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.     

Distribution kinetics of polymer crystallization and the Avrami equation

Cluster distribution kinetics is adopted to explore the kinetics of polymer crystallization. Population balance equations based on crystal size distribution and concentration of amorphous polymer segments are solved numerically and the related dynamic moment equations are also solved. The model accounts for heterogeneous or homogeneous nucleation and crystal growth. Homogeneous nucleation rates follow the classical surface-energy nucleation theory. Different mass dependences of growth and dissociation rate coefficients are proposed to investigate the fundamental features of nucleation and crystal growth. A comparison of moment solutions with numerical solutions examines the validity of the model. The proposed distribution kinetics model provides a different interpretation of the familiar Avrami equation.     

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

We 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     

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.     

A distribution kinetics approach for crystallization of polymer blends

The cluster distribution approach is extended to investigate the crystallization kinetics of miscible polymer blends. Mixture effects of polymer-polymer interactions are incorporated into the diffusion coefficient. The melting temperature, activation energy of diffusion, and phase transition enthalpy also depend on the blending fraction and lead to characteristic kinetic behavior of crystallization. The influence of different blending fractions is presented through the time dependence of polymer concentration, number and size of crystals, and crystallinity (in Avrami plots). Computational results indicate how overall crystallization kinetics can be expressed approximately by the Avrami equation. The nucleation rate decreases as the blending fraction of the second polymer component increases. The investigation suggests that blending influences crystal growth rate mainly through the deposition-rate driving force and growth-rate coefficient. The model is further validated by simulating the experimental data for the crystallization of a blend of poly(vinylidenefluoride)[PVDF] and poly(vinyl acetate)[PVAc] at various blending fractions.     

Gel electrophoretic mobility of single-stranded DNA: the two reptation field-dependent factors

The reptation model is the dominant theory in understanding the electrophoretic separation of single-stranded DNA molecules in gels or entangled polymer solutions. Recently, we showed that the Ogston and reptation regimes are separated by an entropic trapping regime at low field intensities. Here, we report the first comparison of the field-dependent part of the DNA mobility for both small and long reptating molecules. We show that both mobilities increase linearly with field intensity, with the mobility of the longer (comigrating) fragments increasing faster than that of the smaller ones. We compare our results to the predictions of the biased reptation model.     

磁场影响聚合物本体结晶动力学的机理分析

在经典的热力学理论基础上,探讨了磁场对聚合物本体结晶过程的成核与生长的影响,建立了相关结晶动力学理论方程.初步认为,磁场产生的＂磁结晶效应＂可能是由于晶相与非晶相之间磁化率差异导致了两相之间磁化能的差异,也可能由于聚合物体系在结晶前会形成一种有序相,减小了体系的熵值,进而改变了结晶过程中的体系自由能,影响其成核与晶体生长,乃至整个结晶动力学方程.利用Matlab软件结合PLLA的各结晶参数值,绘制了结晶自由能与各成核临界参数之间的函数图像.结果表明,在低过冷度下,较小的自由能扰动可能导致较大的晶核临界参数变化.     

均聚物结晶与熔融化的稳态和亚稳态转变统计理论

基于多重微晶网络结构模型和分子分凝机制建立了高分子晶体的微晶核-和微晶粒-高分子链组模型,推导出了平衡态下高分子预结晶动力学方程,计算出了平衡态下不同尺寸微晶核-和微晶粒-高分子链组的几率分布函数.建立了非稳态下不同尺寸的微晶核-高分子链组的成核演化方程和微晶粒-高分子链组的增长演化方程,求解一般状态下的两个演化方程后,得到了不同时间和不同尺寸的微晶核-和微晶粒-高分子链组的一般密度分布函数.最后根据成核自由能和增长自由能对晶核和晶粒的尺寸大小的依赖性,提出了微晶核-高分子链组和微晶粒-高分子链组存在稳定性的热力学条件和动力学条件,成功地表征为三个特征区(稳态、亚稳态和非稳态).     

