Modified Avrami Equation Research Articles

X-ray induced synthesis of beta tin (β-Sn)

The destabilization of molecular structures via hard X-rays has been previously utilized to synthesize novel compounds. Here we report that the monochromatic X-ray induced decomposition of tin(II) oxalate (SnC2O4) at ambient and 0.6 GPa pressures lead to the formation of beta tin (β-Sn). At 1 GPa, only the degradation of SnC2O4 crystal structure is observed without any indication of β-Sn at the end of irradiation. The maximum transformation yield is achieved at 0.6 GPa suggesting the critical role of intermolecular distance in X-ray induced synthesis of β-Sn. Moreover, a modified Avrami equation is utilized to describe the kinetics and geometry of structural synthesis at ambient and 0.6 GPa. The obtained results demonstrate that X-ray irradiation can induce photochemical synthetic pathways different from conventional methods (e.g., high pressure, temperature, stoichiometric mixing) and that high pressure (HP) can be considered a tool to control X-ray induced photochemistry.

Flow softening and recrystallization accompanied flow in AZ61 magnesium alloy during thermomechanical processing

The present work deals with characterizing the recrystallization accompanied flow and high temperature softening behavior of an extruded AZ61 magnesium alloy. This was supported by conducting a set of hot compression tests at temperatures in the range of 250–450 °C under the strain rate ranging from 0.001 to 0.1s−1. The flow curves at all thermomechanical conditions indicated high fractional softening representing the domination of dynamic recrystallization mechanism. Through a new quantitative approach, “Arrhenius type model”, “modified Avrami equations” and Poliak and Jonas method were simultaneously employed to investigate the kinetic of dynamic recrystallization. It was revealed that the strain required for the same amount of recrystallization fraction increased with decreasing deformation temperature, and at a specified temperature, the required strain increases with increasing strain rate. Interestingly, an anomaly was found at 400 °C under the strain rate of 0.001s−1, where the recrystallization kinetic was faster than that of what was recorded at 450 °C. This anomaly was discussed relying on the nanoprecipitation of γ-phase at the prior boundaries and sub-boundaries which prohibited the grain boundary migration and also the rotation and coalescence of adjacent sub-grains.

Effect of the storage process on quality characteristics of hemp-enriched "tsoureki" a rich-dough baked Greek product.

The effects of the storage process on the quality characteristics of a hemp-enriched "tsoureki" (a rich-dough baked Greek product, rich-dough baked product [RDBP]) were investigated. The wheat flour was substituted with defatted hemp flour at selected ratios (0%-50% hemp:wheat flour). The baked products were stored at 25°C and at specific time intervals (0, 1, 4, 7, 10, and 14 days), and their properties were determined, including moisture content, water activity, structure, texture, color, total phenolic content (TPC), and antioxidant activity. Moreover, analyses of phenolic compounds were performed using quadrupole time of flight liquid chromatography-mass spectroscopy, identifying 14 compounds. Both the first-order kinetic model and modified Avrami equation, including the hemp-to-wheat ratio effect in the rate constant, well described the changes in the quality characteristics. The results showed that storage time and hemp incorporation significantly affected the quality of the product. Water activity decreased from 0.901 to 0.859, whereas moisture content decreased from 30.52%-32.33% (0 days) to 26.97%-27.02% w.b. (14 days) with storage time for all hemp additions. Hardness was greatly affected by hemp flour addition and approached 14.72 and 17.85 N after 14 days of storage for 30% and 50% substitutions, respectively. Springiness and cohesiveness decreased with hemp addition and storage time. The color difference of the hemp-enriched products compared to the control sample increased during storage. TPC increased due to the addition of hemp flour, whereas 14 compounds were identified. Based on property correlation, the hemp-enriched RDBP-tsoureki held its high-quality characteristics for 7 days of storage and contained a significant amount of bioactive compounds. PRACTICAL APPLICATION: Industrially produced, defatted hemp is a promising byproduct that can be used to nutritionally enhance baked goods. Modeling results can be used for the prediction of the properties that define product storage ability and also that the hemp-enriched, rich dough-baked Greek "tsoureki" could be produced while maintaining total phenolic content and antioxidant activity during 7 days of storage. These findings are expected to be used in the future in baked goods industry applications to produce goods with an improved nutritional profile.

