Modelling tie chains and trapped entanglements in polyethylene

A Monte Carlo random walk model was developed to simulate the chain structure of amorphous layers in polyethylene. The chains emerging from the orthorhombic crystal lamellae were either folding back tightly (adjacent re-entry) or performing a random walk (obeying phantom chain statistics) forming statistical loops or tie chains. A correct amorphous density (ca. 85% of the crystalline density) was obtained by controlling the probability of tight folding. Important properties like fracture toughness depend on the number of chains covalently linking together the crystalline regions. The model structure was analysed with a novel numerical topology algorithm for calculating the concentration of tie chains and trapped entanglements. The numerical efficiency of the algorithm allowed molecular cubic systems with a side length of 100 nm to be readily analysed on a modern personal computer. Simulations showed that the concentration of trapped entanglements was larger than the concentration of tie chains and that the thickness of the amorphous layer (L_a) had a greater impact than the crystal thickness (L_c) on the tie-chain concentration. In several other commonly used models, such as the Huang–Brown model, the influence of trapped entanglements and the effect of the L_a/L_c ratio are neglected. Simulations using as input the morphology data from Patel generated results in agreement with experimental rubber modulus data.     

Modelling the amorphous phase and the fold surface of a semicrystalline polymer—the Gambler's Ruin method

A semicrystalline polymer with lamellar morphology consists of alternating amorphous and crystalline regions. If sufficiently long, each molecule in this system traverses both the crystalline and amorphous zones. The amorphous portion is comprised of portions of a molecule that form loops that re-enter the same lamella at some distance from the point of emergence, and bridges that form connections between two different crystal lamellae. (A tight fold is not considered to be a loop). The statistics of loops and bridges are shown to be identical to the classical Gambler's Ruin problem in mathematical statistics. This is a useful observation because the extensive existing literature on the Gambler's Ruin problem allows us immediately to transcribe results to the polymer system. Using this approach, the ratio of the number of loops to the number of bridges is determined to be M, the thickness of the amorphous zone in unit statistical steps. Also, the average number of steps comprising the amorphous run is determined to be 3M+1 for a simple cubic lattice in three dimensions. This modelling leads to a calculation of the minimal fraction of crystal stems involved in tight folding in a semicrystalline polymer. For a simple cubic lattice this is found to be $\text{2}\text{3}$. The effects of crystal structure and stiffness of the chain in the melt on this bound are discussed.     

Modelling the amorphous phase of a melt crystallized,semicrystalline polymer: segment distribution,chain stiffness,and deformation

The analogy between the Gambler's Ruin problem and the statistics of loops and bridges in the amorphous region of lamellar semicrystalline polymers was first recognized by Guttman et al. Results for the loop and bridge distribution compare very well with recent data from Monte Carlo calculations. However, when the molecular weight of the polymer is low, a substantial part of the amorphous region is filled by cilia and free polymer. We examined their relative importance by adapting the matrix formalism developed by DiMarzio and Rubin. The Gambler's Ruin results are recovered for high molecular weight polymer. In addition it will be shown that the effect of the temperature (chain stiffness) can be simulated by rescaling the steplength of a random walk chain. Mean field theories incorporate segment-solvent interactions and allow for non-uniform segment densities by weighting each step according to the local concentrations. Using these weighting factors, we find deformation to be controlled by energetic interactions rather than by entropy. At large strain a ‘necking’ process occurs. However, in the presence of a good solvent, the material is soft and flexible.     

