110 resultados para Lyapunov Exponent


Relevância:

10.00% 10.00%

Publicador:

Resumo:

Isothermal crystallization behavior of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) was investigated by means of differential scanning calorimetry and polarized optical microscopy (POM). The Avrami analysis can be used successfully to describe the isothermal crystallization kinetics of PHBV, which indicates that the Avrami exponent n = 3 is good for all the temperatures investigated. The spherulitic growth rate, G, was determined by POM. The result shows that the G has a maximum value at about 353 K. Using the equilibrium melting temperature (448 K) determined by the Flory equation for melting point depression together with U-* = 1500 cal mol(-1), T-infinity = 30 K and T-g = 278 K, the nucleation parameter K-g was determined, which was found to be 3.14+/-0.07 x 10(5) (K-2), lower than that for pure PHB. The surface-free energy sigma = 2.55 x 10(-2) J m(-2) and sigma(e) = 2.70+/-0.06 x 10-2 J m(-2) were estimated and the work of chain-folding (q = 12.5+/-0.2 kJ mol(-1)) was derived from sigma(e), and found to be lower than that for PHB. This implies that the chains of PHBV are more flexible than that of PHB.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

The isothermal melt and cold crystallization kinetics of poly(aryl ether ketone ether ketone ketone) are investigated by differential scanning calorimetry over two temperature regions. The Avrami equation describes the primary stage of isothermal crystallization kinetics with the exponent n approximate to 2 for both melt and cold crystallization. With the Hoffman-Weeks method, the equilibrium melting point is estimated to be 406 degrees C. From the spherulitic growth equation proposed by Hoffman and Lauritzen, the nucleation parameter (K-g) of the isothermal melt and cold crystallization is estimated. In addition, the K-g value of the isothermal melt crystallization is compared to those of the other poly(aryl ether ketone)s. (C) 2000 John Wiley & Sons, Inc.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

After isothermal crystallization, poly(ethylene terephthalate) (PET) showed double endothermic behavior in the differential scanning calorimetry (DSC) heating scan. During the heating scans of semicrystalline PET, a metastable melt which comes from melting thinner lamellar crystal populations formed between the low and the upper endothermic temperatures. The metastable melt can recrystallize immediately just above the low melting temperature and form thicker lamellae than the original ones. The thickness and perfection depends on the crystallization time and crystallization temperature. The crystallization kinetics of this metastable melt can be determined by means of DSC. The kinetics analysis showed that the isothermal crystallization of the metastable PET melt proceeds with an Avrami exponent of n = 1.0 similar to 1.2, probably reflecting one-dimensional or irregular line growth of the crystal occurring between the existing main lamellae with heterogeneous nucleation. This is in agreement with the hypothesis that the melting peaks are associated with two distinct crystal populations with different thicknesses. (C) 2000 John Wiley & Sons, Inc.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

The crystallization behavior of PHBV, poly(beta -hydroxybutyrate-co-beta -hydrxyvalerate), with nucleating agents under isothermal conditions was investigated. A differential scanning calorimeter was used to monitor the crystallization process from the melt. During isothermal crystallization, the dependence of relative degree of crystallinity on time was described by the Avrami equation. It has been shown that the addition of BN and Tale causes a considerable increase in the overall crystallization rate of PHBV but does not influence the Avrami exponent n, mechanism of nucleation and spherulite growth mode of PHBV. A little of nucleating agent will increase the crystallization rate and decrease the fold surface free energy sigma (e), remarkably. The effect of BN is more significant than that of Talc.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

The nonisothermal crystallization behavior of Ethylene Terephthalate-Ethylene Oxide (ET-EO) segmented copolymers has been studied with the use of differential scanning calorimetry (DSC). The kinetics of PEO in ET-EO segmented copolymer under nonisothermal crystallization conditions has been analyzed with the Ozawa equation. The results show that there is no agreement with Ozawa's theoretical predictions in the whole crystallization process owing to the constraint of ET segments imposed on the EO segments. A distinct two-crystallization process has been investigated by using the Avrami equation modified by Jeziorny to deal with the nonisothermal crystallization data. The value of the Avrami exponent n is independent of the length of soft segments. However, the crystallization rate is sensitive to the length of soft segments. The longer the soft segments, the faster the crystallization will be.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

