General treatment of polymer crystallization kinetics—Part 2. The kinetics of nonisothermal crystallization

The isothermal macrokinetic equation of polymer crystallization has been generalized to cover nonisothermal situations as well. The process of nonisothermal crystallization of poly(caproamide) has been studied experimentally. It is shown that the macrokinetic equation of the autocatalytic type can be used to solve both direct and inverse problems of nonisothermal polymer crystallization. Use of the inverse approach has made it possible to establish the value of the constants of the new kinetic equation. The general statement of the problem of nonisothermal crystallization of polymers in an inhomogeneous temperature field is considered. Inhomogeneous temperature and conversion fields have been calculated for model products of different sizes and configurations.     

Crystallization kinetics of oriented polymers

The increase in the rate of polymer crystallization brought about by mechanical deformation above the polymer glass-transition temperature is examined. For flexible macromolecules, this deformation results in alignment and extension of polymer chains. By hypothesizing that the instantaneous growth rate at a given constant temperature depends uniquely on the polymer chain orientation in the surrounding melt, an explicit expression is obtained for the growth rate of a spherulite in terms of experimentally measurable quantities. Isothermal meltspinning experiments were conducted with poly(ethylene terephthalate) (PET) using a laboratory setup. Very large values of the total crystallinity and significantly enhanced values of the crystallization rate were generated by operating at different temperatures that straddle the temperature of maximum crystallization rate for the quiescent melt. Measured rates of crystallization do, indeed, correlate with the instantaneous amorphous orientation. Furthermore, a masterplot, independent of temperature, is obtained by normalizing the crystallization rate under spinning conditions with that under quiescent conditions. This is the first time that such data have become available, and, given the processing history, such a master plot should be of use in predicting the crystallinity levels in actual nonisothermal industrial experiments.     

Strengthening of poly(butylene adipate-co-terephthalate) by melt blending with a liquid crystalline polymer

Poly(butylene adipate-co-terephthalate) (PBAT) is a soft biodegradable polymer with a low melting temperature. PBAT has been melt-blended with a liquid crystalline polymer (LCP) aiming at preparing a new biodegradable polymer blend with improved mechanical properties. The phase structure and crystalline morphologies of the PBAT/LCP blends were investigated using scanning electron microscopy (SEM), differential scanning calorimetry (DSC), small-angle X-ray scattering (SAXS), and transmission electron microscopy (TEM). It was found that the LCP domains are precisely dispersed in the PBAT matrix and that these domains act as the nuclei for PBAT crystallization. The nonisothermal crystallization temperature from the melt was dramatically shifted from 50°C to about 95°C by the addition of 20% LCP. In addition, the tensile modulus of the prepared blends increases gradually with increasing LCP content, indicating the excellent strengthening effects of LCP on the PBAT matrix. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Crystallization kinetics of poly(phenylene sulfide) (PPS) and PPS/carbon fiber composites

The evolution of crystallinity of neat PPS and of the carbon fiber reinforced polymer under different processing conditions is studied. Crystallization from the amorphous state at low temperatures (cold crystallization), crystallization from the melt during cooling, and crystal melting processes are analyzed using calorimetric techniques under both isothermal and nonisothermal conditions. Cold and melt crystallization kinetics are described using an Avrami equation and an Arrhenius expression for the temperature dependence of the kinetic constant. Also, the melting kinetics of the, reinforced and of the unreinforced polymer are studied in this work. The effect of carbon fibers on the crystallization kinetics of PPS is analyzed, and a comparison of the crystallization behavior of PPS and other semicrystalline thermoplastic matrices, such as poly(etheretherketone) (PEEK), is presented.     