Tensile deformation of semi-crystalline polymers by molecular dynamics simulation

In this work, the microstructure evolution of semi-crystalline polymers during tensile deformation is analyzed by molecular dynamics simulation. A perfect semi-crystalline lamellar structure with crystalline/amorphous interface perpendicular to tensile direction is created with the help of coarse-grained (CG) model of poly(vinyl alcohol) (PVA). During the tensile test, two kinds of strain rates are applied to the lamellar stack to determine the stress–strain curves, yield stresses, and crystallinities. Consistent with experimental findings, two yield points were observed in the semi-crystalline sample which was corresponded to the fine and coarse crystallographic slips in the lamellar structure, where the crystal stems gradually rotated into the direction of applied stress during chain slips. After the second yielding point when the crystal stems had been rotated fully into the direction of applied stress, the lamellar structure was destroyed and it resulted in a decrease of crystallinity. In addition, the increase of the strain rate led to the acceleration of destruction of crystal structures. It is worth noting that the stress induced crystallization was observed in the interfacial region, and newly crystallized beads were belonged to the same microcrystalline domain as crystalline region due to memory effects. This work provides direct comparison of structure evolution between crystalline and amorphous region in semi-crystalline polymers during tensile deformation, and it is helpful for the design and mechanical property analysis of semi-crystalline polymers.     

Molecular mechanisms of the chain diffusion between crystalline and amorphous fractions in polyethylene

We revisit the problem of the molecular mechanism of the chain diffusion between crystalline and amorphous fractions in semicrystalline polyethylene (PE). There exists a long-standing controversy on the nature of the topological point defects which diffuse along the chain stems in crystallites and shift the stems. Namely, the conformational (including gauche conformations) twist-compression (interstitial-like) and the smooth (soliton-like) twist-tension (vacancy-like) localized defects were offered for this role. However, none of the proposed models for the process could explain all the experimental facts which seemed unclear and contradictory. Moreover, it was discovered recently that in PE samples of uncommon morphology (electron beam irradiated samples, fibers and single crystals) the diffusion process has the activation energy about 3 times less than that in common melt-crystallized samples. No explanation ever followed. We have carried out molecular dynamics (MD) simulation of both the defects in a realistic model of PE crystal and obtained estimates for their formation energies and diffusion coefficients. These estimates together with analysis of available experimental data allow to solve both the problems and to propose models for molecular mechanisms of the observed diffusion processes. The agents of the ‘old’ diffusion process are the smooth twist-tension defects. Shifts in a chain stem of a crystallite in a common sample are initiated at the interface to an amorphous region through extended thermal motion of the chain stem in the amorphous region. If the motion causes a strong pull (with a twist) at the chain stem in the crystallite, such motion produces a smooth defect of twist-tension on this stem. The proposed molecular model conforms with available mechanical experiments if one accepts that the process corresponds to the most low temperature (α₁) from the α-peaks observed. The ‘new’ diffusion process results from diffusion of the conformational twist-compression defects in crystallites. The needed sequence of conformations appears near a crystallite as a result of a quick gamma process. Because the state of the semicrystalline polymer is unstable, the position of the boundary between the crystalline and disordered regions fluctuates so that segments of chains pass from disordered to crystalline state (and vice versa). The conformational defects in disordered region are captured through expansion of the crystalline region where they become stable and diffuse along the chains. Our MD estimate for the activation energy of the process E_act ≤ 8.65 kcal/mol is in a good agreement with the experimental value 7 kcal/mol. The diffusion coefficients of both the defects are too high to have effect on the statistics of both of these very slow processes. Therefore the statistics of the ‘old’ process is the statistics of strong thermal pulls at chain stems in crystallites, and the statistics of the ‘new’ process is related to the statistics of fluctuations of the position of the boundaries between crystalline and disordered fractions.     

