Surface Forces Mediated by Charged Polymers: Effects of Intrinsic Chain Stiffness Martin Turesson,* Jan Forsman, and Torbjo ¨rn A ° kesson Theoretical Chemistry, Lund UniVersity, POB 124, S-221 00 Lund, Sweden ReceiVed February 17, 2006. In Final Form: March 30, 2006 The strength and range of surface forces in a system consisting of charged polymers with variable intramolecular stiffness confined between two charged planar surfaces have been investigated by Monte Carlo simulations. The negatively charged surfaces are neutralized by polymers carrying charges of opposite sign. Introducing the intermediate intrinsic stiffness of the chains gives rise to a weaker, but more long-ranged attraction between the surfaces. In the limit of infinitely stiff chains, this bridging attraction is lost, but it is replaced by a strong correlation attraction at short distances. Comparisons with predictions by a correlation-corrected polyelectrolyte Poisson-Boltzmann theory are made. The theory predicts surface attractions that are somewhat too weak, but all qualitative features are correctly reproduced. Given the crudeness of the model, the quantitative agreement is satisfactory. Introduction It is a well-known fact that polymers can alter the interaction between particles in a colloidal suspension. In some cases, polymer brushes form, which can lead to steric stabilization of the system. Flocculation or coagulation may occur as a result of depletion when the polymers do not adsorb on the particles. If the chains have a positive surface affinity, the polymers can stretch from one surface to another, creating an attraction. This phenomenon is known as bridging. 1,2 The bridging mechanism is general and operates between all particles where polymers are attracted to the surfaces. Industrially, polyelectrolytes are of great importance. For example, they are widely used as flocculants or stabilizers in various processes. 3 Many experimental works have shed light on surface forces in the presence of polyelectrolytes, using mainly the surface force apparatus (SFA) 4-13 and the atomic force microscope. 14,15 In these experiments, a large number of parameters can be varied, such as pH, salt concentration, surface properties, the length of the polymers, and so forth, which in turn alter the surface interactions. How polyelectrolytes modify surface forces has also been extensively studied with simulations as well as analytical theories. 1,16-19 Most theoretical studies have, however, been restricted to fully flexible chains. That is, no intrinsic stiffness apart from that due to internal electrostatic repulsion has been considered. Lately, theoretical work involving semiflexible chains have appeared in the literature. 20-23 Recently, Messina studied charged rods outside an oppositely charged surface. 24 These works focused on structural properties and adsorption characteristics, but little attention has been devoted to understanding how intersurface interactions are mediated by stiff polyelectrolytes. This problem will be addressed in the present paper. As we will show, increasing the stiffness leads first to a more long-ranged bridging regime, but if the stiffness of the chains is increased even further, the bridging diminishes and eventually becomes negligible. The extreme limit is the case of infinitely stiffs chain or rods, which form a thin adsorbed layer at the surfaces. In this case, there is a much lower probability of a chain reaching the other surface. Instead, the two layers of polyelec- trolytes near each surface are strongly correlated, which induces substantial attractive forces. In this respect, a rod behaves more like a multivalent ion than a flexible polyion. 25-30 In the present study, the polyions are confined to a slit. We do not include any salt, and the surface charges are balanced by the charged monomers. Still, forces calculated up to 30-40 Å, say, would be relevant at salt concentrations less than 10 mM. Extending the simulations to a system that is open with respect to an ordinary salt, but with a fixed amount of polyions, is straightforward though time-consuming. More interesting, how- ever, is to consider a system in full equilibrium with a bulk, that * Corresponding author. (1) A ° kesson, T.; Woodward, C.; Jo ¨nsson, B. J. Chem. Phys. 1989, 91, 2461. (2) Podgornik, R. J. Polym. Sci. Part B 2004, 42, 3539. (3) Kirk, R. E., Othmer, D. F., Eds. Encyclopedia of Chemical Technology, 3rd ed.; Wiley: New York, 1980. (4) Marra, J.; Hair, M. L. J. Phys. Chem. 1988, 92, 6044. (5) Biggs, S.; Proud, A. D. Langmuir 1997, 13, 7202. (6) Dahlgren, M. A. G.; Waltermo, Å.; Blomberg, E.; Claesson, P. M.; Sjo ¨stro ¨m, L.; A ° kesson, T.; Jo ¨nsson, B. J. Phys. Chem. 1993, 97, 11769. (7) Dahlgren, M. A. G.; Claesson, P. M.; Audebert, R. J. J. Colloid Interface Sci. 1994, 166, 343. (8) O ¨ sterberg, M. J. Colloid Interface Sci. 2000, 229, 620. (9) Rojas, O. J.; Claesson, P. M.; Muller, D.; Neuman, R. D. J. Colloid Interface Sci. 2005, 205, 77. (10) Poptoshev, E.; Claesson, P. M. Langmuir, 2002, 18, 1184. (11) Holmberg, M.; Wigren, R.; Erlandsson, R.; Claesson, P. M. Colloids Surf., A 1997, 129-130, 175. (12) Claesson, P. M.; Poptoshev, E.; Blomberg, E.; Dedinaite, A. AdV. Colloid Interface Sci. 2005, 114-115, 173. (13) Tadmor, R.; Hernande ´z-Zapata, E.; Chen, N.; Pincus, P.; Israelachvili, J. N. Macromolecules, 2002, 35, 2380. (14) Bremmel, K. E.; Jameson, G. J.; Biggs, S. Colloids Surf., A 1999, 155, 1. (15) Lokar, W. J.; Ducker, W. A. Langmuir, 2004, 20, 378. (16) Granfeldt, M. K.; Jo ¨nsson, B.; Woodward, C. E. J. Phys. Chem. 1991, 95, 4819. (17) Podgornik, R.; A ° kesson, T.; Jo ¨nsson, B. J. Chem. Phys. 1995, 102, 9423. (18) Podgornik, R. J. Phys. Chem. 1992, 96, 884. (19) Borukhov, I.; Andelman, D.; Orland, H. J. Phys. Chem. B 1999, 103, 5042. (20) Akinchina, A.; Linse, P. J. Phys. Chem. B 2003, 107, 8011. (21) Schiessel, H. Macromolecules 2003, 36, 3424. (22) Kuznetsov, D.; Sung, W. J. Chem. Phys. 1997, 107, 4729. (23) Kuznetsov, D.; Sung, W. Macromolecules 1998, 31, 2679. (24) Messina, R. J. Chem. Phys. 2006, 124, 014705. (25) Guldbrand, L.; Jo ¨nsson, B.; Wennerstro ¨m, H.; Linse, P. J. Chem. Phys. 1984, 80, 2221. (26) Guldbrand, L.; Nilsson, L.; Nordenskio ¨ld, L. J. Chem. Phys. 1986, 85, 6686. (27) Valleau, J. P.; Ivkov, R.; Torrie, G. M. J. Chem. Phys. 1991, 95, 520. (28) Kjellander, R.; Mare `elja, S. Chem. Phys. Lett. 1984, 112, 49. (29) Kjellander, R.; Mare `elja, S. J. Chem. Phys. 1985, 82, 2122. (30) Tang, Z.; Scriven, L. E.; Davis, H. T. J. Chem. Phys. 1992, 97, 494. 5734 Langmuir 2006, 22, 5734-5741 10.1021/la0604735 CCC: $33.50 © 2006 American Chemical Society Published on Web 05/16/2006