Skip to main content
SpringerLink
Log in

Moment Equations for Chromatography Using Superficially Porous Spherical Particles

  • Published:
Analytical Sciences Aims and scope Submit manuscript

Abstract

New moment equations were developed for chromatography using superficially porous (shell-type) spherical particles, which have recently attracted much attention as one of separation media for fast separation with high efficiency. At first, the moment equations of the first absolute and second central moments in the real time domain were derived from the analytical solution in the Laplace domain of a set of basic equations of the general rate model of chromatography, which represent the mass balance, mass-transfer rate, and reaction kinetics in the column packed with shell-type particles. Then, the moment equations were used for analyzing the experimental data of chromatography of kallidin in a Halo column, which were published in a previous paper written by other researchers. It was tried to predict the chromatographic behavior of shell-type particles having different shell thicknesses. The new moment equations are useful for a detailed analysis of the chromatographic behavior of shell-type spherical particles. It is also concluded that they can be used for the preliminarily optimization of their structural characteristics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. Guiochon, S. Golshan-Shirazi, and A. M. Katti, “Fundamentals of Preparative and Nonlinear Chromatography”, 1994, Academic Press, Boston.

    Google Scholar 

  2. J. E. MacNair, K. D. Patel, and J. W. Jorgenson, Anal. Chem., 1999, 71, 700.

    Article  CAS  PubMed  Google Scholar 

  3. J. S. Mellors and J. W. Jorgenson, Anal. Chem., 2004, 76, 5441.

    Article  CAS  PubMed  Google Scholar 

  4. J. R. Mazzeo, U. D. Neue, M. Kele, and R. S. Plumb, Anal. Chem., 2005, 77, 460A.

  5. F. Gritti and G. Guiochon, Anal. Chem., 2008, 80, 5009.

    Article  CAS  PubMed  Google Scholar 

  6. K. Kaczmarski, F. Gritti, and G. Guiochon, J. Chromatogr., A, 2008, 1177, 92.

    Article  CAS  PubMed  Google Scholar 

  7. F. Gritti and G. Guiochon, J. Chromatogr., A, 2008, 1206, 113.

    Article  CAS  PubMed  Google Scholar 

  8. F. Gritti, M. Martin, and G. Guiochon, Anal. Chem., 2009, 81, 3365.

    Article  CAS  PubMed  Google Scholar 

  9. F. Svec and N. Tanaka (ed.), J. Sep. Sci., 2004, 27, 741.

  10. N. Tanaka and F. Svec (ed.), J. Sep. Sci., 2006, 29, 2407.

  11. G. Guiochon, J. Chromatogr., A, 2007, 1168, 101.

    Article  CAS  PubMed  Google Scholar 

  12. J. J. Kirkland, Anal. Chem., 1992, 64, 1239.

    Article  CAS  Google Scholar 

  13. J. J. Kirkland, F. A. Truszkowski, C. H. Dilks Jr., and G. S. Engel, J. Chromatogr., A, 2000, 890, 3.

    Article  CAS  PubMed  Google Scholar 

  14. J. J. Kirkland, F. A. Truszkowski, and R. D. Ricker, J. Chromatogr., A, 2002, 965, 25.

  15. J. J. DeStefano, T. J. Langlois, and J. J. Kirkland, J. Chromatogr. Sci., 2008, 46, 254.

  16. J. C. Giddings, “Dynamics of Chromatography, Part I, Principles and Theory”, 1965, Marcel Dekker, New York.

  17. J. J. van Deemter, F. J. Zuiderweg, and A. Klinkenberg, Chem. Eng. Sci., 1956, 5, 271.

  18. E. Grushka, L. R. Snyder, and J. H. Knox, J. Chromatogr. Sci., 1975, 13, 25.

  19. C. Horváth and H.-J. Lin, J. Chromatogr., 1976, 126, 401.

  20. J. H. Knox, J. Chromatogr. Sci., 1977, 15, 352.

  21. C. Horváth and H.-J. Lin, J. Chromatogr., 1978, 149, 43.

  22. J. H. Knox, Adv. Chromatogr., 1998, 38, 1.

    CAS  Google Scholar 

  23. D. M. Ruthven, “Principles of Adsorption & Adsorption Processes”, 1984, John Wiley and Sons, New York.

  24. M. Suzuki, “Adsorption Engineering”, 1990, Kodansha/Elsevier, Tokyo/Amsterdam.

  25. E. Kucera, J. Chromatogr., 1965, 19, 237.

  26. M. Kubin, Collect. Czech. Chem. Commun., 1965, 30, 2900.

