Skip to main content
Log in

Relevance and Assessment of Molecular Diffusion Coefficients in Liquid Chromatography

  • Review
  • Published:
Chromatographia Aims and scope Submit manuscript

Abstract

Molecular diffusion plays an important role in high-performance liquid chromatography, especially in fundamental column performance studies. An accurate knowledge of the molecular diffusion coefficients (D m) of compounds selected for column evaluation is therefore crucial. In this review, a general overview is presented of the advantages and drawbacks of correlation-based and experimental methods that can be employed to determine molecular diffusion coefficients. The former include the Wilke–Chang, Scheibel, Reddy–Doraiswamy, Lusis–Ratcliff and Hayduk–Laudie equations, and other empirical correlations based on the Wilke–Chang equation. It is discussed how the association factor (ψ) that is required in several of these correlations can be obtained from the solubility parameter (δ). Frequently used experimental methods include the light scattering, nuclear magnetic resonance, peak parking and Taylor–Aris method, and methods employing microfluidic devices. The principles of these experimental methods are elucidated in detail. Moreover, the influence of several parameters, such as solute characteristics, solvent viscosity, temperature and pressure on the molecular diffusion coefficient is described.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1

Figure reprinted with permission from [8]

Fig. 2
Fig. 3

Figure reprinted with permission from [40]

Fig. 4

Figure reprinted with permission from [41]

Similar content being viewed by others

References

  1. Poling EB, Prausnitz JM, O′Connell JP (1987) The properties of gases and liquids. McGraw-Hill Education, New York

    Google Scholar 

  2. Karaiskakis G, Gavril D (2004) J Chromatogr A 1037:147–189

    Article  CAS  Google Scholar 

  3. Northrop JH, Anson ML (1929) J Gen Physiol 12:543–554

    Article  CAS  Google Scholar 

  4. Dullien FAL (1958) Reconsideration of the diaphragm cell method of measuring diffusion coefficients. The University of British Columbia, Canada

