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Synergistic Effects of Polymers and Surfactants on Depletion Forces Aysen Tulpar,† Robert D. Tilton,‡ and John Y. Walz*,§ Department of Chemical Engineering, Yale UniVersity, New HaVen, Connecticut 06520-8286, Department of Biomedical Engineering and Department of Chemical Engineering, Carnegie Mellon UniVersity, Pittsburgh, PennsylVania 15213, and Department of Chemical Engineering, Virginia Tech, Blacksburg, Virginia 24061 ReceiVed NoVember 1, 2006. In Final Form: December 22, 2006 This work investigates the synergistic effects of a neutral polymer and an anionic surfactant on depletion forces as a function of bulk polymer and bulk surfactant concentration. In this work, we measure the force between a silica particle and a silica plate in aqueous solutions of the polymer and the surfactant using atomic force microscopy. The polymer is the triblock copolymer poly(ethylene oxide-block-propylene oxide-block-ethylene oxide) (Pluronic F108), and the surfactant is sodium dodecyl sulfate (SDS). In F108-only solutions, the force between the silica particle and the silica plate is primarily repulsive for polymer concentrations ranging from 200 to 10 000 ppm. In SDS-only solutions, the net force between the silica surfaces is repulsive at all separations for concentrations below 16 mM SDS and is attractive with a structural force character above 16 mM SDS. When both F108 and SDS are present in the solution, a net attractive force is observed at SDS concentrations as low as 4 mM, a factor of 2 below the critical micelle concentration (cmc). We attribute this synergistic effect to the complexation of F108 with SDS in bulk solution at a critical aggregation concentration (cac) that is less than the cmc, producing a relatively large, charged complex that creates a significant depletion force between the particle and plate.
Introduction Polymers and surfactants in solution are widely used together in both biological and industrial processes to take advantage of their different properties.1 By mixing polymers and surfactants, desired solution or surface properties can be achieved.2,3 For example, the addition of a surfactant to a polymer solution can either increase or decrease the solubility of the polymer. Similarly, the presence of a polymer on a solid surface can either promote or inhibit the adsorption of the surfactant. The main characteristic of these mixed solutions is that the polymer and the surfactant molecules often associate and form complexes via van der Waals forces, hydrogen bonding, electrostatic forces, and/or hydrophobic forces. Polymers and surfactants are also used to tune the stability of suspensions in colloidal processes. The addition of these molecules to colloidal suspensions can induce stabilization of the colloidal suspension by producing a repulsive force between particles, or coagulation of the particles by creating an attractive force. In this manuscript, we investigate the synergistic effect of a neutral polymer and an anionic surfactant on attractive depletion forces. This study is performed by measuring the interaction force profile between a particle and a plate using an atomic force microscope (AFM). The attractive depletion force is caused by the exclusion of a nonadsorbed species (e.g., nanoparticles, micelles, polymers) from the gap region between two surfaces. The resulting concentration difference produces an osmotic pressure imbalance between the gap and bulk, resulting in a net attractive force. * To whom correspondence should be addressed. E-mail: jywalz@ vt.edu. † Yale University. ‡ Carnegie Mellon University. § Virginia Tech. (1) Tirrell, M. Interaction of Surfactants with Polymers and Proteins; CRC Press: Boca Raton, FL, 1993; p 59. (2) Goddard, E. D. J. Colloid Interface Sci. 2002, 256, 228-235. (3) Tilton, R. D. In Encyclopedia of Surface and Colloid Science, 8th updated ed.; Somasundaran, P., Ed.; Marcel-Dekker: New York, 2004.
