EUROPHYSICS LETTERS Europhys. Lett., 32 (6), pp. 499-504 (1995) 20 November 1995 Polyelectrolyte Solutions between Charged Surfaces. I. BORUKHOV(*), D. ANDELMAN (*)(§) and H. ORLAND (**)(@) (*) School of Physics and Astronomy Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Awiv University Ramat-Awiv 69978, Tel-Awiv, Israel (**) Service de Physique Thdorique, CE-Saclay - 91191 Gifsur-Yvette Cedex, France (received 4 July 1995; accepted in final form 5 October 1995) PACS. 61.25Hq - Macromolecular and polymer solutions; polymer melts. PACS. 68.10-m - Fluid surfaces and fluid-fluid interfaces. Abstract. - The effect of electrostatic interactions on the distribution of polymers in a good solvent is investigated for semi-dilute solutions containing charged polymers (polyelectrolytes) and small ions. A man field approach is used to derive two coupled differential equations: a modified Poisson-Boltzmnn equation for the electrostatic potential, and a self-consistent field equation for the polymer order parameter, We compare several monomer charge distributions; smeared, annealed and quenched. The polymers are confined between two charged surfaces, and are in contact with a reservoir of polymers and electrolyte. This makes the annealed and quenched cases equivalent. Non-monotonous profiles are obtained for the case of competing surface interactions: electrostatic adsorption us. short-range desorption. The motivation for studying the behaviour of polyelectrolyte solutions between charged surfaces stems from at least two sources. On the one hand, the presence of polymers (in many cases charged) in a solution has a prominent effect on the stability of colloidal suspen- sions [1,2]. Industrial applications range from stabilization of ink and paint to waste water treatment and paper making131. On the other hand, the presence of proteins and other partially charged biopolymers in the intercellular fluid (aqueous solution) affects the interactions between adjacent membranes [4]. Our model system consists of weakly (positively) charged polymers and small ions in a good solvent between two parallel and uniformly charged surfaces. The small ions are of three kinds: (negative) counter-ions and a 1:l electrolyte composed of (positive) co-ions and (negative) counter-ions. We take all the counter-ions to be identical, but this assumption does not affect the results. The system can be viewed as a combination of two coupled problems[5,6]. The first ($1 Also at: Groupe de Physico-Chimie ThBorique, ESPCI, 10 rue Vauquelin, 75231 Paris Cedex 05, (5s) Also at: Groupe de Physique Statistique, Universit4 de Cergy-Pontoise, 95806 Cergy-Pontoise France. Cedex, France. 0 Les Editions de Physique