Crystallization Of Polymer Melts Research Articles

Mesoscale simulations of spherulite growth during isothermal crystallization of polymer melts via an enhanced 3D phase-field model

A finite difference-based 3D phase-field model is developed to investigate the spherulite growth at the mesoscopic scale during the isothermal crystallization of polyamide (PA) 12. The model introduces a phase-field variable to distinguish the crystalline and amorphous phases of polymers. The phase-field evolution equation is coupled with the heat conduction equation that considers the latent heat of crystallization. The evolution equations introduce both the dimensionless diffusivity and latent heat that are dependent on the crystallization temperature. A high-order finite difference-based numerical framework is applied to the phase-field model. Both the qualitative simulation results of the phase-field model such as the crystal morphologies and the quantitative results including the radial crystal growth rate, degree of crystallinity, and lamellar thickness are validated against experiments. The simulation for single-crystal growth shows that a high crystallization temperature results in a large crystal with a slow radial growth rate. The simulation for multi-crystal growth shows that the crystals impinge on each other and finally fill the whole domain during crystallization, which further demonstrates the capability of the model in simulating the spherulite growth during isothermal crystallization of polymer melts.

A Recollection with Respect to Flow Induced Crystallization in Polymer Melt Processing

Abstract A review is given of the work in the field of flow induced crystallization in polymer melts, as has been carried out during the last twenty five years mostly in Linz. A concise discussion of some results of a recent monograph is given. In this connection polymer melt rheology provides insights into the differences of information, as provided by shear and extensional flow. These differences show up with increased degrees of deformation. One finds four important pictures in this report: An electron micrograph of the crystalline structure in a cross-section perpendicular to the previous flow direction. No branching is found of the tracks, which are lines of intersection with the plane of the cross-section. A ring-shaped sample of polypropylene is shown, which fits into a newly developed apparatus. Because of the large radius secondary flow is avoided. A picture, which was obtained already a long time ago, shows that the relaxation of flow induced structures occurs with polypropylene only at temperatures between 210 and 190°C. Below the latter temperature no relaxation of crystalline structures occurs. The sharp boundary between a highly oriented zone near the duct wall and the spherulitic structure in the interior of samples, which have been extruded through ducts of rectangular cross-section, can readily be explained.

Relaxation and Crystallization of Oriented Polymer Melts with Anisotropic Filler Networks.

The coexistence of nanofillers and shear flow can influence crystallization of polymer melts. However, the microscopic mechanism of the effect is not completely revealed yet. Thus, dynamic Monte Carlo simulations were used to study the effect of the filler networks formed by one-dimensional nanofillers on relaxation and crystallization of oriented polymer melts. The filler networks restrict the relaxation of oriented polymers and impose confinement effect on the chains inside the filler networks, resulting in higher orientation and lower conformational entropy of the inside chains compared to those of the outside chains. Thus, the confined inside chains have stronger crystallizability. During crystallization, the confined chains are nucleated on the filler surface and then form nanohybrid shish-kebab structures. Furthermore, the effect of fillers and chain orientation closely depends on some factors, such as polymer-filler interaction, filler content, and filler spacing. Our simulation results are consistent with some experimental findings. Thus, these results can provide new insights into the mechanism of crystallization of filled polymers and also guide researchers to develop new polymer nanocomposites with high performance.

Examining the role of fluctuations in the early stages of homogenous polymer crystallization with simulation and statistical learning.

We propose a relationship between the dynamics in the amorphous and crystalline domains during polymer crystallization: the fluctuations of ordering-rate about a material-specific value in the amorphous phase drive those fluctuations associated with the increase in percent crystallinity. This suggests a differential equation that satisfies the three experimentally observed time regimes for the rate of crystal growth. To test this postulated expression, we applied a suite of statistical learning tools to molecular dynamics simulations to extract the relevant phenomenology. This study shows that the proposed relationship holds in the early time regime. It illustrates the effectiveness of soft computing tools in the analysis of coarse-grained simulations in which patterns exist, but may not easily yield to strict quantitative evaluation. This ability assists us in characterizing the critical early time molecular arrangement during the primary nucleation phase of polymer melt crystallization. In addition to supporting the validity of the proposed kinetics expression, the simulations show that (i) the classical nucleation and growth mechanism is active in the early stages of ordering; (ii) the number of nuclei and their masses grow linearly during this early time regime; and (iii) a fixed inter-nuclei distance is established.

