Dias nummer 1
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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
1
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
2
Isomorph properties
1)
2)
3)
4)
5)
6)
7)
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
3
Strongly correlating liquids
R
WU
(W ) 2 (U ) 2
[Pedersen et al., PRL 100, 015701 (2008)]
Glass and Time – DNRF Centre for Viscous Liquid Dynamics,
Roskilde University
4
Strongly correlating liquids II
[J. Chem. Phys. 129, 184507 and 184508 (2008)]
Glass and Time – DNRF Centre for Viscous Liquid Dynamics,
Roskilde University
5
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
6
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
7
”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
8
ITPS example
Glass and Time – DNRF Centre for Viscous Liquid Dynamics,
Roskilde University
9
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
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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.
Glass and Time – DNRF Centre for Viscous Liquid Dynamics,
Roskilde University
11
Order-parameter maps
Lennard-Jones:
[Errington, Debenedetti, Torquato,
J. Chem. Phys. 118, 2256 (2003)]
BKS silica:
[Shell, Debenedetti, Panagiotopoulos,
Phys. Rev. E 66, 011202 (2002)]
Glass and Time – DNRF Centre for Viscous Liquid Dynamics,
Roskilde University
12
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.)
Glass and Time – DNRF Centre for Viscous Liquid Dynamics,
Roskilde University
13
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
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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
15
Some phenomenological models
1) Adam-Gibbs entropy model:
0 exp(B / v f )
2) Free-volume model:
3) Energy controlled models:
4) Elastic models:
4a) Shoving model:
4b) MSD version:
0 exp(A / TSC )
0 exp((E0 E ) / kBT )
0 exp(VcG / kBT )
0 exp( 2 / 3 / u 2 )
4c) Leporini version:
0 F (a2 / u 2 )
Glass and Time – DNRF Centre for Viscous Liquid Dynamics,
Roskilde University
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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
Glass and Time – DNRF Centre for Viscous Liquid Dynamics,
Roskilde University
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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
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.
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
18
Single-order-parameter scenario
s(t ) 1 (t ) J11T (t ) J12p(t )
v(t ) 2 (t ) J 21T (t ) J 22 p(t )
All thermoviscoelastic response functions proportional [JCP 126, 074502 (2007)]
Glass and Time – DNRF Centre for Viscous Liquid Dynamics,
Roskilde University
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Glass and Time – DNRF Centre for Viscous Liquid Dynamics,
Roskilde University
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Glass and Time – DNRF Centre for Viscous Liquid Dynamics,
Roskilde University
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pV Nk BT W
Glass and Time – DNRF Centre for Viscous Liquid Dynamics,
Roskilde University
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Glass and Time – DNRF Centre for Viscous Liquid Dynamics,
Roskilde University
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Glass and Time – DNRF Centre for Viscous Liquid Dynamics,
Roskilde University
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Glass and Time – DNRF Centre for Viscous Liquid Dynamics,
Roskilde University
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