Isothermal and nonisothermal crystallization kinetics of MC nylon and polyazomethine/MC nylon composites

Crystallization kinetics of MC nylon (PA6) and polyazomethine (PAM)/MC nylon (PAM/PA6) both have been isothermally and nonisothermally investigated by different scanning calorimetry (DSC). Two stages of crystallization are observed, including primary crystallization and secondary crystallization. The Avrami equation and Mo's modified method can describe the primary stage of isothermal and nonisothermal crystallization of PA6 and PAM/PA6 composite, respectively. In the isothermal crystallization process, the values of the Avrami exponent are obtained, which range from 1.70 to 3.28, indicating an average contribution of simultaneous occurrence of various types of nucleation and growth of crystallization. The equilibrium melting point of PA6 is enhanced with the addition of a small amount of rigid rod polymer chains (PAM). In the nonisothermal crystallization process, we obtain a convenient method to analyze the nonisothermal crystallization kinetics of PA6 and PAM/PA6 composites by using Mo's method combined with the Avrami and Ozawa equations. In the meanwhile, the activation energies are determined to be ?306.62 and ?414.81 KJ/mol for PA6 and PAM/PA6 (5 wt %) composite in nonisothermal crystallization process from the Kissinger method. Analyzing the crystallization half‐time of isothermal and nonisothermal conditions, the over rate of crystallization is increased significantly in samples with a small content of PAM, which seems to result from the increased nucleation density due to the presence of PAM rigid rod chain polymer. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 2844–2855, 2004     

聚苯酯对聚醚醚酮结晶行为的影响

用模压法制备了聚苯酯(Ekonol)／聚醚醚酮(PEEK)复合材料，通过X射线衍射(XRD)、差示扫描量热分析(DSC)考察了PEEK的结晶行为，并测定了复合材料的熔点、结晶温度和玻璃化转变温度。结果表明：Ekonol含量的大小对PEEK的结晶行为产生了直接影响，PEEK的相对结晶度随着Ekonol含量的增加而提高；Ekonol含量小于30％时，对复合材料的熔点、结晶温度和玻璃化转变温度影响不大，但含量大于30％时，材料的结晶温度、熔融温度下降，玻璃化转变温度提高。     

Effect of nucleation mechanism on complex poly(L‐lactide) nonisothermal crystallization process,part 2: Crystallization kinetics analysis

In the first part of this article, we reported the crystalline memory effect on the nonisothermal crystallization of poly(L ‐lactide). The experiments were carried out by using polymer single crystals growth from dilute solution as standard starting material. In this article (Part II), we have analyzed in detail the effect of the melting condition on the overall crystallization kinetics by applying the Nakamura‐Avrami model to DSC results. The absence or the low concentration of foreign infusible heterogeneous nuclei in our system allowed us to exalt the self‐nuclei role in polymer crystallization, to follow their concentration decrease during the melting process and to find the limiting melting temperature for their disappearance. Below such a temperature, a stable equilibrium number of self‐nuclei was observed, probably deriving from ordered structures, persisting in the melt, and originated from the single crystals thickening process during the polymer dynamic melting in the DSC. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

MC尼龙/Dy_2O_3纳米复合材料非等温结晶动力学

采用差示扫描量热法研究铸型(MC)尼龙/Dy_2O_3纳米复合材料的非等温结晶行为,并利用Caze法和Mo法对结晶动力学进行分析,运用Kissinger方法计算MC尼龙的结晶活化能.结果表明,纳米Dy_2O_3起到异相成核的作用,使MC尼龙的结晶峰温升高,结晶总速率增大;添加纳米Dy_2O_3使MC尼龙的结晶活化能增大.     

