Potential theory of the depletion interaction in the colloid-polymer mixtures

Abstract

By developing and making use of the potential theory of the polymer-mediated interaction between spherical colloids, we investigate the many-body effects on the depletion interaction among these colloids in the colloid-polymer mixture. As our main results, we obtain analytic expressions for the polymer end density in the presence of the colloids and the many-body depletion potential acting between these colloids in the "protein" limit. We present a comparison of our theoretical findings with the results of recent computer simulations.

From constrained stochastic processes to the nonlinear sigma model. Two old problems revisited

“…In statistical mechanics, in fact, the probability function of a system of long and flexible polymer chains obeys pseudoSchrödinger equations that, for certain aspects, are similar to those of Fokker-Planck. A nice physical application could be the study of the influence of topological constraints on the interactions in colloid-polymer mixtures [48,49].…”

Polymer-mediated interactions and their effect on the coagulation–fragmentation of nano-colloids: a self-consistent field theory approach

“…Solving eqn (9) with respect to s as a function ofõ and s, substituting the result into eqn (8), and integrating over the space variables according to the formula given by eqn (7) solve the posed problem of calculating the potential of the depletion force. Note that such analytical expansions generally lead to an iterative procedure, 16,58 where each next expansion term is expressed through the previous one. Eqn (9) for the potential s is the linear integral equation that can be solved numerically by expanding s in spherical functions and deriving a set of linear algebraic equations for coefficient of this expansion.…”

Analytic liquid-state theory of the interactions between colloids mediated by reversibly adsorbed polymers

“…The polymer correlation length given by the above equation is specific to the above thread model, the mathematical form of this length being determined by the used approximation. Despite the fact that this length has different mathematical forms in other approaches, 11,13,24,25 it is always approximated based on the same principle of averaging the length describing the ideal polymer system and the typical length of the excluded volume screening. The structure of the correlation functions given by Eq.…”

“…Most important effects involved in the above effective interactions are the osmotic effect induced by the nonuniformities of the polymer density caused by the presence a) E-mail: alexander.chervanyov@cbni.ucd.ie of colloids and the enthalpic effect arising due to increasing the contacts between the adsorbing polymers and the colloid surfaces in the density enhancement layers. The above osmotic effect leads to the occurrence of the so-called "depletion force" that is the most thoroughly studied [11][12][13] type of the PM interactions to date. These attractive depletion interactions are known 1,19 to arise from the unbalanced osmotic pressure caused solely by the entropic repulsion of free polymers from the surface of the colloids.…”