Computer simulation of long polymers adsorbed on a surface. I. Corrections to scaling in an ideal chain

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Abstract
This paper is the first in a series of papers in which polymeradsorption on a surface is studied by computer simulation using the ‘‘scanning method.’’ This method is especially efficient to handle chain systems with finite interactions and geometrical constraints. Here we test the method by applying it to models of a single random walk (without excluded volume) on a simple cubic lattice, which are solved analytically; in the immediately following paper a self‐avoiding walk model is treated. The scanning method is found to be extremely efficient, where walks of up to N=105 steps can be simulated reliably, leading thereby to very precise estimates of transition temperatures and critical exponents. In particular we test carefully for a lattice model the range of validity of scaling functions developed by Eisenrigler, Kremer and Binder [J. Chem. Phys. 7 7, 6296 (1982)] for a continuous model. We pay a special attention to corrections to scaling and demonstrate that they are strong above the transition temperature for 〈R 2〉⊥, the perpendicular part of the mean‐square end‐to‐end distance and for ρ(z), the monomer concentration profile. We show that at T=∞, the asymptotic regime, in which these corrections become negligible, is obtained for N≊40 000 for 〈R 2〉⊥ but a significantly larger N is required for ρ(z). This means that this regime corresponds to a real polymer length that is not realized experimentally.

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