Analysis of the Non-isothermal Crystallization Kinetics of the Polyamide 6/M-lignin Composites

In this study, investigations of the non-isothermal crystallization kinetics of polyamide 6 (PA6) and PA6/m-lignin composites were conducted by differential scanning calorimetry (DSC). The crystallization kinetics of the PA6, including crystallization temperature and rate, were characterized by monitoring the heat flow during cooling. The study found that the crystallization temperature shifted to lower temperatures and the crystallization kinetics slowed down with increasing lignin. Besides, the Avrami equation modified by Jeziorny and Mo’s method were used to study the non-isothermal crystallization kinetics of the neat PA6 and PA6 composites. The curve fit resulting from the modified Avrami equation was not convincing. However, Mo’s method did successfully characterize the overall non-isothermal crystallization kinetics for neat PA6 and the PA6 composites. In addition, the activation energies of the non-isothermal crystallization were calculated by the Kissinger method. It was found that the PA6 composite crystallization rate increased when adding less than 10% lignin. However, the more the content of m-lignin, the slower the crystallization rate. The same conclusion was reached based on the fitting results of the non-isothermal crystallization activation energies.

In-situ observation and crystallization kinetics during the solidification of Cr-containing stainless steel slags

For a sustainable recycling process of Cr-containing stainless steel slags, high chromium recovery through selective crystallization could be achieved when thermophysical properties are controlled based on the crystallization kinetics. The in-situ observation and crystallization kinetics of synthesized Cr-containing slags has been studied. The crystallization characteristics in the CaO–SiO2–Al2O3–MgO–Cr2O3 slag system were investigated by using CLSM (confocal laser scanning microscopy) and DSC (differential scanning calorimetry). Analysis of crystallization kinetics was divided into spinel phase and calcium silicate phase. The growth mechanism of primary spinel phase has been demonstrated through CSD (crystal size distribution) theory with varying temperatures and cooling rates. The crystallization kinetic analysis of calcium silicate phase was performed using the modified Avrami equation and the combined Avrami and Ozawa equation. The Friedman differential isoconversional method was applied for determining the apparent activation energy during non-isothermal crystallization. Observations of crystalline phase morphologies and the precipitated phase was identified by using SEM-EDS (scanning electron microscopy-energy dispersive spectroscopy) and XRD (X-ray diffraction) analyses. The change in the crystallization characteristics were compared with the slag melt structures analyzing by Raman spectroscopy.

Microscale spherical TiO2 powder prepared by hydrolysis of TiCl4 solution: Synthesis and kinetics

Hydrolysis of TiCl4 solution is capable of preparing microscale TiO2 particles. This research studied the synthesis of microscale spherical TiO2 powders and the hydrolysis kinetics. The effects of the flow field generated by different agitators and baffles in the crystallizer, the initial free acid concentration, the initial equivalent TiO2 concentration, and the temperature on the hydrolysis progress and powder morphology were systematically studied. The results show that the flow field in a crystallizer can significantly affect the morphology and particle size of the powders, and the axial flow can improve the sphericity of the powders. The increased free HCl and equivalent TiO2 concentrations in the pregnant solution inhibit the forward hydrolysis reaction, prolong the time to reach equilibrium, and reduce the yield. An appropriate temperature matching the compositions of the pregnant solution is crucial for the powder morphology and size. Powders with sizes ranging from around 5 μm–40 μm can be tuned under controlled flow field, solution compositions, and temperature conditions. In addition, the Cheng and Wunderlich modified Avrami equation was used for the crystallization kinetic modeling. The effects of the free HCl concentration, equivalent TiO2 concentration, and hydrolysis temperature are reflected in the reaction rate constant and active nuclei reduction index. Increasing the free HCl and equivalent TiO2 concentrations will reduce the reaction rate constant and accelerate the deactivation of the active nuclei, thus increasing the final powder size, while increasing the temperature will lead to the opposite results.

Fine-structure constant and hysteresis regimes in the giant squid propagating action potential.

