Many c rite ria have been developed to d escrib e th e quality of a chrom atographic separation. They u se information obtained from a chromatogram such as peak maxima peak minima and points of inflexion to give a numerical value fo r th e quality of th e sep aratio n of mixture components. T here a re two basic ty p e s of c riteria; those which compare th e sep aratio n of a b in ary mixture and th o se which d escrib e th e sep aratio n of a multicomponent mixture.
1.3.1 Binary system criteria
The sim plest and most well known m easure of th e sep aratio n of two peaks in a chromatogram is resolution, R^. This can be defined in two ways ( S nyder and Kirkland, 1979 ):
w here is th e reten tio n volume of component / a n d is th e peak width of th e peak /.
Resolution is a convenient param eter to d escrib e peak sep aratio n since it re la te s th e mean peak width to th e difference in reten tio n volumes - two param eters which determ ine w hether peaks overlap. A resolution, of 2.0, ( ie. Wj + Wj - ~ ) co rresp o n d s to complete peak separation. An a lte rn a tiv e method of calculation is given by :
R , = 1/4 ■ a - 1 ■
f
1
a 1 +
j
. 1 11w here a is th e relativ e reten tio n o r selectiv ity facto r betw een peak i and peak J(k*-/k*^) , ir'j is th e capacity facto r of peak j[(tj-tg )/tg ] and N is th e p late num ber of th e column.
The rela tiv e rete n tio n a is itself a m easure of sep aratio n betw een two peaks b u t w hether th e desired sep aratio n is achieved d ep en d s on th e plate num ber of th e column. R^ and a a re m easures based on chrom atography th eo ry as th e y involve fac to rs related to th e reten tio n of th e components in th e sta tio n a ry phase. T here a re how ever o th er c rite ria which simply u se p ro p e rtie s of th e chromatogram and a re empirical. Examples of th is ty p e of c rite ria a re v alley -to -p eak ratio, V,
and peak separation P ( Debets, Bajema and Doom bos , 1983 ). These m easures a re not affected by peak asym metry. Peak-to-valley ratio is defined as th e h eig h t of th e valley betw een two peaks divided by th e h eig h t of th e smaller of th e two peaks ( see fig u re 1.4 ). If peaks are completely overlapped th e n V is considered to be u n ity and if th e peaks a re resolved to th e baseline th en V will be zero.
The peak separation, P, is defined as th e d ep th of th e valley between two peaks, below a s tra ig h t line connecting th e two peak maxima, divided by th e h eig h t of th e s tra ig h t line above th e baseline a t th e position of th e valley ( see fig u re 1.4 ). P is said to be zero when th e two peaks overlap completely and u n ity if th e y a re resolved a t th e baseline. All of th e se c rite ria may provide a sa tisfac to ry d escrip tio n of th e separation of two a d ja ce n t peaks. They have however been used, in th e p ast, to describ e multicomponent sep aratio n s. This is achieved by calculating th e value of th e c riterio n fo r each pair of a d ja ce n t peaks. The b est sep aratio n is considered to be th e sep aratio n w here th e most poorly sep arated pair of peaks gives th e h ig h est value of th e criterio n . The u sefu ln ess of th is method is questionable since th e se two component c rite ria only u se information about a d ja ce n t peaks and information about th e d eg ree of separation of o th er peaks in th e r e s t of th e chromatogram is completely ignored ( Debets, Bajema and Doornbos, 1983 ).
1.3.2 Multicomponent C riteria
B etter solutions to th e problem of how to ju d g e th e quality of a multicomponent sep aratio n have been su g g ested by Giddings (1960). In th e se c rite ria th e sep aratio n of all p a irs of peaks is tak en into account. A list of multicomponent c rite ria developed in th e last tw enty y e ars is shown in Table 1.1 ( Debets, Bajema and Doornbos, 1983 ). Most of th ese a re summations of two component c rite ria which a re c arried out in such a way th a t stro n g ly overlapping peaks give a g re a te r co ntribution to th e c rite rio n th a n well resolved peaks. Modifications have also been made to th e s e c rite ria u sing w eighting fa c to rs to enhance th e sep aratio n of certain peak p airs and time fac to rs w here th e time for th e separation is tak en into account.
T a b l e 1. 1 Q u a l i t y C r i t e r i a f o r c h r o m a t o g r a m s
1. Total Overlap
(|) = 2 exp ( -2 )