Techniques for the automated optimization of HPLC separations

Ire&in analytical&em&y, vol. 3, no. I, I984

deeply-held views which are rooted in science. Whether this final qualification still permits the optimism I expressed is a question that I leave to the reader.

References

1 Ure, A. (1835) The Philosophy of Manufactures p. 368, Charles Knight, London 2 Taylor, F. W. (1947) The Principles of Scientzjic Management, reprinted in Scientz& Management pp. 25-26, Harper and Row, London

Techniques

5 3 Friedmann, G. (1950) 09 va le Travail Hirmain? p. 344, Gallimard, Paris 4 Braverman, H. (1974) Labour and Monopob Capital, Monthly Review Press, London 5 Haraszty, M. (1977) A Worker in a Worker’s State Penguin Books, West Drayton, UK 6 Freigenbaum, E. A. (1979) in Expert Systems in the Microelectronic Age (Michie, D. ed.), p. 3, Edinburgh University Press, Edinburgh Professor Rosenbrock is at the Control Systems Centre, UMIST, P.O. Box 88, Manchester M60 lQD, UK.

for the automated HPLC separations

optimization

of

The availability of computer controlled HPLC instrumentation has enabled more systematic approaches to be taken to the optimization of chromatographic separations. Many of these approaches are suitable for automated applications. John C. Berridge The optimization of the plate number N, i.e. the Sandwich, Kent, UK HPLC is now firmly established as a reliable and versatile analytical tool for the separation and quantitation of mixtures soluble in liquids. There is a wide variety of modern commercially available instruments which completely satisfjr the requirements of most routine analytical and semi-preparative separations. It is, however, the development of the separation which is usually the most difficult and time-consuming task that faces the chromatographer. With the advent of the low cost microcomputer which can be directly interfaced with a modern chromatograph, the era of trial and error experimentation is now drawing to a close. A growing number of systematic schemes for the optimization of separation are being described in the literature and many of these are suitable for automated applications.

efficiency of the chromatographic separation, has been comprehensively discussed in the literaturel-‘. The value ofk’ is controlled by the eluting power, or solvent strength, of the mobile phase and optimum k’ values generally lie in the range l-10. It is the optimization of (Yvalues, i.e. the selectivity of the separation, which is the major problem. Having decided upon the column type and the instrumental configuration to be used, the greatest effort is then spent optimizing the composition of the mobile phase until a separation of adequate specificity is achieved. The selection of the mobile phase composition has traditionally been carried out by trial and error, but this is steadily being replaced by more formal optimization strategies based on, for example, chemometric techniques4 or on semi-empirical models. Many of these strategies have been, or can easily be applied to the on-line optimization of HPLC separations.

The basic problem The objective of any separation development is to separate the samples of interest within a reasonable analysis time. Separation between peaks on a chromatogram is usually expressed in terms of the resolution R, where R can be related to the variables controlling the separation as shown in equation 1’. R=f(a--

1)fi

( > *j+

where k ’ is the average value of the capacity factors k ‘1 and k’z of two adjacent peaks 1 and 2, cx is the separation factor (k ‘l/k ‘2) and N is the column plate number. For most practical purposes the three terms of the above equation may be optimized separately. 0165.9936/84/WZ.CXl.

Initial requirements There are three essential requirements which must be met by hardware (i.e. the chromatograph plus computer controller) and software (i.e. the computer program) before the totally automated optimization of HPLC separations can be achieved. l The optimization scheme chosen must direct the optimization of the interdependent variables which affect the chromatographic processes in an efficient and reliable way. l Each completed chromatogram must be able to be evaluated in terms of the resolutions that have been achieved and the time the separation has taken: it may also be necessary to identify each peak by reference to a set of standards. 0 1964 Elsevier Science Publishers B.V.

