Overall crystallization kinetics of polymorphic propylene-ethylene random copolymers: A two-stage parallel model of Avrami kinetics

The isothermal crystallization of propylene ethylene random copolymers evolves with a simultaneous formation of two polymorphic forms, monoclinic crystals (α form) and orthorhombic crystals (γ form). The relative content of each polymorph changes during crystallization and impacts the kinetics and mechanisms of growth. The content of γ crystals developed at high levels of transformation increases with the concentration of ethylene and with the crystallization temperature. In this work, the overall crystallization kinetics of copolymers with an ethylene content ranging from 0.8 to 7.5 mol% were followed by DSC and analyzed according to classical Avrami kinetics. For most copolymers, fits to single-stage nucleation and growth models were poor. Following structural models for lamellar growth that account for epitaxial γ branching from α surfaces, the experimental data were modeled with a parallel two-stage kinetic model with excellent fits up to ∼70% transformations. The Avrami exponents obtained from the fits are consistent with a linear spherulitic growth from pre-existing nuclei for the α stage and homogeneous nucleation (linear with time) for the γ stage, and strongly support the postulated structural growth model. The rate constants of each stage follow the expected temperature dependence. Attempts made to extract the interfacial free energies for α and γ crystals from the values of the rate constants are discussed.     

Isothermal crystallization kinetics and melting behavior of polyamide 11/silica nanocomposites prepared by in situ melt polymerization

Polyamide 11 (PA 11)/silica nanocomposites were prepared via in situ melt polymerization by the dispersion of hydrophobic silica in 11‐aminoundecanoic acid monomer. Their isothermal crystallization process and melting behaviors were analyzed by differential scanning calorimetry. The isothermal crystallization kinetics was analyzed by the Avrami equation. The obtained data showed that the model of nucleation and growth of PA 11 was not affected after the incorporation of silica and was a mixture with two‐dimensional, circular, three‐dimensional growth with thermal nucleation. Double and single melting peaks were observed depending on the crystallization temperature. The equilibrium melting point of samples was evaluated, and the spherulites growth kinetics parameters and fold surface free energy were further calculated according to the classical theories. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Nonisothermal crystallization kinetics of AB2 hyperbranched polymer‐filled polypropylene

In this article, nonisothermal crystallization kinetics of polypropylene (PP) and AB₂ hyperbranched polymer (HBP)‐filled PP have been investigated by differential scanning calorimetry. The Avrami analysis modified by Mandelkern and a method combined with Avrami and Ozawa equations were employed to describe successfully the nonisothermal crystallization kinetics of samples. The conclusion showed that HBP can prompt crystallization effectively. Furthermore, in blends of different HBP contents, the value of t_1/2 became smaller with increasing HBP content; however, the crystallization rate of the blend decreased slightly when content of HBP is 5%. An increase in the Avrami exponent showed that addition of HBP influenced the mechanism of nucleation and the growth of PP crystallites. The possible explanation could be attributed to the fractal structure of HBP. The polarized micrographs showed that HBP acts as a heterogeneous nucleation agent, and the nucleation efficiency has increased remarkably in HBP/PP blends. POLYM. ENG. SCI., 53:2535–2540, 2013. © 2013 Society of Plastics Engineers     

Crystallization Kinetics of Cocoa Fat Systems: Experiments and Modeling

Isothermal crystallization kinetics of unseeded and seeded cocoa butter and milk chocolate is experimentally investigated under quiescent conditions at different temperatures in terms of the temporal increase in the solid fat content. The theoretical equations of Avrami based on one-, two- and three-dimensional crystal growth are tested with the experimental data. The equation for one-dimensional crystal growth represents well the kinetics of unseeded cocoa butter crystallization of form α and β′. This is also true for cocoa butter crystal seeded milk chocolate. The sterical hindrance due to high solids content in chocolate restricts crystallization to lineal growth. In contrast, the equation for two-dimensional crystal growth fits best the seeded cocoa butter crystallization kinetics. However, a transition from three- to one-dimensional growth kinetics seems to occur. Published data on crystallization of a single component involving spherulite crystals are represented well by Avrami’s three-dimensional theoretical equation. The theoretical equations enable the determination of the fundamental crystallization parameters such as the probability of nucleation and the number density of nuclei based on the measured crystal growth rate. This is not possible with Avrami’s approximate equation although it fits the experimental data well. The crystallization can be reasonably well defined for single component systems. However, there is no model which fits the multicomponent crystallization processes as observed in fat systems.     

