fundamentals of molecular dynamics for nano-technology applications mario blanco materials and...

Fundamentals of Molecular Dynamics for Nano-technology ApplicationsMario BlancoMaterials and Process Simulation CenterCalifornia Institute of Technology IPAM, October 16, 2002

OutlineHierarchical Multi-scale ModelingBrief Review of QM and MDForce Field Development Long Range Atomic PotentialsLarge Scale MD simulationsFluid Control Nano-valveNEMSChallenges

Material ScienceChemistryQUANTUMMECHANICSMolecular DynamicsForce FieldsHierarchical SimulationsChemistMeso-scaleModelingEquilibrium& Rate Constants

Molecular Self-AssemblyCatalysis

Biochemistry

OrganelleModeling

GeneticEngineering

Pharmaceuticals

SpecialtyChemicals& Catalysts

Metal Alloys

Ceramics

Polymers

ReceptorModeling

C1 Chemistry

Electronic& OpticalMaterials

Cancer Research

Fossil EnergyFuel CellsNanotechnologyAtomsElectronsMoleculesMaterialsDesignFemptosecondsAngstromsMicrosecondsMicronsYearsYardsPicosecondsNanometersSecondsInchesH = E F=maMulti-scale W.A. Goddard III, M. Blanco, 1998

Hierarchical ModelingChemical Engineer

minutess

1 nm

picosec

ENGINEERING

DESIGN

UNIT

PROCESS

DESIGN

hours

years

ELECTRONS => ATOMS => SEGMENTS => GRIDS

TIME

DISTANCE

micron

10 nm

1 A

yards

mm

Force Field

Charges

Segment Averages

Group Additivities

Solubilities

QSPR

Equation of State

Viscosity

Thermal Conductivity

Friction Coefficients

Activity Coefficients

Phase Diagram

ASOG

UNIQUAC

Yield (

Young's (

QUANTUM

MECHANICS

H(=E(

femtosec

nanosec

microsec

MOLECULAR

DYNAMICS

F= M A

seconds

MESOSCALE

DYNAMICS

(= E (

FINITE

ELEMENT

ANALYSIS

PROCESS

SIMULATION

Mechanical EngineerNew generation reactive force fields based purely on first principlesFor metals, oxides, organics.Describes: mechanical properties, chemistry,charge transfer, atomic polarization, etc.Deformation and Failure (dislocations, cracks, etc.)Transport properties(diffusion, thermal transport, etc.) Micromechanical modelingContinuum simulations of real devices and materialsAccurate calculations for bulk phases and molecules (EOS, dissociation curves, etc.)Optical properties

MSC/Caltech Quantum Mechanics (Schrodinger)Periodic Systems (3D & 2D)High Accuracy for Large SystemsFast Results for Large SystemsSolvation (Poisson-Boltzmann)Force FieldsPolarizable, Charge TransferVariable Bond OrdersPhase TransitionsMixed Metal, Ceramic, PolymerMesoScale DynamicsCoarse Grained FFGas DiffusionHybrid MD and Meso DynamicsTribologyEpitaxial GrowthUtilization: Web-based user-friendly tools for nonexpertsMolecular DynamicsLarge Systems (CMM, Parallel)Non-Equilibrium Dynamics ViscosityThermal ConductivitySolvation (Schrodinger)surface tension, contact anglesHybrid QM/MDHierarchical NEIMOPlasticityFormation Twins, DislocationsCrack InitiationInterfacial EnergiesGeneralized Hildebrand SolubilitiesProcess SimulationVapor-Liquid EquilibriaReaction NetworksNanotechnologyNano-electronic DevicesNano electro-mechanical systems (NEMS)

The HamiltonianBorn-Oppenheimer1 e orbitals=LCAOn electron trialsolutionM sufficiently large leads to Hartree-Fock limitCorrelation Energy = Difference between experimental and HF energyE(R) = Energy EigenvaluesFunction of nuclear coordinates

Slater DeterminantsPauli Exclusion PrincipleTwo electrons: anti-symmetrized linear combinationn electrons: Slater Determinantetc

Potential Energy Surface (PES)BondRo = 0.9 2.2 AK = 700 Kcal/mol-A2

Potential Energy Surface (PES)E(R)= A e-CR - B/R6 BuckinhamE(R)=Do{[Ro/R)12]}- 2[Ro/R)6]} Lennard-Jones 12-6Exponential-6