Bond disorder, frustration and polymorphism in the spontaneous crystallization of a polymer melt

The isothermal, isobaric spontaneous crystallization of a supercooled polymer melt is investigated by molecular-dynamics simulation of an ensemble of fully-flexible linear chains. Frustration is introduced via two incommensurate length scales set by the bond length and the position of the minimum of the non-bonding potential. Marked polymorphism with considerable bond disorder, distortions of both the local packing and the global monomer arrangements is observed. The analyses in terms of: i) orientational order parameters characterizing the global and the local order and ii) the angular distribution of the next-nearest neighbors of a monomer reach the conclusion that the polymorphs are arranged in distorted Bcc-like lattices.

Molecular dynamics simulations of monodisperse/bidisperse polymer melt crystallization

We use large scale coarse-grained molecular dynamics simulations to study the kinetics of polymer melt crystallization. For monodisperse polymer melts of several chain lengths under various cooling protocols, we show that short chains have a higher terminal crystallinity value compared to longer ones. They align at the early stages and then cease evolving. Long chains, however, align, fold into lamella structures and then slowly optimize their dangling ends for the remaining simulation time. We then identify the mechanism behind bidisperse blend crystallization. To this end, we introduce a new algorithm (called Individual Chain Crystallinity) that allows the calculation of the crystallinity separately for short and long chains in the blend. We find that, in general, bidispersity hinders crystallization significantly. At first the crystallinity of the long chain components exceeds that of the monodisperse melt, but subsequently falls below the corresponding monodisperse melt curve after a certain “crossover time.” The time of the crossover can be attributed to the time required for the full crystallization of the short chains. This indicates that at the early stages the short chains are helping long chains to crystallize. However, after all short chains have crystallized they start to hinder the crystallization of the long chains by obstructing their motion. Lastly, polymer crystallization upon various thermodynamic protocols is studied. Slower cooling is found to increase the crystallinity value. Upon an instantaneous deep quench and subsequent isothermal relaxation, the crystallinity grows rapidly with time at early stages and subsequently saturates. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016

Acid-insoluble lignin and holocellulose from a lignocellulosic biowaste: Bio-fillers in poly(3-hydroxybutyrate)

This paper deals with the valorization of a lignocellulosic biomass (LC), biowaste from the second generation bioethanol production process. LC was processed in order to isolate its main components: holocellulose (HC) and acid-insoluble lignin (IL). To obtain a biomass free of organic extractives (TE) and low molecular weight polar compounds (W), LC was also subjected to solvent extraction with toluene/ethanol and water. IL, HC and LC were characterized by SEM, FTIR and 13C MAS-NMR. The morphological and structural analysis evidenced successful separation of the two main fractions of the lignocellulosic biomass.LC and its derivatives were used as fillers in poly(3-hydroxybutyrate) (PHB). The blends were characterized through rotational rheometry and DSC. Moreover, the samples were also thermally treated at 190°C, and the effects of the thermal processing on the matrix molecular weight was evaluated by GPC.The addition of IL to PHB affected its rheological properties, significantly enhancing melt stability due to the formation of a percolated filler network within the matrix. Furthermore, SEM analysis demonstrated homogeneous dispersion of the filler and good interfacial adhesion with the matrix. LC and TE acted as pro-degrading agents toward PHB matrix causing a decrease in molecular weight of the polymer during the thermal treatment. The DSC analysis showed that LC, HC, W and TE promoted the polymer melt crystallization, potentially enabling to control physical aging of PHB.To sum up, this study provides an insight on the effect of a lignocellulosic biowaste and its derivatives on the properties of a naturally occurring, biodegradable polyester.

Crumpled globule formation during collapse of a long flexible and semiflexible polymer in poor solvent.

By introducing explicit solvent particles and hydrodynamic interactions we demonstrate that crumpled globules are formed after the collapse of long polymer chains (N = 10(4)) in a poor solvent. During the collapse crumples of all sizes form sequentially, but small crumples are not stable and convert to blobs with Gaussian statistics. The observed effective mean squared distance R(2)(n) ∼ n(0.38) at n > Ne and contact probability index p(n) ∼ n(-0.5) at n ≫ Ne, which is not following either the model of a fractal globule, or the predictions for an equilibrium globule. Polymer chain stiffness pushes the system to form globular crystallite, and this freezes crumpled structure with R(2)(n) ∼ n(0.33) at n > Ne as a stable state. We note that there is some similarity to crumple globule formation and crystallization of polymer melt.

