Skip to main content

Vapor nucleation paths in lyophobic nanopores


In recent years, technologies revolving around the use of lyophobic nanopores gained considerable attention in both fundamental and applied research. Owing to the enormous internal surface area, heterogeneous lyophobic systems (HLS), constituted by a nanoporous lyophobic material and a non-wetting liquid, are promising candidates for the efficient storage or dissipation of mechanical energy. These diverse applications both rely on the forced intrusion and extrusion of the non-wetting liquid inside the pores; the behavior of HLS for storage or dissipation depends on the hysteresis between these two processes, which, in turn, are determined by the microscopic details of the system. It is easy to understand that molecular simulations provide an unmatched tool for understanding phenomena at these scales. In this contribution we use advanced atomistic simulation techniques in order to study the nucleation of vapor bubbles inside lyophobic mesopores. The use of the string method in collective variables allows us to overcome the computational challenges associated with the activated nature of the phenomenon, rendering a detailed picture of nucleation in confinement. In particular, this rare event method efficiently searches for the most probable nucleation path(s) in otherwise intractable, high-dimensional free-energy landscapes. Results reveal the existence of several independent nucleation paths associated with different free-energy barriers. In particular, there is a family of asymmetric transition paths, in which a bubble forms at one of the walls; the other family involves the formation of axisymmetric bubbles with an annulus shape. The computed free-energy profiles reveal that the asymmetric path is significantly more probable than the symmetric one, while the exact position where the asymmetric bubble forms is less relevant for the free energetics of the process. A comparison of the atomistic results with continuum models is also presented, showing how, for simple liquids in mesoporous materials of characteristic size of ca. 4nm, the nanoscale effects reported for smaller pores have a minor role. The atomistic estimates for the nucleation free-energy barrier are in qualitative accord with those that can be obtained using a macroscopic, capillary-based nucleation theory.

