Comparison Between the Various Kinetic Models

3 Comparison Between the Various Kinetic Models of Nonlinear Chromatography 

The solid and liquid film linear driving force models can be written under the same general form of a second order Langmuir kinetic model [1]. We can insert the Langmuir isotherm equation q = qsbC)/ l bC)) in the partial differential equation of tire solid fihn linear driving force model (Eq. 14.3) 

Similarly, insertion in the equation of the liquid film linear driving force model (Eq. 14.5)  

In linear chromatography, bC and q/qs are negligible. Then, the three Eqs. 14.50 (reaction-kinetic model), 14.5 (liquid film linear driving force model), and 14.3 

Provided that the apparent equivalent parameters given by Eqs. 14.79 and 14.80 are used, the three models give the same result. 

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Needless to say, an analysis which will finally allow one to nail down all rates, activation parameters, and equilibrium constants requires a large amount of precise and reliable kinetic data from appropriate experiments, including the determination of isotope effects and the like, as well as a rather sophisticated treatment and solution of the complete kinetic scheme. Then a comparison is necessary between various organosilanes with different types of C-H and C-Si bonds as well as the comparison between the dtbpm and the dcpm ligand systems, not to speak of model calculations in order to understand the molecular origin of the kinetic and thermodynamic numbers. We are presently in the process of solving these problems. 

As with the kinetic analyses of homogeneous rate processes, quantitative comparisons are made between the experimentally measured data for a reaction of interest and the curve shapes of the various rate equations (Table 5.1) to identify the applicable kinetic model. This can be approached in several ways (29,105). One traditional method is to plot graphs of g(a) against time and decide which, from the available expressions (Table 5.1), provides the best (linear) representation, or fit. There is no general agreement on what criteria constitute a best or a satisfactory fit. The... 

The variations of S(0 and N(0 versus time are usually presented as log-log plots. The z and w values give a quantitative description of the flocculation processes under the conditions of the space dimension d, the biopolymer persistence length or rigidity /p, biopolymer size 4 and particle/biopolymer concentration ratio r. Hence z(d, /p, k, x) and w(d, /p, 4, x) values can be calculated for various systems [80], and comparison between experiments and computer models to isolate the key parameters controlling both structure and kinetics is possible upon parameterization of the model with experimental data. 

Droop, M.R. (1983) 25 years of algal growth kinetics - a personal view. Botanica Marina, 26, 99-112. Ducobu, H., Huisman, J., Jonker, R.R. and Mur, L.R. (1998) Competition between a prochlorophyte and a cyanobacterium under various phosphorus regimes Comparison with the Droop model. 

It has been demonstrated on several occasions that mai kinetic quantities such as the rate constants of thermal unimolecular reactions or product yields and Stem-Volmer plots in chemical or photochemical activation, depend only slightly on the particular collision model, as long as situations with the same average energy transfimed per collision are considered. Often, particularly good agreement between various models is observed when is chosen as the basis for such comparisons (see below). 

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