Stokes-Einstein model

Under the condition that the Stokes-Einstein model holds, the translational diffusion coefficient, D, can be represented by Eq. (8.3). the diffusion time, Xd, obtained through the analysis is given by Eq. (8.4). 

The discrepancies between the experimental data and the behavior predicted using the Smoluchowski-Stokes-Einstein model for ksenfluor and ksenphos likely arise from the inadequacies of the simple Smoluchowski-Stokes-Einstein analysis for application to the anthracene/diaryliodonium salt molecular system. For example, the Smoluchowski analysis assumes that the reacting molecules are spherical in... 

The experimental and simulation results presented here indicate that the system viscosity has an important effect on the overall rate of the photosensitization of diary liodonium salts by anthracene. These studies reveal that as the viscosity of the solvent is increased from 1 to 1000 cP, the overall rate of the photosensitization reaction decreases by an order of magnitude. This decrease in reaction rate is qualitatively explained using the Smoluchowski-Stokes-Einstein model for the rate constants of the bimolecular, diffusion-controlled elementary reactions in the numerical solution of the kinetic photophysical equations. A more quantitative fit between the experimental data and the simulation results was obtained by scaling the bimolecular rate constants by rj"07 rather than the rf1 as suggested by the Smoluchowski-Stokes-Einstein analysis. These simulation results provide a semi-empirical correlation which may be used to estimate the effective photosensitization rate constant for viscosities ranging from 1 to 1000 cP. 

In polyisobutylene in the melt and in solution (CC14, CS2), McCall, Douglass, and Anderson 17) found that the activation energies for polymer diffusion increased with polymer concentration from the value at infinite dilution (approaching the pure solvent value) to the value in the melt. Solvent diffusion, and solvent effect on polymer diffusion, were also measured. The Stokes-Einstein model applied to this data yielded molecular dimensions too small by a factor of two or three. 

Various models have been suggested to describe the interdependence of an ion s ionic mobility, its size, and its charge. Three of these models are described later (a) the Stokes-Einstein model, (b) the free-volume, or sieving. 

Fig. 2.8. Comparison of the reorientational correlation time of CIO3F with the Debye-Stokes-Einstein model. The inverse of the correlation time (obtained from 35ci relaxation) is plotted as a function of the ratio of temperature to viscosity. (From Ref. [55])...

On substituting for >a and >b in Equation (1.3), one obtains for the rate constant calculated according to the Stokes-Einstein model ... 

The proper definition of these two correlators is the fundamental issue. Very often the slow correlator is addressed to the orientational self-correlation of the single rigid molecule, see (2.33), which according to the Debye-Stokes-Einstein model (DSE) can be described as a pure Brownian diffusive process [19,42]. Hence the slow correlator becomes... 

The Dynamics of Liquid lodobenzene vs. Debye-Stokes-Einstein Model... 

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