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Surface Forces between Telechelic Brushes Revisited: The Origin of a Weak Attraction Dapeng Cao† and Jianzhong Wu* Department of Chemical and EnVironmental Engineering, UniVersity of California, RiVerside, California 92521 ReceiVed October 13, 2005. In Final Form: January 12, 2006 Telechelic polymers are useful for surface protection and stabilization of colloidal dispersions by the formation of polymer brushes. A number of theoretical investigations have been reported on a weak attraction between two telechelic brushes when they are at the classical contact, i.e., when the surface separation is approximately equal to the summation of the brush thicknesses. While recent experiments have confirmed the weak attraction between telechelic brushes, its origin remains elusive because of conflicting approximations used in the previous theoretical calculations. In this paper, we have investigated the telechelic polymer-mediated surface forces by using a polymer density functional theory (PDFT) that accounts for both the surface-adhesive energy and segment-level interactions specifically. Within a single theoretical framework, the PDFT is able to capture both the depletion-induced attraction in the presence of weakly adhesive polymers and the steric repulsion between compressed polymer brushes. In comparison of the solvation forces between telechelic brushes with those between brushes formed by surfactant-like polymers and with those between two asymmetric surfaces mediated by telechelic polymers, we conclude that the weak attraction between telechelic brushes is primarily caused by the bridging effect. Although both the surfactant-like and telechelic polymers exhibit a similar scaling behavior for the brush thickness, a significant difference has been observed in terms of the brush microstructures, in particular, the segment densities near the edges of the polymer brushes.
1. Introduction Polymers tethered onto a solid surface are useful for colloidal stabilization and for prevention of often undesirable, nonspecific adsorptions.1,2 For example, hydrophilic polymers such as poly(ethylene glycol) (PEG) or poly(ethylene oxide) (PEO) are widely used for improving the biocompatibility of implanted medical devices and for stabilizing liposomes devised as drug carriers.3 A similar concept has been proposed recently for controlling adsorption of biomacromolecules secreted by microorganisms.4 The conformations of one-end-grafted, uncharged linear polymers in a good solvent and interactions between polymer-grafted surfaces have been well-documented.5-9 A widely held theoretical approach was developed by Milner, Witten, and Cates (MWC)10 on the basis of earlier concepts proposed by Alexander11 and more comprehensively by de Gennes.12 This analytical selfconsistent mean-field theory predicts that, in a good solvent and at moderately high surface coverage, the end-grafted polymer * To whom correspondence should be addressed. E-mail:
[email protected]. † Current address: P.O. Box 100, College of Chemical Engineering, Beijing University of Chemical Technology, Beijing 100029, People’s Republic of China. (1) Halperin, A.; Tirrell, M.; Lodge, T. P. AdV. Polym. Sci. 1992, 100, 31-71. (2) Currie, E. P. K.; Norde, W.; Stuart, M. A. C. AdV. Colloid Interface Sci. 2003, 100, 205-265. (3) Castner, D. G.; Ratner, B. D. Surf. Sci. 2002, 500, 28-60. (4) Hoipkemeier-Wilson, L.; Schumacher, J.; Carman, M.; Gibson, A.; Feinberg, A.; Callow, M.; Finlay, J.; Callow, J.; Brennan, A. Biofouling 2004, 20, 53-63. (5) Netz, R. R.; Andelman, D. Phys. Rep. 2003, 380, 1-95. (6) Kreer, T.; Metzger, S.; Muller, M.; Binder, K.; Baschnagel, J. J. Chem. Phys. 2004, 120, 4012-4023. (7) Singh, C.; Pickett, G. T.; Balazs, A. C. Macromolecules 1996, 29, 75597570. (8) Zhulina, E. B.; Borisov, O. V.; Priamitsyn, V. A. J. Colloid Interface Sci. 1990, 137, 495-511. (9) Szleifer, I. Biophys. J. 1997, 72, 595-612. (10) Milner, S. T.; Witten, T. A.; Cates, M. E. Macromolecules 1988, 21, 2610-2619. (11) Alexander, S. J. Phys. IV 1977, 38, 983-987. (12) de Gennes, P. G. Macromolecules 1980, 13, 1069-1075.
