Estimating the activation energy for non-isothermal crystallization of polymer melts

The advanced isoconversional method can be used to determine the effective activation energy of non-isothermal crystallization of the polymer melts. The method has been applied to DSC data on crystallization of poly(ethylene terephthalate) (PET). The resulting activation energy increases with the extent of crystallization from -270 to 20 kJ mol^-1. The variation is interpreted in terms of the Turnbull and Fisher crystallization theory. This revised version was published online in July 2006 with corrections to the Cover Date.     

Influence of the specific surface area on crystallization process kinetics of some silica gels

The influence of the specific surface area on the crystallization processes of two silica gels with different specific surface areas has been investigated in non-isothermal conditions using DTA technique. The activation energies of the crystallization processes were calculated using four isoconversional methods: Ozawa-Flynn-Wall, Kissinger-Akahira-Sunose, Starink and Tang. It has been established that, the decrease of the surface area from S=252.62 m² g⁻¹, in the case of sample GS2, to S=2.52 m² g⁻¹, in the case of sample GS1, has determined a slight increase of the activation energy of the crystallization process of the gels. Regardless of the isoconversional method used, the activation energy (E _α) decreases monotonously with the crystallized fraction (α), which confirms the complex mechanism of gels crystallization. It has been proved that the Johnson-Mehl-Avrami model cannot be applied for the crystallization processes of the studied silica gels.     

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。     

Crystallization kinetics of isotactic polypropylene nucleated with octamethylenedicarboxylic dibenzoylhydrazide under isothermal and non-isothermal conditions

Octamethylenedicarboxylic dibenzoylhydrazide (TMC-300) was used as a nucleating agent for isotactic polypropylene (iPP) for the first time. The Avrami method and the Caze method were used to analyze the isothermal and non-isothermal crystallization kinetics of iPP incorporated with TMC-300, respectively. During isothermal crystallization, the half crystallization time at 130 °C reduces from 130 s of virgin iPP to 44 s after addition of TMC-300, which reflects that TMC-300 increased the crystallization rate of iPP obviously. The crystallization activation energy decreases from 382.5 kJ mol^?1 of virgin iPP to 275.3 kJ mol^?1 of iPP/TMC-300. During non-isothermal crystallization, the crystallization peak temperature of iPP nucleated with TMC-300 was increased by 5.1 °C when compared to that of virgin iPP at the cooling rate of 20 °C min^?1, and both the reduction of half crystallization time and the increase in peak crystallization temperature also justified that the addition of TMC-300 accelerated the crystallization of iPP.

     

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.     

Investigating the kinetics of liquid-free,OSDA-free ZSM-5 zeolite synthesis from iron ore tailings

In this study, ZSM-5, which is a Mobil-type five-type zeolite with well-defined crystal morphology, is successfully synthesized via a seed-assisted, liquid-free method that uses iron ore tailings as a silica source. The ZSM-5 crystallization kinetics at 423, 433, and 443 K and different synthesis times are investigated to identify the nucleation and crystallization mechanisms of the synthesized ZSM-5 zeolites, and results suggest that the crystallization kinetics follow a Kolmogorov-Johnson-Mehl-Avrami-type behavior. The activation energies for the induction and transition periods are 112.38 and 58.35 kJ mol⁻¹, respectively. Furthermore, the Avrami exponent indicates three-dimensional crystal growth from both sporadic and instantaneous nucleation mechanisms. A comparison of our results with previous reports of the ZSM-5 crystallization mechanism demonstrates that the seed crystals play a significant role in nucleation and crystal growth. Finally, seed surface crystallization and new nuclei crystallization dual mechanism has been proposed to describe the crystallization process of ZSM-5.     

KINETICS OF NON-ISOTHERMAL CRYSTALLIZATION OF POLY (ETHYLENE TEREPHTHALATE) MODIFIED BY POLY (ETHYLENE GLYCOL)

The non-isothermal crystallization kinetics of poly(ethylene terephthalate) (PET) modified by poly (ethlene glycol) (PEG) were determined by DSC. The dual linear regression method was used to evaluate the relationship between the reciprocal of t 1/2 ( the half life of crystallization) and the appropriate temperature variable. The parameters such as the activation energy (Ed) for transport, the equilibrium melting temperature (T_m~0),the nucleation parameter (ψ),themaximum crystallization temperature (T_(e, max)), and the kinetic crystallizability (G) for the copolyesters were obtained. The influence of the PEG content in PET chains on the parameters characterizing crystallization kinetics and crystallization thermodynamics was discussed.     

