X t is defined as a function of temperature:. For the non-isothermal crystallization process, the relationship between crystallization time t and the corresponding temperature T can be expressed as follows:. The horizontal temperature axis can be transformed into a time scale. All these curves have the same characteristic sigmoidal shape at various cooling rates due to the spherulite impingement in the later stage of crystallization. It can be seen that, for crystallization completion, a shorter time requires higher cooling rates.
Several methods have been developed to describe the non-isothermal crystallization kinetics of polymers. The Avrami equation was used to describe the primary stages of isothermal kinetics. According to the model, the relative crystallinity X t changes with crystallization time t as follows:. In actual conditions, the temperature changes constantly during non-isothermal crystallization; hence, the parameters n and k have different physical meanings. Therefore, Jeziorney considered the correction of the crystallization rate constants by introducing the cooling rate.
The modified equation is expressed by Jeziorny, :.
The values of Z c are shown in Table 2. Z c is increased by increasing the cooling rate. The data are shown in Table 2. As discussed earlier, this effect was caused by reducing PVDF molecular mobility due to stronger interactions with PVP in the molten state. The Ozawa model is one of the most used kinetic approaches for non-isothermal crystallization process, proposed by extending the Avrami Equation Jeziorny, This model is based on the assumption that the non-isothermal crystallization process can be divided into small isothermal steps. The Ozawa Equation is expressed as:. The Ozawa exponent depends on the dimension of crystal growth.
It can be seen that these figures have poor linear correlations. Changes in slopes indicate that m varies with temperature. Thus, the Ozawa method was not satisfactory for the description of the crystallization kinetics of PVDF films.
Interfaces Crystallization Viscoelasticity
Some authors have declared that the Ozawa model cannot be applied for modeling the crystallization kinetics of polymers that have secondary crystallization Ozawa, ; Yu. It is obvious that the Avrami analysis and its Jeziorny modification could only describe the primary stages of non-isothermal melt crystallization. In order to find a method to describe the non-isothermal crystallization process exactly, Mo and his colleagues suggested a new method Liu et al.
This method is the combination of the Avrami and Ozawa Equations at a given value of X t :. F T has a definite physical and practical meaning. The kinetic parameters are listed in Table 3. The data show that F T increased upon increasing the relative crystallinity. This is also in agreement with other kinetic parameters. Ziabicki developed another approach for non-isothermal crystallization kinetics related to the crystallization progress and crystallization rate-temperature function Ziabicki, Crystallization kinetics of polymers in Ziabicki's model can be described by the following equation first order kinetics :.
With the isokinetic approximation, the semi-crystalline polymer crystallization ability kinetic crystallizability index , G z , was obtained by the integration of Equation 11 over the crystallization range:. The G z parameter expresses the ability of a semi-crystalline polymer to crystallize.
Several methods such as Kissinger, Vyazovkin and Friedman methods are used to evaluate the activation energy for the crystallization process Kissinger, ; Vyazovkin, ; Friedman, ; Omrani et al.
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In fact, the activation energy was closely related to the relative crystallinity degree. In order to calculate approximately reliable values of the effective activation energy, the differential isoconversional method of Friedman and the advanced integral isoconversional method of Vyazovkin were used.
The Friedman Equation is expressed as follows Ma et al. Thus, the activation energy E X t can be calculated from the slope of the straight line. According to the results, the activation energy increased upon increasing the relative crystallinity, suggesting that the crystallization becomes more difficult with an increase in relative crystallinity.
Indeed, one should expect that transmission of the polymer segments from the equilibrium melt to the growth front will be slowed down as crystallization proceeds. It is noteworthy that the sole dependence of the activation energy on relative crystallinity is sufficient to reliably predict the behavior of a substance. The accuracy of such predictions obviously depends on the accuracy of calculating the activation energy. Thus, errors in computing the activation energy must be minimized.
One of the sources of these errors are approximations intentionally used to derive the linear final plots yielding the activation energy. Approximations undeniably induced an error in the values of the activation energies.
To resolve this problem, a non-linear procedure for computing the activation energy by the isoconversional method was developed. An advanced isoconversional method nonlinear was described by Vyazovkin In the present study, a non-linear isoconversional method was applied to the dynamic DSC data of neat PVDF system using the following equation:.
In Equation 12 the temperature integral was determined by the Senum-Yang approximation Senum et al. Each value of X t was minimized to obtain the E a dependence.
The advanced isoconversional method applied the same computational algorithm for isothermal and non-isothermal DSC data. The isoconversional plot trends in Fig. The Jeziorny, Mo and Ziabicki models were applied to describe the crystallization process and appeared to be successful. Kinetic parameters obtained from these mathematical models showed that the crystallization rate of PVDF decreased in the presence of PVP and was affected by the molecular weight of PVP.
Badia, J. Thomas, S. KGaA, Weinheim, Germany, Bahader, A. Bianchi, O. Solids, , 29 Chen, N. Polymer, 43, Fan, W. Freire, E. Friedman, H. Application to a phenolic plastic. C: Polym. Gradys, A. Acta, , He, F.
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Jeziorny, A. Polymer, 19, Ji, G. Kissinger, H.
Holdings: Interfaces Crystallization Viscoelasticity
Lang, M. Lee, W. Polymer, 39, Li, J. Liu, J. Crystallization and phase diagram by differential scanning calorimetry. J Polym. B: Polym. Liu, Z. Lobo, H. Lorenzo, M.
Large-scale ordering of nanoparticles using viscoelastic shear processing
Ma, W. Mancarella, C. Polymer, 18, Martins, J.
becksgf.com/wp-content/176.php We are investigated the structural and mechanical properties of natural products extracted from plants wheat grain and proteins or synthesized from plant biomass.
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