Crystallization Kinetics Of Polymers Research Articles

Shape compensation for carbon fiber thermoplastic composite stamp forming

Shape compensation of tooling for stamp forming of carbon fiber thermoplastic laminated composites is described as a process wherein the virtual twin, FORM3D is utilized to determine the tooling geometry required to produce the desired part geometry in a single step process. FORM3D is a physics-based virtual twin that incorporates anisotropic phenomena including transient heat transfer, thermoviscoelasticity, thermoelastic and crystallization shrinkage, and polymer crystallization and melting kinetics. This procedure for determining the compensated tool geometry is illustrated for a composite laminate constructed of AS4/PEKK prepreg, supplied by Solvay Thermoplastic Composites, for a quasi-isotropic layup of variable thickness and double curvature: major radius of curvature of 1556.7 mm and minor radius of curvature of 75.7 mm. The resulting, compensated shape was shown to agree with the desired geometry within ±0.25 mm.

Application of the NPK Method in the Crystallization Kinetics of High-Density Polyethylene

The Non-Parametric Kinetics (NPK) method, developed in 1998, by Serra, R., Sempere, J. and Nomen, R. has been used by them and other research groups to analyze the thermal behavior of a physical or chemical transformation and thermal stability. However, it was until 2021 that the method was applied for the first time in a cooling process for the determination of the crystallization kinetics of polypropylene, obtaining satisfactory results.
 The advantage of the NPK method is that it does not assume any model for the temperature function, nor for the conversion function to describe the crystallization kinetics. Through a mathematical process, the method provides two vectors: the vector u, which contains the information about the kinetic model, and the vector v, which contains the information about the temperature function.
 The aim of this work is to verify that the NPK method is applicable to the crystallization of high-density polyethylene by comparing the results with the most commonly used models to describe the crystallization kinetics of polymers. The fits obtained were very good and the vector u and v allow us to reproduce the original curves from DSC.

Review on Crystallization Strategies for Polymer Single Crystals

Polymer physics has evolved significantly over the past century, transitioning from the early recognition of the chain structure of polymers to a mature field integrating principles from statistical mechanics, thermodynamics, and condensed matter physics. As an important part of polymer physics, polymer single crystals are crucial for understanding molecular structures and behaviors, enhancing material properties, and enabling precise functionalization. They offer insights into polymer crystallization kinetics, serve as templates for nanofabrication, and have applications in electronics, sensors, and biomedical fields. However, due to the complexity of molecular chain movement, the formation of polymer single crystals is still very difficult. Over the decades, numerous researchers have dedicated themselves to unraveling the mysteries of polymer single crystals, yielding substantial findings. This paper focus on the historical evolution and advancements in polymer single crystal research, aiming to offer valuable insights and assistance to fellow researchers in this field.

Tuning the crystallization and thermal properties of polyesters by introducing functional groups that induce intermolecular interactions.

The performance of sustainable polymers can be modified and enhanced by incorporating functional groups in the backbone of the polymer chain that increases intermolecular interactions, thus impacting the thermal properties of the material. However, in-depth studies on the role of intermolecular interactions on the crystallization of these polymers are still needed. This work aims to ascertain whether incorporating functional groups able to induce intermolecular interactions can be used as a suitable systematic strategy to modify the polymer thermal properties and crystallization kinetics. Thus, amide and additional ester groups have been incorporated into aliphatic polyesters (PEs). The impact of intermolecular interactions on the melting and crystallization behavior, crystallization kinetics, and crystalline structure has been determined. Functional groups that form strong intermolecular interactions increase both melting and crystallization temperatures but retard the crystallization kinetics. Selecting appropriate functional groups allows tuning the crystallinity degree, which can potentially improve the mechanical properties and degradability in semicrystalline materials. The results demonstrate that it is possible to tune the thermal transitions and the crystallization kinetics of PEs independently by varying their chemical structure.

