Eur. Phys. J. E (2008) 27: 435-445
https://doi.org/10.1140/epje/i2008-10392-5

Regular Article

The ideal polymer chain near planar hard wall beyond the Dirichlet boundary conditions

¹ Moscow State University, 119992, Moscow, Russia
² Institute Charles Sadron, 6 rue Boussingault, 67083, Strasbourg Cedex, France
³ Physicochimie Curie, Institut Curie Section Recherche, 26 rue d’Ulm, 75248, Paris, France

^* e-mail: ierukhs@polly.phys.msu.ru

Received: 23 March 2008
Revised: 25 September 2008
Accepted: 17 November 2008
Published online: 23 December 2008

Abstract

We present a new ab initio approach to describe the statistical behavior of long ideal polymer chains near a plane hard wall. Forbidding the solid half-space to the polymer explicitly (by the use of Mayer functions) without any other requirement, we derive and solve an exact integral equation for the partition function G _D(r,r′, N) of the ideal chain consisting of N bonds with the ends fixed at the points r and r′ . The expression for G(r,r′, s) is found to be the sum of the commonly accepted Dirichlet result G _D(r,r′, N) = G ₀(r,r′, N) - G ₀(r,r”, N) , where r” is the mirror image of r′ , and a correction. Even though the correction is small for long chains, it provides a non-zero value of the monomer density at the very wall for finite chains, which is consistent with the pressure balance through the depletion layer (so-called wall or contact theorem). A significant correction to the density profile (of magnitude 1/is obtained away from the wall within one coil radius. Implications of the presented approach for other polymer-colloid problems are discussed.