Depletion forces have been measured in nanoparticle suspensions,4 in surfactant micellar solutions,5-7 and in polymer solutions.8-15 To the best of our knowledge, however, there has not been any work done that focused specifically on the depletion force produced by surfactant-polymer complexes. It should be mentioned that various researchers have investigated colloidal forces in mixed polymer-surfactant systems. For example, Luckham and Klein16 attempted to measure depletion forces between two crossed-mica surfaces in solutions containing poly(ethylene oxide) (PEO). To prevent adsorption of the PEO, the mica surfaces were first equilibrated with Triton X-405 surfactant, which itself would adsorb and block the PEO. No depletion forces were observed, however, which the authors attributed to the displacement of the surfactant from the mica surface by the PEO. Several groups have also measured interparticle forces between surfaces containing mixed layers of adsorbed polymer and surfactant. For example, Philip et al.17 measured the force between super-paramagnetic liquid drops that were covered with an adsorbed SDS-poly(vinyl alcohol) complex. The authors found that the surfactant caused the polymer chains to extend, producing large complexes that generated strong steric repulsive (4) Sharma, A.; Walz, J. Y. J. Chem. Soc., Faraday Trans. 1996, 92, 49975004. (5) Richetti, P.; Kekicheff, P. Phys. ReV. Lett. 1992, 68, 1951-1955. (6) Kekicheff, P.; Nallret, F.; Richetti, P. J. Phys. II 1994, 4, 735-741. (7) Sober, D. L.; Walz, J. Y. Langmuir 1995, 11, 2352-2356. (8) Milling, A.; Biggs, S. J. Colloid Interface Sci. 1995, 170, 604-606. (9) Milling, A. J. J. Phys. Chem. 1996, 100, 8986-8993. (10) Sharma, A.; Tan, S. N.; Walz, J. Y. J. Colloid Interface Sci. 1997, 1, 236-246. (11) Kuhl, T.; Guo, Y.; Alderfer, J. L.; Berman, A. D.; Leckband, D.; Israelachvili, J.; Hui, S. W. Langmuir 1996, 12, 3003-3014. (12) Milling, A.; Kendall, K. Langmuir 2000, 16, 5106-5115. (13) Piech, M.; Walz, J. Y. J. Phys. Chem. B 2004, 108, 9177-9188. (14) Biggs, S.; Prieve, D. C.; Dagastine, R. R. Langmuir 2005, 21, 54215428. (15) Pagac, E. S.; Tilton, R. D.; Prieve, D. C. Langmuir 1998, 14, 5106-5112. (16) Luckham, P. F.; Klein, J. J. Colloid Interface Sci. 1987, 117, 149-158. (17) Philip, J.; Prakash, G. G.; Jaykumar, T.; Kalyanasundaram, P.; MondainMonval, O.; Raj, B. Langmuir 2002, 18, 4625-4631.
10.1021/la063191d CCC: $37.00 © 2007 American Chemical Society Published on Web 02/23/2007
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forces. Other work in this area includes that by Sakai et al.18 and Bremmell et al.19 In this work, we perform force measurements between a 5 µm silica sphere and a flat silica surface in poly(ethylene oxideblock-propylene oxide-block-ethylene oxide) triblock copolymer (Pluronic F108) solutions, in sodium dodecyl sulfate (SDS) solutions, and in F108-SDS solutions. Our hypothesis is that the magnitude of the depletion force should be greater in solutions of F108-SDS than in solutions of either SDS or F108 because of the formation of large, charged F108-SDS complexes in solution. All else being equal, polyelectrolytes are more effective at producing depletion forces than nonionic polymers due to counterion contributions to the osmotic pressure difference between the interparticle gap and the bulk solution.20 In addition, when the interacting surfaces have a net charge of the same sign as the polyelectrolyte, electrostatic effects contribute to excluding the polymers from the gap region, in addition to steric and/or entropic effects. By forming F108-SDS complexes, the bound ionic surfactant imparts a polyelectrolyte character to the otherwise neutral polymer. F108-SDS complexation in solution has been analyzed recently by Braem et al.,21 who determined the critical aggregation concentration (cac, surfactant concentration where surfactant molecules cooperatively aggregate on the polymer chain) of the F108-SDS system to be 0.26 mM SDS in low salt (0.1 mM NaCl) conditions. In this work, we investigate depletion forces produced by the synergistic effects of these complexes.
