Avrami Method Research Articles

Effect of Nano Spinel Ferrites Co0.9Cu0.1Fe2O4 on Non-Isothermal Cold Crystallization Behaviours and Kinetics of Its Composites with Polylactic Acid.

Nanoparticles of spinel ferrites with a composition of Co0.9Cu0.1Fe2O4 (AM NPs) were effectively synthesized via a hydrothermal route. The structure of ferrite nanoparticles was characterized with X-ray diffraction, which showed a single cubic spinel phase. Energy-dispersive X-ray (EDX) spectroscopy and field emission-scanning electron microscopy (FE-SEM) were employed to analyse elemental composition and surface morphology, respectively. Moreover, the effects of the Co0.9Cu0.1Fe2O4 on the morphology of [PLA = polylactic acid] nanocomposites were examined through polarized light optical microscopy (POM) and X-ray diffraction (XRD). The thermal behaviours for tested samples were studied through [DSC = differential scanning calorimetry] and [TGA = thermal gravimetric analysis]. A great number of minor PLA spherulites were detected using POM in the presence of the Co0.9Cu0.1Fe2O4 ceramic magnetic nanoparticles (AM), increasing with AM nanoparticle contents. X-ray diffraction (XRD) analysis showed that the presence of nanoparticles led to an increase in the intensity of diffraction peaks. The DSC findings implied that the crystallization behaviours for the efficient PLA as well as its nanocomposites were affected by the addition of AM nanoparticles. They act as efficient nucleating agents because they shift the temperature of crystallization to a lower value. The Avrami models were used to analyse kinetics data. The experimental data were well described using the Avrami method for all samples tested. The addition of AM to the PLA matrix resulted in a decrease in the crystallization half-time t1/2 values, indicating a faster crystallization rate. TGA data showed that the occurrence of AM nanoparticles decreased the thermal stability of PLA.

Non-isothermal crystallization kinetics behavior of ethylene-methyl acrylate copolymer and ethylene-methyl acrylate copolymer/chloroprene rubber thermoplastic vulcanizate

The non-isothermal crystallization kinetics of the pure ethylene-methyl acrylate copolymer (EMA) and EMA/chloroprene rubber (CR) thermoplastic vulcanizate (TPV) prepared by dynamic vulcanization were extensively investigated using differential scanning calorimetry (DSC). The Avrami method modified by the Jeziorny, the Ozawa and the Mo methods were employed to characterize the non-isothermal crystallization process. The results indicated that the Avrami method modified by the Jeziorny and Mo methods effectively characterized the non-isothermal crystallization behavior of both pure EMA and EMA/CR TPV, while the behavior could not be described by the Ozawa modification method.

Composites made of Ginkgo biloba fibers and polylactic acid exhibit non-isothermal crystallization kinetics

Polymer crystallization affects material microstructure and the final product quality, and the crystallization kinetics that govern this process are critical. In this study, alkali-treated Ginkgo biloba fibers (GFs) were melt blended with polylactic acid (PLA) to obtain GF/PLA blends. The non-isothermal crystallization kinetics of the GF/PLA composites were subsequently investigated using the Avrami, Jeziorny, Ozawa, and Liu-Mo methods, and the crystallization activation energies of the systems were calculated by Kissinger and Friedman models. The results showed that the GFs significantly promoted PLA crystallization, accelerated the crystallization rate, and shortened the crystallization time. The Avrami method showed some deviation from the linear relationship due to the effect of secondary crystallization, while the numeric value obtained by the Jeziorny method increased with the cooling rate. The Ozawa method could only be used in a very narrow range of temperatures, while the Liu-Mo method showed a more desirable fit. Crystallization activation energy calculations showed that the GFs promoted an increase in the crystallization capacity of the blend and a decrease in the effective potential barrier. This resulted in more selective biocomposites than pure PLA, offering greater applicability in domains including tissue engineering and 3D printing.

