Depletion of ideal polymer chains near a spherical colloid particle beyond the Dirichlet boundary conditions

I. Erukhimovich¹, A. Johner² and J. F. Joanny³

¹ Moscow State University, 119992, Moscow, Russia
² Institut Charles Sadron, Université de Strasbourg, CNRS UPR 22, 23 rue du Loess, BP 84047, F-67034, Strasbourg Cedex, France
³ Physicochimie Curie, Institut Curie Section Recherche, 26 rue d’Ulm, 75248, Paris, France

Corresponding author: ierukhs@polly.phys.msu.ru

Received: 8 July 2009
Published online: 20 February 2010

Abstract

We reconsider the depletion interaction of an ideal polymer chain, characterized by the gyration radius R_G and bond length a, and an impenetrable spherical colloid particle of radius R. Forbidding the polymer-colloid penetration explicitly (by the use of Mayer functions) without any other requirement we derive and solve analytically an integral equation for the chain partition function of a long ideal polymer chain for the spherical geometry. We find that the correction to the solution of the Dirichlet problem depends on the ratios R/R _G and R/a. The correction vanishes for the continuous chain model (i.e. in the limit R/R _G → 0 and R/a → ∞) but stays finite (even for an infinite chain) for the discrete chain model. The correction can become substantial in the case of nano-colloids (the so-called protein limit).