brushes exhibit a parabolic local density profile and the surface potential between two brush layers varies as the cube of the compression distance. These theoretical predictions have been validated with results from molecular simulations for various coarse-grained models of grafted polymers.6 Telechelic polymers are linear chains with functional groups at both ends. If the polymer backbone is highly soluble and the ends can be attached to a solid surface, telechelic polymers also provide a steric repulsive layer useful for surface protection. Two types of telechelic polymers have been extensively studied in the literature. One is represented by ABA triblock copolymers, such as PEO-polystyrene (PS)-PEO, where block “A” can be absorbed onto the surface but block “B” cannot.13 The other consists of end-modified homopolymers such as long hydrophilic polymers with a small hydrophobic or ionic group at each end.14,15 Previous experiments and theoretical calculations both indicate that the interaction between two highly stretched telechelic brushes is primarily repulsive, resembling that between two singly tethered polymer brushes.16-19 Nevertheless, a weakly attractive force has also been observed when the two telechelic brushes are near contact; i.e., the separation is about twice the thickness of an isolated brush.14,20,21 The origin of such a weak attraction has been subjected to a number of theoretical analyses.22-29 Witten (13) Dai, L. M.; Toprakcioglu, C. Macromolecules 1992, 25, 6000-6006. (14) Eiser, E.; Klein, J.; Witten, T. A.; Fetters, L. J. Phys. ReV. Lett. 1999, 82, 5076-5079. (15) Berret, J. F.; Serero, Y. Phys. ReV. Lett. 2001, 8704. (16) Bhatia, S. R.; Russel, W. B. Macromolecules 2000, 33, 5713-5720. (17) Klein, J. J. Phys: Condens. Matter 2000, 12, A19-A27. (18) Pham, Q. T.; Russel, W. B.; Thibeault, J. C.; Lau, W. Macromolecules 1999, 32, 5139-5146. (19) Pham, Q. T.; Russel, W. B.; Thibeault, J. C.; Lau, W. Macromolecules 1999, 32, 2996-3005. (20) Wijmans, C. M.; Leermakers, F. A. M.; Fleer, G. J. J. Colloid Interface Sci. 1994, 167, 124-134. (21) Zhulina, E.; Singh, C.; Balazs, A. C. Langmuir 1999, 15, 3935-3943. (22) Milner, S. T.; Witten, T. A. Macromolecules 1992, 25, 5495-5503. (23) Johner, A.; Joanny, J. F. J. Chem. Phys. 1992, 96, 6257-6273.
10.1021/la0527588 CCC: $33.50 © 2006 American Chemical Society Published on Web 02/17/2006
The Origin of a Weak Attraction
and co-workers suggested that the attraction is due to thermal fluctuations of the middle segments near the edge of the polymer brush, which allow the polymer ends to penetrate into the opposite brush to form the bridges.22,25 They predicted that, near the classical contact, the number of bridges is proportional to the mean-square end-to-end distance of the polymer and rises linearly with the compression distance as the telechelic brushes are compressed. Bjorling and Stilbs, on the other hand, argued that the bridge formation suppresses the monomer number density near the surface that results in an entropic attraction.26,27 Another explanation was offered by Zilman and Safran who attributed the attraction to the association of the functionalized chain ends to form clusters.28 More recently, Meng and Russel29 extended the MWC theory to telechelic polymers and predicted that the attraction is due to the combinatorial entropy of the polymer end distribution between two surfaces. The attraction predicted by Meng and Russel is much stronger than that suggested by Witten and co-workers. In all of these theoretical investigations, it was assumed that the anchoring energy is sufficiently strong such that all free ends are permanently attached to the surface. Nevertheless, numerical results from lattice-model self-consistentfield theory20 and Monte Carlo simulations30-34 indicate that both the fraction of bridging and the telechelic-mediated surface forces are sensitive to the chain end-surface interactions explicitly. In this paper, we examine the surface forces mediated by telechelic polymers by using a polymer density