Van der Waals (induced dipoles)Electrostatics (point charges)Do=0.01 to 10 Kcal/molRo=1.0 to 4.0 Aq=-1 to 1

Force Fields

Valence Force Field

Bond Stretch

Bond Angle bend

Torsion

Inversion

Typical ExpressionsDescription Ilustration PotentialForces

y

q

J

Dinmica Molecular: Fuerzas Interatmicas


Electrostatics

van der Waals

Non-Bond Force Field

enlace

Non-bonded

enlace

Repulsive


Bonded

Bonded

R

R0

E

D0

_926274384.unknown

_926274629.unknown

_926274723.unknown

_926274760.unknown

_926274706.unknown

_926274594.unknown

_926274371.unknown

Molecular Mechanicsq = Ri nuclear coordinates (PES)

V(q) from Quantum Mechanics

Hessian Matrix: second derivativesMinimizationYields equilibrium structuresQuantum Mechanics

Molecular DynamicsGeneralized forces

Generalized momentumVerlet algorithmIn cartesian coordinates

150 deg

164 deg

180 deg

Chart1

0.9054962806

0.8490204211

0.76681667

0.6086842635

0.4480418187

0.2648090301

0.107304133

0.0257278916

0

0.0527108022

0.2114707183

158

0.8778858604

1.4451544936

2.146082661

2.999495649

Kcal/mol

Dihedral angle

Energy (Kcal/mol)

C6F14 Dihedral QM energy (B3LYP, 631G*)

del

DihedralCoulomb1-3 includedDihedralKcal/mol627.50955Kcal/mol-eVBondAngle

27.45211500.5939-5.1271800.9054962806-180-1626.370325-1626.3717678659127.92

27.32371520.46551.8831780.8490204211-178-1626.370415-1626.36879127.771

27.25721540.3991.1331760.76681667-176-1626.370546127.644

27.09811560.23990.681740.6086842635-174-1626.370798127.539

27.18990.3317-1.8871720.4480418187-172-1626.371054127.438

26.96941600.11120.1021700.2648090301-170-1626.371346127.433

26.8582162001680.107304133-168-1626.371597127.41

26.93661640.0784-0.4281660.0257278916-166-1626.371727127.403

27.10081660.2426-0.911640-164-1626.371768127.405

27.25371680.3955-1.4741620.0527108022-162-1626.371684127.409

27.46061700.6024-2.3071600.2114707183-160-1626.371431127.422

27.66591720.8077-3.003158-158127.44

27.88051741.0223-3.861560.8778858604-156-1626.370369127.447

28.03231761.1741-4.3641541.4451544936-154-1626.369465127.457

28.18471781.3265-4.8781522.146082661-152-1626.368348127.463

28.18561801.3274-5.1271502.999495649-150-1626.366988127.471

C6F14 charges areB3LYP 631G* Mulliken with constrained torsion for three middle dihedrals and free terminal CF3

del

Coulomb

Point Charges: Coulomb from QM Polarized Charges

Kcal/mol

Dihedral angle

Energy (Kcal/mol)


Energy ComponentsMolecular origin of helicity in Teflon

Chart7

-0.975972.232830.62333.1882.999495649

-0.819281.802330.38032.2492.146082661

-0.666071.420730.17621.4741.4451544936

-0.51681.079230.02570.8650.8778858604

-0.243840.45484-0.07410.1570.2114707183

-0.110550.24379-0.10080.0050.0527108022

00000

0.10101-0.195080.14290.1070.0257278916

0.19021-0.371280.28940.2510.107304133

0.26925-0.500440.44780.4560.2648090301

0.33544-0.591960.59090.6660.4480418187

0.38727-0.650820.74590.8830.6086842635

0.42536-0.680180.82421.0150.76681667

0.44988-0.725170.91581.1470.8490204211

0.45636-0.709020.91451.1530.9054962806

O

torsion

vdw

electrostatic

Force Field

QM B3LYP

f (degrees)

Energy (Kcal/mol)