Theory The net interaction force between the charged particle and the charged plate in our system consists primarily of two components: a repulsive electrostatic force due to the negative charge on both surfaces and an attractive depletion force. Thus,
F(h) ) Fel(h) + Fdep(h)
(1)
As is typical with force measurements between silica surfaces in aqueous solutions, van der Waals forces were not significant.22,23 It should be noted that, at low SDS-F108 ratios, such as those used in these experiments, mixed adsorbed layers form on silica surfaces, which could contribute a short-range, repulsive steric force to the net interaction.21 (No adsorption occurs for large SDS-F108 ratios at which the polymer-surfactant binding is saturated.) However, because the measurements described here focus primarily on the longer-range electrostatic and depletion interactions, such steric contributions are generally not significant. For separation distances larger than several Debye lengths, the electrostatic repulsive force in these systems can be approximated as24
Derjaguin approximation25 to account for the curvature of the particle and thus assumes that the particle radius is much greater than the characteristic length of the interaction (i.e., the Debye length), which is valid for all of the experiments presented here. It should be mentioned that while the addition of either salt (NaCl) or surfactant (SDS) will alter this force, the electrostatic repulsion should be essentially independent of the concentration of the neutral F108 polymer. For a purely electrostatic interaction, eq 1 implies that a semilog plot of the measured force versus the separation distance should yield a straight line with a slope equal to the negative inverse of the Debye length. The depletion force arises from the exclusion of material in solution from the particle-plate gap region at sufficiently small separation distances. This exclusion, which can arise from steric, entropic, or electrostatic effects, produces an osmotic pressure imbalance between the gap and bulk, resulting in an attractive force. For a purely hard sphere system, the depletion force between a spherical particle of radius R and a flat plate can be expressed using a modified form of the Asakura-Oosawa potential26
{
a h h2 for h e 2a +2- Fdep(h) ) -2πF∞aRkT R a 4aR 0 for h > 2a
(3)
where a is the radius of the nonadsorbed polymer molecules, F∞ is the bulk number density, and the factor of 2 in the prefactor term is the correction for a sphere-plate geometry versus a sphere-sphere geometry (again, using the Derjaguin approximation). In addition to assuming purely hard sphere-hard wall interactions, this equation is also restricted to relatively dilute systems since it uses the van’t Hoff relationship to calculate the osmotic pressure. The equation also ignores any effects due to changes in the configuration of the polymer coil. Walz and Sharma20 showed that when the surfaces are charged, the range and magnitude of this force can be increased substantially. Note that, in the results presented below, the concentration of polymer is presented in terms of ppm by mass. An approximate expression for the depletion force in terms of these units can be written as
Fdep(h) ≈ -2π
[
]
(ppm)NA aRkT MW a h h2 for h e 2a +2- (4) R a 4aR 0 for h > 2a
{
Here, κ is the Debye parameter (κ-1 is the Debye length), and the pre-exponential constant B is a function of the surface potentials of the particle and plate, the particle size, and the dielectric constant of the solution. This equation uses the
where ppm is the ppm of the polymer (by mass), MW is the polymer molecular weight, NA is Avogadro’s number, and the density of the polymer solution has been assumed to be 1 g/cm3. As the bulk concentration of the nonadsorbed material increases, confinement of this material in the gap region induces ordering, resulting in the formation of a long-range structural force. This force is characterized by oscillations between repulsion and attraction and has been observed in polymer,27,28 polyelectrolyte,13,14 micellar,5,7,29 and nanoparticle4,30 systems. In our particular experimental system, electrostatic, depletion, and structural forces can act on the particle simultaneously.
(18) Sakai, K.; Yoshimura, T.; Esumi, K. Langmuir 2003, 19, 1203-1208. (19) Bremmell, K. E.; Gameson, G. J.; Biggs, S. Colloids Surf., A 1999, 155, 1-10. (20) Walz, J. Y.; Sharma, A. J. Colloid Interface Sci. 1994, 168, 485-496. (21) Braem, A. D.; Prieve, D. C.; Tilton, R. D. Langmuir 2001, 17, 883-890. (22) Peschel, G.; Belouschek, P.; Mu¨ller, M. M.; Mu¨ller, M. R. Colloid Polym. Sci. 1982, 260, 444-451. (23) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Nature 1991, 353, 239241. (24) Verwey, E. J. W.; Overbeek, J. Th. G. Theory of the Stability of Lyophobic Colloids; Elsevier: Amsterdam, 1948.
