Polymer crystallization from the melt at large undercoolings

Consideration of crystallization kinetics in high-molecular-weight polymers shows that adjacent reentry is unlikely in melt crystallization and that sections of individual chains will crystallize concurrently at several sites. Hence the characteristic crystallization process will be that of a loop of chain with both ends attached to different sites on the crystal surface. Analysis of this process leads to predictions of crystallinity values for various conditions of chain mobility in the crystal and of entanglements in the amorphous regions. Observations on polymers crystallized at high undercoolings where a crystallinity of about 30% is usually observed suggest that the common case is that of a highly entangled amorphous layer and rapid, local annealing of the chains but with no long-range motion in the crystal. This model of loop crystallization is shown to agree with available small-angle neutron scattering data. The overall crystallization kinetics are in accord with surface nucleation controlled growth which also arises out of the Lauritzen-Hoffman adjacent reentry model and has been shown to fit experimental results on growth rates.     

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.     

聚合物片晶中链折叠模型的对称性讨论

 本文从对称的观点讨论了在聚合物片晶中链折叠的问题.提出只有当分子链在折向相反方向后对称性不改变时,近邻规整折叠才是可能的.它是近邻折叠的必要条件.根据折叠时“对称性不变”这一论点,可以预言分子链近邻规整折叠的可能性及可能的折叠方向.     

聚合物片晶中链折叠模型的对称性讨论

本文从对称的观点讨论了在聚合物片晶中链折叠的问题.提出只有当分子链在折向相反方向后对称性不改变时,近邻规整折叠才是可能的.它是近邻折叠的必要条件.根据折叠时“对称性不变”这一论点,可以预言分子链近邻规整折叠的可能性及可能的折叠方向.     

Rough-surface crystallization: Some applications to poly(ethylene oxide)

A model incorporating a rough (disordered) crystal growth surface is capable of treating many of the observations and measurements on the crystal growth of short chains of poly(ethylene oxide) from the melt. A simple preliminary treatment if presented which aims primarily to analyze the growth rate data within one growth “branch,” i.e., for a regime in which crystal thickness is approximately constant. Under these conditions the growth rate is approximately linear with crystallization temperature, as expected for rough growth surfaces, but not for smooth (faceted) ones. Simulation results are included which are in agreement with a simple equation and with experiment. The analysis enables the growth rates for different branches to be compared in a systematic way. A very steep decrease in growth rate with increasing crystal thickness is clearly illustrated, together with some influence of molecular weight. The general trend for chain folding can be seen as a consequence of this steep decrease. Parallel work on systems in which crystal thicknesses vary continuously with crystallization temperature led to the realization that “rounding off” will occur at the crystal perimeter and that this will give rise to an entropic barrier for the crystal advance. This argument is presented in the context of extended-chain and once-folded crystallization, from which it is clear that growth rates should be much lower as crystal thicknesses increase, and for folded-chain as compared with extended-chain crystals. Different morphologies are interpreted in terms of changes in surface structure which are probably due to kinetic as well as equilibrium effects.     

Crystal growth rate in ultrathin films of poly(ethylene oxide)

Many dynamical properties of polymers, including segmental relaxation and chain diffusion, exhibit anomalies in thin‐film samples. We extend the studies of thin‐film dynamics to the case of semicrystalline polymers and present a study of the crystal growth rate for thin films of poly(ethylene oxide). We used optical microscopy and quartz crystal microbalance techniques to characterize the kinetics of crystallization for films with thicknesses from 40 to 1000 nm for a range of temperatures near the melting point. A remarkable slowing down of the crystal growth is observed at all temperatures studied for films with a thickness of less than ～100 nm. The results can be used to suggest reductions of the mobility of chains at the crystal/amorphous interface. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2615–2621, 2001     

Studies on polyethylene crystallized at unusually high supercoolings: Fold length,habit, growth rate,epitaxy

The newly arisen possibility of crystallizing polyethylene at supercoolings much higher than were achievable previously has enabled the study of crystallization to be extended in several directions. Thus, fold length can be followed down to previously inaccessibly low crystallization temperatures, in the present case with sharp fractions, demonstrating the essential independence of the fold length of molecular weight. In this context the thinnest isolated crystal reported so far was obtained (ca. 6 nm). The faceted nature of crystals grown at such low temperatures and high rates has been noted, and is in line with new conceptions of polymer crystal growth. A previous observation of exceptionally high crystal growth rate (ca. 2 m/s) has been supplemented by measurements over a range of crystallization temperatures and the results found to be in good agreement with the predicated regime III behavior in the least theory of Hoffman. Observations of epitaxy on mica, while broadly in line with those by Lovinger, were revealing in several respects. Among these the observation that the substrate can influence the fold length when the chains are parallel to the substrate plane remains unexplained and puzzling.     