Isothermal and nonisothermal crystallization kinetics of novel even‐odd nylon 10 11

Isothermal and nonisothermal crystallization kinetics of even‐odd nylon 10 11 were investigated by differential scanning calorimetry (DSC). Equilibrium melting point was determined to be 195.20°C. Avarmi equation was adopted to describe isothermal and nonisothermal crystallization. A new relation suggested by Mo was used to analyze nonisothermal crystallization and gave a good result. The crystallization activation energies have been obtained to be ?583.75 and ?270.06 KJ/mol for isothermal and nonisothermal crystallization, respectively. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 1637–1643, 2005     

PP/纳米SiO2复合材料的非等温结晶动力学

采用差示扫描量热法研究了聚丙烯（PP）/纳米SiO2复合材料的非等温结晶动力学,研究了纳米粒子的成核活性及复合材料的结晶有效能垒。研究结果表明,纳米SiO2起到异相成核的作用,使PP的结晶峰温升高,结晶总速率增大;增容剂马来酸酐接枝聚丙烯(PP-g-MAH)提高了纳米SiO2的成核活性;添加纳米SiO2使复合材料的结晶有效能垒降低,PP-g-MAH使复合材料的结晶有效能垒增大,但低于纯PP的结晶有效能垒。     

Effect of the pressure on the crystallization behavior of polyamide 66

The crystallization behavior of polyamide 66 under high pressure up to 2500 bar was investigated by the use of dilatometric and calorimetric techniques in nonisothermal and isothermal conditions. The solid–solid Brill transition is detected from the evolution of the specific volume in the PVT diagram. The variation of supercooling was examined under different pressures and temperatures. In nonisothermal conditions, when the same cooling rate is applied, the crystallization supercooling is not changed for different pressures. In isothermal conditions, for a given temperature, a pressure increase extends the crystallization supercooling. By the analysis of melting peaks of samples crystallized in different conditions of pressure and temperature, we can conclude that the increasing of the crystallization supercooling leads to a decrease of the lamellae thickness. Finally, the evolution of the thermodynamic equilibrium melting temperature according to pressure was examined. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 1021–1029, 2001     

Physical properties, crystallization kinetics, and spherulitic growth of well-defined poly(ε-caprolactone)s with different arms

Both well defined star-shaped poly(ε-caprolactone) having four arms (4sPCL) and six arms (6sPCL) and linear PCL having one arm (LPCL) and two arms (2LPCL) were synthesized and then used for the investigation of physical properties, isothermal and nonisothermal crystallization kinetics, and spherulitic growth. The maximal melting point, the cold crystallization temperature, and the degree of crystallinity of these PCL polymers decrease with the increasing number of polymer arms, and they have similar crystalline structure. The isothermal crystallization rate constant (K) of these PCL polymers is in the order of K_2LPCL>K_LPCL>K_4sPCL>K_6sPCL. Notably, the K of linear PCL decreases with the increasing molecular weight of polymer while that of star-shaped PCL inversely increases. The variation trend of K over the number of polymer arms or the molecular weight of polymer is consistent with the analyses of both nonisothermal crystallization kinetics and the spherulitic growth rate. These results indicate that both the number of polymer arms and the molecular weight of polymer mainly controlled the isothermal and nonisothermal crystallization rate constants, the spherulitic growth rate, and the spherulitic morphology of these PCL polymers.     

Monitoring nonisothermal crystallization of thermoplastic polymers using a quartz crystal resonator

A new monitoring device for the nonisothermal crystallization of thermoplastic polymers, polyethylene, polypropylene, polystyrene, and polyamide, is developed utilizing a quartz crystal resonator, and its performance is evaluated by comparing the measurements with the results of DSC thermoanalysis and microscopic observation. The experimental results of four different polymers indicate that the variation of resonant freency of the quartz crystal resonator is a good means to monitor the crystallization process. Though the measurements of melting and crystallization are close to the DSC outcome, more deviation is observed with the new device. The change in crystalline morphology during the crystallization process is also detected from the slope changes of the frequency decrease. In comparison with the microscopic observation of polymer films, it is found that the processes of nucleation and crystal growth in nonisothermal crystallization can be explained with the variation of the resonant frequency of the quartz crystal resonator. In addition, crystallization kinetics is modeled with the Avrami equation. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Poly(hydroxybutyrate)/poly(butylene succinate) blends: miscibility and nonisothermal crystallization

