Crossover behavior in crystal growth rate from n‐alkane to polyethylene

A crystal growth rate equation, parameterized from molecular dynamics simulations of n‐alkanes, is compared to recent experiments on growth rates for polyethylene at high undercooling. The analysis reveals that the growth rate of alkanes and polyethylene can both be described by the same relationship. The appropriate relaxation time is used to describe the kinetic barrier to crystallization. For chains shorter than the entanglement length, this is the Rouse time. For chains longer than the entanglement molecular weight, kinetic limitations are modeled by the local relaxation of an entangled segment at the interface. This model supports a different mechanism for fast crystal growth at high undercooling than that usually inferred from slow growth data near the melting temperature. Use of the crystal growth rate model is illustrated for polyethylene crystallizing under conditions of slow cooling and fast cooling. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2468–2473, 2005     

Crystallization of helical oligomers with chirality selection. I. A molecular dynamics simulation for bare helix

Helical polymers often exhibit pronounced chirality recognition during crystallization. By molecular dynamics simulation, we have already shown that the helical polymers crystallize with or without marked chirality selection depending on structural details of the polymer molecules. We have there classified the helical polymers into two categories: the bare helices made of only backbone atoms which show rather tolerant chirality selection, and the general helices with large side groups showing strict chirality recognition. Polymer crystallization is in general largely hampered and retarded by slow dynamics of the entangled chains, and therefore short helical oligomers are very suitable models for studying the chiral crystallization. We here report on molecular simulations of crystallization in the bare helical oligomer molecules by the use of Monte Carlo and molecular dynamics simulations. First we confirm the low temperature chiral crystal phase and the reversible order-disorder transition. We also observe frequent inversions of the helical sense, and the helix reversal defects propagating along the chains. Then we investigate crystallization from the melt into the chiral crystal phase. We find that the crystallization rate depends very sensitively on the degree of undercooling. The crystallization is found to be the first order transition that conforms well to the traditional picture of crystal growth in small molecules. Even when the crystallization directly into the chiral crystal phase is conducted, marked chirality selections are not observed at the early stage of crystallization; the chains adhere to the crystal surfaces selecting their helical senses rather at random resulting in racemic crystallites. The isothermal crystallization for a sufficiently long time, however, yields lamellar crystals composed of well-developed chiral domains, the growth of which seems to be accomplished through the transition back into the ordered chiral crystal phase.     

Polymer crystallization: Simulation with entropic barrier model and application to specific polymers

The growth of polymer single crystals has been simulated on the basis of a simple two-dimensional ‘entropic barrier’ model. The chain is described by a sequence of growth units. Their additions and removals are determined by rate constants obeying detailed balance. The crystallization is then simulated by a kinetic Monte Carlo algorithm. An application of the model to specific crystallizable polymers (polyethylene, isotactic polystyrene, isotactic polypropylene, polyhydroxybuterate and polypivalolactone) is presented. Input parameter values for the model are derived from the respective surface free energies, bulk enthalpies, melting points and crystallographic repeat lengths. The only free parameter is the length of a polymer growth unit. This is set to half the lamellar crystal thickness at large undercooling. The lamellar thicknesses calculated on this basis are in good agreement with experimental data. An analysis of the growth unit lengths of the different polymers indicates a scaling with the chain persistence length in the melt.     

Crystallization and melting of polyethylene copolymers: Differential scanning calorimetry and atomic force microscopy studies

The Hoffman–Lauritzen theory of secondary, surface nucleation and growth was primarily relied upon for about 40 years after its introduction in about 1960 to rationalize the crystallization of flexible chain polymers into lamellar crystals. However, in about 1998, Strobl and coworkers introduced a different model for crystallization, based on the stage‐wise formation of lamellae. Two major components of this model were as follows: (1) the concept of the formation of a mesomorphic melt as a precursor to crystallization and (2) the control of the melting temperature range of lamellar crystals of homogeneous polyolefin copolymers by an inner degree of order or perfection rather than on the crystal thickness. The first concept is in disagreement with the HL theory and the second with the Gibbs‐Thomson theory, which associates melting temperature with lamella thickness. In the present study, differential scanning calorimetry and atomic force microscopy were successfully employed to monitor the in situ quiescent crystallization of polyethylene homopolymer and copolymer. In the present study, evidence was not found to support the concept of lamellae with equal thickness melting over a broad temperature range. Some evidence was found that might be interpreted to support the concept of a mesomorphic melt as a precursor to crystallization. At present, the model promoted by Strobl and coworkers appears to be at an uncertain stage at which strong proof or disproof are not available. However, this alternative model has injected a new vitality into the study of crystallization of flexible chain polymers. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2369–2388, 2006     

