Directed walk models of semiflexible polymers
by Gerasim Iliev
Abstract: The use of directed walk models to study polymeric systems in a variety of environments has provided much insight into the full self-avoiding walk model of such problems. Many of the previous studies have focused on the behaviour of long, flexible polymers, however on sufficiently small length scales the polymer essentially behaves as a rigid rod. Modifying the usual directed walk models (Dyck paths, Motzkin paths and partially-directed walks) we can obtain models which have a tunable persistence length. These models are subsequently used to study the phenomenon of polymer adsorption at an impenetrable surface in the presence and absence of an elongational force. In such studies, we obtain the phase diagram for each model as a function of the interaction parameter with the adsorbing surface and a stiffness parameter. In all models studied, the adsorbed-desorbed phase transition in the absence of a tensile force is of second order for all finite values of the stiffness. When an elongational force is introduced, several regimes with respect to the stiffness parameter become apparent as we observe the critical value of the desorbing force. Work in collaboration with E. Orlandini and S. Whittington.
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