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

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

2007-12-18

arxiv.org/abs/0712.2941v1

Journal of Statistical Mechanics: Theory and Experiment (2008) P04022

Physics

Condensed Matter

Statistical Mechanics

21 pages, 6 figures

Scientific paper

10.1088/1742-5468/2008/04/P04022

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.

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