Prsentation PowerPoint

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Relaxation and Transport in Glass-Forming Liquids
G. Appignanesi, J.A. Rodríguez Fries, R.A.
Montani Laboratorio de Fisicoquímica, Bahía
Blanca W. Kob
Laboratoire des Colloïdes, Verres et
Nanomatériaux Université Montpellier
2 http//www.lcvn.univ-montp2.fr/kob

• Motivation (longish)
• Democratic motion
• Conclusions

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The problem of the glass-transition

• Most liquids crystallize if they are cooled below
  their melting temperature Tm
• But some liquids stay in a (metastable) liquid
  phase even below Tm
• one can study their properties in the
  supercooled state
• Use the viscosity ? to define a glass transition
  temp. Tg ?(Tg) 1013 Poise
• make a reduced Arrhenius plot log(?) vs Tg/T

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Model and details of the simulation
Avoid crystallization ? binary mixture of
Lennard-Jones particles particles of type A
(80) and of type B (20)
parameters ?AA 1.0 ?AB 1.5 ?BB 0.5
?AA 1.0 ?AB 0.8 ?BB 0.85

• Simulation
• Integration of Newtons equations of motion in
  NVE ensemble (velocity Verlet algorithm)
• 150 8000 particles
• in the following use reduced units
• length in ?AA
• energy in ?AA
• time in (m ?AA2/48 ?AA)1/2

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Dynamics The mean squared displacement

• Mean squared displacement is defined as
• ?r2(t)? ?rk(t) - rk(0)2?

• short times ballistic regime ?r2(t)? ? t2
• long times diffusive regime ?r2(t)? ? t
• intermediate times at low T
• cage effect
• with decreasing T the dynamics slows down
  quickly since the length of the plateau increases

• What is the nature of the motion of the particles
  when they start to become diffusive
  (?-process)?

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Time dependent correlation functions

• At every time there are equilibrium fluctuations
  in the density distribution how do these
  fluctuations relax?
• consider the incoherent intermediate scattering
  function Fs(q,t) Fs(q,t) N-1 ???(-q,t) ??(q,0)?
  with ??(q,t) exp(i q?rk(t))

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Dynamical heterogeneities I

• One possibility to characterize the dynamical
  heterogeneity (DH) of a system is the
  non-gaussian parameter
• ?2(t)
  3?r4(t)? / 5(?r2(t)?)2 1
• with the mean particle displacement r(t) (
  self part of the van Hove correlation function
  Gs(r,t) 1/N ?i ??(r-ri(t) ri(0)) ) ?
• N.B. For a gaussian process we have ?2(t) 0.

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Dynamical heterogeneities II

• Define the mobile particles as the 5 particles
  that have the largest displacement at the time t
• Visual inspection shows that these particles are
  not distributed uniformly in the simulation box,
  but instead form clusters
• Size of clusters increases with decreasing T

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Dynamical heterogeneities III

• The mobile particles do not only form clusters,
  but their motion is also very cooperative

ARE THESE STRINGS THE ?-PROCESS?
Similar result from simulations of polymers and
experiments of colloids (Weeks et al. Kegel et
al.)
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Existence of meta-basins

• Define the distance matrix (Ohmine 1995)
• ?2(t,t) 1/N ?i
  ri(t) ri(t)2

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Dynamics I

• Look at the averaged squared displacement in a
  time ? (ASD) of the particles in the same time
  window
• ?2(t,?) ?2(t- ?/2, t ?/2)
• 1/N ?i ri(t?/2) ri(t-?/2)2

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Dynamics II

• Look at Gs(r,t,t ?) 1/N ?i (r-ri(t)
  ri(t ?)) for times t that are inside a
  meta-basin

• Gs(r,t,t ?) is very similar to the mean curve
  ( Gs(r, ?) , the self part of the van Hove
  function)

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Dynamics III

• Look at Gs(r,t,t ?) 1/N ?i (r-ri(t)
  ri(t ?)) for times t that are at the end of a
  meta-basin, i.e. the system is crossing over to a
  new meta-basin

• Gs(r,t,t ?) is shifted to the right of the
  mean curve ( Gs(r, ?) )
• NB This is not the signature of strings!

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Democracy

• Define mobile particles as particles that move,
  within time ?, more than 0.3
• What is the fraction m(t,?) of such
• mobile particles?

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Nature of the motion within a MB

• Few particles move collectively signature of
  strings (?)

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Nature of the democratic motion in MB-MB
transition

• Many particles move collectively no signature of
  strings

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Summary

• For this system the ?-relaxation process does not
  correspond to the fast dynamics of a few
  particles (string-like motion with amplitude O(?)
  ) but to a cooperative movement of 20-50
  particles that form a compact cluster
• ? candidate for the cooperatively rearranging
  regions of Adam and Gibbs
• Slowing down of the system is due to increasing
  cooperativity of the relaxing entities (clusters)
• Qualitatively similar results for a small system
  embedded in a larger system
• Reference
• PRL 96, 057801 (2006) ( cond-mat/0506577)