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trends in analytical chemistry, vol. 3, no. 1: 1984

There should be comprehensive, two-way communication between all units of the chromatograph and the computer controller. The computer, having accessed the chromatographic data to calculate resolutions and separation time and having calculated a new set of experimental conditions, must be able to set up these the next conditions and automatically initiate experiment.

l

TABLE

I. Mobile

phase blend ratios defining Experiment

a 7 experiment

set

numbers

Relative proportion of organic modifier

MeOH MeCN THF

1

2

3

4

5

6

7

1 0 0

0 1 0

0 0 1

0.5 0.5 0

0 0.5 0.5

0.5 0 0.5

0.33 0.33 0.33

Semi-empirical models The first steps towards automated optimization were taken when commercial instruments became available that could be pre-programmed to carry out a series of isocratic separations in which the mobile phase was modified slightly between each run. This timeconsuming approach is unnecessary, since a very rapid and easily automated procedure is now available which will often yield a good estimate ofthe required isocratic, binary, mobile phase for reversed-phase separations’. A gradient elution programme using water and methanol is run first and this is used to predict the appropriate isocratic mobile phase. It will often be the case, however, that a methanol-water mobile phase does not provide adequate specificity for all the solutes and it will then be necessary to investigate the different selectivities offered by alternative organic modifiers. Until recently there has not been a rational approach to the adjustment of selectivity, but the classification of solvents into a ‘solvent selectivity triangle’ by Snyder’ has provided a major step forward (Fig. 1). The solvent selectivity triangle for reversed-phase separations indicates that maximum selectivity differences will result from the use of methanol, acetonitrile Proton acceptor

Proton donor

Dipole4ipole

Fig. 1. Solvent selectivity triangle for reversed-phase (and normal phase) separations. Water and hexane are used to adjust the solvent strength for reversed-phase and normal phase separations. The comers of the triangle represent binary mixes with equal solvent strength (isoelutropic). Seven experiments carried out at the comers, at th mid-points of the sides and at the trinngle centre will thus explore the maximum selectivity range.

and tetrahydrofuran as organic modifiers. There are simple equations’.’ which allow the substitution of one organic modifier for another, while keeping the solvent strength constant for the average solute. Thus, selectivity changes can be explored while average retention times are kept approximately constant. There are further selectivity advantages to be gained by using mixtures of organic modifiers. If it is the case, as has been proposed’, that ternary mobile phases can provide all the required selectivity, then the method described by Schoenmakers et al.’ can be automated to provide a rapid procedure for optimizing such mixtures. Following the determination ofthe necessary solvent strength from a water-methanol gradient elution run, two equal solvent strength binary mixtures are selected. The capacity factors ofthe solutes are then determined using these two mobile phases. It is now assumed that the logarithm of the individual capacity factors will vary linearly with respect to the composition of mixtures of the two equal strength mobile phases. By considering a suitable optimization criterion, such as the product of resolution factors of adjacent peaks, it is possible to predict an optimum ternary solvent composition (Fig. 2). Initial failure of the procedure will occur when there are major deviations in the linearity of capacity factor dependence upon composition. However, the additional data acquired from the investigation of a separation at the predicted optimum composition can be used to provide a better estimate of the true optimum composition, should that predicted composition not provide an adequate separation. For maximum effectiveness this procedure requires that components are identified in successive chromatograms and, while considerable progress has been made in the automation ofthe procedure”, totally unattended optimization has not been reported to date. Probably the ultimate development of the solvent selectivity triangle approach for reversed-phase separations, the use of tertiary mixtures, has been fully automated and is incorporated as software in a commercially available instrument *. Again, the first step is to run a linear water-methanol gradient to determine the requisite solvent strength. A statistical simplex design of seven experiments (Table I) is then carried out” with equal eluting power mobile phases consisting of up to four components. The solvent *‘Sentinel System’, Du Pont trademark chromatography system.

for automated

predictive

liquid

tnndi in anal$ical ChemisQ, lwl. 3, no. I, 1984

7

3 4,s.

