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The high frequency dynamics of liquids and supercritical fluids

The high frequency dynamics of liquids and supercritical fluids. by Filippo Bencivenga. OUTLINE. Introduction Experimental description Data analysis Experimental results (Dispersions) Experimental results (Relaxations) Conclusions Outlook. Supercritical. Critical Point.

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The high frequency dynamics of liquids and supercritical fluids

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  1. The high frequency dynamics of liquids and supercritical fluids by Filippo Bencivenga

  2. OUTLINE • Introduction • Experimental description • Data analysis • Experimental results (Dispersions) • Experimental results (Relaxations) • Conclusions • Outlook

  3. Supercritical Critical Point LIQUIDS & SUPERCRITICAL FLUIDS (1) Pressure Temperature

  4. csQ Microscopic dynamics(ps) What is missing? What is Known: LIQUIDS & SUPERCRITICAL FLUIDS (2) Qm~2p/r0 Thermodynamic properties Microscopic structure(nm) SC fluids: a few cases Systematic studies: none

  5. Liquid phase Supercritical phase AIM OF THE THESIS Microscopic dynamics ( ps-nm) From a microscopic point of view … … what is the role of inter- and intra-molecular interactions ? … what is the difference between a liquid and a SC fluid ?

  6. Supercritical Liquid H2O NH3 Ne N2 EXPERIMENTS (1)

  7. Pressure connector Cell body out sample Sealing system in out in X-ray beam Scattered beam EXPERIMENTS (2) • Large Volume HP Cells • Low pressures ( Kbar) • “Large” samples ( cm3) • Versatility (High-T & Low-T) Cell body Nut Sample X-ray beam Scattered beam 10 mm

  8. •Q = |kout – kin| 2 kin sin(q) •w=E/ ħ =(Eout– Ein) / ħ No /NiS(Q,w) INELASTIC X-RAY SCATTERING (IXS) Q  nm-1 w  THz lengths nm times ps Q,E No  Eout, kout Sample 2 q Ni  Ein, kin ħ=1

  9. Q = 8 nm-1 N2 1.5 meV IXS SPECTRA T = 87 K N2

  10. [ ] wm’(Q,w) 2 (cTQ)2 m’(Q,w) 1 p [ w2-(cTQ)2-wm’’(Q,w) 2 ] + S(Q,w) = S(Q) DATA ANALYSIS Free EoS Rayleigh-Brillouin Spectrum Free Fix Fix m(Q,t)=(g-1)(cTQ)2exp{-t/tT}+2Gmd(t) +(c∞2-gcT2)Q2exp{-t/ta} m(Q,t)=2nLQ2d(t)+(g-1)(cTQ)2exp{-t/tT} Low-(Q,w) limit Hydrodynamics Free Free Instantaneous relaxation (c∞2-gcT2)Q2exp{-t/ta}+2Gmd(t) Thermal relaxation Structural relaxation WL(Q) max[w2S(Q,w)] taps tT=1/DTQ2

  11. Fully unrelaxed: elastic WL(Q)ta1 ta-1 c∞Q c0Q Fully relaxed: viscous SOUND DISPERSIONS & RELAXATIONS (1) Visco-Elasticity: 1) Low-Frequency limit:c0=cs=g1/2cT 2) High-Frequency limit:c∞ “High” and “low” frequency is with respect tota-1 Structural relaxation WL(Q) W Positive sound dispersion Q

  12. Unrelaxed Relaxed: isothermal WL(Q) W ta-1 c0Q Relaxed Q WL(Q)tT1 c∞Q WL(Q) W Unrelaxed: adiabatic ta-1 csQ Q SOUND DISPERSIONS & RELAXATIONS (2) Isothermal transition: “High” and “low” frequency is with respect to tT-1 1) High-Frequency limit:c∞=cs=g1/2cT 2) Low-Frequency limit:c0=cT Thermal relaxation Structural and thermal relaxations: competing dispersive effects WL(Q) W csQ Structural relaxation tT-1=DTQ2 Structural relaxation Q Negative sound dispersion

  13. RESULTS (DISPERSIONS) kBTQ2 WT2(Q)= MS(Q) Ws(Q)=√gWT(Q) WL=ta-1 W∞(Q)=c∞(Q)Q N2 @400 bar T/Tc=0.69 Good agreement with S(Q) measurements WL(Q) WT(Q)=cT(Q)Q ta-1 WL(Q) max[w2S(Q,w)]

  14. W∞ WL=ta-1 WL~Ws WL Ws ta-1 WT WL=ta-1 WT DISPERSION RELATIONS (N2) DTQ 2 WL=DTQ2

  15. H2O NH3 Ne W L W s WL=DTQ2 WL=DTQ2 WL=DTQ2 DISPERSION RELATIONS c∞ ta-1 WL~Ws DTQ2 W T

  16. M(Q)=1 Elastic M(Q)=1 Elastic M(Q)=0 Viscous M(Q)=0 Viscous COMMON PHENOMENOLOGY (1)

  17. MT(Q)=1 Adiabatic MT(Q)=0 Isothermal COMMON PHENOMENOLOGY (2) Structural relaxation Thermal relaxation W∞(Q) Ws(Q) WT(Q) Ws(Q) Vs. MT(Q)=1 Adiabatic Da2(Q)=W∞2(Q) - Ws2(Q) DT2(Q)=Ws2(Q) - WT2(Q) >> MT(Q)=0 Isothermal Dispersive effect of structural relaxation

  18. CONCLUSIONS (SOUND DISPERSION) • Common evolution with T: • Evidence of a systematic disappearance of the positive dispersion, relatedto the structural relaxation, close to Tc • First experimental observation of an adiabatic to isothermal transition of sound propagation, associated to the thermal relaxation.

