ON A DIFFERENTIAL EQUATION FOR KINETICS OF NON- ISOTHERMAL CRYSTALLIZATION

A new differential equation was derived from the modified first-order kinetic model to describe the polymer crystallization processes. The crystallization experiments were carried out by means of DSC. Poly (ethylene terephthalate) resins were selected as the samples containing different catalysts. The relationships between the parameters obtained from the known Avrami equation and from one in the present paper were discussed. A method for applying the equation to determine the kinetic parameters from a constant heating and a constant cooling curve was proposed.

NON-ISOTHERMAL CRYSTALLIZATION OF POLY(L-LACTIDE)(PLLA) UNDER QUIESCENT AND STEADY SHEAR CONDITIONS

The non-isothermal crystallization of poly（L-lactide） （PLLA） under quiescent and steady shear flow conditions was in situ investigated by using polarizing optical microscopy （POM） with a hot shear stage and wide-angle X-ray diffraction （WAXD）. The shear rate and the cooling rate both play a significant role in the final crystalline morphology and crystallinity. Under quiescent conditions, the morphology assumes different sized spherulites, and its crystallinity dramatically reduces with increasing the cooling rate. On the other hand, the shear flow increases the onset crystallization temperature, and enhances the final crystallinity. When the shear rate is above 5 s^-1, cylindrite-like crystals are observed, furthermore, their content depends on the cooling rate.

Non-isothermal Crystallization Kinetics of Polyamide 6/Diaminemodified MWNTs Nanocomposite

The non-isothermal crystallization kinetics of polyamide 6/diamine-modified multi-walled carbon nanotube （PA6/D-MWNT） nanocomposite was investigated by differential scanning calorimetry （DSC）. The modified Avrami equation, the Ozawa equation and the combined Avrami/Ozawa equation were employed to analyze the non-isothermal crystallization data. The crystallization activation energies were also evaluated by the Kissinger method. It was found that the combined Avrami/Ozawa equation could successfully describe the non-isothermal crystallization process. The results showed that D-MWNTs not only acted as effective heterogeneous nucleating agents for PA6 and noticeably increased the crystallization temperature of PA6, but also influenced the mechanism of nucleation and crystal growth of PA6 and then reduced the overall crystallization rate of the neat PA6 matrix. The crystallization activation energy for the nanocomposite sample was greater than that of the neat PA6, which indicated that the addition of D-MWNTs hindered the mobility of PA6 chain segments.

Non-isothermal Melt Crystallization Kinetics of Anhydrite-Filled Polypropylene Composites

The non-isothermal crystallization kinetics of polypropylene （PP）, PP/anhydrite composites were investigated by differential scanning calorimetry （DSC） with various cooling rates. The Avrami analysis modified by Jeziorny and a method developed by Mo were employed to describe the non-isothermal crystallization process of these samples. The difference in the exponent n between PP and PP/anhydrite composites indicated that non-isothermal kinetic crystallization corresponded to tri-dimensional growth with heterogeneous nucleation. The values of half-time, Zc and F（T） showed that the crystallization rate increased with the increasing of cooling rates for PP and PP/anhydrite composites, but the crystallization rate of PP/anhydrite composites was faster than that of PP at a given cooling rate. The method developed by Ozawa did not describe the non-isothermal crystallization process of PP very well. Moreover, the method proposed by Kissinger was used to evaluate the activation energy of the mentioned samples. The result showed that the activation energy of PP/anhydrite was greatly larger than that of PP.

KINETICS OF NON-ISOTHERMAL CRYSTALLIZATION

A kinetic equation of non-isothermal crystamzation was derived by extending Avrami's equation to the non-isothermal situation. More crystallization information can be obtained from this kinetic equation. The curves of non-isothermal and isothermal crystallizations were analysed and compared for poly (ethylene terephthalate) (PET), and the results were discussed.

Non-Isothermal Crystallization Kinetics of PET Under Solid State Poly condensation

An equation of non-isothermal crystallization kinetics was derived according to a new model and the crystallizations of both the PET samples under solid state polycon-densation and the pre-orientation yarn of high speeding spinning PET were studied with this equation. The results show that there is a good linear relationship between In {-In[1-X(T)]} and lnΦ. The index m in the equation approximately equals to 3 for PET chips and 1. 3 for pre-orientated yarn. At the same temperature, Q(T) decreases with the increase of PET M. W. and the kinetics parameters obtained by Jeziorny' s method indicate that G also decreases with the increase of PET M. W.. Q(T) and Gc show the same varying tendency in the non-isothermal crystallization process.

