions to contract a DOA monolayer. However, the monolayer contraction cannot be explained only from differences in the double-layer free energy emerging from the different degrees of ion-binding. Stern-layer effects seem to be very important as we11 and show a correlation with the effective size of the anions. The results provide new insight into intra- and intermembrane interactions of quaternary ammonium salt surfactants and shed new light on the relative importance of ion-binding and Stern-layer effects. In addition they are of central importance to the understanding of the effects of counterion specificity on the geometry of surfactant aggregates (e.g., micelles, vesicles).

Introduction Recently, a strong interest has grown around the phenomenon of the spontaneous formation of vesicles of dialkyldimethylammonium salt surfactants.’,* Many of these surfactant salts like the fluoride, acetate, and hydroxide salts are very soluble in water, give isotropic solutions up to high surfactant concentrations, and form stable vesicles sporitaneously. This is in sharp contrast to the extensively studied vesicle systems of phospholipid^,^ which require sonication to facilitate vesicle formation and are often unstable, eventually reverting to a liquid-crystalline lamellar phase. In general, these vesicles are not monodisperse either. As the theory concerning the equilibrium statistical mechanics of self-assembly of dilute surfactant solutions is well establi~hed,~’ it is important to have access to equilibrium systems which can be subjected to intensive scrutiny. The dialkyldimethylammonium salt surfactants provide such a system. The theory of the assembly of surfactants can be characterized in terms of the geometric parameter v / a l . Here, v is the volume of the hydrocarbon region of the surfactant, a is the optimal head group area, and I is an optimal hydrocarbon chain length related to its maximum extended length. The theory relates the shape of the aggregates to the value of v / a l (1) spherical micelles, v/al < (2) globular or cylindrical micelles, < u / a f < (3) < v / a l < 1. These criteria demand that vesicles or bilayers, if vesicles are the desired structure, one is normally restricted to double-chained surfactants (larger u). Single-chained surfactants are required for micellar stuctures. The relationship between aggregate geometry and surfactant structure has received considerable but specific counterion effects have remained largely unexplored? The present study deals with specific counterion effects. Attention is given to the possible influence which counterion adsorption and Stern-layer effects can have on the aggregate geometry (via its effect on the optimal headgroup area a ) . In general, counterions will adsorb to some extent to the surfactant headgroups. This ~

~~~

(1) Ninham, B. W.; Evans, D. F.; Wei, G. J. J . Phys. Chem. 1983, 87, 5020. (2) Brady. J. E.; Evans, D. F.; Kachar, B.; Ninham, B. W. J . Am. Chem. Soc. 1984, 106, 4279. (3) Fendler, J. “Membrane Mimetic Chemistry”; Wiley: New York, 1983

and references listed therein. (4) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J . Chem. SOC., Faraday Trans. 2 1976, 72, 1525. ( 5 ) Israelachvili, J. N.; Mitchell, D. J.; Ninham. B. W. Biochim. Bionhvs. . _ Acta.1977, 470, 185. ( 6 ) Carnie, S.; Israelachvili, J. N.; Pailthorpe, B. A. Biochim. Biophys. Acta 1979, 554, 340. (7) Evans, D. F., Ninham, B. W, J . Am. Chem. SOC.,in press. (8) Brady, J.; Evans, D. F.; Warr, G.; Grieser, F.; Ninham, B. W. J . Am. Chem. SOC.,submitted for publication.

0022-3654/86/2090-2145$01.50/0

not only alters the electrostatics on the aggregate surface, but also might change the hydrophobic-hydrophilic nature of the surface through specific interactions of a nonelectrostatic origin9 (dehydration of the surfactants, conformational changes in the surfactant headgroup, etc.) Also, Stern-layer effects, where the distance of closest approach of an unbound counterion to the surface is considered,’~8Jo deserve attention. Here, the size of the ion becomes important because it determines the thickness of the Stern layer and the actual surface potentia1.l’ Specific interactions can greatly change the lateral interactions between surfactants in a monolayer or bilayer. This has been shown recently with measurements on the negatively charged phospholipids ph~sphatidylglycerol’~ and pho~phatidylserine.~ Specific effects have also been found to exist in the spontaneous formation process of vesicles of quaternary ammonium salt surfactants’J3v’4and are evidently responsible for the phenomenon of counterion-dependent cmc’s (critical micelle concentrations) and aggregation numbers in micellar solution^.^^^ They also have shown up dramatically in three-component ionic microemulsions.I6 An understanding of these processes enables one to elucidate specific counterion effects, other than counterion valency. A logical way to attack this problem is to establish first the amount of ion adsorption and second its consquences on the lateral interactions between adjacent surfactant molecules. In the present study use is made of the direct force measurement technique of Israela~hvili.’~Bilayers of the cationic surfactant dioctadecyldimethylammonium bromide (DOABr) are deposited with the Langmuir-Blodgett technique on two molecularly smooth mica surfaces. By bringing these surfaces together in an aqueous solution, it is possible to measure the interaction between the bilayers as a function of the bilayer separation. Because the bilayers carry an electrical surface charge, a repulsive double-layer force is experienced. Fitting the measured double-layer force with theoryi8 allows the surface potential to be estimated, from which (9) Ohshima, H.; Ohki, S. J. Colloid Interface Sci. 1985, 103, 8 5 . (IO) Stigter, D. J . Phys. Chem. 1975, 79, 1015. See also. Beunen, J.; Ruckenstein, E. J . Colloid Interface Sci. 1983, 96, 469. ( 1 1) Hunter, R. “Zeta Potential in Colloid Science”; Academic: London, 1981. (12) Marra, J., Biophys. J., submitted for publication. (13) Talmon, Y.; Evans, D. F.; Ninham, B. W. Science 1983, 221, 1047. (14) Hashimoto, S.; Thomas, J. K.; Evans, D. F.; Mukerjee, S.; Ninham, B. W. J . Colloid Interface Sci. 1983, 95, 594.

