Pr

1
(No Transcript)
2
Relaxation dynamics of glassy liquids Meta-basins
and democratic motion
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 (long)
• strings
• democratic motion
• conclusions

3
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
  (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

4
Dynamics The mean squared displacement

• Mean squared displacement is defined as
• ?r2(t)? ?r(t) - r(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)?

5
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(q?rk(t))

• high T after the microscopic
• regime the correlation decays
• exponentially
• low T existence of a plateau at
• intermediate time (reason cage effect) at long
  times the correlator
• is not an exponential (can be fitted well by
  Kohlrausch-law)
• Fs(q,t) A exp( - (t/ ?)?)

• Why is the relaxation of the particles in the
  ?-process non-exponential? Motion of system in
  rugged landscape? Dynamical heterogeneities?

6
Dynamical heterogeneities I

• One possibility to characterize the dynamical
  homogeneity 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) )

7
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

8
Dynamical heterogeneities III

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

ARE THESE STRINGS THE ?-PROCESS? ARE THESE DH
THE REASON FOR THE STRETCHTING IN THE ?-PROCESS ?
Similar result from simulations of polymers and
experiments of colloids (Weeks et al. Kegel et
al.)
9
Existence of meta-basins

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

10
Dynamics I

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

11
Dynamics II

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

• Gs(r,t,t ?) is shifted to the left of the
  mean curve ( Gs(r, ?) ) and is more peaked

12
Dynamics III

• look at Gs(r,t,t ?) 1/N ?i (ri(t) ri(t
  ?))2 for times t that are at the end of a
  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!

13
Democracy

• define mobile particles as particles that move,
  within time ?, more than 0.3
• what is the fraction of such
• mobile particles?

• fraction of mobile in the MB-MB transition
  particles is quite substantial ( 20-30 ) ! (cf.
  strings 5)

14
Nature of the motion within a MB

• few particles move collectively signature of
  strings (?)

15
Nature of the democratic motion in MB-MB
transition

• many particles move collectively no signature of
  strings

16
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
• Qualitatively similar results for a small system
  embedded in a larger system
• Reference
• cond-mat/0506577