Langmuir 2001, 17, 5693-5695
Polymer-Induced Repulsive Forces at Solid-Liquid and at Liquid-Liquid Interfaces P. Omarjee, A. Espert, and O. Mondain-Monval* Centre de Recherche Paul Pascal, CNRS, Av. A. Schweitzer, 33600 Pessac, France J. Klein*,† Weizmann Institute of Science, 76100 Rehovot, Israel Received February 5, 2001. In Final Form: May 17, 2001
Introduction and Experimental Background Polymers are commonly used to coat colloidal particles in a wide range of systems in order to prevent their coalescence or aggregation.1 In addition to this technological aspect, the issue of interactions generated by the adsorbed macromolecules at the particle-continuous phase interface is of basic interest and has been extensively studied.1,2 Some of the earliest direct studies were carried out using the mica surface forces balance (SFB), which allows the forces between solid surfaces immersed in a solvent to be determined.3 Thus, the force-distance interaction profiles between polymer-covered mica surfaces across a good solvent have been investigated4 and interpreted within a scaling framework.5 More recently, two other techniques were used to determine forcedistance profiles between different pairs of fluid interfaces (oil-water and air-water),6 and the results were compared with a model of adsorbed polymer layers based on a self-consistent mean-field (SCMF) analysis.7 In the present paper, results from the two experimental studies4,6 are critically compared. We find that both sets of data show repulsive interactions that increase exponentially with decreasing surface separation, with characteristic lengths λ which depend on the polymer unperturbed dimensions Rg, in agreement with theoretical expectations. Remarkably, the dependence of these characteristic lengths on Rg is identical (within scatter) for all systems studied and for the three experimental approaches, indicating the robustness of this behavior. Differences in the magnitude of the forces (i.e., the pre-exponential factors) may derive from the different experimental configurations. † Correspondence should be sent to W.I.S. or to: Physical and Theoretical Chemistry Laboratory, Oxford University, Oxford OX1 3QZ, U.K.
(1) Napper, D. H. Polymeric Stabilization of Colloidal Dispersions; Academic Press: London, 1989. (2) Fleer, G.; Cohen Stuart, M.; Scheutjens, J.; Cosgrove, T.; Vincent, B. Polymers at Interfaces; Chapman and Hall: New York, 1993. (3) Klein, J. In Molecular Conformation and dynamics of macromolecules in condensed systems; Nagasawa, M., Ed.; Elsevier: Amsterdam, 1988; p 333-352. Patel, S. S.; Tirrell, M. Annu. Rev. Phys. Chem. 1989, 40, 597 and references therein. (4) Klein, J.; Luckham, P. F. Nature 1982, 300, 429; Macromolecules 1984, 17, 1041; Luckham, P. F.; Klein, J. Macromolecules 1985, 18, 721; J. Chem. Soc., Faraday Trans. 1990, 86, 1363. (5) de Gennes, P. G. Macromolecules 1981, 14, 1637; 1982, 15, 492. de Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell University Press: London, 1979. (6) Mondain-Monval, O.; Espert, A.; Omarjee, P.; Bibette, J.; Leal Calderon, F.; Philip, J.; Joanny, J.-F. Phys. Rev. Lett. 1998, 80, 1778; Macromolecules 1998, 31, 7023. (7) Semenov, A. N.; Bonet-Avalos, J.; Johner, A.; Joanny, J.-F. Macromolecules 1996, 29, 2179; 1997, 30, 1479.