(25) Derjaguin, B. V. Kolloid Z. 1934, 69, 155-164. See also: Hunter, R. J. Foundations of Colloid Science; Oxford Science Press: Oxford, 1987; Vol. I. (26) Asakura, S.; Oosawa, F. J. Chem. Phys. 1954, 22, 1255-1256. (27) Rudhardt, D.; Bechinger, C.; Leiderer, P. J. Phys.: Condens. Matter 1999, 1, 10073-10078. (28) Bechinger, C.; Rudhardt, D.; Leiderer, P.; Roth, R.; Dietrich, S. Phys. ReV. Lett. 1999, 83, 3960-3963. (29) Tulpar, A.; Van Tassel, P. R.; Walz, J. Y. Langmuir 2006, 22, 28762883. (30) Lazzara, G.; Milioto, S.; Gradzielski, M. Phys. Chem. Chem. Phys. 2006, 8, 2299-2312.
Fel(h) ) κB exp(-κh)
(2)
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Whether the net force, which is what is measured, is attractive or repulsive at any given separation will depend on the relative magnitudes of these contributions. Experimental Section Materials. Water was purified with a NANOPure water purification system (Barnstead Thermolyne Corp., Dubuque, IA) that was equipped with a 0.22 µm filter. NaCl (Sigma, St. Louis, MO) was roasted in air at 400 °C for 16 h. The flat substrate used in the AFM measurements consisted of polished fused silica flats (Melles Griot, Irvine, CA) with a diameter of 12.5 mm and a thickness of 3 mm. The flats had a root mean square (rms) roughness of 99% pure, from Fluka Chemical, Milwaukee, WI) was used as received. The concentration of surface-active contaminants was low because surface tension measurements revealed no minimum in the surface tension versus ln(concentration). Solutions. For the surfactant experiments, the SDS solutions were prepared on the same day as the actual experiment to minimize the formation of dodecanol. Pluronic F108 solutions were prepared 1 day prior to the experiment. All solutions were prepared at a background concentration of 0.1 mM NaCl with the exception of the SDS-only solutions, which contained no added salt, and the F108 solutions, which contained 0.1 M NaCl. No pH adjustment was made. Atomic Force Microscopy (AFM). Force-distance measurements were performed with a Multi-mode AFM (Veeco Metrology, Santa Barbara, CA). The force-separation profiles were obtained following the analysis of Ducker et al.31 The silica spheres were attached to AFM cantilevers (Bio-levers, Asylum Research Corporation, Santa Barbara, CA) using a UV-curable epoxy (NEA 123L, Norland Product Inc., Cranbury, NJ). The size of the spheres was measured after each experiment using scanning electron microscopy (SEM). The spring constant (0.006-0.01 N m-1) of each cantilever was determined by the method of Sader.32 Prior to each experiment, the silica plates were rinsed with a 0.1 M NaOH solution, prepared from a 1 N NaOH solution (Fisher Scientific, Fairlawn, NJ), rinsed with purified water and 200 proof ethanol (Pharmco Products Inc., Brookfield, CT), and then rinsed again with purified water. The silica plate and the silica sphere attached to the AFM cantilever were treated with UV radiation (TipCleaner from BioForce Nanosciences, Ames, IA) for 45 min and for 10 min, respectively, to render the surfaces hydrophilic and to remove organic material prior to setting up the AFM. Before the injection of the solutions, the fluid cell was rinsed with 200 proof ethanol, with a 50% ethanol-water mixture, and finally with water. The z-axis of the piezo was calibrated using a silicon calibration reference of 104 nm step height (Silicon-MDT, Moscow, Russia). The calibration was cross-checked by measuring the decay length of double-layer forces in 10-4, 10-3, and 10-2 M NaCl solutions. All solutions were left inside the liquid cell for 15-30 min before data acquisition. Multiple approach and separation runs were performed in each experiment. Scanning frequencies of the approach-separation runs were 0.1 Hz for scan sizes of 80-300 nm, giving approach-retraction speeds ranging between 16 and 60 nm/s. Independent measurements have shown that hydrodynamic forces are negligible at these scan speeds.33 Measurements were performed in the temperature range 22 ( 2 °C. (31) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Langmuir 1992, 8, 18311836. (32) Sader, J. E.; Chon, J. W. M.; Mulvaney, P. ReV. Sci. Instrum. 1999, 70, 3967-3969. (33) Tulpar, A.; Walz, J. Y. Colloids Surf., A, in press.