We present a phase space based phenomenological theory for the steady propagation of the action potential using the Rosenthal-Bezanilla experimental data. Time derivatives of giant squid action potential, its velocity of propagation, the radius of the axon and its capacitance, and the resistivity of axoplasm, yield the total ionic, capacitive, and membrane currents of the charge conserving cable equation. Evidence is presented that the sodium channels lattice has a polarization flip at the inception of the action potential and the corresponding flip reversal at the peak of the action potential while traversing a ferroelectric hysteresis loop. The polarization flip at the inception of the action potential is followed by capacitive polarization current known as gating current. The polarization flip at the peak of the action potential is preceded by a small sodium polarization current associated with sodium current inactivation. Ionic currents and sodium polarization ionic currentsare taken to have the familiar structure, as the product of maximum conductance, driving force, and fraction of open channels. Fractions of open channels are fitted in the lab frame by modified Avrami equations seeded with the value of the fine-structure constant α = 0.0072973... . The existence of sodium channels domains with two different symmetries, albeit only one being stable in squid axon, suggests the possibility of neurons with at least 2 stable states, the necessary condition for storage and retrieval of memories. It is expected that presented results will provide the framework for further analysis of thermodynamic phase changing behavior, the role of quantum mechanics in the flow of ions trough ionic channels and in particular the role of ferroelectric sodium channels lattice behavior in storage and retrieval of memories and nerve excitability.

Isotactic Polybutene-1의 결정화 거동을 개선하기 위한 생분해성 미세결정 셀룰로오스의 적용

The microcrystalline cellulose (MCC) was used for inducing crystallization of the isotactic polybutene-1 (iPB) and the maleic anhydride grafted polybutene-1 (MAPB) was used as a compatibilizer. The crystallization behavior of the composite demonstrated that the addition of MCC could significantly accelerate the crystallization rate of iPB and the addition of MAPB could improve the compatibility between MCC and iPB. Moreover, the properties of the composites with MAPB were better than those without MAPB. The crystal transformation had been completed after storage for 5 days and the form I was formed after storage for 3 days which was faster than pure iPB. The non-isothermal crystallization kinetics data of the composites indicated that the modified Avrami equation could describe the non-isothermal crystallization process of the iPB/MCC composite and the tSUB1/2/SUB of the composites was shortened for 24.32% and 40.27% which indicated that MCC could promote the crystallization of iPB.

Effect of nucleating agents on the non‐isothermal crystallization and degradation kinetics of poly(ethylene terephthalate)

Poly(ethylene terephthalate) (PET) was synthesized by two steps, namely (a) transesterification and (b) polycondensation. Various analytical instruments were used for the characterization of neat PET. The sodium salt of nucleating agents added with PET was synthesized by the in‐situ method under the same experimental conditions. The influence of CO2Na, ONa, SO3Na, PO3Na on the crystallization properties of PET was tested. The aromatic SO3Na nucleated PET exhibited the highest crystallization temperature (Tc) value of 211.4°C with the degradation temperature (Td) value of 446.9°C. The energy of activation (Ea) for the degradation and crystallization of PET was determined using various kinetic models. The modified Avrami equation showed the 3D crystal growth of PET, which was further evidenced by polarized optical microscopy (POM). The second stage of degradation consumed a higher amount of thermal energy. The experimental results were compared with the literature values.

Thermally reduced graphene/polyethylene nanocomposites: effects of graphene on isothermal and nonisothermal crystallization of polyethylene

The crystallization behavior of polyethylene/thermally reduced graphene (PE/TRG) nanocomposites prepared via solvent blending is investigated using a differential scanning calorimeter, and results are compared with PE/carbon black (CB) composites. The effects of TRG and CB concentrations on the crystallization process are studied under isothermal and dynamic conditions. The Avrami and modified Avrami equations provided excellent fits to isothermal and dynamic crystallization kinetics data, respectively. The TRG nanosheets acted as nucleating agents during crystallization attributed to substantial decrease in crystallization half time at higher TRG concentrations. The reduced surface energy of the nanocomposites with incorporation of TRG further confirmed its nucleating behavior.

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.

Melt crystallization and segmental dynamics of poly(ethylene oxide) confined in a solid electrolyte composite

ABSTRACTThe isothermal melt crystallization and the corresponding segmental dynamics, of a high molecular weight poly(ethylene oxide) (PEO) confined by Li7La3Zr2O12 (LLZO) particles in solid electrolyte composites, were monitored by differential scanning calorimetry (DSC) and dielectric relaxation spectroscopy (DRS), respectively. Our results show that the overall crystallinity is positively correlated with the surface area of LLZO particles. The primary and secondary crystallization processes are identified by a modified Avrami equation, while two dynamic modes, the α relaxation and α′ relaxation, were in the DRS measurements. The results reveal an unambiguous correlation between the primary crystallization and the α relaxation, while a correlation between the second crystallization and the α′ relaxation concurrently exist in the electrolyte composites. © 2020 Wiley Periodicals, Inc. J. Polym. Sci. 2020, 58, 466–477