(15) Porte, G.; Appell, J. In “Surfactants in Solution”; Mittal, K. L., Lindman, B., Eds.; Plenum: New York, 1982; Vol. 2, p 805. (16) Evans, D. F.; Mitchell, D. J.; Ninham, B. W. J . Phys. Chem., submitted for publication. (1 7 ) Israelachvili, J. N.; Adams, G. E. J. Chem. Soc., Faraday Trans. 2 1978. 7 4 . 975. (18) Chan, D. Y. C.; Pashley. R. M.; White, L. R. J . Colloid Interface Sci. 1980, 77, 283.

0 1986 American Chemical Society

2146 The Journal of Physical Chemistry, Vol. 90, No. 10, 1986 the binding affinity of the ions can be Next, the monolayer compression isotherm of DOA is measured on an aqueous electrolyte subphue. At a particular headgroup area, the surface pressure of the film is recorded as a function of the electrolyte species present in the subphase. This yields information about changes in the lateral interactions between the surfactants, which is expected to have a relation to the equilibrium surfactant headgroup and hence the curvature of a surfactant aggregate through the geometrical factor u/al. Direct force measurement between (planar) bilayers are also of use in the evaluation of the intervesicle interactions. The latter can be obtained by a simple scaling of the measured bilayer interactionZoas long as the vesicles are large compared to the range of the intervesicle interaction. Apart from the repulsive double-layer interaction, the van der Waals interaction and possibly the ion-ion correlation interaction,21,22which are both attractive, must be taken into account and can cause the aggregation of vesicles into larger structures. The intervesicle interactions are important to explain the phase behavior of surfactant aggregates as a function of the surfactant concentration.* Using the direct force measurement technique, Pashley et al.23 investigated the interactions between bilayers of dihexadecyldimethylammonium acetate and bromide surfactants. Because these surfactants are soluble in water, they could be adsorbed from solution as a bilayer onto the mica surfaces. The advantage of this adsorption from solution method is that the adsorbed bilayers and the surfactants in solution necessarily form an equilibrium system. A disadvantage is that at low electrolyte concentrations, the aggregates in solution have an effect on the measured double-layer force between the adsorbed layers, which is hard to quantify especially when the geometry of the aggregates is unknown. With the Langmuir-Blodgett deposition technique for an insoluble surfactant like DOABr, the solution does not contain any aggregates and provides an infinite reservoir of electrolyte. Finally, it can be expected that the general binding behavior of anions to the quaternary ammonium headgroups responsible for the electrostatics on the amphiphilic surfaces, will not depend sensitively on the precise length of the hydrocarbon tails and the results obtained here with DOA salt surfactants should be of relevance to shorter surfactants as well. Of course, the packing of the surfactants and the geometry of the surfactant aggregates do depend on the hydrocarbon chain length but this can be accounted for4-6 as long as the optimal headgroup area remains approximately the same. Materials and Methods Dioctadecyldimethylammonium bromide (DOABr) surfactants were purchased from Eastman Kodak, Co., Rochester, NY, and recrystallized before use. Water was purified by distillation, treatment overnight with activated charcoal, filtration through a 0.05 pm pore size nucleopore filter, and a final distillation from an all-glass still. The inorganic salts used were of AnalaR grade. AnalaR grade hexane was further purified by double distillation. Monolayer compression isotherms were measured in an allTeflon Langmuir trough; measurement of the surface tension was done using the maximum pull on a vertical rod method as described by Paddy et al.24 DOABr was spread from a 9:l hexane/ethanol spreading solvent on water. Concerning the Langmuir-Blodgett deposition of the surfactants on mica, a series of calibration depositions was carried out on large rectangular mica sheets of 40 cm2 surface area, to obtain the transfer ratios at different deposition pressures. The transfer ratio is the ratio of the area per molecule in the monolayer on water (19) Pashley, R. M. J. Colloid Interface Sci. 1981, 83,531. (20) Verwey, E. J. W.; Overbeek, J. Th.G. “Theory of the Stability of Lyophobic Colloids”; Elsevier: Amsterdam, 1948. (21) Guldbrand, L.; Jonsson, B.; Wennerstrom, H.; Linse, P. J. Chem. Phys. 1984, 80, 2221. (22) Kjellander, R.; Marcelja, S. Chem. Scr.1985, 25, 112. (23) Pashley, R. M.; McGuiggan, P. M.; Ninham, B. W.; Brady, J.; Evans, D. F. J . Phys. Chem., submitted for publication. (24) Padday, J. F; Pitt, A. R.; Pashley. R. M. J. Chem. Soc., Faraday Trans.I 1915, 74.915.