Roles of specific hydrogen-bonding interactions in the crystallization kinetics of polymers

Polyamides hold specific hydrogen-bonding interactions as the hierarchical thermodynamic driving forces for crystallization. Their roles in crystallization kinetics are worthy of further investigation. We performed dynamic Monte Carlo simulations to compare crystallization kinetics among 16-mer melts holding hydrogen-bonding interactions with variable strengths specifically assigned to 2, 4 and 8 monomers on the chain, respectively. The results demonstrate higher densities and strengths of hydrogen-bonding interactions generally accelerating the cooling and isothermal crystallization as well as the lateral growth of lamellar crystals, consistent with the experimental observations of polyamide crystallization. Too strong hydrogen-bonding interactions will slow down polymer diffusion and thus bring retardation to crystallization kinetics. Furthermore, hydrogen-bonding interactions at the central 8–9 monomers make higher crystal growth rates than those at the evenly distributed 5–12 monomers, demonstrating the dominant roles of specific interactions in the hierarchical parallel packing of polymer chains at the lateral growth front of lamellar crystals.

Molecular Weight Distribution Shape Dependence of the Crystallization Kinetics of Semicrystalline Polymers Based on Linear Unimodal and Bimodal Polyethylenes

The manipulation of the crystallization kinetics and crystallinity of polymers without altering their chemical composition, chain structure, or average molecular weight is challenging, while little attention is paid to the role of molecular weight distribution (MWD) shape. In this work, a series of well-defined linear unimodal and bimodal polyethylenes (PEs) with molecular weights ranging from 300 k to 1200 k g/mol were synthesized to serve as a model system to study the impact of bimodal MWD shape on the crystallization kinetics of semicrystalline polymers in comparison with unimodal MWD shape at the same weight-average molecular weight (Mw). It is shown that PEs with a bimodal shape exhibit a faster nucleation rate and crystallization rate with a smaller lamellar width at low isothermal temperatures. A higher crystallization enthalpy of bimodal PEs is shown in non-isothermal experiments. The mechanism behind this is elucidated, which suggests that MWD shapes mainly affect the small-scale nucleation process without altering the large-scale growth process. This first systematic comparative study on the crystallization kinetics of linear unimodal and bimodal PEs gives insight into tailoring the crystallization behavior of semicrystalline polymers from an MWD shape perspective.

Evaluation of relative content and crystallization behavior of homogeneous crystals in poly (lactic acid) by terahertz spectroscopy

Poly (lactic acid) (PLA) is a typical polymer with homogeneous polymorphism. Its different crystal forms have their own crystallization paths, which endow it with special properties. Therefore, it is crucial to study the structure and crystallization behavior of PLA to better understand its properties. Here, we investigate PLA films obtained under different crystallization conditions by terahertz (THz) spectroscopy. The α′, α and their mixed crystal forms of PLA exhibit completely different spectral feature. Based on the frequency of THz characteristic peaks, we further determine the relative contents of α′ form and α form in PLA with mixed crystals, the validity of which is verified by comparing X-ray diffraction (XRD). Furthermore, the change of absorption intensity of different PLA films is significantly different with crystallization time, mainly manifested as the change rate of glassy PLA crystallized at 80 °C is faster than that of molten PLA. We believe that this is because the crystallization of the α form of PLA at 80 °C is at a disadvantage, which reduces the speed of conformational adjustment. The results show that THz spectroscopy can not only characterize the crystal changes of polymers, but can also be an effective method to study the kinetics of polymer crystallization.

Comments on isothermal crystallization kinetics of polymers: Polypropylene at high supercooling

A robust procedure for isothermal kinetic evaluation of Differential Scanning Calorimetry (DSC) measurements of polymers using the Kolmogorov-Johnson-Mehl-Avrami (KJMA) equation is proposed. This procedure takes into account the experimental uncertainties for short (initial deflection) and long (secondary crystallization) measurement times. This procedure is applied to the isothermal crystallization of various commercially available isotactic polypropylenes (iPP) in the temperature range between 10°C and 120°C. Further measurements are performed on unfilled iPP and iPP highly filled with calcium carbonate. The measurements were performed using Fast Differential Scanning Calorimetry (FDSC).Evaluation of the crystallization kinetics indicates homogeneous nucleation in the temperature range of mesophase formation below 60°C. With decreasing temperature, the crystallization is more affected by diffusion control and/or termination of growth at an early crystallization stageDuring α-phase formation (above 60°C), crystallization is heterogeneously nucleated. Depending on the sample, growth occurs at a constant rate or is diffusion controlled.Polypropylene highly filled with calcium carbonate shows an additional α-phase crystallization process. The KJMA evaluation indicates that this process is homogeneously nucleated.