A critical assessment of unbalanced surface stresses as the mechanical origin of twisting and scrolling of polymer crystals

Twisting of polymer lamellae manifested by e.g. appearance of concentric bands in polymer spherulites examined in a polarized optical microscope remains a topic of research and controversy. It has been interpreted variously as resulting from phenomena that take place during growth or from structural features of individual lamellae, or multilamellar aggregates. Phenomena that take place during growth are of general, or even generic character. They include non-linear diffusion processes leading to rhythmic crystallization, or self-induced compositional or mechanical fields generated near the advancing crystal front. Structural features include cumulative reorientation of lamellae at successive isochiral screw dislocations (possibly linked with surface pressure exerted by cilia) or different surface stresses on opposite fold surfaces of individual lamellae, as a result of different levels of congestion of folds.This contribution reviews evidence that has accumulated in favor of lamellar twist induced by surface stresses that result from differential congestion of fold surfaces, as suggested initially (in 1984) and advocated for many years by Keith and Padden. Such differences in fold surface structure are occasionally amenable to experimental (even if only qualitative) verification, as illustrated by polymer decoration of polyethylene single crystals. Twist is expected when a two-fold symmetry parallel to the growth direction exists in the lamellar structure (crystalline core and fold surface). This symmetry often stems from chirality: most frequently atomic (configurational) or stem (conformational) chirality but chirality (or at least asymmetry) may also be introduced by chain tilt.Possible origins of twisting in chiral polymers are also reviewed. In β sheets of fibrous proteins, the origin of twist stems from the atomic chiral centers in the crystalline core of the lamellae and its transfer to higher structural levels via the strong structural identity of the hydrogen-bonded β sheets. However, in a series of synthetic liquid-crystalline main-chain nonracemic chiral polyesters, the lamellar twist sense depends on the odd or even numbers of atoms in the aliphatic segment. For these and other more flexible chiral polymers, often with helical chain conformation, twisting appears to result from surface stresses associated with different fold structure or conformations at opposite fold surfaces, as suggested by a preliminary analysis of the Form III of isotactic poly(1-butene). Such differences in fold conformations result from, but are not directly related to, the specific helical hand of the polymer since they rest on the details of the chain conformation as it reaches the fold surface. This analysis accounts for the lack of one-to-one correspondence between configurational or conformational chirality of the polymer and lamellar twist sense (the one-to-one correspondence applies however for stereoenantiomers of a given polymer).Twist is not the only known non-planar geometry of polymer lamellae. In a few cases, the lamellae are scrolled. Scrolling of polymer lamellae is also easily accounted for by the existence of surface stresses when the two-fold symmetry parallel to the growth direction is absent. Such surface stresses are again linked to disparities in fold volume, as first suggested for poly(vinylidenefluoride) in its γ Form and later for two long paraffins substituted near their middle carbon atom and that crystallize in hairpin fashion, and for scrolled crystals of polyamide 66.The different nature and structure of polymer crystal fold surfaces, therefore, offer an unusual opportunity to decouple surface and bulk contributions and to analyze the origin of non-planar lamellar geometries at a sub-molecular level. Fold structure disparities and resulting unbalanced surface stresses provide a unified explanation for the formation of non-planar (both twisted and scrolled) lamellar crystals. They account for both the diversity of lamellar morphologies produced under the same crystallization conditions and for the similarity of lamellar morphologies produced under very different crystallization conditions.     

Segmental mobility in the noncrystalline regions of nascent polyethylene synthesized using two different catalytic systems with implications on solid-state deformation

Recently, it has been shown that using a single-site catalytic system it is possible to tailor entanglement density in the amorphous region of a semi-crystalline polymer, such as polyethylene, with a molar mass greater than 1 million g/mol. The synthesized polymer can be processed in its solid-state, along uniaxial and biaxial directions. It also shows strong heating rate dependence on melting invoking kinetics in randomization of chains from crystal to amorphous phase. With the help of solid-state NMR the distinction between amorphous regions of the synthesized and commercially available ultra-high molar mass polyethylene is made. For example, the polymer synthesized under the controlled conditions, using a homogeneous single-site catalytic system, shows faster motion of methylene units from the noncrystalline to the crystalline regions compared to commercially available nascent polyethylene synthesized using a Ziegler–Natta (Z–N) catalyst. The differences in chain diffusion, and the resultant ¹³C polarization transfer from the noncrystalline to the crystalline region, are attributed to the difference in entanglement density arising from the polymerization method employed. The two polyethylene samples investigated are of similar molar mass and crystallinity. Conformational changes caused by deformation of the two samples have been characterized and co-relationship with the entanglement density has been established.     