Four blends of poly(hydroxybutyrate) (PHB) and poly(butylene succinate) (PBSU), both biodegradable semicrystalline polyesters, were prepared with the ratio of PHB/PBSU ranging from 80/20 to 20/80 by co-dissolving the two polyesters in N,N-dimethylformamide and casting the mixture. Differential scanning calorimetry (DSC) and optical microscopy (OM) were used to probe the miscibility of PHB/PBSU blends. Experimental results indicated that PHB showed some limited miscibility with PBSU for PHB/PBSU 20/80 blend as evidenced by the small change in the glass transition temperature and the depression of the equilibrium melting point temperature of the high melting point component PHB. However, PHB showed immiscibility with PBSU for the other three blends as shown by the existence of unchanged composition independent glass transition temperature and the biphasic melt. Nonisothermal crystallization of PHB/PBSU blends was investigated by DSC using various cooling rates from 2.5 to 10 °C/min. During the nonisothermal crystallization, despite the cooling rates used two crystallization peak temperatures were found for PHB/PBSU 40/60 and 60/40 blends, corresponding to the crystallization of PHB and PBSU, respectively, whereas only one crystallization peak temperature was observed for PHB/PBSU 80/20 and 20/80 blends. However, it was found that after the nonisothermal crystallization the crystals of PHB and PBSU actually co-existed in PHB/PBSU 80/20 and 20/80 blends from the two melting endotherms observed in the subsequent DSC melting traces, corresponding to the melting of PHB and PBSU crystals, respectively. The subsequent melting behavior was also studied after the nonisothermal crystallization. In some cases, double melting behavior was found for both PHB and PBSU, which was influenced by the cooling rates used and the blend composition.     

A comparison of induction time and crystallization rate for syndiotactic polystyrene

One objective of this study was to measure the crystallization parameters for syndiotactic polystyrene (M_W = 244,000) to support a computer simulation of this material in an injection molding application. A second objective was to introduce a new crystallization rate equation that adequately predicts crystallization rates over a broader temperature range than the Hoffman‐Lauritzen equation. A third objective was to establish a new clearly defined method for determining the true induction time of a semicrystalline polymer as a function of temperature. The new crystallization rate equation introduced in this study has been formulated to give appropriate crystallization rate constants for all the temperatures currently usable with the Hoffman‐Lauritzen equation. In addition, this new equation also predicts appropriate crystallization rate constants outside the range of the Hoffman‐Lauritzen equation from temperatures significantly below the glass transition temperature, T_g, to temperatures significantly above the melting point, T_m. Interestingly, the isolation of the true isothermal induction times from apparent induction times in this study nicely mirrored the isothermal crystallization rates at each specific temperature. Both the true induction time and the crystallization rate curves were found to be similarly unsymmetrical as a function of temperature. Also, the temperature at the minimum induction time and the temperature at the peak crystallization rate determined from nonisothermal crystallization rate measurements were found to be nearly identical. Consequently, the results from this study strongly suggest that there is a significant and potentially very useful relationship between induction time analysis and crystallization rate kinetics.     

Isothermal and nonisothermal crystallization kinetics of fully bio‐based polyamides

We studied the crystallization behaviors of bio‐based BDIS polyamides synthesized from the following biomass monomers: 1,4‐butanediamine (BD), 1,10‐decanediamine (DD), itaconic acid (IA), and sebacic acid (SA). Isothermal crystallization, melting behavior, and nonisothermal crystallization of BDIS polyamides were investigated by differential scanning calorimetry (DSC). The Avrami equation was used to describe the isothermal crystallization of BDIS polyamides. The modified Avrami equation, the Ozawa equation, the modified Ozawa equation, and an equation combining the Avrami and Ozawa equations were used to describe the nonisothermal crystallization. The equilibrium melting point temperature of BDIS polyamide was determined to be 163.0°C. The Avrami exponent n was found to be in the range of 2.21–2.79 for isothermal crystallization and 4.10–5.52 for nonisothermal crystallization. POLYM. ENG. SCI., 56:829–836, 2016. © 2016 Society of Plastics Engineers     

