Relationships for Estimating Optimized Conditions

One such approximate but practically useful relationship, that for the optimized theoretical plate height in Equation [3.42], has already been seen. Note that this approximation for clearly represents a considerable over-simplification, since it suggests that column performance for a well-packed column is independent of the nature of the analyte provided k is sufficiently large, and is also independent of the nature of both the stationary and mobile phases. Nonetheless, this approximate relationship does emphasize the ca ucial importance of particle size in determining the efficiency of an LC column (see Section 3.5.7) and provides a first-order approximation to the value of H under optimum flow conditions. 

Under the same limitations and assumptions as those that allowed evaluation of the approximation for (Equation [3.42]), the final approximate form of Equation [3.40] for the optimum linear velocity u p gives  

Now consider the maximum achievable column efficiency as measured by the number of theoretical plates N pj. For this purpose help is obtained from the water engineers An important relationship used to evaluate flow rates of water through porous media is d Arcy s Law (see http //biosystems.okstate.edu/darcy/). The principles underlying d Arcy s original formulation also apply to liquids other than water and the law can be expressed as follows in a form appropriate to flow of a mobile phase through a bed of stationary phase particles (Scott http //www.chromatography-online.org/)  

Within the same set of approximations as before, it is now possible to evaluate the column length that will give optimum performance when operated at the van Deemter optimum  

Another parameter of interest related to N, is the peak capacity Cp. Under the highly restrictive assumption that all peaks have the same width (taken conservatively as the width of the last-eluting peak), Plate Theory led to 

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