Charge Method

ESP-ElecESP-SplinedihedralFixed ESPESP-SplineMUL-SplineFixed MULPolarized MUL

27.55991.911191.436551500.064630.064860.62450.62330.5939

27.31691.886571.411671520.040010.039980.38030.38030.4655

27.11281.866371.391251540.019810.019560.17510.17620.399

26.96231.849321.37411560.002760.002410.02410.02570.2399

26.86251.838291.36314160-0.00827-0.00855-0.0754-0.07410.1112

26.83581.832661.35756162-0.0139-0.01413-0.1018-0.10080

26.93661.846561.3716916400000.0784

27.07951.866191.391541660.019630.019850.1440.14290.2426

27.2261.886691.412421680.040130.040730.29240.28940.3955

27.38441.908361.434431700.06180.062740.45240.44780.6024

27.52751.928081.454411720.081520.082720.59680.59090.8077

27.68251.951271.47781740.104710.106110.75280.74591.0223

27.76081.961931.488671760.115370.116980.83210.82421.1741

27.85241.975711.502581780.129150.130890.92430.91581.3265

27.85111.974871.501791800.128310.13010.92330.91451.3274

Charge Method

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

Fixed ESP

Fixed MUL

Polarized MUL

Dihedral angle (degrees)

Energy (Kcal/mol)

FF QM geometry

dreiding_msc_exp6.par, fixed charges (164 deg), QM optimized geometriese-emin

angletorsionvdwcoulombE totalangletorsionvdwelectrostaticForce Fieldcoulomb+vdwtorsion+vdwQM B3LYP

1506.847611.354427.5599144.127150-0.975972.232830.62333.1882.856131.256860.03553389042.9994956490.188504351

1527.0042910.923927.3169143.188152-0.819281.802330.38032.2492.182630.983050.01059197872.1460826610.102917339

1547.157510.542327.1128142.413154-0.666071.420730.17621.4741.596930.754660.00083206321.44515449360.0288455064

1567.3067710.200826.9623141.804156-0.51681.079230.02570.8651.104930.562430.00016604540.87788586040.0128858604

1607.579739.5764126.8625141.096160-0.243840.45484-0.07410.1570.380740.2110.00296705920.21147071830.0544707183

1627.713029.3653626.8358140.944162-0.110550.24379-0.10080.0050.142990.133240.00227632060.05271080220.0477108022

1647.823579.1215726.9366140.939164000000000

1667.924588.9264927.0795141.0461660.10101-0.195080.14290.107-0.05218-0.094070.00660515560.02572789160.0812721084

1688.013788.7502927.226141.191680.19021-0.371280.28940.251-0.08188-0.181070.02064850220.1073041330.143695867

1708.092828.6211327.3844141.3951700.26925-0.500440.44780.456-0.05264-0.231190.0365539870.26480903010.1911909699

1728.159018.5296127.5275141.6051720.33544-0.591960.59090.666-0.00106-0.256520.04750576880.44804181870.2179581813

1748.210848.4707527.6825141.8221740.38727-0.650820.74590.8830.09508-0.263550.07524912330.60868426350.2743157365

1768.248938.4413927.7608141.9541760.42536-0.680180.82421.0150.14402-0.254820.06159496530.766816670.24818333

1788.273458.396427.8524142.0861780.44988-0.725170.91581.1470.19063-0.275290.08879182950.84902042110.2979795789

1808.279938.4125527.8511142.0921800.45636-0.709020.91451.1530.20548-0.252660.06125809110.90549628060.2475037194

0.0300383187

0.1733156619

Q factorEq Angle

0180

0.1180

0.2180

0.3180

0.4180

0.5180

0.6179.8

0.7179.7

0.8179.4

0.9177.8

1175.2

1.1172.9

1.2171.2

1.3169.9

1.4168.7

1.5167.8

1.6

1.7

1.8

FF QM geometry

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

torsion

vdw

electrostatic

Force Field

QM B3LYP

f (degrees)

Energy (Kcal/mol)

FF minimized geometry

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Eq Angle

Equilibrium Dihedral Angle f

Equilibrium Dihedral Angle f

FF fixed geometry

Rigid Dihedral changes no minimization

angletorsionvdwcoulombsumtotal

-1808.27800163229.72317624322.964136703140.96531457820.7034018502140.44988387820.7339982842

-1758.23054960649.738534068622.847952615340.81703629030.5551235623140.29098843180.5751028378

-1708.09223276839.814163524122.587051023440.49344731570.2315345877139.94617615640.2302905624

