Mobilities of Reactants

The kinetic system of equations for the concentrations of adsorbed particles coincides with system (50) for ordering of the particles and with system (55) for their disordered distribution. Here the functions Qfr) are determined for the given values 0,- from the solution of algebraic systems that are described in Appendix A. The kinetic equations are solved with given initial conditions Oft — 0), i = A or B. 

For this reason, the local concentrations of the B components will vary and, consequently, the concentrations of the A and V components will also vary. The indicated change in the structure of the system of equations relates to all the levels of the hierarchy. For instance, in a point model with restricted mobility of the B component, the kinetic equation for the function 0 (1) will be written as follows  

The system of constructed Eqs. (31)—(32) describes the elementary processes at the atomic-molecular level and is a unified interrelated system of equations for the entire inhomogeneous lattice. Its solution allows to determine the sought 8j and values and calculate the following 

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Reactions in which a gas or liquid reacts with the surface of a solid are rather common processes in inorganic chemistry. The product that forms as a layer on the surface of the solid may impede the other reactant from contacting the solid. There are several types of behavior that depend on how the product layer affects the mobility of reactants, but in this instance, we will assume that the rate is inversely proportional to the thickness of the product layer. When the rate law is written in terms of the thickness of the product layer, x, the result is... 

Diffusional Problems. The likelihood of diffusional problems will be increased as the active site of the catalyst becomes more sterically hindered and physically buried. These diffusional problems can derive simply from greatly inhibited mobility of reactants and products into and out of the active site, but they can also derive exclusively from diffusional escape of the products whose sizes or other properties affecting mobility are appreciably different from those of the reactant. 

In this Section we continue studies of particle dynamical interactions. For this purpose the formalism of many-particle densities is applied to the study of the cooperative effects in the kinetics of bimolecular A -f B —> 0 reaction between oppositely charged particles (reactants) interacting via the Coulomb forces. We show that unlike the Debye-Hiickel theory in statistical physics, here charge screening has essentially a non-equilibrium character. For the asymmetric mobility of reactants (Da = 0, 0) the joint spatial distri-... 

The main difference between solid-state reactions and those in solution is that of freedom of molecular motion (1-3) due to restriction of mobility of reactants in solids. Another important feature is the heterogeneous progress of reactions (3,4) frequently observed in solid states due to the microscopically heterogeneous states of aggregation or free volume distribution of the reaction media. In the case of poly(methyl methacrylate) (PMMA), which is an organic glass and is usually regarded as an inert matrix for photophysical and photochemical processes, a marked deviation from... 

The treatment given here was based on a number of rather simplifying assumptions in order to delineate a few general principles. More complicated situations can certainly arise, e.g., if the mobilities of reactant and product are different, if a reaction sequence takes place, or if side reactions change the nature of the solid. 

The risk of chemical instability can be assessed from the primary sequence of the protein. The sequence containing labile amino acids such as Asn-Gly and Met would be indicative of potential instability issues. The rate of chemical reactions that alter the primary sequence of the protein is higher in solution conditions and can limit the shelf-life of protein therapeutics. As the mobility of reactants is minimized in the solid state, freeze-drying is often attempted to improve the stability [16]. In such instances, physical instability is a major issue to be dealt with. Freezedrying, also termed as lyophilization, is a dessication process in which the solvent (usually water) is first frozen and then is removed by sublimation in a vacuum [17]. In other words, the protein in solution is frozen, producing discrete ice and solute crystals. The solid ice is sublimed. Controlled heating desorbs any of the tightly bound water. 

MIK Mikhaliov, Yu.M., Ganina, L.V., Kurmaz, S.V., Smirnov, V.S., and Roshchupkin, V.P., Diffusion mobility of reactants, phase equilibrium, and specific features of radical copolymerization kinetics in the nonyl acrylate/2-methyl-5-vinyltetrazole system, J. Polym. Sci. PartB Polym. Phys., 40, 1383, 2002. 

More detailed studies of eleetroeatalytie processes, which incorporate heterogeneous surfaee geometries and finite surface mobilities of reactants, require kinetic Monte Carlo simulations. This stochastic method has been successfully applied in the field of heterogeneous catalysis on nanosized catalyst particles [59,60]. Since these simulations permit atomistic resolution, any level of structural detail may easily be incorporated. Moreover, kinetic Monte Carlo simulations proceed in real time. The simulation of current transients or cyclic voltammograms is, thus, straightforward [61]. 

The mobility of reactants depends not only on the type of reaction as well as the size and shape of reacting groups, but also on the molecular motion and free volume distribution in the matrix polymer. Three types of heterogeneity can be distinguished. Microhetrogeneity due to a heterogeneous free volume distribution would lead to... 

Mobility of reactants translational and rotational diffusion of reacting groups as function of temperature and macromolecular motions size and shape of reacting groups free volume and conformation interactions between reacting groups and matrix cage effect... 

The Maillard reaction rate increases with gradually decreasing water activity and the maximum reaction rate is at a water activity of about 0.7-0.8, which is attributed to the increase in the concentration of reactants (amino compounds and reducing sugars). With further decrease of water activity, the reaction rate decreases. The Maillard reaction does not proceed at all when the water activity decreases to less than 0.2-0.3, because the mobility of reactants is too low. ... 

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