Finite- N effects for ideal polymer chains near a flat impenetrable wall
Department of Mathematics, University of Reading, Reading RG6 6AX, Whiteknights, UK
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Accepted: 25 March 2009
Published online: 14 May 2009
This paper addresses the statistical mechanics of ideal polymer chains next to a hard wall. The principal quantity of interest, from which all monomer densities can be calculated, is the partition function, G N(z) , for a chain of N discrete monomers with one end fixed a distance z from the wall. It is well accepted that in the limit of infinite N , G N(z) satisfies the diffusion equation with the Dirichlet boundary condition, G N(0) = 0 , unless the wall possesses a sufficient attraction, in which case the Robin boundary condition, G N(0) = - G N ′(0) , applies with a positive coefficient, . Here we investigate the leading N -1/2 correction, G N(z) . Prior to the adsorption threshold, G N(z) is found to involve two distinct parts: a Gaussian correction (for z aN 1/2 with a model-dependent amplitude, A , and a proximal-layer correction (for z a described by a model-dependent function, B(z) .
PACS: 82.35.Gh Polymers on surfaces; adhesion – / 61.25.he Polymer solutions – / 05.70.Np Interface and surface thermodynamics –
© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg, 2009