No description available.

<div> <div> <div> <div> <div> <p>Polymer materials are receiving increased attention in the field of materials science, both in academia and industry, with its widespread application from commercial plastics to advanced biomaterials. These include composites in airplanes and automobiles, functional films on monitors in mobile phones and computers, as well as adhesive and coating materials in civil engineering. Despite significate efforts, the major questions and challenges in understanding key properties of polymer materials are still not solved. Such lack of understanding hinders advances in delicate design and controlling of polymers for advanced functional applications. The development of polymer science began with the pioneering work made by Flory and his coworkers at 1950s as commercial synthetic polymer industry started to develop and grow. During the following decades, experimental work guided by theoretical predictions had been the major contribution of our further understanding while the great challenges in experimental techniques at molecular level always blurred critical information in polymer materials. With enhanced ability in computational science, simulation starts to become an essential investigation method to provide thermodynamic insights at this molecular level. Along with great progress in properties prediction with improved accuracy, great challenges still exist in modeling processing of polymer systems, especially in accurate description of dynamic evolution incorporated with various processing conditions resulting macroscopic structural changes like carbon fiber processing from polyacrylonitrile (PAN) precursor in which crystalline regions represent more than 55% of the material by volume. In terms of crystallinity in polymers, with the heated debates over classical crystal-growth models, major questions and challenges are still not solved including the control and determination of molecular conformations and crystal structures as well as mesoscale morphologies, detailed understanding of melting and crystallization. It is clear that molecular scale investigations on crystal structure and crystallization mechanisms as well as predictive simulations of that will be a huge demand in the near future to explore mechanical, optical, and other physical properties in polymeric materials. </p> <p>The purpose of my dissertation is to summarize my major research contributions to our current understanding of crystalline polymers in the aspects of crystal structure determination and crystallization processes at molecular level, and to introduce our effort on simulation software development and indicate possible future directions in the field of molecular modeling of polymer crystals. Three major research topics will be included as the following </p> </div> </div> <div> <div> <p>1. Crystalline and pseudo-crystalline phases of polyacrylonitrile from molecular dynamics; 2. Novel mode of non-crystallographic branching in the initial stages of polymer fibril<br></p></div></div></div><div><div><div> <p>growth;<br> 3. Polymer crystal structure generator and analysis software (PolymerXtal). </p> </div> </div> </div> </div> </div>

No description available.

The melting behavior of polymers can provide information on their crystallization mechanism. However, the origin of the time-dependent low endotherm, or annealing peak, and the extent of melting-recrystallization-remelting during heating are still debated. The crystallization and subsequent melting behavior of isotactic polystyrene are explored in the context of Stroblâ "s 3-Phase model using differential scanning calorimetry (DSC), small angle X-ray scattering (SAXS), and wide angle X-ray diffraction. DSC experiments confirm the existence of a crystallization time-dependent low endotherm, and melting-recrystallization-remelting processes during heating. SAXS analysis using the correlation function confirms that the lamellar thickness increases with crystallization temperature and is independent of time. The spread between equilibrium melting and crystallization temperatures determined in this work (Tfâ"" = 533K, Tcâ"" = 544K) is much smaller than reported by Strobl et al. (Tfâ"" = 562K, Tcâ"" = 598K). These differences are partially attributed to overestimation in lamellar thicknesses calculated through the interface distribution function. Analysis of diffraction broadening shows that the apparent crystal size decreases with crystallization time, suggesting the formation of smaller/less perfect crystals during secondary crystallization. These results are consistent with observations that the glass transition temperature increases with crystallization time and supports the idea that secondary crystallization leads to increased amorphous conformational constraints. These results also suggest that the upward shift of the annealing peak during secondary crystallization is associated with increased amorphous constraints rather than increased crystal dimensions. The lack of distinction between Tfâ"" and Tcâ"" and the evolution of crystal size during crystallization stand in direct contrast with Stroblâ "s model. / Master of Science