Isothermal and nonisothermal crystallization kinetics of irradiated nylon 1212

The crystallization behavior of nylon 1212, irradiated at ⁶⁰Co γ‐rays (50 kGy), was studied by a rheometer, polarized optical microscopy (POM), and differential scanning calorimeter (DSC). The results showed that irradiated nylon 1212 samples exhibited abnormal crystallization behavior during the crystallization process: The Avrami exponent n was calculated and was found to be in the range from 2.06–2.41 for isothermal crystallization, and from 2.67–4.91 for nonisothermal crystallization; the spherulite morphology also changed largely by polarized optical microscopy (POM); the crystallization activation energy ΔE for isothermal and nonisothermal crystallization process of irradiated nylon 1212 are determined to be 57.4 kJ/mol and 78.65 kJ/mol, respectively, which are lower than that of nonirradiated nylon 1212. At the same time, a new method by a combination of the Avrami and Ozawa equations was successfully applied to analyze the noncrystallization process of irradiated nylon 1212. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2326–2333, 2005     

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     

Effect of Heating Rate on Crystallization Kinetics of Amorphous Al91La5Ni4 Alloys by DSC

Crystallization kinetics of Al₉₁La₅Ni₄ amorphous ribbons produced by a melt-spinning method were studied by DSC analysis and X-ray diffraction. The effect of heating rate (from 4 to 200°C min^-1) was investigated in the temperature range from 298 to 700 K. Increases the heating rate from 4 to 200°C min^-1 resulted in increases of the temperature difference between the two stages of the transformation process: crystallization of Al and crystallization of the Al compounds from 148.9 to 167.4 K. The apparent activation energies for the first step, related to Al crystallization, and to the second step related to crystallization of Al₄La and Al₃Ni, were found to be 161±9 and 199±10 kJ mol^-1, respectively. The results indicate the possibility of tailoring the heating treatment to produce the required fraction of the amorphous phase. This revised version was published online in July 2006 with corrections to the Cover Date.     

Study of non-isothermal crystallization of amorphous Cu<Subscript>50</Subscript>Ti<Subscript>50</Subscript> alloy

The crystallization kinetics of amorphous Cu₅₀Ti₅₀ has been studied using differential scanning calorimetry (DSC) under non-isothermal conditions. The curves at different linear heating rates (2, 4, 8 and 16 K min^–1) show sharp crystallization peaks. The crystallization peak shifts to higher temperatures with increasing heating rate. The Kissingers method of analysis of the shift in the transformation peak is applied to evaluate the activation energy (E _c). The KJMA formalism, which is basically developed for isothermal experiments, is also used to obtain E _c and the Avrami parameter (n).The DSC data have been analysed in terms of kinetic parameters, viz. activation energy (E _c), Avrami exponent (n) and frequency factor K ₀ using three different theoretical models. It is observed that the activation energy values derived from KJMA approach and modified Kissinger equation agree fairly well with each other. The activation energy values obtained from normal Kissinger method, and Gao and Wang expression underestimate the activation energy.The financial support provided by All India Council for Technical Education (AICTE), New Delhi (Govt. of India) is gratefully acknowledged.     

Crystallization kinetics of Ti20Zr20Cu60 metallic glass by isoconversional methods using modulated differential scanning calorimetry

The study of crystallization kinetics of amorphous alloys has been a matter of great interest for material researchers for past few decades, since it provides information about the kinetic parameters i.e., activation energy of crystallization and the frequency factor. These kinetic parameters can be calculated by model-free isoconversional methods. Isoconversional methods allow calculating the activation energy as a function of degree of conversion, α. Hence, these methods provide accurate results for multistep processes like crystallization. Model-free methods are categorized as linear and non-linear isoconversional methods. Linear methods are further classified as linear differential and linear integral isoconversional methods. In present work, we have used these isoconversional methods to study the effect of non-linear heating rate, employed by modulated differential scanning calorimetry (MDSC), on the non-isothermal crystallization kinetics of Ti₂₀Zr₂₀Cu₆₀ metallic glass. For Ti₂₀Zr₂₀Cu₆₀, MDSC curves clearly indicate a two-step crystallization process. Both crystallization peaks were studied based on the modified expressions for isoconversional methods by non-linear heating rate. The term corresponding to non-linearity comes out to be (A _T ω/2β)². The effect of non-linear heating rate on measurement of kinetic parameters by isoconversional methods is studied. The activation energy of crystallization is calculated for Ti₂₀Zr₂₀Cu₆₀ metallic glass for various degrees of conversion by linear integral isoconversional methods i.e., Ozawa–Flynn–Wall, Kissinger–Akahira–Sunose, and also with Friedman method which is a linear differential isoconversional method.     

