Phase behavior of Methane Clusters from MD Calculations

1. Phase behavior of Methane Clusters from MD Calculations Ana Proykova University of Sofia Gordon Research Conference on Molecular & Ionic Clusters Centre Paul Langevin, Aussois, France September, 7, 2004

2. Interest in: • What is the actual state (liquid or solid) of a nano-sized particle in a contact with a surface? • Charge dependence of the interaction potential Important for Biology (penetration of gases into cells), Green-house effect, clathrates One way to answer these questions is a simulation of clusters of various atoms and molecules, interacting with different potentials

3. Local icosahedral ordering in the liquid phase - Franck • the structure of atomic liquids and glasses has a polytetrahedral arrangement Is it true for molecular systems? Generally – no! Clusters of octahedral molecules pack in solid structures below their freezing point (size dependent)

4. A toy system: molecular clusters made of octahedral molecules

6. Normal modes of CH4 (ignored in our MD) • Stretches [A1+T2] 3215 (A1) 3104 (T2) {cm -1} • Bends [E + T2] 1412 (E) 1380 (T2) {cm -1} • T2 modes IR active • All modes are Raman active • The symmetric C–H stretching mode of the CH4 molecule in water is a single peak at 2910{cm -1}with a half-width of approximately 5 {cm -1} • Octopole moments of CH4 estimated from the T dependence of second virial coefficients 3.7 10-34 esu. cm 3

7. Molecular dynamics simulations at a constant total energy and free cluster surface: velocity Verlet algorithm for solving the classical equations of motion • N - rigid molecules (the lowest frequency 1380 1/cm is much higher than the fastest inter-molecular vibrations < 250 1/cm) • Lennard-Jones (short-range) & Coulomb (long-range) potential – q on the C-atom is negative (0.2 - 1 e)

8. Range of potential and structure • Long-range – highly strained, highly coordinated, spherical structures : no regular packing. For large size – liquid-like inherent structure • Intermediate ranges – icosahedral structures are dominant • Short – range – decahedral • Very short – fcc structure dominates

9. Potential energy surface ‘seen’ by a CH4 molecule – aligned CH4-dimer

10. A cluster of 50 molecules at 10 K: shell-like structure with vibrating molecules

12. 55 CH4 molecule cluster at 10 K

13. Evaporation of a methane molecule: a 59 cluster at 60 K

14. Phase Diagram • High temperature phase: molecular axes are random, rotational and translational diffusion • Low temperature phase: rotational (librational) diffusion • ΔT = |Ttr.p – Tcr.p |→ 0 for N≤50

15. Numerical diagnostics Radial distribution function Lindemann criterion Normal modes analysis – diagonalization of Hessian

16. The lowest energy starting configuration (no kinetic energy) of a 55-molecule cluster is the icosahedron

17. Radial distribution functions (RDF) for selected structures: ‘real’ indicates the RDF for a 55 molecule cluster at 10 K

18. 10 K The most important pattern is the double peak at 4 A:the nearest neighbors form 'anti-aligned 1' dimers

19. 25 K Higher temperature: no doublet; shell-like structure

20. Double charge: the doublet shrinks into a single peak for all temperatures studied 10 K

21. What new? • The most important finding in this study is that dimers of molecules with a specific mutual anti-ferro orientation play an important role in cluster ordering at low temperatures. This result – not expected for rigid, globular-like molecules – is probably due to the angular dependence of the interaction.

23. Increase of melting temperature for larger charges • Same in octahedral molecules

24. Team • Dr. R. Radev (currently, financial company) • Mr. S. Pisov(U of Sofia – Ass. Prof.) • Ms. E. Daykova(U of Sofia – PhD student) • Mr. H. Iliev(U of Sofia – PhD student)

25. Acknowledgements • NFS – Bulgaria • U of Sofia – Scientific Grants • European Commission grants for mobility • Resources (EPCC, TRACS) • Discussions with R.S. Berry (U of Chicago)

26. Thank you for listening and the Chairs of this meeting for selecting the topic