Oxygen solubility and specific volume of rigid amorphous fraction in semicrystalline poly(ethylene terephthalate)

The existence of rigid amorphous fraction (RAF) in semicrystalline poly(ethylene terephthalate) (PET) is associated with the lamellar stack crystalline morphology of this polymer, the regions where several crystalline lamellas are separated by very thin (20-40 Å) amorphous layers. In contrast, regular or mobile amorphous fraction is associated with much thicker interstack regions. The oxygen transport properties of PET isothermally crystallized from the melt (melt-crystallization) or quenched to the glassy state and then isothermally crystallized by heating above T_g (cold-crystallization) were examined at 25 °C. Explanation of unexpectedly high solubility of crystalline PET was attributed to the formation of RAF, which in comparison with mobile amorphous phase is constrained and vitrifies at much higher than T_g temperature thus developing an additional excess-hole free volume upon cooling. Measurements of crystallinity and jump in the heat capacity at T_g were used to determine the amount of mobile and rigid amorphous fractions. Overall oxygen solubility was associated with the solubility of mobile and rigid amorphous fractions. The oxygen solubility of the RAF was determined and related to the specific volume of this fraction. The specific volume of the RAF showed a direct correlation with the crystallization temperature. It was shown that upon crystallization from either melt or glassy state, the constrained between crystalline lamellas PET chains consisting of the RAF, vitrify at the crystallization temperature and resemble the glassy behavior despite high temperature. When cooled to room temperature, the RAF preserves a memory about the melt state of polymer, which is uniquely defined by the crystallization temperature.     

Toughening semicrystalline poly(lactic acid) by morphology alteration

The incorporation of the triblock copolymer (PDLA-PEG-PDLA) into Poly(l-Lactic Acid) (PLLA) has produced a semicrystalline polymer of substantial modulus and strength. These improvements in mechanical properties could potentially increase the utility of this biomass-based polymer. The blended samples have a continuous amorphous phase with crystalline regions being the discontinuous portion. Micro-Raman spectroscopy revealed that a stereocomplex involving PDLA and PLLA chains exists in the crystalline region. It can be concluded that the poly(ethylene glycol), the flexible midblock component, is necessarily dispersed in these crystalline regions. Both morphological features can contribute to the improvement in mechanical properties. Therefore, the successful toughening of PLA may be achieved due to several mechanisms working synergistically.     

Cold crystallization of poly(ethylene naphthalene-2,6-dicarboxylate) by simultaneous measurements of X-ray scattering and dielectric spectroscopy

The isothermal cold crystallization of poly(ethylene naphthalene-2,6-dicarboxylate) was investigated by simultaneous small and wide angle X-ray scattering and dielectric spectroscopy (DS). By this experimental approach, simultaneously collected information was obtained about the specific changes occurring in both crystalline and amorphous phases during crystallization, namely about the chain ordering through wide angle X-ray scattering, about the lamellar crystals arrangement by means of small angle X-ray scattering, and about the amorphous phase evolution by means of DS. The results indicate that average mobility of the amorphous phase suffers a discontinuous decrease upon passing from the primary to the secondary crystallization regime. We interpret these results assuming that the restriction to the mobility of the amorphous phase occurs mainly in the amorphous regions between the lamellar stacks and not in the amorphous regions within the lamellar stacks.     

