Accurate effective pair potentials for polymer solutions

Dilute or semidilute solutions of nonintersecting self-avoiding walk (SAW) polymer chains are mapped onto a fluid of "soft" particles interacting via an effective pair potential between their centers of mass. This mapping is achieved by inverting the pair distribution function of the centers of mass of the original polymer chains, using integral equation techniques from th e theory of simple fluids. The resulting effective pair potential is finite at all distances, has a range of the order of the radius of gyration, and turns out to be only moderately concentration-dependent. The dependence of the effective potential on polymer length is analyzed in an effort to extra ct the scaling limit. The effective potential is used to derive the osmotic equation of state, which is compared to simulation data for the full SAW s egment model, and to the predictions of renormalization group calculations. A similar inversion procedure is used to derive an effective wall-polymer potential from the center of mass density profiles near the wall, obtained from simulations of the full polymer segment model. The resulting wall-poly mer potential turns out to depend strongly on bulk polymer concentration wh en polymer-polymer correlations are taken into account, leading to a consid erable enhancement of the effective repulsion with increasing concentration . The effective polymer-polymer and wall-polymer potentials are combined to calculate the depletion interaction induced by SAW polymers between two wa lls. The calculated depletion interaction agrees well with the "exact" resu lts from much more computer-intensive direct simulation of the full polymer -segment model, and clearly illustrates the inadequacy-in the semidilute re gime-of the standard Asakura-Oosawa approximation based on the assumption o f noninteracting polymer coils. (C) 2001 American Institute of Physics.