J . Phys. Chem. 1987, 91, 2902-2904
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with coating behavior must be addressed. Because the morphologies adopted by coatings of block copolymers can be controlled in a facile manner by varying their chemical composition we believe that they will prove irtcreasingly useful in developing electrode coatings with specifiable properties. Acknowledgment. This work resulted from a Japan-USA
Cooperative Research Project supported by the Japanese Society for the Promotiod of Science and the U. S. National Science Foundation, and was partially supported by a Grant-in-Aid from the Ministry of Education, Science and Culture, Japan. Registry No. PVI, 26983-77-7; Fe(CN),’, 13408-63-4; C, 7440-44-0; ((lysine)(styrene)(block copolymer)).xHBr, 107474-56-6.
Double-Layer Forces in Ionic Micellar Sotutions R. M. Pashleyt and B. W. Ninham** Department of Chemistry, The Faculties, and Department of Applied Mathematics, Research School of Physical Sciences, Australian National University, Canberra, ACT 2601, Australia (Received: September 29, 1986: In Final Form: December 24, 1986)
Measurements are reported of the force between two molecularly smooth mica surfaces coated with adsorbed bilayers of cetyltrimethylammonium bromide (CTAB) and separated by an aqueous solution of CTAB. Below the critical micelle concentration (cmc), the double-layer forces are well described by assuming the surfactant to be a completely dissociated simple 1:l electrolyte. Above the cmc, micelles and their “bound” counterions do not contribute to the Debye length. Some consequences for colloid stability are discussed.
Introduction Nothing is known concerning the nature and range of double-layer forces between two colloidal particles in the presence of a highly asymmetric electrolyte like a micellar solution. The problem is not academic since many real applications involve ionic detergents with or without hydrophobes which can induce aggregation. To set this study into perspective, recall that all of our intuition on colloid stability derives from the DLVO theory. That theory ascribes to the repulsive electrostatic forces between two particles at separation 1 an asymptotic form F
a
exp(-rol)
(2) The same question occurs in an electrolyte that contains surfactant micelles and their counterions. Here, typical aggregation numbers are N = z , i= 50 and zl >> z 2 . If aggregation is determined in the pseudophase approximation by the law of mass action XM s X s N , then below the cmc the system is a 1:l electrolyte of monomer and counterion. Above the cmc, if the micelles behave as fully charged entities, zl = N , ul = 1, u2 = N , and z2 = 1 since charge neutrality requires zlul z2v2 = 0. Direct application of eq 2 would give
+
(1)
where K { ’ is the Debye screening length. The Debye length is a key parameter that determines stability. It is defined (in cgs units) by
and
(4b) This form applies to an electrolyte C , , Z I A , of ~ density p where C and A denote cation and anion with charge z,q and z2q, respectively. The classical theory begins to break down in many cases of real interest. Several examples serve to illustrate the point. (1) For a dilute suspension of latex spheres in equilibrium with counterions only (or at low salt concentration), two such spheres interact in a complex many-body potential determined by all the other spheres and their associated counterions. The reduction of the problem to an effective two-body interaction is an awkward and unresolved issue.’ The meaning of any effective Debye length is unclear. At close separations of two spheres one expects only counterions to contribute to electrostatic screening because other (highly charged) spheres will be strongly repelled from the region of strong interaction. If the spheres have charge z l , counterions charge z2, and zl >> z2, one might then expect eq 2 to take the form (3) +Department of Chemistry. f Department of Applied Mathematics.
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where psis the surfactant concentration and pcmcthe surfactant concentration at the cmc (in units of molecules per unit volume). For an aggregation number N = 50, the Debye length would be about 4 times smaller (e.g., for CTAB) (eq 4b) than the corresponding value for a simple electrolyte at a concentration of ps 5p ,, (eq 4a). An alternative possibility, as for latex spheres, is to assume that highly charged micelles will behave as co-ions expelled from the region of close double-layer overlap. Were that so, the Debye lengths of the aggregate solution would be much closer to the simple electrolyte values. Yet another hypothesis is to adopt the ion-binding description of micelles; Le., the micelles behave as dressed micelles with effective charge N - Q,where Q / N is the fraction of “bound” counterions, and only the free counterions are assumed to contribute to the observed K ~ - ’ . Above the cmc we therefore have
This equation will be further altered if the micelles are also assumed to contribute to K ~ . (1) Beresfold-Smith, B.; Chan, D. Y . C. Faraday Discuss. Chem. SOC. 1983, 76, 6 5 .
