Kinetic prior, estimation

Equilibrium Concept in Vaporization Kinetics Prior to further discussion of the vaporization equations, it is appropriate to comment on the application of the concepts of equilibrium and of the equilibrium pressure to kinetics. The existence of real equilibrium during the course of decomposition, as well as of decomposition under equilibrium conditions (particularly in a high vacuum), is out of the question. Both concepts are employed rather as categories applied to conceivable situations, in which the direct and the reverse processes (i.e., the vaporization and the condensation) are in a state of equilibrium, thus validating the estimation of the vaporization rate through the rate of the reverse process. For this reason, in describing the decomposition rate the term equivalent pressure is sometimes used. 

It is important to distinguish clearly between the surface area of a decomposing solid [i.e. aggregate external boundaries of both reactant and product(s)] measured by adsorption methods and the effective area of the active reaction interface which, in most systems, is an internal structure. The area of the contact zone is of fundamental significance in kinetic studies since its determination would allow the Arrhenius pre-exponential term to be expressed in dimensions of area"1 (as in catalysis). This parameter is, however, inaccessible to direct measurement. Estimates from microscopy cannot identify all those regions which participate in reaction or ascertain the effective roughness factor of observed interfaces. Preferential dissolution of either reactant or product in a suitable solvent prior to area measurement may result in sintering [286]. The problems of identify-... 

Various model-dependent methods for the comparison of two cumulative dissolution data sets have been proposed (21). Usually, these methods involve prior characterization of both profiles by one to three parameters per profile. In some models, these parameters can be interpreted in terms of the kinetics, the shape, and/or the plateau, but in other instances, they have no physical meaning. One issue that requires some attention is that, in cases where more than one parameter is estimated, a multi-variate procedure for the comparison of the parameters must be applied (9,21). 

NONMEM is a one-stage analysis that simultaneously estimates mean parameters, fixed-effect parameters, interindividual variability, and residual random effects. The fitting routine makes use of the EES method. A global measure of goodness of fit is provided by the objective function value based on the final parameter estimates, which, in the case of NONMEM, is minus twice the log likelihood of the data (1). Any improvement in the model would be reflected by a decrease in the objective function. The purpose of adding independent variables to the model, such as CLqr in Equation 10.7, is usually to explain kinetic differences between individuals. This means that such differences were not explained by the model prior to adding the variable and were part of random interindividual variability. Therefore, inclusion of additional variables in the model is warranted only if it is accompanied by a decrease in the estimates of the intersubject variance and, under certain circumstances, the intrasubject variance. 

Williams et al. [62] also studied the copolymerization of D- and L-enantiomorphs in dioxan solution and obtained transition points similar to those shown for the L-NCA in Fig. 8. However, in these systems the transition occurred at lower P (Fig. 9), a result which is contrary to that expected if a coil-helix transition were responsible for the change in rate. Kinetic analysis was carried out in terms of simultaneous polymerization in both phases following prior adsorption of monomer. (The general procedure was similar to that of Biihrer and Elias [63] (p. 615 et seq.) and was used by them). It was found that only in the associated phase is selectivity essentially complete with no cross-over reactions. The analysis leads to an estimate of Kl d / l l = 1-6 0.6, in reasonable agreement with the value determined directly (p. 615). 

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