The Effective Plate Number

The concept of the effective plate number was introduced and employed in the late nineteen fifties by Purnell (7), Desty (8) and others. Its introduction arose directly as a result of the development of the capillary column, which, even in 1960, could be made to produce efficiencies of up to a million theoretical plates (9). It was noted, however, that these high efficiencies were were only realized for solutes eluted close to the column dead volume, that is, at very low k values. Furthermore, they in no way reflected the increase in resolving power that would be expected from such high efficiencies on the basis of the performance of packed columns. This poor performance, relative to the high efficiencies produced, can be shown theoretically ( and Indeed will be, later in this book) to result from the high phase ratio of capillary columns made at that time. That is the ratio of the mobile phase to the stationary phase in the column. The high phase ratio was 

To compensate for, what appeared to be very misleading efficiencies values, the effective plate number was introduced. The effective plate number uses the corrected retention distance, as opposed to the total retention distance to calculate the efficiency. Otherwise the calculation is the same as that used in the normal calculation of theoretical plates. In this way the effective plate number becomes significantly smaller than the true number of theoretical plates for solutes eluted at low k values At high k values, the the two measures of efficiency tends to converge. In this way the effective plate number appears to more nearly correspond to the column resolving power. In fact, it is an indirect way of trying to define resolution in terms of the number of effective plates in the column. 

The efficiency of column (n) in number of theoretical nlates has bn shown to be given by the following equation, 

Equation (8) describes the relationship between the efficiency of a column in theoretical plates and the efficiency given in effective plates. It is also seen that the calculation of the number of effective plates in a column does not provide an arbitrary measure of the column performance, but is directly related to the number of theoretical plates In the column as defined by the plate theory. It should be noted that as (k ) becomes large, (n) and (N) converge to the same value. 

The effective plate number has an interesting relationship to the function for the resolution of a column that was suggested by Giddings (10). Giddings 

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Column Efficiency. Under ideal conditions the profile of a solute band resembles that given by a Gaussian distribution curve (Fig. 11.1). The efficiency of a chromatographic system is expressed by the effective plate number defined from the chromatogram of a single band. 

Band Asymmetry. The peak asymmetry factor AF is often defined as the ratio of peak half-widths at 10% of peak height, that is, the ratio b/a, as shown in Fig. 11.2. When the asymmetry ratio lies outside the range 0.95-1.15 for a peak of k =2, the effective plate number should be calculated from the expression... 

The idea of the effective plate number was introduced and employed by Purnell [4], Desty [5] and others in the late 1950s. Its conception was evoked as a direct result of the introduction of the capillary column or open tubular column. Even in 1960, the open tubular column could be constructed to produce efficiencies of up to a million theoretical plates [6]. However, it became immediately apparent that these high efficiencies were only obtained for solutes eluted at very low (k ) values and, consequently, very close to the column dead volume. More importantly, on the basis of the performance realized from packed columns, the high efficiencies did not... 

As a secondary consideration, the chromatographer may also need to know the minimum value of the separation ratio (a) for a solute pair that can be resolved by a particular column. The minimum value of (a) has also been suggested [8] as an alternative parameter that can be used to compare the performance of different columns. There is, however, a disadvantage to this type of criteria, due to the fact that the value of (a) becomes less as the resolving power of the column becomes greater. Nevertheless, a knowledge of the minimum value of (cxa/b) can be important in practice, and it is of interest to determine how the minimum value of (aA/B) is related to the effective plate number. 

The peak broadening for the entire chromatographic system,. columns plus the instrument, may thus be estimated from the bandwidth contribution of each component of the system. The effective plate number of the system may then be calculated from Equation 1. 

It is also of interest to the chromatographer to know the minimum (a) value of a pair of solutes that can be separated on a particular column. In fact, this has been suggested, (11), as a basis for comparing the resolving power of different columns. The disadvantage of this type of criteria is that the value of (a) becomes smaller the higher the resolving capacity of the column. Nevertheless, the minimum value of (a) is important in practice and it is of interest to see if it can be related to the effective plate number of the column. 

The effective plate number 7Vcff may be calculated as a function of the separation factor a for a given value of the resolution, R. Derive this relationship. 

Height equivalent to an effective plate. H. The number obtained by dividing the column length by the effective plate number. 

A related measure of system efficiency is the effective plate number,... 

The effective plate number will increase as k increases, and it will approach n at high k values where VM is no longer of significant size compared to Vr. 

Two sample components may only be separated from each other if their k values differ. The effective plate number, NefT, or the effective plate height, Heis used to describe the separation efficiency of a column. 

From equations (12), (13), and (14), it can be seen that the plate number is a measure of the relative peak broadening that has occurred while the sample component passed through the column in time tR. As retention time increases, the value of W increases, that means the peak broadens. If the adjusted retention time, tR, is used, the peak number is called the effective plate number and written as ... 

Combining equations (5), (13) and (15), the effective plate number can be related to the plate number by the following equation ... 

The effective plate number increases with increase of k, and approaches to N at high k values. In general, the effective plate number is a better parameter to describe the performance of a column. It is especially true when we compare the efficiency of the capillary column with the packed column. 

The effective plate number corrects theoretical plates for dead (void) volume and hence is a measure of the true number useful of plates in a column ... 

The effective plate number is related to the retention factor and effective plate number via ... 

N calculated this way using is a measure of the efficiency of the whole system that includes the dead volume. In order to calculate and compare efficiencies of columns alone, it is necessary to use (adjusted retention time) in place of tR in the above expression, to obtain the effective plate number. 

The efficiency of an open tubular column can be measured in several ways, such as by the plate number (N), the effective plate number (Neff), the plate height (H) or the... 

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