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Modelling chromatographic behaviour as a function of pH and solvent composition in RPLC

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Summary

In this work we establish the basic layout of IONICS, an expert system for optimizing the separation of ionogenic solutes in Reversed-Phase Liquid Chromatography, using the pH and the organic-modifier concentration of the mobile phase as parameters. We also present REMO, a front-end system that automates the retention modelling stage, based on a 9-parameter model. This system uses a scale transformation to suppress several numerical problems previously observed and features a strategy for automatic calculation of an initial approximation to the model optimum. The successful application of this system to a set of seven drugs is described. The final models are accurate and have smaller numerical problems. We also describe the use of a genetic algorithm instead of classical non-linear least-squares for fitting the model to the experimental data. Results indicate that genetic algorithms are a valuable, complementary tool for retention modelling.

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Abbreviations

Φ:

constant that, for an experimental design with three equally spaced levels of organic-modifier content, is the value of the middle level.

ε:

constant that, for an experimental design with three equally spaced levels of organic-modifier content, is the reciprocal of the difference between two successive levels.

ϕ:

fraction of organic modifier in the mobile phase

ϕ:

rescaled fraction of organic-modifier content of the mobile phase. For a given experimental design with three equally spaced levels of organic-modifier content, ϕ takes the values −1, 0 and +1 at the minimum, central, and maximum levels.

GA:

genetic algorithm (an optimization algorithm based on special operators that mimic evolutionary techniques)

k:

observed capacity factor

k0 :

capacity factor of neutral species

k 00 :

capacity factor of neutral species in pure water

k Φ0 :

capacity factor of neutral species in a water/organic-modifier mixture, with 100 Φ% organic-modifier

k−1 :

capacity factor of negatively charged species

k 0−1 :

capacity factor of negatively charged species in pure water

k Φ−1 :

capacity factor of negatively charged species in a water/organic-modifier mixture, with 100 Φ% organic-modifier

k1 :

capacity factor of positively charged species

K 0a :

acidity constant of a monoprotic acid HA in pure water

N:

neutral solute

NLLS:

non-linear least-squares optimization algorithm

Q1, Q2 :

second and third coefficients, respectively, of a polynomial model for ln Ka as a function of the fraction of organic modifier (constant pH)

Q Φ1 , Q Φ2 :

second and third coefficients, respectively, of a polynomial model for ln Ka as a function of ϕ, the rescaled fraction of organic modifier (constant pH)

rp :

degree of ionization of a solute at a pH value of p

SA:

strongly acidic solute

SB:

strongly basic solute

Si :

second coefficient of a polynomial model for ln ki as a function of the fraction of organic modifier (constant pH)

S Φi :

second coefficient of a polynomial model for ln ki as a function of ϕ, the rescaled fraction of organic modifier (constant pH)

SSQ:

sum of squares of the differences between calculated and observed values.

Ti :

third coefficient of a polynomial model for ln ki as a function of the fraction of organic modifier (constant pH)

T Φi :

third coefficient of a polynomial model for ln ki as a function of ϕ, the rescaled fraction of organic modifier (constant pH)

t0 :

hold-up time

WA:

weakly acidic solute

WB:

weakly basic solute

References

  1. P. J. Schoenmakers, Optimization of Chromatographic Selectivity. A Guide to Method Development, Elsevier, Amsterdam, 1986.

    Google Scholar 

  2. L. R. Snyder, J. L. Glajch, J. J. Kirkland, Practical HPLC Method Development, Wiley, New York, 1988.

    Google Scholar 

  3. R. M. Lopes Marques, P. J. Schoenmakers, J. Chromatogr.,592, 157 (1992).

    Google Scholar 

  4. P. J. Schoenmakers, S. v. Molle, C. M. G. Hayes, L. G. M. Uunk, Anal. Chim. Acta,250, 1 (1991).

    Google Scholar 

  5. P. J. Schoenmakers, N. Mackie, R. M. Lopes Marques, Optimizing Separations in Reversed-Phase Liquid Chromatography, Chromatographia (1992) in print.

  6. J. C. Berridge, Chemometrics & Intell. Lab. Syst.,3, 175 (1988).

    Google Scholar 

  7. C. K. Bayne, I. B. Rubin, Practical Experimental Designs and Optimization Methods for Chemists, VCH Publishers, Deerfield Beach, Florida, 1986.

    Google Scholar 

  8. G. K. C. Low, A. Bartha, H. A. H. Billiet, L. de Galan, J. Chromatogr.,478, 21 (1989).

    Google Scholar 

  9. P. J. Schoenmakers, H. A. H. Billiet, L. de Galan, J. Chromatogr.,205, 13 (1981).

    Google Scholar 

  10. H. A. H. Billiet, L. de Galan, J. Chromatogr.,485, 27 (1989).

    Google Scholar 

  11. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Reading, Massachussets, 1989.

    Google Scholar 

  12. D. H. Ackley, A Connectionist Machine for Genetic Hillclimbing, Kluwer Academic Publishers, Norwell, Massachussets, 1987.

    Google Scholar 

  13. D. E. Rumelhart, J. L. McClelland, Parallel distributed processing, MIT, Cambridge, Massachussets, 1986.

    Google Scholar 

  14. C. B. Lucasius, M. J. J. Blommers, L. M. C. Buydens, G. Kateman, A Genetic Algorithm for Conformational Analysis of DNA, in L. Davis, ed., The Handbook of Genetic Algorithms, Van Nostrum-Reinhold, 1991.

  15. C. B. Lucasius, G. Kateman, Applications of Genetic Algorithms in Chemometrics, in J. D. Schaffer, ed., Third Int. Conf. on Genetic Algorithms, Morgan Kaufmann, 1989.

  16. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes. The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986.

    Google Scholar 

  17. R. M. Lopes Marques, P. J. Schoenmakers, Proc. 13th. Meeting Port. Chem. Soc., Lisbon, Portugal, 1991.

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Author notes

  1. P. J. Schoenmakers

    Present address: Department AG, Royal Dutch/Shell Laboratory, Badhuisweg 3, 1031 CM, Amsterdam, The Netherlands

Authors and Affiliations

  1. Departamento de Química, Centro de Tecnologia Química e Biológica, 2780, Oeiras, Portugal

    R. M. Lopes Marques

  2. Philips Research, P.O. Box 80000, 5600 JA, Eindhoven, The Netherlands

    P. J. Schoenmakers

  3. Catholic University of Nijmegen, Toernooiveld 1, 6525 ED, Nijmegen, The Netherlands

    C. B. Lucasius & L. Buyden

Authors
  1. R. M. Lopes Marques
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  2. P. J. Schoenmakers
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  3. C. B. Lucasius
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  4. L. Buyden
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Lopes Marques, R.M., Schoenmakers, P.J., Lucasius, C.B. et al. Modelling chromatographic behaviour as a function of pH and solvent composition in RPLC. Chromatographia 36, 83–95 (1993). https://doi.org/10.1007/BF02263843

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  • DOI: https://doi.org/10.1007/BF02263843

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