Crystallization Kinetic Parameters Research Articles

Determining Kinetic Parameters for Isothermal Crystallization of Glasses

Non‐isothermal crystallization techniques are frequently used to determine the kinetic parameters for crystallization in glasses. The techniques are experimentally simple and quick, compared with isothermal techniques. However, the analytical models used for non‐isothermal data analysis, that were derived from models originally developed for describing isothermal transformation kinetics, are fundamentally flawed. The present paper describes a technique for determining the kinetic parameters for isothermal crystallization in glasses, which eliminates most of the common problems that generally make the study of isothermal crystallization laborious and time consuming. In this technique, the volume fraction of a glass that is crystallized as a function of time during an isothermal hold was determined in a separate experiment using differential thermal analysis. The activation energy (345±10 kJ/mole) and Avrami parameter (0.89±0.09) for crystallization of Li2O·2SiO2 glass determined by the present technique are consistent with the similar values reported in the literature.

Effect of nucleating agents on crystallization kinetics of PET

Effects of three nucleating agents concluding talc, sodium benzoate (SB) and an ionomer (Ion., Na+) on crystal- lization of poly(ethylene terephthalate) (PET) were studied by differential scanning calorimetry (DSC) and polarized opti- cal microscope (POM), the parameters of crystallization kinetics were obtained through Avrami and Ozawa equations. The fold surface free energy σe of pure PET and PET/nucleating agent blends was calculated by Hoffman-Lauritzen theory. The results indicate that the three kinds of nucleating agents increase the crystallization rate constant through promoting their nucleating effect for PET crystallization, among which SB is the best one with the same content. The crystallization mode of PET might shift from three-dimensional growth to two-dimensional growth by the addition of the nucleating agents. The values of σe of PET/nucleating agent blends are much less than that of pure PET, and PET/SB (99:1) blend has the least value of σe (18.2 mJ/m2). The conclusion based on Hoffman theory is similar to the analysis by Avrami and Ozawa equa- tions.

Influence of hyperbranched against linear architecture on crystallization behavior of poly(ɛ-caprolactone)s in binary blends with poly(vinyl chloride)

Nonisothermal and isothermal crystallization behaviors of the hyperbranched poly(e-caprolactone) (HPCL)/poly(vinyl chloride) (PVC) and linear poly(e-caprolactone) (LPCL)/(PVC) blends were characterized with various blend composition such as 100/0, 95/5, 90/10, and 80/20, respectively. HPCL was synthesized through polycondensation of AB2 macromonomer while LPCL and PVC were commercially purchased. The architectural characterization performed on 1H NMR spectra revealed that HPCL consisted of about 3 AB2 units and the linear segments consisted of 25 e-CL units. Through the nonisothermal crystallization analyses by modified Avrami approach with DSC crystallization exotherms, it was found that the crystallization rate was retarded by the increase in the noncrystallizable component (PVC) in the blends. This is in good agreement with the results of the isothermal crystallization analyses where time resolved small angle light scattering (SALS) and polarized optical microscopy (POM) were used. The effect of molecular architectural difference between HPCL and LPCL on the crystallization of their binary blends with PVC was elucidated by comparing the crystallization kinetic parameters. Both the nonisothermal and isothermal crystallization analyses showed that the crystallization rates of HPCL/PVC blends was faster than LPCL/PVC blends at given blend compositions. The faster crystallization of the HPCL/PVC blends is ascribed to the two specific architectural characteristics of HPCL; the branched structure and the incorporated long linear segments. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 577–589, 2007

Crystallization study of amorphous Al 82Fe 5Ni 5Ce 8 alloy

The crystallization behavior and thermal stability of Al 82Fe 5Ni 5Ce 8 amorphous alloy, obtained by mechanical alloying, were investigated by using X-ray diffraction (XRD), differential thermal analyzer (DTA) at constant heating rate. One exothermic peak was observed from the continuous heating DTA curves, implying the crystallization process undergoes only one stage. The product phases of crystallization are intermetallic compounds Al 11Ce 3 and Al 3(Fe, Ni). The crystallization kinetic parameters, including activation energy ( E a), Avrami exponent ( n) were determined with isothermal and isochronal analysis method based on the DTA data. The results suggest that the crystallization mechanism is governed dominantly by a three-dimensional diffusion-controlled growth.

