Exact and Monte Carlo study of adsorption of a self-interacting polymer chain for a family of three-dimensional fractals

Abstract

We study the problem of adsorption of self-interacting linear polymers situated in fractal containers that belong to the three-dimensional (3d) Sierpinski gasket (SG) family of fractals. Each member of the 3d SG fractal family has a fractal impenetrable 2d adsorbing surface (which is, in fact, 2d SG fractal) and can be labelled by an integer $b$ ($2\le b\le \infty$). By applying the exact and Monte Carlo renormalization group (MCRG) method, we calculate the critical exponents $\nu$ (associated with the mean squared end-to-end distance of polymers) and $\varphi$ (associated with the number of adsorbed monomers), for a sequence of fractals with $2\le b\le 4$ (exactly) and $2\le b\le 40$ (Monte Carlo). We find that both $\nu$ and $\varphi$ monotonically decrease with increasing $b$ (that is, with increasing of the container fractal dimension $d_f$), and the interesting fact that both functions, $\nu (b)$ and $\varphi (b)$, cross the estimated Euclidean values. Besides, we establish the phase diagrams, for fractals with $b=3$ and $b=4$, which reveal existence of six different phases that merge together at a multi-critical point, whose nature depends on the value of the monomer energy in the layer adjacent to the adsorbing surface.

28 pages, 6 figures

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Cited by in corpus (5)

• Polymer adsorption on a fractal substrate: numerical study
• Hamiltonian walks on Sierpinski and n-simplex fractals
• On the number of contacts of a floating polymer chain cross-linked with a surface adsorbed chain on fractal structures
• Critical behavior of interacting two-polymer system in a fractal solvent: an exact renormalization group approach
• Exact study of surface critical exponents of polymer chains grafted to adsorbing boundary of fractal lattices embedded in three-dimensional space