What are molecular simulations? Introduction. Numerical Tools : Fluid Mechanics

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1 What ar molcular simulations? Introduction MSE 60 Computational Matrials Scinc / CME Molcular Simulations S.E. Rankin Dpartmnt of Chmical and Matrials Enginring Univrsity of Kntucky, Lxington KY August 3, 006 Atomic or molcular-lvl dtail Intrmolcular intractions spcifid Emrging proprtis of population prdictd Simulation : computr usd to simulat configurations of population and how thy volv Numrical statistical mchanics tools Not thory but us thory, validat xprimnts Not xprimnts but usd to validat thoris 1 Numrical Tools : Fluid Mchanics OUR FOCUS In fluid mchanics, limitd analytical solutions For incomprssibl, Nwtonian liquid, Navir-Stoks: Axisymmtric flow nglcting gravity (Poisull) Gnrally, numrical mthod ndd for practical problms Dv ρ p + µ v + ρg Dt R P r v z 1 4 µ L R 0 vz r/r AIChE J (5):

Numrical Tools : Statistical Mchanics Numrical Statistical Mchanics (cont) Idal gas quation Probability of obsrving systm in stat w/ nrgy ε i is Thrmo. Props.

2 Numrical Tools : Statistical Mchanics Numrical Statistical Mchanics (cont) Idal gas quation Probability of obsrving systm in stat w/ nrgy ε i is Thrmo. Props. from canonical partition cofficint Q For N indpndnt particls in 3D box, And for instanc: Pi q Q whr q N! n, n, n 1 x y z i Q N 3/ β ( h /8ma )( nx + ny + nz ) lnq p kt V N, T NkT V πmkt h V Gnrally, dpndnc of nrgis on configuration of atoms complicatd Intrnal dgrs of frdom Amorphous solids and liquids Nanophas matrials Nd numrical mthod to calculat Q E.g. Lnnard-Jons fluid at T.0 (from F&S) 5 6 Rlationship Btwn Exp Sim & Tho Molcular Simulations: Byond Thory REAL LIQUIDS PERFORM EXPERIMENTS EXPERIMENTAL DATA MAKE MODELS COMPARE MODEL LIQUIDS PERFORM SIMULATIONS EXACT PREDICTIONS ASSUMPTIONS COMPARE APPROXIMATE THEORIES SOLVE THEORETICAL PREDICTIONS In addition to solving mor problms, can dirctly obsrv molcular phnomna Adsorption of butan in silicalit by molcular dynamics annrp9/nichol.html TEST OF MODELS TEST OF THEORY Dynamics (fullrn hitting Si) EXPENSE AND TIME Adaptd from M.P. Alln and D.J. Tildsly Computr Simulation of Liquids, Oxford,

Uniqu Insights from Simulation This cours will not focus on.

Carbon nanotubs in watr (J. H. Walthr t al. Molcular Dynamics Simulation of Carbon Nanotubs in Watr, Procdings, Cntr for Turbulnc Rsarch, Stanford Univrsity, 1998.

3 Uniqu Insights from Simulation This cours will not focus on... 3D Ising modl Modl of magntization (spin up/down) 3D modl may hav no analytical solution Simulations asily prformd Hydrophobic hydration forcs in solution Exampl: Carbon nanotubs in watr (J. H. Walthr t al. Molcular Dynamics Simulation of Carbon Nanotubs in Watr, Procdings, Cntr for Turbulnc Rsarch, Stanford Univrsity, 1998.) Quantum mchanics Ab initio and molcular orbital tchniqus Most fundamntal Can do it - mor DOF Finit lmnt mthods Quantum MD simulation of K.T. Thomson & R. Wntzcovitch, J. Chm. Phys :8584. Trat particls of fluid as continuum If intrstd, talk to Tat Tsang about FEM cours Instad, focus on approximat molcular modls and msoscal modls that bridg ths two 9 10 Applications of Molcular Simulations 1 Molcular Simulation Apps Dynamic Mont Carlo Simulation of Sol-Gl Silica Mastr Equation Solution S.E. Rankin t al. Macromolculs000 33:7639. MD of Sol-Gl Silica-Alumina Intrfac S. Blonski and S.H. Garofalini J. Phys. Chm :

4 Molcular Simulation Apps 3 Molcular Simulation Apps 4 Lattic Mont Carlo Surfactant Slf-Assmbly Sharing of crystallin matrials MD of sharing singl-crystal FCC nickl M. F. Horstmyr, M. I. Basks and D. J. Plimpton Acta Matr : Molcular Simulation Apps 5 Molcular Simulation Apps 4 Many biological apps (protin / DNA motion) Traditional transport modling using MD Watr transport in aquaporin Singl-fil diffusion Msoscal Modl of Polymr Tthring Random squntial adsorption of lastic discs

5 Molcular Simulation Apps 6 Kintic Mont Carlo for Crystal Etching Si tching vs. miscut angl Y.C. Huang, J. Flidr, T.A. Nwton and M.A. Hins, J. Chm. Phys :

Elements of Statistical Thermodynamics

Elements of Statistical Thermodynamics 24 Elmnts of Statistical Thrmodynamics Statistical thrmodynamics is a branch of knowldg that has its own postulats and tchniqus. W do not attmpt to giv hr vn an introduction to th fild. In this chaptr,