CHEM 8843: Special Topics: Nonequilibrium Statistical Mechanics Prof. Rigoberto Hernandez [email protected] 8843 Lecture #1 — Rigoberto Hernandez Introduction 1 SPRING 2013
CHEM 8843: Special Topics: Nonequilibrium
Statistical Mechanics
Prof. Rigoberto Hernandez [email protected]
8843 Lecture #1 —Rigoberto Hernandez
Introduction 1
SPRING 2013
8843 Lecture #1 —Rigoberto Hernandez
Introduction 2
Major Concepts • Why am I here? • What is Statistical Mechanics?
– What is Mechanics? – What does statistics have to do with anything? – Do I need to know Classical Mechanics? – Do I need to know Quantum Mechanics? – Do I need to know Thermodynamics?
• What is NONEQUILIBRIUM Statistical Mechanics
• What do I really need to know? – Is this a mathematics course? – Is this a physics course? Where’s the chemistry?
Why and How is Prof. Hernandez
here?
Gratuitous images from my lab!
8843 Lecture #1 —Rigoberto Hernandez
3 Introduction
• Born in Cuba... Spain... Miami, FL • Princeton University " B.S.E. Chemical Engineering & Mathematics, 1989
• University of California, Berkeley " Ph.D. Chemistry w/t Bill Miller, 1993
• Weizmann Institute—Postdoc w/t Eli Pollak • U. of Pennsylvania—Postdoc w/t Greg Voth • GaTech: 1996-present " Assistant Professor (Blanchard Chair) " Associate Professor’02 (Goizueta Chair) " Professor’09 (Vasser Woolley Professor’11)
Academic History
8843 Lecture #1 —Rigoberto Hernandez
4 Introduction
• Humboldt Research Fellowship " Universität Potsdam (Fall’06 & May’08) " Universität München (Spring’07 & June’08)
• Awards: CAREER, Cotrell, Sloan, etc • Honors: ACS Fellow, AAAS Fellow • Panels: BCST/NSF /NIH/ NAS TAB /
TSRC/... • ACS Service
Academic History
Funding & Partners!
8843 Lecture #1 —Rigoberto Hernandez
5 Introduction
• CCMST: Center for Computational Molecular Sciences & Technology: ( ) " IBM SP2 ’01: 72 375 MHz Power3-II’s, 47GB RAM " IBM’04: 56 2.8GHz Pentium4’s
*Dell’05: 152 Intel Xeon’s, 340GB RAM *Dell’07: 98 duo 2.66GHz Woodcrests, 416GB RAM *Penguin’11: 720 2.0GHz AMD Opteron cores, 2240GB RAM, 108TB Disks
• Hernandez Group Machines: " Apple Xserve ’08: 10 quad-core 3.0GHz Xeon’s " 8 Apple Unix or Dell Linux workstations (20” Flat)
Computational Facilities
8843 Lecture #1 —Rigoberto Hernandez
6 Introduction
• Diffusion in Swelling/Contracting/Rotating Colloids – E. Hershkovitz and R. Hernandez; J. Chem. Phys. 122, 014509 (2005). (cond-mat/0501434, doi:10.1063/1.1829252)!– A. V. Popov, J. Melvin, and R. Hernandez; J. Phys. Chem. A 110, 1635-1644 (2006). (doi:10.1021/jp054241a)!– A. V. Popov, and R. Hernandez; J. Chem. Phys. 126, 244506 (2007). (arXiv:0705.0745) – A. V. Popov, and R. Hernandez; J. Chem. Phys. 131, 024503 (2009). (doi:10.1063/1.3168405)!– A. K. Tucker and R. Hernandez, J. Phys. Chem. A 114, 9628-9634 (2010).!– A. K. Tucker and R. Hernandez, J. Phys. Chem. B 115, 4412-4418 (2011).