The present thesis reports computer simulation studies of several phase transition related phenomena in a range of soft-condensed matter systems. A coherent unifying theme of the thesis is the understanding of dynamics of phase transitions through free energy calculations using recently developed efficient non-Boltzmann sampling methods. Based on the system/phenomena of interest, the thesis has been classified into four major parts: I. Isotropic-nematic (IN) phase transition in liquid crystals. II. Nucleation phenomena in gas-liquid transition with particular emphasis on the systems close to the spinodal curve. III. Collapse transition in linear hydrocarbon (n-alkane) chains for a varying range of length, solvent and temperature. IV. Crystallization of unbranched polymer chains in dilute solution, with particular emphasis on the temperature dependent crossover between the rod-like crystalline state and spherical molten globule state. The thesis has been further divided into ten chapters running through the four parts mentioned before. In the following we provide a brief chapter-wise outline of the thesis. Part I deals with the power law relaxation and glassy dynamics in thermotropic liquid crystals close to the IN transition and consists of two chapters. To start with, Chapter I.1 provides an introduction to thermotropic liquid crystals. Here we briefly introduce various liquid crystalline phases, the order parameter used to characterize the IN transition, a few well established theoretical models, and we conclude with describing the recent experimental and computer simulation studies that have motivated the work described in the next chapter. In Chapter I.2, we present our molecular dynamics simulation studies on single particle and collective orientational dynamics across the IN transition for Lebwohl Lasher model, which is a well-known lattice model for thermotropic liquid crystals. Even this simplified model without any translational degrees of freedom successfully captures the short-tointermediate time power law decay recently observed in optical heterodyne detected optical Kerr effect (OHDOKE) measurements near the IN transition. The angular velocity time correlation function also exhibits a rather pronounced power law decay near the IN boundary. In the mean squared angular displacement at comparable time scales, we observe the emergence of a sub-diffusive regime which is followed by a super-diffusive regime before the onset of the longtime diffusive behavior. We observe signature of dynamical heterogeneity through pronounced non-Gaussian behavior in the orientational motion particularly at lower temperatures. Interestingly, this behavior closely resembles what is usually observed in supercooled liquids. We obtain the free energy as a function of orientational order parameter by the use of recently developed transition matrix Monte Carlo (TMMC) method. The free energy surface is flat for the system considered here and the barrier between isotropic and nematic phases is vanishingly small for this weakly first-order transition, hence allowing for large scale, collective, and correlated orientational density fluctuations. We attribute this large scale fluctuations as the reason for the observed power law decay of the orientational time correlation functions. Part II consists of three chapters, where we focus on the age old problem of nucleation and growth, both from the perspective of thermodynamics and kinetics. We account for the rich history of the problem in the introductory Chapter II.1. In this chapter we describe various types and examples of the nucleation phenomena, and a brief account of the major theoretical approaches used so far. We begin with the most successful Classical Nucleation Theory (CNT), and then move on to more recent applications of Density Functional Theory (DFT) and other mean-field types of models. We conclude with a comparison between the experiments, theories and computational studies. In the next chapter (Chapter II.2) we attempt to elucidate the mechanism of nucleation near the gas-liquid spinodal from a microscopic point of view. Here we construct a multidimensional free energy surface of nucleation of the liquid phase from the parent supercooled and supersaturated vapor phase near the gas-liquid spinodal. In particular, we remove the Becker-Doring constraint of having only one growing cluster in the system. The free energy, as a function of the size of the largest cluster, develops a pronounced minimum at a subcritical cluster size close to the spinodal. This signifies a two step nature of the process of nucleation, where the rapid formation of subcritical nuclei is followed by further growth by slower density fluctuations on an uphill free energy surface. An alternative free energy pathway involving the participation of many subcritical clusters is envisaged near the spinodal where the growth of the nucleus is found to be promoted by a coalescence mechanism in contrast to the single particle addition assumption within CNT. The growth of the stable phase becomes progressively collective and spatially diffuse, and the significance of a “critical nucleus” is lost for deeper quenches. In this chapter we present our studies both in 3dimensional Lennard-Jones (LJ) system and Ising model (both 2and 3dimensions). Our general findings seem to be independent of the model chosen. While the previous chapter focuses on relatively well-studied 3-dimensional (3D) LJ system, in Chapter II.3 we present our studies on the characteristics of the nucleation phenomena in 2dimensional (2D) Lennard-Jones fluid. To the best of our knowledge this is the first extensive computer simulation study to check the accuracy of CNT in 2D. Using various Monte Carlo methods, we calculate the free energy barrier for nucleation, line tension, and bulk densities of equilibrium liquid and vapor phases, and also investigate the size and shape of the critical nucleus. The study is carried out at an intermediate level of supersaturation (away from the spinoidal limit). In 2D, a surprisingly large cutoff (rc ≥ 7.0σ where σ is the diameter of LJ particles) in the truncation of the LJ potential is required to obtain converged results. A lower cutoff leads to a substantial error in the values of