Small-angle x-ray scattering and crystallization kinetics of poly(ethylene terephthalate) crystallized in a liquid environment

By small-angle x-ray scattering, a systematic investigation was performed of the long spacing of poly(ethylene terephthalate) (PET) crystallized in a liquid environment. The results indicated that the measured long spacings were temperature dependent and apparently relatively insensitive to liquid type under the conditions studied. The kinetic nucleation model of polymer crystallization was found to adequately explain this dependence. The differences in the long spacings between thermal and liquid-induced crystallization were in part rationalized in terms of the suspected supercoolings involved in the respective processes. Calculation of the spherulite growth rates for liquid-induced crystallization was made on the basis of the kinetic nucleation model and the classic theory of polymer–diluent crystallization. The results were shown to agree with inferential experimental observations of these growth rates and to elucidate the physics underlying liquid–induced crystallization. Finally, use of this growth rate theory in conjunction with a previous model for overall crystallization kinetics was shown to adequately describe and predict the diffusion-limited kinetics observed experimentally for most liquid-induced crystallization situations.     

Estimation of the nucleation and crystal growth contributions to the overall crystallization energy barrier

Classical kinetic theories of polymer crystallization were applied to isothermal crystallization kinetics data obtained by polarized optical microscopy (PLOM) and differential scanning calorimetry (DSC). The fitted parameters that were proportional to the energy barriers obtained allow us to quantitatively estimate the nucleation and crystal growth contributions to the overall energy barrier associated to the crystallization process. It was shown that the spherulitic growth rate energy barrier found by fitting PLOM data is almost identical to that obtained by fitting the isothermal DSC crystallization data of previously self‐nucleated samples. Therefore, we demonstrated that by self‐nucleating the material at the ideal self‐nucleation (SN) temperature, the primary nucleation step can be entirely completed and the data obtained after subsequent isothermal crystallization by DSC contains only contributions from crystal growth or secondary nucleation. In this way, by employing SN followed by isothermal crystallization, we propose a simple method to obtain separate contributions of energy barriers for primary nucleation and for crystal growth, even in the case of polymers where PLOM data are very difficult to obtain (because they exhibit very small spherulites). Comparing the results obtained with poly(p‐dioxanone), poly(ε‐caprolactone), and a high 1,4 model hydrogenated polybutadiene, we have interpreted the differences in primary nucleation energy barriers as arising from differences in nuclei density. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1478–1487, 2008     

Monte Carlo simulations of the exchange kinetics of polymers adsorbed on a solid surface

The exchange kinetics of polymers adsorbing on a solid surface is extensively studied by dynamic Monte Carlo simulations. A model employed simulates a semidilute polymer solution placed in contact with a solid surface that attracts polymer segments by the adsorption interaction (χ_s). The exchange process of polymer chains, between the solution and the adsorbed polymer layer, is examined under various conditions. The exchange kinetics shows two characteristic regimes with increasing chain length. One is the diffusion‐controlled regime found with a small χ_s , and the other the detachment‐controlled regime with a large χ_s . These two regimes are well described by a kinetic theory. Various dynamic quantities show that the diffusion‐controlled regime is not due to sluggish dynamics near the surface, but rather to bulk diffusion of chains. The diffusion‐controlled regime found in this study is considered to appear at the high temperature limit.     

The growth of crystals in solution

The crystallization of sparingly soluble salts from their aqueous supersaturated solutions is discussed from the standpoint of two important applications; scale formation and biological mineralization. Theories of crystal growth are outlined and the importance of kinetic factors in determining the nature of the growing phases is discussed. The kinetic factors can be studied by using a highly reproducible seeded growth technique and under certain conditions secondary nucleation can also be induced on the surface of the inoculating seed crystals. The kinetics of crystallization of the alkaline earth surfaces and the calcium phosphates is discussed. In the latter systems, temperature, supersaturation, surface concentration, pH, ionic strength and the presence of foreign ions are important in determining the nature of the phase which grows on the added seed crystals. The mechanism of the retardation of crystal growth by added crystallization inhibitors is illustrated by the influence of organic phosphonate molecules upon the precipitation of calcium carbonate.     