Non-isothermal Crystallization Kinetics of Kaolin Modified Polyester

Fiber-class modified kaolin and PET have been blended in the twin-screw and granulated to chips containing 4 wt% of kaolin.Non-isothermal crystallization process of kaolin modified polyester was investigated using a differential scanning calorimetry （DSC）,and the addition of kaolin enhances either the melting temperature （Tm） or the crystallization temperature （Tc）.The morphology of kaolin modified polyester,the melt of which is cooled at different cooling rate,was observed by scanning electron microscope （SEM）.The relationship between Tc and cooling rate F was studied.Semi-crystalline phase t1/2 makes an exponential decline with increasing F,and the higher the cooling rate,the shorter the time of crystallization completion.Non-isothermal crystallization kinetics parameters and the activation energy were calculated,indicating that the higher rate of cooling needs the higher relative crystallinity in the unit crystallization time,the crystallization rate increased while speeding up the temperature reduction,and the activation energy ΔE was calculated to be-204.1566 kJ/mol for the non-isothermal crystallization processes by the Kissinger＇s methods.

STUDY OF ACOUSTIC EMISSION DURING NON-ISOTHERMAL CRYSTALLIZATION OF POLYPROPYLENE

In this paper we have presented the results of acoustic emission (AE) during non-isothemal crystallization of polypropylene (PP) melt with mean cooling rate 4℃/min, and discussed the effects of molecular weight (MW) on AE activity. It is shown that the amount of AE ring-down counts during whole crystallization of PP depends on the MW strongly.The copious AE bursts have been observed at the late stage of PPcrystallization. AE bursts are caused by cracking, crazing and cavitation between spherulites and inside spherulites.

Isothermal and Non-Isothermal Crystallization Kinetics of Conductive Polyvinylidene Fluoride/Poly(Ethylene Terephthalate) Based Composites

This work deals with isothermal and non-isothermal crystallization kinetics of electrically conductive polyvinylidene fluoride/poly(ethylene terephthalate) (PVDF/PET) based composites. It completes our previous work in which we related the crystallinity of these conductive PVDF/PET based composites to their through-plane resistivity [1]. Isothermal crystallization was described using the logarithmic form of the Avrami equation and it was observed that the crystallization rate of the PVDF phase inside the composite became slower compared to that of neat PVDF. In non-isothermal crystallization, the Avrami exponent of PVDF phase did not show any noticeable variation;however, that of PET phase, which contains the major part of the conductive carbon black (CB) and graphite (GR) additives, showed an evident decrease compared with neat PET. It was also observed that, at the same cooling rate, the crystallization rate of PVDF and PET phases inside the composite was slower than that of neat PVDF and PET.

KINETICS OF NON-ISOTHERMAL CRYSTALLIZATION OF POLY (ETHYLENE TEREPHTHALATE) MODIFIED BY POLY (ETHYLENE GLYCOL)

The non-isothermal crystallization kinetics of poly(ethylene terephthalate) (PET) modified by poly (ethlene glycol) (PEG) were determined by DSC. The dual linear regression method was used to evaluate the relationship between the reciprocal of t 1/2 ( the half life of crystallization) and the appropriate temperature variable. The parameters such as the activation energy (Ed) for transport, the equilibrium melting temperature (T_m^0),the nucleation parameter (ψ),themaximum crystallization temperature (T_(e, max)), and the kinetic crystallizability (G) for the copolyesters were obtained. The influence of the PEG content in PET chains on the parameters characterizing crystallization kinetics and crystallization thermodynamics was discussed.