60

45

Me OH

MeCN

2

8 min

8 min

3

k’ IO 24

MeOH

27

MeCN

/

4

MeOH w

0 8-

MeCN

8 min .

03

Fig. 2. Steps in the developmentof a reoersed+se separation’: (a) se+ztion using MeOHIHIo 60:40, (b) sejaration using MeCNlHsO 45:55, (c) phase sekction diagram: the optimMI ternary compoJitMnis the bknd of the two binav mixes specijied at the maximumoff(R), (d) sejaration using predictedoptinrum comjosition. Mixture of aromatic phenols and esters separated using a 4 cm column@cked with 5 pan ODS packing:Jow rate 1 ml min-?

8

trends in analytical chmist~,

vol. 3, no. i, 1984

strength is determined by the amount ofwater present. Ideally, standard solutions are also chromatographed under each of the seven experimental conditions and, while this considerably extends the time required to complete the procedure, each component in the seven chromatograms can then be identified. Where standards are not available visual inspection will usually permit a suitable composition to be deduced, but where the complete retention data are available they can be plotted (by computer) as an ‘overlapping resolution map’ (Ref. 7) to precisely predict the optimum mobile phase. In the case of normal phase chromatography the use of an analogous solvent-selectivity triangle provides a similar rational basis for the variation of selectivity12. Normal phase separations are complicated by solute-solvent and solvent-specific localization effects at the silica surface which make automated optimization more difficult using the triangle approach. Nevertheless, there is little doubt that computer software will become available to automate the optimization of normal phase separations, particularly as a more complete understanding of the factors controlling selectivity is gained. varlame i

Chemometric approaches As defined by the Chemometrics Society: ‘Chemometrics is a chemical discipline that uses mathematical and statistical methods (a) to design or select optimal measurement procedures and experiments; and (b) to provide maximum chemical information by analysing chemical data’ (Refs 4 and 13). While the semi-empirical models discussed above obviously embrace some aspects of chemometrics,

Fig. 3. ‘Window diagram’for Ref. 15 with the permission

separation of 10 acids. Reprinted from of the American Chemical Society.

Fig. 4. Two variable simplex optimizations. Dotted lines are response lines, 0 is optimum response ‘9 ABC is initial simplex and D is a new point obtained by reflection of worst point (B).

alternative options to automated HPLC separation optimization are the more general, experimental, optimization techniques.

Window diagrams Originally developed for the selection of mixed stationary phases in gas chromatography, the ‘window diagram’ technique has been shown to be useful in the optimization of HPLC separations14. It is suitable for on-line optimization, although real-time applications have still to be reported. The window diagram technique, as a general optimization strategy, is applicable to the optimization of any HPLC variable. An example of the technique is shown as Fig. 3, which shows a window diagram resulting from the optimization of the separation of five weak acids, where the variable considered was pH. The diagram is produced by plotting the relative retentions for all 10 pairs ofacids against a function ofthe mobile phase pH. The shaded areas, or windows, indicate conditions where separation of peak pairs occurs: the tops of the windows represent conditions where the best separation of the worst separated pair can be achieved. In Fig. 3 the optimum separation occurs at [BMHBI = 0.54. However, the tops of the other windows should not be ignored since they also indicate conditions which may give an adequate separation and which may be preferred for other reasons, such as analysis time. Thus, the window diagram technique is, for one experimental variable, a simple computer compatible

trena3

&

analytical

chemists,

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3, no. I, 1!2?4

strategy which will provide the chromatographer with a global set of optima (the windows) from which the optimum experimental conditions may be chosen. The technique should be of use in most cases in which dependent variables are to be optimized with respect to one or more independent variables15. Unfortunately, in HPLC method development, there are many interdependent variables to be considered. This, coupled with the complexity of producing (and visualizing) multidimensional window diagrams, may restrict the ultimate development of this otherwise elegant approach.