-1657.872857489210.032875028522.356180210340.2619127280139.7158855940

-1607.586080345710.499469121422.298427729340.38397719640.1220644684139.91898475070.2030991566

-1557.248684390911.291543976222.494996842741.03522520980.7733124818140.81847307591.1025874819

-1506.879357157812.423270532822.971166675542.27379436612.0118816381142.58854466082.8726590668

-1456.498328867113.836945495623.704471165144.03974552783.7778327998145.27792224565.5620366516

-1406.128357473615.412526310424.63187082646.172754615.910841882148.76139140079.0455058066

-1355.796484587116.9720146525.648368896348.41686813348.1549554054152.676072760412.9601871664

-1305.534875300518.274815323726.597257841550.406948465710.1450357377156.356927097816.6410415038

-1255.376061868219.043984236427.281439731551.701485836111.4395731081158.894851078919.1789654849

-1205.340223193819.090944222327.550625777251.981793193311.7198804653159.551694335819.8358087418

-1155.423870026118.382104439427.430068525651.236042991110.9741302631158.299972228418.5840866344

-1105.590583923216.65960858127.354048718949.60424122319.3423284951156.049766033116.3338804391

-1055.825602285314.87898009227.549414781148.25399715847.9920844304153.792602114314.0767165203

-1006.120964931313.510514535328.303490698547.93497016517.6730574371152.154118924712.4382333307

-956.501017819413.62638923628.835829055148.96323611058.7013233825150.875025457911.1591398638

-906.839532887413.190132739829.647118503549.67678413079.4148714027151.351493041311.6356074473

-857.187607118413.296361726231.196264560551.680233405111.4183206771154.206468461514.4905828675

-807.481670063412.879886949234.651822469855.013379482414.7514667544159.478288192219.7624025982

-757.80187899412.975521207635.645212537856.422612739416.1607000114161.873706697322.1578211033

-708.036178598312.151371044336.336899609956.524449252416.2625365244161.858185801422.1423002074

-658.187982634611.151529083237.091972121856.431483839716.1695711117160.931581862521.2156962685

-608.26683994110.479627606737.92383109356.670298640716.4083859127160.401510389720.6856247957

-558.260363222410.501405086439.186063902257.947832210917.6859194829162.240803609122.5249180151

-508.16131952211.012753094841.303546489360.477619106120.2157063781167.83964335928.1237577649

-458.108347879812.844702104644.987924151665.94097413625.679061408176.913851242337.1979656483

-407.90666787613.864414038146.744808323668.515890237728.2539775097180.656541622540.9406560285

-357.641897533314.798316009147.954515596770.394729139130.1328164111184.394217711344.6783321173

-307.499293745216.866658140449.451178245173.817130130833.5552174028192.843893543453.1280079494

-257.066952336619.759959113151.048858418577.875769868237.6138571402205.344420930965.6285353369

-206.74104011821.976481102851.508765205980.226286426739.9643736987212.383191033472.6673054394

-156.454415782424.107805448352.536395957283.098617187842.8367044598221.737668260982.0217826669

-106.042511112825.208081178954.991262485186.241854776845.9799420488236.475819278496.7599336844

-55.458464399124.658755171659.645640132389.76285970349.500946975253.9568101536114.2409245596

05.325736991325.812100484460.054512413591.192349889250.9304371612260.3919722695120.6760866755

55.45846439924.658755177459.64564013589.762859711449.5009469834253.9568101605114.2409245665

106.042511109125.208081159654.991262518586.241854787345.9799420593236.475819320696.7599337266

156.454415782324.107805450152.536395957283.098617189642.8367044616221.73766826182.021782667

206.741040117921.976481102651.508765205980.226286426539.9643736985212.383191033472.6673054393

257.066952336619.759959113251.048858418577.875769868237.6138571402205.344420930965.6285353369

307.499293745216.866658138249.451178244273.817130127633.5552173996192.843893539153.128007945

357.641897534814.798316002547.954515595770.39472913330.132816405184.394217708744.6783321147

407.906667881213.864414047346.744808317468.515890245828.2539775178180.65654162240.940656028

458.108347880212.844702106444.987924151665.940974138225.6790614102176.913851243137.1979656491

508.161319522111.012753093841.30354649160.477619106920.2157063789167.83964336128.123757767

