Simulation of Polymer Dynamics in Gels and Melts

Abstract

I have worked on computer simulations of lattice polymer models. Those models describe a polymer as a long chain of segments, connecting neighboring lattice sites. Polymers show interesting behavior if their freedom of movement is restricted, for example if the polymers move through a gel. The gel forms a three-dimensional structure that blocks sideways movements of the polymers. The polymer can only move by diffusion of "stored length" from one end of the chain to the other end. This is called reptation.

We have extended an existing model for a polymer in a gel to simulate a DNA fragment in a gel under the influence of an applied electric field. In weak fields, long fragments move slower than short ones. In this way, fragments of different length can be separated. If the field strength is increased, the fragments orientate themselves parallel to the field, and shorter and longer fragments move with the same velocity. In strong fields, fragments can get trapped in a U-shape, in which the applied field pulls on both ends of the fragment, while the middle cannot move in the direction of the field because of the gel.

We also introduce a new lattice polymer model for polymer solutions (melts). In this model, we simulate many polymers, mutually restricting their freedom of motion. We have investigated a mixture of two mutually repelling polymer types. At high temperatures the polymers are homogeneously distributed but if the temperature is lowered, phase separation sets in. The polymer model turns out to be highly efficient, and is the first where the growth of the phase domains can be directly observed. We have also investigated the composition of the two phases after full phase separation. Each phase consists mostly of one type of polymer, but there is always a small contamination with the other polymer type. If the polymers of one type are not all of equal length, then the shorter polymers will occur more often in the rare phase than the long ones. This is called fractionation.