Nonisothermal crystallization kinetics and morphology of self‐seeded syndiotactic 1,2‐polybutadiene

Subsequent melting behavior after isothermal crystallization at different temperatures from the isotropic melt and nonisothermal crystallization kinetics and morphology of partially melting sPB were carried out by differential scanning calorimetry (DSC), polarized light microscopy (POM), respectively. Triple melting‐endothermic peaks were observed for the polymer first isothermally crystallized at temperatures ranging from 141 to 149°C, respectively, and then followed by cooling at 10°C/min to 70°C. Comparing with the nonisothermal crystallization from the isotropic melt, the nonisothermal crystallization for the partially melting sPB characterized the increased onset crystallization temperature, and the sizes of spherulites became smaller and more uniform. The Tobin, Avrami, Ozawa, and the combination of Avrami and Ozawa equations were applied to describe the kinetics of the nonisothermal process. Both of the Tobin and the Avrami crystallization rate parameters (K_T and K_A, respectively) were found to increase with increase in the cooling rate. The parameter F(T) for the combination of Avrami and Ozawa equations increases with increasing relative crystallinity. The Ziabicki's kinetic crytallizability index G_Z for the partially melting sPB was found to be 3.14. The effective energy barrier Δ? describing the nonisothermal crystallization of partially melting sPB was evaluated by the differential isoconversional method of Friedman and was found to increase with an increase in the relative crystallinity. At the same time, Hoffman‐Lauritzen parameters (U and K_g) are evaluated and analyzed from the nonisothermal crystallization data by the combination of isoconversional approach and Hoffman‐Lauritzen theory. The K_g value obtained from DSC technique was found to be in good agreement with that obtained from POM technique. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 1479–1491, 2006     

Nonisothermal melt and cold crystallization kinetics of poly(aryl ether ether ketone ketone)

Analysis of the nonisothermal melt and cold crystallization kinetics of poly(aryl ether ether ketone ketone) (PEEKK) was performed by using differential scanning calorimetry (DSC). The Avrami equation modified by Jeziorny could describe only the primary stage of nonisothermal crystallization of PEEKK. And, the Ozawa analysis, when applied to this polymer system, failed to describe its nonisothermal crystallization behavior. A new and convenient approach for the nonisothermal crystallization was proposed by combining the Avrami equation with the Ozawa equation. By evaluating the kinetic parameters in this approach, the crystallization behavior of PEEKK was analyzed. According to the Kissinger method, the activation energies were determined to be 189 and 328 kJ/mol for nonisothermal melt and cold crystallization, respectively.     

Isothermal and nonisothermal crystallization kinetics of partially melting nylon 10 12

Nylon 10 12, a newly industrialized engineering plastic, shows a double‐melting phenomenon during melting. Partial melts were obtained when the sample was heated to the temperature between the two melting peaks. A differential scanning calorimeter was used to monitor the energies of the isothermal and nonisothermal crystallization from the partially melted samples. During isothermal crystallization, relative crystallinity develops with a time dependence described by the Avrami equation, with the exponent n = 1.0. For nonisothermal studies, kinetics treatments based on the Avrami and Ozawa equations are presented to describe the crystallization process. It was found that the two treatments can describe the nonisothermal crystallization from the partially melted samples. The derived Avrami and Ozawa exponents are all about 1.0, which means that the partially melted samples crystallize by one‐dimensional growth, which may cause thickening of the lamellae. We calculated the crystallization activation energies for isothermal and nonisothermal crystallization from the partially melted samples. It was found that the activation energy determined by the Kissinger method was not rational, which may be attributed to the free‐nucleation process for nonisothermal crystallization from partially melted samples. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 1311–1319, 2003