the line tension, nucleation barrier, and characteristics of the critical cluster. Note that typically 2.5σ is sufficient for 3D LJ fluids. We observe that in 2D system CNT fails to provide a reliable estimate of the free energy barrier. While it is known to slightly overestimate the nucleation barrier in 3D, it underestimates the barrier by as much as 50% at the saturation ratio S = 1.1(defined as S = P/Pc, where Pc is the coexistence pressure) and at the reduced temperature T* = 0.427(defined as T* = KBT/ ε, where ε is the depth of the potential well). The reason for the marked inadequacy of the CNT in 2D can be attributed to the non-circular nature of the critical clusters. Although the shape becomes increasingly circular and the clusters become more compact with increase in cutoff radius, an appreciable non-circular nature remains even without any cutoff to make the simple CNT inaccurate. Part III again consists of three chapters and focuses on the conformational equilibria. Collapse transition and self-organized structures of n-alkanes in solution. In Chapter III.1 we carry out a brief survey of the existing theories of polymer in solution, with particular emphasis on the collapse process in poor solvents. We also introduce the concept of “hydrophobicity” and “hydrophobic collapse”, which is now a subject enormous interest, partly because it my help in understanding the initial processes involved in protein folding. We briefly discuss the subject of formation of beautiful self-organized structures by block copolymers, and also simple homopolymers which is essentially the focus of the work embodied in the next two chapters. In Chapter III.2 we demonstrated a chain length dependent crossover in the structural properties of linear hydrocarbon (n-alkane) chains using detailed atomistic simulations in explicit water. We identify a number of exotic structures o the polymer chain through energy minimization of representative snapshots collected from molecular dynamics trajectory. While the collapsed state is ring-like(circular) for small chains(CnH2n+2; n ≤ 20) and spherical for very long ones( n = 100), we find the emergence of ordered helical structures at intermediate lengths (n ~ 40). We find different types of disordered helices and toroid-like structures at n = 60. We also report a sharp transition in the stability of the collapsed state as a function of the chain length through relevant free energy calculations. While the collapsed state is only marginally metastable for C20H42, a clear bistable free energy surface emerges only when the chain is about 30 monomers long. For n = 30, the polymer exhibits an intermittent oscillation(characterized by well-developed 1/f noise, where f is the frequency ) between the collapsed and the coil structures, characteristic of two stable states separated by a small barrier. This appears to support a weakly first order phase transition between the extended and the collapsed states. Chapter III.3 extends the study of previous chapter to much longer chains (n ≥ 100), which irreversibly collapse in water into globular forms. Even though the collapsed form has a nearly spherical shape, close inspection shows a propensity towards local ordering in the alignment of the polymer segments. This tendency to maintain alignment in order to maximize the number of contacts leads to a core-shell like structure, where the shell is often characterized by a bent rod-like shape consisting of two adjacent segments running in parallel. A key event associated with the initial stage of collapse seems to be the formation of a skewed ring (or loop) that serves as a “nucleation center” for rest of the chain to collapse into. Time evolution of the radial distribution function of water surrounding the polymer, shows that the density of neighboring water decreases by only about 15-20% from that of bulk water. Even though interior of the ting-like structures is fully devoid of water, solvent accessible surface representation shows that these regions are geometrically/spatially inaccessible to water molecules. We suggest that the role of water is to stabilize such ring-like structures once formed by natural conformational fluctuations of the polymer chain. This view is confirmed by observation of spontaneous formation and melting away of such ring-like entities in a polar aprotic solvent(DMSO). We also comment on the role of the flexibility of polymer chains in determining the collapse kinetics. The last part(Part IV) of the thesis consists of two chapters that deal with the crystallization of linear polymer chains from dilute solution. The way long chain polymers crystallize is drastically different from their small molecule counterparts due to their topological connectivity. Linear polymers often crystallize from dilute solution in the form of thin lamellae with well-defined crystallographic features. In Chapter IV.1 we briefly survey the current theoretical understanding and confusions associated with the highly debated field of polymer crystallization. While the last few decades have seen the development of many successful phenomenological theories, the molecular mechanism of formation of such self-organized lamellae is extremely complex and very poorly understood. There are clearly two distinct steps in polymer crystallization. Firstly, the individual linear polymers must self-organize into bundles of somewhat regular structures. These structures then further aggregate to lamellar form and crystallize into a lattice. In this respect , it has marked similarity to the problem of protein crystallization. In chapter IV.2 we present Brownian dynamics simulation studies of a single polythelene chain of length 500. Such systems can reasonably