Bandbroadening Eddy diffusion

At two conceptual extremes, we might envision that there are only two flow paths an analyte might take as it passes down the column, a slow path and fast path, and that at times the analyte may jump from one to another. There are also two conceptual extremes in traveling between the flow streams (1) diffusion of the analyte molecule between flow streams and (2) a mobile phase flow-mediated transfer between flow streams. The former will be slow in comparison to the latter because diffusion mediated processes are much slower. In the case of eddy diffusion, flow-mediated transfer will overwhelmingly dominate the bandbroadening process. 

The van Deemter Curve and Equation The total plate height for a separation is equal to the sum of all its component plate heights. One such sum is known as the van Deemter Equation, originally pubhshed in 1956 by van Deemter and colleagues. In terms of the bandbroadening expression presented herein it takes the form where the first term represents bandbroadening contributions from eddy diffusion, the second term represents contributions from longitudinal diffusion, and the third term represents contributions from resistance to mass transfer. 

Figure 11.6 The van Deemter Equation plotted as a curve. The full expression is the sum of the three individual components. Eddy diffusion, the A term, a constant, does not change as the mobile linear flow rate changes. Bandbroadening from longitudinal diffusion steadily decreases the shorter the analyte remains on the column, in other words, the faster the flow rate is. Contributions from resistance to mass transfer of the analyte into and out of the stationary phase increase linearly with the mobile phase flow rate. The separation will be most efficient at the flow rate that minimizes plate height, in this case about 0.1 cm/s.

Contributions from longitudinal diffusion are greatest as the flow rate approaches zero at which point, of course, any separation would cease and the band would merely spread out gradually. Eddy diffusion (A) has no flow-related component but does contribute an absolute limit on the how small the overall plate height can be. Finally, the mass transfer term (C w) contributes increasing amounts of bandbroadening as the mobile phase flowrate increases. 

Bandbroadening components can be treated as being additive and include contributions from longitudinal diffusion, eddy diffusion, and resistance to mass transfer. 

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