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Forces between solid-fluid interfaces were measured using the mica surface force balance technique, details of which have been extensively published (see e.g. ref 4 for details of the procedure used to obtain the data appearing in this paper). Forces F(h) are measured between two curved mica (or polymer-covered mica) surfaces as their closest separation h changes, via a direct determination of the bending of a spring on which one of them is mounted. The mean radius of curvature R of the mica sheets is of the order of 1 cm, so that R . h, and in the Derjaguin approximation F(h)/R ) W(h), the interaction energy per unit area between flat parallel plates obeying the same force law.12 Forces were measured between mica surfaces in solutions of poly(ethylene oxide) (PEO, Mw ) 40 000 and 160 000) in toluene and in 0.1 M KNO3 aqueous salt solution;4 both are good to marginally good solvents for the PEO. Following adsorption of the polymer, the forcedistance profiles were determined from the onset of repulsion (for values of the normalized force F(h)/R > ca. (2-20) µN/m) up to high compressions (F(h)/R > 104 µN/ m). Force measurements between oil-water interfaces were carried out as follows: Emulsion droplets (radius R ) ca. 100 nm) of a magnetic fluid (an octane dispersion of Fe2O3) stabilized with a water-soluble surfactant were created in an aqueous medium, with the polymer of interest (see below) adsorbing at the oil-water interface. By imposing a magnetic field, polarized droplet chains align along the field and diffract light, allowing their spacing to be measured precisely. Since a given field corresponds to a known attractive force between the droplets, the opposing repulsive forces F(h) at different separations h may be deduced, and the force profile can be measured from the onset of droplet-chain formation up to the saturation of the ferrofluid magnetization. Normalized forces F(h)/R were measured in the range 1-100 µN/m.8 Disjoining pressure isotherms Π(h) between air-water interfaces were determined using a modified version9 of the porous plate technique first developed by Mysels and Jones.10 A thick liquid lens is formed in the center of a small hole drilled in a porous glass disk fused to a capillary tube and exposed to a constant reference pressure. An applied pressure difference Π causes the fluid to drain forming a flat horizontal liquid film, which stabilizes at a thickness h (measured using an interferometric method11) when the surface force per unit area balances the applied pressure difference (Π(h)). The force-distance profiles are calculated from the disjoining pressuredistance profiles by using the Derjaguin approximation.12 Using the two above methods, we measured the intersurface forces when a statistical copolymer (poly(vinyl alcohol)-co-poly(vinyl acetate), PVA-VAc, of average molecular weights Mw ) 55 000 and 155 000) adsorbs at the emulsion droplet/water interface and at the air-water (8) Leal Calderon, F.; Stora, T.; Mondain-Monval, O.; Poulin, P.; Bibette, J. Phys. Rev. Lett. 1994, 72, 865; J. Phys. II (France) 1996, 6, 1313. (9) Bergeron, V.; Radke, C. J. Langmuir 1992, 8, 3020. Espert, A.; Colin, A.; von Klitzing, R.; Poulin, P.; Zana, R. Langmuir 1998, 14, 4251. (10) Mysels, K.; Jones, M. N. Discuss. Faraday Soc. 1966, 42, 50. (11) Sheludko, A. Adv. Colloid Interface Sci. 1967, 1, 391. (12) Derjaguin, B. V. Kolloidn. Zh. 1934, 69, 155. W(h) for the porous plate method is evaluated from the disjoining pressure as W(h) ) ∫ Π(h′) dh′, integrated from large film thicknesses down to h, and is then converted to F(h)/R ) 2πW(h) (the Derjaguin approximation).
10.1021/la010198g CCC: $20.00 © 2001 American Chemical Society Published on Web 08/11/2001
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Notes
Figure 2. Force-distance profiles between polymer-covered mica surfaces in the distal regime. 9: PEO, Mw ) 1 120 000, mica-water/0.1 M KNO3 interface. 2: PEO, Mw ) 310 000, mica-toluene interface. Data were extracted from ref 4. Data points below ca. 10-20 µN/m are within the range of scatter (ref 4) and are not used for the exponential fit.
Figure 1. Force-distance profiles between polymer-covered interfaces in the distal regime: (a) ×: PVA-VAc, Mw ) 55 000, air-water interface. +: PVA-VAc, Mw ) 55 000, octane-water interface. b: PEO, Mw ) 40 000, mica-toluene interface. [: PEO, Mw ) 40 000; mica-water/0.1 M KNO3 interface. (b) b: PEO, Mw ) 160 000, mica-water/0.1 M KNO3 interface. [: PEO, Mw ) 160 000, mica-toluene interface. ×: PVA-VAc, Mw ) 155 000, octane-water interface. +: PVA-VAc, Mw ) 155 000, air-water interface. Data were extracted from refs 4 and 6. For the SFB profiles, data points below ca. 10-20 µN/m are within the range of scatter (ref 4) and are not used for the exponential fit.
