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.     

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.     

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.     

Vapor Nucleation and Droplet Growth: Cluster Distribution Kinetics for Open and Closed Systems

A theory based on cluster distribution kinetics for single-monomer addition and dissociation is presented as a framework for homogeneous and heterogeneous vapor nucleation and growth dynamics. For continuous cluster and monomer distributions in a well-mixed non-steady-state flow system, population (mass) balance equations yield moment equations for the cluster mass moments. Nuclei are either homogeneously generated or heterogeneously seeded, and subsequent cluster growth occurs by reversible condensation of vapor monomers. The zeroth moment is the number (or moles) of clusters, the first moment is cluster mass, and the second moment gives cluster-size variance. Solutions are proposed for steady-state flow (open) and non-steady-state batch (closed) systems. Experimental data are interpreted by recognizing that droplets typically observed in nucleation experiments have grown much larger than their nuclei. This allows resolution of the large temperature-dependent discrepancy between experiment and classical nucleation theory. Copyright 2000 Academic Press.     

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.     

Kinetics of nonisothermal polymer crystallization

We adopt a cluster size distribution model to investigate the kinetics of nonisothermal polymer crystallization. The time dependencies of polymer concentration, number and size of crystals, and crystallinity (in Avrami plots) are presented for different cooling rates. The incubation period is also investigated at different cooling rates and initial temperatures. The relationship between cooling rates and incubation time is presented graphically and compared with experimental measurements. The initial temperature (relative to melting point) has a significant effect on nonisothermal crystallization. A comparison of moment and numerical solutions of the population balance equations shows the influence of Ostwald ripening. Agreement between modeling results and experimental measurements at different cooling rates supports the application of the distribution kinetics model for nonisothermal crystallization.     

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.     

Modelling Neodymium Oxalate Precipitation with a Moment Approach and a Chebyshev Quadrature Spline Reconstruction

This paper deals with the modelling of the precipitation of decahydrated neodymium oxalate from experimental data. The model takes into account the kinetic laws of primary nucleation, crystal growth and agglomeration and is based on two population balances, one for the crystallites and one for the particles. The population of particles is solved using a quadrature moment approach and then reconstructed by splines using an algorithm proposed by Chebyshev. The particle sizes predicted, at steady state for different experimental conditions, are in very good agreement with the experimental measurements.     

A simulation model for long-chain branching in vinyl acetate polymerization: 1. Batch polymerization

A new simulation model for the kinetics of long-chain branching formed via chain transfer to polymer and terminal double-bond polymerization is proposed. This model is based on the branching density distribution of the primary polymer molecules. The theory of branching density distribution is that each primary polymer molecule experiences a different history of branching and provides information on how each primary polymer molecule is connected with other chains that are formed at different conversions, therefore making possible a detailed analysis on the kinetics of the branched structure formation. This model is solved by applying the Monte Carlo method and a computer-generated simulated algorithm is proposed. The present model is applied to a batch polymerization of vinyl acetate, and various interesting structural changes occurring during polymerization (i.e., molecular weight distribution, distribution of branch points, and branching density of the largest polymer molecule) are calculated. The present method gives a direct solution for the Bethe lattice formed under nonequilibrium conditions; therefore, it can be used to examine earlier theories of the branched structure formation. It was found that the method of moments that has been applied successfully to predict various average properties would be considered a good approximation at least for the calculation of not greater than the second-order moment in a batch polymerization. © 1994 John Wiley & Sons, Inc.     

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.     

The kinetics of homogeneous and two-step nucleation during protein crystal growth from solution

Many experimental reports for the kinetics of crystal nucleation and growth, from an isothermal solution, point to a sigmoidal-like behavior for the process. Here we consider three different nucleation models from the literature and show that all lead to sigmoidal or sigmoidal-like behavior for the kinetics of nucleation. A two-step nucleation process is known to occur within certain supersaturated protein solutions, and it is demonstrated in this report how the sigmoidal law yields kinetic information for the two-step and homogeneous nucleation modes. We propose here that two-step solute-rich associates form in the solution around seed nuclei that are already present at or near the point in time when the solution is prepared. Using this hypothesis, we are able to model the time-dependent volume of the two-step phase per unit volume of solution and show that this compares well with reported experimental data. A kinetic model is given for the proposed process, which leads to a sigmoidal rate law. Additionally, a relation between the initial and final nuclei densities and the induction time is derived. As a result of this study, the conclusion is that two-step activity increases with increasing initial supersaturation or increasing salt concentration.     

