In this thesis, the crystallization and melting of blends of high and low density homogeneous ethylene-1-octene copolymers with appended long chain branches have been investigated in real time by means of time-resolved SALS under cross-polarized and parallel-polarized optical alignments using a charge-coupled device camera (CCD) system, simultaneous small angle-X-ray and wide angle X-ray measurements using synchrotron radiation and differential scanning calorimetry (DSC). For the highest density material studied, our data show that in the case of crystallization at low supercooling, spherulitic growth (primary crystallization) occurs first while the apparent degree of crystallinity is less than 2%. Over 90% of the crystallinity develops after the primary crystallization process. When the average branch content of the blend is 14 branches per 1000 carbons complete spherulites are observed. The internal spherulite disorder is unchanged relative to that obtained for the high density component. When the average branch content of the blend is increased to 58 branches per 1000 carbons, the crystallization rate is faster than that of the moderate increase but the morphology suggested from SALS is consistent with incomplete spherulites. For this case, our data suggest that the domain sizes resulting from the incipient melt phase separation is the likely cause of the accelerated crystal growth. We propose that the incomplete spherulites formed may be a consequence of the competition between amorphous phase separation in the residual melt and crystallization. The results of a numerical study investigating the dynamics of spinodal decomposition in blends of linear Gaussian chains in three dimensions were used to evaluate the effect of branch content on the phase separation kinetics for mixtures of linear Gaussian chains and branched chains. The phase separation kinetics in the branched systems are identical to that of linear mixtures with larger domain sizes. Hence, it may not be possible to detect differences in the time dependence of the structure factor and domain size from scattering measurements if one varies the branch content of the blend. Blends of linear and branched polymers can be treated as blends of linear Gaussian chains even when the branch content is very high.

This dissertation describes computer simulations and theoretical analyses of ordering processes in liquid crystals and polymers. One ordering process in liquid crystals occurs during the isotropic to nematic transition in which point and line defects form and annihilate. Monte Carlo simulations support the newly-derived scaling of the defect density, which was found to scale with time as $-$6/7 in both two and three dimensions, contrary to the mean-field result of $-$1. Frustration was determined to be a key factor in this difference. Another ordering process in liquid crystals is the evolution of inversion walls and loops. Analogous to the model of a shrinking elastic loop in a viscous medium which has been theoretically investigated by deGennes and Brochard, our lattice Monte Carlo simulations of inversion walls and loops show the same scaling behavior with time and the same predicted dependence of shrinkage rate on the orientational diffusion coefficient. Polymer crystallization constitutes the other major topic of this dissertation. The initial stages of crystallization are difficult to study experimentally but by using the united-atom Langevin dynamics method, single and multi-chain crystallization can be simulated. The simulations show that random fluctuations nucleate regions of higher order which in turn can induce further crystallization. Lamellar thicknesses obtained from simulations at various undercoolings showed the same scaling behavior as experimental data from literature. Besides homogeneous nucleation, secondary nucleation was also observed, with the newly-attached chains continuing to undergo conformational changes on the crystal surface. Finally, the phenomenon of lamellar thickening was investigated. Lamellar thickening was observed to occur cooperatively in a stepwise, quantized manner.