Isothermal and Non-Isothermal Crystallization Kinetics of PVDF and PVDF/PMMA Blends

Background:poly(vinylidene fluoride)PVDF and PVDF/PMMA blends have been investigated with a focus on the crystal structure,immiscibility and mechanical properties.However,few reports were found on the crystallization behaviors of PVDF and PVDF/PMMA blends,especially on crystallization kinetics.The article is to report the research on isothermal and nonisothermal crystallization kinetics for PVDF and PVDF/PMMA blends using differential scanning calorimetry(DSC).Results:Besides crystallization temperature and isothermal crystallization activation energy,the Avrami equation exponent of PVDF in blends decreased compared with pure PVDF.The nonisothermal crystallization kinetics of PVDF and PVDF/PMMA(70:30)blends were investigated by Ozawa equation,Jeziorny method and crystallization rate constant(CRC)in detail.The nonisothermal crystallization energy of pure PVDF and its blends were determined by the Kissinger and Vyazovkin’s method.Conclusion:The nucleation and growth mechanism of PVDF in blends changed compared with pure PVDF.The Ozawa equation is not applicable in nonisothermal crystallization kinetics of PVDF and PVDF/PMMA blends.The decreasing of crystallization ability of PVDF in blends were found and confirmed by CRC and the decline of crystallization rate constant in Jeziorny method.Such is opposite to the results of Kissinger’s and Vyazovkin’s method,chances are that these two methods were not used to calculate the nonisothermal crystallization activation energy where the nucleation process was influenced.

INFLUENCE OF SAMPLE THICKNESS ON ISOTHERMAL CRYSTALLIZATION KINETICS OF POLYMERS IN A CONFINED VOLUME

Isothermal crystallization process of polymers in a confined volume was simulated in the case of instantaneous nucleation by use of the Monte Carlo method.The influence of sample thickness on some kinetic parameters of crystallization was quantitatively evaluated.It was found that there was a critical thickness value.Influence of thickness on the crystallization behavior was only found for samples of thickness near and less than the critical value.For thick samples the Avrami plot showed straight lines with a turning point at the late stage of crystallization due to the secondary crystallization.When the thickness was near or less than the critical value a primary turning point appeared in the Avrami plot at the very beginning of the crystallization process.A model was proposed to explain the mechanism of this phenomenon.According to this model the critical thickness value is related to the nucleation density or the average distance between adjacent nuclei,and the primary turning point is an indication of a transformation of crystal growth geometry from a three-dimensional mode to a two-dimensional one.Analysis of experimental results of PEO isothermally crystallized at 53.5℃ was consistent with the proposed model.

Isothermal Crystallization Kinetics of Nylon 10T and Nylon 10T/1010 Copolymers:Effect of Sebacic Acid as a Third Comonomer

Nylon 10T and nylon 10T/1010 samples were synthesized by direct melt polymerization.The isothermal crystallization kinetics of nylon 10T and nylon 10T/1010 was investigated by means of differential scanning calorimetry（DSC）.The crystallization kinetics under isothermal condition has been analyzed by the Avrami equation.It was found that the Avrami equation was well-suited to describe the isothermal crystallization kinetics,combined with the results of the Turnbull-Fisher equation.The values of Tm^0 and Kg were obtained by Hoffman-Weeks and Lauritzen-Hoffman equations,respectively.The activation energies for isothermal crystallization of nylon 10T and nylon 10T/1010 were determined using the Arrhenius equation and found to be-123.24 and-81.86 kJ·mol^（-1）,respectively,which reveals that the crystallization ability of nylon 10T/1010was lower than that of nylon 10T during the isothermal crystallization process.The crystal morphology was observed by means of polarized optical microscopy（POM）and X-ray diffraction（XRD）.It was found that the addition of sebacic acid comonomer did not change the crystal form of nylon 10T,but significantly increased the number and decreased the size of spherulites.

GLOBAL EXISTENCE OF WEAK SOLUTIONS TO THE NON-ISOTHERMAL NEMATIC LIQUID CRYSTALS IN 2D

In this article, we prove the global existence of weak solutions to the non- isothermal nematic liquid crystal system on T2, on the basis of a new approximate system which is different from the classical Ginzburg-Landau approximation. Local in space energy inequalities are employed to recover the estimates on the second order spatial derivatives of the director fields locally in time, which cannot be derived from the basic energy balance. It is shown that these weak solutions satisfy the temperature equation, and also the total energy equation but away from at most finite many ＂singular＂ times, at which the energy concentration occurs and the director field losses its second order derivatives.

LOW MACH NUMBER LIMIT OF A COMPRESSIBLE NON-ISOTHERMAL NEMATIC LIQUID CRYSTALS MODEL

In this paper, we study the low Mach number limit of a compressible nonisothermal model for nematic liquid crystals in a bounded domain. We establish the uniform estimates with respect to the Mach number, and thus prove the convergence to the solution of the incompressible model for nematic liquid crystals.

