Simple Model of glass-formation Itamar Procaccia Institute of Theoretical Physics Chinese University...
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Simple Model of glass-formationSimple Model of glass-formation
Itamar Procaccia
Institute of Theoretical PhysicsChinese University of Hong Kong
Weizmann Institute: Einat Aharonov, Eran Bouchbinder, Valery Ilyin, Edan Lerner, Ting-Shek Lo, Natalya Makedonska, Ido Regev and Nurith Schupper .
Emory University: George Hentschel
CUHK September 2008
Glass phenomenology
The three accepted ‘facts’: jamming, Vogel-Fulcher, Kauzmann
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.
QuickTime™ and a decompressor
are needed to see this picture.
The conclusion was that “defects” do not show any ‘singular’ behaviour , so they were discarded as a diagnostic tool .
The liquid like defects disappear at the glass transition!
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
QuickTime™ and a decompressor
are needed to see this picture.
Rigorous Results(J.P. Eckmann and I.P., PRE, 78, 011503 (2008))
The system is ergodic at all temperatures
Consequences: there is no Vogel-Fulcher temperature!
There is no Kauzman tempearture!
There is no jamming!
(the three no’s of Khartoum)
Statistical Mechanics
We define the energy of a cell of type i
Similarly we can measure the areas of cells of type i
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
A low temperature phase
Note that here the hexagons have disappeared entirely!
QuickTime™ and aCinepak decompressor
are needed to see this picture.
First result :
Specific heat anomalies
The anomalies are due to micro-melting (micro-freezing of crystalline clusters)
We have an equation of state !!!
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
Strains, stresses etc.
We are interested in the shear modulus
Dynamics of the stress
Zwanzig-Mountain (1965)