Analysis of isothermal and nonisothermal crystallization kinetics of nylon 66 was carried out using differential scanning calorimetry (DSC). The commonly used Avrami equation and that modified by Jeziorny were used, respectively, to fit the primary stage of isothermal and nonisothermal crystallizations of nylon 66. In the isothermal crystallization process, mechanisms of spherulitic nucleation and growth were discussed. The lateral and folding surface free energies determined from the Lauritzen-Hoffman treatment are sigma = 9.77 erg/cm(2) and sigma (e) = 155.48 erg/cm(2), respectively; and the work of chain folding is q = 33.14 kJ/mol. The nonisothermal crystallization kinetics of nylon 66 was analyzed by using the Mo method combined with the Avrami and Ozawa equations. The average Avrami exponent (n) over bar was determined to be 3.45. The activation energies (DeltaE) were determined to be -485.45 kJ/mol and -331.27 kJ/mol, respectively, for the isothermal and nonisothermal crystallization processes by the Arrhenius and the Kissinger methods.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

Isothermal and non-isothermal crystallization kinetics of a syndiotactic polypropylene(sPP) sample synthesized by new metallocene catalyst at different annealing temperatures and different cooling rates have been investigated by using differential scanning calorimetry(DSC) and density analysis. The equilibrium melting temperature( T-m(0)) is 158 degrees C by Hoffman-Weeks method. The equilibrium heat of fusion(Delta H-m(0)) is 88J/g in terms of the density analysis and DSC methods. The lateral and end surface free energies derived from the Lauritzen-Hoffman spherulitic growth rate equation are sigma = 5.2erg/cm(2) and sigma(e) = 69erg/cm(2), respectively. The work of chain folding is determined to be q = 33.75kJ/mol. Modified Avrami equation and Ozawa equation can be used to describe the non-isothermal crystallization behavior. And a new and convenient approach by combining the Avrami equation and Ozawa equation in a same crystallinity is used to describe the non-isothermal behavior as well. The crystallization activation energies are evaluated to be 73.7kJ/mol and 73.1kJ/mol for isothermal crystallization and non-isothermal crystallization, respectively. The Avrami exponent n is 1.5 similar to 1.6 for isothermal crystallization procedure, while the Avrami exponent n,is 2.5 similar to 3.5 for non-isothermal crystallization procedure. This indicated the difference of nucleation and growth between the two procedures.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

After isothermal crystallization of the amorphous poly(ether ether ketone), double endothermic behaviour can be found through differential scanning calorimetry experiments. During the heating scan of semicrystalline PEEK, a metastable melt, which comes from the melt of the thinner lamellar crystal populations, can be obtained between these two endotherms. The metastable melt can recrystallize immediately just above the lower melting temperature and form slightly thicker lamellae than the original ones. The thickness and the perfection depend upon the crystallization time and the crystallization temperature. By comparing the TEM morphological observations of the samples before and after partial melting, it can be shown that lamellar crystals, having different thermodynamic stability, form during isothermal crystallization. After partial melting, only the type of lamellar crystal exhibiting the higher thermodynamic stability remains. Wide angle X-ray diffraction measurements shows a slightly change in the crystallinity of the samples before and after the partial melting. Small angle X-ray scattering results exhibit a change in the long period of the lamellar crystals before and after the partial melting process. The crystallization kinetics of the metastable melt can be determined by means of differential scanning calorimetry. The kinetic analysis showed that the isothermal crystallization of the metastable PEEK melt proceeds with an Avrami exponent of n = 1.0 similar to 1.4, reflecting that probably one-dimensional or an irregular line growth of the crystal occurred between the existing main lamellae with heterogeneous nucleation. (C) 1998 Elsevier Science Ltd. All rights reserved.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

Isothermal melt and cold crystallization kinetics of PEEKK have been investigated by differential scanning calorimetry in two temperature regions. During the primary crystallization process, the relative crystallinity develops with a time dependence described by the Avrami equation, with exponent n = 2 for both melt and cold crystallization. The activation energies are -544.5 and 466.7 kJ/mol for crystallization from the melt and amorphous glassy state, respectively. The equilibrium melting point T-m(o) is estimated to be 371 degrees C by using the Hoffman-Weeks approach. The lateral and end surface free energies derived from the Lauritzen-Hoffman spherulitic growth rate equation are sigma=10 erg/cm(2) and sigma(e) = 60 erg/cm(2), respectively. The work of chain folding q is determined as 3.98 kcal/mol. These observed crystallization kinetic characteristics of PEEKK are compared with those of PEEK. (C) 1997 Elsevier Science Ltd.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

