Application of the Avrami, Tobin, Malkin, and Urbanovici–Segal macrokinetic models to isothermal crystallization of syndiotactic polypropylene

Various kinetic equations, namely the Avrami, Tobin, Malkin, and Urbanovici–Segal models, have been applied to describe the kinetics of primary crystallization from the melt state of syndiotactic polypropylene (s-PP) under isothermal conditions. Analysis was carried out using a data-fitting procedure, in which the experimental data were fitted directly to each model using a non-linear multi-variable regression program. The results suggested that the experimental data of s-PP can be best described by the Urbanovici–Segal model, followed by the Avrami, Malkin, and Tobin models, respectively.     

Isothermal and nonisothermal cold crystallization kinetics of poly(<Emphasis Type="SmallCaps">l</Emphasis>-lactide)/functionalized eggshell powder composites

Functionalized eggshell powder (NES) with nucleating surface of calcium phenylphosphonic acid (PPCa) for poly(l-lactide) (PLLA) was compounded with PLLA via melt blending to improve the cold crystallization process of PLLA. The cold crystallization behavior of the PLLA/NES composites was studied by differential scanning calorimetry. The isothermal cold crystallization rates have been enhanced obviously in the PLLA/NES composites than in the neat PLLA, indicative of the excellent nucleating effects of NES on PLLA. For the nonisothermal cold crystallization, the overall crystallization rate of PLLA increased with both increasing NES loadings and heating rate. It was found that the Avrami equation and the combined Ozawa–Avrami model could describe the experiment data successfully.     

Crystallization kinetics study of poly(L‐lactic acid)/carbon nanotubes nanocomposites

Effects of carbon nanotubes (CNT) on the isothermal crystallization kinetics of poly(L ‐lactic acid) (PLLA) were quantitatively investigated using the Avrami equation and the secondary nucleation theory of Lauritzen and Hoffman. CNT via grafting modification with PLLA could well disperse in the PLLA matrix and give significantly enhanced crystallization rate and crystallinity of PLLA as analyzed by differential scanning calorimetry and polarized optical microscopy. Analysis of isothermal crystallization kinetics using the Avrami equation demonstrated that CNT significantly enhanced the bulk crystallization of PLLA. Analysis of spherulite growth kinetics using the secondary nucleation theory of Lauritzen and Hoffman found that CNT could expand the temperature range of the crystallization regime III of PLLA. Values of the nucleation constant (K_g) in crystallization regimes III and II of PLLA both increased with increasing CNT contents. The K_g III/K_g II ratios were found to be close to the theoretical value 2 but were not clearly found to depend on the CNT contents. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 983–989, 2010     

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.     

Crystallization kinetics and crystallization behavior of syndiotactic polystyrene/clay nanocomposites

We investigated the effects of montmorillonite (clay) on the crystallization kinetics of syndiotactic polystyrene (sPS) with isothermal differential scanning calorimetry analyses. The clay was dispersed into the sPS matrix via melt blending on a scale of 1–2 nm or up to about 100 nm, depending on the surfactant treatment. For a crystallization temperature of 240 °C, the isothermal crystallization data were fitted well with the Avrami crystallization equation. Crystallization data on the kinetic parameters (i.e., the crystallization rate constant, Avrami exponent, clay content, and clay/surfactant cation‐exchange ratio) were also investigated. Experimental results indicated that the crystallization rate constant of the sPS nanocomposite increased with increasing clay content. The clay played a vital role in facilitating the formation on the thermodynamically more favorable all‐β‐form crystal when the sPS was melt‐crystallized. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2097–2107, 2001     

聚醚醚酮酮等温结晶动力学的研究

聚醚醚酮酮等温结晶动力学的研究陈艳，王军佐，曹俊奎，那辉，吴忠文（吉林大学化学系，长春，１３００２３）关键词聚醚醚酮酮，等温结晶动力学，差示扫描量热法聚醚醚酮酮（ＰＥＥＫＫ）是在聚醚醚酮（ＰＥＥＫ）基础上开发成功的一种耐热高分子材料。它保持了ＰＥＥＫ...     

Isothermal crystallization studies of poly(butylene terephthalate) composites

Different crystallization kinetic models (Avrami and Tobin) have been applied to study the crystallization kinetics of virgin poly(butylene terephthalate) (PBT) and filled PBT systems under isothermal experimental conditions. The experimental data have been analyzed with a nonlinear, multivariable regression program. The kinetic parameters for the isothermal crystallization have been determined. The analysis results indicate that both models satisfactorily represent the isothermal crystallization kinetics. PBT crystallizes most slowly. The presence of nanoclays or nanofibers, added as fillers, enhances the crystallization rate of PBT composites. An analysis of the kinetic data with the Avrami and Tobin models has shown little change in the crystallization exponent compared with that of virgin PBT. The crystallization rate constant decreases with a rise in the temperature for the two models. This trend has been observed for similar polyester systems reported in the literature. The dispersion of the clay layers in the PBT nanocomposites has been characterized with wide‐angle X‐ray diffraction and transmission electron microscopy. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1344–1353, 2007     

Unified isothermal and non-isothermal modelling of neat PEEK crystallization

A differential generalized Avrami’s law is used to model crystallization kinetic of PEEK in considering that PEEK crystallization results from the contribution of two distinct mechanisms. The form of this equation allows to predict with good accuracy both isothermal and non-isothermal crystallization kinetics. Nevertheless, isothermal model parameters are not entirely satisfactory for predicting non-isothermal crystallization and the identification of kinetic parameters is needed for both isothermal and non-isothermal cases. The results show that the Avrami exponents and Arrhenius activation energies remain constant for both conditions and therefore suggest that these parameters are only material dependent. On the other hand, the other kinetic parameters depend on the crystallization condition and vary with temperature and/or cooling rate.     

