Relaxation and crystal nucleation in polymer glasses

Crystallization of Poly(ethylene terephthalate): A Review

Poly(ethylene terephthalate) (PET) is a thermoplastic polyester with excellent thermal and mechanical properties, widely used in a variety of industrial fields. It is a semicrystalline polymer, and most of the industrial success of PET derives from its easily tunable crystallization kinetics, which allow users to produce the polymer with a high crystal fraction for applications that demand high thermomechanical resistance and barrier properties, or a fully amorphous polymer when high transparency of the product is needed. The main properties of the polymer are presented and discussed in this contribution, together with the literature data on the crystal structure and morphology of PET. This is followed by an in-depth analysis of its crystallization kinetics, including both primary crystal nucleation and crystal growth, as well as secondary crystallization. The effect of molar mass, catalyst residues, chain composition, and thermo-mechanical treatments on the crystallization kinetics, structure, and morphology of PET are also reviewed in this contribution.

Rigid Nuclei and Flexible Nuclei: Appearance and Disappearance of Nuclei in Indomethacin Glass Revealed by a Long-Term Annealing Study

In this study, nucleation/crystallization behaviors of indomethacin glass are discussed with emphasis on the fate of nuclei, which is explained using a notion of "rigid" and "flexible" nuclei. The observation was made mainly by thermal analysis of indomethacin glass after long-term annealing at various temperatures. Formation of nuclei was evaluated by observing cold crystallization behaviors of the annealed glasses, as they should be dominated by the "nuclei form" produced in the glass. Nuclei of forms α and γ, which have opposite stability trends, were found to appear over a wide temperature range. The nuclei of form α were stable even in the presence of other crystal forms, whereas those of form γ were likely to be easily integrated into other crystals during their growth, which was explained by a notion of rigid and flexible nuclei. Moreover, unconventionally fast crystallization in the glass-transition region and the finding of a new crystal form are also reported.

Crystal nucleation in a glass during relaxation well below Tg

Until quite recently, in almost all papers on crystal nucleation in glass-forming substances, it was assumed that nucleation proceeds in a completely relaxed supercooled liquid and, hence, at constant values of the critical parameters determining the nucleation rate for any given set of temperature, pressure, and composition. Here, we analyze the validity of this hypothesis for a model system by studying nucleation in a lithium silicate glass treated for very long times (up to 250 days) in deeply supercooled states, reaching 60 K below the laboratory glass transition temperature, T_g. At all temperatures in the considered range, T < T_g, we observed an enormous difference between the experimental number of nucleated crystals, N(t), and its theoretically expected value computed by assuming the metastable state of the relaxing glass has been reached. Analyzing the origin of this discrepancy, we confirmed that the key parameters determining the nucleation rates change with time as a result of the glass relaxation process. Finally, we demonstrate that, for temperatures below 683 K, this particular glass almost fully crystallizes prior to reaching the ultimate steady-state nucleation regime (e.g., at 663 K, it would take 176 years for the glass to reach 99% crystallization, while 2600 years would be needed for complete relaxation). This comprehensive study proves that structural relaxation strongly affects crystal nucleation in deeply supercooled states at temperatures well below T_g; hence, this phenomenon has to be accounted for in any crystal nucleation model.

Physical Aging Behavior of the Side Chain of a Conjugated Polymer PBTTT

This paper provides a viewpoint of the technology of the fast-scanning calorimetry with the relaxation behavior of disordered side chains of poly[2,5-bis(3-dodecylthiophen-2-yl)thieno[3,2-b]thiophene] (PBTTT-C12) around the glass transition temperature of the side chains (T_g,γ). PBTTT is an ideal model of the high-performance copolymer of poly(alkylthiophenes) with side chains. The γ₁ relaxation process of the disordered side chains of PBTTT was detected as a small endothermic peak that emerges before the γ₂ relaxation process. It shows an increase with increasing temperature as it approaches the glass transition temperature of the disordered side chains of PBTTT. The ductile-brittle transition of PBTTT in low temperatures originating from the thermal relaxation process is probed and illustrated by physical aging experiments. The signature is shown that the relaxation process of the disordered side chain of PBTTT at low temperatures varies from Arrhenius temperature dependence to super Arrhenius temperature dependence at high temperatures. These observations could have significant consequences for the stability of devices based on conjugated polymers, especially those utilized for stretchable or flexible applications, or those demanding mechanical robustness during tensile fabrication or use in a low-temperature environment.

