Multicomponent diffusion when important

No reliable mixture-averaged theory is available for computing the thermal diffusion coefficient D[. When thermal diffusion is important, the rigorous multicomponent theory described next should be used to obtain D[. 

When modeling phenomena within porous catalyst particles, one has to describe a number of simultaneous processes (i) multicomponent diffusion of reactants into and out of the pores of the catalyst support, (ii) adsorption of reactants on and desorption of products from catalytic/support surfaces, and (iii) catalytic reaction. A fundamental understanding of catalytic reactions, i.e., cleavage and formation of chemical bonds, can only be achieved with the aid of quantum mechanics and statistical physics. An important subproblem is the description of the porous structure of the support and its optimization with respect to minimum diffusion resistances leading to a higher catalyst performance. Another important subproblem is the nanoscale description of the nature of surfaces, surface phase transitions, and change of the bonds of adsorbed species. 

For multicomponent liquid mixtures, it is usually very difficult to obtain numerical values of the diffusion coefficients relating fluxes to concentration gradients. One important case of multicomponent diffusion for which simplified empirical correlations have been proposed is when a dilute solute diffuses through a homogeneous solution of mixed solvents. Perkins and Geankoplis (1969) evaluated several methods and suggested... 

For such supramolecular systems, diffusion NMR may be extremely important for the determination of the structure and dynamics of the system. Diffusion is also extremely important in determining the association constant in systems, which on their formation induce a small change in the NMR spectra, and in systems in which chemical shift changes occur for reasons other than complexation, for example when protonation takes place. Diffusion NMR can also easily be used to probe the kinetic stability of multicomponent systems just by monitoring the effect of a small excess of one of the components on the diffusion coefficient of the supramolecular system. 

Thus, in addition to the well-received applications of NMR for structure characterization, there are additional physicochemical aspects of complex macromolecular architectures, biohybrid structures, and aggregates and complexes, which can be investigated using NMR. In particular the measurement of displacements based on PEG NMR for either measuring diffusion or the electrophoretic mobility offers additional information on the size and charge of these various macromolecular architectures and compositions. The inherently available chemical shift information allows the identification of the moving species, which is important in multicomponent systems or when the formation of complexes is studied. 

Throughout the discussion of chromatography, we have focused on pairs of analytes that were difficult to separate and the need for columns of high efficiency. It is important to remember that in multicomponent mixtures, some analytes are not so difficult to separate. In such cases, another principle must be considered, namely, the time required to move all the components through the column. Further, the longer the residence time, the more diffusion effects will spread the band out In a mixture in which two adjacent components have reasonably different k values, then the eluent might be altered when the first component clears the column to reduce the k of the second. This can be done by continuous or concrete step gradients. 

---