Marra

Headgroup area

(B’)

Figure 1. Monolayer compression isotherms of DOA a t 22 “ C on different electrolyte solutions: (a) 1 mM NaAc or 1 m M N a F ; (b) 1 mM NaOH + 2 X M NazCOl or 1 m M N a O H + 1 m M Na,CO,; (c) pure water; (d) 1 mM Na2S04; (e) 1 mM NaCl + 1 mM Na,SO,; (f) 1 mM NaCI; (9) 1 m M NaBr.

to that actually being deposited on the mica. In order to deposit a bilayer, two depositions have to be carried out consecutively. In previous work,25it was found that deposition of a first layer of dipalmitoylphosphatidylethanolamine(DPPE) at a surface pressure of 32 dyn/cm gives a very hydrophobic outer surface (headgroups down on the mica) when the mica is slowly raised out of the water in the Langmuir trough (sides vertical with respect to the water surface). This hydrophobic surface is particulary suitable for deposition of a second layer of other surfactants. In this way a second layer of DOA was deposited at various surface pressures on top of the DPPE layer when the mica is brought down into the water again. In general, the deposited headgroup area appeared to depend on both the applied surface pressure and the electrolyte species present in the subphase in the Langmuir trough. However, at surface pressures >25 dyn/cm, the transfer ratios were always found to be close to 1:l and the deposited headgroup areas follow directly from the measured monolayer compression isotherms (see Results). A detailed description of the Langmuir-Blodgett deposition, analogous to the procedure followed here, can be found in ref 2 5 . Interactions between bilayers of DOA surfactants were measured by using the direct force measurement technique developed by Israelachvilli. This technique is described in detail elsewhere” and only a brief summary will be given here. Use is made of two thin (thickness C 10 Mm) molecularly smooth mica plates, silvered on one side with a high-reflecting silver layer of about 500 A thickness, which are glued down on two cylindrically curved silica-glass disks with a curvature radius R of about 1 cm. Before the silica disks are mounted in the force measurement apparatus, a bilayer is deposited on each mica surface. Once this is done, the glass disks with the mica surfaces attached are transferred under water in small glass beakers from the Langmuir trough to the force measurement apparatus where they are mounted. This procedure is necessary since the bilayers lose their outer monolayer when the surfaces are retracted from the water. One of the silica disks is mounted on a rigid support, and the other, facing the first one, is positioned on a spring with a known spring constant. When the surfaces are brought together, at some stage they will exert a force onto each other, which can be measured through the deflection of the spring. The separation between the two surfaces is measured simultaneously with an optical technique using fringes of equal chromatic order or FECO interferometry.26 From the position and shape of the FECO fringes seen in the spectrometer, the distance D between the two surfaces can be measured with an accuracy of 1-2 A. By measuring the deflection of the spring (the surface force) as a function of the surface separation, the full force law is obtained. The force F(D)is converted into the interaction energy E(D)per unit area between two planar surfaces (25) Marra, J. J. Colloid Interface Sci. 1985, 107,446. (26) Israelachvili, J. N. J . Colloid Interface Sei.1973, 44, 259

Counterion Specificity of Cationic Surfactants

The Journal of Physical Chemistry, Vol, 90, No. 10, 1986 2147

according to E(D) = F(D)/2nR, (the Derjaguin approximation2').