Graphical abstract


  1. 1

    V. Eroshenko, R.-C. Regis, M. Soulard, J. Patarin, J. Am. Chem. Soc. 123, 8129 (2001)

    Article  Google Scholar 

  2. 2

    L. Guillemot, T. Biben, A. Galarneau, G. Vigier, É. Charlaix, Proc. Natl. Acad. Sci. U.S.A. 109, 19557 (2012)

    ADS  Article  Google Scholar 

  3. 3

    Y. Grosu, M. Li, Y.-L. Peng, D. Luo, D. Li, A. Faik, J.-M. Nedelec, J.-P. Grolier, ChemPhysChem 17, 3359 (2016)

    Article  Google Scholar 

  4. 4

    B. Lefevre, A. Saugey, J.-L. Barrat, L. Bocquet, E. Charlaix, P.-F. Gobin, G. Vigier, J. Chem. Phys. 120, 4927 (2004)

    ADS  Article  Google Scholar 

  5. 5

    R. Helmy, Y. Kazakevich, C. Ni, A.Y. Fadeev, J. Am. Chem. Soc. 127, 12446 (2005)

    Article  Google Scholar 

  6. 6

    R. Allen, S. Melchionna, J.-P. Hansen, Phys. Rev. Lett. 89, 175502 (2002)

    ADS  Article  Google Scholar 

  7. 7

    J. Russo, S. Melchionna, F. De Luca, C. Casieri, Phys. Rev. B 76, 195403 (2007)

    ADS  Article  Google Scholar 

  8. 8

    A. Tinti, A. Giacomello, Y. Grosu, C.M. Casciola, Proc. Natl. Acad. Sci. U.S.A. 114, E10266 (2017)

    ADS  Article  Google Scholar 

  9. 9

    S. Bonella, S. Meloni, G. Ciccotti, Eur. Phys. J. B 85, 97 (2012)

    ADS  Article  Google Scholar 

  10. 10

    L. Maragliano, A. Fischer, E. Vanden-Eijnden, G. Ciccotti, J. Chem. Phys. 125, 024106 (2006)

    ADS  Article  Google Scholar 

  11. 11

    A. Laio, A. Rodriguez-Fortea, F.L. Gervasio, M. Ceccarelli, M. Parrinello, J. Phys. Chem. B 109, 6714 (2005)

    Article  Google Scholar 

  12. 12

    S. Meloni, A. Giacomello, C.M. Casciola, J. Chem. Phys. 145, 211802 (2016)

    ADS  Article  Google Scholar 

  13. 13

    M. Amabili, A. Giacomello, S. Meloni, C. Casciola, Phys. Rev. Fluids 2, 034202 (2017)

    ADS  Article  Google Scholar 

  14. 14

    E. Lisi, A. Tinti, A. Giacomello, Cavitation in confinement: a classical nucleation theory approach, in Proceedings of the XXIII Conference of the Italian Association of Theoretical and Applied Mechanics, 2017 (Gechi Edizioni, 2017) pp. 136--146

  15. 15

    J.L. Abascal, C. Vega, J. Chem. Phys. 123, 234505 (2005)

    ADS  Article  Google Scholar 

  16. 16

    G.J. Martyna, M.L. Klein, M. Tuckerman, J. Chem. Phys. 97, 2635 (1992)

    ADS  Article  Google Scholar 

  17. 17

    S. Marchio, S. Meloni, A. Giacomello, C. Valeriani, C. Casciola, J. Chem. Phys. 148, 064706 (2018)

    ADS  Article  Google Scholar 

  18. 18

    S. Plimpton, J. Comput. Phys. 117, 1 (1995)

    ADS  Article  Google Scholar 

  19. 19

    W. E, W. Ren, E. Vanden-Eijnden, J. Chem. Phys. 126, 164103 (2007)

    ADS  Article  Google Scholar 

  20. 20

    E. Vanden-Eijnden, Transition path theory, in Computer Simulations in Condensed Matter Systems: From Materials to Chemical Biology, Volume 1, Lecture Notes in Physics, Vol. 703 (Springer, Berlin, Heidelberg, 2006) pp. 453--493

  21. 21

    L. Maragliano, E. Vanden-Eijnden, Chem. Phys. Lett. 426, 168 (2006)

    ADS  Article  Google Scholar 

  22. 22

    M. Amabili, A. Giacomello, S. Meloni, C.M. Casciola, J. Phys.: Condens. Matter 29, 014003 (2016)

    ADS  Google Scholar 

  23. 23

    A. Giacomello, S. Meloni, M. Chinappi, C.M. Casciola, Langmuir 28, 10764 (2012)

    Article  Google Scholar 

  24. 24

    A. Giacomello, S. Meloni, M. Müller, C.M. Casciola, J. Chem. Phys. 142, 104701 (2015)

    ADS  Article  Google Scholar 

  25. 25

    J.R. Panter, H. Kusumaatmaja, J. Phys.: Condens. Matter 29, 084001 (2017)

    ADS  Google Scholar 

  26. 26

    A. Giacomello, L. Schimmele, S. Dietrich, Proc. Natl. Acad. Sci. U.S.A. 113, E262 (2016)

    ADS  Article  Google Scholar 

  27. 27

    R.J. Allen, C. Valeriani, P.R. ten Wolde, J. Phys.: Condens. Matter 21, 463102 (2009)

    Google Scholar 

  28. 28

    A. Giacomello, M. Chinappi, S. Meloni, C.M. Casciola, Phys. Rev. Lett. 109, 226102 (2012)

    ADS  Article  Google Scholar 

  29. 29

    M. Amabili, S. Meloni, A. Giacomello, C.M. Casciola, J. Phys. Chem. B 122, 200 (2017)

    Article  Google Scholar 

  30. 30

    E. Lisi, M. Amabili, S. Meloni, A. Giacomello, C.M. Casciola, ACS Nano 12, 359 (2018)

    Article  Google Scholar 

Download references


Open Access funding provided by Max Planck Society.

Author information



Corresponding author

Correspondence to Antonio Tinti.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Tinti, A., Giacomello, A. & Casciola, C.M. Vapor nucleation paths in lyophobic nanopores. Eur. Phys. J. E 41, 52 (2018).

Download citation


  • Topical issue: Advances in Computational Methods for Soft Matter Systems