Linear and branched polymers on fractals

Abstract

This chapter provides a pedagogical review on linear polymers on deterministic finitely ramified fractals. The critical properties can be determined exactly by real-space renormalization group technique. This is used to determine the critical exponents of self-avoiding walks on different fractals. The chapter considers the case of linear polymers with attractive interactions, which on some fractals leads to a collapse transition. The fractals also provide a setting where the adsorption of a linear chain near on attractive substrate surface and the zipping-unzipping transition of two mutually interacting chains can be studied analytically. The chapter also discusses the critical properties of branched polymers on fractals. The study of branched polymers on fractal lattices is very instructive for detailed analysis of the system in detail and development of a better understanding of the critical behavior of polymers. It also allows the verification of the general qualitative features of the polymers on fractals that are similar to that in real experimental systems. A good deal of freedom is available for selecting the details of the fractal, and this can be used to find one that represents best the local geometry of the space. The exact values of the critical exponents depend on the details of the fractal. It is more important that the different interactions in the problem, between different monomers, with the substrate, or with a different chain can be handled consistently and satisfactorily in a way that allows exact calculation.