Microstructural Modeling of Thermally-Driven β Grain Growth, Lamellae & Martensite in Ti-6Al-4V

The microstructural kinetics of β grain growth in the β field of a Ti-6Al-4V alloy was studied by a series of controlled heat treatments at constant temperature rates. Heating rates of 5°C/s, 50°C/s and 500°C/s were considered, stopping at different peak temperatures. The thickness evolution of martensitic needles and lamellar α laths, formed on cooling, was also investigated, by soaking the material above its β-transus temperature and cooling down at 5°C/s, 50°C/s, 100°C/s and 300°C/s till ambient temperature. Quantitative microstructural analyses were used to measure the particle dimensions. The β grain growth kinetics was reasonably well described by a modified Avrami equation. The thickness of α lamellae was a function of the cooling rate and the β grain dimension in which they nucleated. The martensite needle thickness was shown to be a function of the cooling rate to which the material was subjected.

The Effect of a Secondary Process on the Analysis of Isothermal Crystallisation Kinetics by Differential Scanning Calorimetry.

This paper demonstrates the application of a modified Avrami equation in the analysis of crystallisation curves obtained using differential scanning calorimetry (DSC). The model incorporates a square root of time dependence of the secondary process into the conventional Avrami equation and, although previously validated using laser flash analysis and infrared spectroscopy, is not currently transferable to DSC. Application of the model to calorimetric data required long-duration isotherms and a series of data treatments. Once implemented, the square root of time dependence of the secondary process was once again observed. After separation of the secondary process from the primary, a mechanistic n value of 3 was obtained for the primary process. Kinetic parameters obtained from the analysis were used in the model to regenerate the fractional crystallinity curves. Comparison of the model with experimental data generated R2 values in excess of 0.995. Poly(3-hydroxybutyrate-co-3-hydroxyvalerate) was used as model polymer due to the prominent secondary crystallisation behaviour that this polymer is known to display.

Synthesis and nonisothermal crystallization kinetics of biodegradable poly(ethylene terephthalate‐co‐ethylene succinate)s

ABSTRACTIn the current work, a series of biodegradable poly(ethylene terephthalate‐co‐ethylene succinate)s (P[ET‐co‐ES]s) were prepared via a traditional melting polycondensation method. First of all, the structures of prepared copolymers were characterized by nuclear magnetic resonance and Fourier transform infrared measurements. Meanwhile, the thermal properties of prepared samples were analyzed by differential scanning calorimetry and thermogravimetric analysis measurements, respectively. Subsequently, the mechanical properties of the P(ET‐co‐ES)s were evaluated, the tensile strength of P(ET‐co‐ES)s decreased with increasing of PES content in copolymer, however, corresponding P(ET‐co‐ES)s exhibited better elongation at break. Next, the biodegradability of P(ET‐co‐ES)s was evaluated using lipase as degrading enzyme. The results presented that the biodegradability of P(ET‐co‐ES)s improved with PES content, the corresponding results were supported by scanning electron microscopy test. Finally, the Mo's modified Avrami equation was employed to analyze the nonisothermal crystallization kinetics of prepared copolymers. The results showed the addition of the PES component improved the crystallization properties of the prepared P(ET‐co‐ES)s. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020, 137, 48422.

Thermal diffusivity and secondary crystallisation kinetics in poly(lactic acid)

The non-steady state technique of laser flash analysis (LFA) was used to record the variation of thermal diffusivity with time during the cold-crystallisation of poly(lactic acid), a grade that contains 4% D stereoisomer. The measured diffusivity data was analysed in terms of the Avrami and Hoffman-Lauritzen models for polymer crystallization and this yielded kinetic data that was comparable to that which originated from DSC. Within the temperature range 88 to 109 °C, mechanistic ‘n’ values of 2.0 ± 0.1 were calculated and a nucleation constant of 6.58 × 10−5 K2 was determined. Measurements of thermal diffusivity were also recorded over a longer time-scale to determine whether thermal diffusivity was a useful indicator of secondary crystallization and this data was analysed using a modified Avrami equation that includes a root-time dependence of the secondary process. Secondary crystallisation rate constants (ks) increased with crystallisation temperature and yielded an activation energy for the secondary crystallisation process of 40 kJ/mol.