Influence of polymer molecular weight on the solid-state structure of PEG/monoolein mixtures

The polar lipid monoolein (MO) and poly(ethylene glycol), PEG, of different molar mass (1500, 4000 and 8000) were melted, mixed and left to solidify at room temperature. Analysis of the solid mixtures by differential scanning calorimetry (DSC) and small angle X-ray scattering (SAXS) revealed that a phase separation occurs when MO is present in sufficient amounts. The molecular weight of the polymer determines the amount of MO that has to be added before a separate MO phase can be detected. To further understand this behaviour, the folding of the polymers and the thickness of the amorphous domains within the lamellar structure of PEG were determined by calculation of the one-dimensional correlation function from the experimental SAXS data. It revealed that the presence of MO makes the crystalline domains of PEG 1500, which crystallizes unfolded, increase at the expense of the amorphous domains. PEG 4000 and PEG 8000 obtain a higher degree of folding when the MO content in the mixtures increases. Furthermore, a second form of MO was detected when it phase separated from PEG 1500 and 4000. This behaviour was argued to be due to the secondary crystallization of the PEGs.     

Diffusivity of n-hexane in poly(ethylene-stat-octene)s assessed by molecular dynamics simulation

Molecular dynamics simulations have been used to study diffusion of n-hexane in wholly amorphous poly(ethylene-stat-octene)s with comonomer contents ranging from 0 to 11.5 mol%. The branches in the polymer increased the specific volume by affecting the packing of the chains in the rubbery state in accordance with experimental data. The diffusion of n-hexane at penetrant concentrations between 0.5 and 9.1 wt% was simulated within time-scales between 0.1 and 0.2 μs. The penetrant diffusivity unexpectedly decreased with increasing comonomer content. The penetrant molecule motion statistics showed that systems with high comonomer content showed a greater tendency for short distance motion (over a sampling period of 3 ps) whereas the systems with lower comonomer content showed penetrant motion over longer distances. It seems that the branches retarded local chain mobility of the polymer thereby trapping the penetrant molecules. All systems studied showed a minimum in penetrant diffusivity at ca. 1 wt% n-hexane and a marked increase in diffusivity at higher penetrant concentrations. The volumetric data for the different polymer-penetrant systems were consonant with additional volumes of the different components. Comparison between simulated diffusivities (for a wholly amorphous polymer) and experimentally obtained diffusivity data for semicrystalline polymers showed that constraining effect of the crystals were substantial for the highly crystalline systems and that it gradually decreased with decreasing crystallinity.     

The amorphous contribution to the modulus of a semi-crystalline polymer

The amorphous contribution to the Young's modulus of a semi-crystalline polymer is calculated for two morphologies: the spherulite and the stacked lamellae structure. Four types of amorphous chains are considered: bridges (or tie molecules); cilia; loops; and floating, unattached chains. The statistics of a polymer chain between two, infinite, impenetrable, parallel walls are used in the modulus calculation. It is found that for each type of amorphous chain, the Young's modulus is greater in the stacked lamellae structure than in the spherulite. The Young's modulus of a cilium, loop and floating chain all increase with increasing chain contour length while the Young's modulus of a bridge passes through a minimum value. The behavior of the Young's modulus as a function of temperature is analogous. These results are discussed in terms of the relative importance of crystalline lamellar impenetrability and the inherent elastic nature of the amorphous chains, in the Young's modulus behavior.     

Morphological responses in thermally conditioned linear low density polyethylene

An octene-modified linear low density polyethylene has been used to examine the mechanisms involved during thermal annealing. Annealing temperatures ranged from 60 to 100°C. Annealing results in crystallinity increments and these respond to two concurrent effects. One involves the segregation from crystalline regions of low molecular weight moieties in the polymer's molecular weight distribution; the other is lamellar thickening, leading to the formation of more highly perfected crystalline domains. In the present polymer, the two effects were found to be in balance at annealing temperatures near 80°C leading to the optimum distribution of crystalline regions in the amorphous portions of the polymer. The effect of thermal conditioning on mechanical properties of the polymer was illustrated in terms of the initial modulus and the polymer's yield strength. The twin mechanisms of molecular fractionation and lamellar thickening were found to influence both of the mechanical property parameters.     