functional theory (PDFT).35 A similar calculation has been recently applied to solvation forces because of multivalent polymers.36 The objective here is to conciliate various interpretations of the telechelic mediated forces by inspecting the solvation forces between the symmetric and asymmetric surfaces and those between surfaces mediated by telechelic polymers and by single-end attachable polymers. In comparison with alternative theoretical methods, PDFT takes the advantages of specifically accounting for the chain end-surface interactions along with the segment-level excluded-volume effects and van der Waals attractions. Furthermore, PDFT allows us to consider, at a certain degree, the correlation effects that are neglected in a typical mean-field theory. We expect that our calculations will also reveal the structural difference between a singly tethered brush and a telechelic brush when both are isolated. 2. Molecular Models We consider a coarse-grained model of telechelic polymers dissolved in a good solvent. The backbone of the telechelic polymers is represented by a freely jointed tangent-sphere chain, and the sticky ends are adhesive to a solid surface. While this simplified model is not intended to represent any specific telechelic polymer used in experiments, it retains the generic features including explicit endsurface interactions, excluded-volume effect, and chain connectivity. For simplicity, the solvent is treated as a continuous medium and all polymer segments are assumed to have the same size. Figure 1a (24) Avalos, J. B.; Johner, A.; Joanny, J. F. J. Chem. Phys. 1994, 101, 91819194. (25) Tang, W. H.; Witten, T. A. Macromolecules 1996, 29, 4412-4416. (26) Bjorling, M.; Stilbs, P. Macromolecules 1998, 31, 9033-9043. (27) Bjorling, M. Macromolecules 1998, 31, 9026-9032. (28) Zilman, A. G.; Safran, S. A. Eur. Phys. J. E 2001, 4, 467-473. (29) Meng, X. X.; Russel, W. B. Macromolecules 2003, 36, 10112-10119. (30) Misra, S.; Nguyen-Misra, M.; Mattice, W. L. Macromolecules 1994, 27, 5037-5042. (31) Misra, S.; Mattice, W. L. Macromolecules 1994, 27, 2058-2065. (32) Nguyen-Misra, M.; Misra, S.; Mattice, W. L. Macromolecules 1996, 29, 1407-1415. (33) Peng, C. J.; Li, J. K.; Liu, H. L.; Hu, Y. Eur. Polym. J. 2005, 41, 637-644. (34) Li, J. K.; Peng, C. J.; Liu, H. L.; Hu, Y. Eur. Polym. J. 2005, 41, 627-636. (35) Cao, D. P.; Wu, J. Z. Macromolecules 2005, 38, 971. (36) Cao, D. P.; Wu, J. Z. Langmuir 2005, 21, 9786-9791.
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Figure 1. (a) Schematic of a telechelic polymer. (b) Definitions of the surface separation “H” and the range of adhesion potential “w”. (c) Solvation forces because of associating polymers. Case I, telechelic polymers between adhesive surfaces; case II, surfactant-like polymers between adhesive surfaces; case III, telechelic polymers between a neutral and an adhesive surface. shows a schematic of a telechelic chain according to our coarsegrained model. The nonsticky backbone segments, denoted as “B”, are represented by neutral hard spheres, and the sticky ends, denoted as A segments, are represented by attractive spheres. The interaction between A and B segments is assumed to be the same as that between two B segments, and the interaction between two A segments is described by a square-well potential35
{
∞ r γσ
(1)
where σ is the segmental diameter and γσ is the square-well width. Throughout this paper, we assume γ ) 1.2 and the attractive energy between two A segments is AA ) 1kT, where k stands for the Boltzmann constant and T stands for the absolute temperature. To examine the adsorption behavior and solvation forces, we consider telechelic polymers confined between two infinitely large parallel plates that are neutral to B segments but can be either attractive or neutral to A segments. In other words, we consider the solvation forces between symmetric surfaces and that between asymmetric surfaces. For an attractive plate, the surface energy for each A segment is represented by a square-well potential att ψAW (z) )
{
-AW 0
0
