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Interaction Forces between a Bare Silica Surface and an r-Alumina Surface Bearing Adsorbed Polyelectrolyte and Surfactant Laurence Meagher,* George Maurdev, and Michelle L. Gee School of Chemistry, The University of Melbourne, Parkville, Victoria 3052, Australia Received August 15, 2001. In Final Form: December 20, 2001 The interactions between silica and R-alumina surfaces with and without polyelectrolyte and combinations of both polyelectrolyte (sodium poly(styrene sulfonate) or PSS) and surfactant (cetyltrimethylammonium bromide or CTAB) have been measured using the atomic force microscope (AFM) colloid probe technique. In this case, silica particles were glued to the AFM cantilever to give a surface of known geometry. The forces between silica and R-alumina in electrolyte only were well described by the Derjaguin-LandauVerwey-Overbeek theory at all separation distances. However, introduction of a solution of negatively charged PSS and mixtures of PSS and a positively charged surfactant, CTAB, at the point of zero charge of R-alumina, modified the interaction forces, introducing short-range steric interactions superimposed onto electrostatic interactions. Thus, the adsorption of strongly charged polyelectrolytes onto net neutral surfaces resulted in a flat conformation with few loops and tails. When PSS and CTAB were added sequentially, the interaction forces were further modified, resulting in weak electrostatic interactions and the presence of attractive van der Waals or bridging forces between the surfaces. The sign of the surfaces was altered from negative to positive in this case. Increasing the concentration of the added CTAB resulted in swelling of the adsorbed layer and an increase in the effective surface potential fitted to the data.
Introduction Investigation of the interfacial properties of polymers, and in particular polyelectrolytes, has been pursued vigorously over the last two decades for both technological and academic reasons. The applications of polyelectrolytes are widespread and encompass thin film applications such as biosensors1 and biocompatibility2 of implant devices to more traditional applications such as dispersants and flocculants in mineral processing.3 For example, in the biomaterials area polyelectrolytes have been used to mask the properties of the underlying substrate and to mimic the glycocalix of cells. Theory for the adsorption of uncharged and charged polymers is quite well advanced due mostly to the work of Scheutjens, Fleer, and co-workers.4 More recently, the use of mean field lattice models5,6 and Monte Carlo simulations7 has added to the understanding of polyelectrolyte adsorption onto neutral and charged surfaces. In general, these models are able to account for many of the experimentally observed features of polyelectrolyte adsorption, such as both increased and decreased adsorption with increases in electrolyte concentration. There has been little theoretical endeavor so far in modeling the adsorption * Corresponding author. Current address: CSIRO Molecular Science, Ian Wark Laboratories, Bag 10, Clayton South, VIC 3169, Australia. (1) Collings, A. F.; Caruso, F. Rep. Prog. Phys. 1997, 60, 1397. (2) Ratner, B. D. In Comprehensive Polymer Science: The Synthesis, Characterization, Reactions and Applications of Polymers; Aggarwal, S. L., Ed.; Pergamon Press: Oxford, 1989. (3) Deutzenberg, H.; Jaeger, W.; Kotz, J.; Philipp, B.; Seidel, C.; Stscherbina, D. Polyelectrolytes: Formation, Characterization and Application; Hanser Publishers: New York, 1994. (4) Fleer, G. J.; Cohen Stuart, M. A.; Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent, B. Polymers at Interfaces, 1st ed.; Chapman and Hall: London, 1993. (5) van de Steeg, H. G. M.; Cohen Stuart, M. A.; de Keizer, A.; Bijsterbosch, B. H. Langmuir 1992, 8, 2538. (6) Linse, P. Macromolecules 1996, 29, 326. (7) Akesson, T.; Woodward, C.; Jonsson, B. J. Chem. Phys. 1989, 91, 2461.
