Kinetic rate constant encounter theory

Two questions are inseparable how to optimize ion radical reactions, and how to facilitate electron transfer. As noted in the preceding chapters, electron transfers between donors and acceptors can proceed as outer-sphere or inner-sphere processes. In this connection, the routes to distinguish and regulate one and another process should be mentioned. The brief statement by Hubig, Rathore, and Kochi (1999) seems to be appropriate Outer-sphere electron transfers are characterized by (a) bimolecular rate constants that are temperature dependent and well correlated by Markus theory (b) no evidence for the formation of (discrete) encounter complexes (c) high dependence on solvent polarity (d) enhanced sensitivity to kinetic salt effects. 

Inner-sphere electron transfers are characterized by (a) temperature-independent rate constants that are greatly higher and rather poorly correlated by Marcus theory (b) weak dependence on solvent polarity (c) low sensitivity to kinetic salt effects. This type of electron transfer does not produce ion radicals as observable species but deals with the preequilibrium formation of encountered complexes with the charge-transfer (inner-sphere) nature (see also Rosokha Kochi 2001). 

The remote transfer in condensed matter is characterized by the position-dependent rate W(r), which is the input data for encounter theory. In its differential version (DET), the main kinetic equation (3.2) remains unchanged, but the rate constant acquires the definition relating it to W(r) ... 

However, at still larger concentrations only DET/UT is capable of reaching the kinetic limit of the Stem-Volmer constant and the static limit of the reaction product distribution. On the other hand, this theory is intended for only irreversible reactions and does not have the matrix form adapted for consideration of multistage reactions. The latter is also valid for competing theories based on the superposition approximation or nonequilibrium statistical mechanics. Moreover, most of them address only the contact reactions (either reversible or irreversible). These limitations strongly restrict their application to real transfer reactions, carried out by distant rates, depending on the reactant and solvent parameters. On the other hand, these theories can be applied to reactions in one- and two-dimensional spaces where binary approximation is impossible and encounter theories inapplicable. 

Thus, electron transfers from a series of unhindered, partially hindered, and heavily hindered aromatic electron donors (with matched oxidation potentials) to photoactivated quinone acceptors are kinetically examined by laser flash photolysis, and the free-energy correlations of the ET rate constants are scrutinized [31]. The second-order rate constants of electron transfers from hindered donors such as hexaethylbenzene or tri-icrt-butylbenzene strongly depend on the temperature, the solvent polarity and salt effects, and they follow the free-energy correlation predicted by Marcus theory (see Figure 20A). Moreover, no spectroscopic or kinetic evidence for the formation of encounter complexes (exciplexes) with the photo-activated quinones prior to electron transfer is observed. 

In contrast, electron transfers from unhindered (or partially hindered) donors such as hexamethylbenzene, mesitylene, di-ferr-butyltoluene, etc. to photoactivated quinones exhibit temperature-independent rate constants that are up to 100 times faster than predicted by Marcus theory, poorly correlated with the accompanying free-energy changes (see Figure 20A), and only weakly affected by solvent polarity and salt effects. Most importantly, there is unambiguous (NIR) spectroscopic and kinetic evidence for the pre-equilibrium formation K c) of long-lived encounter complexes (exciplexes) between arene donor (ArH) and photoexcited quinone acceptor (Q ) prior to electron transfer (A et) [20] (Eq. 95). 

We have applied ab-initio molecular orbital methods in conjunction with reaction rate theory in a systematic procedure for calculating rates for chemical nucleation/reaction processes (12,13). An example of such an approach has been the calculation of the nucleation of SiO, a monomer to silica particle formation. The results of the computations indicate the rate constants are both pressure and temperature sensitive. This sensitivity results from the rate of energy transfer with the surrounding bath gas (M). Higher temperatures and lower pressures both lower the bath gas encounter rate with the growing cluster and therefore the nucleation rate. The individual kinetic steps in a nucleation event can be expressed as follows ... 

In order to take account of the fact that the solvent is made up of discrete molecules, one must abandon the simple hydrodynamically-based model and treat the solvent as a many-body system. The simplest theoretical approach is to focus on the encounters of a specific pair of molecules. Their interactions may be handled by calculating the radial distribution function, whose variations with time and distance describe the behaviour of a pair of molecules which are initially separated but eventually collide. Such a treatment leads (as has long been known) to the same limiting equations for the rate constant as the hydro-dynamically based treatments, including the term fco through which an activation requirement can be expressed, and the time-dependent term in (Equation (2.13)) [17]. The procedure can be developed, but the mathematics is somewhat complex. Non-equilibrium statistical thermodynamics provides an alternative approach [16]. The kinetic theory of liquids provides another model that readily permits the inclusion of a variety of interactions the mathematics is again fairly complex [37,a]. In the computer age, however, mathematical complexity is no bar to progress. Refinement of the model is considered further below (Section (2.6)). 

According to kinetic theory, gas molecules are in constant random motion.When a molecule on the left side of the box happens to hit the pinhole in the partition between the two parts of the box, it passes (or effuses) to the right side.The rate of effusion depends on the speed of the molecules—the faster the molecules move,the more likely they are to encounter the pinhole and pass from the left side of the box to the right side. 

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