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.     

Effects of functionalized graphenes on the isothermal crystallization of poly(L-lactide) nanocomposites

The effects of graphene oxide(GO) with polar groups and functionalized GO(f GO) with nonpolar groups on the isothermal crystallization of poly(L-lactide)(PLLA) were compared. Functionalized GO was obtained by grafting octadecylamine and characterized by FTIR, WAXD and TGA. Isothermal crystallization kinetics of PLLA/GO and PLLA/f GO nanocomposites were investigated by combining DSC data and Avrami equation. The results showed that f GO could improve PLLA crystallization rate more obviously than GO. By analyzing the morphology obtained from POM, SEM and TEM, it was found f GO with large layer space dispersed better in PLLA and supplied more nucleation sites than GO. Therefore, for the multilayer graphene, increasing the layer spaces is important to improve its dispersion in polymers, which will cause the crystal kinetics changing of polymers.     

联苯聚醚醚酮酮的结晶动力学的研究

通过ｄｓｃ 方法对新型聚芳醚酮联苯聚醚醚酮酮（ＰＥＥＫＤＫ） 的等温及非等温熔融结晶动力学进行了研究,运用Ａｖｒａｍｉ 方程分析了其等温结晶行为,求得了等温结晶活化能,平衡熔点,成核参数,并与其它聚芳醚酮类聚合物进行了比较。同时,对ＰＥＥＫＤＫ的非等温结晶动力学也进行了研究。     

固相缩聚PET等温结晶动力学

高聚物等温结晶动力学方面的研究者甚多,由熔融缩聚制备的不同分子量PET的等温结晶动力学及几种不同缩聚催化体系固相缩聚PET的等温结晶动力学已有报道.本文采用一个修正的Avrami方程对固相缩聚PET样品进行系统的等温结晶动力学研究.     

Isothermal and nonisothermal crystallization kinetics of poly(propylene terephthalate)

The kinetics of crystallization of poly(propylene terephthalate) (PPT) samples of different molecular weights were studied under both isothermal and nonisothermal conditions. The Avrami and Lauritzen–Hoffmann treatments were applied to evaluate kinetic parameters of PPT isothermal crystallization. It was found that crystallization is faster for low‐molecular‐weight samples. The modified Avrami equation, and the combined Avrami–Ozawa method were found to successfully describe the nonisothermal crystallization process. Also, the analysis of Lauritzen–Hoffmmann was tested and it resulted in values close to those obtained with isothermal crystallization data. The nonisothermal kinetic data were corrected for the effect of the temperature lag and shifted alone with the isothermal kinetic data to obtain a single master curve, according to the method of Chan and Isayev, testifying to the consistency between the isothermal and corrected nonisothermal data. A new method for ranking of polymers, referring to the crystallization rates, was also introduced. This involved a new index that combines the maximum crystallization rate observed during cooling with the average crystallization rates over the temperature range of the crystallization peak. Furthermore, the effective energy barrier of the dynamic process was evaluated with the isoconversional methods of Flynn and Friedmann. It was found that the energy barrier is lower for the low‐molecular‐weight PPT. The effect of the catalyst remnants on the crystallization kinetics was also investigated and it was found that this is significant only for low‐molecular‐weight samples. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3775–3796, 2004     

Can Classic Avrami Theory Describe the Isothermal Crystallization Kinetics for Stereocomplex Poly(lactic acid)?

Classic Avrami model and its modifications have found diverse applications in describing the thermal and phase behaviors of inorganic metals and organic polymers.The direct introduction of classic Avrami equation to offer quantitative analyses of crystallization kinetic parameters for enantiomeric poly(lactic acid) (PLA) blends may,however,lead to contradictory conclusions.As revealed by this study,during the characterization of isothermal melt and cold crystallization for stereocomplex PLA containing equal-weight poly(L-lactic acid) and poly(D-lactic acid),the kinetic parameters yielded by Avrami equation are not in line with the classic crystallization hypotheses or the direct morphological observations.The underlying mechanisms,to some extent,lie in the generation of stereocomplex crystals (SCs) during the cooling/heating which affects the subsequent crystallization dynamics.The huge gap between the melting enthalpies of 100％ crystalline SCs (142 J/g) and homo-crystals (HCs,93 J/g) is most likely responsible for the confusing kinetic parameters acquired from the deduction of Avrami equation,which is based on the integration of enthalpies as a function of crystallization time.This prompts for great care that the classic Avrami equation is not applicable to accurately describe the crystallization kinetics of stereocomplex PLA,given the generation of SCs prior to crystallization and the coexistence of HCs and SCs during crystallization.     