of polyelectrolytes in the presence of surfactants. Even so, these theories are an extremely useful starting point in understanding the possible effects of surfactant on the interactions responsible for adsorption. The behavior of polyelectrolyte solutions and adsorption of polyelectrolytes to surfaces such as metal oxides are controlled in many instances by electrostatic interactions. These interactions exist between the charged groups along the polymer backbone and between polymer molecules, any simple ions present in solution, and charged groups present on surfaces immersed in polyelectrolyte solutions. With the addition of oppositely charged surfactants to polyelectrolyte solutions, there are additional attractive electrostatic interactions between the oppositely charged groups and hydrophobic interactions between the surfactant hydrocarbon tail and the polymer backbone, respectively. The surfactant molecules tend to form micellelike aggregates on the polyelectrolyte chain in solution at concentrations above the critical aggregation concentration (cac).8 This association is usually highly cooperative, and the cac is generally lower (up to 2-3 orders of magnitude) than the cmc of the surfactant alone.9 The cac value for a particular surfactant/polyelectrolyte combination depends on various parameters, for example, the surfactant headgroup and chain length,9 the polyelectrolyte concentration,10,11 chemical composition12 and linear charge density,8 and the electrolyte concentration of the system.13,14 Because of the electrostatic nature of these interactions, solution conditions such as pH and (8) Hayakawa, K.; Kwak, J. C. T. In Cationic Surfactants; Rubingh, D. N., Holland, P. M., Eds.; Marcel Dekker: New York, 1991. (9) Lindman, B.; Thalberg, K. In Interactions of Surfactants with Polymers and Proteins; Goddard, E. D., Ananthapadmanabhan, K. P., Eds.; CRC Press: London, 1993. (10) Thalberg, K.; Lindman, B. J. Phys. Chem. 1989, 93, 1478. (11) Thalberg, K.; van Stam, J.; Lindblad, C.; Almgren, M.; Lindman, B. J. Phys. Chem. 1991, 95, 8975. (12) Shimizu, T.; Seki, M.; Kwak, J. C. T. Colloids Surf. 1986, 20, 289. (13) Hayakawa, K.; Kwak, J. C. T. J. Phys. Chem. 1982, 86, 3866. (14) Wei, Y. C.; Hudson, S. M. Macromolecules 1993, 26, 4151.
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ionic strength can have a dramatic effect on the adsorbed amount and conformation of polyelectrolyte and/or surfactant molecules adsorbed to a surface. These adsorbed film characteristics (i.e., adsorbed amount and conformation) control the interactions between surfaces bearing adsorbed polyelectrolyte, which in turn control other properties such as stability of a suspension of particles or the biocompatibility of a surface. It is the intrinsic complexity of these systems that makes them a very rich area for investigation. For several decades, it has been possible to measure the interaction forces between smooth, macroscopic surfaces directly using the surface forces apparatus (SFA)15 and more recently with the atomic force microscope16 (AFM) between microscopic surfaces.17,18 These techniques have proven to be extremely useful in studying the adsorption of both uncharged and charged polymers. For synthetic polyelectrolytes in particular, a number of systems have been studied.19-40 These authors have mostly measured the interaction forces in systems where the two interacting surfaces are chemically identical and where the adsorbing polyelectrolyte is of opposite charge to that of the surface. Under these conditions, the interaction forces observed were well described by the Derjaguin, Landau, Verwey, and Overbeek or DLVO theory of colloid stability41,42 at larger separation distances. In addition, forces of a steric nature were usually observed at smaller separation distances as well as attractive bridging forces. (15) Israelachvili, J. N.; Adams, G. E. J. Chem. Soc., Faraday Trans. 1 1978, 74, 975. (16) Binnig, Q.; Quate, C. F.; Gerber, C. Phys. Rev. Lett. 1986, 56, 930. (17) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Nature 1991, 353, 2239. (18) Butt, H.