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computer cornerA new high performance liquid chromatographymultifactor methodology for systematicand simultaneous optimisation of thegradient solvent system and theinstrumental /experimental variablesPedro AraujoInvercanigo, Divisioèn de Qu|èmica Anal|ètica, via Intercomunal Cagua-La Villa, Sector Huete, No. 6, Cagua,Aragua, Venezuela

A simple HPLC methodology is proposed whichtakes into account changes in solvent compositionand analysis time in order to speed up lengthy sep-arations without affecting the chromatographicresolution. The main aspects discussed in the dem-onstration of the proposed approach are: routineanalyses; long execution time separation proc-esses; and an overall treatment of all the parame-ters. The combination of the new methodology andexperimental design tools, such as a Doehlertmatrix, has proved to be a reliable alternative tooptimise simultaneously the HPLC solvent gradientsystem and the instrumental /experimental varia-bles. z2000 Published by Elsevier Science B.V.

Keywords: Chromatographic method development;Multifactor methodology; Experimental design;Chemometrics

1. Introduction

The aim in any chromatographic optimisation isto predict the maximum performance or experi-mental conditions for which two or more peaksare separated from each other at some speci¢clocal maximum and under certain constraints suchas greatest permissible analysis time [ 1,2 ].

Time-consuming separations are impractical inroutine analysis and in separations where the sam-ple can be altered by long exposure to the solventsor the column packing material [ 3^6 ]. Classical

approaches to avoid time-consuming HPLC sepa-rations are trial and error in the combination of sol-vents used as mobile phases, change of the mobileor the stationary phase, change of the £ow rate, etc.However, the alteration of some of these experi-mental variables can result in changes in the reso-lution of the chromatograms [ 7 ]. The experimenterrarely tries to carry out further improvements in thereduction of the analysis time once an optimal set ofconditions that provides a good resolution of thesample has been obtained. Accordingly, the imple-mentation of HPLC multifactor studies, whichinvolve the simultaneous optimisation of the gra-dient solvent system and instrumental /experimen-tal variables, is of great importance [ 1 ].

There is much in the literature concerning theoptimisation of HPLC separations [ 8 ]. Full factorialdesign [ 9 ], simplex design [ 9,10 ] and overlappingresolution map [ 11 ] have often been used to opti-mise either the gradient solvent system or theinstrumental /experimental variables such as £owrate, temperature, pH, additive concentration, etc.The use of experimental design in the simultaneousoptimisation of both gradient and instrumental /experimental variables has been a dif¢cult task,however, because changes in solvent compositionover time represent variations in the eluotropicstrength, which is de¢ned as the ability of the sol-vent system to separate compounds. The eluo-tropic strength, in other words, becomes an extraparameter in the optimisation process. Gradientmixture design has been used to some extent as a

0165-9936/00/$ ^ see front matter ß 2000 Published by Elsevier Science B.V.PII: S 0 1 6 5 - 9 9 3 6 ( 0 0 ) 0 0 0 3 5 - 2

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useful approach to optimise the solvent systemcomposition and the eluotropic strength, but stud-ies involving the simultaneous optimisation of thegradient and instrumental /experimental variableshave not been reported yet in the chemometric lit-erature.

The objective of this article is to propose a newHPLC multifactor methodology which, taking intoaccount systematic and simultaneous changes inthe gradient solvent system and the instrumental /experimental variables, allows the analyst to reduce

the analysis time and optimise the HPLC system viaexperimental design.

2. Software

The two-dimensional HPLC data ¢les in hexadec-imal binary format were converted to ASCII usingsoftware developed by Invercanigo IT supportservices. The statistical analysis was carried outusing the STATGRAPHICS [ 12 ] data analysis pack-age. Microsoft Excel was used for producing the¢nal version of tables and graphs.

3. Methodology

The methodology proposed, summarised in Fig.1, consists of four steps.

Step 1. Selection of the systemIn order to demonstrate the methodology, thesystem chlorophyll a ( I ) and its allomers

Fig. 1. Steps involved in the proposed methodology. A Hewlett-Packard HP 1050 high performance liquid chromatograph with diodearray detector (HPLC-DAD) and a HP LiChrosorb RP 18 column (200U4.6 mm I.D.) particle size 10 Wm was used. The recordedspectral range was set to 400^700 nm with a spectral resolution of 2 nm. The mobile phase consisted of methanol, acetonitrile andwater. All solvents were of HPLC grade (Lab-Scan, Ireland) and the chloropigment samples were supplied by IPASME laboratories,Venezuela.

Table 1Optimal HPLC solvent gradient program used in the separationof the chloropigments

Time( min)

Methanol (%) Acetonitrile (%) Water (%)

0 70 5 1510 70 5 1530 55 45 050 55 45 060 70 5 1570 70 5 15

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hydroxy chlorophyll a ( II ) and methoxylac-tone chlorophyll a ( III ), respectively, wasselected. The mixture was separated usingthe HPLC gradient conditions given in Table1. The HPLC system was operated in propor-tional rate of change mode, i.e. the solventcomposition changes linearly with time. It isimportant to mention that the solvent condi-tions given in Table 1 are the result of a uni-variate optimisation of the gradient system.The chromatogram for the mixture sample ofI, II and III with the recorded peak area andstandard deviations at 432 nm is shown in Fig.2. The elution times were 40.25, 41.05 and41.77 min for II, III and I, respectively, andthe total analysis time was 70 min.Step 2. Selection of the variablesChromatographic performance can beaffected by approximately 50 variables[ 13,14 ]. For HPLC up to 15 factors have beenreported [ 15 ]. The variables selected for opti-misation in this study are £ow rate and analysistime. The variation ranges are 0.5^1.5 ml / minand 0^70 min for £ow rate and analysis time,respectively.Step 3. Selection of the designSequential ( simplex, steepest ascent, evolu-tionary optimisation) and simultaneous (star,central composite, Doehlert ) designs havebeen widely used for optimisation purposes

