Polymer adsorption on a fractal substrate: numerical study

TL;DR

This study investigates how flexible polymers adsorb onto a fractal substrate modeled by a percolation cluster, revealing critical exponents and conformational properties near the adsorption transition.

Contribution

It provides numerical estimates of the surface crossover exponent and adsorption temperature for polymers on fractal substrates, a novel analysis of conformational characteristics in this context.

Findings

Adsorption is weaker on fractal substrates compared to Euclidean surfaces.

Estimated surface crossover exponent: 0.425±0.009.

Adsorption transition temperature: 2.64±0.02.

Abstract

We study the adsorption of flexible polymer macromolecules on a percolation cluster, formed by a regular two-dimensional disordered lattice at critical concentration p_c of attractive sites. The percolation cluster is characterized by a fractal dimension d_s^{p_c}=91/49. The conformational properties of polymer chains grafted to such a fractal substrate are studied by means of the pruned-enriched Rosenbluth method (PERM). We find estimates for the surface crossover exponent governing the scaling of the adsorption energy in the vicinity of the transition point, \phi_s^{p_c}=0.425\pm0.009, and for the adsorption transition temperature, T_A^{p_c}=2.64\pm0.02. As expected, the adsorption is diminished when the fractal dimension of the substrate is smaller than that of a plain Euclidean surface. The universal size and shape characteristics of a typical spatial conformation which attains a polymer chain in the adsorbed state are analyzed as well.