Magnitude increasing with parameter

The enhancement of interaction energy in micropores was discussed in some detail in Chapter 4. It was emphasized that the critical pore width d at which the enhancement first appears increases with increasing diameter a of the adsorbate molecule, since the relevant parameter is the ratio d/a rather than d itself. The quantity a is involved because the magnitude of the dispersion interaction increases as the polarizability, and therefore the size, of the molecule increases (cf. p. 5). 

The relative magnitude of these two activation free energies determines the size and shape of the critical nucleus, and hence of the resulting crystal. If sliding diffusion is easy then extended chain crystals may form if it is hard then the thickness will be determined kinetically and will be close to lmin. The work so far has concentrated on obtaining a measure for this nucleus for different input parameters and on plotting the most likely path for its formation. The SI catastrophe does not occur because there is always a barrier against the formation of thick crystals which increases with /. 

In all liquids, the free-ion yield increases with the external electric field E. An important feature of the Onsager (1938) theory is that the slope-to-intercept ratio (S/I) of the linear increase of free-ion yield with the field at small values of E is given by e3/2efeB2T2, where is the dielectric constant of the medium, T is its absolute temperature, and e is the magnitude of electronic charge. Remarkably S/I is independent of the electron thermalization distance distribution or other features of electron dynamics in fact, it is free of adjustable parameters. The theoretical value of S/I can be calculated accurately with a known value of the dielectric constant it has been well verified experimentally in a number of liquids, some at different temperatures (Hummel and Allen, 1967 Dodelet et al, 1972 Terlecki and Fiutak, 1972). 

There are a number of quantitative features of Eq. (14) which are important in relation to rapid diffusional transport in binary systems. The mutual diffusion coefficient is primarily dependent on four parameters, namely the frictional coefficient 21 the virial coefficients, molecular weight of component 2 and its concentration. Therefore, for polymers for which water is a good solvent (strongly positive values of the virial coefficients), the magnitude of (D22)v and its concentration dependence will be a compromise between the increasing magnitude of with concentration and the increasing value of the virial expansion with concentration. 

The parameter k is termed the interaction factor and the degree of interaction increases with the magnitude of k. When k= 0 equation 7.43 becomes the same as equation 7.30, i.e. the equivalent non-interacting case. 

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