Avrami kinetics

In addition to the above, there are further possibihties. When the rate of guest diffusion between individual layers is very large compared with the rate of nucleation at the edge of the crystal, there exists a situation in which the individual layers appear to fill instantly. In this case, when Avrami kinetics are applied to the system, the diffusion process being observed is not the diffusion of guest species between the layers, but the diffusion of filled layers parallel to the c-axis. Such ID processes will consist of nucleation followed by diffusion control in the vast majority of cases, although phase boundary control is also possible if the rate of advancement of the phase boundary is also very rapid with respect to nucleation. In this case, instantaneous nucleation is not a possibility [18]. 

The gradient of this graph therefore permits the determination of n, and the intercept allows k to be calculated. The advantage of using a Sharp-Hancock plot rather than a least squares fitting process with the Avrami equation is that if Avrami kinetics are not applicable, this can be seen in the former plot, and hence other kinetic models may be investigated. Purely diffusion controlled processes can be identified using a Sharp-Hancock plot n is foimd to be 0.5 in such cases. 

M. Avrami, Kinetics of phase change. II Transformation-time relations for random distribution of nuclei, J. Chem. Phys. 8 (1940) 212. 

One of the earliest attempts to explicitly combine thermodynamics and kinetics in rapid solidification was by Saunders et al. (1985). They examined the equations derived by Davies (1976) and Uhlmann (1972) for predicting TTT diagrams. These were based on Johnson-Mehl-Avrami kinetics for predicting glass formation during rapid solidification where the ruling equation could be given as... 

Many reactions, including recrystallization, can be described by Avrami kinetics. 

The kinetic theory presented by Johnson and Mehl [2] and Avrami [3] predicts the volume fraction transformed, as a function of time, t, during an isothermal phase transformation. The derivation of the Johnson-Mehl-Avrami kinetics is based on the grouping of the three individual partial processes, that is, nucleation, growth, and impingement of growing particles [5],... 

The different combinations of nucleation, growth, and impingement processes give rise to the Johnson-Mehl-Avrami kinetic model [4], which results in the following equation... 

Iguchi [266] considered a mechanism in which growing chains are occluded, and thus become non-propagating, by a process kinetically analogous to the interaction of crystallites growing from the polymer melt and following Avrami kinetics. (It was assumed that chemical transfer and termination reactions do not occur.) The polymerization rate is given by the concentrations of monomer and active centres at any time, i.e. Rp = kp [C ], [M],. If the decay of catalytic activity follows the relationship... 

Viability time courses, collected at NCGRP for a large number of samples for more than 30 years, provide a rich source of informafion on the nature and kinetics of seed deterioration. Time courses follow a sigmoidal pattern, where a period of minor loss in viabilify precedes a cataclysmic phase where severe reductions in viability are observed. Recently, Avrami kinetics, which describe cooperative reactions based on visco-elastic properties (Avrami, 1941), have been used to describe the pattern of seed aging (Walters et al., 2004 Walters et al., 2005) ... 

A highly topical area within the pharmaceutical sciences for which DSC measurements may be of use for kinetic studies is in the study of recrystallization, either on cooling from the melt or from the amorphous state. Classically, such reactions are described by Avrami kinetics (22-24), given by... 

The detailed thermal behaviours of the starch/PLA blends have been studied by DSC [204]. The experimental data was evaluated using the well-known Avrami kinetic model. Starch effectively increased the crystallization rate of PLA, even at a 1 % content, but the effect was less than that of talc. The crystallization rate of PLA increased slightly as the starch content in the blend was increased from 1 to 40 %. An additional crystallization of PLA was observed, and it affected the melting point and degree of crystalhnity of PLA. 

Kose and Kondo studied tbe size effects of cellulose nanofibres on the crystallization behaviour of PLA. They discovered that the smaller size of cellulose nanofibres on tbe nanoscale does not necessarily make a better nucleating agent for PLA. Table 9.1 summarizes the Avrami kinetic parameters for the isothermal crystallization of the PLA and PLA biocomposites with different types of nanocelluloses as compared to PLA composites with talc and nanoclay. With the addition of unmodified and silylated CNCs as nucleating agents, the t 2 value increases with increasing T similar to that of nanoclay and com starch, but opposite to that of talc. Comparing the... 

Crystallisation processes in PEEK have been the subject of many academic papers [10-13]. However, the crystallisation of PEEK generally matches the classic behaviour of other polymers. The effect of time is described by Avrami kinetics ( 3) and secondary crystallisation occurs after the spherulites have impinged. This secondary crystallisation results from an increase in the crystallinity within the spherulites and is probably related to the existence of the low-temperature melting peaks (LTMP) described later. A number of non-isothermal crystallisation models have been developed. 

Melvin Avrami. Kinetics of phase change. I. General theory. Toumal of Chemical Physics. 7(12) 1103-1U2, 1939. 

The overall crystallization of PBl was analyzed by means of the Avrami equation by several authors. The linear relationship between log(— ln(l — Xi) versus log t showed that the results were eompatible with the Avrami kinetic model. Cortaraz and Guzman found a value of n = 2 for all the samples independently of crystallization temperature and moleeular mass. For unfractionated PBl Danusso [165] and Gordon and Hiller [166] found n = 3, whereas Silvestre et al. found values lying between 2 and 3. 

Compute the rate of some reaction that obeys O Avrami kinetics, assuming that the constants n... 

P. J. Barham, R. A. Chivers, and A. Keller, The supercooling dependence of the initial fold length of polyethylene crystallised from the melt Unification of melt and solution crystallisation. Journal of Mat. Science 20 (5), 1625-1630 (1985). M. Avrami, Kinetics of phase changes 1. J. Chem. Phys. 7,1103-1112 (1939). M. Avrami, Kinetics of phase changes II. /. Chem. Phys. 8,212-224 (1940). 

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