Continuous modeling and simulation of flow-swell-crystallization behaviors of viscoelastic polymer melts in the hollow profile extrusion process

The continuous viscoelastic flow, swell and crystallization behaviors of polymer melts experienced within and through out of the die/mould can significantly influence the variation of internal structure, and hence determine the performance and dimension of final products in practical processing. However, traditionally theoretical and experimental methods are difficult to be afforded to this problem. In the study, the continuous viscoelastic flow, swell and crystallization behaviors of polymer melts within and through out of practically used die/mould are investigated by means of finite element-finite difference simulation. The mathematical model of three-dimensional viscoelastic flow of polymer melts is established with Phan-Thien and Tanner constitutive model. The streamface–streamline method is introduced to adjust the swelling free surface of the extrudate. The influence of the thermal and flow state on the crystallization phenomenon are discriminated using a modified Schneider’s approach. A decoupled solving algorithm for the governing equations is introduced and the corresponding penalty finite element-finite difference model is derived. The discrete elastic viscous split stress algorithm incorporating the streamline upwind scheme is adopted to improve calculation stability. The essential viscoelastic flow characteristics, extrudate swell phenomenon and flow induced crystallization of polymer melts in the hollow profile extrusion process are investigated based on the proposed mathematical model and numerical methods. Both the distribution of flow variables within the extrusion die and the variation of crystallization kinetic process within the shaped mould are successfully predicted by means of finite element-finite difference simulation of flow-swell-crystallization continuous behaviors of viscoelastic polymer melts.

Reexamination of shish kebab formation in poly(ethylene oxide) melts

Although recent experiments concerning shear effects on crystallization in polymer melts are inclined to support the oriented network model, two important questions still remain open: the effect of polydispersity on shish formation and the growth mechanism of shish. In this work, a narrowdisperse poly(ethylene oxide) (PEO) is chosen as a model system to clarify the role of polydispersity for shish kebab formation after a pulse of flow. The intact structure of shish kebab observed via scanning electron microscopy (SEM), with a 150 nm wide shish core and perpendicular epitaxially grown kebabs with a long period of about 35 nm, reveals that polydispersity is not a necessary condition for shish kebab formation. On the other hand, two-step shear experiment is utilized to elucidate the growth mechanism of shish. It has been proved in a latest study that shish growth is related to the size of the growing nuclei (interval time) and second step shear rate. In this manuscript, a third factor, shear time in the second step shear, is found to be an effective factor to promote the growth of shish, which might provide a convenient processing method.

Flow-induced crystallization in polymer melts: how Winter’s gelation concept fits into the picture

Nobody could expect that gelation times of many hours, which were observed in quiescent polymer melts below the melting temperature of the spherulites, would play a role in flow-induced crystallization. However, this role became obvious for an iPP, when special polarization optics were employed in the well-known arrangement of the Linkam CSS450 apparatus (parallel glass plate rheometer). With the aid of a λ-plate, the interference color red of first order was created in white polarized light. This sensitive interference color changes quickly into blue, when a small phase difference is added (with subtraction a yellow color is obtained). With the aid of the great number of blue halos, which came up at 145 °C after the cessation of flow, an oriented gelation was identified. It spreads faster over the sample than the spherulites. The unwieldy gelation times, which have been found in quiescent melts, seem to be the consequence of a shortage of nuclei.

A phase-field model for simulating various spherulite morphologies of semi-crystalline polymers

A modified phase-field model is proposed for simulating the isothermal crystallization of polymer melts. The model consists of a second-order phase-field equation and a heat conduction equation. It obtains its model parameters from the real material parameters and is easy to use with tolerable computational cost. Due to the use of a new free energy functional form, the model can reproduce various single crystal morphologies of polymer melts under quiescent conditions, including dendritic, lamellar branching, ring-banded, breakup of ring-banded, faceted hexagonal, and spherulitic structures. Simulation results of isotactic polystyrene crystals demonstrate that the present phase-field model has the ability to give qualitative predictions of polymer crystallization under isothermal and quiescent conditions.

