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? 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 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 the structure of atomic liquids and glasses has a polytetrahedral arrangement has a polytetrahedral arrangement Is it true for molecular systems? 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 } Stretches [A1+T2] 3215 (A1) 3104 (T2) {cm -1 } Bends [E + T2] 1412 (E) 1380 (T2) {cm -1 } Bends [E + T2] 1412 (E) 1380 (T2) {cm -1 } T2 modes IR active T2 modes IR active All modes are Raman active All modes are Raman active {cm -1 }{cm -1 } 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 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) 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) 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 Long-range – highly strained, highly coordinated, spherical structures : no regular packing. For large size – liquid-like inherent structure Intermediate ranges – icosahedral structures are dominant Intermediate ranges – icosahedral structures are dominant Short – range – decahedral Short – range – decahedral Very short – fcc structure dominates 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 High temperature phase: molecular axes are random, rotational and translational diffusion Low temperature phase: rotational (librational) diffusion Low temperature phase: rotational (librational) diffusion ΔT = |T tr.p – T cr.p | → 0 for N≤50 ΔT = |T tr.p – T cr.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. The most important pattern is the double peak at 4 A: the nearest neighbors form 'anti-aligned 1' dimers 10 K

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

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. 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. 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 Same in octahedral molecules

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

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

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