Critical behavior of interacting two-polymer system in a fractal solvent: an exact renormalization group approach

TL;DR

This paper analyzes the critical behavior of two interacting polymers in a fractal solvent using exact renormalization group methods, revealing phase diagrams and contact exponents influenced by lattice topology.

Contribution

It provides the first exact RG analysis of two-polymer systems in 3D Sierpinski Gasket fractals, comparing avoiding and crossing interactions.

Findings

Established phase diagrams for different fractal parameters.

Calculated contact critical exponents at transition points.

Demonstrated the influence of lattice topology on phase behavior.

Abstract

We study the polymer system consisting of two polymer chains situated in a fractal container that belongs to the three--dimensional Sierpinski Gasket (3D SG) family of fractals. Each 3D SG fractal has four fractal impenetrable 2D surfaces, which are, in fact, 2D SG fractals. The two-polymer system is modelled by two interacting self-avoiding walks (SAWs), one of them representing a 3D floating polymer, while the other corresponds to a chain adhered to one of the four 2D SG boundaries. We assume that the studied system is immersed in a poor solvent inducing the intra-chain interactions. For the inter-chain interactions we propose two models: in the first model (ASAWs) the SAW chains are mutually avoiding, whereas in the second model (CSAWs) chains can cross each other. By applying an exact Renormalization Group (RG) method, we establish the relevant phase diagrams for $b=2,3$ and $b=4$ members of the 3D SG fractal family for the model with avoiding SAWs, and for $b=2$ and $b=3$ fractals for the model with crossing SAWs. Also, at the appropriate transition fixed points we calculate the contact critical exponents, associated with the number of contacts between monomers of different chains. Throughout the paper we compare results obtained for the two models and discuss the impact of the topology of the underlying lattices on emerging phase diagrams.