1. 1 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University Strongly correlating liquids and their isomorphs - Simple liquids [van der Waals, metals] - Hidden scale invariance as reflected in the existence of ”isomorphs” - Isomorph invariance: Sorting among non-Arrhenius theories Nicoletta Gnan, Thomas Schrøder, Nick Bailey, Ulf Pedersen, Søren Toxværd, Jeppe Dyre

2. 2 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University Isomorph definition Trivial example: For inverse power-law (IPL) liquids, states with same are isomorphic (with C 12 =1). Main idea: Same potential energy landscape (in temperature scaled units) [arXiv:0905.3497 – JCP (2009)]

3. 3 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University Isomorph properties 1)Isomorphic state points have same excess (configurational) entropy. 2)Isomorphic state points have same (scaled) relaxation time. 3)Isomorphic state points have same (scaled) dynamics. 4)Isomorphic state points have same (scaled) static equilibrium distributions. 5)Isomorphic state points have same... 6)Instantaneous equilibration for jumps between isomorphic state points. 7)A liquid has isomorphs (to a good approximation) if and only if the liquid is strongly correlating, i.e., have strong correlation between equilibrium fluctuations of virial and potential energy.

4. 4 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University Strongly correlating liquids [Pedersen et al., PRL 100, 015701 (2008)]

5. 5 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University Strongly correlating liquids II [J. Chem. Phys. 129, 184507 and 184508 (2008)]

6. 6 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University Results from computer simulations of isomorphs [Kob-Andersen binary Lennard-Jones liquid, arXiv:0905.3497 (2009)]

7. 7 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University Results from computer simulations of isomorphs II [Kob-Andersen binary Lennard-Jones liquid, arXiv:0905.3497 (2009)]

8. 8 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University ”Isochronal superposition” - An isomorph prediction Finding: Whether the relaxation time is increased by decreasing temperature or by increasing pressure, the effect is the same on the spectrum (exception: hydrogen-bonding liquids). See also C. M. Roland, Soft Matter 4, 2316 (2008).

9. 9 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University ITPS example

10. 10 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University Origin of the hidden scale invariance of strongly correlating liquids: ”Extended inverse power-law” (eIPL) potential Strong virial / potential energy correlations are present whenever the potential can be fitted well around first structure peak by Fluctuations are almost not affected by the r-term; thus IPL approximation applies. For details: JCP 129, 184508 (2008); arXiv:0906.0025 (2009).

11. 11 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University Connecting to conventional liquid state theory 1)The melting line is an isomorph. Thus the Lindemann melting criterion must be pressure independent. 2) Rosenfeld’s ”excess entropy scaling” (1977): Transport coefficients (in reduced units) are functions of the excess entropy.

12. 12 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University [Errington, Debenedetti, Torquato, J. Chem. Phys. 118, 2256 (2003)] [Shell, Debenedetti, Panagiotopoulos, Phys. Rev. E 66, 011202 (2002)] BKS silica: Lennard-Jones: Order-parameter maps

13. 13 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University Some conclusions about isomorphs 1)Strongly correlating liquids have ”isomorphs” in their state diagrams, curves along which a number of properties are invariant. 2)The existence of isomorphs reflects a hidden (approximate) scale invariance. Refs: Phys. Rev. Lett. 100, 015701 (2008); Phys. Rev. E 77, 011201 (2008); J. Chem. Phys. 129, 184507 and 184508 (2008) [comprehensive papers]; J. Phys.: Condens. Matter 20, 244113 (2008) [review of the single-parameter scenario] arXiv’s: 0803.2199; 0811.3317; 0812.4960; 0903.2199; 0905.3497; 0906.0025. See poster 7 (Nicoletta Gnan et al.)

14. 14 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University i.e., ”Simple” liquids are the strongly correlating liquids = those with isomorphs in their state diagram Simple: Van der Waals liquids, metallic liquids Complex: Hydrogen-bonding, ionic, covalent liquids

15. 15 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University The isomorph filter Wanted: A theory for the super-Arrhenius temperature dependence IF a universal theory is aimed at, the quantity controlling the relaxation time must be an isomorph invariant.

16. 16 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University Some phenomenological models 1)Adam-Gibbs entropy model: 2)Free-volume model: 3)Energy controlled models: 4)Elastic models: 4a) Shoving model: 4b) MSD version: 4c) Leporini version:

17. 17 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University Applying the filter 1)Adam-Gibbs entropy model: Not isomorph invariant 2)Free-volume model: Not isomorph invariant 3)Energy controlled models: Not isomorph invariant 4)Elastic models: 4a) Shoving model: Isomorph invariant 4b) MSD version: Isomorph invariant 4c) Leporini version: Not isomorph invariant

18. 18 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University Summary - Strongly correlating liquids: van der Waals liquids and metallic liquids (not hydrogen-bonding, ionic, covalent) are simpler than liquids in general These liquids: - have a hidden scale invariance - are “single-parameter liquids” - have isomorphs The isomorph filter allows one to sort among theories for the non-Arrhenius temperature dependence See poster 7 (Nicoletta Gnan et al.) Refs: Phys. Rev. Lett. 100, 015701 (2008); Phys. Rev. E 77, 011201 (2008); J. Chem. Phys. 129, 184507 and 184508 (2008) [comprehensive papers]; J. Phys.: Condens. Matter 20, 244113 (2008) [review of the single-parameter scenario] arXiv’s: 0803.2199; 0811.3317; 0812.4960; 0903.2199; 0905.3497; 0906.0025.

19. 19 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University Single-order-parameter scenario All thermoviscoelastic response functions proportional [JCP 126, 074502 (2007)]

20. 20 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University

21. 21 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University

22. 22 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University

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24. 24 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University

25. 25 Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University