Molecular simulations of the solubility of gases in polyethylene below its melting temperature

We have employed Monte Carlo simulations in the osmotic ensemble to study the solubility of three different gases (N₂, CH₄, CO₂) in polyethylene. The simulations are performed at temperatures below the polymer melting point. Although under such conditions, polyethylene is in a semicrystalline state, we have used simulation boxes containing only a purely amorphous material. We show that under such circumstances, computed solubilities are 4-5 times larger than experimental data. We therefore introduce an original use of the osmotic ensemble to implicitly account for the effects of the complex morphology of semicrystalline materials on gas solubility. We have made the assumption that i) the network formed by polymer chains trapped between different crystallites and ii) the changes in local density from crystalline regions to purely amorphous regions, may be both represented by an ad-hoc constraint exerted on the amorphous phase. A single constraint value emerges, independent of the gas nature, characteristic of the crystalline degree of the polymer. It is concluded that the role of this constraint is mostly to reproduce the effective density of the permeable phase of the real material, indirectly giving insights into the morphology of a semicrystalline polymer.     

Twisting orientation and the role of transient states in polymer crystallization

A possible connection is suggested and explored between non-planer crystal habits in banded polymer spherulites and disordered chain folding in polymers crystallized relatively rapidly from the melt. It is proposed that, when lateral growth faces and fold surfaces are not orthogonal (because chain stems are tilted with respect to the lamellar normal), different degrees of disorder develop at opposite fold surfaces. Resulting differences in surface stress give rise to bending moments, but these are likely to be of transient existence. It is shown that, on this basis, an appealingly simple rationale can be developed to account for the complex and hitherto puzzling observations of Bassett and Hodge on polyethylene spherulites, including S-bending and non-uniform axial twisting in lamellae, and also an empirical correlation between these deformations. Much depends, however, upon interactions between interleaved crystals and upon relaxation of bending moments. Existing evidence in support of the rationale is outlined. Implications with respect to polymers other than polyethylene, and to kinetics of crystallization in general, are discussed briefly. Calculations concerning axial twisting under the influence of surface stresses suggest that the twisted crystals incorporate twist boundaries, possibly formed by aggregation of dislocations generated during the growth of what must initially be relatively disordered crystals. The ‘chiral’ factor determining handedness of twisting in a given crystal is the direction in which chain stems tilt with respect to the lamellar normal.     

Effect of supercritical CO2 on phase structure of PEO/PVAc blends evaluated from SAXS absolute intensity measurement

The effect of supercritical CO₂ on the morphological structure of crystalline/amorphous PEO/PVAc blends was investigated by means of SAXS with the measurement of absolute scattering intensity. The morphological structure of PEO/PVAc exhibited a considerable change upon CO₂ treatment as demonstrated by the drastic increase of scattering intensity, or the enhancement of electron density contrast between the crystalline and amorphous layers in the lamellar stacks, resulting from the swelling of amorphous PEO via the incorporation of CO₂ into the interlamellar (IL) regions and/or the expulsion of PVAc from the IL regions. Upon CO₂ treatment, the crystal and amorphous layer thickness (l_c and l_a, respectively) were both increased. Compared with the increase of l_a, the increase of l_c was relatively significant and was attributed to the occurrence of melting and recrystallization during CO₂ treatment leading to thicker PEO crystals via a depression of equilibrium melting temperature and/or an increase of crystal fold surface free energy. The measured electron density contrast revealed that the distance of segregation in PEO/PVAc blends involved the extralamellar segregation before CO₂ treatments and the swelling of interlamellar region dominated the drastic increase of scattering intensity after CO₂ treatments. The finding of extralamellar morphology was consistent with the magnitude of volume fraction of lamellar stacks in the blends. The lamellar size distribution appeared to be broader and the lamellar stacks more disorganized for the blends after CO₂ treatments according to SAXS one-dimensional correlation function profiles.     