Study on in situ visualization crystallization behavior and secondary nucleation model of polypropylene under supercritical N2

The crystal morphology and crystallization kinetics of polymers under supercritical N2 have an important impact on the polymers’ melt strength as well as the microstructure and properties of microcellular plastic parts. Herein, the self-made in-situ high pressure microscopy system was employed to study the spherulite morphology and crystal growth behavior in high pressure N2. It was found that PP spherulites were significantly refined under supercritical N2. As the N2 pressure was augmented to 20.69 MPa at 130 °C, the spherulite size was reduced to 48.41 μm, refined by 35.84%, indicating that the crystallization behavior of PP can be controlled by pressure regulation. The new growth pattern for spherulite under supercritical N2 was discovered by atomic force microscope (AFM) for the first time. In addition, the spherulite growth rate exhibited a phenomenon that was inhibited first and then promoted. To explore the re-promoting effect of supercritical N2, a secondary nucleation model that considered the effect of additional free energy induced by high-pressure N2, was established. The re-promotion of spherulite growth rate at elevated N2 pressure is attributed to the augment in translational free energy induced by N2, i.e., entropy-driven crystallization. The calculated results of secondary nucleation model achieved a good agreement with the experimental results, and the variation trend of PP spherulite growth rate could be well predicted under supercritical N2.

Kinetics of crystallization mechanisms in poly(3-hexylthiophene) and poly(9,9-dihexylfluorene-alt-2,5-didodecyloxybenzene) conjugated polymers

Conjugated polymers are perceived as promising materials for emerging applications in energy and environment. Kinetics of crystallization processes in conjugated polymers may not only model the processes but also helps in revealing their mechanisms. This paper gives an account of the kinetic investigation on crystallization processes in two known conjugated polymers, poly(3-hexylthiophene) (P3HT) and poly(9,9-dihexylfluorene-alt-2,5-didodecyloxybenzene) (PF6OC12) under non-isothermal conditions by employing the advanced polymer crystallization kinetics approach. Kinetic study suggests that both P3HT and PF6OC12 crystallize by following fairly single-step nucleation and diffusion phenomena. In addition, the diffusion activation energies of P3HT and PF6OC12 obtained are compared and conform to the universal activation energy value of the segmental jump during the diffusion processes in polymers. Nevertheless, while PF6OC12 pursues two-dimensional (2D) growth of spherulites, P3HT on the other hand, follows a rather complex crystallization mechanism. It is noteworthy that the glass transition temperatures of both the conjugated polymers are more or less the same. The obtained kinetic parameters are interpreted in terms of their plausible physical meanings. A thermodynamic expression to determine the transition entropy of polymer crystallization is also derived and discussed.

Determination of polymer crystallization kinetics with the NPK method

Determination of polymer crystallization kinetics with the NPK method

Kinetics of Polymer Crystallization with Aggregating Small Crystallites.

The isothermal crystallization near the glass transition temperature from the melt state of poly(trimethylene terephthalate) has been studied by wide-angle x-ray diffraction (WAXD), small-angle x-ray scattering (SAXS), and optical microscopy. The SAXS and WAXD results show the crystallization mechanism in which the crystalline nodules cover the entire sample with the formation of aggregation regions. The analysis of the SAXS results using Kolmogorov-Johnson-Mehl-Avrami theory indicates that the formation kinetics of the aggregation regions is of three-dimensional homogeneous nucleation type. The analysis of the SAXS profiles using Sekimoto's theory provides the growth velocity and the nucleation rate of the aggregation region. The temperature dependence of the growth velocity of the aggregation region is a natural extrapolation of that of spherulite to the high supercooling region. The temperature dependence of the nucleation rate of the aggregation region is also represented by the parameters of the spherulitic growth rate. The result of the growth velocities of the aggregation region and the spherulite suggests the existence of precursors at the front of the crystal growth.

