On the number of contacts of a floating polymer chain cross-linked with a surface adsorbed chain on fractal structures

Details On the number of contacts of a floating polymer chain cross-linked with a surface adsorbed chain on fractal structures On the number of contacts of a floating polymer chain cross-linked with a surface adsorbed chain on fractal structures

2006-12-04

arxiv.org/abs/cond-mat/0612079v2

Journal of Statistical Mechanics: Theory and Experiment (2007) P02005

Physics

Condensed Matter

Statistical Mechanics

15 pages, 3 figures

Scientific paper

10.1088/1742-5468/2007/02/P02005

We study the interaction problem of a linear polymer chain, floating in fractal containers that belong to the three-dimensional Sierpinski gasket (3D SG) family of fractals, with a surface-adsorbed linear polymer chain. Each member of the 3D SG fractal family has a fractal impenetrable 2D adsorbing surface, which appears to be 2D SG fractal. The two-polymer system is modelled by two mutually crossing self-avoiding walks. By applying the Monte Carlo Renormalization Group (MCRG) method, we calculate the critical exponents $\phi$, associated with the number of contacts of the 3D SG floating polymer chain, and the 2D SG adsorbed polymer chain, for a sequence of SG fractals with $2\le b\le 40$. Besides, we propose the codimension additivity (CA) argument formula for $\phi$, and compare its predictions with our reliable set of the MCRG data. We find that $\phi$ monotonically decreases with increasing $b$, that is, with increase of the container fractal dimension. Finally, we discuss the relations between different contact exponents, and analyze their possible behaviour in the fractal-to-Euclidean crossover region $b\to\infty$.

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