Part I Part II Outline. Thermodynamics in the IS formalism Stillinger- Weber F(T)=-T S conf (, T) +f basin (,T) with f basin (e IS,T)= e IS +f vib (e.

Slides:

Advertisements

Similar presentations

15.5 Electronic Excitation

Advertisements

Gelation Routes in Colloidal Systems Emanuela Zaccarelli Dipartimento di Fisica & SOFT Complex Dynamics in Structured Systems Università La Sapienza, Roma.

Third law of Thermodynamics

Genova, September Routes to Colloidal Gel Formation CCP2004 In collaboration with S. Bulderyev, E. La Nave, A. Moreno, S. Mossa, I. Saika-Voivod,

Activities in Non-Ideal Solutions

Konstanz, September 2002 Potential Energy Landscape Equation of State Emilia La Nave, Francesco Sciortino, Piero Tartaglia (Roma) Stefano Mossa (Boston/Paris)

Potential Energy Landscape Description of Supercooled Liquids and Glasses.

Bad Gastein, January 2005 Gels and Strong Liquids In collaboration with S. Bulderyev,C. De Michele, E. La Nave, A. Moreno, I. Saika-Voivod, P. Tartaglia,

March ACS Chicago Francesco Sciortino Universita’ di Roma La Sapienza Gel-forming patchy colloids, and network glass formers: Thermodynamic and.

IV Workshop on Non Equilibrium Phenomena in Supercooled Fluids, Glasses and Amorphous Materials Pisa, September 2006 Francesco Sciortino Gel-forming patchy.

June Universite Montpellier II Francesco Sciortino Universita’ di Roma La Sapienza Aggregation, phase separation and arrest in low valence patchy.

Viscoelastic response in soft matter Soft matter materials are viscoelastic: solid behavior at short time – liquid behavior after a time  Shear strain;

Control of Chemical Reactions. Thermodynamic Control of Reactions Enthalpy Bond Energies – Forming stronger bonds favors reactions. – Molecules with strong.

The Marie Curie Research/Training Network on Dynamical Arrest Workshop Le Mans, November 19-22, 2005 Slow dynamics in the presence of attractive patchy.

Cluster Phases, Gels and Yukawa Glasses in charged colloid-polymer mixtures. 6th Liquid Matter Conference In collaboration with S. Mossa, P. Tartaglia,

Symmetry-broken crystal structure of elemental boron at low temperature With Marek Mihalkovic (Slovakian Academy of Sciences) Outline: Cohesive energy.

Conference on "Nucleation, Aggregation and Growth”, Bangalore January Francesco Sciortino Gel-forming patchy colloids and network glass formers:

Konstanz, September 2002 Potential Energy Landscape Equation of State Emilia La Nave, Francesco Sciortino, Piero Tartaglia (Roma) Stefano Mossa (Boston/Paris)

Free Energy Landscape -Evolution of the TDM- Takashi Odagaki Kyushu University IV WNEP Round Table Discussion September 22, 2006 Trapping diffusion Model.

Duesseldorf Feb 2004 Duesseldorf February Potential Energy Landscape Description of Supercooled Liquids and Glasses Luca Angelani, Stefano Mossa,

Cosmic Coincidence and Interacting Holographic Dark Energy ncu Suzhou Dark Universe Workshop.

Polymers PART.2 Soft Condensed Matter Physics Dept. Phys., Tunghai Univ. C. T. Shih.

Francesco Sciortino Universita’ di Roma La Sapienza October ISMC Aachen Patchy colloidal particles: the role of the valence in the formation of.

Density anomalies and fragile-to-strong dynamical crossover

Orleans July 2004 Potential Energy Landscape in Models for Liquids Networks in physics and biology In collaboration with E. La Nave, A. Moreno, I. Saika-Voivod,

Patchy Colloids, Proteins and Network Forming Liquids: Analogies and new insights from computer simulations Lyon - CECAM - June Dynamics in patchy.

Physical Gels and strong liquids 5th International Discussion Meeting on Relaxations in Complex Systems New results, Directions and Opportunities Francesco.

STATISTICAL PROPERTIES OF THE LANDSCAPE OF A SIMPLE STRONG LIQUID MODEL …. AND SOMETHING ELSE. E. La Nave, P. Tartaglia, E. Zaccarelli (Roma ) I. Saika-Voivod.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 1 Spontaneous Processes and Entropy Thermodynamics lets us predict whether a process will.

Liquid-Liquid Phase Transitions and Water-Like Anomalies in Liquids Erik Lascaris Final oral examination 9 July

Shai Carmi Bar-Ilan, BU Together with: Shlomo Havlin, Chaoming Song, Kun Wang, and Hernan Makse.

Lecture 5: 2 nd and 3 rd Laws of Thermodynamics 2 nd law: The entropy of an isolated system never decreases. Nernst’s Theorem: The entropy of a system.

T. Odagaki Department of Physics, Kyushu University T. Yoshidome, A. Koyama, A. Yoshimori and J. Matsui Japan-France Seminar, Paris September 30, 2005.

Summary: Isolated Systems, Temperature, Free Energy Zhiyan Wei ES 241: Advanced Elasticity 5/20/2009.

Molecular Dynamics Simulation Solid-Liquid Phase Diagram of Argon ZCE 111 Computational Physics Semester Project by Gan Sik Hong (105513) Hwang Hsien Shiung.

Minimization v.s. Dyanmics A dynamics calculation alters the atomic positions in a step-wise fashion, analogous to energy minimization. However, the steps.

