Microscopic theory of polymer-mediated interactions between spherical particles

Abstract

We develop an analytic integral equation theory for treating polymer-induced effects on the structure and thermodynamics of dilute suspensions of hard spheres. Results are presented for the potential of mean force, free energy of insertion per particle into a polymer solution, and the second virial coefficient between spheres. The theory makes predictions for all size ratios between the spheres and the polymer coil dimension. Based on the Percus-Yevick ͑PY͒ closure, the attractive polymer-induced depletion interaction is predicted to be too weak under athermal conditions to induce a negative value for the second virial coefficient, B 2 cc , between spheres in the colloidal limit when the spheres are much larger than the coil size. A nonmonotonic dependence of the second virial coefficient on polymer concentration occurs for small enough particles, with the largest polymer-mediated attractions and most negative B 2 cc occurring near the dilute-semidilute crossover concentration. Predictions for the polymer-mediated force between spheres are compared to the results of computer simulations and scaling theory.

Small mesoscopic particles in dilute and semidilute solutions of nonadsorbing polymers

“…5,6 The polymer-induced depletion interaction between the particles has a rich structure which depends on the ratio of the particle and chain sizes 7 and on the degree of overlap between the chains, i.e., on whether the polymer solution is dilute or semidilute. 8 For large particle size the depletion interaction closely resembles that for planar walls. 9,10 Here the focus is on small spherical particles whose radius R, though large on a microscopic scale, is much smaller than the radius of gyration R g of an isolated chain in the dilute solution or the Edwards screening length ͑or ''blob'' size͒ 5,6 in the semidilute solution.…”

“…The second virial coefficient, which can be measured by light scattering, is of particular interest, since in protein suspensions its value appears to be correlated with the success of protein crystallization. 18 We make contact with the results of Chatterjee and Schweizer, 8 based on an integral equation approach for arbitrary overlap and with the results of Sear 19 In Sec. V the overlap-dependence of the polymerinduced interaction of a particle with a wall is considered.…”

“…5,6 For the case of a good solvent in three dimensions, the exponent dϪ1/ in Eq. ͑1.4͒ equals 1.3, and F 1 decreases more rapidly with decreasing R than the prediction F 1 ϰR of mean field 17 or integral equation 8 approaches.…”

Excluded-volume polymer-induced depletion interaction between parallel flat plates

“…The inclusion of the excluded-volume effects of the polymer segments has gained increasing attention [8][9][10][11][12][13][14][15][16][17][18] in order to bring the theoretical description closer to real polymer chains. Simplifications can be made in a successful way when relatively small colloidal spheres immersed in a polymer solution are considered [8][9][10][11], whereas a meanfield approach was developed for excluded-volume polymers between two plates [12].…”

“…Simplifications can be made in a successful way when relatively small colloidal spheres immersed in a polymer solution are considered [8][9][10][11], whereas a meanfield approach was developed for excluded-volume polymers between two plates [12]. For more complex systems, reference interaction site models (RISM) have been developed [13][14][15][16] that treat the polymers more realistically than PHS models do. Louis et al [17] recently adopted a Gaussian core model for polymer chains that interact via a penetrable repulsive Gaussian potential.…”