Temperature effects for isothermal polymer crystallization kinetics

We adopt the cluster size distribution model to investigate the effect of temperature on homogeneous nucleation and crystal growth for isothermal polymer crystallization. The model includes the temperature effects of interfacial energy, nucleation rate, growth and dissociation rate coefficients, and equilibrium solubility. The time dependencies of polymer concentration, number and size of crystals, and crystallinity (in Avrami plots) are presented for different temperatures. The denucleation (Ostwald ripening effect) is also investigated by comparing moment and numerical solutions of the population balance equations. Agreement between the model results and temperature-sensitive experimental measurements for different polymer systems required strong temperature dependence for the crystal-melt interfacial energy.     

Molar mass dependent growth of poly(epsilon-caprolactone) crystals in Langmuir films

Poly(epsilon-caprolactone) (PCL) samples with number average molar masses (Mn) ranging from 3.5 to 36 kg.mol-1 exhibit molar mass dependent nucleation and growth of crystals, crystal morphologies, and melting properties at a temperature of 22.5 degrees C in Langmuir films at the air/water (A/W) interface. At surface area per monomer, A, greater than approximately 0.37 nm2.monomer-1, surface pressure, Pi, and surface elasticity exhibit molar mass independent behavior that is consistent with a semidilute PCL monolayer. In this regime, the scaling exponent indicates that the A/W interface is a good solvent for the liquid-expanded PCL monolayers. Pi-A isotherms show molar mass dependent behavior in the vicinity of the collapse transition, i.e., the supersaturated monolayer state, corresponding to the onset of the nucleation of crystals. Molar mass dependent morphological features for PCL crystals and their subsequent crystal melting are studied by in situ Brewster angle microscopy during hysteresis experiments. The competition between lower segmental mobility and a greater degree of undercooling with increasing molar mass produces a maximum average growth rate at intermediate molar mass. This behavior is analogous to spherulitic growth in bulk PCL melts. The plateau regions in the expansion isotherms represent the melting process, where the polymer chains continuously return to the monolayer state. The magnitude of Pi for the plateau during expansion decreases with increasing molar mass, indicating that the melting process is strongly molar mass dependent.     

聚乳酸的非等温结晶行为

用差示扫描量热法(DSC)研究聚乳酸(PLA)从熔体及玻璃态为初始条件下的非等温结晶行为,采用Ozawa方程、Mo法、Khanna法和Kissinger法对结晶动力学参数进行计算处理。 实验结果表明,这几种方法均适合处理PLA的非等温结晶过程,而Khanna法提出的结晶速率系数(CRC)能够方便地评价PLA相对结晶速率的大小。 PLA从玻璃态升温结晶比从熔体降温结晶容易得多,升温过程有利于晶核生成,而降温有利于晶体生长。 升温结晶时,升温速率2.0 ℃/min时,结晶焓(ΔH_c)达到最大为27.1 J/g。 从熔体等速降温过程中,随着冷却速率的降低ΔH_c单调增加,冷却速率为0.25 ℃/min时ΔH_c增加到28.3 J/g。 在较低温度下从玻璃态结晶,主要表现为异相成核的二维生长方式。 在较高的温度下从玻璃态升温结晶及从熔体冷却结晶时,以均相成核的三维生长方式结晶为主。 与升温过程相比,冷却不利于晶核的生成,所以导致冷却过程总体ΔH_c偏低,扩散活化能偏大。     

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.     

