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

Ivan Zivic
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Abstract

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 $ϕ$, 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 $ϕ$, and compare its predictions with our reliable set of the MCRG data. We find that $ϕ$ 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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Ivan Zivic. 2007-02-05. On the number of contacts of a floating polymer chain cross-linked with a surface adsorbed chain on fractal structures. https://doi.org/10.1088/1742-5468%2F2007%2F02%2Fp02005

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