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IntroductionIntroductionIntroductionIntroduction

MSE 620 Computational Materials Science /

CME 599-001 Molecular Simulations

S.E. Rankin

Department of Chemical and Materials Engineering

University of Kentucky, Lexington KY

August 23, 2006

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What are molecular simulations?

�Atomic or molecular-level detail

�Intermolecular interactions specified

�Emerging properties of population predicted

�“Simulation” : computer used to simulate configurations of population and how they evolve

�Numerical statistical mechanics tools

�Not “theory” but use theory, validate experiments

�Not “experiments” but used to validate theories

3AIChE J. 2000 46(5): 878

OUR FOCUS

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Numerical Tools : Fluid Mechanics

�In fluid mechanics, limited analytical solutions

☯For incompressible, Newtonian liquid, Navier-Stokes:

☯Axisymmetric flow neglecting gravity (Poiseulle)

☯Generally, numericalmethod needed forpractical problems

gvv

ρµρ +∇+−∇= 2p

Dt

D

−

∆=

22

14 R

r

L

PRvz

µ0

-1.25 -0.75 -0.25 0.25 0.75 1.25

r/R

vz

http://www.flow3d.com/appl/toilet.htm

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Numerical Tools : Statistical Mechanics

�Ideal gas equation

☯Probability of observing system in state w/ energy εi is

☯Thermo. Props. from canonical partition coefficient Q

☯For N independent particles in 3D box,

☯And for instance:

Q

e

e

eP

i

i

i E

i

E

E

i

β

β

β −

−

−

==∑

Vh

mkTeq

N

qQ

zyx

zyx

nnn

nnnmahN 2/3

21,,

))(8/( 2 where

!

22222

≅== ∑

∞

=

++− πβ

V

NkT

V

QkTp

TN

=

∂

∂=

,

ln

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Numerical Statistical Mechanics (cont)

�Generally, dependence of energies on configuration of atoms complicated

☯Internal degrees of freedom

☯Amorphous solids and liquids

☯Nanophase materials

�Need numerical methodto calculate Q

☯E.g. Lennard-Jones fluidat T=2.0 (from F&S)

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Relationship Between Exp Sim & Theo

REAL LIQUIDS MODEL LIQUIDSMAKE MODELS

PERFORM

EXPERIMENTS

PERFORM

SIMULATIONS

APPROXIMATE

THEORIESASSUMPTIONS

SOLVE

EXPERIMENTAL

DATA

EXACT

PREDICTIONS

THEORETICAL

PREDICTIONSCOMPARE COMPARE

TEST OF

MODELS

TEST OF

THEORY

Adapted from M.P. Allen and D.J. Tildesley Computer Simulation of Liquids, Oxford, 1987.

EXPENSE AND TIME

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Molecular Simulations: Beyond

Theory

�In addition to solving more problems, can directly observe molecular phenomena

☯Adsorption of butane insilicalite by molecular dynamicshttp://www.cacr.caltech.edu/Publications/annreps/annrep92/nichol.html

☯Dynamics (fullerene hitting Si)http://cnls.lanl.gov/~beardm/MolecularDynamics/c60si.html

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Unique Insights from Simulation

�3D Ising model

☯Model of magnetization (spin up/down)

☯3D model may have no analytical solution

☯Simulations easily performed

�Hydrophobic hydrationforces in solution

☯Example: Carbon nanotubesin water(J. H. Walther et al. “Molecular DynamicsSimulation of Carbon Nanotubes in Water,”Proceedings, Center for TurbulenceResearch, Stanford University, 1998.)

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This course will notnotnotnot focus on...

�Quantum mechanics

☯Ab initio and molecularorbital techniques

☯Most fundamental

☯Can do it - more DOF

�Finite element methods

☯Treat particles of fluid as continuum

☯If interested, talk to Tate Tsang about FEM course

�Instead, focus on approximate molecular models and mesoscale models that bridge these two

Quantum MD simulation of K.T. Thomson &

R. Wentzcovitch, J. Chem. Phys. 1998 108:8584.

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Applications of Molecular Simulations 1

�Dynamic Monte Carlo Simulation of Sol-Gel Silica

☯“Master Equation” SolutionS.E. Rankin et al. Macromolcules 2000 33:7639.

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Molecular Simulation Apps 2

�MD of Sol-Gel Silica-Alumina InterfaceS. Blonski and S.H. Garofalini J. Phys. Chem. 1996 100:2201.

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Molecular Simulation Apps 3

�Lattice Monte Carlo Surfactant Self-Assembly

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Molecular Simulation Apps 4

�Shearing of crystalline materials

☯MD of shearing single-crystal FCC nickelM. F. Horstemeyer , M. I. Baskes and D. J. Plimpton Acta Mater. 2000 49:4363

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Molecular Simulation Apps 5

�Many biological apps(protein / DNA motion)

�Traditional transportmodeling using MD

�Water transport inaquaporin

�Single-file diffusion

http://www.ks.uiuc.edu/Gallery/Movies/aquaporins/chemanim1.mpg

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Molecular Simulation Apps 4

�Mesoscale Model of Polymer Tethering

☯Random sequential adsorption of elastic discs

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Molecular Simulation Apps 6

�Kinetic Monte Carlo for Crystal Etching

☯Si etching vs. miscut angleY.C. Huang, J. Flidr, T.A. Newton and M.A. Hines, J. Chem. Phys. 2000 109:5025.