Results Monolayer Compression Isotherms. Figure 1 gives the monolayer compression isotherms of DOA salts at T = 22 OC for different electrolyte species present in the subphase. (The concentration of the original surfactant counterions Br- becomes negligible as soon as the monolayer is spread on water.) The subphase containing 1 mM Na2C03also contained 1 mM NaOH to ensure the complete ionization of the C032- ion. It is clear that the properties of DOA depend strongly on the type of counterion, indicating a pronounced ion specificity. The fluoride, acetate, and carboxylate surfactant monolayers are completely of the liquid-expanded type whereas the sulfate, chloride, and bromide surfactant monolayers all show a phase transition from the liquid phase to the condensed phase. Because this phase transition occurs at different surface pressures for the various counterions, the critical temperature beyond which no phase transition occurs must depend on the type of counterion. An interesting observation is that the ability of the anions to contract the monolayer follows a lyotropic series in the order Br> C1- > F.This is also the order in which the anion becomes increasingly hydrated, suggesting that the specificity of the counterions is directly related to their hydration. The monolayer contraction on a subphase containing a mixture of N a 2 S 0 4and NaCl is intermediate between the observed contractions in the presence of only NaCl or Na2S04. The Equilibrium Headgroup Area. Before the forces between DOA bilayers in various electrolyte solutions could be measured accurately, a problem arose concerning the deposited headgroup area. When the deposition was carried out in pure water, giving a deposited headgroup area of 60 A2 (1:1 transfer ratio at a surface pressure of 32 dyn/cm, see Figure l ) , and 1 m M N a F was subsequently added, some of the surfactant molecules seemed to get pushed out of the bilayers. This became apparent when the interbilayer forces were measured: at a surface separation D N 30 A, the repulsion became much stronger than was expected from the double-layer forces alone. On application of a force FIR N 60 000 mdyn/cm, a layer of material suddenly got squeezed out and the bilayers came to the position D = 0, where bilayer contact occurred before the addition of NaF. Consecutive force vs. distance measurements gave much less repulsive forces, but some additional repulsion at short bilayer separations remained. The same phenomenon, but to a lesser extent, was observed when 1 mM N a O H was added into the apparatus. Then the material between the bilayers was squeezed out at a force FIR 10000 mdyn/cm. These observations are not surprising when the monolayer compression isotherms in Figure 1 are studied again. At a headgroup area of 60 AZ,the surface pressure, and hence the surface energy, increases substantially when NaOH, and especially NaF, is added to the subphase. The pressure can be reduced when the headgroup area becomes larger, which in the case of a deposited bilayer is only possible when a number of surfactant molecules is pushed out of the bilayer. Indeed, no additional bilayer repulsions were observed when the deposition was carried out from a 1 mM NaF-containing subphase, giving a deposited headgroup area of 70 A2 at a deposition pressure of 32 dyn/cm. Following these preliminary investigations, it was decided to deposit bilayers from a subphase containing 1 m M N a F when forces in N a F or alkaline solutions were to be measured. In all other cases, the deposition was done in pure water, choosing a headgroup area of 60 A2. Forces between DOA Bilayers. Figures 2 and 3 give the forces between DOA bilayers as a function of their separation in pure water, solutions of the monovalent ions NaC1, NaF, and NaOH, and solutions of the divalent ions Na2S04and Na2C03. At large separations, only a repulsive double-layer force is measured. At shorter range, typically less than 30 A, the interaction becomes attractive: at the surface separation where the gradient of the (27) Derjaguin, B. V. Kolloidn Zh. 1934, 69, 155.

1

0

L

8

12

16

20

2L

28

32

D (nm) Figure 2. Measured forces between DOA bilayers in various electrolyte solutions at 22 OC: (a) 1 mM NaF; (b) 1 mM NaC1; (c) 1 mM NaOH 2X M Na,CO,; (d) 1 mM Na2S04. The inward and outward jumps are indicated by inward and outward arrows. The solid curves are the theoretical curves with charge regulation in which a Hamaker conJ has been used. stant of 6 X

+

0

16 20 2L 28 32 D (nm) Figure 3. Measured forces between DOA bilayers in various electrolyte solutions at 22 OC: (a) pure water; (b) 1 mM NaCl + 0.1 mM Na2S0,; (c) 1 mM NaF + 1 mM NaOH 0.89 mM Na2C0,; (d) 1 mM NaCl 1.2 mM Na2S04. The inward and outward jumps are indicated by inward and outward arrows. The solid curves are the theoretical curves with charge regulation in which a Hamaker constant of 6 X J has been used.

+

L

8

12

+

surface force equals the spring constant, an instability occurs and the bilayers jump into adhesive contact. The position D = 0, where the surfaces came at rest after an inward jump occurred, appeared to be essentially a hard wall. Because the DOA headgroups are exposed at the bilayer surface, a logical choice is to take D = 0 as the outer Helmholtz plane (OHP) where the diffuse doublelayer charge originates, and also as the van der Waals plane where the van der Waals interaction of hydrocarbon across water becomes infinitely large. With this reference distance, the tail of the force curves in Figures 2 and 3 can now be analyzed by fitting the curves to the theoretical double-layer repulsion based on the Poisson-Boltzmann theory.'* In doing so, it became apparent that the fitted surface charge density was always well below its value for the fully charged bilayer. The easiest way to explain this is through ion binding which partly neutralizes the bilayer surface. By inserting ion binding into the double-layer theory, it becomes possible to obtain the surface potential $o and surface charge uo as a function of the surface separation, and (by extrapolaton) the surface potential and the surface charge density uomexisting when the bilayers are well separated. At shorter separations, the surfaces interact with each other and both the surface potential and the surface charge will change because of a regulation of the ion binding.Iq The general expression for uo" in terms of is (at 25 "C)

2148

The Journal of Physical Chemistry, Vol. 90, No. 10, 1986

Marra

TABLE I: Double-Layer and Adhesion Results for DOA Bilayers at 22 'C"