Figure 1. Forces between a silica sphere and a silica plate in 0.1 M aqueous solutions of F108. Part b is a semilog plot of the data. (Note that not all of the solutions are shown in part b for reasons of clarity.) The slope of each curve of part b in the linear region provides the negative inverse of the decay length of the force.
Results and Discussion Experiments with Pluronic F108. The forces in this work, F, are normalized by the radius of the silica particle, R, since, in the Derjaguin limit (applicable here), the magnitude of the force is proportional to the particle radius.25 Figure 1 shows the force between the silica particle and silica plate as a function of the bulk concentration of F108 at a fixed ionic strength of 0.1 M NaCl. (This relatively high ionic strength was used to screen the electrostatic repulsion between the charged particle and plate sufficiently so that any depletion interaction that might be present could be detected.) The concentration range of F108 is below the critical micelle concentration (cmc) for this polymer, 45 mg/ mL.34 The force profiles show a very slight attraction at ∼5 nm separations but are primarily repulsive. Figure 1b shows a semilog plot of the data. From the slope of these plots, we can determine the decay lengths of the force (34) Alexandridis, P.; Holzwarth, J. F.; Hatton, T. A. Macromolecules 1994, 27, 2414-2425.
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Figure 2. Forces between a silica sphere and a silica plate in aqueous solutions of SDS. Part b is a semilog plot of the data.
profile (the decay length is the distance over which the force drops by a factor of 1/e). At F108 concentrations of 0, 200, 1000, and 10 000 ppm, the decay lengths are 0.68, 0.84, 0.95, and 1.60 nm, respectively. By comparison, the predicted Debye length in 0.1 M NaCl is 0.96 nm. This value should be compared to the measured decay length of 0.68 nm obtained with no added polymer. The fact that our measured decay length is ∼30% lower than that predicted for a purely electrostatic interaction is most likely a result of either surface irregularities at these relatively small separations or the presence of an additional repulsive force, such as the hydration force that has been observed by other researchers with silica-silica interactions.22,23 As the concentration of F108 increases, the decay lengths also increase, such that the value at 10 000 ppm polymer is over twice that of the salt-only system. The exact cause of this trend is difficult to determine, since there are a number of different interactions that can arise upon the addition of polymer. One possible contribution would be a depletion attraction arising from the exclusion of the F108 chains from the gap at small separations. For example, using a Rg of 4 nm and assuming a concentration
SDS conc/mM
calc Debye length/nm
meas decay length/nm
2 4 6 8
6.8 4.8 3.9 3.4
6.4 ( 0.2 4.2 ( 0.3 3.7 ( 0.2 3.2 ( 0.2
of 10 000 ppm, eq 4 predicts Fdep/R values of -0.085 mN/m at contact and -0.064 mN/m at 2 nm separation, which are clearly large enough to significantly alter the force profiles in Figure 1a. Another contributing factor could be the presence of a steric repulsion, which could be important at the relatively small separations shown in Figure 1. Braem et al.21 showed that, in the absence of SDS, F108 will adsorb onto silica surfaces in a homopolymer-like conformation. McLean et al.35 measured the force between adsorbed layers of F108 on silica in 0.15 M NaCl and observed a long-ranged shallow attractive force at ∼10 nm separation and a weak steric repulsion. The authors attributed the attractive force to van der Waals or bridging forces. (The reason for the discrepancy