The phonon theory of liquid matter

Transcription

1 Barcelona, 2012 The phonon theory of liquid matter Dima Bolmatov Queen Mary University of London

2 Kostya Trachenko Dima Bolmatov Vadim Brazhkin

3 Plan Introduction The phonon theory of liquids Results: theory vs experiment Current and future work

4 States of Matter: gases, solids, liquids Gases: energy of ideal monatomic gas, small interactions E=3/2NT+P, k_b=1 Solids: P. Debye's phonon theory, small displacements E=E_0+E_harm+E_anharm Liquids: neither Lev Landau: liquids have no small parameter (no expansion is possible). Landau&Lifshitz, Statistical Physics: Interactions in a liquid are both strong and system-specific Liquid energy can not be calculated in general!

5 Energy and heat capacity of matter A. Granato, J. Non-Cryst. Sol , 376 (2002) Gases: E_gas=3/2NT, k_b=1 Solids: E_solid=3NT, k_b=1, in classical limit Dulong Petit law Liquids: E_liquid=?

6 Liquid heat capacity? can not be done in general form (L. D. Landau and E. M. Lifshitz, Statistical Physics,1964) Over the last 30 years, liquid heat capacity is not mentioned in popular books about liquids: J. M. Ziman, Models of Disorder, Cambridge University Press, Cambridge, J. P. Boon and S. Yip, Molecular Hydrodynamics, Dover, New York, N. H. March, Liquid Metals, Cambridge University Press, Cambridge, R. Zwanzig, Non-Equlibrium Statistical Mechanics, Oxford University Press, J. P. Hansen and I. R. McDonald, Theory of Simple Liquids, Elsevier, New York, 2007.

7 Facts melting point D Wallace, Phys. Rev. E (1998) The same behaviour is seen in complex liquids

8 Two approaches to liquid energy From the gas phase, by switching on interactions in a gas (L&L argument): E=3NT/2+U(r) The exact results exist only for small densities and high temperatures that describe interacting gases, but not real liquids. CVan Der Vaals=CIdeal gas Virial expansions do not work for real dense liquids: vn/v 1 (Allen&Tildesley) For simple models (hard spheres, LJ systems etc), analytical results agree with MD simulations, but still depend on parameters and correlation functions Require knowledge of multiple correlation functions and interatomic potentials, calculations are difficult and approximations are hard to control Correlation functions (especially higher-order) and interatomic potentials are not available beyond very simple liquids (Ar, Xe and LJ-type liquids) RESULT: Not easy to see how CV=3N at low temperature and CV=2N at high temperature

9 Two approaches to liquid energy From the solid phase: Take strong interactions into account from the outset: E=3NT + (?) Brillouin, classical case: Esolid=3NT=NT/2+NT/2+2(NT/2+NT/2). Eliquid=NT+2(NT/2)=2NT, in disagreement with experiments. Led to assume the existence of small crystalline domains with easy cleavage directions J Frenkel: introduced relaxation time τ.

10 Local relaxation events Dynamics in viscous liquids: rattling motion inside cages plus large atomic jumps with cage relaxation. These thermally excited jumps give liquid flow Liquid is a solid for times smaller than τ! Frenkel proposed that liquids support transverse phonons with frequency ω>1/τ High-frequency transverse modes widely observed in liquids experimentally We took up this approach and accounted for the phonon energy

11 The phonon theory of liquids Virial theorem: or Debye function

12 Heat capacity (cv=de/dt ): theory vs experiment

13 Heat capacity (cv=de/dt ): theory vs experiment

14 Heat capacity (cv=de/dt ): theory vs experiment

15 Heat capacity (cv=de/dt ): theory vs experiment

16 Quantum liquids: Helium, P=45 MPa

17 Quantum liquids: Hydrogen, P=50 MPa

18 Quantum liquids: Parahydrogen, P=120 MPa

19 Complex liquids Chloropentafluoroethane (R115)

20 Complex liquids Trifluoromethane (R23)

21 Universal behaviour of liquids near critical point

22 Universal behaviour of liquids near critical point

23 Universal behaviour of liquids near critical point

24 Current and future work Calculation liquid energies and heat capacities of quantum exotic liquids: Hydrogen, Parahydrogen and Helium; organics: Octafluorocyclobutane, Octafluoropropane, Hexafluoroethane, Chloropentafluoroethane and etc. Analytical expression of c_v for 2->3/2 regime. Connection the dynamics (phonon states) and structure (gas phase approach) of liquids: numerical calculations, MD simulations. Description of liquids at microscopic level: spontaneously breaking symmetry, Goldstone excitations and etc. Liquids in confined and restricted geometries.

25 Thank you!