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.     

Nonisothermal cold‐crystallization kinetics of poly(trimethylene terephthalate)

The nonisothermal cold‐crystallization kinetics and subsequent melting behavior of poly(trimethylene terephthalate) (PTT) were investigated with differential scanning calorimetry. The Avrami, Tobin, and Ozawa equations were applied to describe the kinetics of the crystallization process. Both the Avrami and Tobin crystallization rate parameters increased with the heating rate. The Ozawa crystallization rate increased with the temperature. The ability of PTT to crystallize from the glassy state at a unit heating rate was determined with Ziabicki's kinetic crystallizability index, which was found to be about 0.89. The effective energy barrier describing the nonisothermal cold‐crystallization process of PTT was estimated by the differential isoconversional method of Friedman and was found to range between about 114.5 and 158.8 kJ mol^?1. In its subsequent melting, PTT exhibited double‐melting behavior for heating rates lower than or equal to 10 °C min^?1 and single‐melting behavior for heating rates greater than or equal to 12.5 °C min^?1. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4151–4163, 2004     

Isothermal and nonisothermal crystallization kinetics of nylon‐46

Isothermal and nonisothermal crystallization kinetics of nylon‐46 were investigated with differential scanning calorimetry. The equilibrium melting enthalpy and the equilibrium melting temperature of nylon‐46 were determined to be 155.58 J/g and 307.10 °C, respectively. The isothermal crystallization process was described by the Avrami equation. The lateral surface free energy and the end surface free energy of nylon‐46 were calculated to be 8.28 and 138.54 erg/cm², respectively. The work of chain folding was determined to be 7.12 kcal/mol. The activation energies were determined to be 568.25 and 337.80 kJ/mol for isothermal and nonisothermal crystallization, respectively. A convenient method was applied to describe the nonisothermal crystallization kinetics of nylon‐46 by a combination of the Avrami and Ozawa equations. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1784–1793, 2002     

Synthesis and crystallization kinetics of the novel ion exchanger Na<Subscript>4</Subscript>Ti<Subscript>4</Subscript>Si<Subscript>3</Subscript>O<Subscript>10</Subscript> for cesium removal

Thermodynamics and crystallization kinetics of the hydrothermal synthesis of Na₄Ti₄Si₃O₁₀ (NaTS) were systemically studied by both experiments and model simulation. Experimental results showed that the curve of crystallinity with time was a characteristic signmoid in the shape that indicated the crystallization of Na₄Ti₄Si₃O₁₀ was a typical spontaneous nucleation process on the laboratory scale. Crystallization of NaTS belongs to the liquid-liquid transformation mechanism and the reaction is endothermic (ΔH = 15.3 kJ/mol). A mathematic model of crystallization kinetics was developed to simulate the synthesis of NaTS. Runge-Kutta and simplex methods were adopted to solve the partial differential equations. Model results fitted well with the experimental data and showed that the synthesis process belongs to spontaneous nucleation and crystal growth. Moreover, the very small crystal growth constant (5.6·10⁻⁷) and gel dissolution constant (7.0·10⁻⁷) indicate they are the rate-limiting steps of the whole synthesis process.     

Coupling between kinetics and rheological parameters in the flow-induced crystallization of thermoplastic polymers

Flow Induced Crystallization (FIC) is the common term to indicate the acceleration in polymer crystallization kinetics due to the action of flow. FIC is expected to be the result of the coupling between the intrinsic (quiescent) crystallization kinetics and the rheological response of the polymer. The choice of a suitable rheological model, therefore, is a crucial requirement for a successful FIC model. Recent work of our group^[1] has demonstrated that the Doi-Edwards rheological model (DE), based on the concept of chain reptation, can be easily incorporated into classical crystallization models to successful predict the enhancement in nucleation rate under the action of a steady shear flow. In this paper, the interaction between the rheological parameters of the DE model and the crystallization kinetics parameters is investigated in more details. In particular, the effect of the crystallization temperature, which acts on both the polymer relaxation time and the free energy jump between liquid and solid phase, is determined and discussed.     

