DOC PREVIEW
CU-Boulder ASEN 5519 - Interatomic Potentials and Force Fields

This preview shows page 1-2-3-22-23-24-44-45-46 out of 46 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 46 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 46 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 46 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 46 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 46 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 46 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 46 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 46 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 46 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 46 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

Interatomic Potentials and Force FieldsJudith A. Harrison and Guangtu GaoChemistry DepartmentUnited States Naval AcademyAnnapolis, MD [email protected] Potential⎥⎦⎤⎢⎣⎡⎟⎠⎞⎜⎝⎛−⎟⎠⎞⎜⎝⎛=612rσrσ4εU(r)r ε and σ are energy and length parameters, respectively. r is the intermolecular distance. For inert monatomic molecules.Rare Gas Parameters:Ne σ = 2.74 Å ε/kB= 36.2KAr σ = 3.405 Å ε/kB= 121KKr σ = 3.65 Å ε/kB= 163KXe σ = 3.98 Å ε/kB= 232KCombining Rules for Unlike Pairs:jiijσσσ =jiijεεε=Global Minima of LJNClusters – The Magic Number Cluster Structures(Data are from The Cambridge Cluster Database, http://www-wales.ch.cam.ac.uk/)N = 13 E = -44.33εN = 19E = -72.66εN = 25E = -102.37εN = 55E = -279.25εSolvation of Halogens in Rare-Gas ClustersSolvated (12K)Implanted (0K)Fragmented (37K)Ar55Cl27 K42 KAr20Cl2J. A. Harrison & M. G. PrisantDuke University (1990)F. G. Amar and B. J. Berne, J. Phys. Chem. 88 (1984) 6720Br2ArNClusters Potentials:Br-Ar σ = 2.74 Å ε/kB= 143 K LJ potentialAr-Ar σ = 3.405 Å ε/kB = 119.8 K LJ potentialBr-Br: Morse PotentialF. G. Amar and B. J. Berne, J. Phys. Chem. 88 (1984) 6720()()[]{}o2eErrαexp1 DrV −−−−=Ground state: X()()()[]2ooorrβrrαexpVrV −−−−=Excited State: u11ΠVo= 11012.95 Kro= 2.3 Åα= 4.637 Å-1β = 0.879 Å-2F. G. Amar and B. J. Berne, J. Phys. Chem. 88 (1984) 6720Br2ArNClustersInteraction Potential Î Bead-Spring ModelEach polymer contains N spherical beadsAll interact with Lennard-Jones potentialVLJ(r) = 4ε[(σ/r)12 −(σ/r)6] for r < rcVb(r) = VLJ(r) + k r4[(r-r1)(r-r2)] + Vcr < rbrVb(r) = 0 r > rbrk, r1, r2, Vc= obtained from fitting FENE near mean equilibrium bond length. rbr= length at which a bond is considered broken, kSemiflexible chains → add bond-bending terms→ less flexible, smaller NeBackbone – FENE potentialStandard Finite Extensible Nonliner Elastic potentialαCourtesy of Mark. O. Robbins, The Johns Hopkins UniversityK. Kremer and G. S. Grest, J. Chem. Phys. 92, 5057 (1990)S. W. Sides, G. S. Grest, and M. J. Stevens, Phys. Rev. E. 64, 050802 (2001)Adhesion of surface-tethered chains entangled in a polymer melt• tensile pull simulation•2 x 105particles (Nt= 250, chain length)• move bottom wall at constant velocity• Chains attached to bottom wall only• wall-chain interaction Æ LJ• T << Tg• Red = tethered chains• Blue = represent the polymer melt• Green = chains were tethered buthave brokenS. W. Sides, G. S. Grest, and M. J. Stevens, Phys. Rev. E. 64, 050802 (2001)Quantifying the amount of chain scission ∑=tnitfittNNnF,1<F > = Ave fractional chain length<F> = 1 Pure chain pull out<F> = 0 Chain scission at wallNt,i= length of ithchain at end ofsimulation<F> decreases as chain length increases!T > TgT < TgUnited Atom PotentialsHow to build: Molecule are represented by different functional groups, ex., CHngroups. Functional groups are represented as spherical pseudo-atoms. There are bonded and non-bonded interactions among the pseudo-atoms. Potential is the sum the these bonded