Reactive spheres constant

Two Spheres. The steady state diffusion controlled rate constant for two uniformly reactive spheres interacting via a centrosymmetric potential of mean force can be solved numerically and in special cases analytically as given by Eq. 2. For a potential of mean force of zero and no hydrodynamic interaction (NHI), Eq. 2 reduces to the Smoluchowski result (1)... 

According to the Marcus theory [64] for outer-sphere reactions, there is good correlation between the heterogeneous (electrode) and homogeneous (solution) rate constants. This is the theoretical basis for the proposed use of hydrated-electron rate constants (ke) as a criterion for the reactivity of an electrolyte component towards lithium or any electrode at lithium potential. Table 1 shows rate-constant values for selected materials that are relevant to SE1 formation and to lithium batteries. Although many important materials are missing (such as PC, EC, diethyl carbonate (DEC), LiPF6, etc.), much can be learned from a careful study of this table (and its sources). 

This formulation assumes that the continuum diffusion equation is valid up to a distance a > a, which accounts for the presence of a boundary layer in the vicinity of the catalytic particle where the continuum description no longer applies. The rate constant ky characterizes the reactive process in the boundary layer. If it approximated by binary reactive collisions of A with the catalytic sphere, it is given by kqf = pRGc(8nkBT/m)1 2, where pR is the probability of reaction on collision. 

We focus on the effects of crowding on small molecule reactive dynamics and consider again the irreversible catalytic reaction A + C B + C asin the previous subsection, except now a volume fraction < )0 of the total volume is occupied by obstacles (see Fig. 20). The A and B particles diffuse in this crowded environment before encountering the catalytic sphere where reaction takes place. Crowding influences both the diffusion and reaction dynamics, leading to nontrivial volume fraction dependence of the rate coefficient fy (4>) for a single catalytic sphere. This dependence is shown in Fig. 21a. The rate constant has the form discussed earlier,... 

In Eq. (5.25) H2O represents a water molecule initially present outside the coordination sphere of the metal ion, which, as a result of the exchange, has entered the first coordination sphere. It follows that the degree of kinetic reactivity of aquometal ions with complexing agents parallels their kinetic lability toward water exchange. Moreover, since the water exchange rate constants of most metal ions are known, predictions on the rate of complex formation of aquometal ions can be made. 

When the above factors are put under control, the possibility of changing the ligand L in the pentacyano(L)ferrate complexes adds a further dimension for studying systematic reactivity changes, brought out by the controlled modification of the redox potentials of the Fe(II)-Fe(III) redox couples. In this way, the rates of electron transfer reactions between a series of [Fen(CN)5L]re complexes toward a common oxidant like [Coin(NH3)5(dmso)]3+ showed a variation in agreement with Marcus predictions for outer-sphere electron transfer processes, as demonstrated by linear plots of the rate constants versus the redox potentials (123). 

A point of note in the data in Table 1 is the extraordinary range in electron-transfer reactivity that can exist even for outer-sphere reactions among what appear to be closely related reactions. For example, the self-exchange rate constants for Co(NH3)63+/2+ and Ru(bipy)33+/2+ differ in magnitude by 1014. 

Syntactic Foam. Hollow glass, ceramic, or plastic spheres are dispersed in the reactive liquid system before it is cast. When the liquid is polymerized and cured, the hollow spheres make it a unicellular foam. The air bubbles in the cells make it low-density, low dielectric constant and loss, and very resistant to compressive forces such as hydrostatic head in deep-sea equipment. 

Given that inner-sphere pathways are commonly encountered at metal-solution interfaces, as between reactants in homogeneous solution, a key question concerns the manner and extent to which the reactant-electrode interactions associated with such pathways lead to reactivity enhancements compared with weak-overlap pathways (Sect. 3.5.2). A useful tactic involves the comparison between the kinetics of structurally related reactions that occur via inner- and outer-sphere pathways. This presumes that the outer-sphere route yields kinetics which approximate that for the weak-overlap limit. For this purpose, it is desirable to estimate the work-corrected uni-molecular rate constant for the outer-sphere pathway at a particular electrode potential, k° , from the corresponding work-corrected measured value, kCOTr, using [cf. eqns. (10) and (13)]. 

These reactive total cross sections can be considered as the sum of a capture term, which decreases exponentially with energy, and a rigid sphere term, which is constant and should dominate at high collision energies [31]. 

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