A raman LAM study of lamellar thickness of virgin polyethylene powder

The lamellar thickness of polyethylene virgin reactor powder has been successfully measured using the Raman longitudinal acoustic mode (LAM). Relatively high lamellar thicknesses have been found. These values change with polymerization temperature in an unusual way, with lamellar thickness being larger for lower polymerization temperature, i.e., at higher undercooling for crystallization. Agreement within an experimental error of 10% has been obtained between values from LAM and those calculated by the Thompson—Gibbs equation from the melting point measured by differential scanning calorimetry.     

Thermal and mechanical properties of syndiotactic polystyrene/organoclay nanocomposites with different microstructures

The fabrication of syndiotactic polystyrene (sPS)/organoclay nanocomposite was conducted via a stepwise mixing process with poly(styrene‐co‐vinyloxazolin) (OPS), that is, melt intercalation of OPS into organoclay followed by blending with sPS. The microstructure of nanocomposite mainly depended on the arrangement type of the organic modifier in clay gallery. When organoclays that have a lateral bilayer arrangement were used, an exfoliated structure was obtained, whereas an intercalated structure was obtained when organoclay with a paraffinic monolayer arrangement were used. The thermal and mechanical properties of sPS nanocomposites were investigated in relation to their microstructures. From the thermograms of nonisothermal crystallization and melting, nanocomposites exhibited an enhanced overall crystallization rate but had less reduced crystallinity than a matrix polymer. Clay layers dispersed in a matrix polymer may serve as a nucleating agent and hinder the crystal growth of polymer chains. As a comparison of the two nanocomposites with different microstructures, because of the high degree of dispersion of its clay layer the exfoliated nanocomposite exhibited a faster crystallization rate and a lower degree of crystallinity than the intercalated one. Nanocomposites exhibited higher mechanical properties, such as strength and stiffness, than the matrix polymer as observed in the dynamic mechanical analysis and tensile tests. Exfoliated nanocomposites showed more enhanced mechanical properties than intercalated ones because of the uniformly dispersed clay layers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1685–1693, 2004     

Characterization,Solar Reflectance,and Crystal Properties of Polyethylene and Ethylene Copolymer after Thermal Treatment

Various kinds of polyethylene and ethylene copolymers were prepared by non-isothermal crystallization and isothermal crystallization methods. Solar reflectance of all samples was determined by a series of characterization (UV-vis-NIR measurement, wide-angle X-ray diffraction, differential scanning calorimetry analysis, polarized optical microscopy). It was found that lamellar thickness, degree of crystallinity, and microstructure played an important role in affecting the solar reflectance of these polymers. Long-branched chains in ethylene copolymers lowered the solar reflectance by decreasing lamellar thickness and the degree of crystallinity of these polymers. The isothermal crystallization method is a way to promote lamellar thickness and the degree of crystallinity, and make the microstructure more compact.     

Lamellar thickening of polyethylene under high pressure

Single crystal mat (SCM) samples of polyethylene (PE) were prepared from dilute solution of p-xylen, then they were annealed at pressures of 200 and 500 MPa. Lamellar thickness of the original and annealed SCM samples was measured by small-angle X-ray scattering method. Orientation of the molecular chain in those SCM samples was investigated by wide-angle X-ray diffraction pattern. From these X-ray measurements, annealing temperature dependence of the lamellar thickness, i.e., lamellar thickening, under high pressure was obtained. Melting process of the SCM samples was also investigated at 200 and 500 MPa by high pressure differential thermal analysis. Then correspondence between the lamellar thickening and the melting process was studied. The lamellar thickness increases markedly with approaching to the melting temperature of the orthorhombic crystal even in the high pressure region where the high pressure phase (hexagonal phase) appears. The annealing temperature dependence curve of the lamellar thickness at 200 MPa can be superimposed on the curve at 500 MPa by shifting the curve along the temperature scale by 47 K. Large scale lamellar thickening occurs in the orthorhombic crystal phase in the high pressure region. The formation process of extended-chain crystal is discussed. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys, 35: 535–543, 1997     

