Computer simulation of long polymers adsorbed on a surface. II. Critical behavior of a single self-avoiding walk

Abstract

The scanning simulation method is applied to a model of polymer adsorption in which a single self-avoiding walk is terminally attached to an attracting impenetrable surface on a simple cubic lattice. Relatively long chains are studied, of up to 1000 steps, which enable us to obtain new estimates for the reciprocal transition temperature ‖ε‖/kBTa=θa =0.291±0.001 (ε is the interaction energy of a monomer with the surface), the crossover exponent φ=0.530±0.007 and the free energy exponents at Ta, γ1SB =1.304±0.006 and γ11SB =0.805±0.015. At T=∞ we obtain, γ1=0.687±0.005, γ11=−0.38±0.02, and the effective coordination number q=4.6839±0.0001, which are in good agreement with estimates obtained by other methods. At T>Ta we demonstrate the existence of strong correction to scaling for the perpendicular part of the mean-square end-to-end distance 〈R2〉⊥ and for the monomer concentration profile ρ(z) (z is the distance from the surface). At T=∞ the leading correction to scaling term for 〈R2〉⊥ is c/Nψ, where c≊−0.9 and ψ≊0.4 is close to 0.5 obtained for the random walk model in the preceding paper. This means that the asymptotic regime, in which these corrections become negligible, corresponds to a large polymer length that is not realized experimentally. Close enough to Ta we demonstrate for our lattice model the validity of various scaling forms predicted by Eisenriegler, Kremer, and Binder [J. Chem. Phys. 77, 6296 (1982)] for a continuum model on the basis of the n-vector model.