between our measured force profiles and those of McLean et al. is not known, as the only apparent difference in the experiments is that our force measurements were done in the presence of F108 in 0.1 M NaCl solution, while the measurements of McLean et al. were performed in the absence of F108 in solution, that is, with adsorbed polymer only.) A comment should also be made concerning the lack of a significant depletion attraction in Figure 1 at the highest F108 concentration. Specifically, the predicted values of Fdep/R mentioned above (e.g., -0.085 mN/M at contact) are substantially larger than the forces measured with no added polymer. Again, one possible contributing factor here is the presence of an adsorbed polymer layer. While it is known that depletion forces can still arise in the presence of adsorbed polymer,15 it is possible that the force is much weaker than that predicted by the AsakuraOosawa model of eq 3, since this equation assumes purely hard sphere-hard wall interactions between all species. Likewise, a strong steric repulsion would tend to counteract the attractive depletion force. Another issue that should be mentioned concerns the separation distances shown in Figure 1. In performing the AFM experiments, determining the absolute separation distance requires forcing the particle into hard contact with the plate (termed the point of constant compliance), which provides a reference point from which all separations are measured. If this point of constant compliance is not measured correctly, which can result from factors such as surface roughness or problems with interpreting the AFM deflection curves, then the measured separation distances will be less than the true values. While such an error would not affect the measured decay lengths reported in this paper, it would hinder making a comparison between the measured and predicted depletion forces, especially at the relatively small separations shown in Figure 1. While there are clearly a number of complicating factors, especially at the relatively small separation distances shown in Figure 1, the important point that should be emphasized here is that, with only F108 in solution, the force profiles are primarily repulsive at all separation distances. Experiments with SDS. Figure 2 shows the force between the silica particle and the silica plate as a function of the concentration of SDS up to the cmc, 8 mM. These SDS-only solutions contained no added salt. The force is again repulsive at all separations. The decay lengths of the force profiles are in (35) McLean, S. C.; Lioe, H.; Meagher, L.; Craig, V. S. C.; Gee, M. L. Langmuir 2005, 21, 2199-2208.
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Figure 3. Forces between a silica sphere and a silica plate in aqueous SDS micellar solutions. The force profiles have been offset vertically for ease of viewing. Table 2. Decay Lengths of SDS Solutions with 200 and 1000 ppm Pluronic F108a meas decay length/nm SDS conc/mM 0.2 0.4 0.6 0.8 1 2 8 a
calc Debye length/nm 17.6 13.6 11.5 10.1 9.2 6.6 3.4
200 ppm 15.9 ( 1.2 10.8 ( 1.4 10.2 ( 1.3 8.2 ( 0.7 7.3 ( 0.4 6.0 ( 0.7
1000 ppm
Figure 4. Forces between a silica sphere and a silica plate in aqueous SDS micellar solutions and in aqueous SDS solutions with 1000 ppm F108. The force profiles at the two different SDS concentrations have been offset vertically for ease of viewing. Table 3. Decay Lengths of SDS Solutions with 10 000 ppm Pluronic F108a SDS conc/mM
calc Debye length/nm
meas decay length/nm
0.2 0.4 0.6 0.8 2
17.6 13.6 11.5 10.1 6.6
11.1 ( 0.4 9.5 ( 0.6 6.4 ( 0.4 5.8 ( 0.7 2.5 ( 0.4
16.1 ( 0.5 11.0 ( 1.1 8.8 ( 0.4 7.6 ( 0.6 5.0 ( 0.5 1.8 ( 0.2
Background solution contains 0.1 mM NaCl.