Understanding the growth rates of polymer cocrystallization in the binary mixtures of different chain lengths

Polymer materials often contain a polydispersity of molecular lengths. We studied the linear growth rates of polymer lamellar crystals in the binary mixtures of different chain lengths by means of dynamic Monte Carlo simulations. Both chain lengths were chosen large enough to perform chain folding upon crystal growth but not very large to avoid the effect of chain entanglement in the bulk phase. We found that the crystal growth rates exhibit a linear dependence upon the compositions of mixtures. This linear relation implies that the overall crystal growth rates are integrated by the separate contributions of variable-length single polymers, supporting the model of intramolecular crystal nucleation. In each event of crystal growth of single polymers, long chains yield more crystallinity than short chains. This high efficiency explains higher crystal growth rates of long chains than that of short chains, and the explanation is quite different from the traditional view on the basis of their different melting points. In addition, with a partial release of sliding diffusion for crystal thickening, a new dependence of crystal growth rates occurs near the dilute end of long-chain compositions at high temperatures, which can be attributed to the preference of integer-number chain folding at the crystal growth front. The preferred fold lengths may vary with chain lengths and thus influence the crystal growth rates.     

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.     

Crystallization during polymerization of poly-p-xylylene

Crystallization during polymerization of p-xylylene from the gas phase has been studied between 200 and ?196°C. From room temperature to ?17°C the polymer crystal morphology changes in that the crystallinity decreases. In this range the process is thought to be of the successive polymerization and crystallization type. The morphology is in agreement with this mechanism, of the folded-chain β-polymorph type with proper epitactic orientation of the chains with respect to the support surface. At ?78°C an intermediate, poorly crystallized polymer results. At 196°C the reaction is most likely of the simultaneous polymerization and crystallization type. The morphology is, in agreement with the changed mechanism, of a metastable, irregularly folded β-polymorph type with no orientation of the chains relative to the support surface. No significant changes in molecular weight were observed in the polymers produced between 26 and ?196°C.     

Stress induced crystallization in thermoplastic elastomers

Thermoplastic elastomers show considerable flow if they are subjected to large strains. To investigate the influence of stress induced crystallization, elastomers showing stress induced crystallization are synthesized by hydrogenation of poly(butadienes) and poly(styrene-b-butadiene-b-styrene) block polymers. The influence of the methylene sequence length on the crystallization behaviour is evaluated. From stress relaxation experiments, the crystallization kinetic is analyzed. Heterogeneous nucleation and fibrillar crystal growth is detected for all block polymer systems. The kinetic behaviour is described by a preorientation of elastomer chains near the domain surface.Dedicated to Prof. Dr. R. Kosfeld on the occasion of his 60th birthday.     

Growth of n-Paraffin Crystals from Solution and the Effect of Polymers on Themy

The crystallization of n-paraffins has been investigated. The crystallizations were carried out in dilute solution under carefully defined cooling conditions. In some of the runs small quantities of synthetic polymers which were similar in structure to the n-paraffins were added to the solutions. The studies have shown that the habits of the crystals are very sensitive to the growth conditions, that n-paraffins are potent mutual crystal modifers, and that the addition of small amounts of polymers can affect the crystal growth considerably.     

The onset of chain folding in ultralong n-alkanes: An electron microscopic study of solution-grown crystals

Crystallization of extremely pure n-C₁₉₈H₃₉₈ from dilute solution is investigated by electron microscopy and differential scanning calorimetry. This long-chain alkane is capable of crystallizing in the extended form or of folding once or twice and thus provides useful insights into the fundamental process of chain-folded crystal growth. Crystallization conditions that give rise to the different crystal types are identified by measuring the variation in dissolution temperature with crystallization temperature and crystallization time. Examples of each type of crystal are examined in the electron microscope using various techniques. From shadow length measurements we find the crystals to have thicknesses corresponding to integer fractions of the extended chain length, in agreement with previous findings on this and similar materials. However, contrary to all past experience with polyethylenes, refolding was found to occur while in the solvent. This refolding, which here takes place isothermally, also occurs in integral steps, with wider implications discussed. The crystal morphologies are similar in many respects to those obtained from polyethylene; in particular the crystals containing once-folded chains are often lozenge shaped with the folds along {110} growth planes, thus producing clearly defined sectorization made visible by several techniques. Electron diffraction studies show that the chains are substantially perpendicular within the crystals in all cases. In addition, differences in surface regularity between the different crystal types revealed by decoration techniques are discussed.     