Nonisothermal crystallization kinetic behavior of pure ethylene-Vinyl acetate copolymers and ethylene-Vinyl acetate copolymer/nitrile rubber thermoplastic vulcanizate

Thermoplastic vulcanizate (TPV) made from the ethylene-vinyl acetate copolymer (EVA)/nitrile rubber (NBR) blend was fabricated using the dynamic vulcanization method. Differential scanning calorimetry (DSC) was utilized to analyze the nonisothermal crystallization kinetics of both pure EVA and EVA/NBR TPV. The nonisothermal crystallization mechanism was evaluated using the Avrami method modified by Jeziorny, the Ozawa method and the Mo method. The results demonstrate that the nonisothermal crystallization of both pure EVA and EVA/NBR TPV can be adequately described by the Avrami method modified by Jeziorny and the Mo method, while the Ozawa method is not applicable. By elevating the cooling rate, there was a reduction in the crystallization temperature and t1/2 for both pure EVA and EVA/NBR TPV, while the degree of crystallization increased. At the same cooling rate, the crystallization temperature of the EVA/NBR TPV was found to be higher than that of the pure EVA, suggesting that the presence of NBR facilitated the nucleation of the EVA matrix within the EVA/NBR TPV. Moreover, a steric hindrance effect existed in the NBR phase of EVA/NBR TPV at the same cooling rate, resulting in a larger t1/2 compared to that of the pure EVA, indicating hindered crystal growth.

Isothermal crystallization behaviors of isotactic polypropylene with ultrasonically‐modified calcium sulfate whisker as β‐nucleating agent

AbstractIn this work, the effect of calcium sulfate whisker (CSW) and ultrasonically‐modified CSW (UCSW) on the crystal structure and isothermal crystallization of isotactic polypropylene (iPP) is studied by using differential scanning calorimetry (DSC), X‐ray diffraction (XRD), and polarized optical microscopy (POM). UCSW obviously increases heterogeneous nucleation. The isothermal crystallization kinetics of pure iPP, iPP/CSW, and iPP/UCSW composites are analyzed by the Avrami method. Although the Avrami exponent (n) of these samples only changed slightly, the half crystallization time (t1/2) indicates that CSW and UCSW decrease the overall crystallization time and increase the crystallization rate (Rc). POM results show that most crystals are β‐iPP shaped and the spherulite size decreases significantly with the addition of UCSW. The apparent equilibrium temperature of iPP/UCSW composites is lower than that of pure iPP and iPP/CSW composites. The values of β‐iPP fold surface free energy (σe) and the nucleation parameter (Kg) are much lower than that of α‐iPP for these iPP composites. The content of β‐crystal in iPP composites increases due to the addition of UCSW.

An Analysis of the Forgeability of Ti-10V-2Fe-3Al β Titanium alloy using a combined Estrin Mecking and Avrami Material Constitutive Model

A constitutive model was developed to predict the high temperature sub-transus flow behavior of a metastable β Ti-10V-2Fe-3Al alloy, and its applicability for industrial scale forging process has been evaluated using a finite element simulation. Cylindrical samples extracted from a cogged billet of the alloy after β recrystallisation treatment were subjected to hot compression tests at sub-transus temperatures ranging from 720 °C to 780 °C with an increment of 15 °C under varying strain rates from 0.025 to 0.2 s−1. The sub-transus flow curves of the alloy exhibited work hardening followed by dynamic recovery and flow softening beyond the strain equivalent to peak stress. Formation of low angle grain boundaries within the prior β grains and dynamic recrystallisation of β phase were observed to contribute to the flow softening. A constitutive model based on Estrin Mecking and Avrami methods was developed with minimised number of material constants, using the data derived from the hot compression tests. The model was successfully verified using the deformation behaviour measured for the alloy in the region of interest. The constitutive model was implemented into a finite element package as a user subroutine to predict the flow behaviour of industrial scale billets during open die hot forging processes and validated using experimental trials. A fairly good predictive capability with more than 95% convergence for open die forging was achieved, confirming the suitability of the material model developed for predicting sub-transus forgeability of the Ti-10V-2Fe-3Al alloy during industrial scale forging.

