Column efficiency, theoretical plate number

The theoretical plate is a hypothetical measurement of the efficiency of the column. The theoretical plate number should be determined upon first use of the column and the value monitored throughout the column lifetime. Using the last peak in the chromatogram, the measurement of N should be determined it can be calculated using the following equation ... 

As explained elsewhere in this book, resolution in SEC can be expressed in terms of the peak standard deviation and the slope of the calibration curve. As in other HPLC modes, the efficiency of SEC columns can be improved by decreasing particle size. The relationship between column efficiency (or plate number N) and velocity can be expressed i dimensionless (reduced) parameters. The reduced plate height h is equal to the ratio of the height of a theoretical plate and the particle size as shown in Equation (1). The reduced velocity v is equal to the product of the linear velocity and particle size dp divided by the solute diffusion coefficient/), as shown in Equation (2). 

Three separate factors affect resolution (1) a column selectivity factor that varies with a, (2) a capacity factor that varies with k (taken usually as fej). and (3) an efficiency factor that depends on the theoretical plate number. 

The chiral recognition ability of the insoluble (+)-l was estimated by HPLC using a column packed with small particles of l.25 However, this column showed a poor efficiency because of a low theoretical plate number. This defect was overcome by coating soluble poly(TrMA) with a DP of 50 on macroporous silica gel.26 The 1-coated silica gel had higher resistance against compression and longer lifetime than the CSP of insoluble 1. Moreover, the two 1-based CSPs show quite different chiral recognition for several race-mates, which may be attributed to the different orientation of 1 in bulk and on the surface of the silica gel.27... 

The theoretical plate number (AO is inversely related to the amount of zone broadening occurring in a column. The greater the value for N, the more efficient is the column but differences of less than 25% are not very significant. 

If the correctly sized flow cell and connecting tubing are not used, the high efficiency of a column or high theoretical plate number columns cannot be effectively used. The detector cell volume contributes hold-up volume. The larger is the cell volume, the greater the peak broadening. The cell volume... 

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 analytical specifications must prescribe the ultimate performance of the total chromatographic system, in appropriate numerical values, to demonstrate the performance that has been achieved. The separation of the critical pair would require a minimum column efficiency and the number of theoretical plated produced by the column should be reported. The second most important requisite is that the analysis should be achieved in the minimum time and thus the analysis time should also be given. The analyst will also want to know the maximum volume of charge that can be placed on the column, the solvent consumption per analysis, the mass sensitivity and finally the total peak capacity of the chromatogram. The analytical specifications can be summarized as follows. 

Efficiency of column. Usually measured by column theoretical plate number. Relates to peak sharpness or column performance. 

Theoretical plate number, n. Number defining the efficiency of the column or sharpness of peaks. 

In capillary gel electrophoresis, one of the major contributors to band broadening, besides the injection and detection extra-column effects, is the longitudinal diffusion of the solute molecules in the capillary tube [14], The theoretical plate number (N) is characteristic of column efficiency ... 

For practical purposes, several terms need to be defined. These are capacity factor (k ), theoretical plate number (N), height equivalent to one theoretical plate (F1ETP), selectivity (a) and peak asymmetry (b/a). As will be discussed later in specific examples (Sects. 9.2.4 and 9.2.5), these parameters are of crucial importance in monitoring and maintaining HPLC column efficiency. 

When packed into chromatography columns, TRIM beads imprinted with Boc-L-Phe were shown to have column efficiencies and separation abilities superior to ground and sieved bulk material [5]. The theoretical plate number was approximately double that obtained with conventional crushed polymer under the same conditions and the resolution of a racemate was also slightly enhanced. The difference, however, was not that great considering the additional preparation time and effort involved. 

The process of band broadening (Figure 2.1) is measured by the column efficiency or the number of theoretical plates N, equation (2.24)), which is equal to the square of the ratio of the retention time to the standard deviation of the peak. In theory, the value of N for packed columns has only a small dependency on k and may be considered to be a constant for a particular column. Column efficiency in open-tubular systems decreases markedly with increased retention. For this reason open-tubular liquid chromatography systems must be operated at relatively low kf values (see section 2.5.S.2). 

The plate theory assumes that the solute is in equilibrium with the mobile and stationary phases. Due to the continuous exchange of solute between the two phases as it progresses down the column, equilibrium between the phases can never actually be achieved. To accommodate this nonequilibrium condition, a technique originally introduced in distillation theory is adopted, where the column is considered to be divided into a number of cells or plates. Each cell is allotted a finite length and, thus, the solute spends a finite time in each cell. The size of the cell is such that the solute is considered to have sufficient residence time to achieve equilibrium with the two phases. Thus, the smaller the plate, the more efficient the solute exchange between the two phases and, consequently, the more plates there are in the column. As a result, the number of theoretical plates contained by a column has been termed the column efficiency. The plate theory shows that the peak width (the dispersion or peak spreading) is inversely proportional to the square root of the efficiency and, thus, the higher the efficiency, the narrower the peak. Consider the equilibrium that is assumed to exist in each plate then... 

Two related terms are widely used as quantitative measures of chromatographic column efficiency (1) plate height H and (2) plate count or number of theoretical plates N. The two are related by the equation... 

From the experimental data [44], the selectivity of the adsorbents was calculated as the relative retention volume of the separated species. It can be seen in Table 9 that Cs-CPM adsorbent possesses better selectivity than the Ca-CPM one with respect to the separation of the isomers of xylene and ethylbenzene with like properties. The results enabled us to conclude that the separation of the isomers of m- and p-cresol up to the purity degree of 99% can be achieved using the columns with the theoretical plates number (TPN) not exceeding 200, and that for the o- and m-isomers - employing the packed intermediate efficiency columns with TPN of 2000-2500. To separate the same pairs of the species using the Ca-CPM, the capillary columns with the TPN of 20000 were reqnired. 

It follows that the lowest dilution or the highest peaks are obtained if a short and, most importantly, thin column with as high a theoretical plate number as possible, is used. The origin of the separation efficiency of the column must come from its fine,... 

Generally, the column efficiency is expressed in terms of the theoretical plate number N or the height equivalent to a theoretical plate, H ... 

For a given column at optimum flow conditions the maximum efficiency and theoretical plate number can be calculated, as well as the minimum H. 

The number of these theoretical transverse slices of column is known as the theoretical plate number (N) and reflects the number of times a solute partitions between the two phases. is a measure of the efficiency of the column and will determine how broad the chromatogram peaks will be. A column with a high number of theoretical plates will be efficient and will produce narrow peaks. 

One could use more efficient columns resulting in a higher theoretical plate number. In addition, all measures resulting in an improved signal-to-noise ratio (see Tip No. 38) are useful. In this chapter, we will deal with the influence of the injection volume on the peak. 

In HPLC, the flow rate has a profound influence on the separation, because retention times and separation performance (theoretical plate number, efficiency) of a column depend on it. A decreased flow rate results in later elution of the peaks and in increased distance between them and vice versa. The relationship between flow and column efficiency is described by the Van Deemter curve (see Fig. 42-1). 

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