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5th Liquid Matter Conference

5th Liquid Matter Conference. Konstanz, 14-18 September 2002. Potential Energy Landscape Equation of State. Emilia La Nave, Francesco Sciortino, Piero Tartaglia (Roma). Stefano Mossa (Boston/Paris). Potential Energy Landscape. Statistical description of the number, depth and shape.

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5th Liquid Matter Conference

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  1. 5th Liquid Matter Conference Konstanz, 14-18 September 2002 Potential Energy Landscape Equation of State Emilia La Nave, Francesco Sciortino, Piero Tartaglia (Roma) Stefano Mossa (Boston/Paris)

  2. Potential Energy Landscape Statistical description of the number, depth and shape of the PEL basins e IS P IS w

  3. Z(T)= S Zi(T) allbasins i fbasin i(T)= -kBT ln[Zi(T)] fbasin(eIS,T)= eIS+ kBTSln [hwj(eIS)/kBT] + fanharmonic(T) normal modes j

  4. Thermodynamics in the IS formalism Stillinger-Weber F(T)=-kBT ln[W(<eIS>)]+fbasin(<eIS>,T) with Basin depth and shape fbasin(eIS,T)= eIS+fvib(eIS,T) and Number of explored basins Sconf(T)=kBln[W(<eIS>)]

  5. Distribution of local minima (eIS) + Vibrations (evib) Real Space rN evib eIS

  6. F(T)=-kBT ln[W(<eIS>)]+fbasin(<eIS>,T) From simulations….. • <eIS>(T) (steepest descent minimization) • fbasin(eIS,T) (harmonic and anharmonic contributions) • F(T) (thermodynamic integration from ideal gas) In this talk….. Data for two rigid-molecule models: LW-OTP, SPC/E-H20

  7. Basin Free Energy LW-OTP SPC/E S ln[wi(eIS)]=a+b eIS

  8. The Random Energy Model for eIS Hypothesis: e-(eIS -E0)2/2s 2 W(eIS)deIS=eaN -----------------deIS 2ps2 S ln[wi(eIS)]=a+b eIS Predictions: <eIS(T)>=E0-bs 2 - s 2/kT Sconf(T)=aN-(<eIS (T)>-E0)2/2s 2

  9. Gaussian Distribution ? eIS=SeiIS E0=<eNIS>=Ne1IS s2= s2N=N s21

  10. T-dependence of <eIS> (SPC/E)

  11. T-dependence of <eIS> (LW-OTP)

  12. T-dependence of Sconf (SPC/E)

  13. The V-dependence of a, s2, E0 e-(eIS -E0)2/2s 2 W(eIS)deIS=eaN -----------------deIS 2ps2

  14. Landscape Equation of State P=-∂F/∂V|T F(V,T)=-TSconf(T,V)+<eIS(T,V)>+fvib(T,V) In Gaussian (and harmonic) approximation P(T,V)=Pconst(V)+PT(V) T + P1/T(V)/T Pconst(V)= - d/dV [E0-bs2] PT(V) =R d/dV [a-a-bE0+b2s2/2] P1/T(V) = d/dV [s2/2R]

  15. Developing an EOS based on PES properties

  16. SPC/E WaterP(T,V)=Pconst(V)+PT(V) T + P1/T(V)/T

  17. Conclusion I The V-dependence of the statistical properties of the PEL has been quantified for two models of molecular liquids Accurate EOS can be constructed from these information Interesting features of the liquid state (TMD line) can be correlated to features of the PEL statistical properties

  18. Aging in the PEL-IS framework Ti Tf Tf Starting Configuration (Ti) Short after the T-change (Ti->Tf) Long time

  19. P=-∂F/∂V Reconstructing P(T,V) F(V,T)=-TSconf(T,V)+<eIS(T,V)>+fvib(T,V) P(T,V)= Pconf(T,V) + Pvib(T,V)

  20. From Equilibrium to OOE…. P(T,V)= Pconf(T,V)+ Pvib(T,V) If we know which equilibrium basin the system is exploring… • eIS(V,Tf),V,T • log(w) • Pvib • eIS(V,Tf).V • Pconf eIS acts as a fictive T !

  21. Numerical TestsHeating a glass at constant P T P time

  22. Numerical TestsCompressing at constant T Pf Pi T time

  23. Liquid-to-Liquid T-jump at constant V P-jump at constant T

  24. Conclusion II • The hypothesis that the system samples in aging the same basins explored in equilibrium allows to develop an EOS for OOE-liquids depending on one additional parameter • Small aging times, small perturbations are consistent with such hipothesis. Work is requested to evaluate the limit of validity. • This parameter can be chosen as fictive T, fictive P or depth of the explored basin eIS

  25. Perspectives An improved description of the statistical properties of the potential energy surface. Role of the statistical properties of the PEL in liquid phenomena A deeper understanding of the concept of Pconf and of EOS of a glass. An estimate of the limit of validity of the assumption that a glass is a frozen liquid (number of parameters) Connections between PEL properties and Dynamics

  26. References and Acknowledgements We acknowledge important discussions, comments, criticisms from P. Debenedetti, S. Sastry, R. Speedy, A. Angell, T. Keyes, G. Ruocco and collaborators Francesco Sciortino and Piero Tartaglia Extension of the Fluctuation-Dissipation theorem to the physical aging of a model glass-forming liquid Phys. Rev. Lett. 86 107 (2001). Emilia La Nave, Stefano Mossa and Francesco Sciortino Potential Energy Landscape Equation of State Phys. Rev. Lett., 88, 225701 (2002). Stefano Mossa, Emilia La Nave, Francesco Sciortino and Piero Tartaglia, Aging and Energy Landscape: Application to Liquids and Glasses., cond-mat/0205071

  27. Entering the supercooled region

  28. Same basins in Equilibrium and Aging ?

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