1D Classical Density Functional Theory of a Tethered Polymer Layer

2016/12/01 by Davis, Luke Kristopher
#FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Soft Condensed Matter (cond-mat.soft)

paper · doi:10.48550/arxiv.1612.00311

Abstract

A simple application of classical density functional theory is derived and applied to a system of polymers grafted to a plane. The system is assumed to have symmetry in directions parallel to the grafting plane hence it being a '1-dimensional' problem. A quick introduction to using propagators in the theory of chains in the presence of external fields and a numerical algorithm for solving the modified diffusion (or Fokker-Planck) equation are presented. Density profiles are found for hard-sphere chains which agree with results in the literature (see Murat,.., Milner,.., Muhukumar and others) and align with physical expectations of brush formation due to excluded volume. The linear scaling h ≈ (σ)^1/3 N, of brush height with polymerisation N, is reproduced here.

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