Stiffness dependence of critical exponents of semiflexible polymer chains situated on two-dimensional compact fractals

Abstract

We present an exact and Monte Carlo renormalization group (MCRG) study of semiflexible polymer chains on an infinite family of the plane-filling (PF) fractals. The fractals are compact, that is, their fractal dimension df is equal to 2 for all members of the fractal family enumerated by the odd integer b(3<or=b<infinity). For various values of stiffness parameter s of the chain, on the PF fractals (for 3<or=b<or=9 ), we calculate exactly the critical exponents nu (associated with the mean squared end-to-end distances of polymer chain) and gamma (associated with the total number of different polymer chains). In addition, we calculate nu and gamma through the MCRG approach for b up to 201. Our results show that for each particular b, critical exponents are stiffness dependent functions, in such a way that the stiffer polymer chains (with smaller values of s) display enlarged values of nu, and diminished values of gamma. On the other hand, for any specific s, the critical exponent nu monotonically decreases, whereas the critical exponent gamma monotonically increases, with the scaling parameter b. We reflect on a possible relevance of the criticality of semiflexible polymer chains on the PF family of fractals to the same problem on the regular Euclidean lattices.