Diffusion packed column separation

Examination of the parameters in the van Deemter expression (Equation 2.44), term by term, provides a basis for optimizing a packed column separation. The plate height, h, of a packed column may be represented as the sum of the eddy diffusion, molecular diffusion and mass transfer effects. Thus, to attain maximum column efficiency, each term in the plate height equation should be minimized ... 

A column having a smaller HETP value is a good column because diffusion inside the column is small, resulting in better separation. The HETP value is given by the Van Deemter equation, which describes the peak broadening of packed columns through which a non-compressible solvent is moving. 

In the course of attempts to quantitatively and a priori describe separation of macromolecules by SEC, a theory was formulated, which considered the effect of porous structure of the column packing on the diffusion rate of separated macromolecules. The resulting theory of restricted diffusion by Ackers [56], however, rather contradicts the equilibrium conception of SEC. 

A fourth factor is the flow rate of the eluent (mobile phase). A too high rate decreases resolution because there is no time for molecules to diffuse into the pores of the matrix. In contrast, a very slow migration of solvent decreases the resolution by remixing the components by diffusion. The effect of diffusion is minimized if the chromatography is done at low temperature. If short separation times are necessary, pre-packed columns, elevated pressure, or HPLC columns are indispensable. 

Equation (13) gives the minimum analysis time that can be obtained from an open tubular column, when separating a mixture of defined difficulty, under given chromatographic conditions. It is seen that, in a similar manner to the packed column, the analysis time is inversely proportional to the fourth power of the function (a-1) and inversely proportional to the inlet pressure. The contribution of the function of (k1), to the analysis time is not clear and can be best seen by calculation. It is also seen (perhaps a little surprisingly) that the analysis time is completely independent of the diffusivity of the solute in the mobile phase but is directly proportional to the viscosity of the mobile phase. 

For packed columns, typical values [701] are h = 3 and v= 3, so that h/ v= 1. For open columns typically h = 1.5 and v= 5, so that /i/ v= 0.3. Consequently, capillary columns will lead to analysis times that are about three times shorter (for dp— dc) for the same separation (N and k constant). Therefore, in principle, capillary columns are superior to packed columns. Unfortunately, capillary columns cannot always be used. This arises from the occurrence of the diffusion coefficient (Dm) in eqn.(7.6). Typically, Dm is 10,000 times larger in gases than it is in liquids. This necessitates the use of very small particles (typically 5-10 pm) in HPLC columns. If we compare packed and capillary columns with dp= which is a reasonable assumption for GC [702], then capillary columns with very small internal diameters need to be considered for LC [703]. Such very narrow columns impose extreme demands on the instrumentation, and at present open tubular columns cannot be used for practical LC separations. 

MECC separations are conducted in open capillaries, hence eddy diffusion is not problematic. However, the columns behave in many ways like packed columns, with the micelles functioning as uniformly sized and evenly dispersed packing particles. In packed columns, resistance to mass transfer in the mobile phase is reduced (i.e., efficiency improved) when smaller particles are used because the "diffusion distance" between particles is decreased. Average inter-micellar" distance is the analogous parameter in MECC. This distance can be decreased by increasing surfactant concentration. 

Resolution and separations in SEC are described by the van Deemter equation (Eq. 14.7). The main contributions to zone broadening, in order of importance, are as follows. The first factor involves the kinetics of partitioning between the mobile phase and the gel there is a limited rate at which equilibrium can be established, and this rate depends on the solute s diffusion coefficient. Second, differences in the lengths of different stream paths in the packed bed of irregularly shaped particles result in eddy diffusion with an ideally packed column, this is not a significant problem, but in practice, eddy diffusion may be significant. Finally, longitudinal... 

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