good agreement with the calculated Debye lengths, as can be seen from Table 1. Figure 3 shows the onset of a net attractive force at 16 mM (2 × cmc), which we attribute to a depletion force arising from the exclusion of the micelles from the gap region between the silica sphere and the silica plate. As the concentration of SDS increases, the magnitude of the depletion force increases. At higher concentrations (24 mM), we observe a slight repulsion at distances beyond the depletion attraction, which we attribute to the onset of a structural force due to the confinement-induced ordering of the micelles in the gap region. Tulpar et al. conducted very similar measurements to those described here at SDS concentrations up to 50 times the cmc and saw very clear oscillations arising from the ordering of the micelles.29 Experiments with SDS in 200 and 1000 ppm Pluronic F108. In the presence of either 200 or 1000 ppm F108, the net force between the silica particle and the silica plate is found to remain repulsive below 16 mM SDS. The decay lengths of the force curves are given in Table 2. As compared to the SDS-only solutions, which showed good agreement between the measured decay lengths and predicted Debye lengths (Table 1), the decay lengths in these solutions are now slightly smaller than the Debye lengths, suggesting an additional attractive force acting on the particle (i.e., the depletion component). Braem et al.21 found that the critical aggregation concentration (cac) of the F108-SDS system was 0.26 mM in 0.1 mM NaCl; thus, some large, charged complexes would be expected to be present at these conditions.
a
Background solution contains 0.1 mM NaCl.
This additional attractive force can be seen more clearly in Figure 4, which shows the total force profile measured in solutions containing 1000 ppm Pluronic F108 and 16 and 32 mM SDS. As with the SDS-only profile, a net attractive force between the particle and the plate is now observed; however, the magnitude of this attraction is clearly greater in solutions containing the polymer. We should point out that it is likely that the SDS concentration at which a net attraction is observed is most likely lower in solutions containing the polymer than in the SDS-only solutions. However, experiments to determine the exact SDS concentration at which this attraction occurs were not performed. In the 32 mM SDS curves shown in Figure 4, a slight repulsion is again observed in both the SDS-only and SDS-polymer mixtures at distances beyond the onset of the depletion attraction. A comment should be made here concerning the dependence of the measured decay lengths on SDS concentration in the SDSF108 mixtures. Although most of the data presented in Tables 2 and 3 were obtained above the reported cac for this system (0.26 mM SDS), the measured decay lengths still agree relatively well with the predicted Debye lengths, especially at the lowest F108 concentration of 200 ppm. In fact, a log-log plot of the measured decay length versus ionic strength for this 200 ppm system yields a scaling exponent of -0.50, which is the same dependence as that of the bulk Debye length on ionic strength (i.e., κ-1 ∼ I-1/2). What this means is that, even above the cac, the electrostatic screening length in these systems is determined by the total concentration of surfactant in the system. This is a very different behavior than that observed with micelles. For
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Figure 5. Forces between a silica sphere and a silica plate in a 2 mM SDS solution and in a 2 mM SDS solution with 10 000 ppm F108.
example, Tulpar et al.36 found that the electrostatic screening length in SDS solutions became relatively constant with respect to SDS concentration once the critical micelle concentration was reached. The cause of this different screening behavior is currently not understood. However, one possible reason is that the surfactant monomers aggregated on the F108 chains are much more dissociated than those in the micelles and continue to screen the electric fields produced by the charged surfaces, but this is speculation at this point. Another possibility is that, unlike conventional micellization, the free surfactant monomer concentration perhaps continues to rise with increasing surfactant concentration above the cac and, thereby, contributes fully dissociated 1:1 electrolytes to the total electrostatic screening. Because of these complexities, we have not attempted to isolate the depletion-only component of the force in the solutions in which both depletion attraction and electrostatic repulsion forces are observed. Specifically, isolating the depletion component involves subtracting a known electrostatic force from the measured force profile. However, this analysis requires assuming that the electrostatic component is not altered by the polymer-surfactant complexation, which may not be the case. For example, in Figure 4, some of the difference between the SDS-only curves and those with SDS plus 10 000 ppm polymer could be due to changes in the electrostatic repulsion between the particle and plate brought about by the polymer-surfactant complexation. Experiments with SDS in 10 000 ppm Pluronic F108. To further explore the effect of the polymer, we also performed measurements in solutions containing 5000 and 10 000 ppm F108. Because of the similarity of the results, we present here only the results at 10 000 ppm. In the presence of 10 000 ppm polymer, the net force between the silica particle and the silica plate is repulsive below 4 mM SDS. The decay lengths of the force curves are given in Table 3. There is now a significant discrepancy between the decay lengths and predicted Debye lengths, which we again attribute to the presence of a strong depletion attraction between the particle and plate. This can be seen more clearly in Figure 5, which shows the force curves measured in 2 mM SDS only and in 2 (36) Tulpar, A.; Subramanian, V.; Ducker, W. Langmuir 2001, 17, 84518454.
