# liquid chromatography column - Scott R.P.W.

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8r]U0pi

Where, (1) is the length of the column,

(P) is the pressure drop across the column, and (n) is the viscosity of the flowing liquid.

Now, employing equations (10) and (12),

1 - nHmin. ~ 2ï^(âÑ

Thus,

From the 6olay equation, Â = 2Dm

Thus,

32j]Dm

(14)

Employing equation (14) it is possible to calculate the range of efficiencies attainable under operating conditions commonly used for packed columns. The conditions assumed are as follows,

1

Inlet Pressure lOOOIb/sq.in.

Viscosity of Mobile Phase 0.00397 Poises

Diffusivity of the Solute in the Mobile Phase 2.5 X 10~5cm2/sec

The results obtained are shown as a graph relating column efficiency against column radius in figure 4

Figure 4

Graph of Log.Efficiency against Log.Radius for a Capillary Column

Log.Radius (Radius in micron)

It is seen that the 1 micron column can provided an efficiency of over two hundred thousand plates whereas the column 100 micron in radius can provide an efficiency of over two billion theoretical plates (assuming an inlet pressure of 1000 p.s.i). It will be seen later, however, that the practical limitations of present day chromatography equipment render the realization of even a modest performance from LC capillary columns extremely difficult.

References

(1) J C. Giddings,.J. Chrornatogr5( 1961)46.

(2) J. F. K. Huber and J. A. R. J. Hulsman, Anal Chirn. Acta.,Z8( 1967)305.

(3) G. J. Kennedy and J. H. Knox, J Chromatogr. Sc/., 10( 1972)606.

(4) J. N. Done and J. H. Knox, J.Chromatogr. Sci., 10( 1972)606.

(5) J. N. Done, G. J. Kennedy and J. H. Knox, in " Gas Chromatography 1972", (Ed. S. G. Perry), Applied Science PUBLISHERS, Barking, (1973)145.

(6) J. C. Giddings, Anal Chem ,35(1963)1338.

(7) J. C. Giddings," Dynamics of Chromatography M.Dekker (New York) (1965)125.

(8) M. J. E.Golay.in " Gas chromatography /958", (ed.D.H.Desty), Butterworths, London, (1958)36

Chapter 9

Experimental Validation of the Van Deemter Equation

The equations discussed in the previous chapter, that described the variance per unit length of a solute band after passing through an LC column, were all significantly different. It is, therefore, necessary to identify the specific equation that most accurately describes the dispersion that takes place, so that it can be employed with confidence in the design of optimized columns. The different equations were tested against an extensive set of accurately measured experimental data by Katz et a! (1) and, in order to identify the most pertinent equation, their data and some of their conclusions will be considered in this chapter

Reiterating the equations that were examined, they are as follows,

H = a + - + Cu

The Van Deemter equation,(2)

u

The Giddings equation, (3)

è

H = —-— + - + Cu + Du'/2 The Huber equation, (4) E è

h = - + Av1^3 + Cv

The Knox equation, (5)

v

H = —-— + - + Cu + Du2/3 The Horvath equation, (6) E è

u '

- w» “

At first sight, it might appear adequate to apply the above equations to a number of experimental data sets of (H) and (u) and to identify that equation that provides the best fit. Unfortunately, this is of little use as, due to their nature, all five equations would provide an excellent fit to any given experimentally derived data set, provided the data was obtained with sufficient precision. However, all the individual terms in each equation purport to describe a specific dispersive effect. That being so, if the dispersion effect described is to be physically significant over the mobile Phase velocity range examined, all the constants for the above equations derived from a curve fitting procedure must be positive and real. Any equation, that did not consistently provide positive and real values for all the constants, would obviously not be an appropriate and explicit equation to describe the dispersion effects occurring over the range of velocities examined. However, any equation that does provide a good fit to a series of experimentally determined data sets and meet the requirement that all constants were positive and real would still not uniquely identify the correct equation for column design.

When a satisfactory fit of the experimental data to a particular equation, is obtained the constants, (À), (Â), (C) etc. must then be replaced by the explicit functions derived from the respective theory and which incorporate the respective physical properties of solute, solvent and stationary phase. Those physical properties of solute, solvent and stationary phase must then be varied in a systematic manner to change the magnitude of the constants (A), (B),(C) etc. The changes predicted by the equation under examination must then be compared with those obtained experimentally. The equation that satisfies both requirements can then be considered the true equation that describes band dispersion in a packed column

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.

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