Some remarks on flow induced crystallization in polymer melts

This note is concerned about the circumstances, under which flow induced crystallization can take place. In first instance, a discrimination must be made between two temperature ranges. One of these ranges is between the equilibrium melting point of ideal crystals and the melting temperature of spherulitic structures. The other range is below the temperature, where spherulites melt. A second question is, whether one has to do with homogeneous (sporadic) nucleation or with heterogeneous nucleation on so-called defects. In other words, does flow actually cause sporadic nucleation in a homogeneous medium or does it merely activate kind of already existing dormant entities. A third point is the mechanism of the growth of nuclei. The applied specific work is of importance.

Detection of fast and slow crystallization processes in instantaneously-strained samples of cis-1,4-polyisoprene

Cross-linked samples of natural rubber (NR) and synthetic cis-1,4-polyisoprene (IR) were instantaneously expanded to a predetermined strain ratio, αs, using a newly-designed high-speed tensile tester. Crystallization behavior after the cessation of deformation was investigated. The high-cycle wide-angle X-ray diffraction (WAXD) measurements could successfully reveal the drastic progress of crystallization within the first a few hundred milliseconds. Quantitative analysis of diffraction intensity clarified coexistence of fast and slow crystallization processes; time constants τf and τs, and amplitude If and Is, respectively, were estimated for these processes. The values of τf were in the range of 50–200 ms, while τs ranged between 2.5 and 4.5 s. Almost linear dependence of If and Is on αs was clarified. The crystallite size in the directions both parallel and perpendicular to the stretching direction decreased with the increase in time-averaged nominal stress. The crystal lattice deformed almost linearly with the average nominal stress. For the fast process, correlation between crystallization and stress relaxation was not recognized, while linear relationship between them was found for the slow process. In every case, strain-induced crystallization was found to be the major origin of stress relaxation. Based on the results, effects of strain on crystallization of polymer melt were discussed.

Flow-induced crystallization in polymer melts: on the correlation between nucleation and specific work

A new counting technique for nuclei, as found after short-term shearing, has been developed with the aid of the plate-and-plate rheometer Linkam CSS450. For the purpose this apparatus was modified by the introduction of complementary polarizing optics (a polarizer and a λ-plate). With the aid of this technique the density of nuclei could be determined in a new way. When these number densities are plotted against the applied specific work, satisfactory agreement is found with results, which have been obtained previously with a sliding glass plate rheometer. Nevertheless, the limits of validity of the diagrams had to be discussed. A transition from a dynamic description with the aid of the specific work to a purely kinematic description with the aid of the frequency of successful encounters cannot be overlooked. In fact, with increasing specific work the influences of temperature and (non-Newtonian) viscosity appear to fade away.

Coarse-Grained Simulations of Flow-Induced Nucleation in Semicrystalline Polymers

We perform kinetic Monte Carlo simulations of flow-induced nucleation in polymer melts with an algorithm that is tractable even at low undercooling. The configuration of the noncrystallized chains under flow is computed with a recent nonlinear tube model. Our simulations predict both enhanced nucleation and the growth of shish-like elongated nuclei for sufficiently fast flows. The simulations predict several experimental phenomena and theoretically justify a previously empirical result for the flow-enhanced nucleation rate. The simulations are highly pertinent to both the fundamental understanding and process modeling of flow-induced crystallization in polymer melts.

The Effect of Orientation Relaxation on Polymer Melt Crystallization Studied by Monte Carlo Simulations

We use dynamic Monte Carlo simulations to study the athermal relaxation of bulk extended chains and the isothermal crystallization in intermediately relaxed melts. It is found that the memory of chain orientations in the melt can significantly enhance the crystallization rates. The crystal orientation and lamellar thickness essentially depend on the orientational relaxation. Moreover, there is a transition of the nucleation mechanism during the isothermal crystallization from the intermediately relaxed melts. These results explain the mechanism of the self-nucleation by orientation and suggest that in flow-induced polymer crystallization, the orientational relaxation of chains decides the crystal orientation.

