Chromatographic theory plate number

HETP = height equivalent to a theoretical plate. It is derived from the plate theory of distillation which is a confusing concept having no basis in fact in the context of modem chromatographic separations. Nevertheless the terms plate number and plate height are still very widely used. 

However, the T-distribution permits an extension of the plate theory, which is also usable in case of asymmetric peaks. The chromatogram (1 component) is considered to be the result of a pure time delay and a T-distribution response. The procedure implies the fitting of a function f(t) given in Eq. (15) to the chromatographic peak. The asymmetry of the peak determines the new plate number n, decreasing with increasing asymmetry. 

Martin and Synge (3) introduced the important concept of theoretical plates into chromatography. Their concept was derived from partition theory and random statistics, and was related to similar ideas developed for extraction and fractional distillation. They supposed that the column could be divided into a number of sections called theoretical plates, and that solutes (dissolved compounds) could be expected to achieve equilibrium between the two phases (mobile and stationary) that exist within each plate. The chromatographic process, like an extraction process, can be visualized to occur when mobile phase (solvent) is transferred to the next plate, where a new equilibrium is established. Theoretical plate numbers of 1000 or more are common for HPLC columns, which means that 1000 separate equilibria must be established to obtain the same degree of separation by solvent... 

In chromatographic theory, a plate is a transverse section of a cross-sectional area equal to the cross-sectional area of the column. The thickness of the plates is called the HETP, or the height equivalent of a theoretical plate. It is derived from the number of plates divided by the length of the column ... 

While extremely large numbers of theoretical plates are possible with larger diameter columns (22, 23), calculations from chromatographic theory of the Internal diameters and column lengths necessary to achieve relatively high efficiencies in reasonable analysis times Indicate that column diameters of 50 to 100 ym l.d. are necessary for high-resolution SFC (23). For example, more than 10 effective theoretical plates are possible In less than two hours on 30-m long columns of 50 ym l.d. 

Almost all these recent studies have been concerned with the variation of sample distribution between bed and solvent as a function of separation conditions and sample molecular structure. The problem of the number of theoretical plates in the bed (as a function of separation conditions) has been approached from other directions. In the field of gas chromatography the experimental and theoretical unraveling of this problem proceeded quite rapidly after 1955. At the present time our knowledge in the latter area is beginning to have application to liquid chromatographic separations, since the underlying theory for both systems is basically similar. Recent experimental studies of bed plate numbers in... 

In a chromatographic process, a solute is equilibrated many times between the mobile and stationary phases during passage through the column. Each equilibration is equivalent to one equilibrium stage or one theoretical plate. Though in SEC, the concept of the so-called stationary phase, as in other chromatographic separation modes, is not definitive, the theoretical plate number N derived from the plate theory is still used as a measure of column efficiency. 

In classical theory, N was used as a measure of separation power because N increased with greater column length. Height equivalent of a theoretical plate, H, served as a measure of chromatographic efficiency. H in mm or cm is calculated by dividing the column length, I, by the plate number... 

So far the plate theory has been used to examine first-order effects in chromatography. However, it can also be used in a number of other interesting ways to investigate second-order effects in both the chromatographic system itself and in ancillary apparatus such as the detector. The plate theory will now be used to examine the temperature effects that result from solute distribution between two phases. This theoretical treatment not only provides information on the thermal effects that occur in a column per se, but also gives further examples of the use of the plate theory to examine dynamic distribution systems and the different ways that it can be employed. 

Primarily the Plate Theory provides the equation for the elution curve of a solute. Such an equation describes the concentration of a solute leaving a column, in terms of the volume of mobile phase that has passed through it. It is from this equation, that the various characteristics of a chromatographic system can be determined using the data that is provided by the chromatogram. The Plate Theory, for example, will provide an equation for the retention volume of a solute, show how the column efficiency can be calculated, determine the maximum volume of charge that can be placed on the column and permit the calculation of the number of theoretical plates required to effect a given separation. 

Solute equilibrium between the mobile and stationary phases is never achieved in the chromatographic column except possibly (as Giddings points out) at the maximum of a peak (1). As stated before, to circumvent this non equilibrium condition and allow a simple mathematical treatment of the chromatographic process, Martin and Synge (2) borrowed the plate concept from distillation theory and considered the column consisted of a series of theoretical plates in which equilibrium could be assumed to occur. In fact each plate represented a dwell time for the solute to achieve equilibrium at that point in the column and the process of distribution could be considered as incremental. It has been shown that employing this concept an equation for the elution curve can be easily obtained and, from that basic equation, others can be developed that describe the various properties of a chromatogram. Such equations will permit the calculation of efficiency, the calculation of the number of theoretical plates required to achieve a specific separation and among many applications, elucidate the function of the heat of absorption detector. 

Plate Theory. Envision the chromatographic system as a discontinuous process functioning the same as a distillation or extraction system, that, is comprised of a large number of equivalent plates. 

Martin and Synge provided the first theoretical treatment of LLPC by adapting the concept of theoretical plates which had been developed, mainly, for distillation and countercurrent extraction. According to the theory, a chromatographic column is considered to consist of a number of theoretical plates, within each of which perfect equilibrium occurs between the mobile and the stationary phases. Unlike in RPC employing hydrocarbonaceous bonded stationary phases where the retention mechanism is still the subject of contro-... 

For a sufficiently large number of theoretical plates, the closed-form plate theory result (6.6-1) for the chromatographic curve can be approximated by the Gaussian distribution... 

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