Chad Snyder - Exact solution of the thermodynamics and size parameters of a polymer confined to a lattice of finite size: Large chain limit

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      Publication Details (including relevant citation   information):

      C.R. Snyder, C.M. Guttman and E.A. Di Marzio, J. Chem.   Phys. 140, 034905 (2014).

      Abstract:

      We extend the exact solutions of the Di Marzio-Rubin matrix   method for the thermodynamic properties, including chain density,   of a linear polymer molecule confined to walk on a lattice of   finite size. Our extensions enable (a) the use of higher   dimensions (explicit 2D and 3D lattices), (b) lattice boundaries   of arbitrary shape, and (c) the flexibility to allow each monomer   to have its own energy of attraction for each lattice site. In   the case of the large chain limit, we demonstrate how periodic   boundary conditions can also be employed to reduce computation   time. Advantages to this method include easy definition of   chemical and physical structure (or surface roughness) of the   lattice and site-specific monomer-specific energetics, and   straightforward relatively fast computations.We show the   usefulness and ease of implementation of this extension by   examining the effect of energy variation along the lattice walls   of an infinite rectangular cylinder with the idea of studying the   changes in properties caused by chemical inhomogeneities on the   surface of the box. Herein, we look particularly at the polymer   density profile as a function of temperature in the confined   region for very long polymers. One particularly striking result   is the shift in the critical condition for adsorption due to   surface energy inhomogeneities and the length scale of the   inhomogeneities; an observation that could have important   implications for polymer chromatography. Our method should have   applications to both copolymers and biopolymers of arbitrary   molar mass.

      Address (URL): http://dx.doi.org/10.1063/1.4857355