3 4 A

The ‘Sequential Simplex’ method Most HPLC method development, as well as considering many interdependent experimental variables, is carried out against a background of other experimental constraints. For example, an adequate resolution may need to be coupled with a specific time for analysis and an optimum flow rate. In addition, the separation may require gradient elution or control of pH or ion-pair concentration to achieve adequate selectivity. Fortunately, there is a general, multidimensional, optimization strategy which is simple to operate and ideally suited to the optimization of the many interdependent variables occurring in HPLC. The sequential simplex procedure”*” contains one of the most efficient multidimensional, sequential search algorithms for locating an experimental optimum. It has been applied successfully in a wide variety of analytical situationsl*. A simplex is defined as a geometrical figure described by one more point than the number of variables being optimized. Thus, for two variables the simplex will be a triangle, and each of the three vertices corresponds to particular values of the variables at which an experiment is conducted. Moves are made by rejecting the vertex which gives the worst experimental response and reflecting the triangle across the line joining the other two points (Fig. 4) until an optimum is located. This is a very simplified representation of the basic simplex method: there are several rules which are used to ensure moves are made in the correct directions and to ensure that simplexes do not get stuck. The basic procedure is rather inflexible and a more practical version is the ‘modified simplex procedure’ (Ref. 19) where the simplex size is expanded or contracted depending on the relative value of the new result. While higher dimensional optimization problems cannot be represented graphically they are easily handled by computer. The modified simplex procedure has been successfully used for manual optimization of HPLC separations20%21 and, more recently, for the totally automated, real-time optimization of a wide variety of types of HPLC separations22-24. An essential requirement ofthe simplex procedure in HPLC is to have a single response which reflects the quality ofthe separation. This is readily achieved using a Chromatographic Response Function (CRF)20*22*25. The CRF provides a numerical description of the

i

c 0

I

I

I

2

4

6

1

8 min

Fig. 5. Separation of j&wls optimized using TERNOPT with a 7 minute time constraint. Optimum mobile phase MeOH-MeCN-H20,21:27:52.

% Water

Fig. 6. Movements of simplexes during optimization. The initial simplex is ABC: because reflections would exceed the boundary conditions the simplex size is contracted. Contraction and rejlection continue until the optimum is located at a composition of apfioximate~ 50% water and 20% methanol, the remaining30 % being acetonitrile. Figs 5 and 6 were reprinted from Ref. 23 with permission of Elsevier Science Publishers B.V.

quality of a separation which may then be used as the value of the experimental response in the simplex procedure. While the chromatographer is free to design any CRF appropriate for a particular need, a most successful form to date for automated optimization is22:

10

trena!sin analytical chemistry, ml. 3, no.‘], 1984

CRF = 2

Ri +fl(L)

+fi(T.~ - 7’1,) -tf3(T1

- T,,)

i=l

where R is the resolution between adjacent peak pairs and L is the number of peaks detected. TA is a specified analysis time, TL is the retention time of the last eluted peak, TI is the retention time ofthe first eluted peak and To is a specified minimum elution time; all time units are expressed in minutes. This form of the CRF provides the chromatographer with a simple, but extremely flexible means of assigning priorities to various aspects of the separation; for example, speed may be more important than resolution. The ability to quantifir the quality of a separation and to search for a maximum value of this multi-criteria quality provides a powerful means for optimizing all types of HPLC separations. Early applications of the simplex procedure required the intervention of the chromatographer to set new experimental conditions, but the complete automation of the procedure has been reported recently22. Programs for a commercially available microcomputer controlled chromatograph have been written which will optimize isocratic two and three component mobile elution conditions. phases and gradient Both reversed-phase22*23 and normal phase2* separations may be optimized. Fig. 5 shows an example of a reversed-phase separation automatically optimized using a three component mobile phase22 and Fig. 6 shows the movements of the simplexes which occurred during the optimization: convergence on the optimum is rapid and direct. No optimization procedure is without its problems. The simplex procedure can be hampered by noise, but the major problem common to most general optimization procedures is that a local, rather than a global optimum may be located. For example, if the elution order of three components A, B and C changes there will be a local optimum for the order ABC and one for the order BAC. It may, however, be that the elution order at the global optimum is CBA. Alternatively, a local optimum may produce a separation where there is still peak overlap which cannot be recognized by the chromatograph integrator or data system. It has recently been shown that using the resolution enhancement techniques of differentiation2* the chances of the optimization procedure halting at a local optimum can be reduced.

