On the number of contacts of a floating polymer chain crosslinked with a surface adsorbed chain on fractal structures
نویسنده
چکیده
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 ≤ b ≤ 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 → ∞. PACS numbers: 64.60.Ak, 36.20.Ey, 05.40.Fb, 05.50.+q On the number of contacts of crosslinked polymer chains on fractals 2
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