Isothermal Crystallization Kinetics and Melting Behavior of POE-g-MAH Compatibilized PA11/POE Blends

A new Nylon 11（PA11）/polyethylene-octene（POE） blends compatibilized by maleic anhydride grafted mixture polyethyleneocten（POE-g-MAH） was prepared through melt blending method.The isothermal crystallization kinetics and melting behaviors of PA11/POE blends were investigated in detail by differential scanning calorimetry（DSC） and polarized optical microscope.The n values of PA11 blending with POE or POE-g-MAH are almost similar with pure PA11,which indicates that the effect of POE and POE-g-MAH on nucleation and growth of PA11 crystal is slight.The overall crystallization rate of PA11/POE blends are higher than ones of pure PA11 at the same crystallization temperatures,but they decrease significantly when POE-g-MAH is added into PA11/POE blends.DSC heating curves of both PA11 and its blends exhibit two melting peaks,but the two melting peak become weaker when POE-g-MAH is add into PA11/POE blend systems.And the spherulite size is reduced significantly by the addition of POE-g-MAH compared with pure PA11 and PA11/POE blends.

Kinetics of Nonisothermal and Isothermal Crystallization of Metallocene Polyethylene

The kinetics of nonisothermal and isothermal crystallization of metallocene catalyzed and conventional polyethylenes has been studied by differential scanning calorimetry. Using Avrami equation, Ozawa theory and Mo Zhishen method, the experimental data have been analyzed. It is shown that metallocene polyethylene possesses a higher rate of crystallization due to a higher stereoregularity of its molecular chains. Moreover, they have different nonisothermal crystallization mechanisms and identical isothermal crystallization mechanisms.

CHARACTERIZATION OF γ-IRRADIATED CRYSTALLINE POLYMERS Ⅱ ISOTHERMAL CRYSTALLIZATION KINETICS OF γ-RADIATION INDUCED CROSSLINKED POLYAMIDE 1010

Polyamide 1010 is a γ-radiation crosslinkable polymer. After irradiation, it is possible to raise its service temperature up to 240℃ . Network formation greatly changes the crystallization behaviour of the polymer. In the present work, DSC was used to examine its isothermal crystallization kinetics. It is found that in addition to the necessity of more undercooling and the lowering of crystallization rate, the primary crystallization stage of the irradiated polymer is shortened. This effect is more evident with increasing radiation dose and content of enhanced difunctionai erosslinking agent. However, the crystallization mechanism of the primary stage is not changed as evidenced by the constancy of Avrami exponent. The lamella end surface free energy σ_e calculated according to Hoffman's equation is very sensitive to γ-radiation. It increases abruptly in 2—3 fold even though the radiation dose is not high enough. The origin of this phenomenon may be accounted for in terms of network structure of the polymer.

Poly(tetrafluoroethylene) Spherulitic Crystal and Isothermal Crystallization Kinetics

Spherulitic crystals of Poly(tetrafluoroethylene)(PTFE) were observed for the first time in a kind of PTFE composites, and were verified by polarized optic microscopy(POM). Differential scanning calorimetry(DSC) was used to study the isothermal crystallization kinetics of PTFE matrix at different temperatures. The result shows that Avrami exponents are near 3, which may be elucidated that PTFE crystallizes three dimensionally from preexisting nuclei. The result is in accordance with the observations of scanning electric microscopy(SEM) and POM. In addition, the rate of three dimensional crystallization of PTFE is lower than that of the one dimentional crystallization. So the three dimensional crystallization is easier to control than the one dimensional crystallization of PTFE.

Isothermal Crystallization Behavior of Biodegradable Poly (butylene succinate-co-terephthalate) (PBST) Copolyesters at High Undercoolings

Poly （butylene succinatc-co-terephthalate） （PBST） copolycsters were prepared by polycondensation. The crystallization behavior of the as-prepared copolyesters was investigated by depolarized light intensity （DLI） at high undercoolings. According to Avrami equation, the exponent n, independent of the crystallization temperature, is at a range of 2. 5 to 3. 4, which probably corresponds to the heterogeneous mucleation and a 3-dimensional spherulitic growth. The maximum crystallization rate, very useful to polymer processing, was found at about 90℃ based on the half-crystallization time t1/2 analysis.