Strongly correlating liquids and their isomorphs

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

2. Isomorph definition [arXiv:0905.3497 – JCP (2009)] Trivial example: For inverse power-law (IPL) liquids, states with same are isomorphic (with C12=1). Main idea: Same potential energy landscape (in temperature scaled units) Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University

3. Isomorph properties • Isomorphic state points have same excess (configurational) entropy. • Isomorphic state points have same (scaled) relaxation time. • Isomorphic state points have same (scaled) dynamics. • Isomorphic state points have same (scaled) static equilibrium distributions. • Isomorphic state points have same ... • Instantaneous equilibration for jumps between isomorphic state points. • 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. Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University

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

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

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

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

8. ”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). Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University

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

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

11. Connecting to conventional liquid state theory • 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. Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University

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

13. Some conclusions about isomorphs • Strongly correlating liquids have ”isomorphs” in their state diagrams, • curves along which a number of properties are invariant. • 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.) Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University

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

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

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

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

18. Summary • Strongly correlating liquids: • van der Waals liquids and metallic liquids • (not hydrogen-bonding, ionic, covalent) • are simpler than liquids in general 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. • 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.) Glass and Time – DNRF Centre for Viscous Liquid Dynamics, Roskilde University

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

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

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

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

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

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

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