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 spherulitic growth rate data for a molecular weight series of isotactic polystyrene are analyzed in context of the Lauritzen-Hoffman kinetic theory of polymer crystallization. The primary objectives of the study are to critically test the Lauritzen-Hoffinan theory under conditions not rigorously investigated before and to gain a better understanding of the molecular weight dependence of crystal growth rate for isotactic polystyrene. The analyses yield values for fundamental kinetic and thermodynamic quantities associated with polymer crystallization. The physical meaning of the resulting parameters is assessed by comparing these results to those obtained from methods independent of crystal growth rate or crystallization theory altogether. This study differs from others reported in the literature in a number of ways, such as, the narrow molecular weight distribution and the molecular weight range of polystyrenes investigated. Also, growth rate measurements were extended to higher temperatures and a more appropriate kinetic equation for crystal growth rate analysis was applied. The majority of published studies that have used the Lauritzen-Hoffman theory applied an approximated form of the kinetic equation which does not fully describe the temperature dependence of polymer crystallization. The results of the study show that a transition from molecular weight dependent to independent crystal growth rate occurs at a molecular weight of about 250,000 g/mole for isotactic polystyrene. Also, comparison of viscoelastic and crystal growth rate data indicate that the Vogel form of the transport term in the Lauritzen Hoffman kinetic growth rate equation correctly describes the temperature dependence of molecular transport for the crystallization process of isotactic polystyrene. Furthermore, the study suggests that the equilibrium melting temperature for the polymer is significantly higher than the value that has been generally accepted for the past 25 years. The study also provided the opportunity to investigate various other factors and theories associated with polymer crystallization. For example, the theoretical relationship between the crystal's lateral surface free energy, σ, and the characteristic ratio, C_∞, was evaluated. Also, the spherulitic morphology as a function of molecular weight and temperature was examined by scanning electron microscopy, SEM. / Ph. D.

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.

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.

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.

The crystallization and melting behaviors of an ethylene/1-hexene copolymer and series of narrow molecular weight linear polyethylene and poly(ethylene oxide) fractions were studied using a combination of ultra-fast and conventional differential scanning calorimetry, optical microscopy, small angle X-ray scattering, and wide angle X-ray diffraction. In the case of linear polyethylene and poly(ethylene oxide), the zero-entropy production melting temperatures of initial lamellae of isothermally crystallized fractions were analyzed in the context of the non-linear Hoffman-Weeks method. Using the Huggins equation, limiting equilibrium melting temperatures of 141.4 ± 0.8oC and 81.4 ± 1.0oC were estimated for linear polyethylene and poly(ethylene oxide), respectively. The former and the latter are about 4oC lower and 12.5oC higher than these predicted by Flory/Vrij and Buckley/Kovacs, respectively. Accuracy of the non-linear Hoffman-Weeks method was also examined using initial lamellar thickness literature data for a linear polyethylene fraction at different crystallization temperatures. The equilibrium melting temperature obtained by the Gibbs-Thomson approach and the C2 value extracted from the initial lamellar thickness vs. reciprocal of undercooling plot were similar within the limits of experimental error to those obtained here through the non-linear Hoffman-Weeks method. In the next step, the Lauritzen-Hoffman (LH) secondary nucleation theory was modified to account for the effect of stem length fluctuations, tilt angle of the crystallized stems, and temperature dependence of the lateral surface free energy. Analysis of spherulite growth rate and wide angle X-ray diffraction data for 26 linear polyethylene and 5 poly(ethylene oxide) fractions revealed that the undercooling at the regime I/II transition, the equilibrium fold surface free energy, the strength of the stem length fluctuations and the substrate length at the regime I/II transition are independent of chain length. The value of the equilibrium fold surface free energy derived from crystal growth rate data using the modified Lauritzen-Hoffman theory matches that calculated from lamellar thickness and melting data through the Gibbs-Thomson equation for both linear polyethylene and poly(ethylene oxide). Larger spherulitic growth rates for linear polyethylene than for poly(ethylene oxide) at low undercooling is explained by the higher secondary nucleation constant of poly(ethylene oxide). While the apparent friction coefficient of a crystallizing linear polyethylene chain is 2 to 8 times higher than that of a chain undergoing reptation in the melt state, the apparent friction coefficient of a crystallizing poly(ethylene oxide) chain is about two orders of magnitude lower. This observation suggests that segmental mobility on the crystal phase plays a significant role in the crystal growth process. In case of the statistical ethylene/1-hexene copolymer, the fold surface free energies of the copolymer lamellae at the time of crystallization and melting increase with increasing undercooling, approaching the same magnitude at high undercooling. As a result of this temperature dependence, the experimental melting vs. crystallization temperature plot is parallel to the Tm = Tc line and the corresponding Gibbs-Thomson plot is non-linear. This behavior is attributed to the fact that longer ethylene sequences form a chain-folded structure with lower concentration of branch points on the lamellar surface at lower undercooling, while shorter ethylene sequences form lamellar structures at higher undercooling exhibiting a higher concentration of branch points on the lamellar surface. Branch points limit the ability of lamellar structures to relax their kinetic stem-length fluctuations during heating prior to melting. / Ph. D. / Morphology of semi-crystalline polymers is strongly affected by their crystallization conditions. Thermodynamic and kinetic models allow us to understand the crystallization mechanism of a semi-crystalline polymer and relate its crystallization conditions to the final morphology. In this research, we studied the molar mass dependence of the crystallization and melting behaviors of narrow molecular weight distribution linear polyethylene (LPE) and poly(ethylene oxide) (PEO) fractions using a modified Lauritzen-Hoffman (LH) secondary nucleation theory. We have shown that the equilibrium melting temperature of LPE and PEO fractions found from the non-linear Hoffman-Weeks method are within the experimental uncertainty identical with these measured directly for extended chain crystals or derived from a Gibbs-Thomson analysis. The value of the equilibrium fold surface free energy derived from crystal growth rate data using the modified LH theory matches that calculated from lamellar thickness and melting data through the Gibbs-Thomson equation for both LPE and PEO. We reported that the higher segmental mobility of PEO in the crystalline phase leads to significantly lower apparent chain friction coefficients during crystal growth compared to LPE. We also studied the role of short-chain branching in the crystal growth kinetics of ethylene/1-hexene copolymers. We observed that the fold surface free energies during crystallization and during melting are both function of the undercooling while the ratio of the former to the latter decreases with increasing undercooling. We proposed that this behavior may be related to the concentration of short-chain branches at the surface of the lamellae, where higher concentration leads to lower relaxation.