Chromatographic column, HETP

The height equivalent to a theoretical plate (HETP) for a chromatographic column is approximated by the van Deem ter equation (107) ... 

Small particles should be used in gas chromatographic columns since the HETP is directly proportional to particle diameter. However, column permeability is proportional (and pressure drop is inversely proportional) to the square of the particle diameter. Therefore, if particles are too small pressure requirements increase tremendously. 

HETP Height equivalent to a theoretical plate. A measure of the combined effects of axial mixing and finite mass transfer resistance in causing deviations from ideal (equilibrium) behavior in a chromatographic column or in a countercurrent contact system. The definitions of HETP in these two cases are somewhat different,... 

In the presence of similar molecules and impurities, that molecule will also have to compete for the interactive sites on the surface of the stationary phase. The first scientist to assess the composite effects of mass transport in a chromatographic column from a chemical engineering perspective was JJ van Deem ter 241 in the early 1950s. In doing so he derived a more dynamic equation for the HETP which, in simplified form, can be represented as ... 

Band broadening within the chromatographic column is described as a function of mobile phase linear velocity ( ) by the well known van Deemter equation [5] that relates the height equivalent to the theoretical plate (HETP) to u the lower the HETP, the higher the plate number per unit length of a column. It follows that the highest efficiency is obtained for the shortest HETP. The van Deemter equation is ... 

Compared with Bo , which is independent of the interstitial velocity (Eq. 7.32), Steffi is inversely proportional to interstitial velocity (Eq. 7.20). This means that the influence of mass transfer resistance will grow and surpass the influence of axial dispersion at high interstitial velocity, which is almost always the case for preparative chromatographic processes. In some extreme cases, where the mass transfer coefficients are small and the chromatographic column is operated at high flow rates, the HETP equation for the calculation of Nt can even be simplified further to ... 

The concept of HETP was described in Chapter 3, p. 26. The same concept applies here except that HETP for a distillation differs from an HETP for a chromatographic separation, because in a distillation, the entire column is in use at the same time, whereas in a chromatographic column, only a small portion is being used at any one time. 

The efficiency of chromatographic columns is usually measured under conditions of linear adsorption equilibria from pulse tests. The Height Equivalent to a Theoretical Plate (HETP) is calculated from the first moment /ij and the variance of a chromatographic peak obtained in a column of length I by ... 

How do we do this A performance measure of a chromatographic column that is indqwndent of the length is the HETP. The HETP, in turn, depends on the liiiear velocity with which the mobile phase moves through the column ... 

Fortunately, Dutch scientists in the 1950s related the performance of columns in terms of H, the HETP, to a single variable, the linear mobile phase velocity, . This could be calculated from column dimensions and volume flow rates or more simply measured directly using the retention time of an unretained analyte, and the measured column length, L. Three constants, the ABCs of chromatographic column efficiency, combine in the Van Deemter equation (Equation 11.11), to describe how H varies with u for a particular geometry and construction. Three terms sum together, one independent of u, one inversely proportional to it, and one directly proportional to it ... 

The concept of a theoretical plate is introduced to characterize separation of compounds in chromatographic columns. A theoretical plate is a virtual discrete section of the chromatographic column in which equilibrium between the fraction of the analyte in the mobile phase and the stationary phase can occur at the provided conditions. The number of theoretical plates (V) is a measure of column efficiency. It depends on the length of the column (L) and the height equivalent to a theoretical plate (HETP) ... 

From the Van Deemter plot, it is clear that there exists an optimum velocity of mobile phase at which the HETP function attains its minimum. The low HETP value is favorable because it will imply a large number of theoretical plates in the column of a given length (cf. Equation 6.1). Thus, interactions between the sample and the stationary phase will favor differentiation of retention times of various analytes traversing the chromatographic column. 

The efficiency of the chromatographic column is proportional to the reciprocal value of HETP. 

Recall that one measure of the efficiency of a chromatographic column is the number of theoretical plates. This analogy is drawn from distillation The more collection plates in the column, the more effective is the separation. The maximum number of plates (N) is achieved when the distance between them (i.e., the smallest possible height of a plate, HETP) is minimized. 

For a phenomenological description of chromatographic separation, the concept of theoretical plate is often used. Chromatographic column is considered to consist of a large number of theoretical plates, in each of which equilibrium relations between fluid and particle phases hold (Fig. 10.1). Height equivalent to theoretical plate (HETP) and number of theoretical plate (NTP) are then related to column length z as... 

An alternative measure of efficiency, which is independent of the length of a chromatographic column, is the plate height, H (or Height Equivalent of a Theoretical Plate, HETP), and given by... 

In a packed column the HETP depends on the particle diameter and is not related to the column radius. As a result, an expression for the optimum particle diameter is independently derived, and then the column radius determined from the extracolumn dispersion. This is not true for the open tubular column, as the HETP is determined by the column radius. It follows that a converse procedure must be employed. Firstly the optimum column radius is determined and then the maximum extra-column dispersion that the column can tolerate calculated. Thus, with open tubular columns, the chromatographic system, in particular the detector dispersion and the maximum sample volume, is dictated by the column design which, in turn, is governed by the nature of the separation. 

---