-J. Biophys. J. 1991, 60, 1438. (19) Dahlgren, M. A. G.; Claesson, P. M. Prog. Colloid Polym. Sci. 1993, 93, 206. (20) Dahlgren, M. A. G.; Waltermo, A.; Blomberg, E.; Claesson, P. M.; Sjostrom, L.; Akesson, T.; Jonsson, B. J. Phys. Chem. 1993, 97, 11769. (21) Marra, J.; Hair, M. J. Phys. Chem. 1988, 92, 6044. (22) Dahlgren, M. A. G. Langmuir 1994, 10, 1580. (23) Dahlgren, M. A. G.; Claesson, P. M.; Audebert, R. J. Colloid Interface Sci. 1994, 166, 343. (24) Dahlgren, M. A. G.; Hollenberg, H. C. M. Ber. Bunsen-Ges. Phys. Chem. 1996, 100, 1004. (25) Claesson, P. M.; Dahlgren, M. A. G.; Eriksson, L. Colloids Surf., A 1994, 93, 293. (26) Kamiyama, Y.; Israelachvili, J. N. Macromolecules 1992, 25, 5081. (27) Dahlgren, M. A. G.; Hollenberg, H. C. M.; Claesson, P. M. Langmuir 1995, 11, 4480. (28) Claesson, P. M.; Paulson, O. E. H.; Blomberg, E.; Burns, N. L. Colloids Surf., A 1997, 123-124, 341. (29) Abe, T.; Kunihara, K.; Higashi, N.; Niwa, M. J. Phys. Chem. 1995, 99, 1820. (30) Dahlgren, M. A. G. J. Colloid Interface Sci. 1996, 181, 654. (31) Sukhishvili, S. A.; Dhinojwala, A.; Granick, S. Langmuir 1999, 15, 8474. (32) Abe, T.; Higashi, N.; Niwa, M.; Kurihara, K. Langmuir 1999, 15, 7725. (33) Albersdorfer, A.; Sackmann, E. Eur. Phys. J. B 1999, 10, 663. (34) Guenoun, P.; Argillier, J. F.; Tirrell, M. C. R. Acad. Sci., Ser. IV: Phys., Astrophys. 2000, 1, 1163. (35) Osterberg, M.; Laine, J.; Stenius, P.; Kumpulainen, A.; Claesson, P. M. J. Colloid Interface Sci. 2001, 242, 59. (36) Kelley, T. W.; Schorr, P. A.; Johnson, K. D.; Tirrell, M.; Frisbie, C. D. Macromolecules 1998, 31, 4297. (37) Abraham, T.; Giasson, S.; Gohy, J. F.; Jerome, R. Langmuir 2000, 16, 4286. (38) Rojas, O. J.; Claesson, P. M.; Muller, D.; Neuman, R. D. J. Colloid Interface Sci. 1998, 205, 77. (39) Le Berre, F.; Malmsten, M.; Blomberg, E. Langmuir 2001, 17, 699. (40) Maurdev, G.; Meagher, L.; Ennis-King, J.; Gee, M. L. Macromolecules 2001, 34, 4151. (41) Verwey, E. G. W.; Overbeek, J. T. G. Theory of the Stability of Lyophobic Colloids; Elsevier: Amsterdam, 1948. (42) Derjaguin, B.; Landau, L. Acta Physicochim. URSS 1941, 14, 633.
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Occasionally, on the first approach the interaction forces were electrosteric in nature but were described by DLVO theory on subsequent approaches. The interaction of a bare surface with another containing an adsorbed layer of polyelectrolyte has been investigated in a few instances.28,43,44 Incubation of one surface was used as a means of obtaining an adsorbed polyelectrolyte layer, which was then brought toward a second bare surface. More recently, there have been several studies, both surface force45-56 and adsorption experiments,57,58 investigating the adsorption of polyelectrolyte and surfactant coadded and added sequentially. These studies concluded that the presence of the surfactant was very important in determining both the adsorbed amount and conformation of the adsorbed polymer/surfactant layer. In addition, competitive adsorption between the polyelectrolyte and surfactant species played a significant role47,59 in determining the relative adsorbed amounts. In the present study, we have used one silica and one R-alumina surface in the AFM to study the interaction forces between an adsorbed layer containing both poly(styrene sulfonate) (an anionic polyelectrolyte) and cetyltrimethylammonium bromide (a cationic surfactant) and a bare surface. We have chosen to carry out the experiments under solution conditions where the alumina surface is net neutral and electrostatic interactions between the surface and polyelectrolyte are minimized. The order of addition of polyelectrolyte and surfactant was also investigated, as previous studies have indicated that very different interaction forces can be obtained under a variety of adsorption conditions.58,60 The data obtained will be discussed with reference to existing theories of polyelectrolyte adsorption and the interactions between adsorbed layers. Methods and Materials The interaction forces between silica and R-alumina surfaces bearing adsorbed polyelectrolyte/surfactant were measured with a Nanoscope III atomic force microscope (Digital Instruments, Inc.) using the colloid probe method developed by Ducker et al.17,61 In this method, a spherical colloidal particle is attached to the microfabricated cantilever spring used in the AFM, providing a surface of known geometry. To scale the force measurements (43) Hartley, P. G.; Bailey, A. I.; Luckham, P. F.; Batts, G. Colloids Surf. 1993, 77, 191. (44) Hartley, P. G.; Scales, P. J. Langmuir 1998, 14, 6948. (45) Claesson, P. M.; Dedinaite, A.; Blomberg, E.; Sergeyev, V. G. Ber. Bunsen-Ges. Phys. Chem. 1996, 100, 1008. (46) Ananthapadmanabhan, K. P.; Mao, G.