Microscopic Picture of Aging in SiO 2 : A Computer Simulation

Transcription

1 Microscopic Picture of Aging in SiO 2 : A Computer Simulation Katharina Vollmayr-Lee, Robin Bjorkquist, Landon M. Chambers Bucknell University & Göttingen 7 td tb r n (t) 6 R ti t [ns] waiting time tw waiting time windows N p / [/ns] T f =325 K T f =3 K T f =275 K T f =25 K.. t w [ns] Mainz, June 25, 23 Acknowledgments: J. Horbach & A. Zippelius

2 Introduction: Glass V system falls out of equilibrium liquid Crystal Glass Liquid glass crystal T m T log η [Poise] 2 GeO 2 strong glass former Glycerol SiO2 fragile glass former 2 4Ca(NO 3 ) 2 6KNO.4 T /T 3. g [C.A. Angell and W. Sichina, Ann. NY Acad. Sci. 279, 53 (976)] Dynamics: Viscocity η as function of inverse temperature T slowing down of many decades very interesting dynamics strong and fragile glass formers Here: SiO 2 (strong glass former) Below: comparison with fragile glass former

3 System: SiO 2 Properties: rich phase diagram (like H 2 O) density maximum network former strong glass former Model: BKS Potential [B.W.H. van Beest et al., PRL 64, 955 (99)] log η [Poise] 2 GeO 2 strong glass former Glycerol SiO2 fragile glass former 2 4Ca(NO 3 ) 2 6KNO.4 T /T 3. g φ(r ij ) = q iq j e 2 r ij +A ij e B ijr ij C ij r 6 ij O 2 Si & 224 O ρ = 2.32 g/cm 3 T c = 333 K Si network (potential only "spheres")

4 Simulation Runs Molecular Dynamics Simulations T 5 K 376 K Ti T c 2 initial configurations 325 K 3 K T f.33 ns 33 ns 275 K NVT NVE 25 K (Nose Hoover) (Velocity Verlet) aging: time waiting time

5 Generalized Intermediate Incoherent Scattering Function C q (, +t) = N α N α e i q ( r j(+t) r j ()) j= tw +t C q (, +t) =24. ns waiting time C q (, +t) depends on waiting time (colors).2 q=.7 Å - T i =5 K = ns t [ns]

6 Generalized Intermediate Incoherent Scattering Function C q (, +t) =.8 N α N α e i q ( r j(+t) r j ()) j= intermediate equilibrium =24. ns waiting time tw tw +t C q (, +t).6.4 too short three time windows: too short intermediate (scaling) equilibrium (t C eq ).2 q=.7 Å - T i =5 K = ns t [ns] [KVL, J. Roman, J.Horbach, PRE 8, 623 (2)]

7 Generalized Intermediate Incoherent Scattering Function C q (, +t) =.8 N α N α e i q ( r j(+t) r j ()) j= intermediate equilibrium =24. ns waiting time tw +t C q (, +t) q=.7 Å - T i =5 K too short = ns t [ns] three time windows: too short intermediate (scaling) equilibrium (t C eq ) equilibrium curve included in scaling [KVL, J. Roman, J.Horbach, PRE 8, 623 (2)]

8 Mean Square Displacement r 2 (, +t) [Å 2 ] - -2 r 2 (, +t) = T f =25 K T i =5 K = ns N N (r j ( +t) r j ( )) 2 j= =24. ns waiting time tw +t three time windows: [KVL, J. Roman, J.Horbach, PRE 8, 623 (2)] t [ns]

9 Mean Square Displacement r 2 (, +t) [Å 2 ] r 2 (, +t) = T f =25 K T i =5 K = ns cage N N (r j ( +t) r j ( )) 2 j= jump here =24. ns t [ns] waiting time tw +t three time windows: Goal: Single Particle Picture N (not N ) j=

10 Jump Definition.327 ns r n {r n},σ {r n},σ {r n},σ {r n},σ t 7 7 z n (t) [Å] z n (t) [Å] r n σ r n y n (t) [Å] t [ns] r n > 3 σ [KVL, R. Bjorkquist, L.M. Chambers,PRL, 78 (23)]

11 Jump Definition: Aging Dependence r n (t) t t [ns] i waiting time t w waiting time windows

12 Average Jump Length R [Å] T i =5 K : Si-atoms: T f =325 K T f =3 K T f =275 K T f =25 K.. t w [ns] r n (t) R ti t [ns] waiting time tw waiting time windows jump farther than Si-atoms compare: d SiO =.59 Å, d OO = 2.57 Å, d SiSi = 3.3 Å R mostly independent of

