Complex dynamics and phase behavior in non-equilibrium models: From Lorentz models to liquid crystals

This thesis has focused on two classes of simple modes: Lorentz models, where the surrounding solvent is stationary and one solute molecule is allowed to translate and rotate through the resulting network, and a liquid crystal model comprised of hard spherocylindrical particles that are driven by an external rotating electric field. Both of these models are amenable computationally and provide the fundamental physics necessary to capture the complex behavior indicative of the complex dynamics and phase behavior described above.;The Lorentz models studied throughout this work are comprised of a combination of needles and spherical particles. The particular version of the model useful to describing a variety of dynamical regimes, is that of a thick needle diffusing through an array of stationary scatterers. The resulting dynamics of the thick needle in a two-dimensional array of point scatterers shows three regimes of transport, the expected Enskog behavior at low scatterer density, reptative transport that gives rise to enhanced translational diffusion parallel to the long-axis of the needle at intermediate densities and finally a geometric trapping at large densities. The competition between suppression of rotational and translation motion perpendicular to the long-axis of the needle leading to reptation and suppression of the motion of the needle leading to trapping is determined by the ratio of the thickness of the needle to the average inter-particle spacing of the scatterers. In order for the needle to reptate, the length of the needle must be sufficiently longer than the average inter-particle spacing while the width remains somewhat small compared to the inter-particle spacing, creating an effective Edwards tube. A corresponding three-dimensional system is studied, where the scatterers are made spherical.;The second class of models discussed in this thesis, is a simple liquid crystal model. This model is comprised of nematogens formed from hard spherocylinders. The spherocylinders are aligned and driven by an external, rotating electric field. The field is coupled to the nematogens via a dipole along the long-axis of the spherocylinder. The frequency and field-dependent phase behavior is studied. For stationary fields, an overall stabilization of long-range order is observed, accessing liquid crystal phases that would not be accessible otherwise. However, upon rotation of the field, long-range order is seen to decrease. The loss in long-range order is more pronounced with increasing frequency and increasing volume fraction and geometric anisotropy. When a constant frequency is chosen, and the field strength is varied, a reentrant phase behavior is observed. When a low field strength is applied, the long-range order possessed by the system is lost, upon increasing the field strength, the long-range order increases. This work provides an avenue in which to control the phase behavior of liquid crystal system by tuning parameters of an external rotating electric field.;The complex frequency and field dependent phase behavior of driven nematogens indicates that the dynamics of a spherical probe immersed in this system can also be tuned with respect to the parameters of the external field. The frequency dependent dynamics of a spherical probe immersed in driven nematogens is studied. The translational diffusion of the probe increases with increasing frequency, until a frequency of o = 2 ps-1 is reached. After this frequency is reached, a downturn in the diffusion coefficients is observed. At this frequency, the rotational motion of the nematogens show a transition to collision dominated dynamics, indicated by the complex decay of the rotational correlations. These results show that the dynamics of the probe are strongly coupled to the rotational dynamics of the nematogens. This data provides strong evidence suggesting that the transport of a spherical probe in orientable fluids can be controlled by tuning the parameters of the external field.;Overall this thesis provides advances in the description of the underlying physical processes of a variety of materials systems. We are able to accurately obtain transport coefficients and describe correlations of rotational and translational motion with respect to increasing spatial and geometric anisotropy. We are also able to access and control the phase behavior and dynamics in orientable fluids. Moreover, we were able to advance the use of simple Lorentz models and a simple LC model in describing complex dynamics and phase behavior. (Abstract shortened by UMI.)...