Melting behavior,isothermal and nonisothermal crystallization kinetics of nylon 1111

The isothermal and nonisothermal crystallization kinetics of nylon 1111 was extensively studied using differential scanning calorimetry (DSC). The equilibrium melting temperature of nylon 1111 was determined to be 188°C. In this article, the Avrami equation was used to describe the isothermal crystallization behavior of nylon 1111. On the basis of the DSC results, the Avrami exponent, n, was determined to be around 3 during the isothermal crystallization process. Nonisothermal crystallization was analyzed using both the Avrami equation as modified by Jeziorny and an equation suggested by Mo. The larger value of the Avrami exponent, n, during the nonisothermal crystallization process indicates that the development of nucleation and crystal growth are more complicated during the nonisothermal crystallization for nylon 1111, and that the nucleation mode might simultaneously include both homogeneous and heterogeneous nucleations. The isothermal and nonisothermal crystallization activation energies of nylon 1111 were determined to be ?132 kJ/mol and ?121 kJ/mol using the Arrhenius equation and the Kissinger method, respectively. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

Crystallization kinetics of poly(L-lactide-co-meso-lactide)

The crystallization kinetics of poly(L -lactide-co-meso-lactide) were determined over a range of 0% to 9% mesolactide. The kinetics were fit to the nonlinear Avrami equation and then to the Hoffman–Lauritzen equation modified for optical copolymers. The theory was found to fit the data well. The crystallization half-time was found to increase about 40% for every 1 wt % meso-lactide in the polymerization mixture. The change in crystallization rate is driven mainly by the reduction in melting point for the copolymers. The copolymer crystallization kinetics were also determined in the presence of talc, a nucleating agent for polylactide. The theory again fit the data well, using the same growth parameters and accounting for the talc only through the nucleation density term. © 1996 John Wiley & Sons, Inc.     

Crystallization kinetics of two polyesters with different main chain rigidity

The crystallization kinetics of two polyesters, poly(p-phenylene sebacate) (PPS) and poly(p-phenylene isophthalate) (PPI), have been investigated by DSC. The nonisothermal data indicate that the relative crystallization rate of PPI was slower than that of PPS due to the more rigid nature of the PPI the chains. The isothermal crystallization data were analyzed by the Avrami equation, 1 − X_(t) = exp(−ktⁿ). PPS exhibited Avrami exponent (n), values of about 4, indicating that its isothermal crystallization followed a process of homogeneous nucleation, spherical growth and a growth type of interface control. PPI exhibited Avrami exponent values of about 3 indicating its isothermal crystallization followed a process of homogeneous nucleation, a possible disc growth geometry and an interface control growth type. Possibly, the bending structure and rigid nature of PPI forced its growth to follow a three dimensional growth during crystallization.     

Crystallization kinetics of novel poly(aryl ether ketone) copolymers containing 2,7‐naphthalene moieties

To increase the glass transition temperature (T_g) of poly(aryl ether ketone), and to decrease the melting temperature (T_m) and temperature of processing, a series of novel poly(aryl ether ketone)s with different contents of 2,7‐naphthalene moieties (PANEK) was synthesized. We focused on the influence of the naphthalene contents to the copolymer's crystallization. The crystallization kinetics of the copolymers was studied isothermally and nonisothermally by differential scanning calorimetry. In the study of isothermal crystallization kinetics, the Avrami equation was used to analyze the primary process of the crystallization. The study results of the crystallization of PANEK at cooling/heating rates ranging from 5 to 60°C/min under nonisothermal conditions are also reported. Both the Avrami equation and the modified Avrami–Ozawa equation were used to describe the nonisothermal crystallization kinetics of PANEK. The results show that the increase in the crystallization temperature and the content of 2,7‐naphthalene moieties will make the crystallization rate decrease, while the nucleation mechanism and the crystal growth of PANEK are not influenced by the increasing of the content of 2,7‐naphthalene moieties. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 2527–2536, 2006     