mimic the process of crystallization from dilute solutions. Our simulations could successfully reproduce some of the interesting phenomena observed in experiments and very recent computer simulation studies, including multi-center nucleation of rod-like structures within a single polymer chain, an inverse relation between lamellar thickness and temperature etc. But our primary focus has been to understand the nature of the phase transition as one traverses along the melting temperature and the underlying free energy surface. Near the melting temperature we observe a very intriguing fluctuation between the disordered molten globule state and the ordered rod-like crystalline, where these two forms have highly different shape and structure. These fluctuations have strong signature of 1/f noise or intermittency. This clearly indicates the existence of a weakly first order transition, where two widely different states with large difference in values of order parameter are separated by a rather small free energy barrier. This can be related to the experimentally observed density fluctuations that resemble spinodal decomposition. It is important to note that very similar fluctuations have been observed in our previous studies on liquid crystals (Chapter 1.2) and intermediate sized alkalines in water(Chapter III.2) that signifies a universal underlying energy landscape for these systems. We have discussed the scope of future work at the end of each chapter whenever appropriate.

Narrow molecular weight fractions of Poly(ε-caprolactone) were successfully obtained using the successive precipitation fractionation technique with toluene/n-heptane as a solvent/nonsolvent pair. Calorimetric studies of the melting behavior of fractions that were crystallized either isothermally or under constant cooling rate conditions suggested that the isothermal crystallization of the samples should be used for a proper evaluation of the molecular weight dependence of the observed melting temperature and degree of crystallinity in PCL. The molecular weight and temperature dependence of the spherulitic growth rate of fractions was studied in the context of the Lauritzen-Hoffman two-phase model and the Strobl three-phase model of polymer crystallization. The zero-growth rate temperatures, determined from spherulitic growth rates using four different methods, are consistent with each other and increase with chain length. The concomitant increase in the apparent secondary nucleation constant was attributed to two factors. First, for longer chains there is an increase in the probability that crystalline stems belong to loose chain-folds, hence, an increase in fold surface free energy. It is speculated that the increase in loose folding and resulting decrease in crystallinity with increasing chain length are associated with the ester group registration requirement in PCL crystals. The second contribution to the apparent nucleation constant arises from chain friction associated with segmental transport across the melt/crystal interface. These factors were responsible for the much stronger chain length dependence of spherulitic growth rates at fixed undercooling observed here with PCL than previously reported for PE and PEO. In the case of PCL, the scaling exponent associated with the chain length dependence of spherulitic growth rates exceeds the upper theoretical bound of 2 predicted from the Brochard-DeGennes chain pullout model. Observation that zero-growth and equilibrium melting temperature values are identical with each other within the uncertainty of their determinations casts serious doubt on the validity of Strobl three-phase model. A novel method is proposed to determine the Porod constant necessary to extrapolate the small angle X-ray scattering intensity data to large scattering vectors. The one-dimensional correlation function determined using this Porod constant yielded the values of lamellar crystal thickness, which were similar to these estimated using the Hosemann-Bagchi Paracrystalline Lattice model. The temperature dependence of the lamellar crystal thickness was consistent with both LH and the Strobl model of polymer crystallization. However, in contrast to the predictions of Strobl’s model, the value of the mesomorph-to-crystal equilibrium transition temperature was very close to the zero-growth temperature. Moreover, the lateral block sizes (obtained using wide angle X-ray diffraction) and the lamellar thicknesses were not found to be controlled by the mesomorph-to-crystal equilibrium transition temperature. Hence, we concluded that the crystallization of PCL is not mediated by a mesophase. Metallocene-catalyzed linear low-density (m-LLDPE with 3.4 mol% 1-octene) and conventional low-density (LDPE) polyethylene blends of different compositions were investigated for their melt-state miscibility and concurrent crystallization tendency. Differential scanning calorimetric studies and morphological studies using atomic force microscopy confirm that these blends are miscible in the melt-state for all compositions. LDPE chains are found to crystallize concurrently with m-LLDPE chains during cooling in the m-LLDPE crystallization temperature range. While the extent of concurrent crystallization was found to be optimal in blends with highest m-LLDPE content studied, strong evidence was uncovered for the existence of a saturation effect in the concurrent crystallization behavior. This observation leads us to suggest that co-crystallization, rather than mere concurrent crystallization, of LDPE with m-LLDPE can indeed take place. Matching of the respective sequence length distributions in LDPE and m-LLDPE is suggested to control the extent of co-crystallization. / Ph. D.