13 Jump Length Distribution P( R) [/Å]..... d SiO d SiO d SiSi d OO Si-atoms T i =5 K T f =25 K =. ns =.2 ns =.6 ns =.67 ns =8.75 ns =29. ns R [Å] r n (t) R ti t [ns] waiting time tw waiting time windows peak at R j = : reversible jumps peaks at d SiO and d OO exponential decay P( R) independent of

14 Jump Length Distribution strong glass former SiO 2 : P( R) [/Å]..... Si-atoms T i =5 K T f =25 K =. ns =.2 ns =.6 ns =.67 ns =8.75 ns =29. ns R [Å] P( R) independent of exponential decay compare fragile glassformer binary LJ (& polymer) [Warren & Rottler,EPL(29)]

15 Time Averages: Jump Duration t d & Time in Cage t b t d [ns] t b [ns].. T f =275 K T f =3 K T f =325 K T f =25 K T i =5 K.. t w [ns] r n (t) t b t d jump duration td time in cage tb ti t [ns] tw waiting time tw waiting time windows t b not influenced by artifact due to finite simulation run t b independent of!

16 Distribution of Time in Cage P( t b ) P( t b ) [/ns] P( t b ) T f =325 K t b [ns] T f =25 K.. t b [ns] =. ns =.2 ns =.6 ns =.67 ns =8.75 ns =29. ns T i =5 K r n (t) 7 6 time in cage tb ti t [ns] tw waiting time tw waiting time windows P( t b ) independent of! 25 K: powerlaw 325 K: exponential

17 Distribution of Time in Cage P( t b ) P( t b ) [/ns] strong glass former SiO 2 : P( t b ) T f =325 K t b [ns] T f =25 K.. t b [ns] =. ns =.2 ns =.6 ns =.67 ns =8.75 ns =29. ns T i =5 K P( t b ) independent of! compare fragile glassformer (binary LJ &) polymer [Warren & Rottler,EPL(29)]

18 Distribution of Time in Cage P( t b ): T f varied P( t b ) temperature: T f =25 K T f =275 K T f =3 K T f =325 K t b [ns] t eq C =8.75 ns r n (t) ti t [ns] tw waiting time tw waiting time windows time in cage tb = 8.75 ns fixed temperature T f varied crossover power law to exponential

19 Distribution of Time in Cage P( t b ): T f varied P( t b ) temperature: T f =25 K T f =275 K T f =3 K T f =325 K t b [ns] t eq C =8.75 ns C q (, +t) too short q=.7 Å - T i =5 K C intermediate teq equilibrium = ns =24. ns t [ns] = 8.75 ns fixed temperature T f varied crossover power law to exponential at t cross t C eq (arrows)

20 Distribution of Time in Cage P( t b ): T f varied strong glass former SiO 2 : P( t b ) temperature: T f =25 K T f =275 K T f =3 K T f =325 K t b [ns] =8.75 ns [KVL, R. Bjorkquist, L.M. Chambers, PRL (23)] crossover power law to exponential slope power law: -. to -.3 (T f = 25 K to T f = 325 K) at t cross t C eq compare fragile glassformer binary LJ [Warren & Rottler, PRL (23)] slope power law: -.23 to -.34 p τ (τ) (T f =.28 to T f =.37) τ

21 Number of Jumping Particles per Time N p / [/ns] T f =325 K T f =3 K T f =275 K T f =25 K.. t w [ns] t C eq r n (t) ti t [ns] waiting time tw tw waiting time windows N p / depends strongly on waiting time N p / t tw decreasing with increasing compare: soft colloids [Yunker et al.,prl (29)] equilibration at t j eq t j eq t C eq (arrows)

22 Summary: Microscopic Picture of Aging r n (t) 7 td tb 6 R t [ns] ti waiting time tw waiting time windows log η [Poise] 2 GeO 2 strong glass former Glycerol SiO2 fragile glass former 2 4Ca(NO 3 ) 2 6KNO.4 T /T 3. g Aging of SiO 2 : Only -dependence: N p / (not P( R) and P( t b )) P( t b ) crossover power law to exponential at t cross t j eq t C eq [KVL, R. Bjorkquist, L.M. Chambers, PRL, 78 (23)] Compare with Fragile Glassformer: Surprising similar jump dynamics of strong and fragile glass formers P( R) and P( t b ) -independent P( t b ) crossover