• Control and Simulation of Transport on Surfaces – J. M. Moix, T. D. Shepherd, and R. Hernandez; J. Phys. Chem. B 108, 19476-19482 (2004). (doi:10.1021/jp046629w)!– J. M. Moix and R. Hernandez; J. Chem. Phys. 122, 114111 (2005). (cond-mat/0501327, doi:10.1063/1.1870875)!– J. M. Moix and R. Hernandez; Ann. Rep. Comp. Chem. 3, 137-151 (2007).!– J. M. Moix, R. Hernandez, and E. Pollak; J. Phys. Chem. B 112, 206-212 (2008).!– T. Vazhappilly, T. Klamroth, P. Saalfrank, and R. Hernandez; J. Phys. Chem. C 113, 7790-7801 (2009).!
• A Geometric Perspective on TST in Dissipative Systems – T. Bartsch, R. Hernandez, and T. Uzer; Phys. Rev. Let. 95, 058301 (2005). (doi:10.1103/PhysRevLett.95.058301)!– T. Bartsch, T. Uzer and R. Hernandez; J. Chem. Phys. 123, 204102 (2005). (cond-mat/0509425,doi:10.1063/1.2109827)!– T. Bartsch, T. Uzer, J. M. Moix and R. Hernandez; J. Chem. Phys. 124, 244310 (2006). (cond-mat/0604640)!– T. Bartsch, T. Uzer, J. M. Moix, and R. Hernandez; J. Phys. Chem. B 112, 213-218 (2008).!– T. Bartsch, J. M. Moix and R. Hernandez, S. Kawai, and T. Uzer, Adv. Chem. Phys. 140, 191-238 (2008).!– P.L. García-Müller, F. Borondo, R. Hernandez, and R. M. Benito, Phys. Rev. Let. 101, 178302 (2008).!– R. Hernandez, T. Bartsch and T. Uzer, Chem. Phys. 370, 270-276 (2010). "
• MD simulations of Cybotactic Region in GXLs
– J.P.Hallet, C.L.Kitchens, R.Hernandez, C.L.Liotta, C.A.Eckert, Acc. Chem. Res. 39, 531 (2006)!– C.L.Shukla, J.P .Hallet, A.V. Popov, R. Hernandez, C.L. Liotta, C.A. Eckert, J.Phys.Chem.B, 110, 24101 (2006).!– J.L. Gohres, C.L. Kitchens, J.P. Hallett, A.V. Popov, R.Hernandez, C.L. Liotta, C.A. Eckert; J.Phys.Chem.B, 112, 4666 (2008).!– J.L. Gohres, C.L.Shukla, A.V. Popov, R.Hernandez, C.L. Liotta, C.A. Eckert; J.Phys.Chem.B, 112, 14993 (2008).!– J. L. Gohres, A.V.Popov, R. Hernandez, C.L. Liotta, C.A. Eckert, J.Chem.Theory Comput. 5, 267-275 (2009). "
Nonequilibrium Chemistry & Materials
http://www.chemistry.gatech.edu/rig/!8843 Lecture #1 —Rigoberto Hernandez
7 Introduction
• A Stochastic Model for Polymerization – M. T. Vogt and R. Hernandez; "A two-dimensional polymer growth model," J. Chem. Phys. 115, 1575-1585 (2001).
(doi:10.1063/1.1380709)!– M. T. Vogt and R. Hernandez; "A three-dimensional polymer growth model," J. Chem. Phys. 116, 10485-10491 (2002). "
(doi:10.1063/1.1477455)!– Y. Qin, A. V. Popov, and R. Hernandez, "Stochastic models for polymerization reactions under nonequilibrium conditions," Ann. Rep.
