SCALING EXPONENT OF COMPACT POLYMER CONFORMATIONS IN NON HOMOGENEOUS MEDIA
We studied compact conformations of a ring polymer adsorbed on the non homogeneous (e. g. porous) substrates. Substrates are represented by the generalization of modified rectangular (MR) lattice – a hierarchically constructed family of fractal lattices embedded in 2d space and parameterized with an integer p >1. Analyzing the exact set of recursive relations for arbitrary value of p, we established an asymptotic form of a number of conformations. As a correction to the leading exponential factor we obtained the stretched exponential factor with the exponent s = 1/2 on each member of the fractal family. Although it is believed that the critical exponent s on fractal lattices is determined not only by the fractal dimension of the underlying lattice but also by other lattice parameters, here we found that s had the same value on different fractals with the same fractal dimension (df = 2).
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