Bias in isothermal time-to-event studies due to approach to test temperature

Oxidative induction time (OIT), constant temperature stability (CTS) and isothermal crystallization are examples of isothermal time-to-event (TTE) measurements obtained using differential scanning calorimetry. In TTE experiments, a test specimen is heated/cooled at a constant rate from the setup temperature to an isothermal test temperature. Once the test temperature is achieved, a clock is started and the time to the thermal event (e.g., onset to oxidation, thermal decomposition or crystallization exotherm peak) is measured. Such TTE values may be used to rank stability of the material at the test temperature. Some portion of the reaction of interest, however, takes place during the pre-isothermal period as the test specimen approaches the test temperature. This amount of reaction is unmeasured and represents a bias in the resultant TTE value. An equation has been derived and numerically integrated to estimate this bias. This approach shows that the bias is dependent upon the activation energy of the test reaction, the heating/cooling rate used and the temperature range between the melting temperature and the test temperature. For commonly used heating rates, the bias for OIT and CTS tests is small. Further, the myth that isothermal crystallization kinetics determinations required high cooling rates is dispelled with the bias of less than 0.9 min resulting from heating rates as low as 10°C min^–1. Knowledge of magnitude of this bias permits the selection of experimental conditions without the expense of high heating/cooling rate apparatus or extra cost cooling accessories.     

Real-time image analysis and numerical simulation of isothermal spherulite nucleation and growth in polyoxymethylene

A method of analysing nucleation and crystallization kinetics, based on real time image analysis and hot stage optical microscopy, has been used to investigate the isothermal crystallization of different grades polyoxymethylene. The data were compared with results from differential scanning calorimetry (DSC), using a simple numerical simulation to model the effects of finite smaple thickness on the form of the isothermal DSC curves. This simulation was then used to predict the microstructural development in a bulk sample for different boundary conditions, taking into account latent heat evolution and diffusion during crystallization.     

Interpretation of the nonisothermal crystallization kinetics of polypropylene using a power law nucleation rate function

A nucleation rate function is proposed for use in analyzing the overall crystallization kinetics of polymers. This function allows for the possibility that the nucleation rate varies substantially during the crystallization. This feature is particularly useful in analyzing nonisothermal crystallization, but it can be used to analyze isothermal crystallization as well. The nucleation rate function was used in the derivation of a modified transformation kinetics equation of the Avrami type. The modified Avrami equation was found to be suitable for kinetics analysis for the data obtained from nonisothermal crystallization at rapid cooling rates. Kinetics parameters used to describe nonisothermal crystallization under rapid cooling rates are presented and discussed. These include crystallization induction time, plateau (crystallization) temperature, crystallization half-time, crystallization rate constant, Avrami index, and newly defined quantities called nucleation index, geometric index, and nucleation rate constant. The procedure used to obtain the nucleation rate constant and nucleation index for the nucleation rate function is described and illustrated by application to the analysis of the crystallization kinetics of polypropylene. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1077–1093, 1997     

Deposition and crystallization studies of thin amorphous solid water films on Ru(0001) and on CO-precovered Ru(0001)

The deposition and the isothermal crystallization kinetics of thin amorphous solid water (ASW) films on both Ru(0001) and CO-precovered Ru(0001) have been investigated in real time by simultaneously employing helium atom scattering, infrared reflection absorption spectroscopy, and isothermal temperature-programmed desorption. During ASW deposition, the interaction between water and the substrate depends critically on the amount of preadsorbed CO. However, the mechanism and kinetics of the crystallization of approximately 50 layers thick ASW film were found to be independent of the amount of preadsorbed CO. We demonstrate that crystallization occurs through random nucleation events in the bulk of the material, followed by homogeneous growth, for solid water on both substrates. The morphological change involving the formation of three-dimensional grains of crystalline ice results in the exposure of the water monolayer just above the substrate to the vacuum during the crystallization process on both substrates.     

Reflection–absorption infrared spectroscopy investigation of the crystallization kinetics of poly(ethylene terephthalate) ultrathin films

Reflection–absorption infrared spectroscopy was used to study the crystallization behavior of poly(ethylene terephthalate) (PET) ultrathin films. The crystallinity of ultrathin films was estimated by the fraction of trans conformers of PET. The isothermal and nonisothermal crystallization kinetics of ultrathin films with different thicknesses were investigated. The thinner PET film showed slower kinetics during isothermal crystallization than the thicker film. Moreover, the final crystallinity of films with various thicknesses were reduced with decreasing thickness. An Avrami equation was used to fit the acquired results. The Avrami exponents decreased with the film thickness. As for the nonisothermal crystallization, the cold‐crystallization starting temperature shifted to a lower temperature as the film thickness increased. The influence of the substrate on the crystallization kinetics of the films was also studied. The half‐crystallization times and final crystallinities of ultrathin films adsorbed onto a self‐assembled‐monolayer‐treated surface and an untreated substrate were clearly different, although their thickness dependence was similar. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4440–4447, 2004     