A simplified semi-analytical model for the filling and cooling process in plastic molding

The effects of the operational conditions on the filling and cooling process in plastic molding are studied. First, a semianalytical model is developed to study the effects of thermal boundary conditions and imposed pressure on the velocity profile and blocking time in the filling stage of the molding process. To do so, a lubrication approximation type model is developed in which the shear viscous heating terms are neglected to simplify the governing equations. Using an equipped mold, molding experiments are conducted to validate the model predictions by using a well-controlled injection molding machine. Comparing the model and experimental results shows a reasonable agreement among them. Second, regarding the cooling process, a modified Avrami equation is used to capture the polymer crystallization in variable cooling rates. The model results show that the cooling time and the final solid fraction decrease by increasing the cooling rate.

Analysis of Changes of Particle Size Distribution and Biological Composition of Flocs in Wastewater During the Growth of Algae

The process of growth of algae can be described using the images from microscopic analysis. The new approach to assessment of the growth dynamics of algae used the data of granulometric composition of liquid medium and the modified Avrami equation relating to the crystallisation process. This paper presents a comparison of both methods (granulometric and microscopic) for the analysis of the dynamics of changes in the growth of algae in wastewater. The experimental set-up consisted of four glass tanks filled with biologically treated sewage, in which algae grew. The cultivation of algae was carried out for 8 weeks. During this period, the granulometric analysis and microscopic observations of sewage were conducted. The study demonstrated that with increase in the size of flocs in treated sewage, biomass of algae was also increased. Therefore, the results obtained with the method of laser diffraction are in agreement with microscopic observation of flocs. Granulometric analysis could be, next to microscopic analysis, a method for the estimation of the dynamics of changes in the growth of algae in sewage. This knowledge will allow to selection of a suitable method of wastewater treatment and algal separation.

Non-isothermal crystallization kinetics of continuous glass fiber-reinforced poly(ether ether ketone) composites

Current studies on crystallization kinetics for glass fiber-reinforced poly(ether ether ketone) mainly focused on short glass fiber-reinforced composites and their isothermal crystallization. It is worth noting that continuous glass fiber-reinforced poly(ether ether ketone) composite (CGF/PEEK) possesses relatively higher mechanical performance than short fiber-reinforced PEEK under high temperature. Here, for the first time, we investigate the non-isothermal crystallization kinetics and melting behavior of CGF/PEEK by differential scanning calorimetry at four different cooling rates. By evaluating the crystallite size of CGF/PEEK using X-ray diffraction, it is found that with the decreasing cooling rate, the crystallite size distribution evolves more uniform, and the size of crystallites enlarges. Besides, by systematical analysis, we find the modified Avrami equation can well describe crystallization behavior of the CGF/PEEK. The higher Avrami value of CGF/PEEK than pure PEEK indicates that CGF could introduce a more complex geometry effect on the crystallization. The addition of CGF greatly reduces the absolute value of crystallization activation energy of PEEK, suggesting that CGF can reduce the nucleation energy barrier. The obtained results illustrate that CGF can accelerate the nucleation rate due to heterogeneous nucleation while reduce the growth rate due to retarded polymer chain mobility. And the cooling conditions can influence crystal growth and morphology.

Non-isothermal crystallization kinetics of poly(3-hydroxybutyrate)/EVA 80 blends enhanced by NH4Cl as a nucleating agent

The crystallization kinetics of poly(3-hydroxybutyrate) (PHB), PHB/NH4Cl composites, PHB/ethylene-vinyl acetate (EVA 80) blends and PHB/EVA 80/1 mass% NH4Cl blends were studied under non-isothermal conditions. The modified Avrami equation and the MO approach were found to successfully describe the non-isothermal crystallization process. It was found that the inverse half time of crystallization and the values of Avrami rate constant, K, of PHB increased with decreasing EVA 80 content, increasing cooling rate and the addition of NH4Cl. Moreover, the crystallization mechanism remains unchanged in spite of the EVA 80 content and the presence of NH4Cl. Furthermore, the effective energy barrier of the non-isothermal crystallization process, EX(t), was evaluated with the isoconversional methods of Friedman. The EX(t) values of PHB/NH4Cl composites are much lower than those of pure PHB. Moreover, EX(t) values of PHB in PHB/EVA 80/1 mass% NH4Cl increase with increasing EVA content. A large number of small PHB spherulites were observed by polarized optical microscopy in the presence of NH4Cl.