Encounter radius

On the other hand, if the rate constant for the quenching step exceeds that expected for a diffusion-controlled process, a modification of the parameters in the Debye equation is indicated. Either the diffusion coefficient D as given by the Stokes-Einstein equation is not applicable because the bulk viscosity is different from the microviscosity experienced, by the quencher (e.g. quenching of aromatic hydrocarbons by O, in paraffin solvents) or the encounter radius RAb is much greater than the gas-kinetic collision radius. In the latter case a long-range quenching... 

Encounter radii, R, for reaction between hydrated electrons and various ions [17], the corrected encounter radius, i H, incorporating the hydrodynamic effect, and the sum of the hydrated electron and ion crystallographic radii, Rc... 

Similarly, the contact quenching of 1,2-benzanthracene fluorescence by carbon tetrabromide in 1,2-propanediol or mineral oil has an encounter radius 0.8 nm [7]. This is again a reasonable encounter radius and the ir orbital configuration of the fluorophor 1,2-benzanthracene is not encouraging. 

Typical decay functions of the expectation value of (N) were evaluated by Clifford et al. The initial value of (AO was not N0 but about 20% less. The model is therefore able to account for the reaction of pairs initially formed within an encounter radius of one another. 

The term on the right, outside the braces, is the diffusion-limited rate for encounters of uncharged species e and X whose total diffusion constant is DeX and whose encounter radius is rex. N is Avogadro s number... 

There is rarely much information available on either the hydrodynamic radius of a species and the encounter radius Rc. ft is often assumed that Rc = Ra + Rb, and if Ra and 7 b are also approximately equal, Eqs (9.37) and (9.47) may be combined to give a simple expression for the rate constant ... 

The rate at which ligand molecules are bound by a receptor is equal to the intrinsic reaction rate constant kon times the ligand concentration at the receptor surface, L evaluated at r = s 5 is often termed the encounter radius. At steady state, this must be equal to the ligand diffusion rate (moles/time) to the receptor surface (the diffusive flux multiplied by the surface area, again evaluated at r = s). This provides the second boundary condition needed for Eq. (29) ... 

The radius of charge distribution of the hydrated electron has been estimated by several methods. The values obtained from hydration energies, encounter radius, i.e. the radius required to account for experimental diffusion controlled rate coefficients, and Jortner s cavity-continuum model are all in the range 0.25—0.30 nm [33]. This clearly indicates that the electron is not associated with a single water molecule only, but rather that the charge of the electron is smeared out over 3—4 water molecules. 

The encounter-rate constants and k can usually be estimated from physical properties of the two reactants (i.e., the diffusion coefficient and encounter radius), using Equations 4-64 and 4-66. Therefore, the relative importance of diffusion vs reaction in determining the overall rate of reaction can be estimated by using the definitions of k and in Equation 4-62. 

In all these studies by Jonah et al., no estimate of the variation of encounter radius or diffusion coefficient was made, though they were presumed to be small changes with electrolyte concentration. In studies on aqueous solutions of LiCl (0—14mldm ) or CsCl (0—6 mol dm ) at 293 K containing electron scavengers nitrobenzene, IrCl or Fe(CN) , Hankiewicz and Schulte-Frohlinde [120] produced hydrated electrons by pulse radiolysis and observed the decays. For reactions between eaq and nitrobenzene, the rate coefficient was independent of the caesium chloride concentration (just as the viscosity is independent of CsCl concentration), while with lithium chloride, the rate coefficient decreased exponentially with LiCl concentration (the viscosity is 0.001 exp (0.059 [LiCl] Pa s). They estimated that the reaction radius, R, was constant to within 5% over all the change of electrolyte concentration... 

V(r) is the interaction potential between e"and S, and is the effective encounter radius. In diffusion-limited reactions between singly charged ions, V(r) is the Coulomb potential. 

Following the radiolysis of the solvent, localised clusters of highly reactive particles are formed which have a non-uniform distribution. After a short period of time, the clusters of ions spread by diffusion to form a uniform distribution which can be characterised by homogeneous theories of chemical kinetics. However, before scavenging steady state conditions can be achieved there is a transient period whose lifetime varies as a I nD ) where a is the encounter radius and D the mutual diffusion coefficient. 

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