Barrier theories

Barnes and Hunter [290] have measured the evaporation resistance across octadecanol monolayers as a function of temperature to test the appropriateness of several models. The experimental results agreed with three theories the energy barrier theory, the density fluctuation theory, and the accessible area theory. A plot of the resistance times the square root of the temperature against the area per molecule should collapse the data for all temperatures and pressures as shown in Fig. IV-25. A similar temperature study on octadecylurea monolayers showed agreement with only the accessible area model [291]. 

The tortuous-path and barrier theories consider the effects of the media on the electrophoretic mobility in a way similar to the effect of media on diffusion coefficients discussed in a previous section of this chapter. The tortuons-path theory seeks to determine the effect of increased path length on electrophoretic mobility. The barrier theory considers the effects of the barrier or media conductivity on the electrophoretic mobility. 

In a more extensive development of the tortnons-path and barrier theories, Boyack and Giddings [45] considered the transport of solnte in a simple geometrical system similar to that used in the diffnsion analysis of Michaels [241] bnt with added tortuosity effects. The effective mobility in this system was found to be... 

FIG. 29 Obstruction factor from barrier theory of Boyack and Giddings for fibers. (Reprinted with permission Ref. 45, Copyright 1963, Academic Press.)... 

Alternatively one can make use of No Barrier Theory (NBT), which allows calculation of the free energy of activation for such reactions with no need for an empirical intrinsic barrier. This approach treats a real chemical reaction as a result of several simple processes for each of which the energy would be a quadratic function of a suitable reaction coordinate. This allows interpolation of the reaction hypersurface a search for the lowest saddle point gives the free energy of activation. This method has been applied to enolate formation, ketene hydration, carbonyl hydration, decarboxylation, and the addition of water to carbocations. ... 

J. P. Guthrie, No Barrier Theory Calculating Rates of Chemical Reactions from Equilibrium Constants and Distortion Energies, ChemPhysChem 2003,4, 809. 

FIGURE 31.10 Radon-resistant barrier theory. (Adapted from U.S. EPA, Radon-Resistant Construction Techniques for New Residential Construction—Technical Guidance, EPA/625/2-91/032, U.S. Environmental Protection Agency, Washington, DC, February 1991.)... 

According to the diffusion layer theory, for which the transport process is rate-limiting, kT kR, so that k = kT. According to the interfacial barrier theory, for which the surface reaction is rate-limiting, kR kT, so that it, = R-... 

The interfacial barrier theory is illustrated in Fig. 15A. Since transport does not control the dissolution rate, the solute concentration falls precipitously from the surface value, cs, to the bulk value, cb, over an infinitesimal distance. The interfacial barrier model is probably applicable when the dissolution rate is limited by a condensed film absorbed at the solid-liquid interface this gives rise to a high activation energy barrier to the surface reaction, so that kR kj. Reaction-controlled dissolution is somewhat rare for organic compounds. Examples include the dissolution of gallstones, which consist mostly of cholesterol,... 

Another class of thermodynamic barrier theories focuses on the large increases in the elastic constants that accompany glass formation. (These theoretical approaches seem especially appropriate to polymer fluids below the crossover temperature Fj.) In particular, the barrier height governing particle displacement in the shoving model [57] is taken to be on the order of the elastic energy GqoVo required to displace a particle on a scale comparable to the interparticle distance,... 

The decrease in the alpha factor to values below a = 1 can be due to a decrease in either kL or a or both. Two theories are commonly used to explain the reduction in kp. the barrier effect and the hydrodynamic effect. In the barrier theory, the presence of the surfactants at the phase interface creates an additional resistance to mass transfer due to diffusion through the surfactant layer. In the hydrodynamic theory, the layer of surfactant molecules at the gas-liquid interface depresses the hydrodynamic activity (Gurol and Nekouinaini, 1985). 

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