The purpose of this work is to critically examine the Lauritzen-Hoffman (LH) secondary nucleation barrier model of polymer crystallization. One of the major criticisms of the LH theory was that it predicted divergence of the lamellar thickness and crystal growth rate at finite undercoolings - the so-called “δ𝑙 catastrophe." Within this work, it has been shown that the "δ𝑙 catastrophe" can be eliminated by considering all of the implications of the Hoffman-Miller reptation approach. Combination of this approach and the lattice-strain theory of Hoffman and Miller (which predicts curved face crystals) eliminates two of the major criticisms of the LH theory within a single theoretical framework. Through studies performed in this work, the LH theory has been modified in such a way as to extend its utility to higher undercoolings. Physically meaningful nucleation parameters can be obtained with the modified LH theory if the viscoelastic parameters characterizing the transport of chain segments to the growth front are known a priori. Crystal growth and melting behavior were studied in the case of linear and cyclic polydimethylsiloxanes. An equilibrium melting temperature (T_m) of 250K was determined by the Hoffman-Weeks extrapolation method for a linear PDMS fraction with <M_n>=62,700 g/mol. This value is 12°C higher than that previously cited in the literature. From the kinetic studies, a fold crystal/melt interfacial free energy of 10.2 erg/cm² was determined which corresponds to a work of chain folding of 2.5 kcal/mol. Studies performed on the cyclic PDMS fractions confirmed that the configuration entropy decreases with decreasing molecular weight. Additionally, the studies on the cyclic PDMS fractions have shown that the σ-C_∞ relationship of Hoffman and coworkers fails for cyclic systems. The crystal growth rates, T_m, and lamellar thicknesses of polytetrafluoroethylene have been determined in this work. T_m has been shown to be 331±2°C. By atomic force microscopy and theoretical arguments it has been shown that the lamellar thicknesses of polytetrafluoroethylene, over the temperature range studied, is on the order of 1000Å. These thicknesses correspond to quantization of the folds, from which it was shown that meaningful analysis of the growth rate data is impossible. / Ph. D.