-Z.; Goddard, E. D.; Tirrell, M. Colloids Surf. 1991, 61, 167. (47) Shubin, V.; Petrov, P.; Lindman, B. Colloid Polym. Sci. 1994, 272, 1590. (48) Shubin, V. Langmuir 1994, 10, 1093. (49) Dhoot, S.; Goddard, E. D.; Murphy, D. S.; Tirrell, M. Colloids Surf. 1992, 66, 91. (50) Kjellin, U. R. M.; Claesson, P. M.; Audebert, R. J. Colloid Interface Sci. 1997, 190, 476. (51) Muir, I.; Meagher, L.; Gee, M. Langmuir 2001, 17, 4932. (52) Rojas, O. J.; Neuman, R. D.; Claesson, P. M. J. Colloid Interface Sci. 2001, 237, 104. (53) Claesson, P. M.; Fielden, M. L.; Dedinaite, A.; Brown, W.; Fundin, J. J. Phys. Chem. B 1998, 102, 1270. (54) Fielden, M. L.; Claesson, P. M.; Schillen, K. Langmuir 1998, 14, 5366. (55) Dedinaite, A.; Claesson, P. M.; Bergstrom, M. Langmuir 2000, 16, 5257. (56) Dedinaite, A.; Claesson, P. M. Langmuir 2000, 16, 1951. (57) Esumi, K.; Masuda, A.; Otsuka, H. Langmuir 1993, 9, 284. (58) Neivandt, D. J.; Gee, M. L.; Tripp, C. P.; Hair, M. L. Langmuir 1997, 13, 2519. (59) Shubin, V.; Linse, P. J. Phys. Chem. 1995, 99, 1285. (60) Maurdev, G.; Gee, M. L.; Meagher, L. Manuscript in preparation. (61) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Langmuir 1992, 8, 1831.
Interaction Forces between Silica and R-Alumina correctly, the spring constant must be known accurately. This was achieved using the resonance method proposed by Cleveland et al.62 This method gives the spring constant with an error of approximately 10%. An average value calculated from a sample of 10 cantilevers was used to scale the raw data obtained from the interaction force experiments. The fittings and tubing used for injecting solutions into the AFM fluid cell were constructed from either Teflon or KelF polymers to facilitate rigorous cleaning. These fittings, fluid cell, and O-ring and the syringe used to inject solutions were cleaned using the following procedure. First, the individual parts were placed in a 1% surfactant solution (RBS 35, Pierce USA) overnight. Next, they were rinsed thoroughly with purified water and soaked in AR grade ethanol overnight. The ethanol was subsequently replaced followed by another overnight soak. These components were finally rinsed with distilled AR grade ethanol and blown dry using a high-velocity stream of nitrogen. The R-alumina surfaces were cleaned in steamed polypropylene beakers. Polyethylene bottles were used to make solutions so as to avoid contamination of the alumina surfaces by silica present in solution. The bottles were rigorously cleaned by steaming for 2-3 h, soaking in surfactant solution for 2 days, and rinsing copiously with purified water and ethanol. The bottles were left filled with purified water for at least 1 day before an experiment. All operations were carried out in a laminar flow clean cabinet to minimize any particulate contamination. The spherical silica particles, prepared by a modified Stober method,63,64 were a gift from Allied Signal (Illinois) and had a diameter of 4-5 µm. The flat surfaces used in this study were pure R-alumina single crystals (Melles Griot, Rochester, NY) and were polished to give peak to trough and root-mean-square roughness values of 1.4 and 0.16 nm, respectively (approximately 800 × 800 nm area). These flat surfaces were cleaned by immersion in a 1% surfactant solution (RBS 35, Pierce USA) overnight. Next, they were rinsed thoroughly with purified water and soaked in AR grade ethanol overnight. The surfaces were again rinsed with purified water and immersed in a 30% nitric acid solution for 30 min, rinsed thoroughly in purified water, and finally blown dry with a high-velocity nitrogen stream. Both the spherical silica and flat R-alumina surfaces and the AFM fluid cell were then placed under a low-wavelength UV light in the presence of water vapor for 2-3 h to ensure that they