On the crystal growth kinetics of ultra‐toughened biobased polyamide 410: New insights on dynamic crystallization

AbstractThe influence of elastomeric poly (octene‐co‐ethylene) on the crystallization of polyamide 410 in PA‐410/POE‐g‐MA blends was systematically analyzed using a non‐isothermal crystallization kinetics approach. A novel power‐law criterion was employed to characterize the crystallization regimes (primary and secondary) as a function of cooling rate to understand the nature of crystal arrangement vis‐a‐vis various kinetic models proposed by Avrami, Jeziorny (modified Avrami method), Ozawa and Liu‐Mo. The activation energy pattern with fractional crystallinity from onset to fully developed crystals is discussed as per Friedman's theory. The POE phase acted as a weak nucleating agent for PA 410. The effect of elastomer on crystallization rate constant remained almost unchanged regardless of the blend composition. This insensitivity is attributed to (1) nucleating effect of POE‐g‐MA (because of resemblance in the molecular scheme) and (2) hindrance effect through the formation of an interfacial network; these two effects nearly offset one another. Our study illustrates the crucial dependence of acceleration of cooling that is, acceleration required for attaining a certain fraction of crystallinity with composition (threshold elastomer concentration), on an interfacial network in binary blends.

PHASE-TRANSFORMATION DYNAMICS AND CHARACTERIZATION OF PRECIPITATES IN THE Cu-3Ti-3Ni-0.5Si ALLOY

In this paper we investigated the phase-transformation dynamics of the Cu-3Ti-3Ni-0.5Si alloy by applying the Avrami method to phase-transformation dynamics and electrical conductivity based on the relationship between the electrical conductivity and the volume fraction of precipitates in the Cu-3Ti-3Ni-0.5Si alloy. The results corroborated well with the experimental data. The microstructure and precipitated phases were characterized by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The analysis of the selected-area electron-diffraction patterns indicated that the precipitates formed in the matrix of the Cu-3Ti-3Ni-0.5Si alloy during aging, correspond to the Ni3Ti, Ni3Si, and Ni2Si phases. According to the values of formation enthalpy and cohesive energy determined by first-principle calculations, the formation of the Ni2Si phase is more favorable compared to the Ni3Si and Ni3Ti phases, and the Ni3Ti exhibits improved structural stability compared to the Ni2Si and Ni3Si phases.

Functional Thermal Stable Samples: Non-isothermal Calorimetric Analysis of MoO3–V2O5–TeO2 Oxide Glasses

In this research, xMoO3–(60 − x)V2O5–40TeO2 oxide glasses with (0 ≤ x ≤ 60) have been prepared by common melt-quenching method. Differential scanning calorimetry (DSC) at different heating rates (φ) was used to study non-isothermal thermal analysis, and also to gain more insight in to the Hruby index thermal stability, crystal growth index (n), glass forming tendency and so calorimetric characteristics of the present glasses. Also, the effects of the heating rate and MoO3 content on the glass transition temperature (Tg) and crystallization temperature (TCr) were studied. Further structural investigations were done by FESEM, EDX and Map. The glass transition temperature, glass transition region, the temperature corresponding to the onset of crystallization (Tx) and also the crystallization temperature were obtained at different heating rates; heating rate dependence of these parameters was employed estimate the key kinetic parameters of glass transition and crystallization activation energy by using Moyinhan, Ozawa, Kissinger and Avrami methods. Calorimetric curves were used to plot the specific heat capacity curves versus temperature at the constant pressure. In addition, the compositional dependence of the heat capacity and fragility parameter were investigated. Generally, results of this work show that the glass with x = 20 mol% has the highest thermal stability and glass forming tendency and samples having 10 and 20% of MoO3 are the optimal samples (with the least fragility) for thermomechanical applications and also in optical fibers.

