HPLC : Separation Efficiency

The overriding purpose of a chromatographic separation is just that, to separate two or more compounds contained in solution. In analytical chemistry, a quantitative metric of every experimental parameter is desired, and so separation efficiency is measured in plates. The concept of plates as a separation metric arose from the original method of fractional distillation, where compounds were separated based on their volatilities through many simultaneous simple distillations, each simple distillation occurred on one of many distillation plates. In chromatography, no actual plates are used, but the concept of a theoretical plate, as a distinct region where a single equilibrium is maintained, remains. In a particular liquid chromatographic separation, the number of theoretical plates and the height equivalent to a theoretical plate (HETP) are related simply by the length of the column

Where N is the number of theoretical plates, L is the length of the column, and H is the height equivalent to a theoretical plate. The plate height is given by the variance (standard deviation squared) of an elution peak divided by the length of the column.

The standard deviation of an elution peak can be approximated by assuming that a Gaussian elution peak is roughly triangular, in that case the plate height can be given by the width of the elution peak squared times the length of the column over the retention time of the that peak squared times 16.

Using the relationship between plate height and number of plates, the number of plates can also be found in terms of retention time and peak width

In order to optimize separation efficiency, it is necessary in maximize the number of theoretical plates, which requires reducing the plate height. The plate height is related to the flow rate of the mobile phase, so for a fixed set of mobile phase, stationary phase, and analytes; separation efficiency can be maximized by optimizing flow rate as dictated by the van Deemter equation.

The three constants in the van Deemter equation are factors that describe possible causes of band broadening in a particular separation.

A is a constant which represents the different possible paths that can be taken by the analyte through the stationary phase, it decreases if the packing of the column is kept as small as possible. B is a constant that describes the longitudinal diffusion that occurs in the system. C is a constant that describes the rate of adsorption and desorption of the analyte to the stationary phase. A, B and C are constant for any given system (with constant analyte, stationary phase, and mobile phase), so flow rate must be optimized accordingly. If the flow rate is too low, the longitudinal diffusion factor (Bv) will increase significantly, which will increase plate height. At low flow rates, the analyte spends more time at rest in the column and therefore longitudinal diffusion in a more significant problem. If the flow rate is too high, the mass transfer term (Cv) will increase and reduce column efficiency. At high flow rates the adsorption of the analyte to the stationary phase results in some of the sample lagging behind, which also leads to band broadening.