Effect of molecular weight on crystallization and melting of poly(trimethylene terephthalate). 1: Isothermal and dynamic crystallization

The crystallization behavior of poly(trimethylene terephthalate) as a function of molecular weight was investigated under isothermal and dynamic cooling conditions using a differential scanning calorimeter (DSC) and polarized light optical microscopy (POM). THe overall rate of bulk crystallization increased with molecular weight. An Avrami analysis of the isothermal crystallization kinetics indicated that the crystallization rate constant increased with increasing molecular weight. The Avrami exponent, n, approached 2 and was nearly independent of both molecular weight and temperature. The modified Avrami analysis developed by Jeziorny and Ozawa was applied to the dynamic crystallization data. At the same cooling rate, higher molecular weight resulted in a narrower crystallization peak, higher onset crystallization temperature, and larger rate constant (Z_t)^1/n. Higher molecular weight resulted in larger cooling function of dynamic crystallization K(T) and lower Ozawa exponent m. For dynamic crystallization, the average value of the Avrami exponent varied from 3.4 to 3.8 and the average value of the Ozawa exponent changed from 2.3 to 2.6 as the number‐average molecular weight changed from 13,000 to 67,000. Morphology studies indicated that both the isothermal crystallization and the dynamic crystallization of PTT from the melt were thermal nucleation processes, and for a fixed temperature between 190°C and 210°C, the nucleation density increased with increasing the molecular weight.     

Crystallization and melting behavior of 1,2‐syndiotactic polybutadiene

1,2‐Syndiotactic polybutadiene was synthesized at ?30°C using the catalyst system CrCl₂(dmpe)₂‐MAO. The syndiotactic index of the butadiene sequences, expressed as a percentage of syndiotactic pentads [rrrr], was evaluated by ¹³C‐NMR measurements. WAXD and SAXS techniques were employed to characterize the crystalline structure of the polymer. The thermal behavior of the polybutadiene was investigated by differential scanning calorimetry. 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. Polybutadiene isothermally crystallizes from the melt according to regime II of crystallization described by Lauritzen–Hoffman secondary nucleation theory. Nonisothermal crystallization kinetics were elaborated using the Ziabicki and Avrami methods modified by Jeziorny. The equilibrium melting temperature was calculated. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 1680–1687, 2004     

Polylactide/nano‐ and micro‐scale silica composite films. II. Melting behavior and cold crystallization

Nonisothermal crystallization of polylactide (PLA)/silica composites prepared by (i) directly blending the PLA with nanoscale colloidal silica sol and by (ii) a sol–gel process are studied by differential scanning calorimeter (DSC) at various heating rates. Samples quenched from the molten state exhibited two melting endotherms (T_ml and T_mh) due to melt‐recrystallization during the DSC scans. Lower heating rate and the presence of silica particles generate a lower peak intensity ratio of T_ml /T_mh. The nonisothermal crystallization kinetics is analyzed by modified Avrami model, Ozawa model, and Liu‐Mo models. The modified Avrami and Liu‐Mo models successfully described the nonisothermal cold crystallization processes, but Ozawa is inapplicable. The nucleation constant (K_g) is calculated by modified Lauritzen‐Hoffman equation and the activation energy by Augis‐Bennett, Kissinger, and Takhor models. These calculated parameters indicate consistently that the nanoscale silica particles seem to form more heterogeneous nucleation to increase crystallization, but microscale one form hindrance to retard crystallization. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Kinetics of isothermal and nonisothermal crystallization of novel poly(arylene ether ether sulfide)s

