Kolmogorov–Johnson–Mehl–Avrami kinetics for non-isothermal phase transformations ruled by diffusional growth

We report on the functional form of the rate of the transformed volume fraction in non-isothermal phase transitions occurring by nucleation and diffusional growth. The microscopic growth rate is computed by solving the diffusion problem for time-dependent diffusion coefficient. The growth law is further employed in the Kolmogorov–Johnson–Mehl–Avrami (KJMA) theory for describing the time dependence of the transformed volume at constant heating rate. It is demonstrated that the transformation rate separates in the product of volume fraction and actual temperature functions. In the framework of the KJMA approach this factorization is exact. It is also shown that for real systems (due to the high values of the reduced activation energies for nucleation and growth), the kinetics is in excellent agreement with the stretched exponential function appropriate for isothermal transformations.     

Kinetics of the shear-induced isotropic-to-lamellar transition of an amphiphilic model system: a nonequilibrium molecular dynamics simulation study

The shear-induced isotropic-to-lamellar phase transition in the amphiphilic systems in the vicinity of the quiescent order-to-disorder transition point is investigated by the large-scale parallel nonequilibrium molecular dynamics simulations of simple amphiphilic model systems. There is a shear-induced upward shift of the ordering temperature. The initial isotropic phase orders into a lamellar phase perpendicular to the shear vorticity. The phase diagram as a function of temperature and shear rate is established. The dependency of the ordering transition on interaction strength and shear rate is rationalized by the competition between shear rate and chain relaxation. The time evolution of morphology reveals that the shear-induced ordering proceeds via nucleation and growth, a signature of a first-order phase transition. At low shear rate, a single ordered domain grows after an incubation period. With increasing shear rate ordering speeds up, but eventually develops in a lamellar system with disordered shear bands. The time dependence of the order parameter follows that of the mean-squared end-to-end distance, shear viscosity, and bulk pressure, and follows an Avrami scheme with an Avrami exponent between 2 and 4.     

Scenarios of heterogeneous nucleation and growth studied by cell dynamics simulation

The dynamics of phase transformation due to homogeneous nucleation has long been analyzed using the classic Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory. However, the dynamics of phase transformation due to heterogeneous nucleation has not been studied systematically even though it is vitally important technologically. In this report, the author studies the dynamics of heterogeneous nucleation theoretically and systematically using the phenomenological time-dependent Ginzburg-Landau (TDGL)-type model combined with the cell dynamics method. In this study the author focuses on the dynamics of phase transformation when the material is sandwiched by two supporting substrates. This model is supposed to simulate phase change storage media. Since both homogeneous and heterogeneous nucleations can occur simultaneously, the author predicts a few scenarios of phase transformation including homogeneous nucleation regime, heterogeneous nucleation regime, and the homogeneous-heterogeneous coexistence regime. These predictions are directly confirmed by numerical simulation using the TDGL model. The outcome of the study was that the KJMA formula has limited use when heterogeneous nucleation exists, but it could still give some information about the microscopic mechanism of phase transformation at various stages during phase transformation.     

Crystallisation kinetics of some archetypal ionic liquids: isothermal and non-isothermal determination of the Avrami exponent

The properties of ionic liquids give rise to applications in diverse technology areas including mechanical engineering, mining, aerospace and defence. The arbitrary physical property that defines an ionic liquid is a melting point below 100 °C, and as such, an understanding of crystallisation phenomena is extremely important. This is the first report dealing with the mechanism of crystallisation in ionic liquids. Assuming crystallisation of the ionic liquids is a thermal or mass diffusion-controlled process, the values of the isothermal Avrami exponent obtained from three different ionic liquids with three different anions and cations all indicate that growth occurs with a decreasing nucleation rate (n=1.8-2.2). For one of the ionic liquids it was possible to avoid crystallisation by fast cooling and then observe a devitrification upon heating through the glass transition. The isothermal Avrami exponent of devitrification suggested growth with an increasing nucleating rate (n=4.1), compared to a decreasing nucleation rate when crystallisation occurs on cooling from the melt (n=2.0). Two non-isothermal methods were employed to determine the Avrami exponent of devitrification. Both non-isothermal Avrami exponents were in agreement with the isothermal case (n=4.0-4.15). The applicability of JMAK theory suggests that the nucleation event in the ionic liquids selected is a random stochastic process in the volume of the material. Agreement between the isothermal and non-isothermal techniques for determining the Avrami exponent of devitrification suggests that the pre-exponential factor and the activation energy are independent of thermal history. The heating rate dependence of the glass transition enabled the calculation of the fragility index, which suggests that the ionic liquid is a "strong" glass former. This suggests that the temperature dependence of the rate constant could be close to Arrhenius, as assumed by JMAK theory. More generally, therefore, it can be concluded that there is nothing unusual about the crystallisation mechanism of the ionic liquids studied here.     