MELTING CRYSTALLIZATION BEHAVIOR OF NYLON 66

Analysis of isothermal and nonisothermal crystallization kinetics of nylon 66 was carried out using differentialscanning calorimetry (DSC). The commonly used Avrami equation and that modified by Jeziorny were used, respectively, tofit the primary stage of isothermal and nonisothermal crystallizations of nylon 66, In the isothermal crystallization process,mechanisms of spherulitic nucleation and growth were discussed. The lateral and folding surface free energies determinedfrom the Lauritzen-Hoffman treatment are σ= 9.77 erg/cm~2 and σ_e= 155.48 erg/cm~2, respectively; and the work of chainfolding is q = 33.14 kJ/mol. The nonisothermal crystallization kinetics of nylon 66 was analyzed by using the Mo methodcombined with the Avrami and Ozawa equations. The average Avrami exponent n was determined to be 3.45, Theactivation energies (ΔE) were determined to be -485.45 kJ/mol and -331.27 kJ/mol, respectively, for the isothermal andnonisothermal crystallization processes by the Arrhenius and the Kissinger methods.     

Crystallization of a melt spun Fe-Ni based metallic glass

The crystallization kinetics of a melt spun Fe-Ni based alloy has been investigated, with both isothermal and continuous heating experiments, by means of differential scanning calorimetry. The alloy presents two separated crystallization processes. In order to perform the kinetic analysis of a melt spun metallic glass and to decide which kinetic model agrees better with the experimental crystallization data as the crystallized fraction x. We compare the experimental dependence of ln(k0f(x)) vs. (1-x) and that predicted, assuming different model equations for f(x). Both crystallization processes follow the JMAE equation and the master curve is the same for isothermal and non-isothermal data. This revised version was published online in July 2006 with corrections to the Cover Date.     

Ti基化学镀Ni-P和Ni-P-Cg镀层晶化动力学

利用化学镀技术在Ti基体材料表面制备了Ni-P合金镀层和Ni-P-Cg复合镀层。利用SEM、XRD和EDS等分析了镀层的晶化过程,用差热分析仪研究了Ni-P合金镀层和复合镀层的晶化动力学,运用Ozawa、Freeman-Carroll、Achar和Coats-Redfern方法对非等温动力学数据进行了分析和比较。结果发现,复合镀层的特征温度T_m和晶化激活能E均高于Ni-P合金镀层,而热焓值｜ΔH｜却低于Ni-P镀层;计算出Ni-P合金镀层和Ni-P-Cg复合镀层晶化激活能分别为308.9 kJ·mol^-1和412.99 kJ·mol^-1、指前因子A分别为58.03 s^-1和77.84 s^-1,确定了Ni-P合金镀层和复合镀层晶化动力学方程。     

乙烯-辛烯共聚物/淀粉共混体系的非等温结晶动力学

通过差示扫描量热仪(DSC)研究了乙烯-辛烯共聚物/淀粉共混体系的非等温结晶动力学,用Jeziorny和Ozawa方程描述了结晶动力学过程.共混物的结晶温度和结晶焓强烈依赖于淀粉含量和冷却速率.结果表明,随着冷却速率的增加,每个试样的结晶放热曲线均变宽,并向低温区移动.当温度一定高时,所有试样均具有较快的结晶速率. Jeniorzy方程可以较好地描述POE/淀粉共混物的非等温结晶模式,而Ozawa方程对于POE/淀粉共混体系不太适合.     

Ellipsometry as a probe of crystallization kinetics in thin diblock copolymer films

We present results on the use of ellipsometry as a novel probe for the crystallization kinetics in thin films of a diblock copolymer. Ellipsometry makes use of the change in polarization induced upon the reflection of light from a film-covered substrate to enable the calculation of the refractive index and thickness of the film. The information obtained with these measurements can be compared with information from differential scanning calorimetry, with the additional advantages that small sample volumes and slow cooling rates can be employed and that expansion coefficients can be determined. By studying the temperature dependence of these quantities, we are able to measure the crystallization kinetics within very small volumes (∼10⁻¹⁰ L) of a poly(butadiene-b-ethylene oxide) diblock copolymer. Through a comparison of two different poly (ethylene oxide) block lengths, we demonstrate a reduction in both the crystallization and melting temperatures as the domain volume is reduced. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3448–3452, 2006     

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.     