Effects of Glass Transition and Structural Relaxation on Crystal Nucleation: Theoretical Description and Model Analysis

In the application of classical nucleation theory (CNT) and all other theoretical models of crystallization of liquids and glasses it is always assumed that nucleation proceeds only after the supercooled liquid or the glass have completed structural relaxation processes towards the metastable equilibrium state. Only employing such an assumption, the thermodynamic driving force of crystallization and the surface tension can be determined in the way it is commonly performed. The present paper is devoted to the theoretical treatment of a different situation, when nucleation proceeds concomitantly with structural relaxation. To treat the nucleation kinetics theoretically for such cases, we need adequate expressions for the thermodynamic driving force and the surface tension accounting for the contributions caused by the deviation of the supercooled liquid from metastable equilibrium. In the present paper, such relations are derived. They are expressed via deviations of structural order parameters from their equilibrium values. Relaxation processes result in changes of the structural order parameters with time. As a consequence, the thermodynamic driving force and surface tension, and basic characteristics of crystal nucleation, such as the work of critical cluster formation and the steady-state nucleation rate, also become time-dependent. We show that this scenario may be realized in the vicinity and below the glass transition temperature, and it may occur only if diffusion (controlling nucleation) and viscosity (controlling the alpha-relaxation process) in the liquid decouple. Analytical estimates are illustrated and confirmed by numerical computations for a model system. The theory is successfully applied to the interpretation of experimental data. Several further consequences of this newly developed theoretical treatment are discussed in detail. In line with our previous investigations, we reconfirm that only when the characteristic times of structural relaxation are of similar order of magnitude or longer than the characteristic times of crystal nucleation, elastic stresses evolving in nucleation may significantly affect this process. Advancing the methods of theoretical analysis of elastic stress effects on nucleation, for the first time expressions are derived for the dependence of the surface tension of critical crystallites on elastic stresses. As the result, a comprehensive theoretical description of crystal nucleation accounting appropriately for the effects of deviations of the liquid from the metastable states and of relaxation on crystal nucleation of glass-forming liquids, including the effect of simultaneous stress evolution and stress relaxation on nucleation, is now available. As one of its applications, this theoretical treatment provides a new tool for the explanation of the low-temperature anomaly in nucleation in silicate and polymer glasses (the so-called "breakdown" of CNT at temperatures below the temperature of the maximum steady-state nucleation rate). We show that this anomaly results from much more complex features of crystal nucleation in glasses caused by deviations from metastable equilibrium (resulting in changes of the thermodynamic driving force, the surface tension, and the work of critical cluster formation, in the necessity to account of structural relaxation and stress effects) than assumed so far. If these effects are properly accounted for, then CNT appropriately describes both the initial, the intermediate, and the final states of crystal nucleation.

Competition between Structural Relaxation and Crystallization in the Glass Transition Range of Random Copolymers

Structural relaxation in polymers occurs at temperatures in the glass transition range and below. At these temperatures, crystallization is controlled by diffusion and nucleation. A sequential occurrence of structural relaxation, nucleation, and crystallization was observed for several homopolymers during annealing in the range of the glass transition. It is known from the literature that all of these processes are strongly influenced by geometrical confinements. The focus of our work is copolymers, in which the confinements are caused by the random sequence of monomer units in the polymer chain. We characterize the influence of these confinements on structure formation and relaxation in the vicinity of the glass transition. The measurements were performed with a hydrogenated nitrile-butadiene copolymer (HNBR). The kinetics of the structural relaxation and the crystallization was measured using fast differential scanning calorimetry (FDSC). This technique was selected because of the high sensitivity, the fast cooling rates, and the high time resolution. Crystallization in HNBR causes a segregation of non-crystallizable segments in the macromolecule. This yields a reduction in mobility in the vicinity of the formed crystals and as a consequence an increased amount of so-called "rigid amorphous fraction" (RAF). The RAF can be interpreted as self-assembled confinements, which limit and control the crystallization. An analysis of the crystallization and the relaxation shows that the kinetic of both is identical. This means that the Kohlrausch exponent of relaxation and the Avrami exponent of crystallization are identical. Therefore, the crystallization is not controlled by nucleation but by diffusion and is terminated by the formation of RAF.

Enthalpy Relaxation, Crystal Nucleation and Crystal Growth of Biobased Poly(butylene Isophthalate)

The crystallization behavior of fully biobased poly(butylene isophthalate) (PBI) has been investigated using calorimetric and microscopic techniques. PBI is an extremely slow crystallizing polymer that leads, after melt-crystallization, to the formation of lamellar crystals and rather large spherulites, due to the low nuclei density. Based upon quantitative analysis of the crystal-nucleation behavior at low temperatures near the glass transition, using Tammann's two-stage nuclei development method, a nucleation pathway for an acceleration of the crystallization process and for tailoring the semicrystalline morphology is provided. Low-temperature annealing close to the glass transition temperature (T_g) leads to the formation of crystal nuclei, which grow to crystals at higher temperatures, and yield a much finer spherulitic superstructure, as obtained after direct melt-crystallization. Similarly to other slowly crystallizing polymers like poly(ethylene terephthalate) or poly(l-lactic acid), low-temperature crystal-nuclei formation at a timescale of hours/days is still too slow to allow non-spherulitic crystallization. The interplay between glass relaxation and crystal nucleation at temperatures slightly below T_g is discussed.