聚苯撑苯并二噻唑的甲基磺酸溶液的相转变过程及其动力学研究

 用退偏振光强度法及偏光显微镜研究了溶致性液晶高分子聚苯撑苯并二噻唑的甲基磺酸溶液(PBT/MSA)由液晶相至各向同性相(N→I转变),及由各向同性相至液晶相(I→N转变)的相变过程.液晶相的形成(I→N)服从Av-rami方程,Avrami指数为1左右,表明该体系的液晶相是以一维棒状方式形成的.相转变温度与浓度有关,提高温度可加速在应力下液晶相长程有序结构的形成.     

聚苯撑苯并二噻唑的甲基磺酸溶液的相转变过程及其动力学研究

用退偏振光强度法及偏光显微镜研究了溶致性液晶高分子聚苯撑苯并二噻唑的甲基磺酸溶液(PBT/MSA)由液晶相至各向同性相(N→I转变),及由各向同性相至液晶相(I→N转变)的相变过程.液晶相的形成(I→N)服从Av-rami方程,Avrami指数为1左右,表明该体系的液晶相是以一维棒状方式形成的.相转变温度与浓度有关,提高温度可加速在应力下液晶相长程有序结构的形成.     

聚对苯二甲酸1,3-丙二酯的自晶种成核等温结晶动力学

研究了自晶种成核对聚对苯二甲酸1,3-丙二酯(PTT)结晶行为的影响.示差扫描量热结果表明,经过自晶种成核处理后,PTT的结晶温度明显增加.应用Avrami方程分析了PTT等温结晶动力学,Avrami指数n的平均值为3.34,表明初级结晶为三维球晶生长.自晶种成核导致结晶活化能和链折叠功减小,促进PTT的结晶.     

KINETICSOF TRANSITION FROM ISOTROPIC TO CHOLESTERIC PHASE FOR A THERMOTROPIC CELLULOSE DERIVATIVE

The kinetics of mesophase formation of a thermotropic hydroxyethyl cellulose acetatefrom isotropic phase to cholesteric mesophase has been studied by means of depolariz-ing transmittance method. Avrami type analysis of the data gives an exponent n close to1, which suggests the nucleation followed by rod-like growth. It means that the kineticbehavior of phase transition from isotropic to cholesteric mesophase is very similar to thatof the mesophase formation from isotropic to nematic mesophase.     

Induced crystal G phase through intermolecular hydrogen bonding VII. Influence of non-covalent interactions on mesomorphism and crystallization kinetics

A series of intermolecular hydrogen bonding complexes, 2,2'-bipyridine: p- n-alkoxybenzoic acids (BP : nABA) was isolated from liquid crystalline p-n-alkoxybenzoic acids (nABA) (where n represents alkoxy carbon numbers, 3 to 10 and 12) and a non-mesogen, 2,2'-bipyridine (BP). The thermal and phase behaviour of these complexes was studied by thermal microscopy and differential scanning calorimetry (DSC). These studies revealed the induction of tilted smectic F and crystal G phases. The structural elucidation pertaining to the formation of intermolecular hydrogen bonding was carried out by a detailed IR spectral investigation. Comparative crystallization kinectic studies using DSC, performed on two representative compounds, showed different forms of the crystallization process. The magnitudes of the Avrami exponent n suggests two different mechanisms operate for individual members leading to sporadic three-dimensional growth. Nevertheless, an overall unique mechanism is predicted to operate at each crystallization temperature investigated, while the Avrami constant b shows a temperature dependence suggesting a strong influence of alkoxy terminal groups on the rates of nucleation.     