Modeling the crystallization kinetics of polymers displaying high levels of secondary crystallization

The isothermal crystallization of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) was evaluated using a range of models, namely, Avrami, simplified Hillier, Tobin, Malkin, Urbanovici–Segal, Velisaris–Seferis, and Hay. Two methods of model evaluation were used: determination of the parameters through traditional double log plots and curve fitting via nonlinear, multivariable regression. Visual inspection of the cumulative crystallization curves, calculation of the R2 value and standard error of the regression, and evaluation of the returned parameters were used to assess which model best describes the experimental data. The Hay model was found to generate the best fit, closely followed by the Velisaris–Seferis parallel model, suggesting that primary and secondary crystallization occur concurrently. The Avrami, Malkin, and Tobin models were found to perform well when the data is restricted to the region where primary crystallization dominates; however, they could not be used to successfully model the entire crystallization process. This work highlights the importance of selecting the most appropriate model for analyzing kinetics, especially when high levels of lamellar thickening and infilling occur during crystallization.

Tailored growth of graphene oxide liquid crystals with controlled polymer crystallization in GO-polymer composites.

Graphene Oxides (GOs) have been frequently employed as fillers in polymer-based applications. While GO is known to nucleate polymer crystallization in GO-polymer composites reinforcing the mechanical properties of semicrystalline polymers, its counter effect on how polymer crystallization can alter the microstructure of GO has rarely been systematically studied yet. In this work, we study the GO nematic liquid crystal (LC) phase during polymer crystallization focusing on their hierarchical structures by employing in situ small/wide-angle X-ray scattering/diffraction (SAXS/WAXD) techniques. We found that GO LC and polymer crystals co-exist in the GO/polymer complex, where the overall liquid crystallinity is influenced by polymer crystallization. While polymer crystallizes in bulk or at the interface depending on the cooling rate, the interfacial crystallization of poly(ethylene glycol) (PEG) on GO improves both GO alignment and orientation of PEG crystal. This work provides an opportunity to develop a hierarchical structure of GO-based crystalline polymer nanocomposites, whose directionality can be controlled by polymer crystallization under proper cooling rates.

Polymer Crystallization under Confinement by Well-Dispersed Nanoparticles

We explore the role of nanoparticle (NP) size and loading on the kinetics of polymer crystallization, in particular, the crystal growth rate (G), under conditions where the NPs and polymers are uniformly mixed. While there are significant differences with variations in NP size and loading, the measured G data fall into an apparently universal curve when we consider them on the basis of confinement. In particular, we find that the ratio of polymer volume, VPEO, to the NP surface area, SANP, is the most appropriate confinement metric in the 10–100 nm range, which includes typical lamellar spacings in semicrystalline polymers (5–50 nm). Similarly, we find that the fraction of polymer crystallized also decreases with increasing confinement. We thus posit that the formation of a bound layer at the attractive NP interface is the key driver in these situations. Because the volume fraction of the bound polymer layer of thickness δ is (δ × SANP)/VPEO, these results support the notion that, in addition to confining the polymer and reducing its equilibrium melting point, the NPs serve to “remove” a certain fraction of the PEO from the crystallization process by binding “irreversibly” to them. Additionally, when combined with the fact that the formation of a bound layer slows down NP dynamics, we emphasize that the bound polymer critically affects crystallization kinetics from both a structural and a dynamical perspective. These results strongly parallel our earlier work on the glass transition temperature of amorphous polymers intimately mixed with NPs where material properties are critically determined by the formation of a bound layer.

