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 IEI/kBTa = Ba = 0.291 ± 0.001 (E is the interaction energy ofa monomer with the surface), the crossover exponent ~ = 0.530 ± 0.007 and the free energy exponents at Ta, r~B = 1.304 ± 0.006 and r~~ = 0.805 ± 0.015. At T = 00 we obtain, rl = 0.687 ± 0.005, rll = -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 (R 2) 1 and for the monomer concentration profile p(z) (z is the distance from the surface). At T = 00 the leading correction to scaling term for (R 2) 1 is c/ HI', where cz -0.9 and ",zO.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.= -dkB T and denote their critical values by Ta and Ba

Conformational properties of a polymer tethered to an interacting flat surface

“…Interestingly, the minimum was located near the CAP e c ¼À0.29 of the model system. 12,16 Above e c /R 2 S increased slowly with e, while below e c it grew rapidly with the decrease in interaction. The minimum /R 2 S became more obvious with increasing chain length.…”

“…16 The scaling behavior of the parallel component /R 2 S xy is not affected by the surface. For a finite chain length, we have examined whether the scaling law in Equation (1) still exists for a tethered chain on an interacting surface.…”

“…At the CAP, the scaling behavior is also valid, even for finite chain lengths. 16 For a small chain length n and at e above the CAP, the perpendicular component /R 2 S z is influenced by the surface and the correction to scaling becomes important. 16 At e¼0, /R 2 S z can be expressed as…”

“…The CAP e c was estimated to be about À0.29 for polymers on the simple cubic lattice. [9][10][11][12]16,18,19 In this work, we studied how the conformational properties of the chain change from a desorbed state for e4e c to an adsorbed state for eoe c . We found that both the mean square end-to-end distance /R 2 S and the mean square radius of gyration /R G 2 S have a minimum near e c .…”

“…[13][14][15][16][17] Every walk step that contacts the surface is assigned an interaction energy e (in units of k B T, where k B is the Boltzmann constant and T is the temperature). It is well accepted that a single chain adsorbed on an attractive surface exhibits a phase transition from a desorbed state to an adsorbed state when the adsorption strength increases beyond a critical value.…”