No description available.

This work investigates the influence of microstructure and cooling and heating rates on the physical and chemical properties of fast crystallizing polymers. The primary objectives were to 1) utilize advanced methodologies to accurately determine the fundamental thermodynamic value of equilibrium melting temperature (Tmo) for the semi-crystalline polymer poly(ether ketone ketone) (PEKK), 2) increase understanding of the influence of microstructure (random versus blocky) of functionalized semi-crystalline polymers on physical and chemical properties, and 3) understand the influence of additive manufacturing process parameters on semi-crystalline polymer crystallization and final properties. All objectives utilized the advanced characterization technique of fast scanning calorimetry (FSC) using the Mettler Toledo Flash DSC 1. The first half of this work focuses on the high-performance semi-crystalline aromatic polymer poly(ether ketone ketone) (PEKK) with a copolymerization ratio of terephthalate to isophthalate moieties (i.e., T/I ratio) of 80/20. Due to the fast heating and cooling rates of the Flash DSC, PEKK underwent melt-reorganization upon heating at slow heating rates. This discovery resulted in utilizing a Hoffman-Weeks linear extrapolation of the zero-entropy production temperature to establish a new equilibrium melting temperature of 382 oC. Additionally, a new NMR solvent, dichloroacetic acid, was discovered for PEKK, allowing for comprehensive NMR analysis of PEKK for the first time. Diphenyl acetone (DPA) was discovered as a novel, benign gelation solvent for PEKK, enabling heterogeneous gel-state bromination and sulfonation to afford blocky microstructures. The gel state functionalization process resulted in a blocky microstructure with runs of pristine crystallizable PEKK retained within the crystalline domains, and amorphous domains containing the functionalized PEKK monomers. The preservation of the pristine crystalline domains resulted in enhanced physical and chemical properties compared to the randomly functionalized analogs. Additionally, heterogeneous gel state functionalization of PEKK gels prepared from different solvents and gelation temperatures resulted in differences in crystallization behavior between blocky microstructures of the same degree of functionalization. This result demonstrates that the blocky microstructure can be tuned through controlling the starting gel morphology. The second half of this work focuses on understanding the influence of cooling and heating rates on the melting, crystal morphology, and crystallization kinetics on isotactic polypropylene (iPP), iPP-polyethylene copolymers (iPP-PE), and iPP/iPP-PE blends and using this information to gain understanding of how these polymers crystallize during the additive manufacturing processes of powder bed fusion (PBF) and material extrusion (MatEx). The crystallization kinetics of iPP, iPP-PE copolymers, and iPP/iPP-PE blends exhibited bimodal parabolic-like behavior attributed to crystallization of the mesomorphic crystal polymorph at low temperatures and the α-form crystal at high temperatures. Incorporation of non-crystallizable polyethylene fractions both covalently and blended as a secondary component, resulted in decreasing crystallization rates, inhibition of crystallization, and decreased crystallizability. Additionally, the non-isothermal crystallization behavior of these systems shows that the non-crystallizable fractions influence the crystal nucleation density and temperature at which polymorphic crystallization occurs. Utilizing in-situ IR thermography in the PBF system, the heating and cooling rates observed for a single-layer PBF print were used to mimic the PBF process by FSC. Partial melting in the printing process leads to self-seeding and increased crystallization onset temperatures upon cooling, which influences the final part melting morphology. Nucleation from surrounding powder and partially melted crystals greatly influences the crystallization kinetics and crystal morphology of the final part. Utilizing rheological experiments and process-relevant cooling rates observed in the MatEx process, the miscibility of iPP/iPP-PE blends influenced the nucleation behavior and crystallization rates, subsequently leading to differences in printed part properties. / Doctor of Philosophy / The crystalline morphology of semi-crystalline polymers depends on their microstructure and thermal history. The resultant crystalline morphology greatly affects the physical and chemical properties. In the first part of this work, the effect of microstructure on material properties is explored. Block copolymer microstructures consist of two or more blocks of distinct polymer segments covalently bonded to one another. This leads to self-organization of the components into unique structural order that would not be attainable if the polymer segments were randomly bonded together. This structural order enhances material properties; thus, block copolymers are advantageous for many applications. However, synthesis of block copolymers can be tedious and expensive. Thus, additional methodologies for block copolymer synthesis are desired. In this work blocky (i.e., statistically non-random) copolymers are synthesized through a facile post-polymerization functionalization method. These