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MULTIDIMENSIONAL CHROMATOGRAPHY

This document provides an overview of multidimensional chromatography (MDCH), focusing on its principles and measurement challenges. It addresses topics such as uncertainty, information content, peak capacity, and measurement descriptors. Key issues highlighted include extremely high numbers of isomers, low concentrations, and missing standards, along with the limitations imposed by existing hardware. Additionally, the work explores the effects of temperature programming, probability of peak overlaps, and the integration of various chromatographic techniques, contributing to a comprehensive understanding of MDCH methodologies and their practical implications.

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MULTIDIMENSIONAL CHROMATOGRAPHY

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  1. MULTIDIMENSIONALCHROMATOGRAPHY Jiří ŠEVČÍK Prague, the Czech Republic MDCH-GENERAL

  2. ABOUT • UNCERTAINTY • MULTIDIMENSIONALITY • INFORMATION CONTENT • MULTIDIMENSIONAL HW MDCH-GENERAL

  3. PROBLEMS of measurements • residual error of a complex response model MDCH-GENERAL

  4. extremly high number of isomers low concentration levels missing - standards - generally valid QSPR models limited hardware possibilities PROBLEMS of measurements MDCH-GENERAL

  5. DESCRIPTORS of measurement MDCH-GENERAL

  6. what is ULTIMATE UNCERTAINTY complementarity causality ultimate uncertainty probability MDCH-GENERAL

  7. EXPRESSING UU • for one-dimensional system MDCH-GENERAL

  8. EXPRESSING UU • UU is determined by system efficiency (for one-dimensional system) MDCH-GENERAL

  9. PROBABILITY of the retention position • x position • lmean component density x MDCH-GENERAL

  10. PROBABILITY of the difference in the retention position • x0difference • asaturation factor of sep space X x0 t1 t2 MDCH-GENERAL

  11. PEAK CAPACITY • nc peak capacity • asaturation factor of sep space X x0 t1 t2 MDCH-GENERAL

  12. PEAK CAPACITYin isothermal mode • peak width = (a+btx) x0 t1 t2 MDCH-GENERAL

  13. PEAK CAPACITYin a linear temperature program mode • peak width = (a) x0 t1 t2 MDCH-GENERAL

  14. PEAK CAPACITYcomparison of operation modes MDCH-GENERAL

  15. PROBABILITY of peak overlapping • n compounds inx0 x0 t1 t2 MDCH-GENERAL

  16. PROBABILITY of peak clusters overlapping • pn number of clusters with the same number of compounds x0 t1 t2 MDCH-GENERAL

  17. CLUSTERS (n-tets) in one-dimensional chromatography MDCH-GENERAL

  18. WHAT isthe chromatographicdimension • chromatography (a constant value of KD) • switching (a straight inlet-separation-detector) MDCH-GENERAL

  19. WHAT ismultidimensional • chromatography (within one run changes of KD for the same analyte) • switching (within one run multiplication of any part of trajectory inlet-separation-detector) MDCH-GENERAL

  20. WHAT ishyphenation • can be multi-d-chromatography (HPLC-GC) • can be multi-d-switching (FID-MS) • interface of different techniques MDCH-GENERAL

  21. PEAK CLUSTERS in multidimesional chromatography • pn number of clusters with the same number of compounds KD3 KD2 KD1 MDCH-GENERAL

  22. PEAK CAPACITY in multidimesional chromatography • nc(d) maximum number of separated peaks KD3 KD2 KD1 MDCH-GENERAL

  23. RELATIVE PEAK DENSITY in multidimensional chromatography MDCH-GENERAL

  24. WHAT isthe information content • uncertainty (entropy) prior to an experiment and after it • probability that some input and output events will happen MDCH-GENERAL

  25. WHAT isthe information content • input P(Ii) prior to an experiment - there is an analyte i • output P(Ok) after the experiment – there will be a measurable signal (larger than LOD) • conditional probability MDCH-GENERAL

  26. CONDITIONAL PROBABILITIES • P(Ok/Ii) there will be the output - measurable signal larger than LOD when there will be the analyte i as the input • P(Ii/Ok) there will be the analyte i as the input when there will be the output - measurable signal larger than LOD MDCH-GENERAL

  27. PROBABILITIES in chromatography output/input relation aposteriory probability output prob m k 1 P(Ok/Ii) P(Ii/Ok) m k 1 P(Ok) apriori probability 1 i n 1 1 P(Ii) 1 i n MDCH-GENERAL

  28. UNCERTAINTY (ENTROPY) of • a priori status H(I) prior to an analysis • a posteriori status H(I/Ok) after the signal Ok has been measured • a posteriori status H(I/O) after the analysis has been performed MDCH-GENERAL

  29. UNCERTAINTY (ENTROPY) of • a priori status H(I) prior to an analysis MDCH-GENERAL

  30. UNCERTAINTY (ENTROPY) of a posteriori status H(I/Ok) after the signal Ok has been measured MDCH-GENERAL

  31. UNCERTAINTY (ENTROPY) of • a posteriori status H(I/O) after the analysis has been performed MDCH-GENERAL

  32. INFORMATION CONTENT • the difference between uncertainties before and after the analysis has been carried out multidimensional MDCH-GENERAL

  33. INFORMATION CONTENTways of quantification • integration • assumption of the normal distribution of the data and of the measuring error • a histogram • an approach based on maximum peak capacity • an approach based on real peak capacity MDCH-GENERAL

  34. QUANTIFICATIONusing peak capacity • separation system configuration(efficiency, selectivity, operational modes) • sample composition(number of compounds, chromatographic similiarities and overlap) MDCH-GENERAL

  35. INFORMATION CONTENTin multidimensional chromatography MDCH-GENERAL

  36. INFORMATION based GC INSTRUMENTATION • multidimensional column systems IF (RIA)i= a THEN (RIA)k= c AND (RIA)k= d • hyphenated techniques P(SA)k <<>> P(SB)k • expert systems lim Σ(ε)i= 0 MDCH-GENERAL

  37. multidimensional chromatographySYSTEMS serial parallel KD1 <> KD2 <> KDd MDCH-GENERAL

  38. multidimensional chromatographySERIAL SYSTEMS recycle comprehensive tandem MDCH-GENERAL

  39. SWITCHING MODESin multidimensional chromatography MDCH-GENERAL

  40. PROCESS OF IDENTIFICATION • matching actual found pattern with true one - peak identification (noise reduction, integration, deconvolution) - peak correlation (similarity link) - analyte identification (match with standards) • redundant information content MDCH-GENERAL

  41. MS-SIM separation of GC non separated isomers MDCH-GENERAL

  42. FUTURE INSTRUMENTATION • principle of additivity of partial probabilities MDCH-GENERAL

  43. FUTURE INSTRUMENTATION • HW miniaturization • SW deconvolution routines multidimensional statistics MDCH-GENERAL

  44. ABOUT • UNCERTAINTY • MULTIDIMENSIONALITY • INFORMATION CONTENT • MULTIDIMENSIONAL HW MDCH-GENERAL

  45. . MULTIDIMENSIONAL chromatography is the analytical approach to the Bohr principle of complementarity. MDCH-GENERAL

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