558.260363222410.501405057739.186063905557.947832185617.6859194576162.240803602222.5249180081

608.26683994110.479627606737.92383109356.670298640716.4083859127160.401510389720.6856247957

658.187982634711.151529083237.091972121856.431483839716.1695711117160.931581862521.2156962685

708.036178598312.151371044336.336899609956.524449252416.2625365244161.858185801422.1423002074

757.80187899412.975521207635.645212537856.422612739416.1607000114161.873706697322.1578211033

807.481670063412.879886949234.651822469855.013379482414.7514667544159.478288192219.7624025982

857.187607117913.296361720531.196264565751.68023340411.418320676154.206468461414.4905828674

906.839532886413.190132734729.647118511249.67678413239.4148714043151.351493041211.6356074472

956.501017819513.626389239528.835829051948.9632361118.701323383150.875025457911.1591398639

1006.120964931313.510514535328.303490698547.93497016517.6730574371152.154118924712.4382333307

1055.825602285314.87898009227.549414781148.25399715847.9920844304153.792602114314.0767165203

1105.590583923216.659608580827.354048719249.60424122329.3423284952156.049766033116.3338804391

1155.423870025718.382104451127.430068523351.236043000110.9741302721158.299972229518.5840866355

1205.340223193819.090944221427.550625777851.98179319311.719880465159.551694335819.8358087418

1255.376061868219.04398423327.281439732651.701485833811.4395731058158.894851078819.1789654848

1305.534875300518.274815323726.597257841550.406948465710.1450357377156.356927097816.6410415038

1355.79648458716.972014651825.648368894748.41686813358.1549554055152.676072760312.9601871663

1406.128357473615.412526311324.631870825746.17275461065.9108418826148.76139140079.0455058067

1456.498328867113.836945496223.704471164944.03974552823.7778328002145.27792224575.5620366516

1506.879357157812.423270531122.971166676642.27379436552.0118816375142.58854466062.8726590666

1557.248684390911.291543976222.494996842741.03522520980.7733124818140.81847307591.1025874819

1607.586080345710.499469121422.298427729340.38397719640.1220644684139.91898475070.2030991566

1657.872857489210.032875028522.356180210340.2619127280139.7158855940

1708.09223276839.814163524122.587051023340.49344731570.2315345877139.94617615640.2302905624

1758.23054960649.738534068622.847952615340.81703629030.5551235623140.29098843180.5751028378

1808.27800163229.723176243722.964136702540.96531457840.7034018504140.44988387820.7339982842

FF fixed geometry

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torsion

vdw

coulomb

torsion (degrees)

Energy (Kcal/mol)

Force Field: dreiding_msc_exp6.par

FF QM geometry _absolute

0

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0

0

0

0

0

total energy

torsion angle (degree)

Energy (kcal/mol)