    Google Scholar 

  5. Song H, Desmet G, Cabooter D (2015) Anal Chem 87:12331–12339

    Article  CAS  Google Scholar 

  6. Sitaraman R, Ibrahim SH, Kuloor NR (1963) J Chem Eng Data 8:198–201

    Article  CAS  Google Scholar 

  7. Wilke CR, Chang P (1955) AIChE J 1:264–270

    Article  CAS  Google Scholar 

  8. Li J, Carr PW (1997) Anal Chem 69:2530–2536

    Article  CAS  Google Scholar 

  9. Reddy KA, Doraiswamy LK (1967) Ind Eng Chem Fund 6:77–79

    Article  CAS  Google Scholar 

  10. Hayduk W, Minhas BS (1982) Can J Chem Eng 60:295–299

    Article  CAS  Google Scholar 

  11. Miyabe K (2011) J Sep Sci 34:2674–2679

    Article  CAS  Google Scholar 

  12. Miyabe K, Isogai R (2011) J Chromatogr A 1218:6639–6645

    Article  CAS  Google Scholar 

  13. Edward JT (1970) J Chem Educ 47:261–270

    Article  CAS  Google Scholar 

  14. Miyabe K, Isogai R (2013) Anal Sci 29:467–472

    Article  CAS  Google Scholar 

  15. Scheibel EG (1954) Ind Eng Chem 46:2007–2008

    Article  CAS  Google Scholar 

  16. Lusis MA, Ratcliff CA (1968) Can J Chem Eng 46:385–387

    Article  CAS  Google Scholar 

  17. Hayduk W, Laudie H (1974) AIChE J 20:611–615

    Article  CAS  Google Scholar 

  18. Othmer DF, Thakar MS (1953) Ind Eng Chem 45:589–593

    Article  CAS  Google Scholar 

  19. King CJ, Hsueh L, Mao K-W (1965) J Chem Eng Data 10:348–350

    Article  CAS  Google Scholar 

  20. Heinisch S, Desmet G, Clicq D, Rocca J-L (2008) J Chromatogr A 1203:124–136

    Article  CAS  Google Scholar 

  21. Liekens A, Denayer J, Desmet G (2011) J Chromatogr A 1218:4406–4416

    Article  CAS  Google Scholar 

  22. Vanderheyden Y, Cabooter D, Desmet G, Broeckhoven K (2013) J Chromatogr A 1312:80–86

    Article  CAS  Google Scholar 

  23. Cabooter D, Decrop W, Eeltink S, Swart R, Ursem M, Lestremau F, Desmet G (2010) Anal Chem 82:1054–1065

    Article  CAS  Google Scholar 

  24. Li J, Carr PW (1997) Anal Chem 69:2550–2553

    Article  CAS  Google Scholar 

  25. Leahy DE (1986) J Pharm Sci 75:629–636

    Article  CAS  Google Scholar 

  26. Bondi A (1964) J Phys Chem 68:441–451

    Article  CAS  Google Scholar 

  27. Abraham MH, McGowan JC (1987) Chromatographia 23:243–246

    Article  CAS  Google Scholar 

  28. Reid RC, Prausnitz JM, Sherwood TK (1977) The properties of gases and liquids. McGraw-Hill, New York

    Google Scholar 

  29. Olander DR (1961) AIChE J 7:175–176

    Article  CAS  Google Scholar 

  30. Hayduk W, Cheng SC (1971) Chem Eng Sci 26:635–646

    Article  CAS  Google Scholar 

  31. Atwood JG, Goldstein J (1984) J Phys Chem 88:1875–1885

    Article  CAS  Google Scholar 

  32. Czworniak KJ, Andersen HC, Pecora R (1975) Chem Phys 11:451–473

    Article  CAS  Google Scholar 

  33. Krahn W, Schweiger G, Lucas K (1983) J Phys Chem 87:4515–4519

    Article  CAS  Google Scholar 

  34. Rusu D, Genoe D, van Puyvelde P, Peuvrel-Disdier E, Navard P, Fuller GG (1999) Polymer 40:1353–1357

    Article  CAS  Google Scholar 

  35. Carr HY, Purcell EM (1954) Phys Rev 94:630–638

    Article  CAS  Google Scholar 

  36. Stejskal EO, Tanner JE (1965) J Chem Phys 42:288–292

    Article  CAS  Google Scholar 

  37. Cohen Y, Avram L, Frish L (2005) Angew Chem In Ed 44:520–554

    Article  CAS  Google Scholar 

  38. Miyabe K, Matsumoto Y, Ando N (2009) Jap Soci Anal Chem 25:211–218

    CAS  Google Scholar 

  39. Kobayashi H, Tokuda D, Ichimaru J, Ikegami T, Miyabe K, Tanaka N (2006) J Chromatogr A 1109:2–9

    Article  CAS  Google Scholar 

  40. Miyabe K, Ando N, Guiochon G (2009) J Chromatogr A 1216:4377–4382

    Article  CAS  Google Scholar 

  41. Kamholz AE, Weigl BH, Finlayson BA, Yager P (1999) Anal Chem 71:5340–5347

    Article  CAS  Google Scholar 

  42. Culbertson CT, Jacobson SC (2002) Michael Ramsey. J Talanta 56:365–373

    Article  CAS  Google Scholar 

  43. Broboana D (2011) Mihai Balan C, Wohland T, Balan C. Chem Eng Sci 66:1962–1972

    Article  CAS  Google Scholar 

  44. Häusler E, Domagalski P, Ottens M, Bardow A (2012) Chem Eng Sci 72:45–50

    Article  Google Scholar 

  45. Miložič N, Lubej M, Novak U, Žnidaršič-Plazl P, Plazl I (2014) Chem Biochem Eng Q 28:215–223

    Article  Google Scholar 

  46. Fröba AP, Leipertz A (2005) Diffusion fundamentals, vol 2, pp 63.1–63.25

  47. Gulari E, Brown RJ, Pings CJ (1973) AIChE J 19:1196–1204

    Article  CAS  Google Scholar 

  48. Corti M, Degiorgio V (1975) J Phys C Sol Sta Phys 8:953–960

    Article  CAS  Google Scholar 

  49. Sitkowski J, Bednarek E, Bocian W, Kozerski L (2008) J Med Chem 51:7663–7665

    Article  CAS  Google Scholar 

  50. Bocian W, Kawęcki R, Bednarek E, Sitkowski J, Williamson MP, Hansen PE, Kozerski L (2008) Chem Eur J 14:2788–2794

    Article  CAS  Google Scholar 

  51. Knox JH, McLaren L (1964) Anal Chem 36:1477–1482

    Article  CAS  Google Scholar 

  52. Miyabe K, Matsumoto Y, Guiochon G (2007) Anal Chem 79:1970–1982

    Article  CAS  Google Scholar 

  53. McCoy BJ, Moffat AJ (1986) Chem Eng Commun 47:219–224

    Article  CAS  Google Scholar 

  54. Aris R (1956) Proc R Soc A 235:67–77

    Article  Google Scholar 

  55. Taylor G (1953) Proc R Soc A 219:186–203

    Article  CAS  Google Scholar 

  56. Gritti F, Shiner SJ, Fairchild JN, Guiochon G (2014) J Chromatogr A 1334:30–43

    Article  CAS  Google Scholar 

  57. Janssen LAM (1976) Chem Eng Sci 31:215–218

    Article  CAS  Google Scholar 

  58. Kong CY, Watanabe K, Funazukuri T (2013) J Chromatogr A 1279:92–97

    Article  CAS  Google Scholar 

  59. Lin R, Tavlarides LL (2010) J Chromatogr A 1217:4454–4462

    Article  CAS  Google Scholar 

  60. d’Orlye F, Varenne A, Gareil P (2008) J Chromatogr A 1204:226–232

    Article  Google Scholar 

  61. Song H, Vanderheyden Y, Adams E, Desmet G, Cabooter D (2016) J Chromatogr A 1455:102–112

    Article  CAS  Google Scholar 

  62. Chakraborty D, Bose N, Sasmal S, Dasgupta S, Maiti TK, Chakraborty S, DasGupta S (2012) Anal Chim Acta 710:88–93

    Article  CAS  Google Scholar 

  63. Kamholz AE, Schilling EA, Yager P (2001) Biophys J 80:1967–1972

    Article  CAS  Google Scholar 

  64. Brody JP, Yager P (1997) Sens Actuators, A 58:13–18

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Deirdre Cabooter.

Ethics declarations

Funding

Huiying Song greatly acknowledges the Chinese Scholarship Council for funding (grant number 201207040025).

Conflict of interest

The authors declare no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Published in the topical collection Young Investigators in Separation Science with editors D. Mangelings, G. Massolini, G. K. E. Scriba, R. M. Smith and A. M. Striegel.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Song, H., Cabooter, D. Relevance and Assessment of Molecular Diffusion Coefficients in Liquid Chromatography. Chromatographia 80, 651–663 (2017). https://doi.org/10.1007/s10337-016-3204-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10337-016-3204-z

Keywords

Navigation