Comp. Chem. 4, 173-199 (2008). (doi:10.1016/S1574-1400(08)00010-8) "
• A Lattice Model for Polymerization – R. Hernandez and F. L. Somer; "Stochastic dynamics in irreversible nonequilibrium environments. 2. A model for thermosetting
polymerization," J. Phys. Chem. B 103, 1070 (1999). (abstract, doi:10.1021/jp9836269)!– F. L. Somer and R. Hernandez; "Stochastic dynamics in irreversible nonequilibrium environments. 4. Self-consistent coupling in
heterogeneous environments," J. Phys. Chem. B 104, 3456 (2000). (doi:10.1021/jp9928762) – M. Vogt and R. Hernandez; "An idealized model for nonequilibrium dynamics in molecular systems," J. Chem. Phys. 123, 144109
(2005). (cond-mat/0501328, doi:10.1063/1.2052594) "
• Biophysics & Bioinformatics – C. R. Locker and R. Hernandez; "A minimalist model protein with multiple folding funnels," Proc. Natl. Acad. Sci. USA 98, 9074-9079
(2001). (doi:10.1073/pnas.161438898) – P. Doruker, R. L. Jernigan, I. Navizet and R. Hernandez; "The important fluctuation dynamics of large protein structures are preserved
upon renormalization," Int. J. Quant. Chem. 90, 822-837 (2002). (In the Per-Olov Lowdin Festschrift issue.) (doi:10.1002/qua.955) – C.-S. Liu, R. Hernandez, and G. B. Schuster; "The mechanism for radical cation transport in duplex DNA oligonucleotides,"
J. Am. Chem. Soc. 126, 2877-2884 (2004). (doi:10.1021/ja0378254) – S. Zhong, J. M. Moix, S. Quirk, and R. Hernandez; "Dihedral-angle information entropy as a gauge of secondary structure propensity,"
Biophys. J. 91, 4014-4023 (2006). (doi:10.1529/biophysj.106.089243) – S. Quirk, S. Zhong, and R. Hernandez, "De novo identification of binding sequences for antibody replacement molecules," Proteins:
Struct. Func. Bioinfo. 76, 693-705 (2009). (doi:10.1002/prot.22382) – G. Ozer, E. Valeev, S. Quirk and R. Hernandez; "Adaptive steered molecular dynamics of the long-distance unfolding of Neuropeptide
Y," J. Chem. Theory Comput., 6, 3026-3038 (2010). "
http://www.chemistry.gatech.edu/rig/!8843 Lecture #1 —Rigoberto Hernandez
8 Introduction
Nonequilibrium Chemistry & Materials
8843 Lecture #1 —Rigoberto Hernandez
Introduction 9
CHEM 8843 Lectures…
• Major Concepts • Roughly two 40-minute sessions separated
by a 5-minute break • Interactive • Think-Pair-Share
A! B!C! D!
Statistical Mechanics
• The microscopic theory could also be: – Quantum mechanics – QED or relativistic mechanics – etc.
• “statics” vs. “mechanics” vs. “dynamics” • Nonequilibrium requires motion (an EoM)
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Macroscopic Theories
Microscopic Theories
Thermodynamics
Classical Mechanics
Statistical Mechanics
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Nonequilibrium Statistical Mechanics
• Averages • Correlation functions • Stationary vs. Nonstationary • Local (or ohmic) vs. Nonlocal Response • Uniform vs. Nonuniform Response • Rates (Exponential Decay) • Particles vs. Distributions
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Undergrad PCHEM, Part I Atkins, Chapters 1-2
• Gases – Gas Laws or Equations of State (P,V,T,n)
• Perfect/Ideal • Real Gases (van der Waals & virial equations)
– Principle of Corresponding States – Nonideality (and phase transitions out of a gas!)
