Simulations of grafted polymers in a good solvent

TL;DR

This paper uses advanced simulation techniques to study grafted polymers near surfaces, providing precise estimates of critical exponents and insights into the adsorption transition, with results aligning with field theoretic predictions.

Contribution

The study introduces improved simulation methods for grafted polymers, yielding more accurate critical exponents and clarifying the nature of the adsorption transition.

Findings

Cross-over exponent is smaller than 1/2.

Results agree with re-summed field theoretic epsilon-expansion.

Provides improved estimates for entropic critical exponents.

Abstract

We present improved simulations of three-dimensional self avoiding walks with one end attached to an impenetrable surface on the simple cubic lattice. This surface can either be a-thermal, having thus only an entropic effect, or attractive. In the latter case we concentrate on the adsorption transition, We find clear evidence for the cross-over exponent to be smaller than 1/2, in contrast to all previous simulations but in agreement with a re-summed field theoretic $\epsilon$-expansion. Since we use the pruned-enriched Rosenbluth method (PERM) which allows very precise estimates of the partition sum itself, we also obtain improved estimates for all entropic critical exponents.