The kinetics of crystallization have been studied for a series of novel poly(ether ether sulfide)s based on a biphenyl moiety in the backbone (M_n = 14.3K, 19.1K), referred to as biphenyl sulfide (T_g = 142°C, T_m = 347°C) and phenyl moieties in the backbone (M_n = 8.1K, 19.9K, 34K), referred to as phenyl sulfide (T_g = 100°C, T_m = 243°C). Isothermal melt crystallization kinetics were analyzed based on the Avrami equation. Avrami exponents close to three were obtained for the phenyl sulfides, independent of molecular weight or crystallization temperature, which implies growth of three-dimensional spherulitic superstructures following heterogeneous nucleation. For the biphenyl sulfides, values closer to 2 were obtained for the exponent, also independent of molecular weight or crystallization temperature, which could imply the incomplete development of three-dimensional superstructures following heterogeneous nucleation. Nonisothermal crystallization kinetics were also studied by cooling from the melt; in all cases studied, the Ozawa analysis could not well describe the evolution of crystallinity, probably because of the inapplicability of some of the inherent assumptions in this type of analysis. The data were analyzed using the conventional form of the Avrami equation, which yielded good fits. This semiquantitative method of analysis yields a reduced rate constant that was found to increase with increasing cooling rate and decreasing molecular weight. The results of the isothermal and nonisothermal crystallization studies carried out on the poly(ether ether sulfide)s have been compared wherever possible to the results available for PPS and PEEK.     

Thermal analysis of isothermal crystallization kinetics in blends of cocoa butter with milk fat or milk fat fractions

The kinetics of isothermal crystallization of binary mixtures of cocoa butter with milk fat and milk fat fractions were evaluated by applying the Avrami equation. Application of the Avrami equation to isothermal crystallization of the fats and the binary fat blends revealed different nucleation and growth mechanisms for the fats, based on the Avrami exponent. The suggested mechanism for cocoa butter crystallization was heterogeneous nucleation and spherulitic growth from sporadic nuclei. For milk fat, the mechanism was instantaneous heterogeneous nucleation followed by spherulitic growth. For milk fat fractions, the mechanism was high nucleation rate at the beginning of crystallization, which decreased with time, and plate-like growth. Addition of milk fat fractions did not cause a significant change in the suggested nucleation and growth mechanism of cocoa butter.     

Nonisothermal crystallization kinetics of high‐density polyethylene/barium sulfate nanocomposites

The high‐density polyethylene (HDPE)/barium sulfate (BaSO₄) nanocomposites had been successfully prepared by melt‐blending. Nonisothermal melt‐crystallization kinetics of neat HDPE and HDPE/BaSO₄ nanocomposites was investigated with differential scanning calorimetry under different cooling rates. The nonisothermal crystallization behavior was analyzed by Ozawa, Avrami, and combined Ozawa–Avrami methods. It was found that the Ozawa method failed to describe the nonisothermal crystallization behavior of neat HDPE and HDPE/BaSO₄ nanocomposites. The modified Avrami method by Jeziorny was only valid for describing the middle stage of crystallization but was not able to describe the later stage of neat HDPE and HDPE/BaSO₄ nanocomposites crystallization. The value of Avrami exponent n for neat HDPE ranged from 3.3 to 5.7 and for HDPE/BaSO₄ nanocomposites ranged from 1.8 to 2.5. It is postulated that the values of n close to 3 are caused by spherulitic crystal growth with heterogeneous nucleation, whereas simultaneous occurrence of spherulitic and lamellar crystal growth with heterogeneous nucleation account for lower values of n. The combined Ozawa–Avrami method by Mo and coworkers (Polym. Eng. Sci., 37(3) , 568 (1997)) was able to satisfactorily describe the crystallization behavior of neat HDPE and HDPE/BaSO₄ nanocomposites. In addition, the activation energy of nonisothermal crystallization was determined using the Kissinger (J. Res. Natl. Bur. Stand., 57(4) , 217 (1956)) method, showing that the crystallization activation energy of HDPE/BaSO₄ nanocomposites was lower than that of neat HDPE. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