Crystallization behaviors of poly(ethylene terephthalate) (PET) with monosilane isobutyl-polyhedral oligomeric silsesquioxanes (POSS)

The crystallization behaviors of poly(ethylene terephthalate) (PET) with monosilane isobutyl-polyhedral oligomeric silsesquioxanes (POSS) were investigated in detail. It is observed that POSS acts as an effective nucleating agent under appropriate concentration in the PET system. Polarized optical microscopy (POM) results showed that POSS improved the nucleation density of PET. Besides, the transmission electron microscopy (TEM) observation demonstrated POSS dispersed mostly at the nanometer scale throughout the PET matrix. The crystal structures of POSS and PET/POSS were analyzed using wide-angle X-ray diffraction (WAXD). Moreover, non-isothermal crystallization kinetics of PET and PET/POSS were studied using Mo’s method. The PET/POSS system demonstrated the lower value of F(T) than pure PET, indicating that the lower cooling rate was required to attain a specified relative crystallinity for the system. The comparison of the crystallization activation energy (ΔE) showed that the POSS nanoparticles improved the crystallization of PET through an acceleration of the nucleation process. Furthermore, the isothermal crystallization behaviors were also investigated using classic Avrami method. Overall, POSS can act as a nucleating agent and greatly improve the crystallization of PET through accelerating the nucleation process.

PLGA Barrier Materials from CO2. The influence of Lactide Co-monomer on Glycolic Acid Polyesters

The combination of the predicted polymer market growth and the emergence of renewable feedstocks creates a fantastic opportunity for sustainable polymers. To replace fossil-based feedstock, there are only three alternative sustainable carbon sources: biomass, CO2, and existing plastics (via mechanical and/or chemical recycling). The ultimate circular feedstock would be CO2: it can be electrochemically reduced to formic acid derivatives that subsequently can be converted into useful monomers such as glycolic acid. This work is part of the European Horizon 2020 project “Ocean” in which the steps from CO2 to glycolic acid are developed. Polyglycolic acid (PGA) and poly(lactide-co-glycolide) (PLGA) copolyesters with high lactic acid (LA) content are well-known. PGA is very difficult to handle due to its high crystallinity. On the other hand, PLGAs with high LA content lack good oxygen and moisture barriers. The aim of this work is to understand the structure–property relationships for the mostly unexplored glycolic acid rich PLGA copolymer series and to assess their suitability as barrier materials. Thus, PLGA copolymers with between 50 and 91 mol % glycolic acid were synthesized and their properties were evaluated. Increased thermal stability was observed with increasing glycolic acid content. Only those containing 87 and 91 mol % glycolic acid were semicrystalline. A crystallization study under non-isothermal conditions revealed that copolymerization reduces the crystallization rate for PLGA compared to polylactic acid (PLA) and PGA. While PGA homopolymer crystallizes completely when cooled at 10 °C·min–1, the copolymers with 9 and 13% lactic acid show almost 10 times slower crystallization, which is a huge advantage vis-à-vis PGA for processing. The kinetics of this process, modeled with the Jeziorny-modified Avrami method, confirmed those observations. Barrier property assessment revealed great potential for these copolymers for application in barrier films. Increasing glycolic acid content in PLGA copolymers enhances the barrier to both oxygen and water vapor. At room temperature and a relative humidity below 70% the PLGA copolymers with high glycolic acid content outperform the barrier properties of polyethylene terephthalate.

Thermal behavior and soil biodegradation for blends of poly(hydroxybutyrate)/ethylene vinyl acetate copolymer (EVA 60) with 1 mass% NH4Cl

Poly(hydroxybutyrate) (PHB)/ethylene vinyl acetate copolymer (EVA 60) blends in the ratio from 90:10 to 30:70 by weight, where vinyl acetate content 60 mol%, and its composite with 1 mass% NH4Cl, were investigated by utilizing differential scanning calorimetry and polarizing optical microscopy. The experimental results showed that all investigated blend compositions exhibited two separate glass transition temperatures, corresponding to their components, suggesting immiscibility of PHB with EVA 60. The values of melt crystallization peak temperature and melting peak temperature of PHB in the blend and its composites were found to be almost composition independent, while the crystallinity percentage was slightly decreased with increasing the content of EVA 60 and increased in the presence of NH4Cl compared to pure PHB. The modified Avrami equation and the combination of Avrami and Ozawa methods were utilized to analyze the non-isothermal melt crystallization process successfully. Moreover, the presence of NH4Cl shortened the crystallization half-time and an increase in Avrami crystallization constant at various cooling rates. Polarized optical micrographs of PHB composites showed a large number of small, averaged sized spherulites compared with pure PHB. Additionally, a large number of small round no birefringence regions was appeared in the PHB/EVA 60 blend, which increased with increasing EVA 60 content, indicating a phase separation of PHB and EVA 60. The biodegradation for PHB composites in soil was tested via mass loss percentage and SEM. The results revealed that the biodegradability of PHB component in the blend was enhanced with an addition of NH4Cl and slightly decreased with increasing EVA 60 content. Such results make PHB/EVA60/1 mass%NH4Cl composites a promising candidate to substitute synthetic polymers derived from petroleum.

