Skip to main content
Log in

Spatial correlations of interatomic voids in molecular liquids studied using Delaunay simplices

  • Published:
Journal of Structural Chemistry Aims and scope Submit manuscript

Abstract

Pair correlation functions are calculated for interatomic voids determined using Delaunay simplices. Various modifications of these functions are suggested in relation to the problem formulated. In the simplest case, this correlator is a conventional radial distribution function g(r), but its calculation employs the centers of voids, but not the centers of atoms. For analysis of nonuniform systems, it is suggested that a “weighted” radial distribution function be used, where pair distances are taken with weights that depend on the volume of the voids. To study structural differences between molecular liquids (e.g., alkane isomers) we use the partial radial distribution functions that take into account only relatively “wide” voids. The ion-void distance distribution functions define voids in the hydration shells of ions an aqueous salts.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. B. Bokii, Crystal Chemistry [in Russian], Moscow State University, Moscow (1960).

    Google Scholar 

  2. R. W. G. Wyckoff, Crystal Structures, Vol. 1, Wiley, New York (1963).

    Google Scholar 

  3. J. L. Finney and J. Wallace, J. Non-Cryst. Solids, 43, 165–180 (1981).

    Article  CAS  Google Scholar 

  4. M. Wilson and P. A. Madden, Phys. Rev. Lett., 80, 532–535 (1998).

    Article  CAS  Google Scholar 

  5. M. Wilson, P. A. Madden, N. N. Medvedev, et al., J. Chem. Soc., Faraday Trans., 94, No. 3, 1221 (1998).

    Article  CAS  Google Scholar 

  6. V. P. Voloshin, S. Beaufils, and N. N. Medvedev, J. Mol. Liq., 96/97, 101–112 (2002).

    Article  Google Scholar 

  7. G. F. Voronoi, Studies of Primitive Parallelohedra [in Russian], A Collection of Papers, Vol. 2, Ukrainian SSR Academy of Sciences, Kiev (1952).

    Google Scholar 

  8. B. N. Delaunay, Petersburg School of Number Theory [in Russian], USSR Academy of Sciences, Moscow (1947), pp. 196–316.

    Google Scholar 

  9. A. Okabe, B. Boots, K. Sugihara, and S. N. Chiu, Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, Wiley, Chichester (2000).

    Google Scholar 

  10. N. N. Medvedev, Voronoi-Delaunay Method in Structural Studies of Noncrystalline Systems [in Russian], Siberian Division, Russian Academy of Sciences, Novosibirsk (2000).

    Google Scholar 

  11. N. N. Medvedev, Dokl. Ross. Akad. Nauk, 337, No. 6, 767–771 (1994).

    CAS  Google Scholar 

  12. M. G. Alinchenko, A. V. Anikeenko, N. N. Medvedev, et al., J. Phys. Chem. B, 108, 19056–19067 (2004).

    Article  CAS  Google Scholar 

  13. N. N. Medvedev, Voronoi’s Impact on Modern Science, Book 2, P. Engel and H. Syta (eds.), Inst. Math., Kiev (1998), pp. 164–175.

    Google Scholar 

  14. A. V. Anikeenko, M. G. Alinchenko, V. P. Voloshin, et al., LNCS, 3045, 217–226 (2004).

    Google Scholar 

  15. V. P. Voloshin and N. N. Medvedev, Zh. Strukt. Khim., 46, No. 1, 96–100; 101–105 (2005).

    Google Scholar 

  16. C. Beisbart, M. Kerscher, and K. Mecke, Mark Correlation: Relating Physical Properties to Spatial Distributions, in: Morphology of Condensed Matter, K. Macke and D. Stoyan (eds.), Springer, Heidelberg (2002).

    Google Scholar 

  17. C. Ferradini and J.-P. Jay-Gerin (eds.), Excess Electrons in Dielectric Media, CRC Press, London (1991).

    Google Scholar 

  18. W. F. Schmidt, Liquid State. Electronics of Insulating Liquids, CRC Press, New York (1997).

    Google Scholar 

  19. M. G. Martin and J. I. Siepmann, J. Phys. Chem., B102, 2569–2575 (1998).

    Google Scholar 

  20. M. G. Martin and J. I. Siepmann, ibid., B103, 4508–4515 (1999).

    Google Scholar 

  21. D. Paschek and A. Geiger, ibid., 4139–4148.

  22. A. V. Anikeenko, Yu. I. Naberukhin, N. N. Medvedev, et al., Radial Distribution of Voids around Ions in Water, 6th Liquid Matter Conference, 2–6 July, Utrecht, p. 202.

  23. O. Ya. Samoilov, Structure of Aqueous Solutions of Electrolytes and Ion Hydration [in Russian], USSR Academy of Sciences, Moscow (1957).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text Copyright © 2006 by M. G. Alinchenko, A. V. Anikeenko, V. P. Voloshin, N. N. Medvedev, D. Paschek, A. Appelhagen, and A. Geiger

__________

Translated from Zhurnal Strukturnoi Khimii, Vol. 47, Supplement, pp. S122–S128.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alinchenko, M.G., Anikeenko, A.V., Voloshin, V.P. et al. Spatial correlations of interatomic voids in molecular liquids studied using Delaunay simplices. J Struct Chem 47 (Suppl 1), S119–S125 (2006). https://doi.org/10.1007/s10947-006-0386-5

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10947-006-0386-5

Keywords

Navigation