Thermal stability and crystallization kinetics of Se–Te–Sn alloys using differential scanning calorimetry

The present article deals with the differential scanning calorimetric (DSC) study of Se?CTe glasses containing Sn. DSC runs are taken at four different heating rates (10, 15, 20 and 25?K?min^?1). The crystallization data are examined in terms of modified Kissinger, Matusita equations, Mahadevan method and Augis and Bennett approximation for the non-isothermal crystallization. The activation energy for crystallization (E _c) is evaluated from the data obtained at different heating rates. Activation energy of glass transition is calculated by Kissinger??s relation and Moynihan theory. The glass forming tendency is also calculated for each composition. The glass transition temperature and peak crystallization temperature increases with the increase in Sn % as well as with the heating rate.     

Thermal decomposition of cycloadducts of vinylnaphthalenes with electron-deficient dienophiles

Light transmittance was measured during heating of thin NaPO₃ glass plates at different heating rates. According to the results, the crystallization of orthorhombic textured NaPO₃ glass proceeds from sample surfaces into their interior due to the foregoing surface nucleation. The glass surface crystallization process resulted in the sigmoidal decrease of the optical transmittance. Elaborated data lead to the activation energy of glass surface crystallization of the value of 182.8 kJ mol ^-1.     

Non-isothermal crystallization kinetics of poly(trimethylene terephthalate)/poly(ethylene 2,6-naphthalate) blends

The glass-transition temperature and non-isothermal crystallization of poly(trimethylene terephthalate)/poly(ethylene 2,6-naphthalate) (PTT/PEN) blends were investigated by using differential scanning calorimeter (DSC). The results suggested that the binary blends showed different crystallization and melting behaviors due to their different component of PTT and PEN. All of the samples exhibited a single glass-transition temperature, indicating that the component PTT and PEN were miscible in amorphous phase. The value of T_g predicted well by Gordon-Taylor equation decreased gradually with increasing of PTT content. The commonly used Avrami equation modified by Jeziorny, Ozawa theory and the method developed by Mo were used, respectively, to fit the primary stage of non-isothermal crystallization. The kinetic parameters suggested that the PTT content improved the crystallization of PEN in the binary blend. The crystallization growth dimension, crystallization rate and the degree of crystallinity of the blends were increased with the increasing content of PTT. The effective activation energy calculated by the advanced iso-conversional method developed by Vyazovkin also concluded that the value of E_a depended not only on the system but also on temperature, that is, the binary blend with more PTT component had higher crystallization ability and the crystallization ability is increased with increasing temperature. The kinetic parameters U^* and K_g were also determined, respectively, by the Hoffman-Lauritzen theory.     

Crystallization in glasses monitored by thermomechanical analysis

Thermomechanical analysis (TMA) can be used as a sensitive tool to follow crystallization behavior in non-crystalline materials. Newly developed method is based on slowing down of sample deformation caused by viscous flow above the glass transition due to macroscopic crystal growth. It is shown that a typical TMA sigmoidal curve reasonably well corresponds to direct measurement of crystal growth kinetics by means of optical microscopy. The method has been used to study crystallization kinetics in Ge₃₈S₆₂ glass. The TMA measurement is able to detect earlier stages of crystallization than obtained by differential scanning calorimetry measurement. The activation energy obtained from the shift of extrapolated end of TMA curve with heating rate (E = 263 ± 7 kJ mol^?1) is similar to the activation energy of ??-GeS₂ crystal growth in Ge₃₈S₆₂ glass (E _G = 247 ± 23 kJ mol^?1) obtained from direct optical microscopy measurements.     

