Resistance to Mass Transfer in the Mobile Phase

Dispersion Due to Resistance to Mass Transfer Resistance to Mass Transfer in the Mobile Phase 

Marcel Dekker, Inc. 270 Madison Avenue, New York, New York 10016 

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The dispersion of a solute band in a packed column was originally treated comprehensively by Van Deemter et al. [4] who postulated that there were four first-order effect, spreading processes that were responsible for peak dispersion. These the authors designated as multi-path dispersion, longitudinal diffusion, resistance to mass transfer in the mobile phase and resistance to mass transfer in the stationary phase. Van Deemter derived an expression for the variance contribution of each dispersion process to the overall variance per unit length of the column. Consequently, as the individual dispersion processes can be assumed to be random and non-interacting, the total variance per unit length of the column was obtained from a sum of the individual variance contributions. 

When u E, this interstitial mixing effect was considered complete, and the resistance to mass transfer in the mobile phase between the particles becomes very small and the equation again reduces to the Van Deemter equation. However, under these circumstances, the C term in the Van Deemter equation now only describes the resistance to mass transfer in the mobile phase contained in the pores of the particles and, thus, would constitute an additional resistance to mass transfer in the stationary (static mobile) phase. It will be shown later that there is experimental evidence to support this. It is possible, and likely, that this was the rationale that explains why Van Deemter et al. did not include a resistance to mass transfer term for the mobile phase in their original form of the equation. 

In 1967, Huber and Hulsman [2] introduced yet another HETP equation having a very similar form to that of Giddings. Their equation included a modified multipath term somewhat similar in form to that of Giddings and a separate term describing the resistance to mass transfer in the mobile phase contained between the particles. The form of their equation was as follows ... 

The ratio of the resistance to mass transfer in the mobile phase to that in the stationary phase (Rms) will indicate whether the expressions can be simplified or not. Now, (Rms) will be given by. 

Rms ratio of resistance to mass transfer in the mobile phase to that in the stationary phase... 

Van Deemter considered peak dispersion results from four spreading processes that take place in a column, namely, the Multi-Path Effect, Longitudinal Diffusion, Resistance to Mass Transfer in the Mobile Phase and Resistance to Mass Transfer in the Stationary Phase. Each one of these dispersion processes will now be considered separately... 

On page 6, it was shown that in the front half of the peak, there will be a net transfer of solute from the mobile phase to the stationary phase and thus the resistance to mass transfer in the mobile phase will dominate. At the rear half of the peak there is a net transfer of solute from the stationary phase to the mobile phase and in this case the resistance to mass transfer in the stationary phase will dominate. Then if the resistance to mass transfer in the stationary phase is greater than that for the mobile phase, the rear part of the peak will be broader than the front half. In which case,... 

Figure 1.4 Variation of the resistance to mass transfer in the mobile phase, C , and stationary phase, Cj, as a function of the capacity factor for open tubular columns of different internal diameter (cm) and film thickness. A, df 1 micrometer and D, 5 x 10 cm /s B, df 5 micrometers and D, 5 x 10 cm /s and C, df - 5 Micrometers and 0, 5 x 10 cm /s.

Equation (3), however, was developed for a gas chromatographic column and in the case of a liquid chromatographic column, the resistance to mass transfer in the mobile phase should be taken into account. Van Deemter et al did not derive an expression for fi(k ) for the mobile phase and it was left to Purnell (3) to suggest that the function of (k ), employed by Golay (4) for the resistance to mass transfer in the mobile phase in his rate equation for capillary columns, would also be appropriate for a packed column in LC. The form of f (k ) derived by Golay was as follows,... 

It is seen that the first term differs from that in the Giddings equation, in that it now contains the mobile phase velocity to the power of one half. Nevertheless, again when ul/2 >> E, the first term reduces to a constant similar to the Van Deemter equation. The additional term for the resistance to mass transfer in the mobile phase is an attempt to take into account the... 

It is seen that the composite curve obtained from the Huber equation is indeed similar to that obtained from that of Van Deemter but the individual contributions to the overall variance are different. Although the contributions from the resistance to mass transfer in the mobile phase and longitudinal diffusion are common to both equations, the (A) term from the Huber equation increases with mobile phase flow-rate and only becomes a constant value, similar to the multipath term in the Van Deemter equation, when the mobile velocity is sufficiently large. In practice, however, it... 

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. 

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