Theory of Polymers on Fractal Lattices
Nowadays, There is much interest in the statistics of polymers (both of linear chain type and also branched) in good solvents1. The most salient feature of real polymers is the “excluded-volume” effect: the physical fact that no two different monomers composing the polymer can occupy the same spatial position at the same time. In the case of a linear chain polymer without the excluded-volume constraint the chain is Markovian (Gaussian) and can be modelled as a random walk (RW); whereas with inclusion of this constraint the chain becomes non-Markovian and corresponds to a self-avoiding random walk (SAW). In the case of branched polymers we call the analogous case excluded-volume-branched-polymers (EVB) and distinguish them from simple randomly branched polymers (RB), where no such restrictions apply. The statistical properties of SAW and EVB on several kinds of fractal lattices have been extensively discussed in recent years2–7. The motivation for analysing the statistical features of polymers on fractals comes from the wish to understand the controversial (and much studied) problem of establishing the critical behaviour of saw on random media8–10.
KeywordsRandom Walk Configurational Entropy Simple Random Walk Fractal Lattice Sierpinski Gasket
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