Limited Fraction of Crystallized Side Chains in Bottlebrush Poly(n-alkyl methacrylate)s

Crystallinity of bottlebrush polymers due to side chain crystallization has been considered to be related to the length of the side chains only under the assumption of complete participation of crystallization by all side chains.Recent experimental results revealed that in poly(n-alkyl methacrylate)s a fraction of side chains could not crystallize due to constraints imposed by the trapped main chain entanglements and required expansion of main chain-main chain distance.This result renders the original simplified consideration of the origin of crystallinity in bottlebrush polymers questionable.In this work,we introduce a new parameter fc,the fraction of crystallizable side chains,to better describe the crystallinity of bottlebrush polymers.A linear relationship between the melting enthalpy and the number of alkyl groups in side chains for bottlebrush polymers reported repeatedly indicates that fc remains essentially unchanged when bottlebrush polymers had the same main chain structure and grafting degree but different side chain lengths.The slope of the above-mentioned linear relationship is thus AHCH2×fc,where AHCH2 stands for the melting enthalpy of one mole alkyl group packed into the crystal.With a known value of fc,it is possible to estimate the value of AHCH2.In case of poly(n-alkyl methacrylate)s,we estimated AHCH2 of hexagonal crystal being at most 5.74 kJ/mol with the knowledge of possibly smallest fc of 0.67 obtained from small angle X-ray scattering data.Therefore,the crystallinity of bottlebrush polymer would be calculated based on the equation Xc = fc×Nc/N with N and Nc being the number of alkyl groups in a side chain and those packed in the crystalline structure,respectively.Both chemical structure and grafting degree of bottlebrush polymers affect fc.     

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     

Bioinspired synthesis of calcium carbonate hollow spheres with a nacre-type laminated microstructure

In this Article, we combine the characters of hyperbranched polymers and the concept of double-hydrophilic block copolymer (DHBC) to design a 3D crystal growth modifier, HPG-COOH. The novel modifier can efficiently control the crystallization of CaCO(3) from amorphous nanoparticles to vaterite hollow spheres by a nonclassical crystallization process. The obtained vaterite hollow spheres have a special puffy dandelion-like appearance; that is, the shell of the hollow spheres is constructed by platelet-like vaterite mesocrystals, perpendicular to the globe surface. The cross-section of the wall of a vaterite hollow sphere is similar to that of nacres in microstructure, in which platelet-like calcium carbonate mesocrystals pile up with one another. These results reveal the topology effect of the crystal growth modifier on biomineralization and the essential role of the nonclassical crystallization for constructing hierarchical microstructures.     

Effect of stereosequence length on crystallization kinetics of propylene oxide polymers

Crystallization kinetics of crystalline fractions of propylene oxide polymers made with different catalysts have been studied by isothermal dilatometric and microscopical measurements. Isothermal microscopical measurements indicate that spherulite growth in these polymers proceeds from predetermined nuclei. The half time for spherulitic appearance is less than, but of the same order as, the half time for complete crystallization. Only by taking this factor into account can the dilatometric data be represented by the Avrami equation. The deviation of the crystallization isotherm from that predicted from the microscopical data using the Avrami theory is attributed to a secondary crystallization process taking place within the spherulite. Crystallization continues long after spherulites completely occupy the available volume in the polymer. By assuming that the secondary crystallization proceeds as a first-order process in the uncrystallized, but crystallizable, portions of the melt, it is shown that the crystallization isotherms can be completely described in terms of four parameters. These are: (1) the time constant for the primary crystallization process; (2) the time constant for nucleation; (3) the time constant for the secondary crystallization process, and (4) the extent of secondary crystallization. The important conclusions of these studies are: the rates of nucleation and of spherulitic growth are far more dependent on temperature than on stereoregularity; the ratio of the rate of the secondary crystallization process to that of the primary crystallization process is almost independent of temperature, but increases with increasing stereoregularity of the polymer.     

高分子在氧化铝纳米孔道中受限结晶的研究进展

高分子材料在微纳米尺度常常表现出不同于本体的物理性质.对结晶性高分子来说,在纳米受限空间的成核机理、结晶结构和动力学特征都与本体材料有所不同.本文总结了近年来基于多孔氧化铝纳米模板(AAO)开展的高分子受限结晶的研究进展,重点介绍了本课题组的工作.研究发现,在AAO模板中,高分子结晶的过冷度大大增加,成核机理从本体的异相成核转变为均相成核或表面成核;高分子结晶结构通常表现为各向异性,动力学因素、热力学因素和界面性质均对取向结构有重要影响;受限情况下高分子结晶速率大大降低,表现出"成核控制"的动力学特征;空间受限使高分子结晶度降低,倾向于形成亚稳态晶型.最后,对该领域尚待解决的问题进行了展望.     

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     

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