Simple Model of glass-formation

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Simple Model of glass-formation
Itamar Procaccia Institute of
Theoretical Physics Chinese 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
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Glass phenomenology
The three accepted facts 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 Tgt0.5 the system is a
fluid for T smaller - dynamical relaxation
slows down considerably.
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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 gt 0.8
For 0.3 lt T lt 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., PRE, 78,
011503 (2008))
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 nos 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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Summary
The 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
Since nothing gets singular, statistical
mechanics is useful
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).
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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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