We develop a self-consistent field theory of polymer dynamics, based on a functional integral approach, which is analogous to the existing equilibrium self-consistent field theory for polymers. We apply a saddle-point approximation to the exact dynamical theory, which generates a set of mean-field equations for the time-dependent density and mean force field. We also develop a method of treating the single-chain dynamics exactly, subject to this mean-field, resulting in a functional Fokker-Planck equation that must be solved along with the mean-field equations in a self-consistent manner. To test the self-consistency, we apply the theory to the simple but non-trivial case of np Brownian particles in one dimension interacting via a short-range repulsion in a harmonic external potential. Results for the non-interacting case agree with the literature. The interacting case demonstrates physically sensible interaction-dependent dynamics, such as an increased broadening of the density field when the repulsion is increased. We also examine the dynamics of a binary system with two distinct particle species. We calculate the center-of-mass trajectories for colliding distributions of species A and B, and observe that when the difference of repulsion strengths between like and unlike species chi is greater than a threshold value (between chi = 0.3 and chi = 0.4), the two species do not mix (indicating the onset of phase segregation).
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OGU.10214/3171 |
| Date | 08 December 2011 |
| Creators | Grzetic, Doug |
| Contributors | Wickham, Robert |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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