1 Evaluating Chromatograms

Transcription

1 3 1 Evaluaing Chromaograms Hans-Joachim Kuss and Daniel Sauffer Chromaography is, in principle, a diluion process. In HPLC analysis, on dissolving he subsances o be analyzed in an eluen and hen injecing 0 μl, he peak volume exiing he column is greaer han 0 μl. This is a consequence of he chromaographic condiions. Depending on he column dimensions, here is a criical injecion volume, which, if exceeded, leads o addiional peak broadening. If one dissolves he subsances o be analyzed in a weaker eluen, as is generally done when he gradien eluion echnique is used, hen he injecion volume ha can be oleraed is increased significanly. The efficiency (Fig. 1.1) of he column is defined by he plae number and he seleciviy of he separaion of wo componens is given by he separaion facor α. The ime aken for an eluen or carrier gas molecule o run hrough he column wihou reenion is he mobile phase hold-up ime M. This ofen corresponds approximaely o he ime of he appearance of he firs peak in he chromaogram. If one uses oo srong an eluen, all componens o be separaed are elued a he hold-up ime because hey are no held back on he column. Differences in he ineracions of he subsances wih he saionary phase lead o differen reenion imes, S, in he saionary phase. To achieve a separaion, S mus be greaer han M. R = M + S (1.1) k = (1.) S M u L = (1.3) M The sum of M and S yields he measured reenion ime R (Fig. 1.) and he quoien of S and M is he reenion facor k, which is no dependen on he column dimensions or he flow, as is R. Wih increasing pressure he flow and Quanificaion in LC and GC: A Pracical Guide o Good Chromaographic Daa Edied by Hans-Joachim Kuss and Savros Kromidas Copyrigh 009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISB: vch01.indd :17:19

2 4 1 Evaluaing Chromaograms Figure 1.1 Efficiency is dependen on he peak widh, seleciviy on he reenion facor quoien. Figure 1. Reenion imes are measured a he apex of each peak. Unreained componens elue a he mobile phase hold-up ime. he linear velociy increase in parallel. The linear velociy u is calculaed by dividing he column lengh, L, by M. 1.1 Efficiency The ideal peak shape is described by a symmeric Gaussian peak (Fig. 1.3), characerized by he reenion ime R and he sandard deviaion of he reenion ime, which is a measure of he peak widh. R = (1.4) w 50% =.35 (1.5) w 13% = 4 (1.6) 140vch01.indd :17:19

3 1. EMG Model 5 Figure 1.3 Characerisic parameers of a Gaussian peak. Besides he well known graphic mehods, can be calculaed using he area A and heigh H: R HP = π A (1.7) Combining Eqs. (1.4) and (1.7) i can be seen ha can be deermined from he reenion ime, area and heigh. R R P H = π A (1.8) A = (1.9) H π P These equaions only apply o isocraic separaions. For low k values, one usually finds smaller plae numbers han for higher k values. The exra column volume V ec leads o an addiional consan peak broadening. The smaller earlier peaks are influenced more srongly by his han he laer peaks. 1. EMG Model In pracice, peaks ofen have a ailing, which can be described as a Gaussian peak wih an overlaid exponenial funcion (exponenial modified Gauss funcion 140vch01.indd :17:0

4 6 1 Evaluaing Chromaograms Figure 1.4 The asymmery facor is measured a 10% of he heigh. (EMG) [1]). The increase in he Gaussian peak is influenced less by he exponenial ail wih he ime consan τ han by he decreasing porion of he peak. The reenion ime is shifed o a slighly higher value, as is he peak widh. = R + τ (1.10) The values of and τ are no deermined by he inegraion mehod used. The exen of he ailing, which is measured a 10% of he peak heigh, is represened by he asymmery facor A f (Fig. 1.4). A f a = (1.11) b According o he EMG model, he plae number is calculaed as: R a + b = 41.7 b a (1.1) In he range τ/ = Tamisier-Karolak [] found an empirical equaion: τ b = a (1.13) This equaion can only be used if he asymmery facor can be esimaed. Therefore he valley beween he peaks mus no be greaer han 9% of he heigh of he smaller peak. In pracice, he asymmery facor a he peak s half heigh is of more use. If he valley beween he peaks is greaer han 49%, inegraion wih he perpendicular drop mehod is very prone o errors, because he second peaks sis on he firs peak. 140vch01.indd :17:0