symmetrize charges

Rigid Dihedral changes no minimization

angletorsionvdwcoulombsum

-1808.280128.4284525.02841.73657

-1758.229858.4522924.968841.65094

-1708.082458.6000324.873541.55598

-1657.847988.9751524.781441.60453

-1607.542419.7293624.744342.01607

-1557.1865611.074324.815143.07596

-1506.804713.330925.035945.1715

-1456.4228316.961525.426348.81063

-1406.0669922.443225.973354.48349

-1355.7614229.821626.624262.20722

-1305.5269538.025527.28970.84145

-1255.3795644.614327.88977.88286

-1205.3292946.841928.415680.58679

-1155.3795743.649528.872177.90117

-1105.5269636.57129.321871.41976

-1055.7614328.477429.848664.08743

-1006.06721.698130.473258.2383

-956.4228517.379231.036954.83895

-906.8047116.130431.562554.49761

-857.1865818.913832.397558.49788

-807.5424226.892433.468967.90372

-757.8479938.732134.586781.16679

-708.0824647.300735.509790.89286

-658.2298545.066936.150689.44735

-608.2801235.178136.765880.22402

-558.2298531.332637.901777.46415

-508.0824568.970140.2015117.25405

-457.84798287.58744.1609339.59588

-407.542411009.0349.1521065.72441

-357.186561916.3451.48121975.00776

-306.80471605.8947.94521660.6399

-256.42283991.36640.43381038.22263

-206.066991934.7322.03971962.83669

-155.7614215595-60.998915539.76252

-105.526955.55E+07-261.25655490044.27095

-55.3795619085.767.963319159.04286

05.3292910633.9152.75610791.98529

55.3795721608.42.6234721616.40304

105.526966.32E+07-206.30363199699.22396

155.7614313901.2-23.844313883.11713

206.0671847.0424.51661877.6236

256.422851041.2643.39481091.07765

306.804711745.5554.60851806.96321

357.186582002.0754.56572063.82228

407.542421007.6347.44311062.61552

457.84799279.43141.6825328.96149

508.0824667.282538.5798113.94476

558.2298532.059637.22277.51145

608.2801236.609836.702881.59272

658.2298546.570636.299791.10015

708.0824548.462135.519392.06385

757.8479839.347734.253781.44938

807.5424127.029832.765267.33741

857.1865618.779731.415657.38186

906.804715.884230.437853.1267

956.4228317.086129.896553.40543

1006.0669921.369929.73957.17589

1055.7614228.11629.778863.65622

1105.5269536.197129.535871.25985

1155.3795643.314529.135977.82996

1205.3292946.612128.640580.58189

1255.3795744.532828.046277.95857

1305.5269638.086627.373470.98696

1355.7614329.983426.686562.43133

1406.06722.656726.068654.7923

1456.4228517.189325.57549.18715

1506.8047113.548525.218845.57201

1557.1865811.266525.012343.46538

1607.542429.8868824.935942.3652

1657.847999.0933424.947741.88903

1708.082468.677824.996541.75676

1758.229858.4906125.034141.75456

1808.280128.4284525.02841.73657

24.9688

symmetrize charges

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

torsion

vdw

sum

coulomb

torsion (degrees)

Energy (Kcal/mol)

Force Field: dreiding_msc_exp6.par

expo-6 vdw F...F

dreiding_msc_exp6.par, fixed charges (164 deg), QM optimized geometriese-emin

angletorsionvdwcoulombE totalangletorsionvdwcoulombEffcoulomb+vdwtorsion+vdwDihedralQM B3LYP

1506.847611.354425.2511144.1271506.847611.354425.2511144.12736.605518.2021502.999495649

1527.0042910.923925.0069143.1881527.0042910.923925.0069143.18835.930817.928191522.146082661

1547.157510.542324.8017142.4131547.157510.542324.8017142.41335.34417.69981541.4451544936

1567.3067710.200824.6507141.8041567.3067710.200824.6507141.80434.851517.507571560.8778858604

1607.579739.5764124.5512141.0961607.579739.5764124.5512141.09634.1276117.156141600.2114707183

1627.713029.3653624.5248140.9441627.713029.3653624.5248140.94433.8901617.078381620.0527108022

1647.823579.1215724.6266140.9391647.823579.1215724.6266140.93933.7481716.945141640

1667.924588.9264924.7706141.0461667.924588.9264924.7706141.04633.6970916.851071660.0257278916

1688.013788.7502924.919141.191688.013788.7502924.919141.1933.6692916.764071680.107304133

1708.092828.6211325.079141.3951708.092828.6211325.079141.39533.7001316.713951700.2648090301

1728.159018.5296125.2234141.6051728.159018.5296125.2234141.60533.7530116.688621720.4480418187

1748.210848.4707525.3794141.8221748.210848.4707525.3794141.82233.8501516.681591740.6086842635

1768.248938.4413925.4587141.9541768.248938.4413925.4587141.95433.9000916.690321760.76681667

1788.273458.396425.5509142.0861788.273458.396425.5509142.08633.947316.669851780.8490204211

1808.279938.4125525.5499142.0921808.279938.4125525.5499142.09233.9624516.692481800.9054962806

Q factorEq Angle

0180

0.1180

0.2180

0.3180

0.4180

0.5180

0.6179.8

0.7179.7

0.8179.4

0.9177.8

1175.2

1.1172.9

1.2171.2

1.3169.9

1.4168.7

1.5167.8

1.6

1.7

1.8

expo-6 vdw F...F

00002.9994956490

00002.1460826610

00001.44515449360

00000.87788586040

00000.21147071830

00000.05271080220

000000

00000.02572789160

00000.1073041330

00000.26480903010

00000.44804181870

00000.60868426350

00000.766816670

00000.84902042110

00000.90549628060

torsion

vdw

coulomb

Eff

QM B3LYP

torsion+vdw

Torsion (degrees)