Crystallization of polymers in variable external conditions. III: Experimental determination of kinetic characteristics

In two recent papers [1,?2] a new model of non-isothermal crystallization kinetics has been proposed. We are discussing now the possibility of experimental determi-nation of material characteristics appearing in the model. These include relaxation time, τ, and athermal nucleation function, B_ath. Two kinds of experiments are discussed: isothermal and non-isothermal, with constant cooling or heating rate. The following approach should be valid for polymers characterized by not too high crystallization rates, like polyethylene terephthalate (PET), polytrimethylene terephthalate (PTT, Corterra^®), polypropylene and others. Preliminary experiments on isotactic polypropylene and polyvinylidene fluoride will illustrate possibilities of the suggested experimental procedures.     

半结晶聚合物注射成型中结晶动力学的数值模拟

对半结晶聚合物注射成型过程及其结晶过程进行偶合模拟,分析了二者的相互影响.具体是在注射成型数值模拟中考虑结晶动力学效应,分别在本构方程、能量方程及材料物性参数方程中引入反映结晶效应的参数;同时在结晶动力学计算中考虑流动诱导效应,从能量的角度提出并使用修正的动力学模型,用材料流动过程的耗散能表征流动对结晶的影响.通过对等规聚丙烯(iPP)和聚对苯二甲酸乙二醇酯(PET)两种半结晶聚合物注射过程模拟结果的分析比较,证实成型过程具有加速结晶的作用.同时,材料的结晶也对注射成型加工过程,尤其是保压与冷却过程的温度场分布有较大的影响.     

Analysis of the nonisothermal crystallization kinetics in three linear aromatic polyester systems

Melt or cold crystallization kinetics has a strong bearing on morphology and the extent of crystallization, which significantly affects the physical properties of polymeric materials. Nonisothermal crystallization kinetics are often analyzed by the classical Johnson–Mehl–Avrami–Kolmogorov (JMAK) model or one of its variants, even though they are based on an isothermal assumption. As a result, during the nonisothermal (e.g. constant heating or cooling rate) crystallization of polymeric material, different sets of model parameters are required to describe crystallization at different rates, thereby increasing the total number of model parameters. In addition, due to the uncorrelated nature of these model parameters with the cooling or heating rate, accurate modeling at any intermediate condition is not possible. In the present work, these two limitations of the conventional approach have been eliminated by exhibiting the existence of a functional relationship between cooling or heating rate and effective activation energy during nonisothermal melt or cold crystallization in three linear aromatic polyesters. Furthermore, it has been shown that when the JMAK model is used in conjunction with this functional relationship, it is possible to precisely predict the experimental nonisothermal melt or cold crystallization kinetics at any linear cooling or heating rate with a single set of model parameters.     

TG and DSC kinetics of thermal decomposition and crystallization processes

The simplen ^th order model equation combined with the Arrhenius approach of the temperature dependency of the reaction rate constant is widely used in thermal analysis. The new Mettler software package for thermal analysis, GraphWare TA72 allows to access a full model comprising the power law and the crystallization kinetics (AvramiErofe'ev). The kinetics of the following reactions are studied to illustrate some applications:

thermal decomposition of dissolved dibenzoylperoxide, (dynamic and isothermal DSC measurement)

crystallization of polyethylene terephthalate (PET) (isothermal DSC measurements).

The kinetic model applied and the accuracy of the kinetic data obtained are discussed by means of a comparison of a predicted behaviour with the kinetic data measured isothermally.     

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.     

Isothermal crystallization kinetics,morphology, and thermal conductivity of graphene nanoplatelets/polyphenylene sulfide composites

Graphene nanoplatelets (GNP) and polyphenylene sulfide (PPS) were used as filler and matrix, respectively, to produce composites. The PPS/GNP thermal composites were prepared via a melt blending method. The effects of GNP on crystallization behavior and kinetics, morphology, and thermal properties of PPS/GNP composites were investigated. To determine the isothermal crystallization kinetics parameters and isothermal crystallization activation energy, the Avrami model was used to comparatively analyze the relevant DSC experimental data. The results show that GNP provides an obvious heterogeneous nucleation effect on PPS to accelerate the crystallization and decrease isothermal crystallization activation energy. Thermal conductivity values of PPS/GNP composites with various GNP contents revealed that GNP remarkably increases thermal conductivity of composites mainly via a layered dispersion in PPS matrix. Thermal conductivity also increased with increasing GNP content, which was further improved at elevated temperatures. The thermal conductivities of PPS composite containing 30 mass% of GNP were 1.156 and 1.350 W m^?1 K^?1 at 30 and 110 °C, respectively, indicating an increase of more than 3 times compared with the neat PPS.