茂金属间规立构聚丙烯结晶动力学研究

用ＤＳＣ和密度法对茂金属间规立构聚丙烯（ｓＰＰ）样品进行了等温和非等温结晶动力学研究．测得平衡熔点Ｔ０ｍ为１５８℃,平衡熔融热焓ΔＨ０ｍ为３７ｋＪ／ｍｏｌ,侧表面自由能σ＝５２ｅｒｇ／ｃｍ２,折叠链表面自由能σｅ＝６９ｅｒｇ／ｃｍ２,链堆砌功ｑ＝３３７５ｋＪ／ｍｏｌ．对非等温结晶过程研究表明,由熔体结晶的ｓＰＰ具有非均相成核,三维球状生长机理．成核与生长活化能ΔＥ＝７３１ＫＪ／ｍｏｌ     

Carbon nanoparticles as effective nucleating agents for polypropylene

The effect of four nucleating agents on the crystallization of isotactic polypropylene (iPP) was studied by differential scanning calorimetry (DSC) under isothermal and non-isothermal conditions. The nucleating agents are: carbon nanofibers (CNF), carbon nanotubes (CNT), lithium benzoate and dimethyl-benzylidene sorbitol. Avrami?s model is used to analyze the isothermal crystallization kinetics of iPP. Based on the increase in crystallization temperature (T _c) and the decrease in half-life time (τ_½) for crystallization, the most efficient nucleating agents are the CNF and CNT, at concentrations as low as 0.001 mass%. Sorbitol and lithium benzoate show to be less efficient, while the sorbitol needs to be present at concentrations above 0.05 mass% to even act as nucleating agent.     

Flash DSC crystallization study of blown film grade bimodal high density polyethylene (HDPE) resins. Part 2. Non‐isothermal kinetics

Non‐isothermal ultra‐fast cooling crystallization tests were conducted on three blown film grade bimodal high density polyethylene (HDPE) resins using a fast differential scanning calorimeter, the Flash DSC. Non‐isothermal tests were performed at cooling rates between 50 and 4000°K/s, and the data were analyzed using the modified Avrami model by Jeziorny (Polymer, 1978 , 19, 1142). Non‐isothermal data were used to propose a new method named crystallization–time–temperature–superposition, and the two activation energies were obtained for each of the resins. This is very useful for obtaining theoretical crystallization kinetics data at different cooling rates, allowing its use in ultra‐fast cooling polymer processes such as blown film. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1822–1827     

固相缩聚PET等温结晶动力学

高聚物等温结晶动力学方面的研究者甚多,由熔融缩聚制备的不同分子量PET的等温结晶动力学及几种不同缩聚催化体系固相缩聚PET的等温结晶动力学已有报道.本文采用一个修正的Avrami方程对固相缩聚PET样品进行系统的等温结晶动力学研究.     

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.

     

热处理对尼龙1010固态结晶和玻璃态热松驰的影响

本文用DSC首先论证淬火尼龙1010试样在DSC曲线上出现的放热峰是冷结晶峰,然后研究淬火尼龙1010在不同热处理条件下,冷结晶峰和玻璃态热松驰峰的变化规律。实验结果表明,等温结晶时间较短,试样的固态结晶速率较快;等温结晶时间较长,固态结晶速率较慢,这可能与在Tg区域等温所形成的新氢键有关。当升高等温温度时,固态结晶速率加快。在低于Tg的不同温度退火,玻璃态热松弛峰的峰高及热焓在281K达最大值,进而确定对玻璃态热松驰影响最敏感的温度区间是277～284K。     

Isothermal and nonisothermal crystallization kinetics of poly(propylene terephthalate)

