Relaxation dynamics of glassy liquids: Meta-basins and democratic motion

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 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

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 • 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) )

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 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

10. ASD changes strongly when system leaves MB 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. 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