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

摘要

We study the interaction problem of a linear polymer chain, floating infractal containers that belong to the three-dimensional Sierpinski gasket (3DSG) family of fractals, with a surface-adsorbed linear polymer chain. Eachmember of the 3D SG fractal family has a fractal impenetrable 2D adsorbingsurface, which appears to be 2D SG fractal. The two-polymer system is modelledby two mutually crossing self-avoiding walks. By applying the Monte CarloRenormalization Group (MCRG) method, we calculate the critical exponents$\phi$, associated with the number of contacts of the 3D SG floating polymerchain, 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) argumentformula for $\phi$, and compare its predictions with our reliable set of theMCRG data. We find that $\phi$ monotonically decreases with increasing $b$,that is, with increase of the container fractal dimension. Finally, we discussthe relations between different contact exponents, and analyze their possiblebehaviour in the fractal-to-Euclidean crossover region $b\to\infty$.