Energy (Kcal/mol)

quantum

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Eq Angle

Equilibrium Angle

K to Kcalmol

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

QM B3LYP

Mullikencharges from c6f14 at 168 deg minimized b3lyp 6-31G*

HETATM1C2RESA4440.001280.004241.55465C_34400.48001

HETATM2C3RESA4441.42194-0.006272.19046C_34400.52938

HETATM3C4RESA4441.42654-0.390223.70106C_34400.52951averagesumCorrection

HETATM4C5RESA4442.75127-0.027644.43256C_34400.479850.5046875-0.03007-0.01002333330.51471083330

HETATM5F10RESA444-0.643621.118931.96217F_13-0.2639-0.26737875-0.2573554167

HETATM6F11RESA444-0.68236-1.087241.97328F_13-0.26961

HETATM7F12RESA4442.18801-0.902591.52489F_13-0.26803-0.0001

HETATM8F13RESA4441.957071.228592.04823F_13-0.26785

HETATM9F14RESA4440.411140.2544.32218F_13-0.268020

HETATM10F15RESA4441.23128-1.726673.79756F_13-0.26815C=0.5148

HETATM11F16RESA4443.80117-0.37183.64941F_13-0.26954F=-0.2574

HETATM12F17RESA4442.772771.30574.6481F_13-0.26393

-0.12028

Terminal CF3

HETATM1C1RESA444-0.00164-0.005840.00158C_34400.789980.79001

HETATM2C6RESA4442.93532-0.735885.80283C_34400.79004-0.24329

HETATM3F7RESA4440.38902-1.19697-0.46283F_13-0.23944CF2Terminal CF3

HETATM4F8RESA444-1.243570.24036-0.43144F_13-0.24504FCFC

HETATM5F9RESA4440.819330.94229-0.47089F_13-0.24541-0.260.52-0.240.72

HETATM6F18RESA4443.19636-2.035185.62773F_13-0.23926

HETATM7F19RESA4443.96284-0.171986.44881F_13-0.2452200

HETATM8F20RESA4441.82926-0.605076.54835F_13-0.24537

ESP

HETATM1C1RESA444-0.00164-0.005840.00158C_34400.39623

HETATM2C2RESA4440.001280.004241.55465C_34400.12469

HETATM3C3RESA4441.42194-0.006272.19046C_34400.21118

HETATM4C4RESA4441.42654-0.390223.70106C_34400.18554

HETATM5C5RESA4442.75127-0.027644.43256C_34400.11969

HETATM6C6RESA4442.93532-0.735885.80283C_34400.39125FCCF3 FCF3 C

HETATM7F7RESA4440.38902-1.19697-0.46283F_13-0.11772-0.092641250.160275-0.11457666670.39374

HETATM8F8RESA444-1.243570.24036-0.43144F_13-0.11173-0.090.18-0.130.39

HETATM9F9RESA4440.819330.94229-0.47089F_13-0.11745-0.100030.6583466667

HETATM10F10RESA444-0.643621.118931.96217F_13-0.092400

HETATM11F11RESA444-0.68236-1.087241.97328F_13-0.08703

HETATM12F12RESA4442.18801-0.902591.52489F_13-0.10471

HETATM13F13RESA4441.957071.228592.04823F_13-0.09518

HETATM14F14RESA4440.411140.2544.32218F_13-0.0896CF2 FCF2 CCF3 FCF3 C

HETATM15F15RESA4441.23128-1.726673.79756F_13-0.09952Mulliken-0.260.52-0.240.72

HETATM16F16RESA4443.80117-0.37183.64941F_13-0.08378ESP-0.090.18-0.130.39

HETATM17F17RESA4442.772771.30574.6481F_13-0.08891

HETATM18F18RESA4443.19636-2.035185.62773F_13-0.11532

HETATM19F19RESA4443.96284-0.171986.44881F_13-0.11056

HETATM20F20RESA4441.82926-0.605076.54835F_13-0.11468

RExpo-6Nose-KleinExpo-6RDiagonal LJ12-6

1.03491023.949895273721082.2928701679Ro3.382501.0349Ro2.95

1.1349664.09951423026950.3122667943Do0.050921.1349Do7.35E-0237.00000

1.2349428.56615918052512.1175486793Z15.000001.2349

1.3349275.5987855176980.42384477581.3349

1.4349176.7374840732408.13409125931.4349

1.5349113.0583095067179.38051580241.5349