electrolyte concn monovalent 1 mM NaF 1 mM NaCl 1 m M NaOH

2 X lo-' M Na2C03 1 mM Na,SO,

3 X lo-' M (pure water) 1 mM NaCl 1 niM NaF 1 mM NaOH 1 mM NaCl

+

BO-

$0-9

divalent

0.1 mM Na2S04 0.89 mM Na2C03 1.2 mM Na2S04

mV

C/m2

A2/charge

178 154 97 35 213 72 49 40

0.0603 0.0367 0.0172 0.0063 0.0214 0.0122 0.0132 0.0100

265 436 930 2540 748 1308 1209 1595

K, M-' monovalent divalent

EO9

Do

20 60

0.32 3.18

3.6 2.2

30

0.96 0.64 1.43

3.2 4.1 3.0

dyn/cm

A

9

0 12

0 75 12

20 12

30

"The presence of a background electrolyte concentration of 3 X M with a binding constant K = 75 M-' is always taken into account separately. Go = surface potential; uoo = surface charge; K = binding constant; Eo = adhesion energy; Do = equilibrium separation. where uoQis expressed in C/A2 and Cj is the concentration in moles/liter of theIZhionic species with valency zj. When binding of an anionic monovalent ion C to a cationic bilayer takes place, the binding can be described through an intrinsic binding constant Kc using a mass-action law relating the ion concentration in the bulk [C-1, to the number density of bound ions on the surface [SC],. The association constant Kc for the reaction

where [Sf],, the surface density of charged unbound surfactant headgroups, is (for any surface separation) given by (3) In eq 3, use is made of the Boltzmann distribution of ions in a potential field. With the total surfactant density [SIo= [S'], [SC], we have for the net charge density

+

go

= e[S+Io

(4)

and the final expression where the surface potential and surface charge are related to each other via the binding constant (for any surface separation) becomes KC

=

(e[SIo - 'To) exp(-e$o/kr) .o[C-I-

(5)

When several ionic species C, of valency zi bind simultaneously to the surfactant headgroups, eq 4 will contain more terms. However, a mass-action equation similar to eq 3 can be written down for each ionic species as long as a 1:l binding mode is assumed to exist where each anion binds to only one surfactant headgroup. Of course, this will also complicate the relationship between uo and go (in terms of several binding constants), but equations analogous to eq 5 can be derived readily. It has been shown previo~sly'~ that this so-called surface charge regulation model gives double-layer forces which are intermediate between the predicted forces when the surfaces are supposed to interact at constant surface potential or at constant surface charge, respectively. It appeared that even in ''puren water a considerable amount of ion binding to the bilayers has to be taken into account. From the measured Debye length, the ionic concentration seems to be about 3 X M (assumed to be monovalent) and must mainly stem from ions leaking out of the glassware, the stainless steel force measurement apparatus, and dissolved CO,. This effect is disturbing but can be separated out by assigning a separate binding constant to the background electrolyte. When this is taken into account, the binding of the other electrolyte species can be investigated independently. The analyzed double-layer parameters Go" and uomand the binding constants are given in Table I. In the present study, it was noted that the theoretical force curves calculated with charge regulation were very close to the predicted force curves at constant potential, whereas the constant surface charge case always clearly predicted too repulsive forces. F ions do not appear to bind at all but C1- ions do. That there is a difference between the binding affinity of F and C1- ions is

already clear from the observation in Figure 2 that the forces between DOA bilayers in a 1 mM NaF solution are more repulsive than in a 1 mM NaCl solution. Note that addition of 1 mM NaCl or N a F to pure water results in an increase of the net surface charge density. This is a consequence of the lowering of the surface potential through the screening effect of the added electrolyte which decreases the surface concentration and hence the binding of HC03- ions to the DOA headgroups (the binding affinity of C1- ions to the headgroups is much lower than the binding affinity of the background electrolyte). Addition of 1 mM NaOH results in an interbilayer force that is much weaker. However, it must be remembered that at pH 11, all the dissolved CO, is present in the divalent carboxylate ion C032-form. From the measured pH 5.4 in pure water and the literature values for the dissociation constants of H 2 C 0 3and HCO; it is readily calculated that the equilibrium C032- concentration must be about 2 X M. Assuming that only the C032- ions bind to the surfactants, a binding constant Kco, = 20 M-' was inferred. In a medium containing 1 mM NaOH, 1 mM NaF, and 0.89 mM Na2C03, the same value for Kco, emerged assuming again no OH- binding. The agreement indicates that the binding affinity of OH- ions is probably very small and unimportant in solutions containing Na2C03. Addition of Na2S04, or mixtures of Na2S04and NaCl, leads to interbilayer forces which also indicate considerable binding of the sulfate counterions. The adhesion force Fo was measured as the force needed to separate two curved bilayers in adhesive contact. This adhesion force between curved bilayers is related to the interfacial free energy per unit area, Eo,of two planar bilayers at their equilibrium separation D = Do by21 Eo = F0/2aR

(6)

( R is the curvature radius of the two curved surfaces). At D = Do, the interaction forces between two planar bilayers is zero.28 Measured values for Eo are given in Table I. Assuming that the origin of the adhesion force stems completely from the sum of the van der Waals force and the double-layer force, we have at the distance D = Do for the adhesion free energy (7) The first term on the right of eq 7 is the expected form for the (nonretarded) van der Waals attraction with A the Hamaker constant. The second term is the double-layer force at D = Do. For hydrocarbon interacting across water, the theoretically expected value for the Hamaker constant is about 6 X J.29 (For bilayer separations less than the bilayer thickness, which is about 50 A, the van der Waals contribution from the mica surfaces can safely be ignored.29) Using this value, together with the theoretically extrapolated magnitude of the double-layer force near bilayer contact, we can obtain values for Do from the measured Eo with the help of eq 7. Although this procedure must be ap(28) Marra, J. J . Colloid Interface Sci., in press. (29) Mahanty, J.; Ninham, B. W. 'Dispersion Forces"; Academic: New York, 1976.

