Growth and dissolution of crystal nuclei in poly(l-lactic acid) (PLLA) in Tammann's development method

Effects of Structural Relaxation of Glass-Forming Melts on the Overall Crystallization Kinetics in Cooling and Heating

In the theoretical treatment of crystallization, it is commonly assumed that the relaxation processes of a liquid proceed quickly as compared to crystal nucleation and growth processes. Actually, it is supposed that a liquid is always located in the metastable state corresponding to the current values of pressure and temperature. However, near and below the glass transition temperature, Tg, this condition is commonly not fulfilled. In such cases, in the treatment of crystallization, deviations in the state of the liquid from the respective metastable equilibrium state have to be accounted for when determining the kinetic coefficients governing the crystallization kinetics, the thermodynamic driving force of crystallization, and the surface tension of the aggregates of the newly evolving crystal phase including the surface tension of critical clusters considerably affecting the crystal nucleation rate. These factors may greatly influence the course of the overall crystallization process. A theoretical analysis of the resulting effects is given in the present paper by numerical solutions of the J(ohnson)-M(ehl)-A(vrami)-K(olmogorov) equation employed as the tool to model the overall crystallization kinetics and by analytical estimates of the crystallization peak temperatures in terms of the dependence on cooling and heating rates. The results are shown to be in good agreement with the experimental data. Possible extensions of the theory are anticipated and will be explored in future analysis.

Radial growth rate of near-critical crystal nuclei in poly(l-lactic acid) (PLLA) in Tammann's two-stage development method

The specific features of crystal nucleation widely determine the morphology of the evolving crystalline material. Crystal nucleation is, as a rule, not accessible by direct observation of the nuclei, which develop with time. This limitation is caused by the small size (nanometer scale) of the critical nuclei and the stochastic nature of their formation. We describe an experimental approach to the determination of specific features of the cluster size distribution employing fast scanning calorimetry at scanning rates up to 10 000 K s^-1. The surviving cluster fraction is determined by selectively melting/dissolving clusters smaller than the critical size corresponding to the highest temperature of a short spike positioned between the nucleation and the development stage in Tammann's two-stage method. This approach allows for estimating the time evolution of the radius of the largest detectable clusters in the distribution. Knowing this radius as a function of nucleation time allows for determining a radial growth rate. In the example of poly(l-lactic acid) (PLLA), the order of magnitude estimate of radial growth rates of clusters of about 2-5 nm yields values between 10^-5 and 10^-3 nm s^-1. The radial growth rate of micrometer-sized spherulites is available from optical microscopy. The corresponding values are about three orders of magnitude higher than the values for the nanometer-sized clusters. This difference is explainable by stochastic effects, transient features, and the size dependence of the growth processes on the nanometer scale. The experimental and (order of magnitude) classical nucleation theory estimates agree well.

Young's modulus of the different crystalline phases of poly (l-lactic acid)

Young's modulus of α'- and α-crystals of poly (l-lactic acid) (PLLA), more precisely, of aggregates of isotropically arranged lamellae, has been estimated based on dynamic-mechanical analysis of sets of isotropic film samples containing largely different though well-defined amounts of crystals. Evaluation of the modulus of elasticity of these film samples yielded the dependence of Young's modulus as a function of the enthalpy-based crystallinity, increasing with the crystal fraction in the assessed range, from zero to about 75% crystallinity. Extrapolation towards 100% crystallinity suggests values of Young's modulus of around 3.7 and 4.6 GPa for isotropic aggregates of α'- and α-crystals, respectively, being only slightly higher than the modulus of the unaged glassy amorphous phase of 3.0 GPa. Noting the inherent anisotropy of the crystal modulus, suggested in the literature, the average modulus determined in this work seems to be controlled by weaker interchain secondary bonding but not the modulus in chain direction. Great effort has been undertaken to minimize errors by keeping the lamellar thickness in samples of different crystallinity constant, and by providing evidence for independence of the moduli on the spherulitic superstructure.

Kinetics of inherent processes counteracting crystallization in supercooled monatomic liquid

Crystallization of supercooled liquids is mainly determined by two competing processes associated with the transition of particles (atoms) from liquid phase to crystalline one and, vice versa, with the return of particles from crystalline phase to liquid one. The quantitative characteristics of these processes are the so-called attachment rateg+and the detachment rateg-, which determine how particles change their belonging from one phase to another. In the present study, acorrespondence rulebetween the ratesg+andg-as functions of the sizeNof growing crystalline nuclei is defined for the first time. In contrast to the well-known detailed balance condition, which relatesg+(N)andg-(N)atN=nc(wheren_cis the critical nucleus size) and is satisfied only at the beginning of the nucleation regime, the foundcorrespondence ruleis fulfilled at all the main stages of crystallization kinetics (crystal nucleation, growth and coalescence). On the example of crystallizing supercooled Lennard-Jones liquid, the rateg-was calculated for the first time at different supercooling levels and for the wide range of nucleus sizesN∈[nc;40nc]. It was found that for the whole range of nucleus sizes, the detachment rateg-is only≈2% less than the attachment rateg+. This is direct evidence that the role of the processes that counteract crystallization remains significant at all the stages of crystallization. Based on the obtained results, a kinetic equation was formulated for the time-dependent distribution function of the nucleus sizes, that is an alternative to the well-known kinetic Becker-Döring-Zeldovich-Frenkel equation.

