Pseudo-binary gradients

Compositions of the solvents in pseudo-binary gradients (A — or A —1) which are equivalent to the ternary gradients of figure 6.7. 

The most useful secondary parameter for the optimization of the selectivity in programmed solvent LC is the nature of the modifter(s) in the mobile phase. The selectivity can be varied by selecting various solvents (pure solvents for binary or ternary gradients mixed solvents for pseudo-binary gradients). Analogous to the situation in isocratic LC, it is possible to use different modifiers (and hence to obtain different selectivity) while optimum retention conditions are maintained for all solutes. This possibility to optimize the selectivity in programmed solvent LC will be discussed below. 

From the above we may conclude that many of the ternary gradients which may be used in LC can be seen as special forms of binary gradients. Of course, this conclusion is no longer correct if we do not restrict the discussion to linear gradients and allow the shape of the gradient for one solvent to be different from that for another. However, it may be difficult to find applications for which such complicated ternary gradients can be proved to yield better results than the simpler (pseudo-) binary ones. 

The product rule for the divergence operator is applied to both terms on the right-hand side of equation (9-27). In any coordinate system, the divergence of the product of a scalar and a vector is expanded as a product of the scalar and the divergence of the vector plus the scalar (i.e., dot) product of the vector and the gradient of the scalar. This vector identity was employed in equation (9-14). The pseudo-binary mass transfer equation for component i is... 

In fact, comparing the estimated diffusion coefficients of Pb(N03)3, with the related experimental values [5], an increase in the experimental D values is found in lead (II) nitrate concentrations below 0.025M. This can be explained not only by the initial Pb(N03)2 gradient, but also by a further HjO flux. Consequently, as H3O+ diffuses more rapidly than NO3" or Pb , the lead(II) nitrate gradient generates its own HNO3 flux. Thus, the PbfNOjtj/water mixture should be considered a ternary system. However, in the present experimental conditions we may consider the system as pseudo-binary, mainly for c. OIM, and consequently, take the meastrred parameter, D, as the main diffusion coefficient, D. ... 

The selectivity in programmed solvent LC may be varied by varying the solvents used or by the application of ternary or even more complicated gradients. However, most ternary gradients can in fact be reduced to binary ones using mixed (pseudo-) solvents. 

If the variation of the solid diffusion coefficient with Uthium concentration is significant, then the diffusion equation is nonlinear and the above simplification does not apply. For an electrode composed of spherical particles, a pseudo-two dimensional approach is required, in which the radial diffusion equation (Equation 17) is solved at each mesh point across the porous electrode. A set of radial nodes is then required to compute the radial solid concentration profile at each linear position in the electrode. Note that Eiquation 17 is derived using the gradient in chemical potential, and assumes only that volume changes are negligible and that aU current is carried by electrons in the solid phase. The chemical diffusion coefficient, D used in Equation 17 is related to the binary diffusion coefficient derived from the Stefan-MaxweU equations, V, (also aGled the binary interaction parameter), by the relationship presented earlier (Equation 13) for concentrated solutions ... 

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