Effect of heat-treatment on cobalt–molybdenum system

The binary oxide Co–Mo oxides were prepared by mixing the propagate amounts of aqueous cobalt nitrate and ammonium molybdate solutions at pH 5.0 to give ratio of Mo/Co = 1, followed by evaporation of water and by decomposition of the deposit at different temperatures from 200–900 °C. The obtained samples before and after heat-treatment were subjected to XRD and IR techniques to examine their structure. From both of them, it can be observed that, by increasing the temperature of heat-treatment the cobalt–molybdate oxide is strongly observed and cobalt–molybdate hydrate decreased. The lines characteristic for cobalt–molybdate hydrate is absented for heated sample at 900 °C indicating that cobalt–molybdate oxide is only oxide formed at this temperature. The crystallization kinetic parameters were studied from DSC curves at different heating rates by using different methods. The crystallization process occurred with three mechanisms and bulk crystallization.

Isothermal crystallization behavior of poly(trimethylene terephthalate) at high undercoolings

After successfully being commercialized in the 1990s, poly(trimethylene terephthalate) (PTT) has drawn more and more attention due to its superior characteristics, such as elastic recovery, chemical resistance and resilience in comparison with poly (ethylene terephthalate) (PET) and poly (butylene terephthalate) (PBT) [1, 2]. PTT is a typical semicrystalline polymer material and many reports were focused on its crystallization behaviors recently. Huang and Chang [3] investigated the crystallization behavior for PTT from the melt and analyzed the kinetics in the temperature range from 451 K to 483 K, some important parameters for crystallization such as equilibrium melting temperature(Tm 0 = 521 K), lateral surface-free energy (r),work of chain folding (q) were also reported. Crystallization kinetics parameters of PET, PTT and PBT were compared by Chuah [4], it could be concluded that PTT crystallized faster than PET but slower than PBT at the same degree of undercooling. Hong and his coworkers [5] took note of the inaccuracy of Chang and Huang in determining the work of chain folding (q) and gave a more reasonable value of 27.2 kJ mol, they also investigated the regime behaviors of PTT crystallization using the secondary crystallization theory [6] and found the boundaries between the classical regime I fi II and regime II fi III are located at 488 and 468 K, respectively. We also carried out the kinetics analysis of PTT crystallization including the secondary crystallization process using a new mathematical model constructed by us [7]. Much of the above work has concentrated on the measurement of overall rate of crystallization or the measurement of spherulitic growth rate of PTT crystallization from melt at low and moderate degrees of undercooling (DT = Tm –Tc, Tc is crystallization temperature), yet a detailed overall kinetics analysis at high undercoolings (DT > 70 K), especially in the temperature range where the fastest crystallization rate would occur is still lacking. However, study of the behavior of a semicrystalline polymer crystallizing in this temperature range is of great importance from both theoretical and practical view points. Of theoretical importance is the mechanism of nucleation, the growth geometry of crystals and the formation of polymer fine structure during crystallization. The practical importance is that such crystallization data may be very useful to polymer processing such as fiber spinning and injection molding, because most polymer shaping processes need a very fast crystallization rate to shorten the solidifying time. The importance also arises from the effect of final crystallinity on the physical and chemical properties of polymers. In this study, we present the isothermal crystallization behavior of PTT from 356 K to 465 K, the overall crystallization kinetics data in the temperature range 356–450 K was reported for the first time. Poly(trimethylene terephthalate) samples with different molecular weights were obtained by the polycondensation of terephthalic acid in the melt phase with 1,3-propandediol using different reaction time Y. Xu (&) H.-b. Jia Department of Polymer Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, P. R. China e-mail: njust_xuy@hotmail.com

Crystallization kinetics for simulation of processing of various polyesters

AbstractThe approach to determine crystallization kinetic parameters based on the DSC nonisothermal crystallization experiments is applied to poly(butylene terephthalate) (PBT) and poly(ethylene‐2,6‐naphthalate) (PEN). The differential form of the Nakamura equation and master curve approach are used. The isothermal induction times are obtained from nonisothermal induction times according to the concept of induction time index. The correction of temperature lag between the DSC furnace and the sample is incorporated. The corrected nonisothermal crystallization kinetic data is shifted with respect to an arbitrarily chosen reference temperature to obtain the master curve. By fitting the obtained master curve with the Hoffman‐Lauritzen equation, the model parameters for the crystallization rate constant are obtained. The relative crystallinity measured at different cooling and heating rates is described by these model parameters. © 2006 Wiley Periodicals, Inc. J Appl PolymSci 102: 2847–2855, 2006