Counterion Specificity of Cationic Surfactants proached with caution, since a macroscopic theory is extrapolated into the molecular regime, the results in Table I for Doshow that already a small difference in Docan lead to a large change in Eo. In a way, the distance Do can be called the distance range of a short-range hydration repulsion between the bilayers which together with the double-layer force) regulates the adhesion energy between two planar bilayers;28 see curve a in Figure 3. The differences between Do in various electrolyte solutions are likely to be related to the difference in the size of the trapped counterions between two bilayers in adhesive contact. Do is larger for C032than for SO-: counterions, showing that the former has a larger hydration radius than the latter. It is expected that the lesser the hydration of the ions is the greater their binding affinity will be. Indeed, the binding constant Kso, was found to be larger than Kco,. The same is true for the lesser hydrated C1- ion as compared to the strongly hydrated F and OH- ions. The force curves in Figures 2 and 3 are fitted with the theoJ. However, the surface retical Hamaker constant A = 6 X separations where experimentally an inward jump occurred were always a little farther out than predicted theoretically, and the predicted surface forces below 25 A surface separation were somewhat too repulsive. Possible reasons for this will be given in the Discussion section. It is evident from the previous observations in Figures 1-3 that the various monovalent and divalent ions induce different surface interactions. It is interesting to investigate how much of the observed differences between the various monolayer compression isotherms in Figure 1 can be explained through the differences in the diffuse double-layer free energy of the monolayers. Now, the double-layer contribution IIel to the observed surface pressure II is given byZo

ne'=

d$,"

where eq 1 for uoDmust be used. For monovalent electrolyte of concentration C (moles/liter), the integration is straightforward and yields

Here, ne'is obtained in J/A2. Using the values in Table I for pure water, 1 mM NaCI, and 1 mM NaF, the calculated values for riel are 1.O,1.7, and 2.9 dyn/cm, respectively, at headgroup areas of about 60-70 A. The occurrence of phase transitions in the monolayer isotherms makes an exact analysis impossible, but it can be seen that the monolayer isotherm on pure water is indeed shifted upward by about 2 dyn/cm when a 1 mM N a F subphase is used. On the other hand, the monolayer isotherm on a 1 mM NaCl subphase is well below the one on pure water whereas theory predicts that the He' on a 1 mM NaCl subphase is larger than on pure water. It also can be shown that when eq 8 is used for the monolayer isotherms on 1 mM N a 2 S 0 4 and 1 mM N a 2 C 0 3 subphases, a value IIel < 1 dyn/cm results, Le., lower than the values for IIel on the monovalent electrolyte containing subphases. Nevertheless, the isotherms are seen to be quite expanded. Apparently, the lateral interactions between DOA salt surfactants cannot be explained from double-layer theory alone and another explanation involving Stern-layer effects related to the nature of the counterions must be sought. Discussion From the previous results, it has emerged that both lateral interactions in a DOA monolayer and interactions beween bilayers of DOA surfactants exhibit a pronounced ion specificity. Large hydrated counterions like the fluoride, hydroxide, and acetate ions give expanded monolayer compression isotherms. Pashley et al.23 and Brady et ale8report that like what has been found here for fluoride and hydroxide, acetate counterions also do not bind to the DOA headgroups. Following the lyotropic series F > C1> Br-, the smaller the (hydrated) anion, the more contracted the

The Journal of Physical Chemistry, Vol. 90, No. 10, 1986 2149 monolayer compression isotherm becomes and the stronger the counterions bind to the DOA bilayer. Pashley et aLZ3found that the intrinsic binding constant KBris about 6 times larger than the Kcl found in the present study, in agreement with this expectation. Also, the somewhat more hydrated C032-ions show a lesser degree of binding than ions. However, the monolayer contraction in Figure 1 cannot be explained from the decrease in the double-layer free energy alone. Especially, when divalent counterions are added, the double-layer free energy is quite small and cannot explain the fairly expanded nature of the monolayer isotherms. The latter indicates a significant repulsive lateral interaction between the surfactant headgroups. It should be remembered that the surface potentials given in Table I are potentials at the outer Helmholtz plane. The previous observations indicate that the actual potential at the surfactant headgroups is quite different. This is only possible when a finite gap or a Stern layer exists between the OHP and the headgroups. The idea of a Stern layer between the OHP and the headgroups has also been used by Ninham et a1.]S8to explain the unusual properties of didodecyldimethylamnium hydroxide vesicles. The drop in the potential across the Stern layer is proportional to its thickness." Here the nature of the counterions plays a role, since the width of the