Model of processing‐induced microstructure formation in polymeric materials

A general, mechanistic, kinetic model is presented to predict polymer microstructure formation during processing. Applications of the model are presented for three specific cases. The model represents polymer molecules as Kramers chains which may or may not have nucleated. Three forces (hydrodynamic, Brownian, and intermolecular) that act on polymer molecules during processing were considered, which resulted in the presentation of the model as a diffusion equation. The input parameters account for the rheological and thermal history of the polymer melt, the specific type of polymer molecule, and the initial morphology. The solution of the diffusion equation yields a probability distribution function from which the transient and equilibrium morphology can be determined. The three specific cases were chosen to illustrate the versatility of the model and include: the extensional flow‐induced growth of extended chain crystals; the orientation of stiff molecules in solution undergoing shear flow well above the crystallization temperature; and the formation of folded chain vs. extended chain crystals in an extensional flow. Data are available for the first two cases and agree favorably with the model predictions. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2571–2585, 1999     

Enthalpy relaxation in the cooling/heating cycles of polypropylene/organosilica nanocomposites: I: Non-isothermal crystallization

Non-isothermal crystallization of the neat isotactic polypropylene homopolymer (PP-0) and of a series of nanocomposites (PNC) containing up to 4.68 vol.% of organosilica was studied in the standard DSC mode during constant-rate cooling from the melt state.Analysis of the nucleation parameters derived from cooling rate dependencies of the temperatures for the onset of crystallization exotherms revealed a slight but systematic increase of the nucleation barrier for lamellar crystallization of PP in the PNC concomitant to stronger restrictions to transport of PP segments across the melt/lamellar crystal interface. The overall crystallization rate data for the PNC were consistent with the assumption of two separate contributions from the initial (unconstrained), and the subsequent (constrained) growth mechanisms, respectively.The obtained results were considered as evidence for the coexistence in undercooled PP melts of the PNC of initial crystal nucleation and growth sites characteristic for the neat PP-0, and the basically different sites (presumably, PP chains anchored by both ends to the surfaces of two adjacent nanoparticles).     

Confined crystallization of cylindrical diblock copolymers studied by dynamic Monte Carlo simulations

We report dynamic Monte Carlo simulations of polymer crystallization confined in the cylindrical microdomains of diblock copolymers. The microdomains were prepared via spontaneous microphase separation from homogeneous melt, and the major component was then frozen in a vitreous amorphous state to make a hard confinement to the crystallization of the minor component. We found that during the isothermal crystallization at high temperatures, crystal orientations are dominantly perpendicular to the cylinder axis at the early stage of crystal nucleation and remain to the final state; while if the block junctions are broken before crystallization, crystal orientations are dominantly parallel at the early stage of crystal nucleation, and eventually other orientations take the place of parallel preferences. Analysis of bond orientations in the heterogeneous melts demonstrates the microscopic origin of oriented crystal nucleation.     

Confinement Effects on the Crystallization of Poly(ethylene oxide) Nanotubes

In this work, we show the effects of nanoconfinement on the crystallization of poly(ethylene oxide) (PEO) nanotubes embedded in anodized aluminum oxide (AAO) templates. The morphological characteristics of the hollow 1D PEO nanostructures were evaluated by scanning electron microscopy (SEM). The crystallization of the PEO nanostructures and bulk was studied with differential scanning calorimetry (DSC) and wide-angle X-ray diffraction (WAXD). The crystallization of PEO nanotubes studied by DSC is strongly influenced by the confinement showing a strong reduction in the crystallization temperature of the polymer. X-ray diffraction (XRD) experiments confirmed the isothermal crystallization results obtained by DSC, and studies carried out at low temperatures showed the absence of crystallites oriented with the extended chains perpendicular to the pore wall within the PEO nanotubes, which has been shown to be the typical crystal orientation for one-dimensional polymer nanostructures. In contrast, only planes oriented 33, 45, and 90° with respect to the plane (120) are arranged parallel to the pore's main axis, indicating preferential crystal growth in the direction of the radial component. Calculations based on classical nucleation theory suggest that heterogeneous nucleation prevails in the bulk PEO whereas for the PEO nanotubes a surface nucleation mechanism is more consistent with the obtained results.