Columns HETP equation

Effect of Mobile Phase Compressibility On the HETP Equation for a Packed GC Column... 

It is seen that the HETP equation, as derived by Van Deemter, now applies only to a point distance (x) from the inlet of the column. Now, it has already been shown that... 

Thus, the complete HETP equation for a packed GC column that takes into account the compressibility of the carrier gas will be... 

The HETP equation is not simply a mathematical concept of little practical use, but a tool by which the function of the column can be understood, the best operating conditions deduced and, if required, the optimum column to give the minimum analysis time calculated. Assuming that appropriate values of (u) and (Dm) and (Ds)... 

A number of HETP equations were developed other than that of Van Deemter. Giddings developed an alternative form that eliminated the condition predicted by the Van Deemter equation that there was a finite dispersion at zero velocity. However, the Giddings equation reduced to the Van Deemter equation at velocities approaching the optimum velocity. Due to extra-column dispersion, the magnitude of which was originally unknown, experimental data were found not to fit the Van Deemter... 

Hence the term "HETP equation" for the equation for the variance per unit length of a column. 

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 Van Deemter equation remained the established equation for describing the peak dispersion that took place in a packed column until about 1961. However, when experimental data that was measured at high linear mobile phase velocities was fitted to the Van Deemter equation it was found that there was often very poor agreement. In retrospect, this poor agreement between theory and experiment was probably due more to the presence of experimental artifacts, such as those caused by extra column dispersion, large detector sensor and detector electronic time constants etc. than the inadequacies of th Van Deemter equation. Nevertheless, it was this poor agreement between theory and experiment, that provoked a number of workers in the field to develop alternative HETP equations in the hope that a more exact relationship between HETP and linear mobile phase velocity could be obtained that would be compatible with experimental data. 

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. 

The rate theory examines the kinetics of exchange that takes place in a chromatographic system and identifies the factors that control band dispersion. The first explicit height equivalent to a theoretical plate (HETP) equation was developed by Van Deemter et al. in 1956 [1] for a packed gas chromatography (GC) column. Van Deemter et al. considered that four spreading processes were responsible for peak dispersion, namely multi-path dispersion, longitudinal diffusion, resistance to mass transfer in the mobile phase, and resistance to mass transfer in the stationary phase. 

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 ... 

Equation 6.84 shows that the column HETP is the sum of the independent contributions of the axial dispersion (molecular diffusion and eddy diffusion), the film mass transfer resistance, the pore diffusion, and slow kinetics of adsorption-desorption. By comparing Eqs. 6.84 and 6.57a, we obtain ... 

It is convenient to separate these contributions to the column HETP and to distinguish the number of mixing stages, Noisp, the number of mass transfer stages, Nm, and the apparent number of theoretical plates. Nap = L/H. These various contributions are described by the following equations... 

Equation 10.35 assumes the additivity of the variances of independent contributions, which is only approximate in nonlinear cJiromatography [1]. Since the column HETP is proportional to the band variance, we have... 

Lee [33] derived another plate-height equation that should be valid for nonlinear chromatography. He used the same assumption as made previously by Rnox and Pyper [30] and by Shirazi and Guiochon [27]. He assumed that the column HETP is the sum of two independent contributions which are due to the nonlinear behavior of the isotherm and to the mass transfer kinetics, respectively ... 

The smaller the HETP is, the better the column. The older 6 mm diameter packed columns would have values from 1 to 3 mm/plate, whereas values of 0.25 mm/plate are common for capillary columns. One equation to determine the number of theoretical plates and the HETP is the van Deemter equation shown below ... 

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