Bulk enthalpy of melting of poly (l-lactic acid) (PLLA) determined by fast scanning chip calorimetry

The bulk enthalpy of melting of α-crystals of poly (l-lactic acid) (PLLA) has been evaluated by fast scanning chip calorimetry (FSC), by analysis of the correlation between the measured enthalpy of melting of sets of samples of different crystallinity and the corresponding heat capacity at 90°C, that is at a temperature higher than the glass transition temperature of the bulk amorphous phase and lower than the melting temperature. Extrapolation of this relationship for crystals formed at 140°C towards the heat capacity of fully solid PLLA yields a value of about 104.5±6 J/g when melting occurs at 180-200°C. The analysis is based on the presence of a two-phase structure, that is, absence of a vitrified rigid amorphous fraction (RAF) at the temperature of analysis of the solid fraction of the material (90°C). Formation and vitrification of an RAF was suppressed by avoiding both continuation of primary crystallization and secondary crystallization during cooling the system from the crystallization temperature of 140°C to 90°C, making use of the high cooling capacity of FSC. Small-angle X-ray scattering (SAXS) confirmed distinct thickening of initially grown lamellae which only is possible if these lamellae are not surrounded by a glassy RAF. Linear crystallinity values obtained by SAXS and calorimetrically determined enthalpy-based crystallinities agree close to each other. This article is protected by copyright. All rights reserved.

A double-population chaotic self-adaptive evolutionary dynamics model for the prediction of supercritical carbon dioxide solubility in polymers

Solubility of gas in polymers is an important physico-chemical property of foam materials and widely used in the preparation and modification of new materials. Under the conditions of high temperature and high pressure, the dissolution process is a nonlinear, non-equilibrium and dynamic process, so it is difficult to establish an accurate solubility calculation model. Inspired by particle dynamics and evolutionary algorithm, this paper proposes a hybrid model based on chaotic self-adaptive particle dynamics evolutionary algorithm (CSA-PD-EA), which can use the iterative process of particles in evolutionary algorithms at the dynamic level to simulate the mutual diffusion process of molecules during dissolution. The predicted solubility of supercritical CO₂ in poly(d,l-lactide-co-glycolide), poly(l-lactide) and poly(vinyl acetate) indicated that the comprehensive prediction performance of the CSA-PD-EA model was high. The calculation error and correlation coefficient were, respectively, 0.3842 and 0.9187. The CSA-PD-EA model showed prominent advantages in accuracy, efficiency and correlation over other computational models, and its calculation time was 4.144-15.012% of that of other dynamic models. The CSA-PD-EA model has wide application prospects in the computation of physical and chemical properties and can provide the basis for the theoretical calculation of multi-scale complex systems in chemistry, materials, biology and physics.

Stability of Crystal Nuclei of Poly (butylene isophthalate) Formed Near the Glass Transition Temperature

Tammann’s two-stage crystal-nuclei-development method is applied for analysis of the thermal stability of homogenously formed crystal nuclei of poly(butylene isophthalate) (PBI) as well as their possible reorganization on transferring them to the growth temperature, using fast scanning chip calorimetry. Crystal nuclei were formed at 50 °C, that is, at a temperature only slightly higher than the glass transition temperature, and developed to crystals within a pre-defined time at the growth temperature of 85 °C. The number of nuclei, overcritical at the growth temperature, was detected as a function of the transfer-conditions (maximum temperature, heating rate) by evaluation of the developed crystal fraction. For different size-distributions of crystal nuclei, as controlled by the nucleation time, there is detected distinct reduction of the nuclei number on heating to maximum temperatures higher than about 90 to 110 °C, with the latter value holding for longer nucleation time. Longer nucleation allows for both increasing the absolute nuclei number and generation of an increased fraction of larger nuclei. Heating at 1000 K/s to 140–150 °C causes “melting” of even the most stable nuclei. While direct transfer of crystal nuclei from the nucleation temperature (50 °C) to the growth temperature (85 °C) reveals negligible effect of the transfer-heating rate, in-between heating to higher temperatures is connected with distinct nuclei-reorganization above 85 °C on heating slower than 1000–10.000 K/s. The performed study not only provides specific valuable information about the thermal characteristics of crystal nuclei of PBI but also highlights the importance of proper design of Tammann’s nuclei development experiment for analysis of nuclei numbers. With the evaluation of critical rates of temperature-change for suppression of non-isothermal formation of both nuclei and crystals, the kinetics of crystallization of the slow crystallizing PBI is further quantified.