A lattice model of the translational dynamics of nonrotating rigid rods [electronic resource]
- Ying Lung Steve Tse.
- Physical description
- 1 online resource.
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|3781 2011 T||In-library use|
- We present a lattice model of oriented, nonrotating, rigid rods in three dimensions with random walk dynamics and an algorithm to simulate the model. We use the ideas of the Doi-Edwards (DE) theory, which was originally developed for a system of rods that both translate and rotate in continuous space, to predict the dependence of the translational diffusion constant of the rods in the perpendicular direction, on the (dimensionless) concentration in the semidilute regime. We find that the transnational perpendicular diffusion constant is proportional to the inverse square of the concentration. The theory is based on a `tube model' for the constraints imposed on the motion of a rod by the surrounding rods. Simulations of the model confirm that the scaling predicted by DE ideas and that the nature of the agreement is similar to that for the rotational diffusion constant in the original DE theory. We formulate a quantitative theory for the prefactor in the scaling relationship using only DE ideas, but it predicts a proportionality constant that is much too small. To explain this discrepancy, we modify the DE approach to obtain a more accurate estimate of the average tube radius, and we take into account two effects, called `leakage' and `drift', that are caused by perpendicular motions of rods that are ignored by the original DE theory. The theory of leakage takes into account the fact that the ends of a rod are less effective than the middle of the rod for blocking the motion of nearby rods. The theory of drift takes into account that the tube that any one rod is in can move in the perpendicular direction without changing its structure as a result of the perpendicular motion of the rods that form the tube. With these changes, the theory predicts a prefactor that is in much better agreement with the simulations. The simulations find that, as the concentration is increased, the approach to the limit of DE scaling is slow, and the -2 power in the DE scaling law is never quite achieved even at the highest concentration simulated. We propose a new scaling relationship that explains the deviations from the DE scaling relationship. Finally, we study the self and total density-density space time correlation functions for this model and propose a simple theory for the short time behavior of these functions based on a one-dimensional two-component lattice gas model.
- Publication date
- Submitted to the Department of Chemistry.
- Ph.D. Stanford University 2011
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