Dr. Juan Alvarez (University of Toronto & York University)
Self-avoiding polygons and walks in slits
Abstract: A polymer can be modeled by a self-avoiding walk or a self-avoiding polygon. This talk will briefly describe several problems involving these walk models of polymers: collapse, localization, adsorption, steric stabilization, and sensitized flocculation. I will then describe in detail the last two problems, which involve a polymer in a confined geometry. The basic model is a self-avoiding walk or a self-avoiding polygon confined between two parallel walls. In two dimensions, this model involves self-avoiding walks or self-avoiding polygons in the square lattice between two parallel confining lines. Interactions of the polymer with the confining walls are introduced by energy terms associated with edges in the walk or polygon which are at or near the confining lines. We use transfer-matrix methods to investigate the forces between the walk or polygon and the confining lines, as well as to investigate the effects of the confining slit's width and of the energy terms on the thermodynamic properties of the walks or polygons in several models. The phase diagram found for the self-avoiding walk models is qualitatively similar to the phase diagram of a directed walk model confined between two parallel lines, as was previously conjectured. However, the phase diagram of one of our polygon models is found to be significantly different and we present numerical data to support this. For that particular model we prove that, for any finite values of the energy terms, there is an infinite number of slit widths where a polygon will induce a steric repulsion between the confining lines. |
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