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.     

Kinetics of polymer crystallization from the melt (calorimetric approach)

Crystallization kinetics for 12 polymers including polyolefins, polyesters, polyurethanes, polysiloxanes was measured by the evolution of heat in a modified Calvet-type calorimeter over wide temperature ranges. The results are analyzed in terms of the Avrami equation and a comparison between calorimetric and dilatometric results is carried out. It is concluded that, although in the majority of cases experimental results do not obey the Avrami equation, for some polymers the agreement is rather good. The Avrami parameter obtained, however, depends on the experimental technique. Possible reasons for this disagreement are discussed. Analysis of the calorimetric crystallization rate in the vicinity of the melting point by using the kinetic theory of crystallization shows that the growth is controlled by surface (two-dimentional) nucleation. Energy parameters for the crystallites were determined and it is shown that the surface energy of the crystallites depends on the molecular structure of the polymer. Temperature dependence of the calorimetric crystallization rate of the polymers for which crystallization rates could be determined above and below the maximum rate are analyzed using a kinetic equation with common approximations for the transport term. The influence of melting conditions on the crystallization rate was studied. The results indicate heterogeneous nucleation in the polymer melt. It is concluded that this may be due both to impurities and to high regularity of macromolecules in the polymer melt.     

Nonisothermal bulk crystallization studies of high density polyethylene using light depolarizing microscopy

The quiescent nonisothermal bulk crystallization kinetics of two high-density polyethylene resins were investigated by a modified light-depolarizing microscopy (LDM) technique. The technique allows studies at average cooling rates up to 2500°C/min. The polymer was found to crystallize at a pseudo-isothermal temperature even at these very high cooling rates. The overall bulk crystallization rate increased rapidly as the cooling rate and supercooling increased. Crystallization kinetics was analyzed by Avrami analysis. Avrami exponents near 3 suggested spherical growth geometry and instantaneous nucleation at predetermined sites. Observation of spherulites by optical microscopy together with a number density of spherulites that changed little with increase in cooling rate or supercooling supported this model of crystallization behavior. Analysis of the half-time of crystallization based on the Lauritzen and Hoffman secondary nucleation theory indicated that the regime II-III transition was found to occur at a degree of supercooling of approximately 22°C. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 681–692, 1998     

Concentration control for protein crystallization via a continuously-fed crystallization chamber

A continuously-fed crystallization chamber that allows for kinetic path control through the crystallization phase diagram (from labile/nucleation to metastable/growth) was fabricated and used to crystallize lysozyme. A lumped kinetic model was developed, and parameters for heterogeneous nucleation kinetics were determined. Heterogeneous nucleation was found to have faster nucleation kinetics and slower growth kinetics than homogeneous nucleation, as expected. The major contributions of the new device are (1) to allow better control of the chemical environment for studies of crystal nucleation and growth, and (2) to allow lumped-model analysis of those studies to extract kinetic parameters.     

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     

Crystallization kinetics and morphology of poly(butylene succinate‐co‐adipate)

The crystallization kinetics of biodegradable poly(butylene succinate‐co‐adipate) (PBS/A) copolyester was investigated by using differential scanning calorimetry (DSC) and polarized optical microscopy (POM), respectively. The Avrami and Ozawa equations were used to analyze the isothermal and nonisothermal crystallization kinetics, respectively. By using wide‐angle X‐ray diffraction (WAXD), PBS/A was identified to have the same crystal structure with that of PBS. The spherulitic growth rates of PBS/A measured in isothermal conditions are very well comparable with those measured by nonisothermal procedures (cooling rates ranged from 0.5 to 15 °C/min). The kinetic data were examined with the Hoffman–Lauritzen nucleation theory. The observed spherulites of PBS/A with different shapes and textures strongly depend on the crystallization temperatures. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3231–3241, 2005     

溶剂诱导聚合物结晶的研究进展

溶剂诱导结晶(SINC)又称为液体诱导结晶,它是结晶性高聚物在溶剂(或包括其蒸汽)作用下,在低于通常Tg下诱导结晶,而在高于通常Tg时能加速结晶的现象。本文主要对溶剂诱导结晶的机理、动力学和形态学进行了讨论。     

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.     

Fluctuation‐assisted crystallization of an iPP/PEOc polymer alloy prepared on a single multicatalyst reactor granule

The new fluctuation‐assisted mechanism for nucleation and crystallization in the isotactic polypropylene/poly(ethylene‐co‐octene) alloy has been studied. We found that the liquid–liquid phase separation (LLPS) had a dominant influence on the crystallization kinetics through the nucleation process. After LLPS, the nucleation of crystallization mainly occurred at the interface of the phase‐separated domains. It is because that the concentration fluctuations of the LLPS induced the motion of polymer chains and possibly some segmental alignment and/or orientation in the concentration gradient regions through interdiffusion, which could assist the formation of nuclei for crystallization. In other words, the usual nucleation energy barrier could be overcome (or at least partially) by the concentration fluctuation growth of LLPS in the unstable regions. This could be viewed as a new kind of heterogeneous nucleation and could be an addition to the regular nucleation and growth mechanism for crystallization. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 166–172, 2009     

高分子结晶理论的新概念与新进展

回顾了传统的高分子结晶成核与生长模型,指出了该模型在应用中遇到的一些问题;同时总结了Strobl根据近年小角X射线散射结果提出的高分子结晶新机理-中介相机理.介绍了Strobl等构建的热动力学图解对熔体、中介相和片晶的转变过程,阐述了各相间的平衡转变温度、潜在的转变热以及表面自由能,说明了处于熔体和晶体之间的中介相的热动力学性质是理解高分子结晶过程的重要依据.     

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.     

Quiescent crystallization of polypropylene: Experiments and modeling

The quiescent crystallization of several polypropylenes (PPs) was examined using Differential Scanning Calorimetry (DSC) and Polarized Optical Microscopy (POM). The half‐times of crystallization were obtained from the DSC thermographs employing the Avrami/Nakamura equation to fit and predict crystallization kinetics under isothermal and nonisothermal conditions. The induction times under nonisothermal conditions were estimated from isothermal crystallization data and used in conjunction with the Nakamura model in order to capture the crystallization behavior of the studied PPs. The Avrami/Nakamura model is found to fit and predict the nonisothermal crystallization data of the various PPs well over a range of cooling rates supporting its use in the simulation of polymer processes of industrial relevance. POM was used in line with parallel plate rheometry (Anton Paar, MCR 502) under no flow conditions to study the shape and growth rate of crystals of various PP resins at different temperatures or cooling rates. The growth rate of crystals is impeded exponentially with increase of temperature. The various PP resins of different molecular architecture have shown different nucleation and growth rate characteristics behavior under similar processing conditions. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1259–1275     

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.     

低密度聚乙烯/乙丙烯三元共聚(LDPE/EPO)共混体系的结晶动力学

用DSC方法研究了LDPE/EPO共混体系的等温及非等温结晶动力学,对LDPE/EPO共混体系的等温结晶动力学研究表明,共混物是三维生长的异相成核,共混物在各个结晶温度下的结晶过程都是以方式K_g(Ⅱ)进行的.采用联系Avrami方程和Ozawa方程导出的新非等温结晶动力学方程,处理了LDPE/EPO共混体系,得到了非等温结晶过程的一些基本参数,新方程很好地描述了此共混体系的非等温结晶动力学过程.     

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.     

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.