Reactants, interpenetration

Topley and Hume [453], in a study of the dehydration of CaC03 6 H20, assumed the rapid initial formation of (on average) a single nucleus on the surface of each particle of reactant, represented as a sphere of radius a. In the absence of preferential surface development, the reaction interface penetrates the reactant at equal rates in all inward directions (kG = dr/df) and the volume of material reacted at time t is that volume of a sphere, having its centre at the site of surface nucleation and of radius kGt, which falls within the reactant. The fractional reaction, the zone of interpenetrating spheres, at time t is... 

Outer-Sphere Electron Transfer The minimal interpenetration of the coordination spheres of the reactants is inherent in any mechanistic formulation of the outer-sphere process for electron transfer. As such, steric effects provide a basic experimental criterion to establish this mechanism. Therefore we wish to employ the series of structurally related donors possessing the finely graded steric and polar properties described in the foregoing section for the study of both homogeneous and heterogeneous processes for electron transfer. 

N. Sutin, Brookhaven National Laboratory Strictly speaking, the outer-sphere and inner-sphere designations refer to limiting cases. In practice, reactions can have intermediate outer-sphere or inner-sphere character this occurs, for example, when there is extensive interpenetration of the inner-coordination shells of the two reactants. Treating this intermediate situation requires modification of the usual expressions for outer-sphere reactions — particularly those expressions that are based upon a hard-sphere model for the reactants. 

Primary steric effects are due to repulsions between electrons in valence orbitals on atoms which are not bonded to each other. They are believed to result from the interpenetration of occupied orbitals on one atom by electrons on the other resulting in a violation of the Pauli exclusion principle. All steric interactions raise the energy of the system in which they occur. In terms of their effect on chemical reactivity, they may either decrease or increase a rate or equilibrium constant depending on whether steric interactions are greater in the reactant or in the product (equilibria) or transition state (rate). 

Interpenetration of Reactants. A detailed structural examination (Figure 1) reveals the inherent difficulties in attempting to define a "contact" separation for reactants of the type considered here. In spite of the deceptively high symmetry (e.g., the Tg point group assumed in Figure 1 and (13)), the... 

In view of the emphasis on interpenetration of reactants in the previous section, one may well wonder about the validity... 

The upshot of the results presented above is that a suitable QMT or SCT model which allows for interpenetration of reactants, albeit still within the realm of "outer-sphere" exchange, yields quite satisfactory detailed agreement with experiment and leads to a mechanism characterized by a modest, but nevertheless significant, degree of quantum behavior in both the electronic and nuclear aspects of the process, compactly represented by i<, 0.17 and V = 3.5. The rather small value of... 

An expression has been derived by Marcus34 and Hush35 for A0 assuming the solvent to be a structureless dielectric continuum characterized by the macroscopic dielectric constants Dop and Ds. D0p and Ds are the optical and static dielectric constants, respectively, and Dop = n2 where n is the index of refraction in the visible spectral region. In the limit that the reactants can be treated as two non-interpenetrating spheres, AQ is given by equation (23). 

Equation (33) is only an approximation for real molecules in that it assumes both a single value for r and structureless, spherical reactants. In fact, it has been suggested for Fe(H20)63+/2+ selfexchange that a significant feature of the reaction may be the interpenetration of the coordination spheres in order to enhance electronic orbital overlap.12 In addition, for low-symmetry cases, electronic coupling can have an angular dependence if rotational correlation times within the... 

Two limiting pathways for the Tt -n transfer are possible. The first involves electron transfer between the edges of two coplanar bipyridine rings, and the second involves interpenetration of the coordination shells of the two reactants so that electron transfer between two parallel bipyridine rings, becomes possible. Assuming that 10% of an Ru 4d-electron is delocalized over the three bipyridine rings, and that the transfer... 

There is an instructive error in this paper which leads to an important safeguarding principle in making balances. Namely, when a sub-region of a process has been assumed to be uniform, balances that involve its properties must be taken over the whole of it. In simple situations there is little inclination to do otherwise, but in complex cases this may be the effect of a differential balance over another interpenetrating phase. See Aris for a full analysis [9]. We assume spherical particles of radius, R, and call the profile of concentration at time, a, c(r,a). If D is the diffusivity of the reactant and k the rate constant per unit volume of catalyst. 

Impregnation of the porous network with PFSA-type ionomer imparts high proton concentration and conductivity to the layer. The high proton concentration is beneficial for the ORR activity of the CCL but it is detrimental for catalyst stability. Simultaneous percolation in the interpenetrating networks of the solid Pt/carbon matrix, ionomer electrolyte, and pores ensures efficient transport of electrons, protons, chemical reactants (H2, methanol, O2, etc.), and product water to or from Pt. 

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