Solutions and Mixtures Chapter 15 # Components > 1 Lattice Model  Thermody. Properties of Mixing (S,U,F,  )

T. Odagaki and T. Ekimoto Department of Physics, Kyushu University Ngai Fest September 16, 2006.

Thermodynamics and dynamics of systems with long range interactions David Mukamel S. Ruffo, J. Barre, A. Campa, A. Giansanti, N. Schreiber, P. de Buyl,

Mainz, November Francesco Sciortino Gel-forming patchy colloids and network glass formers: Thermodynamic and dynamic analogies Imtroduzione.

Physics 361 Principles of Modern Physics Lecture 14.

Fundamentals of DFT R. Wentzcovitch U of Minnesota VLab Tutorial Hohemberg-Kohn and Kohn-Sham theorems Self-consistency cycle Extensions of DFT.

The thermodynamical limit of abstract composition rules T. S. Bíró, KFKI RMKI Budapest, H Non-extensive thermodynamics Composition rules and formal log-s.

Lecture 23: Applications of the Shell Model 27/11/ Generic pattern of single particle states solved in a Woods-Saxon (rounded square well)

Thermodynamics and dynamics of systems with long range interactions David Mukamel.

18.3 Bose–Einstein Condensation

* Studying energy flow in chemical changes allows us to predict what is possible and what is not. * 1 st Law of Thermodynamics PE tends only to decrease.

Symmetry-broken crystal structure of elemental boron at low temperature With Marek Mihalkovič (Slovakian Academy of Sciences) Outline: Cohesive energy.

The first law of Thermodynamics. Conservation of energy 2.

Thermodynamics. Free Energy When a system changes energy, it can be related to two factors; heat change and positional/motion change. The heat change.

J Villamil, Franklin Magnet HS1 Spontaneous Processes and Entropy Thermodynamics lets us predict whether a process will occur but gives no information.

 State Function (°)  Property with a specific value only influenced by a system’s present condition  Only dependent on the initial and final states,

42C.1 Non-Ideal Solutions This development is patterned after that found in Molecular Themodynamics by D. A. McQuarrie and John D. Simon. Consider a molecular.

Thermodynamics and dynamics of systems with long range interactions David Mukamel.

Intermolecular Forces and Liquids and Solids Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Maximum Work 1 Often reactions are not carried out in a way that does useful work. –As a spontaneous precipitation reaction occurs, the free energy of.

Pattern Formation via BLAG Mike Parks & Saad Khairallah.

Introduction to Entropy. Entropy A formal attempt to quantify randomness by relating it to the amount of heat “wasted” by a thermodynamic process. The.

The average occupation numbers

Equilibrium Carrier Statistics

Bangalore, June 2004 Potential Energy Landscape Description of Supercooled Liquids and Glasses.

The Third Law of Thermodynamics

Entropy Chapter 16-5.

Einstein Model of Solid

7. Ideal Bose Systems Thermodynamic Behavior of an Ideal Bose Gas

Chapter 4 CHM 341 Fall 2016.

Thermal Energy & Heat Capacity:

Semiconductor Physics

Area and Volume How to … Calculate the area of a square or rectangle

Institute for Theoretical Physics,

Presentation transcript:

Part I Part II Outline

Thermodynamics in the IS formalism Stillinger- Weber F(T)=-T S conf (, T) +f basin (,T) with f basin (e IS,T)= e IS +f vib (e IS,T) and S conf (T)=k B ln[  ( )] Basin depth and shape Number of explored basins Free energy

The Random Energy Model for e IS Hypothesis:  e IS )de IS = e  N de IS e -(e IS -E 0 ) 2 /2  2 2222 S conf (e IS )/N=  - (e IS -E 0 ) 2 /2  2 Gaussian Landscape

Predictions of Gaussian Landscape

T-dependence of SPC/ELW-OTP T -1 dependence observed in the studied T-range Support for the Gaussian Approximation

BMLJ Configurational Entropy BMLJ Sconf

Non Gaussian Behaviour in BKS silica

Density minimum and C V maximum in ST2 water inflection = C V max inflection in energy Density Minima P.Poole

Eis e S conf for silica… Esempio di forte Non-Gaussian Behavior in SiO 2 Non gaussian silica Sconf Silica

Maximum Valency Model ( Speedy-Debenedetti ) A minimal model for network forming liquids SW if # of bonded particles <= Nmax HS if # of bonded particles > Nmax V(r) r Maximum Valency The IS configurations coincide with the bonding pattern !!!

Square Well 3% width Generic Phase Diagram for Square Well (3%)

Square Well 3% width Generic Phase Diagram for N MAX Square Well (3%)

Energy per Particle Ground State Energy Known ! (Liquid free energy known everywhere!) It is possible to equilibrate at low T ! (Wertheim)

Specific Heat (Cv) Maxima Cv

Viscosity and Diffusivity: Arrhenius

Stoke-Einstein Relation

Dynamics: Bond Lifetime

It is possible to calculate exactly the basin free energy ! Basin Free energy

S vib S vib increases linearly with the number of bonds S conf follows a x ln(x) law S conf does NOT extrepolate to zero

Self-consistent calculation ---> S(T) Self consistence

Take home message: Network forming liquids tend to reach their (bonding) ground state on cooling (eIS different from 1/T) The bonding ground state can be degenerate. Degeneracy related to the number of possible networks with full bonding. The discretines of the bonding energy (dominant as compared to the other interactions) favors an Arrhenius Dynamics Network liquids are intrinsically different from non- networks, since the approach to the ground state is hampered by phase separation

Frenkel-Ladd (Einstein Crystal)

Excess Entropy Thermodyan mics A vanishing of the entropy difference at a finite T ?