H or HETP

The parameter N is universally referred to as the plate number, but an alternative means of quoting efficiency is in terms of opiate height, H or HETP. Plate number and plate height are inversely related by the equation... 

With effects causing asymmetrical spreading assumed negligible, the plate height h (or HETP, height equivalent to a theoretical plate) for a gaussian distribution may be defined as variance per unit length of column ... 

N. This definition is somewhat artificial, because actually there is no fixed value of N on the column. The rate theory redefines the plate height (H or HETP) as follows ... 

The resulting equation and its components are shown in Figure 22.3. The sum curve is quasi-hyperbolic, exhibiting a minimum value of H (or HETP) at an optimum carrier velocity ( opt) I min = A + iVBC and Fopt = V BC. Equation 22.10 can be compared with Equation 21.8 for liquid chromatography. Also, as in Equation 21.6 used in liquid chromatography, N = 16(rr/fF) in gas chromatography. 

A useful way of describing efficiency is by taking into account the length of the column L, in this way calculating the height equivalent to a theoretical plate H or HETP ... 

As the value of N is proportional to column length, L, the other parameter H or HETP, the so-called height equivalent to a theoretical plate, is Introduced as... 

HETP = height equivalent to a theoretical plate, m, or ft HTU = height of a transfer unit, m or ft Lm = liquid rate, kg-mols/h, or lb mols/hr m = slope of the equilibrium line X = mol fraction of the more volatile component in the liquid phase... 

The efficiency of chromatographic systems can be defined by the height equivalent to a theoretical plate (HETP or plate height, symbol H) or by the reduced plate height ... 

What is H anyway The original interpretation, taken from distillation theory, was height equivalent to a theoretical plate, or HETP. We have seen that this concept was inadequate, and the preceding discussion of the van Deemter equation has presented it as a measure of the extent of spreading of an analyte zone as it passes through a column. Thus, a more appropriate term might be column dispersivity. In fact, another, independent approach to the theory of chromatography defines H as... 

Since the value of N depends on column length, a more useful term is plate height, (h), or height equivalent to one theoretical plate (HETP). This term is derived as shown below ... 

L/N) of this relationship, which is called the plate height (H) or the height equivalent of a theoretical plate (HETP). Thus ... 

In 1952, Martin and Synge were the first to describe column efficiency in terms of H, an equilibrium step or HETP (height equivalent to a theoretical plate) and peak broadening or variance in the elution process [2,3]. However, in 1956, van Deemter et al. realised that most band broadening occurs during the elution process in the column [4]. Column band broadening processes are the subject of the next section. 

Data measured with chemically oxidked packing particles made out of phosphor bronze. In this application, much h her HETPs were demonstrated for the same or aimilar packing that were not specially surfaoe>treated. 

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

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 ... 

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... 

HETP can be related to the experimental parameters through the Van Deemter [59] or Knox [60] equations. It is possible to describe the dependence of H on u since H is a. function of the interstitial mobile phase velocity u. In the case of preparative chromatography, where relatively high velocities are used, these equations can very often be simplified into a linear relation [61, 62]. 

I. Height Equivalent of a Theoretical Plate or Plate Height (HETP or H)... 

To develop an HETP equation it is necessary to first identify the dispersion processes that occur in a column and then determine the variance that will result from each process per unit length of column. The sum of all these variances will be (H), the Height of the Theoretical Plate or the total variance per unit column length. There are a number of methods used to arrive at an expression for the variance resulting from each dispersion process and these can be obtained from the various references provided. However, as an example, the Random-Walk Model introduced by Giddings (5) will be employed here to illustrate the procedure.The theory of the Random-Walk processes itself can be found in any appropriate textbook on probability (6) and will not be given here but the consequential equation will be used. 

The identification of the pertinent HETP equation must, therefore, be arrived at from the results of a sequential series of experiments. Firstly, all the equations must be fitted to a series of (H) and (u) data sets and those equations that give positive and real values for the constants of the equations identified. The explicit form of those equations that satisfy the preliminary data, must then be tested against a series of data sets that have been obtained from different chromatographic systems. Such systems might involve columns packed with different size particles or employ mobile phases or solutes having different but known physical properties. 

Efficiency of the distillation column is measured by the height equivalent to a theoretical plate, abbreviated HETP or simply h. The length of the column is L, thus h=L/n. The h value is independent of L, whereas the n value is dependent on L. 

As long as dumped packing in commercial columns is properly wetted [more than 1000 lb/(h)(ft2) or 5000 kg/(h)(m2)], the following HETP values will result in a workable column ... 

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