Reaction Rates and Transition Pathways

The overall objective of these studies is to unravel mechanisms of interfacial PT. This requires identification of collective coordinates (or reaction coordinates) and transition pathways of transferring protons. Differences in activation energies and rates of corresponding mechanism due to distinct polymer constituents, acid head groups, side chain lengths, side chain densities, and levels of hydration have to be examined. Comparison with experimental... 

Unimolecular gas phase studies try to isolate reacting molecules from their environment. Insofar as this is successful, gas phase studies provide the most unambiguous data on the intramolecular forces which control reaction rates and pathways. The energetic and conformational requirements of transition state species are of paramount interest, and with the stringent limitations placed on the data by modern reaction rate theories, the results may be critically examined and meaningfully evaluated. A critical survey of the data leading to the rejection of some and a selection of the best parameters in others, has been one of our primary concerns. Transition state theory has been assumed, and the methods and criteria employed in the calculations are based on this theory. They are outlined very briefly for each... 

Another critical need identified in Database Needs for Modeling and Simulation of Plasma Processing (Database, 1996) is the measurement of thermodynamic data for species of interest in plasmas (radicals and ions). Such data provide benchmarks for comparison with calculated potential energy surfaces, allow energetically unfavorable reaction pathways to be identified, and supply information necessary to estimate unknown reaction rates by transition state theory. Such thermodynamic information is a critical tool in understanding deposition and etching processes and in evaluating the optimum conditions for plasma reactors (Kruis et al, 1992). 

More elaborate and ambitious studies on the dissolution reactions of silica were conducted by Xiao and Lasaga (1994, 1996). Their objective was to provide full descriptions of the reaction pathway of quartz dissolution in acidic and basic solutions, from the adsorption of H2O or OH on a site, the formation of possible reaction intermediates and transition states, to the hydrolysis of the Si-O-Si bonds. Also, their aim was to extract kinetic properties such as changes in activation energy, kinetic isotope effects, catalytic and temperature effects, and the overall rate law form. The reaction mechanisms investigated were... 

Recently, Chandler and coworkers [46,47] revisited this idea and developed an elegant and promising methodology for the computation of reaction pathways and transition rates in molecular systems. 

On the basis of the examples given above, it is reasonable to suggest that the underlying principles for optimization of the overall reaction rate with respect to the choice of metal ion are similar. That is, there are basically three states along the reaction pathway which determine the most suitable choice of metal ion. These are (1) the reactant state with bound metal and substrate before the proton transfer step, (2) the intermediately created free OH nucleophile and, (3) the subsequent transition state associated with... 

Table 10.4 lists the rate parameters for the elementary steps of the CO + NO reaction in the limit of zero coverage. Parameters such as those listed in Tab. 10.4 form the highly desirable input for modeling overall reaction mechanisms. In addition, elementary rate parameters can be compared to calculations on the basis of the theories outlined in Chapters 3 and 6. In this way the kinetic parameters of elementary reaction steps provide, through spectroscopy and computational chemistry, a link between the intramolecular properties of adsorbed reactants and their reactivity Statistical thermodynamics furnishes the theoretical framework to describe how equilibrium constants and reaction rate constants depend on the partition functions of vibration and rotation. Thus, spectroscopy studies of adsorbed reactants and intermediates provide the input for computing equilibrium constants, while calculations on the transition states of reaction pathways, starting from structurally, electronically and vibrationally well-characterized ground states, enable the prediction of kinetic parameters. 

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