The thermal properties of ethylene propylene copolymer-grafted-acrylic acid (EP-g-AA) were investigated by using differential scanning calorimetry (DSC). Compared with the ethylene propylene copolymer (EP), the peak values of the melting temperature (T-m) of the propylene sequences in the grafted EP changed a little, the crystallization temperature (T-c) increased about 8-12 degrees C, and the melting enthalpy (Delta H-m) increased about 4-6 J/g. The isothermal crystallization kinetics of grafted and ungrafted samples was carried out by DSC. Within the scope of the researched crystallization temperature, the Avrami exponent (n) of the ungrafted sample was 1.6-1.8, and that of grafted samples were all above 2, which indicated that the grafted monomer could become the crystal nuclei for the crystallization of propylene sequence. With increasing grafted monomer content, the crystallization rate of propylene sequence in grafted EP increased; it might be the result of rapid nucleation rate and crystal growth rate.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

Isothermal melt and cold crystallization kinetics of PEDEKmK linked by meta-phenyl and biphenyl were investigated by differential scanning calorimetry in two temperature regions. Avrami analysis is used to describe the primary stages of the melt and cold crystallization, with exponent n = 2 and n = 4, respectively. The activation energies are -118 kJ/mol and 510 kJ/mol for crystallization from the melt and the glassy states, respectively. The equilibrium melting point T-m(0) is estimated to be 309 degrees C by using the Hoffman-Weeks approach, which compares favorably with determination from the Thomson-Gibbs method. The lateral and end surface free energies derived from the Lauritzen-Hoffman spherulitic growth rate equation are sigma = 8.45 erg/cm(2) and sigma(e) = 45.17 erg/cm(2), respectively. The work of chain folding q is determined as 3.06 kcal/mol. These observed crystallization characteristics of PEDEKmK are compared with those of the other members of poly(aryl ether ketone) family. (C) 1997 John Wiley & Sons, Inc.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

The thermal properties of ethylene-propylene copolymer grafted with glycidyl methacrylate (EP-g-GMA) were investigated by using differential scanning calorimetry (DSC). Compared to the plain ethylene-propylene copolymer (EP), peak values of melting temperature (T-m) of the propylene sequences in the grafted EP changed a little, crystallization temperature (T-c) increased about 8-12 degrees C, and melting enthalpy (Delta H-m) increased about 4-6 J/g. The isothermal and nonisothermal crystallization kinetics of grafted and ungrafted samples was carried out by DSC. Within the scope of the researched crystallization temperature, the Avrami exponent (n) of ungrafted sample is 1.6-1.8, and those of grafted samples are all above 2. The crystallization rates of propylene sequence in EP-g-GMA were faster than that in the plain EP and increased with increasing of grafted monomer content. It might be attributed to the results of rapid nucleation rate. (C) 1996 John Wiley & Sons, Inc.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

The surface of superground Mn-Zn ferrite single crystal may be identified as a self-affine fractal in the stochastic sense. The rms roughness increased as a power of the scale from 10(2) nm to 10(6) nm with the roughness exponent alpha = 0.17 +/- 0.04, and 0.11 +/- 0.06, for grinding feed rate of 15 and 10 mu m/rev, respectively. The scaling behavior coincided with the theory prediction well used for growing self-affine surfaces in the interested region for magnetic heads performance. The rms roughnesses increased with increase in the feed rate, implying that the feed rate is a crucial grinding parameter affecting the supersmooth surface roughness in the machining process.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

The crystallization and melting behaviours of a multiblock copolymer comprising poly(ether ether ketone) (PEEK) and poly(ether sulfone) (PES) blocks whose number average molecular weights <((M)over bar (n)'s)> were 10 000 and 2900, respectively, were studied. The effect of thermal history on crystallization was investigated by wide-angle X-ray diffraction measurement. A differential scanning calorimeter was used to detect the thermal transitions and to monitor the energy evolved during the isothermal crystallization process from the melt. The results suggest that the crystallization of the copolymer becomes more difficult as compared with that of pure PEEK. The equilibrium melting point of the copolymer was found to be 357 degrees C, about 30 degrees C lower than that of pure PEEK. During the isothermal crystallization, relative crystallinity increased with crystallization time, following an Avrami equation with exponent n approximate to 2. The fold surface free energy for the copolymer crystallized from the melt was calculated to be 73 erg cm(-2), about 24 erg cm(-2) higher than that of pure PEEK. Copyright (C) 1996 Elsevier Science Ltd.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

Based on Jeziorny theory, the kinetics of phase transition of poly(ester-imide) has been determined under non-isothermal condition by using differential scanning calorimetry (DSC). Avrami exponent n, kinetic parameters G(c) and rate constant Z(c) were derived and discussed.