Monte Carlo simulations of single crystals from polymer solutions

A novel "anisotropic aggregation" model is proposed to simulate nucleation and growth of polymer single crystals as functions of temperature and polymer concentration in dilute solutions. Prefolded chains in a dilute solution are assumed to aggregate at a seed nucleus with an anisotropic interaction by a reversible adsorption/desorption mechanism, with temperature, concentration, and seed size being the control variables. The Monte Carlo results of this model resolve the long-standing dilemma regarding the kinetic and thermal roughenings, by producing a rough-flat-rough transition in the crystal morphology with increasing temperature. It is found that the crystal growth rate varies nonlinearly with temperature and concentration without any marked transitions among any regimes of polymer crystallization kinetics. The induction time increases with decreasing the seed nucleus size, increasing temperature, or decreasing concentration. The apparent critical nucleus size is found to increase exponentially with increasing temperature or decreasing concentration, leading to a critical nucleus diagram composed in the temperature-concentration plane with three regions of different nucleation barriers: no growth, nucleation and growth, and spontaneous growth. Melting temperatures as functions of the crystal size, heating rate, and concentration are also reported. The present model, falling in the same category of small molecular crystallization with anisotropic interactions, captures most of the phenomenology of polymer crystallization in dilute solutions.     

Environmental stress cracking resistance of polyethylene: The use of CRYSTAF and SEC to establish structure–property relationships

Nineteen commercial high‐density polyethylene resins made with different polymerization processes and catalyst types were analyzed by high‐temperature size exclusion chromatography and crystallization analysis fractionation. The information obtained with these characterization techniques on the polymer chain structure was correlated to environmental stress cracking resistance. Environmental stress cracking resistance increases when the molecular weight and concentration of polymer chains that crystallize in trichlorobenzene between 75 and 85 °C increase. Polymer chains present in this crystallization range are assumed to act as tie molecules between crystal lamellae. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1267–1275, 2000     

Spherulitic morphology in polyethylene and isotactic polystyrene: Influence of diffusion of segregated species

Morphological consequences of a localized diffusion of segregated species at crystal growth fronts have been studied in two specific contexts: (1) variation of texture in spherulites grown in unfractionated polyethylene over a range of crystallization temperatures mostly in regime II, and (2) development of elongated lamellar habits in spherulites of a polymer (isotactic polystyrene) whose native crystal habit is regularly polygonal. In relation to (1) it is shown that, as crystallization temperature is varied, there is a correlation between mean thickness of stacks of lamellae and an averaged diffusion range of segregated molecules of lower molecular weight. It is noted that lamellar organization appears to be significantly different in polyethylene fractions. In relation to (2) it is shown that principal contributors to the evolution of spherulitic texture from hedritic precursors are fragmentation of lamellae by screw dislocations and radially biased growth under the influence of concentration gradients of segregated species.     

Study of bundle formation during crystallization in polymer blends

The development of texture which exists in polymer spherulites grown from single phase melts containing an appreciable amount of noncrystallizable material was investigated. This texture generally consists of lamellar bundles separated by amorphous regions, both of which are typically 0.1–1 μm thick. A space–time finite element model previously developed by us was used to simulate the growth of a group of polymer lamellae. The model determines the impurity concentration field in the melt surrounding the growing lamellae and tracks the growth of each lamella. Important variables are the initial melt concentration of noncrystallizable material, the mass diffusion coefficient of noncrystallizable species, lamellar thickness, long period, and the rate of molecular attachment at the growth front. Under certain conditions, bundles did indeed develop during the simulations. These results were used to predict bundle thicknesses. The predictions of bundle texture were compared to actual textures observed in blends of syndiotactic and atactic polystyrene. It was found both experimentally and numerically that bundle thickness was a strong function of crystallization temperature and a relatively weak function of both the initial composition of noncrystallizable species and the degree of crystallinity of the lamellar stack. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 873–888, 1998     