Kinetic study of the electrocrystallization of calcium carbonate on metallic substrates

It is of practical and theoretical importance to understand how physico-chemical factors influence the mechanisms of calcium carbonate crystallization. The present paper focuses on the effect of the nature of metallic substrates (stainless steel, soft steel and copper) in the nucleation/growth process of electrochemically deposited calcium carbonate. An in situ experimental procedure based on image analysis was used to observe and characterize the crystals on the polarized surface: their number, the surface coverage and several morphometric parameters were quantified. Experimental results were fitted with a mathematic model based on a diffusion-controlled process that allowed to determine the kinetic parameters of crystallization. The results showed that the nature of the metallic substrate did not act on the crystaline variety of the deposit (calcite) but strongly influences the nucleation/growth process. Copper substrate produced a high number of nuclei and a large surface coverage compared with soft steel and stainless steel where the number of crystals and the surface coverage are lower. Whatever the substrate, the lateral growth rate decreased during the experiment. With stainless steel, the growth was significant and with soft steel the growth of crystals was not homogeneous.

Crystallization and microstructure of Li2O–Al2O3–SiO2 glass containing complex nucleating agent

The crystallization and microstructure of Li2O–Al2O3–SiO2 (LAS) glass ceramic with complex nucleating agents (TiO2+ZrO2+P2O5+/or F−) are investigated by differential thermal analysis (DTA), X-ray diffraction (XRD) and scanning electron microscopy (SEM), and the effects of P2O5 and F− on the crystallization of LAS glass are also analyzed. The introduction of both P2O5 and F− promotes the crystallization of LAS glass by decreasing the crystallization temperature and adjusting the crystallization kinetic parameters, allows a direct formation of β-spodumene without the transformation of LiAl(SiO3)2 into β-spodumene and as a result, increases the crystal size and crystallinity of LAS glass ceramic.

Influence of chemical modification of wood on the crystallisation of polypropylene

The mechanical properties of wood/polypropylene composites depend strongly on interfacial adhesion between components. However, the application of chemical modification to improve compatibility can influence the supermolecular structure of polypropylene matrix. The experimental material comprised two most common Polish timber species pine wood (Pinus silvestris L.) as a softwood species and beech wood (Fagus silvatica L.) as a hardwood species. The size of wood sawdust ranged from 0.5 to 1.0 mm. Three different types of wood/PP mixture were prepared: (1) PP – untreated wood, (2) PP – NaOH treated wood and (3) PP – esterified wood with maleic anhydride. In this work, the kinetic parameters of crystallization of PP by differential scanning calorimetry were investigated. It is interesting that crystallisation of PP depends on the kind of wood. The chemical treatment of wood caused changes of crystal conversion and half crystallisation time of polypropylene matrix.

Effect of microalloying on glass-forming ability and crystallization kinetics of Zr52.5Cu17.9Ni14.6Al10Ti5 alloy

Zr 52.5 Cu 17.9 Ni 14.6 Al 10 Ti 5 bulk metallic glass prepared using sponge zirconium was microalloyed with 0.1 at.%B + 0.2 at.%Si + 0.1 at.%Pb. The effect of microalloying on the glass-forming ability and thermal stability of the alloy is studied. The crystallization kinetic parameters are determined by means of a Kissinger plot. The interrelation between these parameters is discussed.

Novel phosphate glass/polyamide 6 hybrids: Miscibility, crystallization kinetics, and mechanical properties

AbstractThe miscibility, crystallization kinetics, and mechanical properties of a novel low Tg phosphate glass (Pglass)/polyamide 6 hybrid material were investigated. Here, we report the first evidence for miscibility of inorganic phosphate glass and organic polymer prepared by blending both components in the liquid phase using conventional polymer processing methods. From classical melting point depression measurements, we obtained a chi interaction parameter (χ) of −0.067 for the Pglass/polyamide 6 hybrid, indicating that the inorganic glass and polyamide 6 are miscible. The crystallization kinetic parameters for the hybrids were determined using the Avrami approach and found to depend on the volume fraction of Pglass present in the system. In addition, we studied both the dynamic and static mechanical behavior of the hybrids. The results showed a single Tg that decreased by up to 10 °C with increasing phosphate glass volume percent for the hybrids, giving further evidence for the hybrid component miscibility and plasticizing action of the phosphate glass in the pure polyamide 6, respectively. The tensile (static) mechanical properties of the hybrids were found to be remarkably similar to those obtained from typical polymers plasticized with relatively low molecular weight compounds. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 441–450, 2006

