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

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Those characteristics of the chromatogram that have theoretical significance will be discussed later, but some common measurements that can be taken from the chromatogram are given now. The elapsed time between the dead point and the peak maximum is called the retention time, and the time between the dead point and the peak maximum the adjusted retention time. If the retention time is multiplied by the mobile phase flow-rate, the product is called the retention volume . Similarly, multiplying the adjusted retention time by the flow-rate gives the adjusted retention volume.

In order to obtain a rational relationship between GC and LC the symbols used for the above parameters of the chromatogram are taken from those recommended by the Gas Chromatography Discussion 6roup and IEUPAC.

These terms and symbols are now generally accepted for use in both GC and LC.

dead time, to dead volume, Vo retention time, tr retention volume, Vr adjusted retention time, tr' adjusted retention volume, Vp'

One further parameter ought to be mentioned, which to some extent is arbitrary, but can be a useful measure of column performance, and that is resolution. The value taken from the chromatogram, which is normally recognized as a measure of the resolution of two peaks, is the ratio of the distance between the peak maxima and the sum of the peak widths at 0.6065 of the peak height.

LC Column Theories

There are two basic theories that deal with the processes that occur in a chromatographic column, the Plate Theory and the Rate Theory, both of which are essential to understand the function of the column and column design. The first theory to be developed was the Plate Theory, which was presented in an exponential form by Martin and Synge (10) in 1945. The theory was developed further to a more precise and useful form by Said (11). The publication by Said passed almost unnoticed and this more useful form of the Plate Theory was not generally known until reported by Keulemans

(12). The Rate Theory for packed columns was first developed by Van Deemter etal (13) in 1956 for (GC) but is directly applicable to LC. Since that time, a number of other forms of the Rate Theory for packed columns have been developed and in due course will be discussed. However, it appears that the form introduced by Van Deemter is still the simplest and the most reliable for use in column design. The Rate Theory for capillary columns was developed by Golay (14) in 1958 and has been used unchanged or modified since that time. The Golay equation that arises from his Rate Theory is not only applicable to capillary columns, but also to injection valves and

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connecting tubes and consequently, is also used, to evaluate extra column dispersion.

References

(1) M. S. Tswett, Khromphylii Rastitelnom i Zhivotnom Mire, Izd.

Karbasnikov, Warsaw, 191

(2) J.H.Knox,K.K.Unger and H Muel 1 er, J.Liq.Chromatogr,b{ 1983) 1

(3) ” HPLCFittings,T.Upchurch,Oak Harbor,Wa., 1988.

(4) V.L.McGuffin andM.Novotny, J.Chromatogr.,2bb(\9B'3)'38\

(5) C.Barra,S.M.Han and M.Novotny, J. Chromatogn,ZQb( 1987)75

(6) e.Katz,K.L.Ogan and R.P.W.Scott, J.Chromatogr,2¹( 1984)65

(7)" Small Bore Liquid Chromatography CoiumnS ,(Ed. R.P.W.Scott),

John Wiley and Sons,Chichister,1984

(8) E.Katz and R.P.W.Scott, J. Chromatogr,25Z( 1982)159

(9) E.P.Kroeff,R.A.Owens,E.L.Cambell.,R.D.Johnson and H.I.Marks,

J. Chromatogr,461 (1989)45

(10) AJ.P.Martin and R.L.M.Synge, BiochemJ.,35,(1941) 1358

(11) A.S.Said, Am.inst Chem.EngJ.7i 1956)477

(12)" Gas Chromatograph?(2nd Ed.),A.I.M.Keulemans,Reinhold Publishing Company,Amsterdam, 1959

(13) J.J.Van Deemter,F.j.Zuiderweg and AKlinkenberg, Chem.Eng.5ci. 5(1956)24

CHAPTER 2

The Plate Theory

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.

There are two methods of developing the Plate Theory, that given by Martin and Synge (I) and that given by Said (2,3). Both methods were originally developed for gas chromatography (GC) but are equally applicable to liquid chromatography (LC). The first, developed by Martin and Synge leads to a binomial expression which, unfortunately, is approximate and has severe limitations for subsequent use in determining column parameters. However, it was the first approach to a rational explanation of chromatographic development.

The Plate Theory, in whatever form, assumes that the solute is, at all times, in equilibrium with both the mobile and stationary phase. Due to the continuous exchange of solute between the mobile and stationary phases as it progresses down the column, equilibrium between the phases is, in fact, never actually achieved. As a consequence, to develop the Plate Theory, the column is considered to be divided into a number of cells or plates. Each cell is allotted a finite length, and thus, the solute spends a finite time in each cell. The size of the cell is such that the solute is considered to have sufficient time to achieve equilibrium with the two phases. Thus, the smaller the plate, the more efficient the solute exchange between the two phases in the column and consequently the more plates there are in a given column. This Is why the number of Theoretical Plates in a column is termed

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