Polymer Adsorption on Fractal Walls

TL;DR

This study investigates how polymers adsorb onto fractally rough walls of different dimensions using renormalization group methods, revealing a transition from continuous to first-order adsorption as wall roughness increases.

Contribution

It provides exact results for deterministic fractal walls and numerical evidence for random walls, showing how the adsorption transition depends on wall fractal dimension.

Findings

Adsorption transition is continuous for low wall dimension.

Crossover exponent increases with wall dimension.

Transition becomes first-order beyond a threshold wall dimension.

Abstract

Polymer adsorption on fractally rough walls of varying dimensionality is studied by renormalization group methods on hierarchical lattices. Exact results are obtained for deterministic walls. The adsorption transition is found continuous for low dimension $d_w$ of the adsorbing wall and the corresponding crossover exponent $\phi$ monotonically increases with $d_w$, eventually overcoming previously conjectured bounds. For $d_w$ exceeding a threshold value $d_w^*$, $\phi$ becomes 1 and the transition turns first--order. $d_w^*>d_{saw}$, the fractal dimension of the polymer in the bulk. An accurate numerical approach to the same problem with random walls gives evidence of the same scenario.