Resistance to Mass Transfer in the Mobile and Stationary Phases

3 Resistance to Mass Transfer in the Mobile and Stationary Phases 

Clearly these dispersive processes will increase in relative importance as the mobile phase flow rate increases and as the diffusion rates decrease (the opposite to the dependence for longitudinal diffusion discussed above). This is because the faster the mobile phase (and slower the inter-phase diffusion) the greater the extent to which the molecules originally far from the stationary phase interface will be swept ahead of the molecules that made it into the stationary phase and were retained there for some time. A detailed discussion (Scott http //www.chromatography-online.org/), based on that originally derived by van Deemter, of the form of this dependence of band dispersion on resistance to mass transfer, gives  

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Three main independent contributions to band spreading inside the column have been identified (32) as longitudinal molecular diffusion, the unevenness of flow through the nonhomogeneous packing, and the resistances to mass transfer in the mobile and stationary phases. 

Relative contribution (%) of resistance to mass transfer in the mobile and stationary phases to the column plate height for undecane at 130°C for a 0.32 mm internal diameter open tubular columns in gas chromatography... 

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. 

It is clear that, in LC, the resistance to mass transfer in the mobile phase (albeit within the pores of the particle) is much greater than the resistance to mass transfer in the stationary phase and, thus, simplifying equations (23) and (24), by ignoring the dispersion contribution from the resistance to mass transfer in the stationary phase, will be quite valid. 

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.

The effects of mass transfer are different in the stationary and mobile phases. The resistance to mass transfer in the mobile phase varies with the reciprocals of mobile phase velocity and the diffusivity of the species. The resistance to mass transfer inside the stationary phase varies with the reciprocal of diffusivity and is proportional to the radius of the adsorbent granules attached to the chromatography plate, or the structural complexity of the internal pores in chromatographic paper. For both types of mass-transfer resistance, band stretching is proportional in each direction, as measured from the geometrical spot center, and increases in magnitude the greater the resistance. 

Note the absence of the A term and the separate resistance to mass transfer in the mobile phase. Cm, and and in the stationary phase, Cg. This equation can be written even more specifically and we have... 

This process is not instantaneous and a finite time is required for the solute to transfer by diffusion through the mobile phase in order to enter the stationary phase. Thus, the molecules close to the stationary phase will enter it immediately, whereas those some distance from the stationary phase will enter it sometime later. However, as the mobile phase is moving, during the time the molecules are diffusing toward the stationary phase, they will be swept along the column and thus away from those molecules that were closer to the stationary phase and entered it rapidly. This causes the solute peak to be dispersed (spread) the process is called resistance to mass transfer in the mobile phase (see Figure 2.8). 

Now, the diffusivity of the solute in the mobile phase (Dm(o)) will on average be about the same as that in the stationary phase, viz., 1.5 x 10 cm /sec. The particle diameter (dp) in LC is usually about 5 microns and the film thickness of the stationary phase about 0.1 micron. As in a GC column, the interparticle turbulence will reduce the actual diffusivity of the solute between the particles and, consequently, the resistance to mass transfer between the particles. The mobile phase within the particles, however, is static and, thus, the solute diffusivity is not enhanced. Therefore, there will remain a resistance to mass transfer in the mobile phase within the particle but, as the mobile phase is not moving, it again will appear as a resistance to mass transfer in the stationary phase. Thus,... 

Resistance to mass transfer in the mobile phase, stationary phase, and stagnant mobile phase... 

However, the major contributing factor contributing to band broadening is the C term, in which the resistance to mass transfer can be represented as the composite of the resistance to mass transfer in the mobile phase Cg and that in the stationary phase C. ... 

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