Effect of multi-step annealing above the glass transition temperature on the crystallization and melting kinetics of semicrystalline polymers

Fast scanning calorimetry (FSC) measurements were carried out for multi-step, isothermal, crystallized poly (butylene terephthalate) to quantify the effect of single-step to triple-step annealing above Tg (40 °C interval below the previous annealing temperature) on the crystallization/melting kinetics. In the case of double-step annealing, two endothermic peaks were observed on the FSC curves due to the melting of the crystal formed during the 1st step (base crystal; BC) and 2nd step (thermal history crystal; THC). The crystallization rate of the THC decreased due to the spatial restriction of the pre-existing BC. The melting kinetics of the THC were not affected by the time of 1st step crystallization. If the sample was re-heated to the 1st step temperature (Tc1) after multiple annealing, the thermal history of the previous annealing was completely erased. Moreover, in the re-annealing process at Tc1, secondary crystallization showed the same behavior as that expected from the result of single-step annealing.

Crystallization Kinetics of Semi-Crystalline Polymer Studied with Fast Scanning Calorimetry

Crystallization Kinetics of Semi-Crystalline Polymer Studied with Fast Scanning Calorimetry

A Note for Probabilistic Model of Polymer Crystallization in Temperature Gradients

A polymer crystallization kinetics model is the most important way to characterize the crystallization rate of polymers. Because polymers are poor heat conductors, the cooling of thick-walled shapes results in temperature gradients. Piorkowska (Piorkowska, E. J. Appl. Polym. Sci., 2002, 86: 1351–1362.) derived the probabilistic analytical model of polymer crystallization in temperature gradients based on the Avrami equation. However, there are some misunderstandings when using this model. Here, isotactic polypropylene (iPP) is chosen as a model polymer and its crystallization is studied in a temperature gradient field. Based on the results of the Monte Carlo method, the probabilistic model methodology is discussed. The results show that when the product has a large temperature gradient and a large temperature difference, the probabilistic model cannot be used directly; instead, it is necessary to use the average probabilistic model. This means that the sample should be divided into several smaller parts and the probabilistic model used separately for each small part. The values are then averaged to obtain the mean conversion degree of the melt into spherulites for the whole product. The effects of the division number are also discussed. The goal of the present paper is to better understand the polymer crystallization kinetics model in terms of temperature gradients.

Effect of heat transfer coefficient, draw ratio, and die exit temperature on the production of flat polypropylene membranes

In this work, a stable numerical scheme has been developed for the 1.5-dimensional film casting model of Silagy et al. [Polym. Eng. Sci. 36, “Study of the stability of the film casting process,” 2614–2625 (1996)] utilizing the viscoelastic modified Leonov model as the constitutive equation and energy equation coupled with the crystallization kinetics of semicrystalline polymers taking into account actual temperature as well as cooling rate. The model has been successfully validated on the experimental data for linear isotactic polypropylene taken from the open literature. Drawing distance, draw ratio, heat transfer coefficient, and die exit melt temperature were systematically varied in the utilized model in order to understand the role of process conditions in the neck-in phenomenon (unwanted film width shrinkage during stretching in the post die area) and crystalline phase development during flat film production. It is believed that the utilized numerical model together with the suggested stable numerical scheme as well as obtained research results can help to understand a processing window for the production of flat porous membranes from linear polypropylene considerably.

Modeling of oriented crystallization kinetics of polymers in the entire range of uniaxial molecular orientation

Closed-form analytical formulas describing kinetics of oriented crystallization under constant or variable amorphous orientation and isothermal or non-isothermal conditions are derived, valid in the whole range of orientation. Master relation for the deformation free energy vs. orientation factor, or tensile stress, is derived accounting for non-linear effects of finite chain extensibility. The Avrami-Evans model is expanded to account for the effects of orientation in thermodynamic driving force of nucleation and crystal growth.Involvement of predetermined and spontaneous nucleation varies strongly with the orientation and leads to domination of spontaneous nucleation at high orientations. Crystallization half-time involving separated or coexisting predetermined and spontaneous nucleation is discussed.A formula predicting equal contribution of both nucleation modes vs. orientation factor and temperature is derived and ranges of domination of the modes are discussed. Example computations illustrate the model predictions for an example polymer (PLLA) and are in good agreement with the experimental results.