Plate number effective

Effective plate number is actually a measure of the band broadening in the stationary phase and is calculated by using adjusted retention times  

At high k, there is little difference between plate numbers and effective plate numbers. Effective plate numbers are mostly used in gas chromatography. 

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 

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

Equation (18) displays the relationship between the column efficiency defined in theoretical plates and the column efficiency given in effective plates. It is clear that the number of effective plates in a column is not aii arbitrary measure of the column performance, but is directly related to the column efficiency as derived from the plate theory. Equation (18) clearly demonstrates that, as the capacity ratio (k ) becomes large, (n) and (Ne) will converge to the same value. 

With the introduction of capillary open tube columns (Chapter 4) it became possible to obtain chromatograms corresponding to hundreds of thousands (even 10 ) of theoretical plates as evaluated via Equation [3.20] or [3.21]. However, as a consequence of the issues discussed in Section 3.4.6, such enormous efficiencies could be obtained only for compounds with very low k values, i.e., those that eluted very close to the column dead volume. To provide a more realistic measure of column efficiency in such cases, the effective plate number (Ng) was defined by replacing t, by (L—tg) in Equations [3.20-3.21], where tg is the elution time after injection for unretained solutes  

The proof of the relationship between Ng and N is given elsewhere (Scott http //www.chromatography-online.org/). The correction factor (based on k ) applied to N has a limiting value of 0.25 when k is close to unity (solute is barely retained), but for large k it approaches unity thus Ng as defined in Equation [3.24] does account to some extent for the variation of N with k, discussed above. 

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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... 

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. 

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

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. 

Speed of separation Column capacity Retention factor, k Selectivity factor a Effective plate number, N... 

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

Eddy diffusion, 28, 31, 34 Effective plate number, 16 Einstein equation, 35 Electrochemical detectors in LC, 208 Electron capture detector (ECD), 127-129 Eluent strength function, 49-51, 159, 160— 162... 

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. 

In addition to the theoretical plate number, an effective plate number N is defined by substituting tp in rel. (17c) with tp. The formula for N will be... 

Rel. (18) shows how N depends on chromatographic retention time tp, and since tp is compound related (index i" omitted), it also shows that N (as well as n) are compound dependent. Both rel. (17c) and (18) can be used to measure the theoretical plate number or effective plate number based on experimental data obtained with a given column. This measurement is useful in practice to select columns (higher n gives lower peak broadening) and also to assess the loss in performance of a column after a certain period of usage. 

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 ... 

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