Transient and athermal effects in the crystallization of polymers. I. Isothermal crystallization

The isothermal crystallization of poly(propylene) and poly(ethylene terephthalate) was investigated with differential scanning calorimetry and optical microscopy. It was found that the induction time depends on the cooling rate to a constant temperature. The isothermal crystallization of the investigated polymers is a complex process and cannot be adequately described by the simple Avrami equation with time‐independent parameters. The results indicate that crystallization is composed of several nucleation mechanisms. The homogeneous nucleation occurring from thermal fluctuations is preceded by the nucleation on not completely melted crystalline residues that can become stable by an athermal mechanism as well as nucleation on heterogeneities. The nucleation rate depends on time, with the maximum shortly after the start of crystallization attributed to nucleation on crystalline residues (possible athermal nucleation) and on heterogeneities. However, the spherulitic growth rate and the exponent n do not change with the time of crystallization. The time dependence of the crystallization rate corresponds to the changes in the nucleation rate with time. The steady‐state crystallization rate in thermal nucleation is lower than the rate determined in a classical way from the half‐time of crystallization. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1835–1849, 2002     

Isothermal crystallization kinetics of poly(trimethylene terephthalate) under the influence of self-seeding nucleation

The effect of self-seeding nucleation on the crystallization behavior of poly(trimethylene terephthalate) (PTT) was studied. Differential scanning calorimetry (DSC) indicated that the crystallization temperature of PTT notably increased after self-seeding nucleation. Avrami equation was applied in the analysis of the isothermal crystallization process of PTT. The resulting average value of the Avrami exponent at n = 3.34 suggests that primary crystallization may correspond to a three-dimensional spherulitic growth. Self-seeding nucleation, leading to a decrease in active energy for crystallization and chain folding work, promotes the overall crystallization process of PTT. Translated from Acta Polymerica Sinica, 2006, (3): 414–417 (in Chinese)     

Bulk and solution crystallization kinetics of isotactic polybutene-1

The crystallization kinetics of an unfractionated sample of isotactic polybutene-1 have been studied from the melt and from dilute solutions in amyl acetate by the dilatometric method. The kinetics of bulk crystallization followed the Avrami equation for most of the transformation with a deviation towards the end of the crystallization process. The Avrami exponent is found to be temperature dependent with the value of n ≈ 3 at high undercooling (indicating a homogeneous nucleation process) and n ≈ 4 at lower undercooling (indicating a heterogeneous nucleation process). The temperature coefficients of the rate constants indicate a nucleation controlled process of crystallization.     

NMR approach to the kinetics of polymer crystallization. 1. Cis-1,4-polybutadiene

The isothermal crystallization kinetics of cis-1,4-polybutadiene (PB) in bulk, was studied over the temperature range 193 to 235 K, using ¹H pulsed high-resolution FT-NMR. Analysis of the spectral line area and width, corresponding to the resonance of protons bonded to noncrystalline chain segments, yields two major results:

• (i) The line area variations are associated with the overall progression of crystallization in the sample, which is shown to obey on Avrami law. The time exponent n and rate constant k were determined for each isotherm; their temperature dependence reflects the nucleation and crystal growth mechanisms and provides an estimate of relevant thermodynamic parameters.
• (ii) The line-width is assumed to be closely related to a statistical network with the average mesh size determined by a random distribution of crystallites. Finally, concomitant spin-lattice relaxation time (T₁) measurements show an increase of this parameter which parallels the development of the crystalline fraction.

     

成核剂对PHBV等温结晶行为的影响

用DSC方法测定了氮化硼及滑石粉成核剂对 (β 羟基丁酸酯 与 β 羟基戊酸酯 )共聚物 (简称PHBV)等温结晶行为的影响 .结果表明 ,Avrami方程指数n、成核机理、晶体生长方式基本上不受成核剂的影响 .少量的成核剂可使结晶成核自由能降低 ,结晶速率加大 ,其中氮化硼的效果最为显著     

Simulations of polymer crystallization under high pressure

High pressure crystallization of polypropylene was studied by means of PVT measurements and computer simulations. The isothermal crystallization behaviour were described by using a model which takes into account the effect of pressure on the temperature dependence of nucleation rate and linear growth rate. The agreement between the simulation and the experiments was seen in the tendency that the crystallization was accelerated by the high pressure. The non-isothermal crystallization behavior was also simulated by applying a generalized Avrami equation. The simulation curves well reproduced the experimental values below relative crystallinity 0.5 and below 100 MPa.     