Isothermal and nonisothermal crystallization kinetics of nylon-11

Analysis of the isothermal, and nonisothermal crystallization kinetics of Nylon-11 is carried out using differential scanning calorimetry. The Avrami equation and that modified by Jeziorny can describe the primary stage of isothermal and nonisothermal crystallization of Nylon-11. In the isothermal crystallization process, the mechanism of spherulitic nucleation and growth are discussed; the lateral and folding surface free energies determined from the Lauritzen–Hoffman equation are ς = 10.68 erg/cm² and ς_e = 110.62 erg/cm²; and the work of chain folding q = 7.61 Kcal/mol. In the nonisothermal crystallization process, Ozawa analysis failed to describe the crystallization behavior of Nylon-11. Combining the Avrami and Ozawa equations, we obtain a new and convenient method to analyze the nonisothermal crystallization kinetics of Nylon-11; in the meantime, the activation energies are determined to be −394.56 and 328.37 KJ/mol in isothermal and nonisothermal crystallization process from the Arrhonius form and the Kissinger method. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 70: 2371–2380, 1998     

Crystallization kinetics and morphology of poly(trimethylene terephthalate)

In this work, the isothermal crystallization kinetics of polytrimethylene terephthalate (PTT) was first investigated from two temperature limits of melt and glass states. For the isothermal melt crystallization, the values of Avrami exponent varied between 2 and 3 with changing crystallization temperature, indicating the mixed growth and nucleation mechanisms. Meanwhile, the cold crystallization with an Avrami exponent of 5 indicated a character of three-dimensional solid sheaf growth with athermal nucleation. Through the analysis of secondary nucleation theory, the classical regime I→II and regime II→III transitions occurred at the temperatures of 488 and 468 K, respectively. The average work of chain folding for nucleation was ca. 6.5 kcal mol⁻¹, and the maximum crystallization rate was found to be located at ca. 415 K. The crystallite morphologies of PTT from melt and cold crystallization exhibited typical negative spherulite and sheaf-like crystallite, respectively. Moreover, the regime I→II→III transition was accompanied by a morphological transition from axialite-like or elliptical-shaped structure to banded spherulite and then non-banded spherulite, indicating that the formation of banded spherulite is very sensitive to regime behavior of nucleation.     

Nonisothermal crystallization of highly‐filled polyolefin/calcium carbonate composites

Nonisothermal crystallization kinetics of highly‐filled polyolefin composites was studied by means of differential scanning calorimetry (DSC). Two types of commercial calcium carbonate based fillers (modified with stearic acid and nonmodified one) were used for our investigations. In order to evaluate the crystallization kinetics changes of composites, the Avrami theory modified by Jeziorny was used. Validity of mineral fillers modification with stearic acid has been proved by thermal analysis. Because of the suppression of the heterogeneous nucleation effect resulting from calcium carbonate with stearic acid modification, an increase in the processability of highly‐filled polyolefin cast films might occur. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 41201.     

Nonisothermal crystallization behavior of poly (butylene terephthalate)–poly (ethylene terephthalate‐co‐isophthalate‐co‐sebacate) segmented copolyesters

In this paper, two different analytical methods were applied to investigate nonisothermal crystallization behavior of copolyesters prepared by melting transesterification processing from bulk polyesters involving poly (butylene terephthalate) (PBT) and ternary amorphous random copolyester poly(ethylene terephthalate‐co‐isophthalate‐co‐sebacate) (PETIS). The results show that the half‐time of crystallization of copolyesters depended on the reaction time and decreased with the content of ternary polyesters in the amorphous segment. The modified Avrami model describes the nonisothermal crystallization kinetics very well. The values of the Avrami exponent range from 2.2503 to 3.7632, and the crystallization kinetics constant ranges from 0.0690 to 0.9358, presenting a mechanism of three‐dimensional spherulitic growth with heterogeneous nucleation. Ozawa analysis, however, failed to describe the nonisothermal crystallization behavior of copolyesters, especially at higher cooling rate. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 1232–1238, 2003