interface, respectively. Measurements were taken both in 0.1 M aqueous salt solution and in salt-free water: the agreement of the force-distance characteristics in both these conditions confirms that they are dominated by steric effects due to the polymer rather than by double-layer electrostatic repulsions as might arise from charging of the surfaces. Results and Discussion To compare the different sets of data obtained with these three techniques, we plot in Figure 1 the F/R versus distance profiles obtained with polymers of comparable molecular weights (Figure 1a, PEO 40 000 with PVAVAc 55 000; Figure 1b, PEO 160 000 with PVA-VAc 155 000). We also plot, in Figure 2, the F/R versus distance profile obtained with the SFB in PEO solutions of other molecular weights (310 000 and 1 120 000). The disjoining pressure versus film thickness profiles (for the case of the fluid-fluid interfaces) were transformed into F/R versus distance profiles using the Derjaguin approximation.12 Our main observation from Figures 1 and 2 is that the
profiles are qualitatively similar: the forces decay exponentially with comparable characteristic distances for both types of interface. We note that the measured forces between polymers adsorbed at the solid surfaces are roughly 1 order of magnitude larger than those measured between polymers adsorbed at the fluid interfaces, a point considered further below. Theoretically, the variation of interaction with separation between two surfaces covered with an adsorbed polymer layer immersed in a good solvent is expected to depend on the regime of distance between the plates.5,7 At small surface separations, the polymer volume fraction is essentially due to the presence of loops, and two regimes of force behaviors are expected depending on the range of distance considered. At strong compressions (small surface separations, or “proximal” regime), the repulsive interaction energy is expected to vary as a power law h-p, where p ) 1.25-1, depending on whether the compressed interacting layers are in the semidilute or in the concentrated regime.4,5 A second (“central”) regime is expected at intermediate separations,5 where the interaction energy should scale as h-2. Such behavior was indeed qualitatively compatible with force measurements performed with the SFB in these two separation regimes.4 In the regime of large distances and weak interactions (the “distal” regime), that is, when the opposite polymer layers just start to overlap and interact, one expects the contribution of polymer tails to dominate. The interaction in this regime is expected to decay exponentially, with a decay length comparable to the free coil size, largely because the segment density profile in this distal regime is generally taken to decay in this manner [see e.g. ref 1 and also ref 4]. More recent calculations using an SCMF approach7 provide an explicit calculation of this, and the following law is expected for the repulsive force between two interfaces a distance h apart bearing adsorbed polymers:
F(h)/R ) A exp(-h/λ)
(1)
where A is a prefactor and λ is a length that is proportional to the polymer coil gyration radius Rg: λ ∼ Rg. In the regime that we focus on here, the forces are indeed exponentially decaying and are fitted to eq 1. In Figure 3, we plot the best-fit λ values versus the corresponding
Notes
Figure 3. Scaling of the force-distance profile characteristic length λ with the polymer coil gyration radius Rg(obtained as detailed in refs 4 and 6). The values of λ are deduced from the best fits to the data of Figures 1 and 2. b: PEO, mica-toluene interface. [: PEO, mica-water/0.1 M KNO3 interface. 1: PVAVAc, octane-water interface. ×: PVA-VAc, air-water interface. (Data for the PVA-VAc system include λ values for the full set of three molecular weights at two different temperatures, taken from ref 6).
polymer coil gyration radius for all three cases. The linear scaling of λ with Rg over the entire range of parameters is striking and in good agreement with the predictions: we find λ ) CRg, with C ) 0.8 ( 0.15. The differences in the prefactor A between the PVAVAc (at water/air or water/oil interfaces) and the PEO (at solid/water or solid/toluene interfaces) is attributable to the different polymer/solvent systems as well as to the different experimental configurations. Thus, the PVAVAc adsorbance at the oil-water interface, which lies between 1.5 and 2.2 mg/m2, is significantly lower than the PEO adsorbance at the mica/liquid interface, which is around 4 mg/m2; one expects a higher segment concentra-
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tion in the overlapping regions to lead to stronger repulsion. In addition, the vinyl acetate groups on the opposing copolymer layers in the fluid-fluid experiments may undergo some attractive interaction thereby reducing the absolute repulsion measured. Finally, the mobility of the adsorbed polymer on the highly curved fluid emulsion surfaces may also result in some reduction of the absolute repulsion when the layers are compressed (as chains can respond by moving sideways). All these effects would result in a lower absolute repulsion between the fluid-adsorbed compared with the solid-adsorbed polymers, which is indeed what we observe qualitatively, though we have not attempted a more quantitative estimate. Finally, we recall that the solvency of the two polymers studied in their respective solvents (i.e., the magnitude of the excluded volume effect) may differ, which could be tested by measuring the interactions between mica plates in the presence of PVA-VAc. In conclusion, we have measured and compared the forces between different polymers adsorbed at different surfaces, as determined by three different methods involving liquid-liquid, liquid-air, and liquid-solid interfaces. In the distal regime (weak interactions at the onset of overlap), the forces are exponentially decaying with characteristic distances depending linearly on the polymer chain gyration radius. Such qualitative behavior is very general and is not expected to depend on the type of interfaces or details of the polymer-good solvent system (in contrast to the pre-exponential factors or absolute magnitudes, which may be system-dependent as discussed above). The results compare well with theoretical predictions attributing the repulsive forces to the compression of the outermost part of the surface-adsorbed layers. Acknowledgment. J.K. thanks the Deutsches-Israelische Program (DIP) and the US-Israel BSF for support. O.M.-M. thanks J. F. Joanny for useful discussions. LA010198G