Diffusion of single elements and steric limitations in kinetic theory of nucleation and crystallization

Translational and rotational diffusion equation of single elements in solution in the external orienting potential forces has been formulated. The equation should govern long-range diffusion effects in the kinetics of nucleation and crystal growth. Boundary conditions, adequate to the reversible reaction of cluster growth typical for kinetic model of nucleation and accounting for steric limitations, has been proposed. Uniaxial single elements in uniaxial orienting force field are considered.Depression of the concentration of single elements at the cluster boundary as controlled by kinetic factors, is predicted i. e., chemical rate constants, finite translational and rotational diffusion, supercolling, and steric limitations. Effective rate constants, controlled by long-range diffusion of single elements at steric limitations present, have been used. Two dimensionless kinetic factors (i. e., reduced addition-reaction rate constant and reduced rotational diffusion constant), supercooling, and steric tolerance anlge range, control process kinetics and distribution of single elements in the cluster's surroundings. Rate reduction factor responsible for the effects of long-range diffusion at steric limitations present is defined and applied for kinetic models of nucleation and crystal growth in unoriented and oriented systems.Computation examples are performed for a wide range of the model variables, and rate reduction effects of several orders of magnitude are predicted. The dominating role ranges of particular model variables, i. e., kinetic, thermodynamic, or steric variables, are discussed.     

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.     

Phase transitions and the nucleation of catalytic nanostructures under the action of chemical, physical, and mechanical factors

Basic concepts of first-order phase transitions are formulated, and the state of the art in this field is considered using nanoparticle nucleation and growth as examples. General equations are presented to describe the nanoparticle size distribution function; the average nanoparticle radius; and the density, morphology, and composition of the new phase. Examples are given to illustrate the catalytic effect of nanoparticles on the kinetics of first-order phase transitions in multicomponent systems. The effect of the acidity (pH) of the medium on phase transitions in solutions and the effect of mechanical stress on the nucleation, evolution, and properties of quantum dots are considered.     

Particle nucleation and growth models

This review concentrates on the progress of modeling the nucleation process of particles by the balanced nucleation-growth (BNG) process. The BNG model will be compared with other models that try to predict material nucleation. Compared to other models, the BNG model allows quantifying the nucleation rate, maximum growth rate, and supersaturation during the nucleation period as a function of nucleation efficiency and maximum growth rate of the crystals. From this model, equations are derived that correlate the number of stable crystals formed with molar addition rate of reactants, solubility of the crystals, and temperature. The BNG model predicts the experimental result that many crystallization processes result in a limited number of crystals followed by growth. The model also predicts that factors like diffusion and kinetically controlled growth process, Ostwald ripening agents and growth restrainers control the crystal number. Equations are given for each of the variables that agree with experiments. The BNG model predicts the conditions for renucleation (formation of new crystals during precipitation). It leads to new equations for the prediction of crystal number and crystal size during controlled continuous precipitation in the continuous stirred tank reactor (CSTR) as a function of precipitation conditions.     

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).     

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     

聚合物单晶生长的三维相场模拟研究

利用元胞自动机方法与相场模型的结合建立新型三维模拟相场模型.同时,为模拟真实的、三维的高分子结晶的过程,采用元胞自动机方法离散方程,且元胞几何形状的选取符合真实聚合物晶格扩散方式的物理规律,以及新建立的相场模型套用间规聚丙烯的实验参数.利用该模型模拟了多种三维立方体或者薄层的晶体形貌及其相互之间的演化过程,包括正方形、长方形、菱形、六边形、多层单晶等.通过模拟结果与真实形貌作对比来证明所建立的相场模型真实可靠性.