The kinetics of crystallization of poly(propylene terephthalate) (PPT) samples of different molecular weights were studied under both isothermal and nonisothermal conditions. The Avrami and Lauritzen–Hoffmann treatments were applied to evaluate kinetic parameters of PPT isothermal crystallization. It was found that crystallization is faster for low‐molecular‐weight samples. The modified Avrami equation, and the combined Avrami–Ozawa method were found to successfully describe the nonisothermal crystallization process. Also, the analysis of Lauritzen–Hoffmmann was tested and it resulted in values close to those obtained with isothermal crystallization data. The nonisothermal kinetic data were corrected for the effect of the temperature lag and shifted alone with the isothermal kinetic data to obtain a single master curve, according to the method of Chan and Isayev, testifying to the consistency between the isothermal and corrected nonisothermal data. A new method for ranking of polymers, referring to the crystallization rates, was also introduced. This involved a new index that combines the maximum crystallization rate observed during cooling with the average crystallization rates over the temperature range of the crystallization peak. Furthermore, the effective energy barrier of the dynamic process was evaluated with the isoconversional methods of Flynn and Friedmann. It was found that the energy barrier is lower for the low‐molecular‐weight PPT. The effect of the catalyst remnants on the crystallization kinetics was also investigated and it was found that this is significant only for low‐molecular‐weight samples. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3775–3796, 2004     

Isothermal and nonisothermal crystallization kinetics of novel biobased poly(ethylene succinate-<Emphasis Type="Italic">co</Emphasis>-ethylene sebacate) copolymers from the amorphous state

In this work, the isothermal and nonisothermal crystallization kinetics of three novel biobased poly(ethylene succinate-co-ethylene sebacate) (PESSe) copolymers was systematically investigated with differential scanning calorimetry under different crystallization conditions from the amorphous state. For the isothermal cold crystallization kinetics study, the Avrami equation could well describe the crystallization process of PESSe at various crystallization temperatures. All three PESSe copolymers crystallized through the same crystallization mechanism; moreover, the overall isothermal cold crystallization rate of PESSe decreased with increasing ethylene sebacate (ESe) comonomer content. The nonisothermal cold crystallization kinetics of PESSe was also studied at different heating rates. With increasing ESe content or heating rate, the nonisothermal cold crystallization exotherm of PESSe copolymers shifted to high temperature range. Both the crystallization rate parameter and crystallization rate coefficient of PESSe copolymers decreased with increasing ESe content, indicating that PESSe copolymer with higher ESe content crystallized more slowly than that with lower ESe content. The Ozawa equation was used to analyze the nonisothermal cold crystallization kinetics of PESSe copolymers, which was found to fit the crystallization process very well.     

Crystallization kinetics of poly(hexamethylene succinate)

Isothermal and nonisothermal crystallization kinetics of polyester 64 have been investigated by means of differential scanning calorimetry and optical microscopy. The Avrami analysis has been performed to obtain the kinetic parameters of primary crystallization. These indicate a three-dimensional spherulitic growth on heterogeneous nuclei for the isothermal crystallization, whereas an sporadic nucleation becomes dominant in the nonisothermal crystallization. The maximum crystallization rate of polyester 64 was deduced to take place at a temperature close to −3 °C. Polarizing light microscopy showed that spherulites with a negative birefringence are formed during isothermal crystallization, whereas transmission electron microscopy indicates that the b crystallographic axis is aligned parallel to the spherulitic radius.     

Isothermal crystallization kinetics study on aqueous solution of poly(vinyl methyl ether) by FTIR and optical microscopy method

A study on the isothermal crystallization kinetics of aqueous solution of poly (vinyl methyl ether) (PVME) was carried out by Fourier transform infrared (FTIR) and optical microscopy respectively. IR spectra of PVME solution were measured as a function of time under the isothermal crystallization conditions. With the process of crystallization, the phase of solution changes from transparent state to opaque one within around 1-2 min for 40 or 45 wt % PVME sample, the C-H symmetric stretching bands (nus(CH3)) shift to lower wave number 2823 cm(-1). The red shift of nus(CH3) absorption band was not observed in the transparent noncrystallization area. Using the temperature jump method, we determined the growth rate of ice crystal between the glass transition temperature Tg and the melting temperature Tm. At the different crystallization temperatures Tc, the different morphologies and dimension of ice crystal are also observed.     

Thermophysical analysis and modeling of the crystallization and melting behavior of PLA with talc

The crystallization kinetics and the melting behavior of PLA and PLA with talc are investigated by dynamic scanning calorimeter and optical microscopy. The polymorphic aspect of PLA was highlighted by analyzing the melting process throughout heating after isothermal crystallization. The melting process of PLA with 5 mass% talc (PLAT5) shows the same thermal transitions as for PLA alone. The thermodynamic melting temperature of PLA and PLAT5 is determined to be 167.7 °C. The effects of the temperature and the cooling rate on the crystallization kinetics of PLA are analyzed. Finally, a simple and efficient protocol is defined to model the isothermal and the non-isothermal crystallization taking into account the polymorphism of PLA. Good agreement is found between the predictions of the proposed model and the experimental results under isothermal and non-isothermal conditions.     