Stern layer should be related to the counterion size. With this, it can be explained why monolayers on a Na2C03 subphase are quite expanded while the double-layer potential at the OHP is only small. The introduction of small counterions like C1- leads to much higher double-layer potentials but gives contracted monolayer isotherms. To quantify this matter further is only possible when the dielectric constant in the region between the headgroups and the O H P is known. Force measurements cannot resolve this issue and only from the analysis of the monolayer compression isotherm can we obtain an idea about the actual headgroup size and headgroup interactions in a surfactant aggregate. The binding constants are evaluated by using the existing potential at the OHP. Because the plane in which the counterions bind is probably somewhat further in, it is clear that the procedure followed here to obtain the magnitude of the binding constants is only an approximation and this might explain why the Kso, is lower in a mixture of NaCl and N a 2 S 0 4than in a solution of N a 2 S 0 4only. In solutions of quaternary ammonium hydroxide surfactants, small vesicles are formed spontaneously which become larger when, for example, bromide counterions are added.' The increase in the value of the geometric factor u / d , which is responsible for the vesicle growth is as we now understand only partly due to the decrease of the double-layer free energy and probably mostly due to the decrease of the potential drop across the Stern layer. From the monolayer compression isotherms, it can now be predicted that upon titration of hydroxide vesicles with Na2C03,the size of the vesicles should remain fairly constant. The stability of the vesicles against aggregation however should decrease. It was noted that at small bilayer separations, the predicted repulsion was somewhat too large. Several explanations can be given for this discrepancy. It may be questioned whether continuum double-layer theory holds at surface separations where the separation is smaller than the average distance between two surface charges (discreteness of charge effects). Also, the simple charge regulation model that has been used might then become inadequate. Furthermore, the work of Kjellander and Marcelja22 should be mentioned, in which an extra attractive interaction is predicted to exist comparable to the van der Waals interaction due to correlations between adsorbed (but laterally mobile) ions on the surfaces and correlations between ions (especially divalent ions) in the diffuse double layers. Unfortunately, the theory has not been worked out completely and an unresolved issue is the deconvolution of the surface charge regulation and the ion-ion correlation effect. Whatever the precise cause may be, the interbilayer interactions in Figures 2 and 3 can be predicted correctly by using a Hamaker constant of (8-10) X lo-'' J, i.e., slightly higher than the theoretical hydrocarbon-water Hamaker constant of 6 X J.28

J . Phys. Chem. 1986, 90, 2150-2156

2150

Overall, the simple double-layer theory with charge regulation as used in this study is able to describe the experimental data extremely well. Acknowledgment. I acknowledge Professor B. W. Ninham and

Drs. J. N. Israelachvili and R. M. Pashley for discussions and valuable comments. Registry No. DOA’F, 461-16-5; DOA’AcO-, 13308-45-7; DOAfOH-, 51822-75-4; DOA’Cl-, 107-64-2; DOA+Br-, 3700-67-2; (DOA+)2S0,2-, 18469-21-1; (DOA+)2C032-,100683-04-3.

Voltammetry at Polymer-Modifled Statlonary and Rotating Microelectrodes. Application to Determinatlon of Electron-Transfer Rates at Polymer/Solution Interfaces Thomas E. Mallouk, Vince Cammarata, Joseph A. Crayston, and Mark S. Wrighton* Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 021 39 (Received: September 26, 1985; In Final Form: January 10, 1986)

Voltammetric behavior of rotating disk and band microelectrodes with critical dimensions of 0.25-25 pm has been examined in solutions containing electroactive species. The microelectrode is fabricated to be in the plane but about 4 mm off the rotation axis of an insulating rotating disk. Such electrodes exhibit mass transport limited current densities which are 5-30 times higher than their macroscopiccounterparts. This enhanced mass transport rate follows from equations previously derived for rotating ring electrodes. Rotating microelectrodes were functionalized with polymers derived from N,N’-bis((p-trimethoxysilyl)benzyl)-4,4’-bipyridinium(I, [(BF‘Q2+),],,,J, N,N’-bis((trimethoxysilyl)propyl)-4,4’-bipyridinium (11, [ (PQ2+)JSu~), and 1,I’-bis[N-(3-(triethoxysilyl)propyl)carboxamide]cobalticenium (111, [CO(C~R)~+],,,,,~). Steady-state currents, measured as a function of rotation rate for thermodynamically favored, polymer-mediated reductions of Ru(NH3)3+, C~(bpy),~+, and Cr3+-phenanthrolinecomplexes, are in quantitative agreement with theory for such polymer-mediated redox processes. Values of rate constants for the polymer/redox couple electron-exchange reactions are found to be in the range 3 X l o 5 to > 4 X 107 M-1 s-I. Rough agreement was found between measured rate constants and those calculated from the Marcus outer-sphere cross-reaction relation, although the calculated values were systematically higher.