Optical monitoring of polyesters injection molding

AbstractAn optical fiber sensor similar to the one developed by Thomas and Bur1 was constructed for the monitoring of the crystallization of three polyesters during the injection molding process. The polyesters studied were: polybutylene terephthalate (PBT), polytrimethylene terephthalate (PTT), and polyethylene terephthalate (PET). With this optical system it was possible to obtain, in real time, some essential parameters of the polyester crystallization kinetics at different processing conditions. Thus, a study of the influence of injection molding variables on the nonisothermal crystallization kinetics of these polyesters was done. The processing variables were: mold wall and injection temperatures, Tw and Ti, respectively; flow rate, Q; and holding pressure, Ph. The experiments were done following a first order central composite design statistical analysis. The morphology of the samples was analyzed by polarized light optical microscopy, PLOM. The signal of the laser beam during the filling and the crystallization stages of the injection molding of these materials was found to be reproducible. The measurements showed that this system was sensitive to variations of the crystallization of different types of polymers under different processing conditions. The system was not able, however, to monitor the crystallization process when the crystallinity degree developed by the sample was very low, as in the PET resin. It was also observed that Tw and Ti were the most influential variables on the crystallization kinetics of PBT and PTT. Due to its slower crystallization kinetics, PTT was found to be more sensitive to changes in these parameters than the PBT. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 99: 563–579, 2006

Mullite crystallization mechanism obtained from kinetic parameters determination for seeded and non-seeded gel

Mullite crystallization kinetics was studied using a non-isothermal method. The mullite crystallization parameters obtained from seeded gels were compared with those obtained from non-seeded gels. The phase evolution was studied by X-ray diffraction (XRD) and the thermal events associated to heating treatment by differential thermal analysis (DTA). The crystallization kinetic parameters were obtained using the methodology developed by R.A. Ligero, which is based on Johnson–Mehl–Avrami (JMA) kinetic model. The Avrami exponent (1.9), the apparent activation energy (980 kJ/mol) and the rate constant (3.68 × 10 30 s −1) were determined by this model, for both seeded and non-seeded processes, resulting in similar values for each parameter. Based on the apparent activation energy and rate constant values, one should conclude that mullite crystallization is not controlled by nucleation. On the other hand, Avrami exponent ∼2 is an indicative that the process is controlled by the nucleation step. These controversies are discussed in this paper, based on experimental procedure, model limitation and literature information.

Two heating rates as a method for calculating the kinetic parameters of crystallization in a glassy system

AbstractVarious experimental methods are currently employed for determining the kinetic parameters of crystallization in a glassy system. These parameters include the activation energy E(kJ/mol), the Avrami exponent or the reaction order (n) and the frequency factor K0 (s–1). In the present work, a new method is derived from Johnson–Mehl–Avrami (JMA) equation to calculate the kinetic parameters of crystallization. The method starts with determining the activation energy E. The method depends on obtaining the same vol‐ume fraction of crystallization x(t) at two heating rates. Next, the reaction order n and the frequency factor K0 are determined successively. The present method is straightforward and involves no assumptions in addition to those involved in obtaining JMA equation. The new technique has successfully predicted the crystallization parameters of Ge10Te35As55 glasses during non‐isothermal annealing. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Crystallization and melting behavior of homogeneous and heterogeneous linear low‐density polyethylene resins

AbstractThe crystallization behavior of homogeneous and heterogeneous linear low‐density polyethylenes (LLDPE) was investigated by evaluating the characteristics of melting traces obtained by differential scanning calorimetry (DSC). Based on the isothermal experimental results, the concept of the effective nucleation induction time is suggested. In the initial crystallization stage, the Avrami equation in conjunction with the effective induction time can be used to successfully describe the overall crystallization kinetics. Avrami exponents 2, 1.5, and 1 were found to apply in regimes III, II, and IM, respectively, as identified by the modified Hoffman‐Lauritzen (MHL) equation. The kinetic parameters estimated from evaluating the linear crystallization behavior during spherulitic growth experiments using polarized light microscopy (PLM) are in agreement with the overall crystallization kinetic parameters obtained from DSC experiments. POLYM. ENG. SCI., 45:1140–1151, 2005. © 2005 Society of Plastics Engineers