5 1.3 Chromaogram 7 The plae number is dependen on he column lengh and he paricle size. If one divides he column lengh by he plae number, he plae heigh H (μm) is obained. Dividing H by he paricle size d P, one obains he reduced plae heigh h, i.e. he number of paricles due o one plae. H L = (1.14) H h = (1.15) d P In heory, he minimum possible value for h is, bu in pracice, a value of 3 is usually accepable in real chromaograms. The hree effecs: flow inhomogeneiy A, diffusion broadening B in compeiion wih he flow and deerioraion of he componen exchange C wih increasing flow are overlaid, o produce a Van Deemer Hu-curve. The essenial saemen is ha here is a linear velociy u a which he plae heigh H has a minimum. A column has he highes separaing performance a his flow, which is characerized by he linear velociy u op. In HPLC one usually works above he opimal flow, acceping a loss in he opimal separaing performance because oherwise he analysis imes would become oo long. The corresponding broadening of he peak is paricularly dependen on he componen exchange erm C, which causes he increasing slope of he Hu curve. 1.3 Chromaogram A chromaogram is a graphical represenaion of all peaks eluing from he column superimposed on he baseline. The areas and heighs of he peaks usually increase linearly in accordance wih he amoun of injeced componen. The inegraion sysems enable an auomaed esimaion of he area, heigh and oher characerisic parameers. The separaion is usually carried ou on a C18 column in HPLC and on a capillary column in GC. The separaing abiliy of a column is characerized by he plae number, which deermines he peak widh relaive o he reenion ime. A ypical value for HPLC is and for GC plaes. s p R = 1 (1.16) If he sandard deviaion of he peak is 1% of he reenion ime R, he plae number is vch01.indd :17:0

6 8 1 Evaluaing Chromaograms 1.4 Seleciviy The aim of chromaography is a separaion, which is characerized by he differen reenion imes of wo peaks succeeding one anoher. A very efficien column wih a high plae number is no guaranee of an efficien separaion. The seleciviy is characerized by he separaion facor α, which is he quoien of he wo reenion facors. k α = k1 (1.17) An α of 1.1 implies ha he reenion ime s of he second peak is 10% longer han he reenion ime of he firs peak. The resoluion R, a measure of he qualiy of he separaion beween wo peaks, depends no only on he disance beween he wo peaks bu also on he peak widh, which can be found graphically as he peak widh a half heigh w 50%. R = 1.18 w R + w R1 50% 150% (1.18) An R of 1.5 is known as baseline separaion, alhough only R = is really separaion o he baseline. If he reenion imes of wo successive peaks lie sufficienly far away from each oher hen we have a separaion down o he baseline. If no, he peaks merge ogeher and he valley beween hem decreases unil only a broadened peak can be seen. One does no have any chance of recognizing wheher several componens hide under he visible peak a (almos) he same reenion ime. This can be resolved only by variaion of he separaing condiions or wih one or more specific deecors. References 1 J. P. Foley, J. G. Dorsey, Equaions for Calculaion of Chromaographic Figures of Meri for Ideal and Skewed Peaks, Anal. Chem. 55, 1983, S. L. Tamisier-Karolak, M. Tod, P. Bonnardel, M. Czok, P. Cardo, Daily validaion procedure of chromaographic assay using gaussoexponenial modelling, J. Pharm. Biomed. Anal. 13, 1995, vch01.indd :17:0