    Article  CAS  Google Scholar 

  27. E. Grushka, M. N. Myers, P. D. Schettler, and J. C. Giddings, Anal. Chem., 1969, 41, 889.

    Article  CAS  Google Scholar 

  28. E. Grushka, J. Phys. Chem., 1972, 76, 2586.

  29. M. Suzuki and J. M. Smith, Chem. Eng. Sci., 1971, 26, 221.

    Article  CAS  Google Scholar 

  30. M. Suzuki and J. M. Smith, Adv. Chromatogr., 1975, 13, 213.

    CAS  Google Scholar 

  31. K. Miyabe and G. Guiochon, Adv. Chromatogr., 2000, 40, 1.

    CAS  PubMed  Google Scholar 

  32. K. Miyabe and G. Guiochon, J. Sep. Sci., 2003, 26, 155.

  33. R. K. Marcus, J. Sep. Sci., 2008, 31, 1923.

  34. K. Miyabe and G. Guiochon, J. Phys. Chem. B, 2002, 106, 8898.

  35. K. Miyabe, A. Cavazzini, F. Gritti, M. Kele, and G. Guiochon, Anal. Chem., 2003, 75, 6975.

    Article  CAS  PubMed  Google Scholar 

  36. K. Miyabe and G. Guiochon, J. Sep. Sci., 2004, 27, 853.

  37. K. Miyabe, Anal. Chem., 2007, 79, 7457.

    Article  CAS  PubMed  Google Scholar 

  38. K. Kaczmarski and G. Guiochon, Anal. Chem., 2007, 79, 4648.

    Article  CAS  PubMed  Google Scholar 

  39. A. Cavazzini, F. Gritti, K. Kaczmarski, N. Marchetti, and G. Guiochon, Anal. Chem., 2007, 79, 5972.

    Article  CAS  PubMed  Google Scholar 

  40. F. Gritti, A. Cavazzini, N. Marchetti, and G. Guiochon, J. Chromatogr., A, 2007, 1157, 289.

  41. K. Miyabe, J. Chromatogr., A, 2008, 1183, 49.

  42. K. Kaczmarski, J. Chromatogr., A, 2011, 1218, 951.

  43. F. Gritti, I. Leonardis, D. Shock, P. Stevenson, A. Shalliker, and G. Guiochon, J. Chromatogr., A, 2010, 1217, 1589.

  44. F. Gritti, I. Leonardis, J. Abia, and G. Guiochon, J. Chromatogr., A, 2010, 1217, 3819.

  45. K. Horváth, F. Gritti, J. N. Fairchild, and G. Guiochon, J. Chromatogr., A, 2010, 1217, 6373.

  46. F. Gritti and G. Guiochon, J. Chromatogr., A, 2010, 1217, 8167.

  47. F. Gritti and G. Guiochon, J. Chromatogr., A, 2011, 1218, 907.

  48. N. Marchetti, A. Cavazzini, F. Gritti, and G. Guiochon, J. Chromatogr., A, 2007, 1163, 203.

  49. F. Gritti and G. Guiochon, J. Chromatogr., A, 2007, 1166, 30.

  50. F. Gritti and G. Guiochon, J. Chromatogr., A, 2007, 1169, 125.

  51. F. Gritti and G. Guiochon, J. Chromatogr., A, 2007, 1176, 107.

  52. N. Marchetti and G. Guiochon, J. Chromatogr., A, 2007, 1176, 206.

  53. F. Gritti and G. Guiochon, J. Chromatogr., A, 2009, 1216, 63.

  54. J. A. Abia, K. S. Mriziq, and G. A. Guiochon, J. Chromatogr., A, 2009, 1216, 3185.

  55. M. E. Young, R. A. Carroad, and R. L. Bell, Biotechnol. Bioeng., 1980, 22, 947.

    Article  CAS  Google Scholar 

  56. C. R. Wilke and P. Chang, AIChE J., 1955, 1, 264.

    Article  CAS  Google Scholar 

  57. R. E. Treybal, “Mass-Transfer Operations”, 1980, McGraw-Hill, New York.

  58. R. C. Reid, J. M. Prausnitz, and B. E. Poling, “The Properties of Gases and Liquids”, 1987, McGraw-Hill, New York.

  59. J. Li and P. W. Carr, Anal. Chem., 1997, 69, 2530.

    Article  CAS  PubMed  Google Scholar 

  60. J. Li and P. W. Carr, Anal. Chem., 1997, 69, 2550.

    Article  CAS  PubMed  Google Scholar 

  61. R. B. Bird, W. E. Stewart, and E. N. Lightfoot, “Transport Phenomena”, 2002, John Wiley & Sons, New York.

  62. E. J. Wilson and C. J. Geankoplis, Ind. Eng. Chem. Fundam., 1966, 5, 9.

  63. J. C. Giddings, Anal. Chem., 1967, 39, 1027.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Science and Engineering for Research, University of Toyama, 3190 Gofuku, Toyama, 930-8555, Japan

    Kanji Miyabe

Authors
  1. Kanji Miyabe
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kanji Miyabe.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Miyabe, K. Moment Equations for Chromatography Using Superficially Porous Spherical Particles. ANAL. SCI. 27, 1007–1017 (2011). https://doi.org/10.2116/analsci.27.1007

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.2116/analsci.27.1007

Search

Navigation