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Finite- N effects for ideal polymer chains near a flat impenetrable wall

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Abstract

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) = - \( \xi\) G N ′(0) , applies with a positive coefficient, \( \xi\) . Here we investigate the leading N -1/2 correction, \( \Delta\) G N(z) . Prior to the adsorption threshold, \( \Delta\) G N(z) is found to involve two distinct parts: a Gaussian correction (for z \( \lesssim\) aN 1/2 with a model-dependent amplitude, A , and a proximal-layer correction (for z \( \lesssim\) a described by a model-dependent function, B(z) .

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Author notes

  1. J. U. Kim

    Present address: UNIST, Ulsan, Korea

Authors and Affiliations

  1. Department of Mathematics, University of Reading, Reading RG6 6AX, Whiteknights, UK

    M. W. Matsen, J. U. Kim & A. E. Likhtman

Authors
  1. M. W. Matsen
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  2. J. U. Kim
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  3. A. E. Likhtman
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Correspondence to M. W. Matsen.

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Matsen, M.W., Kim, J.U. & Likhtman, A.E. Finite- N effects for ideal polymer chains near a flat impenetrable wall. Eur. Phys. J. E 29, 107–115 (2009). https://doi.org/10.1140/epje/i2009-10454-2

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  • DOI: https://doi.org/10.1140/epje/i2009-10454-2

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