Central to the study of electrocatalysis a t polymer-modified electrodes are measurements of electron-transfer rates between solution substrates and surface-bound redox centers. Often, transient voltammetric techniques, which are useful in performing kinetic analyses at the electrode/polymer and electrode/solution interface,]-, are not applicable to the study of the polymer/solution interface. Transient techniques are less useful, because the current associated with oxidation or reduction of the electroactive polymer often dominates the transient response. Steady-state voltammetric techniques (using, for example, polymer-coated rotating disk electrodes) can, however, yield kinetic information concerning the polymer/solution interface. This problem has been elucidated in considerable theoretical detail by Anson and Saveant and their c o - ~ o r k e r s . The ~ basic electron-relay scheme corresponding to one case in their theoretical treatment, case C (no substrate permeation of the polymer film), is shown in Scheme I. In this scheme, the rate constant for electron cross-exchange, ket, can be determined experimentally by measuring ik, the electron exchange limited current, at a rotating disk electrode (RDE). The experimentally observed current, iobsd,at a RDE is related to ik by eq 1 .4 The subscript notation used is consistent with that of ref 1/iobsd= 1 / i L

+ 1 / i E + 1 / i k + ( 1 / K - l ) i o b s d / i E i L (1)

4: iL is the Levich or solution mass transport limited current, iE (1) Bard, A. J.; Faulkner, L. R. Electrochemical Meihods; Wiley: New York, 1980. (2) (a) Matsuda, H.; Ayabe, Y. Z . Elektrochem. 1955, 29, 494. (b) Nicholson, R. S.; Shain, I. Anal. Chem. 1965, 37, 190. (c) Nicholson, R. S. Anal. Chem. 1965, 37, 1351. (d) Nicholson, R. S.; Shain, I. Anal. Chem. 1964,36,706. (e) Nicholson, R. S.; Shain, I. Anal. Chem. 1965, 37, 178. (0 Klingler, R. J.; Kochi, J. K. J. Phys. Chem. 1981, 85, 1731. (g) Heinze, J. Ber. Bunsenges. Phys. Chem. 1981, 85, 1096. (3) (a) Howell, J. 0.;Wightman, R. M. Anal. Chem. 1984,56, 524. (b) Howell, J. 0.; Wightman, R. M. J. Phys. Chem. 1984,88, 3915. (4) (a) Andrieux, C. P.; Dumas-Bouchiat, J. M.; Savbnt, J.-M. J . Electroanal. Chem. 1982, 131, 1. (b) Andrieux, C. P.; Savtant, J.-M. J. Electroanal. Chem. 1982, 134, 163. (c) Anson, F. C.; Savtant, J.-M.; Shigehara, K.J . Phys. Chem. 1983,87,214. (d) Anson, F. C.; Savbant, J.-M.; Shigehara, K. J. Am. Chem. SOC.1983, 105, 1096. (e) Andrieux, C. P.; Saveant, J.-M. J. Electroanal. Chem. 1982, 142, 1 .

SCHEME I: Mediated Redox Reaction of a Solution Redox Reagent at a Polymer-Modified Electrode

Electrode

+,,$gr

Electrolyte Solutton

is the maximum polymer current, and K is the equilibrium constant for the cross-exchange redox reaction occurring at the polymer/ solution interface. Experimentally, in order to measure k,,, the aim is to make iE and iL sufficiently large that the ik term dominates in eq 1. A large value of iE is achieved by minimizing the polymer thickness, and a large value of iL is achieved by using a large rotation rate. In previous studies in these laboratorie~,~ kinetic data in quantitative agreement with the theory4 were obtained at a polymer-modified RDE. These and other studies6*’have shown that the practical upper limit for reliable measurements of k,, at an RDE is about 5 X lo5 M-I s-’. The reason for this limitation is that turbulent flow occurs at the RDE for rotation rates higher than about IO4 rpm. ( 5 ) Harrison, D. J; Wrighton, M. S. J. Phys. Chem. 1984, 88, 3932. (6) Lewis, T. J.; White, H. S.; Wrighton, M. S. J. A m . Chem. SOC.1984, 106, 6947. (7) (a) Leidner, C. R.; Murray, R. W. J. Am. Chem. SOC.1985,107, 551. (b) Pickup, P. G.; Leidner, C. R.; Denisevich, P.; Murray, R. W. J. Electroanal. Chem. 1984, 164, 39. (c) Ikeda, T.; Schmehl, R.; Denisevich, P.; Willman, K.; Murray, R. W. J. Am. Chem. SOC.1982, 104, 2683. (d) Leidner, C. R.; Murray, R. W. J. Am. Chem. SOC.1984,106, 1606. (e) Ikeda, T.; Leidner, C. R.; Murray, R. W. J. Am. Chem. Soc. 1981,103, 7422. (f) Ikeda, T.; Leidner, C. R.; Murray, R. W. J. Eleciroanal. Chem. 1982, 138, 343. (8) Pickup, P. G.; Kutner, W.; Leidner, C. R.; Murray, R. W. J . Am. Chem. SOC.1984,106, 1991. (h) Denisevich, P.; Abruna, H. D.; Leidner, C. R.; Meyer, T. J.; Murray, R. W. Inorg. Chem. 1982, 21, 2153.

0 1986 American Chemical Societv 0022-3654/86/2090-2150%01.50/0