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# Relaxation dynamics of glassy liquids: Meta-basins and democratic motion - PowerPoint PPT Presentation

Relaxation dynamics of glassy liquids: Meta-basins and democratic motion. G. Appignanesi, J.A. Rodr í guez Fries, R.A. Montani Laboratorio de Fisicoqu í mica, Bah í a Blanca W. Kob. Laboratoire des Collo ïdes, Verres et Nanomatériaux Universit é Montpellier 2

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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

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 Newton’s 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

• 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)?

• 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?

• 2(t) is large in the caging regime

• maximum of 2(t) increases with decreasing T  evidence for the presence of DH at low T

• define t* as the time at which the maximum occurs

• 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) )

• 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

• 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.)

T=0.5

• we see meta-basins (MB)

• with decreasing T the residence time increases

• NB: Need to use small systems (150 particles) in order to avoid that the MB are washed out

• define the “distance matrix” (Ohmine 1995)

• 2(t’,t’’) = 1/N i|ri(t’) – ri(t’’)|2

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

• 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

• 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!

• 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%)

Nature of the motion within a MB

• few particles move collectively; signature of strings (?)

Nature of the democratic motion in MB-MB transition

• many particles move collectively; no signature of strings

K. Binder and W. KobGlassy Materials and

Disordered Solids: An Introduction to their

Statistical Mechanics (World Scientific,

Singapore, 2005)

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