Single-site kinetic model

In contrast to kinetic models reported previously in the literature (18,19) where MO was assumed to adsorb at a single site, our preliminary data based on DRIFT results suggest that MO exists as a diadsorbed species with both the carbonyl and olefin groups being coordinated to the catalyst. This diadsorption mode for a-p unsaturated ketones and aldehydes on palladium have been previously suggested based on quantum chemical predictions (20). A two parameter empirical model (equation 4) where - rA refers to the rate of hydrogenation of MO, CA and PH refer to the concentration of MO and the hydrogen partial pressure respectively was developed. This rate expression will be incorporated in our rate-based three-phase non-equilibrium model to predict the yield and selectivity for the production of MIBK from acetone via CD. 

Our simplest continuous microheterogeneous model assumes that the luminophore exists in a distribution of spectroscopically different environmental sites. For a tractable, yet plausible, model each site is assumed to be quenched by normal Stem-Volmer quenching kinetics. For luminescence decays each individual component is assumed to give a single exponential decay with the following impulse response ... 

Substituting these expressions into the equations above yields a new expression that enables the interaction kinetics to be readily modeled for single-site, reversible binding between a protein and a single ligand ... 

The model followed single-site, nondissociative, Langmuir-Hinshelwood poisoning. This resulted in the same adsorption coefficients for deactivation and start-of-cycle kinetics. 

REDUCTION KINETICS SINGLE-SITE VERSUS TWO-SITE MODEL... 

A general kinetic model should accommodate all chemical processes known to affect the dechlorination process. These include (1) reductive dechlorination takes place on the iron surface, rather than in the aqueous phase, so adsorption must occur (2) other components in the system may affect the dechlorination reaction by competing for the reaction sites (3) surface sites for reduction and for sorption may not be the same, as for the system with PCE and TCE where dechlorination takes place on the reactive sites, but most of the adsorption is clearly on the nonreactive sites (Burris et al., 1995). In the following section we will first discuss a single-site model similar to the one used by Johnson et al. (1998), which has accounted for the first two observations, then develop a two-site model that will also take the third observation into consideration. We aim to illustrate how coadsorbates in the iron system will affect adsorption and reduction of chlorinated solvents. TCE will be used as an example since relevant adsorption and reduction data are available, from which the required parameters for simulation could be estimated. 

A single site model assumes only one type of surface sites, i.e., the same type of sites is responsible for trichloroethylene adsorption and reduction. The kinetic model developed herein is based on the following reaction... 

In order to explain the degradation kinetics of TCE and PCE, for which the adsorption onto the nonreactive sites is significant (Burris et al., 1995), a two-site model is developed. The basic assumption for the single-site model, i.e., pre-adsorption equilibrium followed by reductive dechlorination, is still valid here. In addition, the two-site model assumes that there are both reactive and nonreactive sites on the iron surface, and while the adsorption of TCE and coadsorbate can occur on both types of sites, reductive dechlorination of TCE only takes place on the reactive sites. Coadsorbate is not involved in redox reactions. The reaction scheme for this model is ... 

Careful analysis of the kinetic data for the reduction of CN by Mo nitrogenase from A. vinelandii shows that at high concentrations of CN a constant rate of reduction is observed, that rate depends only on the pH of the solution [128], This observation is inconsistent with the earlier proposal that CN and HCN bind independently, and the revised model is one in which the CN binds to a single site (Figure 21). 

Model Fitting to Mixing-Cell Data Multiple-site kinetic models have been used to describe pesticide and herbicide movement in soils (15,16,17), cesium migration in columns (18), and strontium migration in a sandy aquifer over a twenty-year time period (1L). The results of the selective extraction procedures in all experiments discussed here suggest that a multi-site model should provide a better fit of the data than a single-site model. This hypothesis is supported by the variances in Table I, with the possible exception of selenium. 

Langmuir-Hinshelwood rate expressions of all the reactions of the network were used in the kinetic modeling of the HDN of quinoline by Satterfield et al. (80, 81, 88). Their assumption that there is a single catalytic site for all reactions is too simple. Nevertheless, they collected an impressive body of kinetic data and pinpointed the reactions that were close to equilibrium and those which were kinetically significant. Gioia and Lee (100) extended these studies to higher pressures (up to 15 MPa H2). Only one model survived their regression analysis of the kinetic data. In this model, it was necessary to assume that 1,2,3,4-THQ reacted directly not only to o-propylaniline but also to propylbenzene (PB) and propylcyclohexene (PCHE). Their analysis does not appear to be very reliable, however. First,... 

We compare in Figure 6.20 two profiles that were calculated as numerical solutions of the equilibrium-dispersive model, using a linear isotherm. The first profile (solid line) is calculated with a single-site isotherm q = 26.4C) and an infinitely fast A/D kinetics (but a finite axial dispersion coefficient). The second profile (dashed line) uses a two-site isotherm model q — 24C - - 2.4C), which is identical to the single-site isotherm, and assumes infinitely fast A/D kinetics on the ordinary sites but slow A/D kinetics on the active sites. In both cases, the inverse Laplace transform of the general rate model given by Lenhoff [38] (Eqs. 6.65a to h) is used for the simulation. In the case of a surface with two t5q>es of adsorption sites, Eq. 6.65a is modified to take into accoimt the kinetics of adsorption-desorption on these two site types. 

An answer to the puzzling problem of the kinetics of skeletal isomerization may be found in a recent proposal, by Frennet and his co-workers (62), that hydrocarbon adsorption involves not a single site but an ensemble of several contiguous sites of the surface (seven to eight). When using the model of bimolecular dehydrogenation steps, one should always replace the first equation in Scheme 15 by... 

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