Conclusions - the future The advent of low cost, microcomputer-controlled HPLC systems has enabled the goal of totally automated separation optimization to be realized. There is already a diverse range of schemes of potential and proven ability from which the chromatographer may choose. While it may be dangerous to look too far into the future there is no doubt that interest in this area will increase greatly. Extensions of the overlapping resolution mapping approach will include the automatic selection of the column stationary phase26

which will undoubtedly also be included in chemometric approaches. The generality of chemometric techniques means that they will be applied to multiparameter optimization of many different types of separations. It is unlikely to be many years before the goal of totally automated method development is achieved.

References

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Snyder, L. R. and Kirkland, J. J. (1979) Introduction to Modern Liquid Chromatography, 2nd edn, Wiley, New York Kaiser, R. E. and Oelrich, E. (1981) Optimisation in HPLC, Verlag, Heidelberg Halasz, I. and Gorlitz, G. (1982) Ang. Chem. Znt. Ed. 21, 50 Kowalski, B. R. (1981) Trends Anal. Chem. 1, 71 Schoenmakers, P. J., Billet, H. A. and de Galan, L. (1981) J. Chromatogr. 205, 13 Snyder, L. R. (1978)J. Chromatogr. Sci. 16, 223 Glajch, J. L., Kirkland, J. J., Squire, K. M. and Minor, J. M. (1980) J. Chromatogr. 199, 57 Jandera, P., Churacek, J. and Colin, H. (1981) J. Chromatogr. 214, 35 Schoenmakers, P. J., Drouen, A. C. J. H., Billet, H. A. and de Galan, L. (1981) Chromatographia 15, 688 Drouen, A. C. J. H., Billet, H. A. H., Schoenmakers, P. J. and de Galan, L. (1982) Chromatographia 16, 48 Lehrer, R. (1981) Am. Lab. (Fairfield) 13, 113 Glajch, J. L., Kirkland, J. J. and Snyder, L. R. (1982) J. Chromatogr. 238, 262 Vandeginste, B. G. M. (1982) Trends Anal. Ck. 1, 210 Deming, S. N. and Turoff, M. L. H. (1978) Anal. Chem. 50,546 Laub, R. J. (1981) Znt. Lab. 11, 16 Spendley, W., Hext, G. R. and Himsworth, F. R. (1962) Technornetrics4, 441 Deming, S. N. and Morgan, S. L. (1973) Anal. Chem. 45,278A Deming, S. N. and Parker, L. R. (1978) Crit. Rev. Anal. Chem. 7, 187 Nelder, J. A. and Mead, R. (1965) Comput. J. 7, 308 Watson, M. W. and Carr, P. W. (1979) Anal. Chem. 51, 1835 Fast, D. M., Culbreth, P. H. and Sampson, E. J. (1982) Clin. Chem. 28, 444 Berridge, J. C. (1982) J. Chromatogr. 244, 1 Bet-ridge, J. C. (1982) Anal. Proc. 19, 472 Bet-ridge, J. C. (1982) Chromatographia 16, 172 Wegscheider, W., Lankmayr, E. P. and Budna, K. W. (1982) Chromatographia 15, 498 Kirkland, J. J., Glajch, J. L. and Charikofsky, J. G. (1982) 183rd American Chemical Society Meeting, Las Vegas, paper 134, American Chemical Society, Washington DC

Dr John C. Benidge is at Pfizer, Central Research, Sandwich, Kent, CT13 SNJ, UK. LETTERS TO TrAC

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