were clean and completely hydrophilic.65 The average time between removing the surfaces from the UV lamp and injection of the first solution was 15 min. The water used to prepare the KBr and PSS/CTAB/KBr solutions was purified initially by reverse osmosis and then fed into a Milli-Q Plus water purification system. The water produced has a resistivity of 18.2 MΩ cm and a low dissolved silica concentration, unlike water prepared by distillation in a glass still. Water prepared in this manner does not result in contamination of alumina by silica as has been shown previously.66 Analytical grade KBr, HBr, and KOH were used as received, the latter being for the adjustment of pH. Sodium poly(styrene sulfonate) (PSS) was obtained from Polysciences Inc. (Warrington, PA) and had a molecular weight of 177 000 and a Mw/Mn ratio of 1.1 indicating a low degree of polydispersity. Cetyltrimethylammonium bromide (CTAB) was obtained from Eastman Kodak (Rochester, NY) and was further purified by twice recrystallizing from an ethanol/acetone mixture. The general procedure used in AFM interaction force measurements was as follows. The clean surfaces were mounted into the AFM apparatus and brought to within 30 µm separation, and a solution of KBr at pH 5.6 was injected and allowed to equilibrate for approximately 30 min. Force curves were then obtained to ensure that the surfaces were free of contamination. The solution pH was then varied in a consistent manner (high to low), and force curves were obtained in order to determine the (62) Cleveland, J. P.; Manne, S.; Bocek, D.; Hansma, P. K. Rev. Sci. Instrum. 1993, 64, 1. (63) Stober, W.; Fink, A.; Bohn, E. J Colloid Interface Sci. 1968, 26, 62. (64) Barder, T. J.; DuBois, P. D. U.S. Patent No. 4,983,369, Jan 1991. (65) Vig, J. R. J. Vac. Sci. Technol., A 1985, 3, 1027. (66) Larson, I.; Drummond, C. J.; Chan, D. Y. C.; Grieser, F. Langmuir 1997, 13, 2109.
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Figure 1. Interaction forces measured between silica and R-alumina surfaces immersed in 10-3 M KBr solutions of various pH values: (b) pH 9.2, (9) pH 6.9, ([) pH 6.3, (2) pH 5.65, (1) pH 5.4, (O) pH 4.7, (]) pH 4.58, and (0) pH 3.75. pH at which the R-alumina surface was net neutral (point of zero charge or pzc). Next, a solution containing polyelectrolyte and surfactant or polyelectrolyte alone was injected and allowed to equilibrate with the surfaces. The particular solution injected and the sequence of addition at this stage were predetermined from the adsorption schemes termed coaddition or sequential addition. The PSS and CTAB concentrations were always 100 ppm and 5.5 × 10-5 M, respectively, and all solutions were prepared in a background electrolyte solution containing 10-3 M KBr. For the coaddition adsorption scheme, a solution of PSS and CTAB was prepared and allowed to equilibrate for 24 h at its natural pH. The pH of this solution was then adjusted to the predetermined pzc of the R-alumina surface before injection into the AFM cell. For the sequential addition scheme, a solution of PSS, again with pH adjusted to the predetermined pzc of the R-alumina surface, was injected into the AFM cell. After equilibration, a solution containing CTAB only was injected. Occasionally, another CTAB solution of higher concentration was injected at a later time. Equilibration times of 12 h were used for all solutions containing PSS and CTAB, whether present as a mixture or not. At least five force curves were obtained for each solution condition, and the rate of approach was varied to investigate any approach rate dependence of the measured forces. Both sequential and coaddition experiments were carried out at least twice using different silica particles. The radius of the silica sphere was measured using a high-powered optical microscope (final magnification ) 1800×). This technique has an approximate accuracy of 10%. The data were analyzed and scaled using a custom-designed computer program.67 In this analysis, the linear compliance region obtained when the surfaces were in hard contact was used to calibrate the photodetector signal and define zero separation. All force curves presented here had very linear compliance regions (R2 > 0.99).
