chem 8843 special topics: nonequilibrium statistical...

CHEM 8843: Special Topics: Nonequilibrium

Statistical Mechanics

Prof. Rigoberto Hernandez [email protected]

8843 Lecture #1 —Rigoberto Hernandez

Introduction 1

SPRING 2013


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!


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


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!


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


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


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!


•  The microscopic theory could also be: – Quantum mechanics – QED or relativistic mechanics –  etc.

•  “statics” vs. “mechanics” vs. “dynamics” •  Nonequilibrium requires motion (an EoM)


Introduction 12

Macroscopic Theories

Microscopic Theories

Thermodynamics

Classical Mechanics



Introduction 13

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


Introduction 16

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


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…


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)


Introduction 19

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


Introduction 21


Introduction 22

Syllabus—Schedule

•  Due dates for problem sets, exam dates, and due date for the paper


Introduction 23

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


Introduction 24

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)


Introduction 25

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…


Introduction 26

Course Web Site

•  web.chemistry.gatech.edu/rig/courses/13a/ •  Username: “CHEM8843” •  Password: “isfun”


Introduction 27

Syllabus—Topics

•  Rough outline as deviations will likely occur

chem 8843 special topics: nonequilibrium statistical...

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