Crystallization kinetics of polypropylene with hyperbranched polyurethane acrylate being used as a toughening agent

The crystallization kinetics of polypropylene (PP) with hyperbranched polyurethane acrylate (HUA) being used as a toughening agent was studied by isothermal and nonisothermal differential scanning calorimetry (DSC). The presence of a small amount of HUA (2-7%) remarkably influences the crystallizability of PP. An addition of HUA leads to an increase in the number of effective nuclei, thus resulting in an increase of crystallization rate and a stronger trend of instantaneous three-dimensional growth. For isothermal crystallization, Avrami exponents were determined to be about 2.97 for pure PP and 3.51 for the HUA/PP blend containing 5% HUA (HUA-PP). The half crystallization time (t_1/2) of pure PP was measured to be 8.43 min, while being 3.28 min for HUA-PP at the crystallization temperature of 132 °C. The nonisothermal crystallization kinetics of HUA/PP blends was analyzed by Avrami, Ozawa and Kissinger methods. It has also been proved that an addition of HUA could increase the crystallization rate of PP. Moreover, the crystallization activation energies of pure PP and HUA-PP were estimated by Kissinger and Friedman methods.     

Crystallization characteristics of polymer blends. I. Polyethylene and polystyrene

Blends of polyethylene and polystyrene have been prepared to study the effect of the morphology on their crystallization characteristics since the polymers are known to phase separate. The polymer component present in least amount formed a dispersed phase of discrete spherical particles whose number and size altered with blend composition. However, close to 50% composition cylindrical rods of polyethylene dispersed in polystyrene were observed. With polyethylene in excess the kinetics of crystallization were insensitive to the morphology, but with polyethylene present as the dispersed phase they became dependent on the size and number of the spheres, and in particular on the nucleation density. When the number of spherical particles exceeded that of heterogeneous nuclei, larger supercoolings, and so presumably homogeneous nucleation, were required for crystallization to develop further. The degree of crystallization of the blends then became dependent on the temperature of crystallization rather than on time, and the isothermal crystallization appearing to be instantaneous.     

Isothermal crystallization behavior of PP and PP-g-GMA copolymer at high undercooling

The study involves synthesis of polypropylene grafted with glycidyl methacrylate (PP-g-GMA) using three different initiators, benzoyl peroxide, dicumyl peroxide and tertiary butyl cumyl peroxide (TBSP). Among the peroxides used, dicumyl peroxide resulted in considerable reduction of molecular weight of the resulting graft copolymer. The melting/crystallization behavior and isothermal crystallization kinetics of PP homopolymer and PP-g-GMA copolymers were studied with differential scanning calorimetry (DSC) at high undercooling (44–60°C). The results showed that the degree of crystallinity and overall crystallization rate of copolymers is greater than that of virgin PP. Among the three initiators used, TBCP exhibited lowest half crystallization time. The isothermal crystallization kinetics of the PP and copolymers was described with the Avrami equation and Sestak-Berggren (SB) equation. The Avrami exponent n of the PP and copolymers were found to be in the range 1.03 to 1.41 at high undercooling conditions employed in this study. The agreement between the values of n calculated from SB kinetics and Avrami equation is satisfactory with few exceptions. The crystallization rate of PP-g-GMA copolymer was found to be more sensitive to temperature. The isothermally crystallized samples showed a single melting peak for PP while a double peak at lower temperature was recorded for PP-g-GMA copolymer samples. The equilibrium melting point was deduced according to Hoffman-Weeks theory. The decrease of recorded for the PP modified with GMA suggests that the thermodynamic stability of the PP crystals is influenced by the chemical interactions.     

Isothermal crystallization kinetics of poly(ethylene terephthalate)s of different molecular weights

The isothermal crystallization kinetics and morphology of poly(ethylene terephthalate) (PET) polymers of different molecular weights have been studied by means of differential scanning calorimetry and transmission microscopy (TM). The kinetic parameters of Avrami exponent n, the rate constant k, half time t _1/2, rate at 50 % crystallinity, τ _1/2 for crystallization of different PETs were evaluated from double logarithmic plots of log {?ln[1 ? X(t)]} versus log t, where X(t) is extent of crystallinity at a given crystallization temperature. The crystallization rate of polymers with high molecular weight found to be lower than that of polymers with low molecular weight, at the same crystallization temperature. It was found that the nucleation mechanism and growth dimension of polymers with low molecular weight are different from those of polymers with high molecular weight. The results of TM and isothermal crystallization kinetics showed a consistent trend for the crystallization of all PET polymers studied, comprising a primary stage and a secondary stage. The activation energy in the PET polymers of low molecular weight was found to be lower than that of polymers with high molecular weight.