Results and Analysis In Figure 1 are presented the forces between a spherical silica particle and an R-alumina flat surface, divided by the radius of the silica particle, while immersed in 10-3 M KBr aqueous solutions of various pH. At high pH values, the interaction forces were repulsive, indicating that the surfaces have the same sign charge (i.e., negative). Decreasing the solution pH results in less repulsive interaction forces as the potential on both surfaces decreases in magnitude. As the solution pH was decreased further, the interaction forces become increasingly attractive as the R-alumina surface passes through its pzc (67) Chan, D. Y. C.; Ip, L.; Venters, S. AFM Analysis; University of Melbourne: Parkville, Australia, 1994.
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Figure 3. Fitted potential (ψ0) versus pH for R-alumina and silica surfaces immersed in 10-3 M KBr. Figure 2. Interaction forces measured between silica and R-alumina surfaces immersed in 10-3 M KBr aqueous solutions at (b) pH 7.75 (fitting parameters: ψ0,SiO2 ) -65 mV, ψ0,Al2O3 ) -25 mV, κ-1 ) 9.39 nm) and (2) pH 4.6 (fitting parameters: ψ0,SiO2 ) -42 mV, ψ0,Al2O3 ) +9 mV, κ-1 ) 9.39 nm).
and its surface charge becomes positive. At pH values lower than the pzc of the alumina surface, heterocoagulation or attractive electrostatic interactions between the now oppositely charged (opposite sign) surfaces resulted. The arrows in Figure 1 indicate where the surfaces jumped to contact. This occurs when the gradient of the force exceeds the spring constant of the AFM cantilever, resulting in an instability. Nonequilibrium force data from this type of unstable region have not been included in any figures presented here. The interaction forces presented in Figure 1 are well described by the Derjaguin, Landau,42 Verwey, and Overbeek41 theory of colloid stability at all separation distances. Two examples, comparing the experimental data with numerical predictions calculated using the DLVO theory, are presented in Figure 2 at solution pH values of 7.75 and 4.6. The theoretical curves were calculated via the algorithm of McCormack68 for the electrical double layer contribution and using a nonretarded Hamaker constant of 1.8 × 10-20 J, calculated by Larson et al.,66 for the SiO2/water/Al2O3 system using Lifshitz theory.69 The Derjaguin approximation70 was used to convert the interaction energy between flat plates to the force for a sphere interacting with a flat plate. For the data obtained in 10-3 M KBr at pH 7.75, surface potentials of -65 and -25 mV for the silica and R-alumina surfaces, respectively, were used to fit the experimental data. Values for the surface potential of silica at all pH values were obtained from the electrokinetic data of Larson et al.66 The surface potential of the silica surface was then set to the appropriate value, and the potential for the alumina surface was allowed to vary until the best fit was obtained. At a solution pH of 4.6, surface potentials of -42 and +9 for the silica and R-alumina surfaces, respectively, were used to fit the experimental data. The data in Figure 2 lie between the constant charge (upper) and constant potential (lower) boundary conditions for the solution of the nonlinear Poisson-Boltzmann equation. This fitting procedure was carried out at all solution pH values, a summary of which is presented in Figure 3. This figure clearly demonstrates the solution pH ranges where the
R-alumina surface was negatively and positively charged as well as the pH at which it was net neutral (the pzc). The pzc for this particular alumina surface was approximately pH 5 and varied slightly from experiment to experiment (from pH 5.0 to 5.9), presumably because of the nitric acid cleaning treatment employed.71 In Figure 4 are presented the interaction forces between silica and R-alumina surfaces immersed in a preequilibrated solution containing both 100 ppm PSS and 5.5 × 10-5 M CTAB (i.e., coaddition) at pH 5.5 (pHpzc ) 5.5). The critical micelle concentration (cmc) for CTAB in 0.001 M KBr electrolyte is 0.75 × 10-3 M.72 Data obtained at two different approach rates (0.059 and 0.59 µm s-1) are included for comparison. Under these approach rate conditions, the hydrodynamic repulsive force generated,73 even at the faster rate, was negligible at all but the smallest separation distances. The data are well described by DLVO theory, except at small separation distances (