and non-bounded interactions terms. Potential parameters are obtained from fitting the experimental and quantummechanical data.Dihedral termθBonded interactions:Bond term , Morse function, or rigid.Angle termP. van der Ploeg et al. Mol. Phys. 49, 233 (1983)()∑+=ωωnsVEncos1Non-bonded interactions: Lennard-Jones potential and Coulomb potential.J. Hautman and M.L. Klein, J. Chem. Phys. 91, 4994 (1989)J. Hautman and M. L Klein, J. Chem. Phys. 93, 7483 (1990)J. Ryckaert & A. Bellemans. Faraday Discuss. Chem. Soc. 66, 95 (1978)()∑−=0llkEll()∑−=0θθϑθkEModeling Alkylthiol Chains S(CH2)nCH3 CH3CH2CH2CH2CH2CH2SdSCdccθCCFunctional groups: S, CH2, and CH3.Bonds are rigid: dCC=1.53Å and dSC=1.82Å.Intramolecular potential:(1) Bond angle term (2) Dihedral angle term(3) LJ interaction between atoms greater than fourth nearest neighborsIntermolecular (chain-chain) potential:LJ potential between all sites on different Chains.()2021θθθ−= kVb()()()() () ()φφφφφφ5544332210coscoscoscoscosaaaaaaVt+++++=J. Hautman and M.L. Klein, J. Chem. Phys. 91, 4994 (1989)J. Hautman and M. L Klein, J. Chem. Phys. 93, 7483 (1990)Self-Assembled Monolayers: Alkanethiol Chains on Au (Au--S(CH2)nCH3)AuCH3CH2CH2CH2CH2CH2SdSCdccSurface Potential: Au--S()()()3o312o12zzCzzCzV−−−=Polarizability of Kr about the same as CH2/CH3Use Kr on Ag(111) experimental data to fix parameters(model zCourtesy of Scott Perry, University of HoustonImproving the Model - All-Atom Representation(J.P. Bareman and M.L. Klein, J. Phys. Chem. 94, 5202 (1990))CHHCH2Group:CHHHCH3Group:Using C and H atoms to represent the CHngroups.dCC=1.53Å , dCH= 1.040Å, and H-C-H bond angles are all tetrahedral.Interactions between atoms on different chains (used for studies of bulk n-alkanes)6BrrCAeV(r) −=−A, B, C = parametersD. E. Williams, J. Chem. Phys. 47, 4680 (1967)Intramolecular and molecule-surface potential = same as united atomJ.P. Bareman and M.L. Klein, J. Phys. Chem. 94, 5202 (1990)Improvement over the united-atom model:(1) Better representation of the collective tilt of the chains in LB films.(2) Better estimation of the effective diameters of long chains.(3) United atom cannot reproduce tilt angles ExperimentUnited AtomAll AtomW. Mar & M. L. Klein, Langmuir 10, 188 (1994)All-Atom Representation yields herringbone structureA. Ulman, Chem. Rev. 96, 1533 (1996)Can MD simulations predict the experimentally determined structure?L. Zhang, W. A. Goddard III, & S. Jiang, J. Chem. Phys. 117, 7342 (2002)Need an accurate surface interaction potential.()⎥⎦⎤⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛−=−=1RR2S-expχ 2χχDEe2eRe= equilibrium position determined to fit the ab initio interatomicS-Au distanceDe= Dissociation energyS = Scale factor (binding energy of thiolate with Au and energy difffor a thiol adsorbed on different sites (fcc, hcp, atop, bridge)Parameter fits with POLYGRAF (DMOL, Molecular Simulations, Inc.)III & IV = c(4x2) superlattice(4 chains / unit cell)II = herringbone (2 chains/unit cell)I = one chain/unit cellV = 4 chains / unit cell= Au= S= hydrocarbonbackboneoR30 33 ×L. Zhang, W. A. Goddard III, & S. Jiang, J. Chem. Phys. 117, 7342 (2002)J. A. Harrison, et al., “The Friction of Model Self-Assembled Monolayers”, inEncyclopedia of Nanoscience and Nanotechnology, Vols. 3,


View Full Document

CU-Boulder ASEN 5519 - Interatomic Potentials and Force Fields

Documents in this Course
Lecture

Lecture

13 pages

Load more
Download Interatomic Potentials and Force Fields
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Interatomic Potentials and Force Fields and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Interatomic Potentials and Force Fields 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?