TRANSFORMATION KINETICS ACTIVATION VOLUME

The hysteresis loop is considered a dynamic property because the kinetics of activated processes should depend on the observation time. The limit of long observation times is important in geophysics for simulating processes occurring over geological time scales. Kinetics experiments are the most important tool in this respect because the study of hysteretic transitions is otherwise limited to measurements taken under nonequilibrium conditions. 

Extensive measurements of the kinetics to determine rate constants for the nanocrystal transition have been made only on the CdSe system (Chen et al. 1997, Jacobs et al. 2001). Both the forward and reverse transition directions have been studied in spherically shaped crystallites as a function of pressure and temperature. The time-dependence of the transition yields simple transition kinetics that is well described with simple exponential decays (see Fig. 5). This simple rate law describes the transformation process in the nanocrystals even after multiple transformation cycles, and is evidence of the single-domain behavior of the nanocrystal transition. Rate constants for the nanocrystal transition are obtained from the slope of the exponential fits. This is in contrast to the kinetics in the extended solid, which even in the first transformation exhibits complicated time-dependent decays that are usually fit to rate laws such as the Avrami equation. 

The measurements of activation volumes and activation energies in both transition directions reveal that the forward and reverse transition kinetics differs. (These 

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We have mentioned above the tendency of atoms to preserve their coordination in solid state processes. This suggests that the diffusionless transformation tries to preserve close-packed planes and close-packed directions in both the parent and the martensite structure. For the example of the Bain-transformation this then means that 111) -> 011). (J = martensite) and <111> -. Obviously, the main question in this context is how to conduct the transformation (= advancement of the p/P boundary) and ensure that on a macroscopic scale the growth (habit) plane is undistorted (invariant). In addition, once nucleation has occurred, the observed high transformation velocity (nearly sound velocity) has to be explained. Isothermal martensitic transformations may well need a long time before significant volume fractions of P are transformed into / . This does not contradict the high interface velocity, but merely stresses the sluggish nucleation kinetics. The interface velocity is essentially temperature-independent since no thermal activation is necessary. 

There are two different basic approaches in the control of selectivity in chemical transformations. In a kinetically controlled reaction the difference between the volumes of activation leading to the isomers must be considered, whereas in a thermodynamically controlled reaction the difference in the volumes of reaction is important. 

The kinetics of excretion are a direct consequence of the kinetics of metabolic transformations. The faster a drug is metabolized, the faster its elimination can be expected. In accordance with this assertion, rats given R,S( ), S(+), and R(-)-amphetamine, were found to excrete less (+)-p-hydroxy-amphetamine than its (-)-isomer this may be the basic explanation of the more pronounced pharmacological properties of the dextro-, compared to the levoampheta-mine. For the hypnotic agent hexobarbital, the ehmination half-life in man is about three limes longer for the more active (-l-)-isomer then for the less active ( )-isomer. This was attributed to a difference in hepatic metabolic clearance and not in volumes of distribulion or plasma binding between the enantiomers. " ... 

An interesting kinetic study deals with the solution-mediated phase transformation of COT and COD into the thermodynamically stable COM [50]. The experimental conditions were adjusted so that either COT or mixtures of COD and COM crystallized initially as confirmed by X-ray diffraction powder patterns. The systems were then aged in contact with the mother liquid, and the transformation of COT or COD into COM was followed by monitoring the total crystal volume as a function of time (by Coulter counter) and determining (by thermo-gravimetric analysis) the relative proportion of the crystal hydrates at fixed time intervals. In addition, supersaturation profiles (i.e., activity products) were determined by solution calcium analysis. In all cases the transformation was completed within approximately 80-100 h. 

FIG. 6 Kinetic analysis of solution-mediated phase transformation of in situ precipitated calcium oxalate trihydrate (COT) into calcium oxalate monohydrate (COM), (a) Solution analysis Variation of ion activity product vs. time, (b) Solid phase analysis Total crystal volume (curve 1) and volume fractions of COT (curve 2) and COM (curve 3) vs. time. 

Pressure is a fundamental physical property that affects various thermodynamic and kinetic parameters. Pressure dependence studies of a process reveal information about the volume profile of a process in much the same way as temperature dependence studies illuminate the energetics of the process (83). Since chemical transformations in SCF media require relatively high operating pressures, pressure effects on chemical equilibria and rates of reactions must be considered in evaluating SCF reaction processes (83-85). The most pronounced effect of pressure on reactions in the SCF region has been attributed to the thermodynamic pressure effect on the reaction rate constant (86), and control of this pressure dependency has been cited as one means of selecting between parallel reaction pathways (87). This pressure effect can be conveniently evaluated within the thermodynamic framework provided by transition state theory, which has often been applied to reactions in solutions (31,84,88-90). This theory assumes a true chemical equilibrium between the reactants and an activated transition... 

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