23 PAST: Fragile Glass Former (Binary LJ): clusters of jumping particles self-organized criticality [KVL & Baker,EPL(26)] granular fluid: simulation and hydrodynamic theory [KVL,T.Aspelmeier,A.Zippelius,PRE 2] PRESENT: Strong & Fragile Glass Former Similar? SiO 2 : scaling (χ 4,P(C q )) together with H. Castillo SiO 2 : defects & jumps together with A. Zippelius Acknowledgments: Supported by SFB 62, NSF REU grants PHY & REU Thanks to J. Horbach, A. Zippelius & University Göttingen.

24 Binary Lennard-Jones: Clusteranalysis (Simultaneous) x P(s) T=.5 T=.25 T=.35 T=.38 T=.4 t -4-6 T=.43 simultaneously jump.part. s

25 Binary Lennard-Jones: Clusteranalysis (Space-Time Cluster) x s= P(s) t extended cluster s T=.5 T=.25 T=.35 T=.38 T=.4 T=.43

26 Summary of Granular Fluid Work Damped Sound Waves Fluctuating Hydrodynamic Theory: DT q 2 3Γ 2T (full solution) S(q,ω) well approximated transport coefficients agree with kinetic theory S(q,ω) η=.5 ε=.8 Simulation: q=.2 q=.3 q=.4 q=.5 Hydrodynamic Theory: q=.2 q=.3 q=.4 q=.5.5 ω.5 [KVL, T. Aspelmeier, A. Zippelius,PRE 83, 3 (2)]

27 Theory: Fluctuating Hydrodynamics t δn = iqn u t u = iq ( ) p p δn+ ρ n T δt t δt = D T q 2 δt 3Γ 2T δt iq 2p dn u Γ fluctuating number density δn( q,t) = n n longitudinal flow velocity u( q,t) = u q q fluctuating temperature δt = T T [Noije et al., PRE 59, 4326 (999)] ν l q 2 u+ξ l ( + dχ n χdn ) δn+θ

28 Generalized Intermediate Incoherent Scattering Function C q (, +t) = N α N α e i q ( r j(+t) r j ()) j= C q (, +t) T i =5 K = ns q=.7 Å - =24. ns t [ns] small: = &t 5 5 ns: T i good approx. no plateau decay -dependent intermediate: plateau -indep. decay -dependent time superposition? large: -indep. equilibrium

29 Generalized Intermediate Incoherent Scattering Function C q (, +t) MF: C q (, +t) = Cq ST (t)+cq AG ( ) h(tw+t) h() Superposition: C q (, +t) = Cq ST (t)+cq AG = ns =24. ns O q=.7 Å t/t Cq r =.49 ns.7 ns.96 ns 8.83 ns 6.67 ns ns ( t t Cq r () ) small: no time superposition intermediate: time superposition large: superposition includes equilibrium curve LJ: [Kob & Barrat, PRL 78, 24 (997)]

30 Generalized Intermediate Incoherent Scattering Function ( ) C q (, +t) = Cq ST (t)+cq AG h(tw+t) h() Is h dependent on C q? C q (, +t) T i =5 K T f =25 K =.49 ns.7 ns.96 ns 8.83 ns 6.67 ns ns q =2.7 Å - q =3.4 Å - q =4.6 Å - q =5.5 Å - q =6.6 Å C q=.7å - (, +t) small: no superposition intermediate: superposition of C q (C q ) h indep.of C q large: superposition includes equilibrium curve LJ: [Kob & Barrat, EPJ B 3, 39 (2)]

31 Dynamic Susceptibility χ 4 (, +t) = N α [ (f s (, +t)) 2 f s (, +t) 2] f s (, +t) = N α N α e i q ( r j(+t) r j ()) j= C q (, +t) = f s χ 4 Fs /χ4 max (-Fs) q=.7 O χ 4 Fs /χ4 max (-Fs) q=.7 SiO ns.4946 ns.9666 ns ns ns ns.8826 ns ns ns ns ns ns ns ns.4946 ns.9666 ns ns ns ns.8826 ns ns ns ns ns ns ns

32 Local Incoherent Intermediate Scattering Function Incoherent Intermediate Scattering Function 2 P(Cq) q=2.7 O Cqfix=.3 b=2 M= CqO.4 q=3.4 q= CqO CqSi q=.7 q= CqSi