Molecular dynamics study of polymer crystallization in the presence of a particle

AbstractWe have used molecular dynamics simulations with a coarse‐grained model to study the effect of a particle on the crystallization of polymer melt. We analyzed in particular a bond order parameter to characterize the nucleation and crystallization process. Our calculations show that the presence of a particle modifies the free energy landscape of polymer melts, locally induces the ordering of polymer melts near the particle surface, and thus enhances the polymer crystallization. Because the interaction between the particle and polymers is repulsive, our results suggest that the origin of the enhancement for polymer crystallization is entropic. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2161–2166, 2007

Epitaxial polymer crystal growth influenced by partial melting of the fiber in the single-polymer composites

We report dynamic Monte Carlo simulations of polymer melt crystallization induced by the same species of the fiber. We found that partial melting on the lateral surface of the fiber postpones the epitaxial crystal growth of the matrix, while the crystal growth rate has been little affected. The delay can be attributed to the recrystallization on the lateral surface of the fiber due to the prior melting. In addition, we observed the highly stretched status of those polymers melted from the fiber, which is responsible for an instant initiation of the recrystallization at a low temperature. The relevance of our results to the experimental observations of isotactic polypropylene has been discussed.

Crystallization-Induced Fluid Flow in Polymer Melts Undergoing Solidification

The influence of processing conditions on the morphology of solidified semicrystalline polymer materials formed under dynamic melt processing conditions has been of concern for decades.1 Although there has been much recent progress in modeling the kinetics and origin of polymer spherulitic crystallization,2,3 the influence of fluid flow and the viscous properties of the undercooled polymer melt on the crystallization morphology have received relatively little attention due to the great computational problems involved in modeling and the experimental difficulties in observing this phenomenon. It is often argued that the macromolecules of the undercooled melt can diffuse to the crystal growth front during crystallization,4 and fluid flow processes are simply ignored. While this assumption may be a reasonable approximation under low undercooling conditions, one may well wonder whether this situation remains true under the conditions of rapid solidification that normally arise during polymer material processing. Flow in the undercooled polymer melts has not been studied much experimentally previously because of the lack of methods of sufficient temporal and spatial resolution to discriminate between the crystalline and amorphous phases during the course of the crystallization process. It is well-known, however, that the formation of commercial semicrystalline polymeric products by injection moldings, film extrusions, film blowing, etc, can be accompanied by the formation of unwanted defects (voids, pores, and other imperfections) and that the ultimate properties of these materials can be appreciably affected by processing conditions.5 The present study indicates that rapid fluid flow can occur in a model undercooled polymer melt (a common commercial polymer, isotactic polypropylene) during the course of crystallization under confinement conditions (simply crystallizing polymer film between cover glasses). We have also observed a similar behavior (not yet published) in crystallizing poly(ethylene oxide) (PEO) melts, indicating some degree of generality for the phenomenon. The isotactic polypropylene (iPP) polymer employed in this work was a commercial grade polymer obtained from the Αldrich Chemical Co., and we show typical results for an isothermal crystallization temperature of 138 °C. The “weight” and “number” molecular masses Mw and Mn were about 340 000 and 97 000, respectively, so this polymer was rather polydisperse, typical of commercial material. The carbon black (CB) relative mass of the probe particles to the polymer matrix was relatively low, 0.5%. The iPP and CB were mixed by meltpressing repeatedly (five times) on a hot plate at 200 °C. Samples for the crystallization and flow measurements were prepared by pressing the melt mixtures between two cover glasses into thin films having a thickness of about 30 μm, thus providing a model confinement environment for the polymer melt crystallization process. Our optical microscope (Carl Zeiss JENA, made in Germany), equipped with a CCD camera (HV1301UC, made by the Da Heng Co. in Beijing), was used to image flows in the undercooled melts by following the motion of CB particles during isothermal crystallization. The resolution of the CCD camera in the x and y directions was about 0.2 μm. A homemade dual-temperature microscope hot stage provided a temperature control, with a temperature uncertainty of ( 0.1 °C. The iPP samples were first melted at 200 °C for 10 min to melt the crystallized structures formed in the course of the previous sample history and then were rapidly transferred to a crystallization temperature below the melting temperature (160 °C). Figure 1 shows a serial of micrographs of the iPP sample during isothermal crystallization at 138 °C. The present work not only considers the standard problem of characterizing the spherulite growth, but also considers how spherulite growth induces flow in the surrounding polymer melt by observing the motion trajectories of CB particles in the undercooled iPP “melt”. The basic concept of our measurement can be understood from the following nautical analogy: The undercooled melt can be viewed as a sea and the growing spherulites as islands that grow up out of this sea. The CB particles are convected by the fluids, providing information about the prevailing local “currents” in the undercooled polymer melt.