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 11, 1987 2903
Double-Layer Forces in Ionic Micellar Solutions The characterization of micellization through the ion-binding model X, F? XsN-QX2Qhas been shown2 to emerge naturally and quantitatively from a Poisson-Boltzmann description of the free energies of aggregation; Le., the “bound” ions are physical adsorption excesses, and which of the above formulas should apply is quite unclear. The issue takes on more importance if we consider that in most real situations involving ionic surfactants (e.g., detergency) the presence of hydrophobes like dirt particles, hydrophobic molecules, or oil contaminants can induce surfactant aggregation well below the cmc. Such a suspension may contain highly charged swollen micellar aggregates. In this situation, then, stability will be much enhanced over that expected from standard theory. For mixed systems comprised of both cationic and anionic monomers, the mixed micelles formed in, say, near equimolar situations will have much less bare charge than for cationic or anionic micelles alone. There will be little ion binding because the surface charge and potential are lowered, and any of eq 2-5 could apply. At the level of rigorous theory, what is known is extremely limited. For an asymmetric electrolyte, the pair distribution f u n ~ t i o nfor ~ , ~ions i and j has the form
I
bilayer contact at 0 - 6 4nm
0
and c is the salt concentration in mol L-I. The second term in this perturbation expansion vanishes identically for a symmetric electrolyte. For very large zIthe formulas go over the case to counterions only: Le., zl disappears from the expressions as for eq 3. But for intermediate values of zI, as for micelles, the effective Debye length is not easily estimated; e.g., even for a 2:1 electrolyte the second term of eq 7 is large, and the formula is invalid4 even at M. Consequently, inference of effective bound charge5 on micelles from techniques like light scattering is a bit of a problem. Analysis of these experiments depends critically on correct choice of the Debye length. In these circumstances we are reduced to experiment. With this in view we have obtained the Debye lengths of CTAB solutions well above the cmc from the measured interaction forces between CTAB bilayers.
Materials and Methods The CTAB used in these experiments was obtained from BDH (>98% assay) and was used directly after atomic and ion analysis confirmed the composition of the sample to better than 1%. All of the solutions were made up in water purified by mixed-bed ion-exchange, activated charcoal treatment, nucleopore (50 nm) filtration, and triple distillation. The water was allowed to equilibrate with atmospheric C02and so had a pH value typically of about 5.7 and a conductivity less than 10 p S cm-I. All force measurements were carried out at 25 “C, which is well above the Krafft temperature for CTAB. CTAB bilayers were adsorbed onto two facing, curved mica crystals, and the double-layer forces between them were measured over a range of concentrations from the cmc (where the bilayer first adsorbs) to 20 times the cmc. Several detailed descriptions of the procedure and techniques have been given previously,6 and these will not be repeated here. (2) Evans, D. F.; Mitchell, D. J.; Ninham, B. W. J . Phys. Chem. 1984,88, 6344. (3) Mitchell, D. J.; Ninham, B. W. Phys. Reu. 1968, 174, 280. (4) Mitchell, D. J.; Ninham, B. W. Chem. Phys. Lett. 1978, 53, 397. (5) Mitchell, D. J.; Ninham, B. W.; Evans, D. F. J . Colloid Interface Sci. 1984, 101, 292. (6) Israelachvili, J. N.; Adams, G. E. J . Chem. SOC.,Faraday Trans 1 1978, 74, 975.
30
TABLE I
where the Debye length B has the asymptotic expansion
(7)
20
Figure 1. Forces (F)measured between two mica surfaces with adsorbed bilayers immersed in a 1.8 X M CTAB solution. The distance D is measured relative to the bare mica surfaces, and the total interaction force is scaled by the mean radius R of the curved surfaces (see text). The solid line is the calculated (constant charge) Poisson-Boltzmann double-layer interaction with a nonretarded van der Waals attraction (with a Hamaker constant of 1.5 X J). The bilayer surfaces have a charge corresponding to about 25% dissociation.
lo-’ 2 x 10-3
1
10
0 I nm
ICTAB1. M
+ O(c3/*In c)
I
* ’
5 x 10-3 10-2 1.8 x 10-2 a Obtained
Kn-lSa
8,
100 85 78
70 60
from “best-fit” theoretical force curve.
