Column Efficiency

Many a u th o rs have su g g ested th e concept of th e chrom atographic sep aratio n efficiency to monitor column condition. Biddlingm eyer and W arren (1984) review ed th e v ario u s methods available fo r calculating column efficiency. They sta te d th a t column efficiency alone cannot give

any indication of w hether th e column is able to se p a ra te a given mixture of compounds and th a t column efficiency is only a m easure of how well th e column has been packed and th e d eg ree of k inetic band broadening. T herefore it can be seen th a t efficiency and perform ance a re two se p ara te term s. Perform ance being th e ability to c a rry o u t a p articu la r separation - high efficiency alone will not g u aran tee th is.

Several param eters affect th e determ ination of column perform ance. These include elu en t composition, viscosity, velocity, tem perature, column length, packing ty p e, packing size and m easurement and calculation method chosen. I t is th e re fo re v ital to s ta te u n d e r what conditions efficiency has been calculated, as well as what method has been used. Many methods make no e ffo rt to remove any co n trib u tio n obtained from th e liquid chrom atography system and so th e value fo r efficiency obtained is th e to tal efficiency for th e whole system . One m easure of p articu lar in te re s t is H or HETP ( h eig h t equivalent to a th eo retical plate ) as it a d ju s ts for th e len g th of th e column. HETP { or H ) refle cts th e ratio of column efficiency to column len g th whilst th e o th er u ses th e in v erse ratio. ( Generally it is not used as chrom atographers a re conditioned to p re fe r a high value of N ra th e r th an a low value of H \ )

1.3.4.1 Measurement and calculation methods

In analytical chrom atography peaks a re often assum ed to be Gaussian in shape and because of th is N is defined as follows

N = (1-13)

o2

Where PJ. is th e reten tio n volume and é is th e v arian ce in volume u n its. (} can be w ritten in term s of th e peak width divided by a constant. The value of th e co n stan t depends upon w here th e w idth is m easured on th e peak, ie. 4%, 50%, or 100% of peak height. This can be incorporated into th e above equation

a

Where a is a co n stan t, th e value of which depends on th e p ercen tag e of th e peak h eig h t a t which th e width, is m easured.

Several approaches a re available fo r th e calculation of peak variance. The following is a list of d ifferen t calculation methods: inflection method, width a t half height, ta n g e n t method, h e ig h t/a re a method, moment method and asym m etry-based methods. Biddlingm eyer and Warren (1984) teste d each of th e calculation methods for accu racy and consistency. The moments and asym metric methods were found to be th e most accu rate. The sim plest methods, ie. m easuring th e width a t half h eig h t and m easuring th e width using tan g en tial lines p ro jected to th e base line, were found to be th e least accu rate, b u t w ere th e easie st to calculate. 1.3.4.2 Moment Method

In th is method no assum ptions a re made about th e peak shape. The c h a ra c te ristic s of th e peak a re ex p ressed in term s of sta tistic a l moments. Peak area is th e zero th moment, th e f ir s t moment is th e mean (for Gaussian peaks th is is th e peak maximum) and th is o ccurs a t th e c en tre of mass. The second moment is th e peak v arian ce and th e th ird and fo u rth moments a re m easures of skew ness. The second moment may th e re fo re be used in place of peak v arian ce to calculate N.

1.3.4.3 Asymmetric Methods

Two ty p e s of asym metric methods a re available. The sim pler of th e two u se s an empirical ratio of th e peak w idths e ith e r side of th e peak maxima m easured a t 10% peak h eight. This ratio has th e a d v an tag e of satisfy in g th e ch ro m ato g rap h er’s in tu itiv e idea of peak asym m etry and is easy to m easure. I t however lacks any th eo retical basis, b u t th is should not preclu d e its use.

The o th er method u se s an exponentially modified Gaussian peak to r e p re s e n t peak skew ness. This function c o n sists of a Gaussian function combined with an exponential decay function. The to tal v arian ce is;

= " 'o + T'

T and a a re not as easy to u se as th e o th e r ratio and re q u ire s th e use of a microcomputer fo r th e ir calculation b u t have th e ad v an tag e of being a fundam ental m easure of peak asym m etry.

1.3.4.4 Exponentially Modified Gaussian Methods

The u se of exponentially modified Gaussian peaks has been investigated as a more accu rate descrip tio n of chrom atographic peaks ( Jeansonne and Foley, 1992, Foley and Dorsey, 1983, Grushka, 1972, and Yau, 1977 ). The exponentially modified Gaussian model may be ju stifie d since it is known th a t in tra and ex tra column effects have th e effect of skewing peaks causing th e changes in v arian ce produced by exponentially modified Gaussian peak functions. The u se of th e c o rre c t model is im portant - th e u se of th e in co rrect model may lead to g re a t inaccuracies in plate counts and variances. The most fre q u e n tly used formula fo r th e num ber of plates for real peaks is :

BIA + 1.25

This formula includes th e asym m etry ( using th e B/A asym m etry ratio as shown in fig u re 1.7 ) of th e peak in th e calculation of th e num ber of th eo retical equilibrium sta g es ( ie. plates ) co rresponding to th e operation of th e column.

1.3.4.5 Choice of Method

Since th e re a re many d ifferen t methods of calculating efficiency which do not always give equivalent values it is im portant to decide why efficiency is to be m easured before choosing which method to use. Generally m ethods which a re least sen sitiv e to peak asym m etry a re th e b e st choice b u t if th e only objective is to monitor th e efficiency of a column over a period of time th e n any of th e methods may be useful. If comparisons a re to be made with columns of d ifferen t size or d ifferen t packings th en a more acc u ra te method which gives a c o n sisten t r e s u lt is req u ire d . With any evaluation of column efficiency th e capabilities and limitations of th e calculation methods used must be tak en into account. When evaluating re p o rte d efficiencies contained within lite ra tu re or commercial information it is difficult to make any d irec t com parisons due to th e lack of any sta n d ard isa tio n of experim ental conditions.