Theoretical Plates

The column was 10 m long, 1 mm I.D. packed with Partisil Silica Gel 20 mm particle diameter. At the optimum flow rate (i.e., 10 ml/min.) the column gave a quarter of a million theoretical plates. However, the chromatogram shown in figure 34 was obtained at a flow rate of 38 ml/min. and, thus, as it was operated well above its optimum velocity, the column only gave an efficiency of 160,000 theoretical plates. As the chromatographic data was acquired and processed by a computer portions of the chromatogram could be expanded and these are shown as inserts in the figure. It is seen that the apparently confused peaks at the start of the chromatogram are, in fact, well

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

. It is clear that open tubular columns are ideal for this type of separation problem. In fact, it would be impossible to separate the components of gasoline efficiently with a packed column, even one that is 50 ft long, and even if the inherent long analysis times could be tolerated. In addition this type of separation demands the maximum number of theoretical plates and therefore not only must open tubes be used but tubes of relatively small diameter to produce the maximum number of theoretical plates. In fact, several hundred thousand theoretical plates will be necessary and so the column must also be very long. As has already been discussed, it is necessary to use small radius open tubular columns with a split injection system. Furthermore, as a result of the wide range of molecular weight of the components present, gasoline has a relatively wide boiling range and so will require a temperature program that will heat the column to 200 ˚C or more. A thermally

nbsp;      Figure 12. Graph of Log. Maximum Efficiency against Particle Diameter It is seen from figure 12 that changing the particle diameter from 1 to 20 micron results in an efficiency change from about 3500 theoretical plates to nearly 1.5 million theoretical plates and furthermore, this very high efficiency is achieved at an inlet pressure of only 3000 p.s.i.. It is also seen that the maximum available efficiency increases as the particle diameter increases. This is because, as already discussed, if the pressure is limited, in order to increase the column length to provide more theoretical plates, the permeability of the column must be increased to allow the optimum mobile phase velocity to be realized. It is possible to increase the

nbsp;                                     dXs = KdXm                                       (2) Consider three consecutive plates in a column, the (p-1), the (p) and the (p+1) plates and let there be a total of (n) plates in the column. The three plates are depicted in Figure 2.   Figure 2. Three Consecutive Theoretical Plates in a Column   Let the volumes of mobile phase and stationary phase in each plate be (vm) and (vs) respectively, and the concentrations of solute in the mobile and stationary phase in each plate be Xm(p-1), Xs(p-1), Xm(p), Xs(p), Xm(p+1), and Xs(p+1), respectively. Let a