• Thermodynamics – First Law: (Energy Conservation) – Paths: Adiabatic, Isothermal, Reversible, Isenthalpic, Etc. – Path Functions, E.g., Work (w), Heat (q) – State Functions, E.g., Internal Energy—U(S,V,N), Enthalpy—
H(S,P,N) – Differential forms in natural or unnatural variables – Heat Capacity – Additive and Nonadditive Thermodynamic Quantities
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Introduction 17
Undergrad PCHEM, Part II Atkins, Chapters 3-4
• Thermodynamics – Second Law: (Total Entropy Increases)
• Needed to define Entropy & Temperature! (dS=dqrev/T) • Spontaneous Processes • Carnot Cycles & Efficiency of Engines • Claussius Inequality (dS≥dq/T)
– Third Law: (T≥0K) – More Free Energies: Helmholtz—A(T,V,N), Gibbs—G(T,P,N)
• Criteria for Spontaneity • Differential Forms…
– Legendre Transforms & Maxwell Relations
• Phase Diagrams (and classifying phase transitions) • Phase Rule • Clapeyron Equation along a coexistence Line
• Surfaces, Bubbles, Cavities, Droplets…
8843 Lecture #1 —Rigoberto Hernandez
Introduction 18
Undergrad PCHEM, Part III Atkins, Chapters 5-7
• Thermodynamics of Chemical Equilibria – Mixtures:
• Simple Mixtures • Solutions • Nonideal Mixtures
– Phase Diagram: • VLE (One Component) • Multi-Phase & Multiple Components
– Chemical Reactions – Returning to Equilibrium After Perturbations
• Thermodynamics of Nonideal Solutes – Ionic Solutions (5.13) – Electrochemistry (6.5-6.8)
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Undergrad PCHEM, Part IV Atkins, Chapters 21,22 & 24
• Macroscopic Kinetics & Microscopic Dynamics – Dynamics in Gases (Kinetic Model) – Dynamics (Transport) in Liquids
• Measurement using Electrolytes • Conclusion: Brownian Dynamics • Fick’s Law and Diffusion Equation
– Chemical Kinetics • Rate Laws (Elementary, Complex, Reaction Order…) • Rate Theory
– Collision Theory – Transition State Theory
• Master Equation: Diffusion, Convection, Reaction • Arrhenius Rate Theory (Including Solvent Effects!)
– Experimental Probes • Microscopic (E.g., Molecular Beams or Single-Molecule) • Macroscopic
Think-Pair-Share Q
• Which is your major/discipline? A. Chemistry B. Physics C. Other Science D. Chemical & Biochemical Engineering E. Other Engineering
8843 Lecture #1 —Rigoberto Hernandez
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8843 Lecture #1 —Rigoberto Hernandez
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Syllabus—Schedule
• Due dates for problem sets, exam dates, and due date for the paper
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Syllabus—Problem Sets
• (4) Problem Sets: – Scores: (out of 5 possible points)
• +1 = anything with your name handed in • +1 = a reasonable attempt on most or all problems • +1 = for the graded first problem • +2 = for an additional graded problem
– You may collaborate, but you must write your own solution!
• No late problem sets will be accepted. – Problem sets will be handed out at 1-2 weeks prior
to the deadline
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Syllabus—Exams
• 2 Term Exams: – One crib sheet HAND-WRITTEN allowed per
exam – Some material from 1st term may be included in
2nd exam – Higher/Lower of two term exams contributes
30%/20% to overall grade – Expect curves to adjust for multiple testing
procedure – Oral make-up exams (for excused absences)
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Syllabus—Textbooks • Textbooks:
– BH: J-L Barat and J-P Hansen, ”Basic Concepts of Simple and Complex Liquids” (Cambridge University Press, UK, 2003)
– EM: D. J. Evans and G. Morriss, ”Statistical Mechanics of Nonequilibrium Liquids,” 2nd Edition (Cambridge University Press, UK, 2008)
• Supplementary (but not required) Textbooks: – David Chandler, “Introduction to Statistical Mechanics” – Robert Zwanzig, “Nonequilibrium Statistical Mechanics”
• Look at other suggestions for reference
• Office hours on Monday’s after lecture…
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Course Web Site
• web.chemistry.gatech.edu/rig/courses/13a/ • Username: “CHEM8843” • Password: “isfun”
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Syllabus—Topics
• Rough outline as deviations will likely occur