Electrical conductivity and crystallization kinetics of amorphous Se 0.81In 0.19 films

The temperature dependence of the DC conductivity ( σ ) of amorphous Se and Se 0.81In 0.19 thin films, prepared by thermal evaporation, has been studied. The incorporation of In atoms in a Se matrix leads to an increase in the electrical conductivity of Se 0.81In 0.19 and to a decrease in the thermal activation energy of conduction from 0.57 to 0.24 eV. The change in σ with time during the amorphous-to-crystalline transformation is recorded for Se 0.81In 0.19 films at different isothermal temperatures in the range 343–373 K. The results indicate that the micro-heterogeneous structures of the films have a remarkable influence on the electrical conductivity during the amorphous-to-crystalline transition. The formal crystallization theory of Avrami has been used to calculate the kinetic parameters of crystallization. The activation energy of the amorphous-to-crystalline transformation is found to be 0.82 and 1.29 eV, respectively, for the two stages of crystallization during the time period of the transformation process.

Isothermal crystallization kinetics of PP in PP/Mg(OH)2 composites

AbstractThe crystallization and melting behavior of PP/Mg(OH)2 composites was investigated, and the crystallization kinetic parameters and thermal characteristics were investigated according to the Avrami method. Optical polarizing microscope (POM) analysis suggested that the presence of Mg(OH)2 particles gave rise to an increase in the number of nuclei and a decrease in PP spherulitic size. The Avrami exponent n of the PP and composites increased with increasing crystallization temperature, and markedly deceased with the addition of low Mg(OH)2 content. A significant increase in crystallization kinetic constant, and a decrease in crystallization half time of PP were observed in the presence of Mg(OH)2 particles, indicating a heterogeneous nucleating effect of Mg(OH)2 upon crystallization of PP. The melting temperature and equilibrium melting temperature of PP in the composites decreased with increasing the Mg(OH)2 content, which is directly related to the size of the PP crystals. The difference of PP melting enthalpies in the PP and composites demonstrated that the presence of Mg(OH)2 can effectively enhance the crystalline of PP. The crystallization thermodynamics of PP and composites were studied according to the Hoffman theory. Surface free energy of PP chain folding for crystallization of PP/Mg(OH)2 composites was lower than that of PP, confirming the heterogeneous nucleation effect of Mg(OH)2. However, the evaluation of the nucleation activation energy of PP suggested the presence of a large amount of Mg(OH)2 particles in the PP matrix reduced the mobility of PP segments and restricted the development of PP nucleation. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1914–1923, 2005

Interaction between light and crystallizing polymer: a simulation study

A study of light transmission through a crystallizing polymer has been carried out by graphic simulations, consisting of sporadic and pre-determinate nucleation and growth of disks (spherulites) in a rectangular area. Interaction between a light beam crossing a sample of polymer has been described by a series of simple graphical rules, accounting for both absorption and scattering. Results of the code well reproduce the experimental behavior observed in the literature of main beam light intensity emerging from a crystallizing polymer sample and allows a better understanding of the interaction between light and nucleating/growing units. Emerging light behavior calculated by the simulation has been adopted as the basis to suggest the dependence of the light scattering coefficient upon crystallization kinetic parameters.

Effect of thallium on the crystallization kinetics of the chalcogenide glasses GeSe<Subscript>2</Subscript> and GeSe<Subscript>4</Subscript>

The structure identification of the quenched compositions GeSe 2 , GeSe 4 , GeSe 2 Tl and GeSe 4 Tl has been confirmed by energy dispersive X-ray analysis (EDX), X-ray diffraction (XRD) and differential thermal analysis (DTA). The differential thermal analysis curves of the compositions under investigation were recorded at the heating rates 5, 10, 20, 30 and 50°C min -1 . Addition of thallium to GeSe 2 and GeSe 4 results in decreasing the glass transition temperature T g , the crystallization temperature T c and the melting temperature T m . The effect of heating rates on the transition temperatures ( T g , T c and T m ) was studied and the variation of the crystallization peak temperature T p position was used to calculate the activation energy. The kinetic parameters of crystallization for the devitrification processes have been determined by three methods and discussed on the basis of Johnson-Mehl-Avrami model.