Simple kinetic models isothermal Langmuir kinetics

Kinetic models referred to as adsorption models have been proposed, especially for olefin polymerisation with highly active supported Ziegler-Natta catalysts, e.g. MgCl2/ethyl benzoate/TiCU AIR3. These models include reversible processes of adsorption of the monomer (olefin coordination at the transition metal) and adsorption of the activator (complexation via briding bonds formation). There are a variety of kinetic models of this type, most of them considering the actual monomer and activator concentrations at the catalyst surface, m and a respectively, described by Langmuir-Hinshelwood isotherms. It is to be emphasised that M and a must not be the same as the respective bulk concentrations [M] and [A] in solution. Therefore, fractions of surface centres complexed by the monomer and the activator, but not bulk concentrations in solution, are assumed to represent the actual monomer and activator concentrations respectively. This means that the polymerisation rate equation based on the simple polymerisation model should take into account the... 

The kinetics of acid hydrolysis of the p-methoxybenzaldehyde-O-acyloximes (7) in SDS micelles modified by BuOH has also been fitted to the PIE model [86]. The substrates differ only in their hydrophobicities, and while the acetyl derivative partitions between water and micelles, the octanoyl derivative is wholly micelle-bound. The simple PIE model fits rate data in dilute HCl [Eq. (6)], but it underpredicts observed rate constants in more concentrated acid. This increased rate was analyzed in terms of a model that does not involve a constant value of a but allows concentrations of reactive and inert ions, and Na" ", in the micellar pseudophase to increase, following Langmuir isotherms [106]. This model was reasonably satisfactory except at high 1-butanol concentration. Alternatively, the rate data in more concentrated acid can be fitted in terms of Eq. (12). 

Our library contains FRFs for four simple isothermal mechanisms Langmuir kinetics, film resistance model, micropore diffusion, and pore-surface model. For each mechanism, a short description with the model equations is given, together with the expressions for the first-order FRF Fx p(w), and two second-order FRFs, F2,pp(w, w) and F2,pp(w, —[Pg.293]

Such a model should be as simple as possible, without however missing any of the underlying thermodynamic and physicochemical factors which cause electrochemical promotion. In particular it will be shown that even the use of Langmuir-type adsorption isotherms, appropriately modified due to the application of potential (or equivalently by the presense of promoters) suffice to describe all the experimentally observed rules G1 to G7 as well as practically all other observations regarding electrochemical promotion including the effect of potential on heats of adsorption as well as on kinetics and reaction orders. 

The transient response experiments were analyzed by a dynamic isothermal PFR model, and estimates of the relevant kinetic parameters were obtained by global nonlinear regression over all runs. It was found that a simple Langmuir approach could not represent the data accurately, and surface heterogeneity had to be invoked. The best fit was obtained using a Temkin-type adsorption isotherm with coverage-dependent desorption energy ... 

At higher partial pressures, the behavior becones nonlinear, and more complex models are required to describe the observed equilibrium data. A frequently used model for monomolecular layer adsorption is the Langmuir isotherm equation. This equation is derived from simple mass-action kinetics. It assumes that the surface of the pores of the adsorbent is homogeneous and that the forces of interaction between the adsorbed molecules are negligible. Let/be the fraction of the surface covered by adsorbed molecules. Therefore, 1 -/ is the fraction of the bare surface. Then, the net rate of adsorption is the difference between the rate of adsorption on the bare surface and desorption from the covered surface ... 

The Langmuir model [12] is commonly used to process chemisorption isotherms because it is relatively simple and it can be used in developing several kinetic equations. It is based on two fundamental assumptions ... 

Lineweaver-Burk plot A double-reciprocal plot used to determine the two constants featured in simple enzyme kinetic equations such as Michaelis-Menten kinetics, Monod kinetics, and in similar adsorption isotherm models such as the Langmuir adsorption isotherm. The constants are determined from the intercept with the y-axis and the gradient (see Fig. 26). It was devised and published in 1934 by American chemist Hans Lineweaver (1907-2009) and American biochemist Dean Burk (1904-1988). 

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