Enthalpy Relaxation of Polyamide 11 of Different Morphology Far Below the Glass Transition Temperature

Polyamide 11 (PA 11) samples of different supermolecular structure, including the crystal-free glass and semi-crystalline PA 11 of largely different semi-crystalline morphology, were prepared by fast scanning chip calorimetry (FSC). These samples were then annealed at different temperatures well below the glass transition temperature T_g. The main purpose of the low-temperature annealing experiments was the calorimetric detection of mobility of chain segments at temperatures as low as −40 °C (≈T_g − 80 K) where still excellent impact resistance is predicted. It was found that annealing PA 11 at such low temperature, regardless the thermal history and supermolecular structure including crystallinity as well as crystal shape and size, permits distinct enthalpy relaxation at rather short time scale with the structural changes reverting on subsequent heating as detected with pronounced sub-T_g-enthalpy-recovery peaks. The main glass transition, associated to large-amplitude segmental mobility, as well as relaxations at temperatures only slightly below T_g are even more distinctly sensitive to the crystal morphology. In contrast to spherulitically grown lamellar crystals, presence of high-specific-surface area nanometer-sized ordered domains causes a shift of the glass transition temperature of the amorphous phase to higher temperature, proving stronger coupling of ordered and amorphous phases than in case of lamellae. In addition, the increased coupling of the crystalline and amorphous phases slows down the cooperative rearrangements on annealing the glass slightly below T_g. The performed study contributes to further understanding of the spectrum of structural relaxations in PA 11 including the effect of presence of crystals. Enthalpy relaxation and consequently the reduction of entropy at temperatures slightly below T_g strongly depends on the semi-crystalline morphology, while an only minor effect is seen on low-temperature annealing at T_g − 80 K, possibly indicating different molecular mechanisms for the processes occurring in both temperature ranges. The low-temperature process even seems proceeding in the crystalline fraction of the material.

Physical Ageing of Polystyrene: Does Tacticity Play a Role?

The ageing kinetics of amorphous atactic (a-PS), isotactic (i-PS), and syndiotactic (s-PS) polystyrene were studied by means of flash-differential scanning calorimetry. The specimens were aged for up to 2 h at six different ageing temperatures: the optimum ageing temperature, that is, the temperature at which the enthalpy overshoot at the glass transition is maximal for the given elapsed time, and five ageing temperatures ranging from 20 to 80 K below the optimum ageing temperature. A logarithmic increase of the enthalpy overshoot with ageing time is observed for specimens at their optimum ageing temperatures. For temperatures significantly lower than the optimum, there is a range where the enthalpy overshoot is constant, but for higher temperatures (still below the optimum), a logarithmic increase is also observed. Moreover, the ageing kinetics appear to depend on tacticity, with s-PS and i-PS exhibiting the slowest and fastest ageing kinetics, respectively, and a-PS exhibiting ageing kinetics between these two extremes.

Reply to "Comment on 'Glass Transition, Crystallization of Glass-Forming Melts, and Entropy"' by Zanotto and Mauro

A response is given to a comment of Zanotto and Mauro on our paper published in Entropy 20, 103 (2018). Our arguments presented in this paper are widely ignored by them, and no new considerations are outlined in the comment, which would require a revision of our conclusions. For this reason, we restrict ourselves here to a brief response, supplementing it by some additional arguments in favor of our point of view not included in our above-cited paper.

Nanometer scale thermal response of polymers to fast thermal perturbations

Nanometer scale thermal response of polymers to fast thermal perturbations is described by linear integro-differential equations with dynamic heat capacity. The exact analytical solution for the non-equilibrium thermal response of polymers in plane and spherical geometry is obtained in the absence of numerical (finite element) calculations. The solution is different from the iterative method presented in a previous publication. The solution provides analytical relationships for fast thermal response of polymers even at the limit t → 0, when the application of the iterative process is very problematic. However, both methods give the same result. It was found that even fast (ca. 1 ns) components of dynamic heat capacity greatly enhance the thermal response to local thermal perturbations. Non-equilibrium and non-linear thermal response of typical polymers under pulse heating with relaxation parameters corresponding to polystyrene and poly(methyl methacrylate) is determined. The obtained results can be used to analyze the heat transfer process at the early stages of crystallization with fast formation of nanometer scale crystals.