Kn-’.b
A
95 89 79 66
54 Calculated from
eq 5.
Results and Discussion The measured force F between the mica surfaces (of mean radius R ) with adsorbed bilayers as a function of separation distance D is given in Figure 1 for a CTAB concentration of about 20 times the cmc. The adsorbed bilayer thickness on each surface was about 3.2 nm, which is in good agreement with earlier measurements.’ The parameter F I R plotted is equal to ~ T E , where E is the corresponding interaction energy per unit area between flat surfaces.* The solid line is the “best-fit” theoretical curve obtained by using a numerical solutiong to the nonlinear Poisson-Boltzmann equation and also includes a nonretarded van der Waals attraction which gives a force maximum only at very small separations (COS nm). The theoretical curve was calculated for 1:l (monovalent) electrolyte since we do not have an interaction theory which would include the charged surfactant aggregates. It is quite remarkable that the simple theory describes the observed interaction so well. The Debye lengths obtained from these best-fit curves over a wide CTAB concentration range are given in Table I. It is quite clear from these results that if we assume that the micelles are 25% dissociated and that only these counterions contribute to the Debye length, we can calculate the observed values quite accurately from eq 5. Not only does this value of 25% binding give the Debye lengths, but the magnitude of the forces between the adsorbed bilayers is also accurately obtained by using this value. That is, the bilayers also appear to exhibit a similar degree of dissociation. The good fit to the 1:l electrolyte double-layer theory also supports the counterions-only hypothesis, even though there must be a significant density of micelles between the surfaces at separations greater than, say, 10 nm. The slight reduction in force at large separations (see Figure l ) , which was not observed at lower concentrations, could be related to the presence of highly charged, micellar co-ions. The value obtained here from the degree of dissociation of CTAB micelles and bilayers is also in good agreement with the (7) Pashley, R. M.; Israelachvili, J. N. Colloids Surf. 1981, 2, 169. (8) Derjaguin, B. V. Kolloid-Z. 1934, 69, 155. (9) Chan, D.Y. C.; Pashley, R. M.; White, L. R. J . Colloid Interface Sci. 1980, 77, 283.
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values obtained from conductivity measurements around the cmc of about 28%.1° However, our recent measurements differ considerably with an earlier interaction measurement at 4 times the cmc' in both degree of dissociation and Debye length, which were lower. In the earlier work, however, additional electrolytes were present and the pH value was much higher, at about 9.0. Presumably, the presence of significant concentrations of Cl- and OH- in the earlier work caused the lower values, although this needs further investigation.
Conclusions Direct force measurements between charged CTAB bilayers in micellar solutions up to 20 times the cmc indicate that the interaction forces can be accurately and simply modeled assuming that 25% of the micellar Br- ions are dissociated and act as free, screening electrolyte. One implication of the observations is that, even below the cmc in the presence of hydrophobes which can induce micellization, a colloidal suspension will be considerably more stable against flocculation than would otherwise be expected.
(10) Hartley, G. S.; Collie, B.; Samis, C. S. Trans. Faraday Soc. 1936, 32, 795.
Acknowledgment. We thank Joyce Evans and D. F. Evans for interest and assistance with this project.
Stochastic Behavior in the Formation of Condensed Coumarin Films at the Mercury-Solution Interface R. Srinivasan and R. de Levie* Chemistry Department, Georgetown University, Washington, D.C. 20057 (Received: September 30, 1986; In Final Form: January 14, 1987)
Coumarin exhibits a capacitance "pit" at the interface between mercury and aqueous 0.1 M NaC104 at 15 OC. The capacitance transients show stochastic behavior, from which the rates of nucleation and growth can be determined separately.
