SPHERICALLY SYMMETRIC RANDOM WALKS III. POLYMER ADSORPTION AT A HYPERSPHERICAL BOUNDARY

TL;DR

This paper uses a novel hyperspherical lattice model to analyze polymer adsorption at a boundary, revealing different phase transition behaviors depending on the hypersphere's dimensionality.

Contribution

It introduces a model for random walks on non-integer dimensional hyperspheres to study polymer adsorption, uncovering phase transition types and scaling behaviors.

Findings

Second-order phase transition for 0<D<4, D≠2

First-order phase transition for D>4

Logarithmic scaling at D=4

Abstract

A recently developed model of random walks on a $D$-dimensional hyperspherical lattice, where $D$ is {\sl not} restricted to integer values, is used to study polymer growth near a $D$-dimensional attractive hyperspherical boundary. The model determines the fraction $P(\kappa)$ of the polymer adsorbed on this boundary as a function of the attractive potential $\kappa$ for all values of $D$. The adsorption fraction $P(\kappa)$ exhibits a second-order phase transition with a nontrivial scaling coefficient for $0<D<4$, $D\neq 2$, and exhibits a first-order phase transition for $D>4$. At $D=4$ there is a tricritical point with logarithmic scaling. This model reproduces earlier results for $D=1$ and $D=2$, where $P(\kappa)$ scales linearly and exponentially, respectively. A crossover transition that depends on the radius of the adsorbing boundary is found.