Optimization to Maximize Column Efficiency

Now the physical origins of the general functional form of the van Deemter equation are understood  

Clearly d H/du 0, so the condition dH/du = 0 does indeed describe a minimum (not maximum) value for H  

Since generally diffusion is much faster in a mobile liquid (D /Dj, 1) and the film thickness is a small fraction of the particle diameter (dp/dp 1), the second terms in both numerator and denominator of Equation [3.40] can be ignored relative to the corresponding first terms thus u p( is (approximately) directly proportional to the diffusion coefficient in the mobile phase (D ,) and inversely proportional to the particle diameter (dp). Also, Upp, varies with the nature of the analyte via k, and to some extent on the quality of the column packing via Tm  

To determine the optimum value Uppt, i.e., the value of u that gives a minimum value of H and thus a maximum value of N, the hyperbolic function in Equation [3.39] must be differentiated with respect to u  

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