Band broadening plate height

As stated previously, additional information on the sample is obtainable from band broadening (plate height) measurements. If plate height is measured as a function of flow velocity at a fixed retention level, a linear relationship is obtained, as predicted by Equation 7. The slope of the line yields the diffusivity D of the sample, and the intercept provides the polydispersity a. . The D value translates into a value for the average particle diameter d via the Stokes-Einstein relationship... 

Assuming a Gaussian profile, the extent of band broadening is measured by the variance or standard deviation of a chromatographic peak. The height of a theoretical plate is defined as the variance per unit length of the column... 

To determine how the height of a theoretical plate can be decreased, it is necessary to understand the experimental factors contributing to the broadening of a solute s chromatographic band. Several theoretical treatments of band broadening have been proposed. We will consider one approach in which the height of a theoretical plate is determined by four contributions multiple paths, longitudinal diffusion, mass transfer in the stationary phase, and mass transfer in the mobile phase. 

Efficiency Degree of band broadening for a given retention time. It is expressed as the number of theoretical plates, N, or as the height equivalent to a theoretical plate, HEPT. 

The efficiency, or plate count of a column N is often calculated as 5.54 (tr/a)2, where tr is the retention time of a standard and a is the peak width in time units at half-height.1 2 5 This approach assumes that peaks are Gaussian a number of other methods of plate calculation are in common use. Values measured for column efficiency depend on the standard used for measurement, the method of calculation, and the sources of extra-column band broadening in the test instrument. Therefore, efficiency measurements are used principally to compare the performance of a column over time or to compare the performance of different columns mounted on the same HPLC system. 

The efficiency of a chromatographic separation can be described by the height equivalent of a theoretical plate (H), where lower values of H correspond to more efficient separations. The Van Deemter equation describes the relationship between H and mobile phase flow velocity (u) as the sum of three major terms, A, B, and C, each of which represents a different contribution to band broadening in a chromatographic column. 

Here, A is the random path, B the longitudinal molecular diffusion and C the RTMT contributions with the velocity of the mobile phase u shown separately. H is referred to as the Height Equivalent to a Theoretical Plate and is terminology borrowed from distillation. While the distillation HETP is not truly applicable, the terminology has persisted. It can be shown that the H in this expression is the equivalent to variance/unit length. This is the expression introduced by Van Deemter and co-workers in 1956 in a discussion of band broadening. 

The band broadening may be characterised by a plate height, and its causes provide a basis for understanding why modem chromatography is such an efficient separation technique. 

In liquid chromatography (LC) the plate height H is related to the various band broadening terms as described by the van Deemter equation ... 

Both the number of theoretical plates and the height eqnivalent to a theoretical plate estimate the band broadening occnrring in the separation system, either related to the whole capillary tnbe (AT) or to the portion of the capillary occupied by the analyte (H). The higher is N (or lower is H) the narrower are the recoded peaks in the electropherogram. 

In packed columns, all three terms contribute to band broadening. For open tubular columns, the multiple path term, A, is 0, so bandwidth decreases and resolution increases. In capillary electrophoresis (Chapter 26), both A and C go to 0, thereby reducing plate height to submicron values and providing extraordinary separation powers. 

Dingenen [9], who studied the effect of the mobile phase velocity on the height equivalent to a theoretical plate (HETP) at different temperatures for benzotriazole derivatives, obtained the results shown in Figure 22, which represents the HETP values found for methanol and the hexane-ethanol mixture. Both curves of Figure 22 clearly demonstrate that the kinetic circumstances are less favorable at low temperatures. A slow mass transfer between the two phases clearly determines the band-broadening process at temperatures below 20°C. This... 

Band broadening arises from three principal mechanisms, one of which depends on the mean velocity of the carrier and two of which are independent of . The latter two represent nonidealities in instrument and sample. The total variance of an eluting peak is the sum of variances contributed by each bandbroadening mechanism. Expressed as plate height H, which is the total variance divided by column length L (12), the zone broadening is described by... 

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