Thermal behavior of syndiotactic E-1,2-poly(3-methyl-1,3-pentadiene)

Syndiotactic E-1,2-poly(3-methyl-1,3-pentadiene) was synthesized with the catalyst system Fe(bipy)₂Cl₂-MAO. The thermal stability and kinetic parameters of degradation were determined by thermogravimetric analysis. The isothermal crystallization kinetics were described by means of the Avrami equation, which suggested a three-dimensional growth of crystalline units, developed by heterogeneous nucleation, followed by a secondary crystallization stage. Syndiotactic E-1,2-poly(3-methyl-1,3-pentadiene) isothermally crystallizes from the melt according to regime II of crystallization described by Lauritzen-Hoffman secondary nucleation theory. Non-isothermal crystallization kinetics were elaborated using different approaches. The equilibrium melting temperature was calculated. The kinetic and thermodynamic data were compared with those obtained from syndiotactic 1,2-poly(1,3-butadiene), which is the first example of 1,2 polydienes family.     

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.     

Crystallization kinetics and multiple melting phenomena of a flame‐retardant phosphorus containing copolyester

Melt, cold isothermal crystallization kinetics, and multiple melting phenomena are investigated by differential scanning calorimetry (DSC) for a flame‐retardant phosphorus containing copolyester. The crystallization kinetics was investigated by the Avrami equation. The Avrami exponent is about 2.6 for melt crystallization and about 2 for cold crystallization. The crystallization activation energy for melt crystallization and for cold crystallization is −64.7 and 145.5, respectively. Three melting endotherms are found in the DSC scan, and they are explained in terms of secondary crystallization, primary crystallization, and recrystallization during the scan. A strong evidence of a two‐stage crystallization mechanism was also observed in the DSC isothermal experiment and X‐ray diffraction. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2269–2277, 1999     

Nonisothermal crystallization studies on poly(4‐hydroxybutyric acid‐alt‐glycolic acid)

The crystallization behavior of a new sequential polyester constituted by glycolic acid and 4‐hydroxybutyric acid has been studied under nonisothermal conditions. Nonisothermal melt crystallization has been followed by means of hot‐stage optical microscopy (HSOM), with experiments performed at different cooling rates. Two crystallization regimes have been found, which is in good agreement with previous isothermal studies and with the different spherulitic morphologies that were observed. The kinetics of both glass and melt crystallizations has also been studied by differential scanning calorimetry (DSC) and considering the typical Avrami, Ozawa, and Cazé analyses. Only the last gave Avrami exponents, which were in good agreement with those measured under isothermal conditions, suggesting a spherulitic growth with a predetermined nucleation. Isoconversional data of melt and glass nonisothermal crystallizations have been combined to obtain the Hoffman and Lauritzen parameters. Results again indicate the existence of two crystallization regimes with nucleation constants close to those deduced from isothermal DSC experiments. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 121–133, 2008     

Effect of ZnO nanofillers treated with triethoxy caprylylsilane on the isothermal and non-isothermal crystallization of poly(lactic acid)

The crystallization of PLA-silane surface-treated ZnO nanocomposites was investigated by DSC and compared to that of neat PLA. Several modes of crystallization were considered: isothermal and non-isothermal cold crystallization and also isothermal and non-isothermal melt crystallization. The kinetics of cold crystallization were studied using different methods, namely the Avrami and Ozawa-Flynn-Wall models, to calculate activation energies and kinetic constants. In contrast to what is typically observed when the foreign particles are added in a polymer matrix, the silane surface-treated ZnO delayed the crystallization of PLA and made it more difficult to start. The nucleation activity of the ZnO nanoparticles, ?, was calculated and found to be greater than 1 (? = 1.7). This indicated that ZnO played an anti-nucleating role in the crystallization of PLA nanocomposites. This effect has been linked mainly to the interactions between the silane groups onto the surface of nanoparticles and PLA macromolecules. These interactions which reduce the mobility of polymer chains have been evidenced by rheological experiments.     

Effect of wood flour as nucleating agent on the isothermal crystallization of poly(lactic acid)

The effect of wood flour (WF) as an efficient nucleating agent on the isothermal melt crystallization and isothermal cold crystallization behavior of poly(lactic acid) (PLA) was investigated by differential scanning calorimeter and polarized optical microscopy. It was found that the incorporation of 4 wt% WF promoted the crystallization of PLA about 4.2%. Polarized optical microscopy results showed the Maltese cross of the samples. The presence of the 4 wt% WF may increase the nucleation density, leading to the increase of the spherulites; however, the size of the spherulites decreased, and the structure became incomplete. The Avrami model was applied to analyze the isothermal crystallization kinetics. It is concluded that the addition of WF modified the crystallization process of PLA (the value of Avrami exponent changed). Various parameters, such as the crystallization half time and crystallization rate constant, reflect that 4 wt% WF significantly improves the crystallization process. The observations in this article indicate that WF is an efficient nucleating agent of PLA. Copyright © 2016 John Wiley & Sons, Ltd.