[ 16^19 ]. A uniform shell design developedby Doehlert [ 20 ] was selected. The numberof experiments dictated by this kind of matrixis calculated according to the expressionK 2+K+1 where K represents the number ofvariables to be studied or optimised. The dis-tribution of the experimental points for thetwo selected variables in this study is shownin Fig. 3 where factor 1 is the £ow rate andfactor 2 is the analysis time. The coded levelsand the correspondent natural levels are givenin Table 2. For factor 1 the three coded levels

Fig. 2. Chromatograms of the chloropigments sample under study. I, chlorophyll a; II, hydroxy chlorophyll a; III, methoxylactonechlorophyll a. The peak area in absorbanceUseconds is given in brackets.

Fig. 3. Distribution of the experimental points for two varia-bles according to the Doehlert matrix.

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denoted by 0.866, 0 and 30.866 represent£ow rates of 0.57, 1 and 1.43 ml / min, respec-tively. For factor 2 the ¢ve coded levelsdenoted by 31, 30.5, 0, 0.5 and 1 represent¢ve different analysis times (970 min) in con-junction with ¢ve new gradient solvent condi-tions for the analysis of the mixture of I, II andIII. The systematic selection of these condi-tions is explained in step 4.Step 4. Projections of the solvent compositionHPLC program against the analysis time inorder to establish the analysis times and sol-vent conditions according to the number oflevels imposed by the designA graph of the solvent composition against theanalysis time is required in order to determinethe natural levels or experimental conditionsto be assessed for factor 2. A gradual shift ofthe movable solvent axis along the time axisresults in a new gradient condition in conjunc-tion with a reduction in analysis time. The sol-vent axis of the solvent composition vs. anal-ysis time graph derived from Table 1, formethanol, acetonitrile and water (Fig. 4) canbe moved in ¢ve equally-spaced intervals of8 min (0, 8, 16, 24 and 32 min) which corre-spond to the ¢ve coded levels of factor 2 speci-

¢ed by the Doehlert design (31, 30.5, 0, 0.5and 1). Fig. 4 shows the new solvent condi-tions (shaded rhombus) when the solvent axisis shifted by 24 min along the time axis. A sum-mary of the experimental conditions obtainedby using the proposed methodology is givenin Table 2. The total analysis times (70, 62, 54,46 and 38 min) result from deducting theequally-spaced intervals of 8 min from the ini-tial analysis time of 70 min.

3.1. Experimental response

The experimental response selected in the anal-ysis of the mixture sample under the conditionsgiven in Table 2 was the peak area of each compo-nent measured at 432 nm. The precision of the chro-matograms was checked by running sample dupli-cates.

4. Results

Fig. 5 shows the chromatograms obtained underthe conditions derived from the methodology pro-posed at 432 nm. A good resolution has been

Fig. 4. New solvent conditions (shaded rhombus) after moving the solvent axis along the analysis time axis by 24 min.

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obtained in the chromatograms run at 70, 62, 54 and46 min. The peaks tend to overlap when 38 minanalysis time is used. Statistical comparisonbetween the peak areas at 62, 54, 46 min andthose obtained at 70 min analysis time revealedthat there is not any signi¢cant difference betweenthem when a t-test was applied at the 95% con¢-dence level. The chromatograms obtained underexperimental conditions 1 and 3 revealed that theresults are independent of the £ow rate rangeselected. The same conclusion can be deducedfrom experimental conditions 6 and 2.

The optimal conditions selected from the resultswere 46 min and 0.57 ml / min, which represent areduction of 34.28% and 43% in analysis time and£ow rate, respectively. Further reduction of 42% inanalysis time and 50% in £ow rate (40 min and 0.5ml / min) were obtained by performing additionalexperiments selected according to the principlesdescribed in the methodology proposed.

The results obtained using the methodology pro-posed, have clearly shown that it is possible to opti-mise systematically and simultaneously the £owrate, the solvent composition and the analysistime without affecting the resolution of the chroma-tograms. Thus the methodology proposed can beconsidered a reliable approach to speed up lengthyseparations, which is quite signi¢cant in routineanalysis.

Fig. 5. Chromatograms obtained after running the sample under the conditions given in Table 2. The numbers represent theexperiment number according to the Doehlert matrix.

Table 2Coded and natural levels for the variables selected in this study

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4.1. Further applications

The proposed methodology was applied in theHPLC separation of orto, meta and para cresol inantiseptic products and polyaromatic hydrocar-bons in synthetic mixtures and reductions of 25%and 34% in analysis time respectively wereachieved. Experimental details of these separationswill be discussed in a paper to be submitted forpublication.

5. Conclusions

The methodology proposed represents an ef¢-cient and easily accomplishable approach to theproblem of reduction of analysis time in lengthyHPLC separations, and enables the analyst to searchfor optimal HPLC chromatographic conditions ofgradient and instrumental /experimental variablesvia experimental design.

Acknowledgements

The author is indebted to Invercanigo for permis-sion to publish this article. I also gratefully acknowl-edge the Analytical Division of Invercanigo Italyand the Venezuela National Supervisory Commit-tee of the IPASME laboratories for their invaluablecollaboration.

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Pedro Araujo is Analytical and Chemometrician Consultant forInvercanigo Division Venezuela. He is currently working asAnalytical Abstractor and Indexer for the Royal Society of Chemistryat 32 Southleigh Road, Clifton, Bristol BS8 2BH, UK. E-mail:Pedro.Araujo@btinternet.com

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