Column efficiency and plate number

If a solution of a pure sample is injected into a liquid chromatograph, a measure of the width of the resultant chromatographic peak will give an indication as to how much the dilution and diffusion of the sample has occurred. The less this happens, the more efficient is the column and the higher the plate number. This can be a useful measure of column performance and can be calculated in various ways. 

In SEC, the efficiency of a column or a set of columns is generally calculated for a peak due to a low-molecular-mass species. For truly monodisperse polymers such as proteins, similar efficiencies should be expected, but experience has shown that lower efficiencies are observed for high-molecular-mass species. A further point to be wary of when comparing column efficiencies is to note whether the quoted plate number is per unit length of column (e.g. per foot or per metre) or per column. A typical SEC column with a length of 60 cm and containing a 5 /im styrene/divinylbenzene resin would have a plate number of about 50000. 

Following on from this, it is possible to calculate the plate height H or height equivalent to a theoretical plate , HETP, thus  

A further modification of eqn (1.6) takes into account the particle size of the column packing material and yields a parameter called the reduced plate height h  

The plate number is affected by several variables, including the particle diameter, eluent viscosity and flow rate, the internal volume of the apparatus and the rate of equilibration. The internal volume of the equipment is obviously important and should be minimized by using small-bore tubing ( 0.01 i.d.), keeping the lengths as short as possible. 

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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. 

Fig. 1.18. Examples of chromatographic separation of a ihree-componcnt sample mixture and possible ways lo improve the separation during HPLC melhtxl development. tA) Satisfactory separation. (B) Unsatisfactory separation — ttw low retention. The elution strength of the mobile phase should be decreased. (C) Good resolution, but too long time of separation. The elution strength of the mobile phase should be increased. (D) Unsatisfactory separation — too low column efficiency. The plate number should be increased by using finer packing panicles or a longer column. (E) Unsatisfactory separation — gixxl retention and column efficiency, but too low separation selectivity. The components of the mobile phase can be changed, a ternary or a quaternary mobile phase, selective mobile phase additives, or another type of the stationary phase can be used.

In isocratic elution, resolution depends on the column efficiency or plate number N, the selectivity a, and the retention factor k, all of which can be experimentally influenced through systematic changes in individual chromatographic parameters. In the isocratic mode of separation, resolution is determined from... 

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). 

The separation of the critical pair would require a minimum column efficiency and, so, the number of theoretical plated produced by the column must be reported. The... 

It follows that as the variance of the peak is inversely proportional to the number of theoretical plates in the column then the larger the number of theoretical plates, the more narrow the peak and the more efficiently the column has constrained the band dispersion. As a consequence the number of theoretical plates in a column has been given the term Column Efficiency and is used to describe its quality. 

The performance of the HPLC system should be evaluated from the column efficiency and the symmetry of the peak. The column efficiency is determined as the number of theoretical plates, N, which should be greater than 5000. It is calculated as follows ... 

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). 

Foley and Dorsey (1983) have considered the effect of peak tailing on column efficiency and concluded that measuring peak widths at half height (equation (2.26)) substantially overestimates the number of theoretical plates of a tailed peak. Thus resolution (equations (2.46) and (2.47))... 

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... 

Efficiency or Plate Number (N)—A measure of column performance. N is calculated from retention times and peak widths (Eq. 2.10 and 2.11). 

For a given number of plates the retention volume and the peak width are proportional to the effective volume of each plate i.e. for two columns of identical plate number, the column with the smaller HEPT, H, that is, the shorter column will have the smaller peak width. The amount present at the peak maximum will be unchanged but the volume of gas required to elute the peak will be less, the concentration in that gas will be higher, and the recorded peak height will be greater. In assessing the efficiency of a column the HEPT is important in addition to the plate number. Since H decreases with decrease in df (liquid film thickness), as is shown by Equation 13.1 and df in its own turn is dependent upon the ratio of the liquid phase to solid support, a small proportion of stationary phase (so that the film thickness is reduced) improves the column efficiency. 

H, HETP H is the height equivalent to a theoretical plate also called the equilibrium step height. It is a measure of column efficiency, H is approximately 0.5 mm in a GC capillary column and 0.01 mm in HPLC. H = L/N where L is column length, N is number of theoretical plates in a column. /fcALC is the practical plate height of a column, Z/ min is the theoretical minimum plate height at optimmn linear velocity and maximum column efficiency, and may be calculated in terms of the retention or capacity factor of a column see A eir, van Deemter equation, capacity factor and coating efficiency. 

Number of theoretical plates N, refers to the number of separation steps in a column, is used to describe the efficiency of a column for a given separation and is calculated using observed retention times see column efficiency and effective theoretical plates. 

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 ... 

The quantitative measures of column efficiency are the plate height and plate number. The plate height, H, is defined as the length of column that participates in one mass transfer equilibrium between the stationary phase and the mobile phase. The plate number, N, is the measure of the total number of plates in a column. The two terms are related to each other through the column length, L, by the expression N = L/H. The value of N can be measured from the chromatogram using the equation... 

The high efficiency of GC was evident in Figure 1.1. Efficiency can be expressed in plate numbers, and capillary columns typically have plate numbers of several hundred thousand. As one might expect, an informal competition seems to exist to see who can make the column with the... 

The measurement and control of carrier gas flow is essential for both column efficiency and for qualitative analysis. Column efficiency depends on the proper linear gas velocity which can be easily determined by changing the flow rate untU the maximum plate number is achieved. Typical optimum values are 75 to 90 mL/min for 1/4" outside diameter (o.d.) packed columns 25 mL/min for 1/8" o.d. packed columns and 0.75 mL/min for a 0.25 fim i.d. open tubular column. These values are merely guidelines the optimum value for a given column should be determined experimentally. 

Thus, the plate theory supplies an approximate description of the spreading of a component band. If the chromatographic peak width is known, one can calculate the number of theoretical plates, which characterize the column efficiency and hence the equivalent height of a theoretical plate ... 

Taking into account that in chromatograpliic use the number of theoretical plates refers to one single component, it is not suitable for describing the separation of two components or the separation i)ower of a column. Therefore, for this purpose, N is replaced by the column efficiency and H by the relative width of a peak. 

Modern column LC has been developed to a very high level by the introduction of selective stationary phases of small particle sizes, resulting in efficient columns with large plate numbers per metre. The development of HPLC equipment has been built upon the achievements in column technology, but the weakest part is still the detection system. UV/vis and fluorescence detectors offer tremendous possibilities, but because of their specificity it is possible to detect components only at very low concentrations when using a specific chromophore or fluorophore. 

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