Crystallization kinetics of amorphous Fe75-xCuxSi9B16

In this work the influence of Cu admixtures on the crystallization process of amorphous Fe-Si-B alloys is studied, based on measurements of differential thermal calorimetry of the series Fe_75-xCu_xSi₉B₁₆ (x=0, 1, 2, 2.8 and 3.5) during their heating with different heating rates. The first crystallization stage can not be traced for any of the amounts of Cu content examined, while the second stage is observed only when the Cu content is 1 at%. The activation energy as estimated with Kissinger's method for the third crystallization stage has a mean value of 326 kJ mol^-1 and with the isoconversional Flynn, Wall and Ozawa method is almost constant when 0.05<a<0.6 and exhibits a small monotical decrease when a>0.6. The main crystallization peak can not be described by means of a single JMA-type function. This revised version was published online in August 2006 with corrections to the Cover Date.     

Non-isothermal crystallization kinetics of a Si–Ca–P–Mg bioactive glass

In this work, the crystallization process of a SiO₂–3CaO·P₂O₅–MgO glass was studied by non-isothermal measurements using differential thermal analysis carried out at various heating rates. X-ray diffraction at room and high temperature was used to identify and follow the evolution of crystalline phases with temperature. The activation energy associated with glass transition, (E _g), the activation energy for the crystallization of the primary crystalline phase (E _c), and the Avrami exponent (n) were determined under non-isothermal conditions using different equations, namely from Kissinger, Matusita & Sakka, and Osawa. A complex crystallization process was observed with associated activation energies reflecting the change of behavior during in situ crystal precipitation. It was found that the crystallization process was affected by the fraction of crystallization, (x), giving rise to decreasing activation energy values, E _c(x), with the increase of x. Values ranging from about 580 kJ mol^?1 for the lower crystallized volume fraction to about 480 kJ mol^?1 for volume fractions higher than 80 % were found. The Avrami exponents, calculated for the crystallization process at a constant heating rate of 10 °C min^?1, increased with the crystallized fraction, from 1.6 to 2, indicating that the number of nucleant sites is temperature dependent and that crystals grow as near needle-like structures.     

Crystallization kinetics study of melt-spun Zr66.7Ni33.3 amorphous alloy by electrical resistivity measurements

In this paper, the electronic transport properties of as-spun Zr_66.7Ni_33.3 alloys were studied in detail by a combination of electrical resistivity and absolute thermoelectric power measurements over a temperature range from 25 up to 400 °C. Moreover, the isochronal and isothermal crystallization kinetics of Zr_66.7Ni_33.3 glassy alloy has been investigated based on the electrical resistivity measurements. The comparative study of the crystallization kinetics of these binary amorphous alloys was carried out, for the first time to our knowledge, using an accurate method for electrical resistivity measurements. In the isochronal heating process, the apparent activation energy for crystallization was determined to be, respectively, 371.4 kJ mol⁻¹ and 382.2 kJ mol⁻¹, by means of Kissinger and Ozawa methods. The Johnson–Mehl–Avrami model was used to describe the isothermal transformation kinetics, and the local Avrami exponent has been determined in the range from 2.97 to 3.23 with an average value of 3.1, implying a mainly diffusion-controlled three-dimensional growth with an increasing nucleation rate. Based on an Arrhenius relationship, the local activation energy was analyzed, which yields an average value E_x = 376.2 kJ mol⁻¹.

     

How much is the accuracy of activation energy affected by ignoring thermal inertia?

This work estimates the magnitude of the effect of thermal inertia on the value of the activation energy determined from heat-flux differential scanning calorimetry (DSC) data. The estimates are obtained via analysis of the literature data on crystallization of copper and thermal degradation of isotactic polystyrene (iPS). The copper crystallization data have been obtained for very large masses (200 mg) and fast heating rates up to 80 K min⁻¹. The iPS degradation data have been collected on small masses (3 mg) and at the heating rates up to 20 K min⁻¹. For crystallization of copper, the Kissinger activation energy obtained from the DSC data corrected for thermal inertia is 34% larger than the value estimated from uncorrected data. This difference drops to 8% and becomes statistically insignificant when the fastest heating rate used is decreased to 10 K min⁻¹. For iPS degradation, the difference in the isoconversional activation energies estimated, respectively, from corrected and uncorrected DSC data is less than 3% and is not statistically significant. Overall, the effect of thermal inertia on the activation energy appears negligible provided that DSC measurements are conducted on smaller samples and at slower heating rates, that is, as advised by the International Confederation for Thermal Analysis and Calorimetry (ICTAC) recommendations. It is suggested that the difference in the activation energies should generally be within the typical 5-10% uncertainty as long as the product of the time constant and the maximum heating rate does not exceed 2-3 K.