Abstract
We have studied the compact phase conformations of semi-flexible polymer chains confined in two dimensional nonhomogeneous media, modelled by fractals that belong to the family of modified rectangular (MR) lattices. Members of the MR family are enumerated by an integer p and fractal dimension of each member of the family is equal to 2. The polymer flexibility is described by the stiffness parameter s, while the polymer conformations are modelled by weighted Hamiltonian walks (HWs). Applying an exact recurrence equations method, we have found that partition function ZN for closed HWs consisting of N steps scales as , where constants and depend on both p and s. We have calculated numerically the stiffness dependence of the polymer persistence length, as well as various thermodynamic quantities (such as free and internal energy, specific heat and entropy) for a large set of members of the MR family. Analysis of these quantities has shown that semi-flexible compact polymers on MR lattices can exist only in the liquid-like (disordered) phase, whereas the crystal (ordered) phase has not appeared. Finally, behavior of the examined system at zero temperature has been discussed.
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