  19. RESULTS (RELAXATIONS) Liquid Supercritical STRUCTURAL RELAXATION TIME ta(Q)=ta(0)exp{-AQ} A≈0.2 ÷ 0.05 nm ta(0)exp{E/kBT} E(KJ/mol) • H2O • NH3 • N2 • Ne

  20. ( c∞ ta(0) tc Liquid Supercritical = cs 2tc -1(Q) • H2O • NH3 • N2 • Ne W∞(Q) [ W∞(Q)=c∞Q ta(Q) tc(Q) 2 2 = ] ) Ws(Q) EoS COMPLIANCE RELAXATION TIME Q  0

  21. Liquid Supercritical • H2O • NH3 • N2 • Ne 1 <t>  √(d4/M)*(r2T) COMMON PHENOMENOLOGY <t> <l> oP. Giura et al.; Unpublished (2006)

  22. STRUCTURAL RELAXATION STRENGTH D2a=c∞2- cs2 =Cr • H2O • NH3 • N2 • Ne Linesdensity

  23. CONCLUSIONS • Common phenomenology: • Negative sound dispersion Thermal relaxation • Positive sound dispersionStructural relaxation • Activation behavior (≈bond’s energy) oftabelow Tc • Collision-like behaviorofta(tc)above Tc • D2a density(correlation with the parameter “a”?) • Structural relaxation related to intermolecuar interactions

  24. OUTLOOK  H2O  NH3 N2Ne • Extend the Tc/T range: • high-T for H2O &NH3 • low-T for Ne & N2 Other classes of fluids !

  25. ACKNOWLEDGEMENTS • M. Krisch, F. Sette, G. Monaco and all the ID28-ID16 staff (ESRF) • A. Cunsolo, L. Melesi (ILL) • G. Ruocco (Universitá “La Sapienza”, Roma) • L. Orsingher (Universitá di Trento) • A. Vispa (Universitá di Perugia)

  26. DE/E ≈ 10-8 Monochromator Si (n,n,n) 6.5 m DE/E ≈ 10-4 ≈ Undulators Pre-Monochromator Si (1,1,1) qB Toroidal mirror 75 m IXS BEAMLINE (ID-28) 5 Analyzers Si (n,n,n) Analyzer Si (n,n,n) Q 2q qB 5 Detectors Detector T-scan ≈ mK sample DE/E ≈ 10-2

  27. H2O @ 400 bar STATIC STRUCTURE FACTORS N2 @ 400 bar

  28. ( c∞ ta(0) tc = cs 2tc -1(Q) w=tc-1 M(∞) ta tc = M(0) W∞(Q) [ EoS ta(Q) tc(Q) 2 2 = ) ] Ws(Q) COMPLIANCE RELAXATION TIME M(∞) w=ta-1 M-1(0) M-1(∞) M(0) W∞(Q)=c∞Q

  29. D2m(Q)exp{-t/tm(Q)} INSTANTANEOUS RELAXATION Gm(Q)=rg(Q) Linesdensity 2Gm(Q)d(t) g(Q)=<Gm(Q)/r> 2Gm(Q)d(t) Gm(Q)r D2m(Q)r tm(Q)const Gm(Q)D2m(Q)tm(Q) Gm(Q)Q2 tm(Q)<<ps Intramolecular degree of freedom?

  30. VISCOSITY (Q-dependence) hL(Q)=r[D2a(Q)ta(Q)+Gm(Q)/Q2] hL(Q)=hLexp{-BQ}

  31. VISCOSITY (T-dependence) hL/hSconstant

  32. OUTLOOK Disappearance of the positive dispersion? O2  H2O  NH3 N2Ne Supercritical Study high T/Tc and P/Pc region of the SC plane Liquid Vapor F. Gorelli et al.; Unpublished (2005)

  33. r(Q,t)=SjeiQRj(t) t ∫ = dt 0 1 Im p MEMORY FUNCTION S(Q,w) D1 -1 [ iw+ [ = D2 S(Q) iw+ D3 iw+ iw+ … THEORETICAL FORMALISM S(Q,w) F(Q,t)=<r*(Q,0)r(Q,t)> Time Fourier Transform dm1(Q,t) dm3(Q,t) dm2(Q,t) dF(Q,t) MEMORY EQUATION m3(Q,t’) m4(Q,t’) m1(Q,t’) m2(Q,t’) m1(Q,t-t’) m3(Q,t-t’) m2(Q,t-t’) F(Q,t-t’) dt’ m2(Q,w)

  34. RELATIVE RELAXATION STRENGTH NH3 H2O N2 Ne

  35. RELATIVE RELAXATION AMPLITUDE H2O NH3 N2 Ne

  36. NEGATIVE DEVIATIONS H2O NH3 N2 Ne

  37. Thermodynamics Microscopic structure (nm) Microscopic dynamics (ps) Liquid Indium Qm  r-1/3 S(0) cT Nitrogen cQ <dr2> x-1 LIQUIDS & SUPERCRITICAL FLUIDS Qm~2p/r0

  38. elastic viscous t, relaxation time t >> 2p/w t << 2p/w A (t) A (t) t t VISCOELASTICITY 2p/w P (t) t

  39. RELAXATION TIME (Q-dependence) ta(Q)=ta(0)exp{-AQ}

  40. Tc Tc Tc RELAXATION TIME (T-dependence) ta(0)=t0exp{Ea/kBT} Tc

  41. Tc Tc Tc Tc RELAXATION STRENGTHS D2a=c∞2- cs2

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