Avrami Kinetic Equation Research Articles

Time‐resolved wide‐angle X‐ray scattering measurements during the isothermal crystallization and ferroelectric phase‐transition processes of a vinylidene fluoride/trifluoroethylene copolymer

AbstractThe time‐resolved measurement of wide‐angle X‐ray scattering was performed with a synchrotron radiation source during the processes of the isothermal crystallization and ferroelectric phase transition of a vinylidene fluoride/trifluoroethylene copolymer with 73 mol % vinylidene fluoride. When the sample was cooled rapidly from the melt to the temperature region of the paraelectric high‐temperature phase, the peak position of the 200/110 reflection shifted toward the higher angle side and the half‐width became narrower. This indicated an increase in the crystallite size with a more compact chain‐packing mode. Even when the temperature jump was made from the melt into the region of the ferroelectric or low‐temperature phase, the crystallization of the high‐temperature phase was first observed before the appearance of the low‐temperature phase. This was consistent with a prediction based on the so‐called Ostwald state rule: the thermodynamically unstable but kinetically preferable high‐temperature phase can appear first even when the thermodynamically more stable low‐temperature phase should be created. The time‐dependent intensity changes were analyzed with the Avrami kinetic equation. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4175–4181, 2004

Kinetics and equilibrium parameters of Hg(II) adsorption on silica–dithizone

Sı́lica–dithizone (Sil-dtz) was synthesized and used to adsorb Hg(II) in solution at pH 6.0. Increasing the temperature accelerates the mass transfer of Hg(II) to the silica surface. The kinetic data were evaluated using the traditional pseudo-first-order Lagergren equation and an alternative Avrami kinetic equation. From the latter equation, two regions presenting distinct kinetic parameters were found, at 25 and 35 °C, and the use of the parameter n was also related to the determination of distinct kinetic orders. Variations of the adsorption kinetic rate in relation to the time and the temperature were also calculated and are discussed. The adsorption isotherms data were well fitted to the Freundlich model. Interestingly, good adsorption data correlation of the Langmuir model and experimental values was observed only at 45 and 50 °C, suggesting, for this temperature range, the formation of complexes with the proportion Hg:dithizone 1:1 on the silica surface.

An alternative Avrami equation to evaluate kinetic parameters of the interaction of Hg(II) with thin chitosan membranes

In this work, thin chitosan membranes were utilized as an adsorbent for the removal of Hg(II) from aqueous solutions. A rise of temperature accelerates the mass transfer of Hg(II) to the membranes, surfaces. The kinetic data did not present a good fitting to the traditional Lagergren adsorption kinetic equations. An alternative Avrami kinetic equation was employed and successfully fitted to the kinetic adsorption quantities. From this new equation, two regions presenting distinct kinectic parameters were found, and the use of the parameter n was also relationed to the determination of the kinetic order. Variations of the adsorption kinetic rate in relation to the time, the initial Hg(II) concentration, and the temperature were also calculated and are discussed.

Non-random nucleation and the Avrami kinetics

Abstract The theory available for obtaining the time evolution of the transformation for a nucleation and growth process, the well-known Kolmogorov-Johnson-Mehl and Avrami kinetic equation, is not accomplished for non-random nucleation processes. However, non-random nucleation protocols are very common; for example in first-order phase transitions where position-dependent nucleation protocols arise from the modification of the nucleation rates in the regions around the growing grains. The present paper attempts to study the effect of these position-dependent nucleation protocols in the overall kinetics of the transformation. Monte Carlo simulations of such processes are performed, and the deviations of the resulting kinetics of the transformation from the Avrami equation are analysed in detail. Consideration of the different effects resulting from the nucleation protocol allows us to model the transformation. A modified Avrami equation is obtained and compared with Monte Carlo simulations, giving excellen...

Synthesis of nanometric zirconia powders by hydrothermal reactions of Zr (IV) peroxide precursors

Hydrothermal reaction of a Zr(IV) peroxide precursor in the temperature range 110-180°C was used to produce nanocrystalline zircon ia powders. Cubic metastable ZrO2 is formed with or without the presence of is formed with or without the presence of 2O3 or CeO2 as stabilising agents. After firing 2h at 1000°C the pure ZrO2 powder remains cubic while the doped powders transforms to tetragonal ZrO2. The influence of Zr concentration and treatment temperature on the crystallite sizes are presented. The kinetic constant for the nucleation of cubic zirconia phase was also calculated according to Avrami's kinetic equation.

Modeling of Non-Random Nucleation Protocols

AbstractNon random nucleation processes are a subject of much interest in the study of first order phase transformations. However, the theory available to obtain the time evolution of the transformation for a nucleation and growth process, the well known Kolmogorov, Johnson-Mehl and Avrami kinetic equation (KJMA), is not accomplished if the nucleation process is nonrandom. Therefore, KJMA does not give an adequate description of the transformation kinetics.In the present paper, a non-random nucleation protocol resulting from a reduced nucleation rate due to the nearby presence of other growing grains is considered. Monte-Carlo simulations of such processes are performed, and the deviations from the Avrami kinetics observed are analyzed in detail.

The kinetics of hydration of calcium sulphate hemihydrate: A critical comparison of the models in the literature

The hydration of calcium sulphate hemihydrate to produce calcium sulphate dihydrate (gypsum plaster) has been the subject of several kinetic models, two of the most notable of which were proposed in a series of conflicting papers by Ridge and Schiller. Evidence was put forward in support of both these and other models but no model has gained universal support. Numerical calculations are used to compare these models with each other and with the Avrami kinetic equation in this paper. It is shown that at least for some ranges of data all three approaches are compatible and that within the limits of the experimental evidence presented so far there is no conclusive evidence which justifies the use of one model rather than the others.

Kinetics and mechanistic aspcts of the interconversion process CrO2 ⇌' CrOOH. Isotopic effect

Abstract The kinetics and mechanistic aspects concerning with the interconversion process CrO2⇌' CrOOH have been studied. The oxidation process appears to be governed by an Avrami kinetics equation. However, the back reaction obeys to an onedimensional duffusion kinetics model in which the hydrogen diffuse along the empty tunnels that parallel to the c-axis are present in the rutile-type structure. the isotopic effect concerning with the reduction process have also been studied.

Relationship between the morphological character of 5-nitroacetylsalicylic acid crystals and the decomposition rate in a humid environment.

Two morphologically different crystals, column-shaped and ramified, were sorted under a microscope from a recrystallized batch of 5-nitroacetylsalicylic acid. Their degradation rates in the solid state were quantitatively studied and the progress of decomposition was observed under a polarizing microscope. Plots of the ratio decomposed against the reaction time were sigmoidal under all reaction conditions, and Avrami's kinetic equation was applicable to this reaction below 40% degradation. The reactivity of the ramified crystals was greater than that of the column-shaped crystals under all experimental conditions. Although the parameter B of Avrami's equation, which is assumed theoretically to be proportional to the product of the number of latent reaction nuclei and the voluminal growth rate varied by a factor of 104 at maximum under various experimental conditions, the ratio of B between ramified and column-shaped crystals remained fairly constant under all the conditions tested, and was about five. The results of observation of the decomposing crystals under a polarizing microscope agreed well with Avrami's theory of the formation and growth of reaction nuclei.