Imaging of nonlinear optical response in biopolyesters via second harmonic generation microscopy and its dependence on the crystalline structures

Nonlinear optical response in various polyhydroxyalkanoates (PHAs) was investigated via second harmonic generation microscopy (SHGM). It was revealed that the second harmonic generation (SHG) efficiency depended on both the polymer chemical structure and the crystalline structure. Among the PHAs studied, the microbial polyesters, poly(R-3-hydroxybutyrate) (PHB) and poly(R-3-hydroxyvalerate) (PHV) showed strongest SHG activity, which could be attributed to hydrogen bonding that enhanced hyperpolarizability of the carbonyl groups in the crystalline lamellar core, and the noncentrosymmetric arrangement of the SHG moieties. The β- and γ-type poly(β-propiolactone) demonstrated different SHG efficiency due to the different packing scheme of the chain stems in the crystal lattice despite the same chain conformation. In addition, SHG response in the banded spherulite varied with the lamellar orientation. Furthermore, SHGM was applied for 3-D imaging of PHB spherulite in PHB/poly(?-caprolactone) blends via optical sectioning of the thick film at different depths. For PHB/poly(l-lactide) (PLLA) blends, SHGM revealed that the PHB twisting lamellae formed from the melt confined between the preformed PLLA twisting lamellae had the same twisting period as the latter, which could not be observed under polarized optical microscope. Due to the advantages, SHGM is expected to find more applications in characterization of nonlinear optical (NLO) materials with heterogeneous structures.     

Constraints in semicrystalline polymers: Using quasi-isothermal analysis to investigate the mechanisms of formation and loss of the rigid amorphous fraction

The nanoscale phase behavior of a semicrystalline polymer is important for mechanical, thermal, optical and other macroscopic properties and can be analyzed well by thermal methods. Using quasi-isothermal (QI) heat capacity measurements, we investigate the formation behavior of the crystalline, mobile amorphous, and rigid amorphous fractions in poly(trimethylene terephthalate), PTT. The crystal and rigid amorphous phases comprise the total solid fraction in PTT at temperatures above T_g, the glass transition temperature of the mobile amorphous fraction. PTT was quasi-isothermally cooled step-wise from the melt which causes its crystalline fraction to be fixed below 451 K. Between the high temperature fulfillment of the T_g step and 451 K, the temperature dependent rigid amorphous fraction (RAF) is completely determined. For PTT, most of the RAF vitrifies between 451 K and T_g step by step during QI cooling after the crystals have formed. The constraints imposed by the crystal surfaces reduce the mobility of the highly entangled polymer chains. We suggest the vitrification of RAF proceeds outward away from the lamellar surfaces in a step by step manner during QI cooling. Upon reheating, devitrification of RAF occurs at a temperature above its previous vitrification temperature, due to the effects of densification brought by physical aging during the long period of quasi-isothermal treatment. Finally, we consider recent concepts related to jamming, which have been suggested to apply to filled polymer systems, and may also be applicable in describing constraints exerted by crystal lamellae upon the RAF.     

Relationship between the crystallization behavior and the warpage of film‐insert‐molded parts

The dimensional variation of an injection‐molded, semicrystalline polymer part is larger than the variation of an amorphous polymer part because the shrinkage of a crystalline polymer is generally greater than the shrinkage of an amorphous one. We investigated the warpage of film‐insert‐molded (FIM) specimens to determine the effect of the crystallization behavior on the deformation of FIM parts. More perfect crystalline structures and higher crystallinity developed in the core region of the FIM specimens versus other regions. Relatively imperfect crystalline structures and low crystallinity developed in the adjacent regions of the inserted films, whereas a thin, amorphous skin layer developed in the adjacent regions of the metallic mold wall. The crystallizable substrate in the FIM specimens caused very large warpage because nonuniform shrinkage occurred in the thickness direction of the specimens. Therefore, the warpage of an experimentally prepared FIM poly(butylene terephthalate) specimen was greater than that predicted numerically because of its complex crystallization behavior. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011