blocky copolymers result in enhanced physical and chemical properties compared to the randomly synthesized analogs. This work shows blocky functionalization of a new polymer under new post-polymerization conditions and expands upon the synthesis methodology for block copolymers. In the second part of this work, the effect of heating and cooling rates on the formation of crystals during additive manufacturing is explored. Additive manufacturing modalities of powder bed fusion and material extrusion consist of rapid heating and cooling processes, which can affect how crystals form and ultimately affect the final printed part properties. Using a technique called fast scanning calorimetry, the different heating and cooling rates that the polymer witnesses during printing can be mimicked, and the formation of crystals under these different conditions can be replicated. This mimicking analysis can be related to the printing process and be used to help guide printing processes to enhance printed part properties.

The crystallization and melting behavior of linear polyethylene and of a series of random ethylene/styrene copolymers was investigated using a combination of classical and temperature modulated differential scanning calorimetry. In the case of linear polyethylene and low styrene content copolymers, the temporal evolutions of the melting temperature, degree of crystallinity, and excess heat capacity were studied during crystallization. The following correlations were established: 1) the evolution of the melting temperature with time parallels that of the degree of crystallinity, 2) the excess heat capacity increases linearly with the degree of crystallinity during primary crystallization, reaches a maximum during the mixed stage and decays during secondary crystallization, 3) the rates of shift of the melting temperature and decay of the excess heat capacity lead to apparent activation energies that are very similar to these reported for the crystal ac relaxation by other techniques. Strong correlations in the time domain between the secondary crystallization and the evolution of the excess heat capacity suggest that the reversible crystallization/melting phenomenon is associated with molecular events in the melt-crystal fold interfacial region. In the case of higher styrene content copolymers, the multiple melting behavior at high temperature is investigated through studies of the overall crystallization kinetics, heating rate effects and partial melting. Low melting crystals can be classified into two categories according to their melting behavior, superheating and reorganization characteristics. Low styrene content copolymers still exhibit some chain folded lamellar structure. The shift of the low melting temperature with time in this case is tentatively explained in terms of reorganization effects. Decreasing the crystallization temperature or increasing the styrene content leads to low melting crystals more akin to fringed-micelles. These crystals exhibit a lower tendency to reorganize during heating. The shift of their melting temperature with time is attributed to a decrease in the conformational entropy of the amorphous fraction as a result of constraints imposed by primary and secondary crystals. To further understand the mechanism of formation of low melting crystals, quasi-isothermal crystallization experiments were carried out using temperature modulation. The evolution of the excess heat capacity was correlated with that of the melting behavior. On the basis of these results, it is speculated that the generation of excess heat capacity at high temperature results from reversible segmental exchange on the fold surface. On the other hand, the temporal evolution of the excess heat capacity at low temperature for high styrene content copolymers is attributed to the reversible segment attachment and detachment on the lateral surface of primary crystals. The existence of different mechanisms for the generation of excess heat capacity in different temperature ranges is consistent with the observation of two temperature regimes for the degree of reversibility inferred from quasi-isothermal melting experiments. In a second project, the chain length and temperature dependences of spherulitic growth rates were studied for a series of narrow fractions of poly(ethylene oxide) with molecular weight ranging from 11 to 917 kg/mol. The crystal growth rate data spanning crystallization temperatures in regimes I and II was analyzed using the formalism of the Lauritzen-Hoffman (LH) theory. Our results are found to be in conflict with predictions from LH theory. The Kg ratio increases with molecular weight instead of remaining constant. The chain length dependence of the exponential prefactor, G0, does not follow the power law predicted by Hoffman and Miller (HM). On this basis, the simple reptation argument proposed in the HM treatment and the nucleation regime concept advanced by the LH model are questioned. We proposed that the observed I/II regime transition in growth rate data may be related to a transition in the friction coefficient, as postulated by the Brochard-de Gennnes slippage model. This mechanism is also consistent with recent calculations published by Toda in which both the rates of surface nucleation and substrate completion processes exhibit a strong temperature dependence. / Ph. D.

