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How Mysterious is the Mysterious Glass How Mysterious is the Mysterious Glass Transition?Transition?
Itamar Procaccia
The Weizmann Institute of Science
Weizmann Institute: Einat Aharonov, Eran Bouchbinder, Valery Ilyin, Edan Lerner, Ting-Shek Lo, Natalya Makedonska, Ido Regev and Nurith Schupper .
Emory University: George Hentschel
Leiden, August 25 2008
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Glass phenomenology
The three common conceptes: jamming, Vogel-Fulcher, Kauzmann
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A very popular model: a 50-50 binary mixture of particles interacting via soft repulsion potential
With ratio of `diameters’ 1.4
Simulations: both Monte Carlo and Molecular Dynamics with 4096 particles enclosed in an area L x L with periodic boundary conditions. We ran
simulations at a chosen temperature, fixed volume and fixed N. The units of mass, length, time and temperature are
Previous work (lots): Deng, Argon and Yip, P. Harrowell et al, etc: for T>0.5 the system is a “fluid”; for T smaller - dynamical
relaxation slows down considerably.
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QuickTime™ and a decompressor
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The conclusion was that “defects” do not show any ‘singular’ behaviour , so they were discarded as a diagnostic tool .
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The liquid like defects disappear at the glass transition!
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For temperature > 0.8
For 0.3 < T < 0.8
Associated with the disappearance of liquid like defects there is an increase of typical scale
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Rigorous Results(J.P. Eckmann and I.P., arXiv:0802.3404)
The system is ergodic at all temperatures
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Consequences: there is no Vogel-Fulcher temperature!
There is no Kauzman tempearture!
There is no jamming!
(the three no’s of Khartoum)
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Statistical Mechanics
We define the energy of a cell of type i
Similarly we can measure the areas of cells of type i
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Denote the number of boxes available for largest cells
Then the number of boxes available for the second largest cells is
The number of possible configurations W is then
Denote
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A low temperature phase
Note that here the hexagons have disappeared entirely!
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First result :
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Specific heat anomalies
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The anomalies are due to micro-melting (micro-freezing of crystalline clusters)
We have an equation of state !!!
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SummarySummaryThe ‘glass transition’ is not an abrupt transition, rather a very smeared out
phenomenon in which relaxation times increase at the T decreases .
There is no singularity on the way, no jamming, no Vogel-Fulcher, no Kauzman
We showed how to relate the statistical mechanics and structural information in a quantitative way to the slowing down and to the relaxation functions.
We could also explain in some detail the anomalies of the specific heat
Remaining task: How to use the increased understanding to write a proper theory of the mechanical properties of amorphous solid materials. (work in progress).
Since nothing gets singular, statistical mechanics is useful
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E. Aharonov, E. Bouchbinder, V. Ilyin, N. Makedonska, I. Procaccia and N. Schupper,Direct Identification of the Glass Transition: Growing Length Scale and the Onset of Plasticity, Europhys. Lett. 77, 56002 (2007) . Also: cond-mat/0608305 .
Valery Ilyin, Edan Lerner, Ting-Shek Lo, Itamar Procaccia, Statistical Mechanics of the Glass Transition in One-Component Liquids with Anisotropic Potential, Phys. Rev. Lett.,99, 135702 (2007) . Also: arXiv:0705.1043v1
Valery Ilyin, Nataliya Makedonska, Itamar Procaccia, Nurith Schupper, Mechanical Properties of Glass Forming Systems, Phys. Rev. E 76, 052401 (2007). Also: arXiv:0705.1834v1
H. G. E. Hentschel, V. Ilyin, N. Makedonska, I. Procaccia and N. Schupper, Statistical mechanics of the glass transition as revealed by a Voronoi tesselation, Phys. Rev. E 75, 050404 (2007) Also: cond-mat/0608443 .
H.G.E.Hentschel and Itamar Procaccia, Theory of Relaxation Dynamics in Glass-Forming Hydrogen-Bonded Liquids, Phys.Rev. E.77,031507 (2008). Also: arXiv:0709.4404
Some references:
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• Valery Ilyin, Itamar Procaccia, Ido Regev, Nurith Schupper, • Ageing and Relaxation in Glass Forming Systems, Phys. Rev. E 77,
061509 (2008) Also: arXiv:0803.2602
Jean-Pierre Eckmann and Itamar Procaccia, Ergodicity and Slowing Down in Glass-Forming Systems with Soft Potentials: No Finite-Temperature Singularities, Phys. Rev. E, 78, 011503 (2008)., Also: arXiv:0802.4346
Edan Lerner and Itamar Procaccia, Quantitative Theory of a Relaxation Function in a Glass-Forming System, Phys. Rev. Lett., submitted. Movie: Avi(9M), Mpeg ( 4M). Also: arXiv:0804.1205
Edan Lerner, Itamar Procaccia and Ido Regev, Quantitative Theory of a Time-Correlation Function in a One-Component Glass-Forming Liquid with Anisotropic Potential, PRE., submitted. Also: arXiv:0806.3685
• H. G. E. Hentschel, Valery Ilyin and Itamar Procaccia, Non-Universality of the Specific Heat in Glass Forming Systems, Phys. Rev. Lett., submitted. Also:arXiv:0808.2736
H. G. E. Hentschel, Valery Ilyin, Itamar Procaccia and Nurith Schupper, Theory of Specific Heat in Glass Forming Systems. Phys. Rev. E, submitted. Also::arXiv:0808.2138
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Strains, stresses etc.
We are interested in the shear modulus
Dynamics of the stress
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Zwanzig-Mountain (1965)
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