Nonisothermal Crystallization Kinetics of Acetylated Bamboo Fiber-Reinforced Polypropylene Composites.

The crystallization behavior of bamboo fiber (BF) reinforced polypropylene (PP) composites (BPCs) was investigated using a differential scanning calorimeter (DSC). The results showed that unmodified BF as a nucleation agent accelerated the crystallization rate of the PP matrix during cooling whereas there is no significant effect on the improved crystallization rate in BPCs with acetylated BFs. Based on the Avrami method, Avrami–Ozawa method, and Friedman method, the corresponding crystallization kinetics of PP reinforced with different acetylation levels of BFs were further analyzed. The results demonstrated that the crystal growth mechanism of the PP matrix for BPCs with unmodified and various acetylated BFs exhibited tabular crystal growth with heterogeneous nucleation. A higher cooling rate is required to achieve a certain relative crystallinity degree at the unit crystallization time for BPCs with a higher weight percent gain (WPG) of acetylated BFs (WPG >13%). Furthermore, based on the Friedman method, the lowest crystallization activation energy was observed for the BPCs with 19% WPG of acetylated BFs.

Effects of acetylation on the thermal decomposition kinetics of makino bamboo fibers

In this study, makino bamboo (Phyllostachys makinoi) fibers were acetylated with different solution ratios of acetic anhydride/dimethylformamide using a liquid phase reaction. This reaction resulted in the production of acetylated bamboo fibers (BFs) with the following weight percent gains (WPGs): 2, 6, 9, 13, and 19%. The effects of the acetylation level on the thermal decomposition kinetics of bamboo fibers were evaluated by thermogravimetric analysis. The results revealed that as the acetylation level increased, both the onset and maximum decomposition temperatures increased. In addition, four model-free iso-conversional methods, the Friedman method, Flynn–Wall–Ozawa method, the Starink method, and the modified Coats–Redfern method, were used to determine the thermal decomposition kinetics. Accordingly, the activation energies of thermal decomposition with conversion rates ranging between 10% and 70% were 191–196, 190–191, 192–194, 182–186, 186–191, and 189–201 kJ/mol for unmodified BFs and acetylated BFs with WPGs of 2, 6, 9, 13, and 19%, respectively. There were no significant dependencies among them. Furthermore, the Avrami method was used to determine the reaction order of unmodified BFs (0.47), which was lower than those of acetylated BFs (0.55–0.74).

Phase Transformation Kinetics of a FCC Al0.25CoCrFeNi High-Entropy Alloy during Isochronal Heating

The phase transformation kinetics of a face-centered-cubic (FCC) Al0.25CoCrFeNi high-entropy alloy during isochronal heating is investigated by thermal dilation experiment. The phase transformed volume fraction is determined from the thermal expansion curve, and results show that the phase transition is controlled by diffusion controlled nucleation-growth mechanism. The kinetic parameters, activation energy and kinetic exponent are determined based on Kissinger–Akahira–Sunose (KAS) and Johnson–Mehl–Avrami (JMA) method, respectively. The activation energy and kinetic exponent determined are almost constant, indicating a stable and slow speed of phase transition in the FCC Al0.25CoCrFeNi high-entropy alloy. During the main transformation process, the kinetic exponent shows that the phase transition is diffusion controlled process without nucleation during the transformation.

Effect of Cold Rolling on the Phase Transformation Kinetics of an Al0.5CoCrFeNi High-Entropy Alloy.

