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plate number was introduced. The effective plate number is calculated in the same way as column efficiency, but uses the corrected retention distance, as opposed to the total retention distance in conjunction with the peak width. As a consequence, the effective plate number is significantly smaller than the number of theoretical plates at low (k') values. The column efficiency and the effective plate number converge to the same value at high (k') values. It follows, that the effective plate number more nearly corresponds to the actual resolving power of the column.  Although the theoretical plate, as defined by the plate theory, has a practical significance and can be used in column design, the concept of the effective plate is not theoretically unsound and is related directly to the theoretical plate. The efficiency of a column (n), in number of theoretical plates, has been shown to be given by the following equation,  

Column Efficiency The column efficiency is defined as the number of theoretical plates in the column. As discussed in the plate theory, the faster the equilibrium process, the smaller the plates and thus, the greater the number of plates in the column. It is therefore important to know how to determine the number of plates a column possesses and the relationship of the number of theoretical plates in the column to the properties of the chromatogram. Starting with the Poisson form of the elution equation, the peak width at the points of inflexion (which corresponds to twice the standard deviation of the normal elution curve) can be found by equating the second differential of the elution equation to zero and

can be determined and an expression for the retention volume (Vr) obtained. The expression for (Vr) will disclose those factors that control solute retention. The Plate Theory The plate theory needs to assume that the solute, during its passage through the column, is always in equilibrium with the mobile and stationary phases. However, equilibrium between the phases never actually occurs. To take this non-equilibrium condition into account, the column is considered to be divided into a number of cells or plates. Each plate is allotted a specific length and, thus, the solute will spend a finite time in each plate. The size of the cell is chosen to provide sufficient residence time for the solute to establish equilibrium with the two phases. Thus, the smaller the plate, the faster will equilibrium and the more plates there will be in the column. Consequently, the number of theoretical plates contained in a column will be directly related to the equilibrium rate and, for this

of the eluted peak, from the plate theory will be,                                                            where X(n) is the concentration of the solute in the mobile phase leaving the (n)th plate, (v) is the volume passed through the column in plate volumes, and (n) is the number of theoretical plates in the column.   If the sample consisted of pure  mobile phase containing no solute, then Xi = 0 and                        

condition and allow a simple mathematical treatment of the chromatographic process, Martin and Synge (1) borrowed the plate concept from distillation theory and considered the column consisted of a series of theoretical plates in which equilibrium could be assumed to occur. In fact each plate represented a 'dwell time' for the solute to achieve equilibrium at that point in the column and the process of distribution could be considered as incremental. This approach has been discussed in Plate Theory and Extensions . Employing this concept an equation for the elution curve can be easily obtained and, from that basic equation, others  can be developed that describe the various properties of a chromatogram. Such equations have permitted the calculation of efficiency, the number of theoretical plates required to achieve a specific separation and among many applications, elucidate the function of the heat of absorption detector. The Plate Theory, however, does little to

, as the composition of the mobile phase in each section will not be constant but will decrease along the plate. Furthermore, as the separation progresses, the lengths of sections (X), (Y) and (Z) will continually increase. Such a system is extremely difficult to treat theoretically particularly as the boundaries are not as sharp as those depicted in Figure 3. In fact, the overall effect is as though the separation was carried out sequentially on three separate sections of a plate, each section having a different stationary phase and mobile phase. In each section, the separation will then be achieved by elution development, but the overall effect will be a form of gradient elution. The complexity of the system increases with the number of solvents used and, of course, their relative concentrations. The process can be simplified considerably by pre-conditioning the plate with solvent vapor from the mobile phase before the separation is started.