Semicrystalline polymers are an important class of materials for their prevalence in today's markets and their desirable properties. These properties depend on the early stages of the polymer crystallization process where a crystal nucleates from the polymer melt. This nucleation process is conventionally understood via an extension of Classical Nucleation Theory to polymers (CNTP). However, recent experimental and simulation evidence points to nucleation mechanisms that do not agree with the predictions of CNTP. Specifically, these experiments suggest a previously unrecognized role of nematic phases in mediating the melt"“crystal transtion. To explain these observations, several new theories of nucleation alternate to CNTP have emerged in the literature, all of which suggest specific modifications to the free energy landscape (FEL) near-equilibrium. To address these theoretical controversies, this dissertation aimed to study the equilibrium phase behavior of polymers via Monte Carlo (MC) simulations. Simulating equilibrium phase behavior of polymer melts is not a trivial task due to the large free energy barriers involved. Throughout this research, we employed a combination of strategies to speed up these molecular simulations. First, we employed a domain decomposition to divide the simulation box into multiple independent simulations that execute independent MC trajectories in parallel. The novel GPU-accelerated MC algorithm successfully and accurately simulated the phase behavior of bead spring chains. Additionally, it sped up MC simulations of Lennard Jones chains by up to 10 times. In its current form, the GPU-accelerated algorithm did not achieve significant speedups to improve outcomes of simulating large polymer melts with detailed potentials. We recommended various strategies to improving the current algorithm. This reality motivated the use of biased MC simulations to study the phase behavior of polymers more expediently without the need for GPU acceleration. Specifically, the latter part of the Dissertation employed Wang Landau MC (WLMC) simulations to build phase diagrams and expanded ensemble density of states (EXEDOS) simulations to construct FELs. Phase diagrams from WLMC simulations divided volume-temperature space into melt, nematic and crystal phases. Then, FELs from EXEDOS simulations at equilibrium provided direct access to the relative stability and minimum free energy paths between coexistant states. By employing a two-dimensional EXEDOS sampling in both crystal and nematic order for hard bead semiflexible oligomers with a stepwise bending stiffness, we built FELs that show that the crystalline transition cooperatively and simultaneously formed crystal and nematic order. This nucleation mechanism was not in agreement with predictions from CNTP or newer theoretical formulations. To investigate the sensitivity of the phase behavior to the employed polymer model, we then employed WLMC simulations to build phase diagrams for a number of different polymer models to ascertain their impact on the resulting nucleation mechanism. We found that the phase behavior was sensitive to the form of the bending stiffness potential used. Chains with a stepwise bending stiffness yielded the previously mentioned cooperative and simultaneous crystal and nematic ordering. In contrast, chains with a harmonic bending stiffness potential crystallized via a two-step nucleation process, first forming a nematic phase that nucleates the crystal. The latter nucleation mechanism was in line with predictions from new theories of nucleation that incorporate the nematic phase as a precursor. Furthermore, we found that it is important to correct for excluded volume differences when comparing chains with soft and hard beads or chains with differing bending stiffnesses.