Collapse Transition‐Assisted Crystallization in P3HT Solution

Understanding the multiple phase transitions such as collapse transition, phase separation, and crystallization in solutions is of fundamental importance to control the solution structure of conjugated polymers in device processing. Combining in situ synchrotron radiation small and wide‐angle X‐ray scattering, ultrasensitive differential scanning calorimetry, ultraviolet–visible absorption spectroscopy, and polarized optical microscopy, we investigate the order–disorder transitions in poly(3‐hexylthiophene)/toluene solutions during cooling and heating processes. We demonstrate the occurrence of collapse transition of polymer chains from a random coil state to a lower dimensional network prior to the onset of crystallization during cooling in solution. This conformational preordering can lead to the formation of a lyotropic liquid crystalline phase, which is of great significance to the crystallization and ordering in polymer films, and further to promote its electric performance. It is examined that the mobility of films cast from chain‐collapsed solutions can be one order of magnitude higher than that from isotropic solutions with random‐coiled conformations. Thus, the conformational preordering in solutions is proposed to be a more efficient way than the postannealing of films to improve the electric performance of conjugated polymer films. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1105–1114     

Poly(thiodiethylene adipate): Melting behavior,crystallization kinetics,morphology, and crystal structure

The melting behavior and crystallization kinetics of poly(thiodiethylene adipate) (PSDEA) were investigated with differential scanning calorimetry and hot‐stage optical microscopy. The observed multiple endotherms, commonly displayed by polyesters, were influenced by the crystallization temperature (T_c) and ascribed to melting and recrystallization processes. Linear and nonlinear treatments were applied to estimate the equilibrium melting temperature for PSDEA with the corrected values of the melting temperature. The nonlinear estimation yielded a higher value by about 9 °C. Isothermal crystallization kinetics were analyzed according to Avrami's treatment. Values of Avrami's exponent close to 3 were obtained, independently of T_c, in agreement with a crystallization process originating from predetermined nuclei and characterized by three‐dimensional spherulitic growth. As a matter of fact, space‐filling spherulites were observed by optical microscopy at all T_c's. The rate of crystallization became lower as T_c increased, as usual at a low undercooling, the crystallization process being controlled by nucleation. Moreover, the crystal structure of PSDEA was determined from powder X‐ray diffraction data by full profile fitting. A triclinic unit cell containing two polymer chains arranged parallel to the c axis was found. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 553–566, 2004     

Effect of molecular architecture on quiescent and shear‐induced crystallization of polyethylene

The aim of this work is to investigate the effect of the molecular structure of polyethylene on the crystallization kinetics. In static conditions, the increase of the degree of branching leads to the decrease of the crystallization temperature, the melting temperature, and the crystallinity. Indeed, the crystal thickness is controlled by the length of PE segments between branching. The effect of preshear on crystallization kinetics was studied by following the dynamic modulus along the time after a treatment of constant shear rate. Particularly, the effect of the shear rate was investigated. The enhancement of crystallization kinetics appears directly linked to the relaxation time of the melt polymer. Expressed by the Weissenberg number, a “master curve” is obtained independent of the amount and length of branching, leading to the conclusion that the nucleation due to shear is conditioned by the molecular architecture mainly via its effect on the relaxation time. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1597–1607, 2006     

Crystallization of polyethylene at high pressure: A kinetic view

A model for the crystallization kinetics of polymers is outlined and is used to interpret observations of the crystallization of polyethylene at high pressures. This model introduces a distinction between σ_e the lamellar surface energy which controls the lamellar thickness, and σ_e′, the surface nucleus surface energy which controls the growth rate. Differential scanning calorimetry and electron microscopy data for several polyethylenes crystallized at pressures of up to 8 kb are presented. From the dependence of lamellar thickness on the crystallization undercooling at 5 kb, it is found that σ_e increases markedly with pressure leading to the formation of very thick crystals at high pressures. The magnitude of the increase in σ_e is in agreement with σ_e values calculated from the dependence of melting temperatures on pressure. The nucleus surface energy σ_e′ is not expected to vary significantly with pressure, and estimates of growth rates of 5 kb which indicate that the growth rate does not vary significantly with pressure at constant under-cooling confirm this. Fractionation effects and the differences in behavior between different polyethylenes are also discussed.     