Introduction The metalsolution interface has proven to be a good place to study the stochastic behavior associated with phase formation, because the interfacial concentrations can be controlled conveniently and accurately, and changed rapidly, through the externally applied potential. In the case of Faradaic processes, the resulting phase transformations can then be monitored by measuring the corresponding current; in the absence of a Faradaic process, the consequent changes in interfacial capacitance or charge density can be used instead. The earliest observations were those of Kaischev and Mutaftschiev on the electrodeposition of mercury onto platinum,'*2 experiments which have since been extended to different electrodeposited metals, different substrates, and different laboratories. (For a fairly recent review of these and other stochastic observations, see ref 3.) Most of these measurements reflected the heterogeneity of the substrate surface used. Subsequently, Kaischev and Budevski et al. reported stochasticity in the electrodeposition of silver monolayers on single-crystal faces of Ag," observations which are only possible after screw dislocations (providing self-perpetuating, low-energy nucleation sites) had been removed from the metal surface. Such observations have been extended recently to cadmium.' Stochastic behavior can also be observed a t the atomically smooth interface between mercury and an aqueous solution, when the latter contains organic molecules which can form two-di(1) Kaischev, R.; Mutaftschiev, B. 2.Phys. Chem. 1955, 204, 334. (2) Kaischev, R.; Mutaftschiev, B. Electrochim. Acta 1965, 10, 643. (3) de Levie, R. Adu. Electrochem. Electrochem. Eng. 1985, 13, 1. (4) Budevski, E.; Bostanov, W.; Vitanov, T.; Stoinov, Z.; Kotzewa, A.; Kaischev, R. Electrochim. Acta 1966, 1 1 , 1697. Phys. Status Solidi 1966, 13, 577. (5) Bostanov, V.; Obretenov, W.; Staikov, G.; Roe, D. K.; Budevski, E. J. Crystal Growth 1981, 52, 761. (6) Obretenov, W.; Bostanov, V.; Popov, V. J. Electroanal. Chem. 1982, 132, 273. (7) Bostanov, V.; Naneva, R. J. Electroanal. Chem. 1986, 208, 153
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mensional films at the interface. Use of a liquid metal electrode obviates the need for removing crystal imperfections, and greatly facilitates measurement reproducibility. Examples of the formation of organic films at the mercury-water interface, which exhibit stochasticity, are those of isoquinoline,* 3-methylisoquinoline: and thymine.I0 Here we report on another such neutral compound, coumarin, which is capable of forming a two-dimensional condensed film at the mercury-solution interface and exhibits stochasticity in the formation of this film. Griffiths and Westmore",'* first reported the strong adsorption of coumarin at the interface between mercury and aqueous 0.1 M KCl, and its effects on the polarographic reduction of nickel ions. These observations were extended by Partridge et al.13J4 who concluded that, depending on the applied potential, coumarin in aqueous 1 M Na2S04adsorbs in one of two different orientations, one parallel to the electrode surface, the other perpendicular to it, a conclusion essentially confirmed by Damaskin et ai.15 More detailed studies of the adsorption of coumarin in a variety of aqueous electrolytes were reported by Moussa et al.'6.'7 Authors from that same laboratory also reported that adsorbed coumarin strongly inhibits the reduction of Cd(I1) and of Pb(I1) * ~none ~ ~ of from 1 N H2S04and 1 N HC104, r e s p e c t i ~ e l y . ~In (8) Gierst, L.; Franck, C.; Quarin, G.; Buess-Herman, C. J. Electroanal. Chem. 1981, 129, 353. (9) Buess-Herman, C.; Quarin, G.; Giewrst, L. J . Electroannl. Chem. 1983, 148, 97. (10) Sridharan, R.; de Levie, R. J. Phys. Chem. 1982, 86, 4489. (1 1) Griffiths, V. S.; Westmore, J. B. J . Chem. SOC.1962, 1704. (12) Griffiths, V. S.; Westmore, J. B. J. Chem. SOC.1963, 4941. (13) Partridge, L. K.; Tansley, A. C.; Porter, A. S. Electrochim. Acta 1966, 1 1 , 517. (14) Partridge, L. K.; Tansley, A. C.; Porter, A. S. Electrochim. Acta 1969, 14, 223. (15) Damaskin, B. B.; Dyatkina, S. L.; Petrochenko, S. I. Elektrokhim. 1969, 5 , 935. (16) Moussa, A. A,; Ghaly, H. A.; Abou-Romia, M. M. Electrochim. Acta 19.
0 1987 American Chemical Society
