Modeling the configurational entropy of supercooled liquids and a resolution of the Kauzmann paradox

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1 Modeling the configurational entropy of supercooled liquids and a resolution of the Kauzmann paradox Dmitry Matyushov Arizona State University Glass and Entropy II, Aberystwyth, April, 2009

2 activated events Chemistry: Glass science: Entropy paradigm: configurational entropy locked in the cooperative regions of Adam and Gibbs, entropic droplet, etc. Rationale: Question: Temperature is low, events happen infrequently (same in chemistry?) Does the success of AG equation imply the success of the paradigm (does configurational entropy drive activated transitions)? Or, maybe, this all occurs in the dynamics only (Garrahan & Chandler)?

3 entropies Observation: Excess and configurational entropies often work equally well in fitting AG relation Need: Models producing both excess and configurational entropies (very few)

4 computer models vs laboratory experiment Is that only the vibrational component that makes the difference? I other words: Do available computer models describe fragile glass formers?

5 ...back to entropies Common configurational entropy : Stillinger s configurational entropy (in fact definition of the basin vibrational free energy): Gaussian model: Observation: Question: The behavior of the Gaussian enumeration function is incorrect in the low temperature limit near the Kauzmann temperature Can we obtain a non Gaussian enumeration function with the expected asymptote?

6 low temperature dipolar hard spheres Stell s Pade solution: Inverse Laplace: P(e) is the distribution of energies e It is nearly Gaussian, but with the width scaling approximately linearly with T It is virtually impossible to see non Gaussian distribution by looking at P(e), the underlying non Gaussian landscape reflects itself in the temperature dependence of the width!

7 inherent structures vs energies First transition: Fluid of oppositely oriented and randomly displaced dipolar chains Second transition: Smectic phase PRE, 76 (2007)

8 liquid liquid transition: the resolution of the Kauzmann paradox Kauzmann temperature is zero in the analytical model The in silico fluid loses thermodynamic stability at approaching the state of zero configurational entropy transforming into a different liquid through a first order phase transition.

9 phenomenology of excitations Excitations characterized by energy and entropy Projecting real space on configuration space: x is the population of the excited state, This is seen for computer glass formers!

10 thermodynamics of excitations Weiss theory of ferromagnetism! When the second terms is dominant, one gets a 1/T decrease of the configurational entropy and a 1/T scaling of the configurational heat capacity. This is the case of fragile liquids! Criticality and a mean field first order transition must be parts of the model!

11 performance against experiment Fragile liquids are found to universally have a first order liquid liquid transition below T g and above T K (dipolar hard spheres!). JCP 126 (2007)

12 correlation between parameters The reduced excitation parameters satisfy the relations (fragile liquids only): Entropy of excitations appears as the only parameter describing fragility.

13 dynamics of excitations Dynamical events occur through infrequently created hot regions of excitations which themselves do not contribute much to the thermodynamics of the liquid. JCP 126 (2007)

14 relaxation time

15 comparison to dielectric data

16 more mysteries (water) Fitting the data to the excitations model gives weak first order transition for water confined in nanopores.

17 nanoconfined water at water/protein interface (MD simulations) Fluctuations of the electrostatic potential at protein s active site show a weak first order singularity. It mostly comes from water, while protein motions are slaved to water mobility. PRE, 78 (2008)

18 conclusions Enumeration function is non Gaussian in its wing close to the point of ideal glass > distribution of inherent structures gains T dependence (width) > 1/T scaling of the configurational/excess heat capacity. Excitations model yields non Gaussian landscape and predicts a LL transition below T g. Fragile liquids differ from strong liquids by an order of magnitude larger width of excitation energies. Equation for the relaxation time can be derived based on the excitations model that involves the configurational heat capacity instead of configurational entropy of the Adam Gibbs theory.