The AFM observation of linear chain and crystalline conformations of ultrahigh molecular weight polyethylene molecules on mica and graphite

Atomic force microscopy (AFM) has been applied to visualize expanded linear chain and compact crystalline conformations of ultrahigh molecular weight polyethylene (PE) molecules deposited on mica and graphite from diluted solutions at elevated temperatures. Isolated PE chains are visualized on mica with the apparent negative AFM height and the contour length much shorter than the molecular length. The chain conformations have both the kinked random‐coil sites and the sites of the unexpectedly large two‐dimensional expansion. The crystalline conformations on mica are small single‐molecule rod‐like nanocrystallites and the isolated block‐type “edge‐on” nanolamellae comprising several PE molecules. Noticeable fluctuations of the fold length in the range of approximately 10–20 nm around the averaged value of about 15 nm are observed for nanocrystallites and on tips of some nanolamellae. The explanation of the experimentally observed features of chain surface conformations on mica is proposed. It implies the immobilization of PE molecules in the nm‐thickness salt layer formed on mica surface at ambient conditions after PE deposition and the presence along the chain of multiple expanded chain folds. Only isolated lamellae and lamellar domains of a monolayer height are observed on graphite samples. The substrate/polymer epitaxial incommensurability important for the observation of the PE linear chain surface conformations is discussed from the comparison of the results obtained for mica and graphite, the coil‐to‐crystal intramolecular transformation is assumed to be inhibited on mica surface. The slow disintegration of the original gel structure of PE stock‐solution used for the high‐temperature depositions was found to result in the characteristic large‐scale morphological heterogeneity of the samples. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 766–777, 2010     

New insight into melting and crystallization behavior in semicrystalline poly(ethylene terephthalate)

After isothermal crystallization, poly(ethylene terephthalate) (PET) showed double endothermic behavior in the differential scanning calorimetry (DSC) heating scan. During the heating scans of semicrystalline PET, a metastable melt which comes from melting thinner lamellar crystal populations formed between the low and the upper endothermic temperatures. The metastable melt can recrystallize immediately just above the low melting temperature and form thicker lamellae than the original ones. The thickness and perfection depends on the crystallization time and crystallization temperature. The crystallization kinetics of this metastable melt can be determined by means of DSC. The kinetics analysis showed that the isothermal crystallization of the metastable PET melt proceeds with an Avrami exponent of n = 1.0 ∼ 1.2, probably reflecting one‐dimensional or irregular line growth of the crystal occurring between the existing main lamellae with heterogeneous nucleation. This is in agreement with the hypothesis that the melting peaks are associated with two distinct crystal populations with different thicknesses. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 53–60, 2000     

Continuum theory of polymer crystallization

We present a kinetic model of crystal growth of polymers of finite molecular weight. Experiments help to classify polymer crystallization broadly into two kinetic regimes. One is observed in melts or in high molar mass polymer solutions and is dominated by nucleation control with G approximately exp(1/TDeltaT), where G is the growth rate and DeltaT is the supercooling. The other is observed in low molar mass solutions (as well as for small molecules) and is diffusion controlled with G approximately DeltaT, for small DeltaT. Our model unifies these two regimes in a single formalism. The model accounts for the accumulation of polymer chains near the growth front and invokes an entropic barrier theory to recover both limits of nucleation and diffusion control. The basic theory applies to both melts and solutions, and we numerically calculate the growth details of a single crystal in a dilute solution. The effects of molecular weight and concentration are also determined considering conventional polymer dynamics. Our theory shows that entropic considerations, in addition to the traditional energetic arguments, can capture general trends of a vast range of phenomenology. Unifying ideas on crystallization from small molecules and from flexible polymer chains emerge from our theory.     

Nanoconfinement as a tool to study early stages of polymer crystallization

This article promotes the idea that crystallization experiments under confinement can be an interesting tool to learn more about the early stages of polymer crystallization in bulk systems. Based on various results from the recent literature, it is demonstrated that crystalline forms that are metastable, transient, or inaccessible in bulk samples can be easily obtained and studied in nanoscopic compartments. This is interesting in the light of the recent discussion about thermodynamic reasons for the temporary occurrence of a mesophase at the growth front of crystals in bulk polymers, in particular, about a hexagonally packed mesophase in polyethylene. The experimental findings for nanoconfined methylene sequences seem to support indirectly thermodynamic approaches explaining the occurrence of a mesophase based on the small thickness of the crystal at the growth front. A first estimate for the critical crystal thickness d_mc defining the transition from hexagonal to orthorhombic packing in case of confined methylene sequences is provided based on results for side chain polymers. Further perspectives of crystallization experiments on confined systems are discussed. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1556–1561, 2008