Thermodynamic enhancement factor

The expression d In a/d In c is known as the thermodynamic factor and is a special case of the Wagner factor (or thermodynamic enhancement factor) which plays an important role for the kinetic properties of electrodes. This term indicates the deviation from ideality of the mobile component. For ideal systems this quantity becomes 1 and comparison with Pick s first law yields... 

The enhancement factors here are very large, in fact, among the larger nonideal corrections encountered in chemical engineering thermodynamics. (Enhancement factors for other mixtures at cryogenic conditions of 10 and larger have been reported, i Note that at T = 35°C and P = 255.3 bar, the solubility of naphthalene is enhanced by a factor of more than 17 700 above its ideal value however, its total solubility is still small at less than 2 mol %. 

The term in square brackets in Eq. (138) expresses the variation of activity coefficient of the neutral species with concentration. Thus, in addition to the statistical contribution to diffusion, expressed by the familiar gradient-in-concentration term, there is a chemical driving force due to the variation of free energy with composition and hence position. The term in square brackets is known as the thermodynamic enhancement factor and was identified by Darken [1948]. The diffusion coefficient A is known as the chanical diffusion coefficient, and its use is appropriate whenever diffusion takes place in an appreciable concentration gradient and when ideal solution laws cannot be applied to the solute. The concept was extended by C. 

It was found that chemical diffusion is reasonably fast in all of the intermediate phases in this system. The self-diffusion coefficients are all high and of the same order of magnitude. However, due to its large value of thermodynamic enhancement factor W, the chemical diffusion coefficient in the phase Li,Sn, is extremely high, approaching 10 cm s, which is about two orders of magnitude higher than that in typical liquids. These data are included in Table 3. 

The chemical diffusion coefficient is related to the self-diffusion coefficient by a term known as the thermodynamic enhancement factor. We will not explore the literature on Dchem as this again is extensive and would only serve... 

Equation (6) links, in a simple way, the thermodynamically important stability constants Kox and /Cred of a complex in different oxidation states with experimentally measurable redox potentials EH and EHa. Therefore it provides an easy way to obtain the ratio of KoxIKted, which is a theoretically useful parameter known as the binding enhancement factor (BEF). We propose that a better description for this ratio would be the reaction coupling efficiency (RCE) since binding by so-called molecular switches may be reduced or enhanced, depending upon the particular system involved. Equation (6) also allows the calculation of Kox if Kted is known or vice versa. 

Based on Eq. (4.4), the enhancement factor E is defined as the enhancement on the maximum flux J"max of a drug across skin by increasing the (kinetic) diffusivity and/or the (thermodynamic) solubility in the stratum corneum.79 Thus... 

In the acidic route (with pH < 2), both kinetic and thermodynamic controlling factors need to be considered. First, the acid catalysis speeds up the hydrolysis of silicon alkoxides. Second, the silica species in solution are positively charged as =SiOH2 (denoted as I+). Finally, the siloxane bond condensation rate is kinetically promoted near the micelle surface. The surfactant (S+)-silica interaction in S+X 11 is mediated by the counterion X-. The micelle-counterion interaction is in thermodynamic equilibrium. Thus the factors involved in determining the total rate of nanostructure formation are the counterion adsorption equilibrium of X on the micellar surface, surface-enhanced concentration of I+, and proton-catalysed silica condensation near the micellar surface. From consideration of the surfactant, the surfactants first form micelles as a combination of the S+X assemblies, which then form a liquid crystal with molecular silicate species, and finally the mesoporous material is formed through inorganic polymerization and condensation of the silicate species. In the S+X I+ model, the surfactant-to-counteranion... 

The phase equilibrium equations for the interface may also need to be modified for the influence of additional species on the thermodynamic properties at the interface. A case in point is sour water stripping, in which reactions in the liquid phase create additional species (including ions), which affect the interfadal equilibrium. Enhancement factors have been derived for many cases and there is no sin-... 

If contact with a rough surface is poor, whether as a result of thermodynamic or kinetic factors, voids at the interface are likely to mean that practical adhesion is low. Voids can act as stress concentrators which, especially with a brittle adhesive, lead to low energy dissipation, i/f, and low fracture energy, F. However, it must be recognised that there are circumstances where the stress concentrations resulting from interfacial voids can lead to enhanced plastic deformation of a ductile adhesive and increase fracture energy by an increase in [44]. 

It should be kept in mind that all transport processes in electrolytes and electrodes have to be described in general by irreversible thermodynamics. The equations given above hold only in the case that asymmetric Onsager coefficients are negligible and the fluxes of different species are independent of each other. This should not be confused with chemical diffusion processes in which the interaction is caused by the formation of internal electric fields. Enhancements of the diffusion of ions in electrode materials by a factor of up to 70000 were observed in the case of LiiSb [15]. 

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