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Figure 6. Forces between a silica sphere and a silica plate in aqueous SDS solutions with 10 000 ppm F108. The force profiles have been offset vertically for ease of viewing.
Figure 7. Comparison of forces between a silica sphere and a silica plate in SDS solutions and in SDS solutions with 10 000 ppm F108. The force profiles at the two different SDS concentrations have been offset vertically for ease of viewing.
mM SDS plus 10 000 ppm F108. At 4 mM SDS and 10 000 ppm polymer (Figure 6), the force profile displays a net attraction. Recall that, in SDS-only solutions, the onset of a net attractive force was not observed until 16 mM SDS, and no depletion force was observed in 10 000 ppm F108-only solutions. At 6 ppm SDS (Figure 6), the onset of oscillations in the profile can be discerned, again indicating the development of ordering in the gap region. Figure 7 compares the forces measured in 8 mM SDS-only solutions and in 16 mM SDS-only solutions with those measured in solutions of 8 mM SDS and 16 mM SDS in 10 000 ppm Pluronic F108, respectively. There is a significant depletion force in the presence of the polymer at 8 mM SDS, while in SDS-only solutions the force is purely electrostatic and repulsive. In 16 mM SDS and 10 000 ppm F108, we observe a clear structural force profile (evidenced by the net repulsion seen around 10 nm
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speculated that SDS surrounds the hydrophobic poly(propylene oxide) (PPO), forming a “bottlebrush” structure.21 Therefore, when SDS binds to F108, the resulting complex may be regarded as a large polyelectrolyte. The elongation of the polymer due to the repulsion between the charged surfactant micelles along the polymer chain is termed the polyelectrolyte effect.39 The magnitude and range of the depletion force produced by a polyelectrolyte are greater than those for a nonionic polymer, as discussed elsewhere.14,15,27 One reason for this is because, in the polyelectrolyte system, the counterions along the polyelectrolyte chain are also excluded from the gap region. In this work, we have measured the manifestation of the polyelectrolyte effect in the enhanced strength of depletion forces.
Conclusions
Figure 8. Forces between a silica sphere and a silica plate in an 8 mM SDS solution, in an 8 mM NaCl solution with 10 000 ppm F108, and in an 8 mM SDS solution with 10 000 ppm F108.
separations), while, in 16 mM SDS-only solutions, we observed a depletion force only without any structural component (see also Figure 3). Figure 8 summarizes the importance of the presence of both the surfactant and the polymer on the depletion force between two silica surfaces. Here, we keep the total ionic strength constant at 8 mM. The force curve measured in the 8 mM SDS-only solution overlaps almost perfectly with that measured in 8 mM NaCl plus 10 000 ppm F108. The force is mainly electrostatic in origin, and the decay length, given in Table 1, is governed by the concentration of SDS or NaCl. The presence of F108 in NaCl-only solutions does not affect the electrostatic force, which is expected for a purely electrostatic force. When both F108 and SDS are present in the solution, a depletion force is observed. While the exact structure of the F108-SDS complex is not known, it is well established in the literature that SDS forms micellelike clusters on poly(ethylene oxide) (PEO).37,38 It is also (37) Cabane, B. J. Phys. Chem. 1977, 81, 1639-1645.
The force between a silica plate and a silica surface is repulsive in a neutral triblock copolymer solution, Pluronic F108, and in an anionic surfactant solution, SDS, below 16 mM. Above 16 mM SDS, a significant depletion force develops. When both SDS and F108 are present in solution, the onset of the depletion force occurs at
