Diffusivity activation volume

The mobility of the boundary should be closely related to die volume diffusion process in the solid, and would therefore be expected to show an Anlienius behaviour widi an activation energy close to the volume diffusion activation energy. 

The influence of pressure on the cage effect was studied by Neuman and colleagues [95-98]. They measured the influence of pressure on the cage effect for competition between recombination and diffusion for the 1,1-dimethylethoxy radical pairs generated from bis(l,l-dimethylethyl)hyponitrite. The empirical activation volume difference (AF(f for the... 

In this equation, kjy is the rate constant for the diffusion-limited formation of the encounter complex, d is the rate constant for diffusion apart, and ka is that for the activation step, i.e. M-L bond formation. Based on the steady-state approximation for the encounter complex concentration, the apparent rate constant for the on reaction is kon = k kj (k - ,+ka), and the activation volume is defined as... 

In the free volume theory, translational diffusion of a lipid molecule in the bilayer occurs only when a free volume larger than a certain critical size appears in the vicinity of the lipid molecule. The free volume theory implies that the smaller the overall volume, the lower the probability for a molecule to associate with a free volume of a critical size. The molecules diffuse slower if the probability for a molecule to associate with a free volume of critical size is small. With increasing pressure, the overall volume decreases and the lateral diffusion is thus reduced. The activation volume for diffusion in the LC phase was calculated using the expression ... 

Table 4.9 gives a summary of diffusion data for divalent cations in aluminous garnets, with the relative activation volume. Although estimation of activation volume is still largely uncertain, its evaluation is essential when dealing with the wide baric regimes encountered in petrologic studies. As shown in the third column of table 4.9, the presence of AF implies substantial modifications of Qj on the kbar scale of pressure. 

Since the design of the measuring cell for field modulation studies is not very critical it was relatively easy to study also the pressure-dependence of ion-pair dissociation and ionic recombination (1 4). Here also the values (Table II) for the activation volumes show the essentially diffusion controlled aspects of the association-dissociation phenomena, since the calculated values, essentially the pressure dependence of the viscosity, and the experimentally determined values agree rather well. 

Taking into consideration the fact that the activation volume of the diffusion process is small compared to that of the chemical reaction, it follow that ... 

The activation volume for diffusion, as measured by the pressure dependence of the diffusivity, is zero to within experimental accuracy [13, 14]. This is unexpected for defect-mediated diffusion, as in such cases, the activation volume for diffusion should consist of the sum of the volume of formation of the defect and the activation volume for the defect migration, and this is usually measurable. 

The postulated C-N heterocoupling requires diffusion of the two radicals either in the solvent-solute surface layer or in the bulk solution. In both cases one expects that the reaction rate should decrease with increasing solvent viscosity. To achieve the latter, the CdS-Si02-catalyzed photoaddition of 2,5-DHF to azobenzene was conducted at pressures ranging from 0.1 to 120 MPa [164]. Both the formation rates of the addition and reduction products 13c and 16 (R = R = Ph) decrease with increasing pressure and from a plot of In(rate) vs. pressure activation volume AF are obtained as 17.4 + 3.4 and 15.8 + 2.3 cm mol , for 13c and 16, respectively (Figure 25). 

In the CAM assay, the concentrations are in a dynamic state, i.e. they are not in a steady state. They ultimately dilute into an infinite volume. But the simple model can be expected to give at least semi-quantitative guidance for the early events, where the active volume is limited by the diffusion distance. 

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