On the number of contacts of two polymer chains situated on fractal structures

Abstract

We study the critical behavior of the number of monomer-monomer contacts for two polymers in a good solvent. Polymers are modeled by two self-avoiding walks situated on fractals that belong to the checkerboard (CB) and X family. Each member of a family is labeled by an odd integer b, $3\le b\le\infty$ . By applying the exact Renormalization Group (RG) method, we establish the relevant phase diagrams whereby we calculate the contact critical exponents $\varphi$ (for the CB and X fractals with b = 5 and b = 7). The critical exponent $\varphi$ is associated with power law of the number of sites at which the two polymers are touching each other.