The solid state phase transformation kinetics of as-cast and cold rolling deformed Al0.5CoCrFeNi high-entropy alloys have been investigated by the thermal expansion method. The phase transformed volume fractions are determined from the thermal expansion curve using the lever rule method, and the deformed sample exhibits a much higher transformation rate. Two kinetic parameters, activation energy (E) and kinetic exponent (n) are determined using Kissinger– Akahira–Sunose (KAS) and Johnson–Mehl–Avrami (JMA) method, respectively. Results show that a pre-deformed sample shows a much lower activation energy and higher kinetic exponent compared with the as-cast sample, which are interpreted based on the deformation induced defects that can promote the nucleation and growth process during phase transformation.

Kinetics of crystallization for polypropylene/polyethylene/halloysite nanotube nanocomposites

The aim of this study is to investigate the kinetics of non-isothermal crystallization of polypropylene/high-density polyethylene/halloysite nanotube (PP/HDPE/HNT) nanocomposites using three methods, that is, Avrami equation, combined Ozawa–Avrami method (hereafter called Mo model), and Kissinger equation. The Avrami exponent ( n) is in the range of 1–2 for all the PP/HDPE/HNT nanocomposites indicating instantaneous nucleation while the crystallization rate constant ( Zt) values of PP/HDPE increased with the addition of HNT. This proved that addition of HNT increases the crystallization rate. The reduction of half crystallization time ( t 1/2) for PP/HDPE as the increasing HNT loading indicates faster crystallization rate. In the Mo model, the cooling rate chosen at unit crystallization time F( T) values for PP/HDPE decreases with the addition of HNT. Kissinger equation showed that the activation energy ( E a) of crystallization for the PP/HDPE decreases with the addition of HNT. All the results demonstrated that HNT can accelerate the crystallization rate for the PP/polyethylene blends.

Effect of thermal relaxation on residual stress and microstructure in the near-surface layers of dual shot peened Inconel 625

Thermal relaxation behavior of residual stress and microstructure in the near-surface layers of dual shot peened Inconel alloy 625 was investigated by X-ray diffraction method. Residual stress on the top surface layer was significantly relaxed in the first 15 min at the elevated temperatures of 500°C, 600°C, and 700°C. However, there was still high maximum compressive residual stress in subsurface layers. The relaxation behavior of residual stress has contributed to the thermally activated process. The activation enthalpy Δ H and m were calculated according to the Zener–Wert–Avrami method, the values of which were 1.59 eV and 0.4934, respectively. Microstructural evaluation revealed that it was slightly changed in the near-surface layers after various isothermal treatments. Accordingly, high level of compressive residual stress and dislocation density resulted in the retained mechanical properties of dual shot peened Inconel 625, which was discussed based on the relaxation of microstructure and microhardness.

The crystallization of polypropylene/halloysite fibers

The halloysite (HNT) in the form of nanotubes was used as an agent for the improved mechanical, thermo-mechanical as well as surface properties of polypropylene (PP) fibers. The halloysite is the nanoadditive that can affect differently the crystallization of PP in the non-oriented and oriented systems. The structure and mechanical properties of PP and PP/HNT fibers depended on the crystallinity and crystallization kinetics of PP at the fiber preparation. The Avrami method on the determination of isothermal crystallization kinetics parameters as well as an estimation of melting and crystallization temperatures and melting and crystallization enthalpies was used for the study of thermal behavior of polypropylene/halloysite non-oriented and oriented blends and fibers. Morphological structure, mechanical and thermo-mechanical properties of polypropylene/halloysite fibers were observed. An influence on all assessed properties was evaluated from the point of halloysite content in the PP and/or PP fibers. The increased HNT content in the non-oriented PP/HNT blends at the isothermal crystallization increases the rate crystallization (decreased t1/2 and free energy σe, increased K) of PP in comparison with the pure PP. The crystallinity of PP in the oriented PP/HNT fibers is not primarily affected by addition of the HNT content 3 mass% and does not change their mechanical and thermo-mechanical properties. 5 mass% HNT increases the crystallinity of PP in PP/HNT fibers expressing mainly the decrease in tenacity at the break, Young’s modulus and shrinkage.

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.