等规聚丙烯自成核的等温结晶动力学

近年来 ,有关等规聚丙烯 (i PP)的自成核研究已引起了人们的关注 [1 ] ,但有关其结晶动力学的报道并不多见 .Carfagna等 [2 ]用膨胀计法研究了 i PP在未完全熔融重结晶情况下的等温结晶动力学 ,得到的 Avrami指数远远小于 3 .张新远等[3 ] 研究了 i PP未完全熔融情况下的非等温结晶动力学 .到目前为止 ,i PP自成核的熔体降温等温结晶动力学尚未见报道 .本文在 i PP自成核研究的基础上 [4] ,用 DSC方法研究了 i PP自成核在较高温度下的等温结晶动力学 ,讨论了结晶机理 .结果表明 ,在本实验的自成核条件下 ,i PP依然是三维球晶生长 ,…     

Crystallization kinetics of dilute polyethylene solutions

The crystallization kinetics of a high molecular weight fraction of linear polyethylene was studied in dilute solutions of p-xylene, n-hexadecane, and decalin by dilatometric methods. For all solvents and temperatures, the experimental isotherms could be quantitatively described by the Avrami formulation for the complete transformation. This result is unique in the realm of polymer crystallization, since marked deviations from this theory are usually observed in more concentrated systems. The Avrami exponent is found to be n = 4 in all cases. The temperature coefficients of the rate constants are indicative of a nucleation controlled process. The data fit either a two-dimensional or three-dimensional nucleation mode, and a discrimination can not be made between these two cases. The interfacial free energies are found to be independent of the solvent medium. It is also shown that, irrespective of the type of nucleation control governing the kinetics, the same type governs the crystallite thickness of the lamella-like crystals that are formed.     

Heterogeneous nucleation on the crystallization poly(ethylene terephthalate)

The crystallization behavior of poly(ethylene terephthalate) (PET) with disodium terephthalate (DST) as nucleating agent was investigated. A detailed analysis of the crystallization course from the melt was made with the Avrami expression. The results demonstrated that DST additive can promote the PET crystallization rate in its entire crystallizable temperature range, and the acceleration degree of DST decreases with increasing temperature after a temperature higher than 180 °C. The values of the Avrami exponent indicated that the crystallization mode in Avrami theory is not suitable for the crystallization of these polymers, and the mechanism of the heterogeneous nucleation on PET crystallization is discussed. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2135–2144, 2003     

Single-crystal model for the bulk crystallization kinetics of poly(ethylene oxide) and polystyrene

Approximations in the Avrami treatment of impingement which arise when the growing crystalline bodies are rods or disks are discussed, with particular reference to the single-crystal model. This model, previously fitted to the isolated primary crystallization of polymethylene, is extended to discuss the growth of the composite lamellar structures, axialites, and spherulites, and is here fitted to the crystallization of poly(ethylene oxide) and polystyrene. Both polymers are found to yield anomalous values of the Avrami exponent when analyzed in terms of the conventional Avrami equation. The new analysis reveals similarities in the behavior of all three polymers. The residual deviations remaining after the fit of the model to polymethylene and poly(ethylene oxide) follow the same pattern, and the temperature dependence of the rate constants associated with the model is similar for all three polymers.     

Isothermal crystallization kinetics of Fe<Subscript>75</Subscript>Cr<Subscript>5</Subscript>P<Subscript>9</Subscript>B<Subscript>4</Subscript>C<Subscript>7</Subscript> metallic glass with cost-effectiveness and desirable merits

In this work, the isothermal crystallization kinetics of cost-effective Fe₇₅Cr₅P₉B₄C₇ metallic glass with a combination of desired merits synthesized by industrial ferro-alloys without high-purity materials was evaluated by Johnson–Mehl–Avrami approach using differential scanning calorimeter. The Avrami exponents at all isothermal annealing temperatures range from about 2.93 to 4.61, indicating a three-dimensional diffusion-controlled growth with an increasing nucleation rate during the isothermal crystallization. Meanwhile, the Avrami exponent firstly increases from 2.93 at the initial time to a maximum value of 4.61 and then decreases to 4.09 with the increment of the isothermal annealing temperature, which can be attributed to the atomic diffusion in the alloy. Additionally, the trend of the local Avrami exponent variations at different isothermal annealing temperatures reflects a variable crystallization mechanism during the crystallization process. Moreover, the local activation energy determined by Arrhenius equation gradually decreases from about 412 to 383 kJ mol^?1 during the present isothermal crystallization, further revealing that the process is dominated by a three-dimensional diffusion-controlled growth with an increasing nucleation rate, which provides useful insights into the formation of the present alloy.