1.634972.14485453482.50889106161.6349

1.734945.91400273239.40189195981.7349

1.834929.129587412119.38714954811.8349

1.934918.4109782589.75193828481.9349

2.034911.58078914464.97074714912.0349

2.13497.23922738142.53913524592.1349

2.23494.48779381551.2791451282.2349

2.33492.75056408290.6183211952.3349

2.43491.65887761290.27035531442.4349

2.53490.97707668840.08841959272.5349

2.63490.5547520868-0.00442247982.6349

2.73490.2960715577-0.04921735212.72c6f142.7349

2.83490.1401014638-0.06817976532.8349

2.93490.0481942594-0.07345672432.95klein2.9349

3.0349-0.0040871393-0.07172687573.0349

3.1349-0.0321346031-0.06666026173.1349

3.2349-0.0455947068-0.06025571233.2349

3.3349-0.0504741764-0.05357836193.38us3.3349

3.4349-0.0504811748-0.04717113573.4349

3.5349-0.0478782164-0.04128640153.5349

3.6349-0.0440233318-0.03601715093.6349

3.7349-0.0397124952-0.03137144463.7349

3.8349-0.0353955623-0.0273145473.8349

3.9349-0.0313118552-0.02379255253.9349

4.0349-0.0275748245-0.02074537634.0349

4.1349-0.024224532-0.01811364374.1349

4.2349-0.0212598723-0.01584209614.2349

4.3349-0.0186580979-0.01388103744.3349

4.4349-0.0163864328-0.01218670384.4349

4.5349-0.0144087973-0.01072106874.5349

4.6349-0.0126895409-0.00945137534.6349

4.7349-0.0111953709-0.00834956234.7349

4.8349-0.0098962153-0.00739167364.8349

4.9349-0.0087654724-0.00655729754.9349

5.0349-0.0077799269-0.00582905775.0349

5.1349-0.0069194957-0.00519216345.1349

5.2349-0.0061669022-0.00463401965.2349

5.3349-0.0055073351-0.00414389125.3349

5.4349-0.0049281194-0.00371261775.4349

5.5349-0.004418416-0.00333237145.5349

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Expo-6

Nose-Klein

R (A)

Energy (Kcal/mol)

DihedralPolarizedvanderWaalsFixedChargeFixed-PolarizedQM B3LYPTotal FFvdw+fixedQ1-3 includedDihedralQM B3LYP627.50955Kcal/mol-eVBondAngle

8.1710627.45211500.59390.946482.1971.60312.9994956492.067170.5043.14348-5.1271800.9054962806-180-1626.370325-1626.3717678659127.92

8.0016927.32371520.46550.777111.5521.08652.1460826611.537169.9742.329111.8831780.8490204211-178-1626.370415-1626.36879127.771

7.8442927.25721540.3990.619711.0150.6161.44515449361.137169.5741.634711.1331760.76681667-176-1626.370546127.644

7.6922227.09811560.23990.467640.5870.34710.87788586040.701169.1381.054640.681740.6086842635-174-1626.370798127.539

7.35426.96941600.11120.129420.1150.00380.21147071830.2168.6370.244420.1021700.2648090301-170-1626.371346127.433

7.2245826.858216200000.05271080220168.437001680.107304133-168-1626.371597127.41

7.059726.93661640.0784-0.164880.025-0.053400.003168.44-0.13988-0.4281660.0257278916-166-1626.371727127.403

6.917527.10081660.2426-0.307080.123-0.11960.02572789160.122168.559-0.18408-0.911640-164-1626.371768127.405

6.784727.25371680.3955-0.439880.268-0.12750.1073041330.274168.711-0.17188-1.4741620.0527108022-162-1626.371684127.409

6.6796627.46061700.6024-0.544920.438-0.16440.26480903010.492168.929-0.10692-2.3071600.2114707183-160-1626.371431127.422

6.6001927.66591720.8077-0.624390.611-0.19670.44804181870.727169.164-0.01339-3.003158-158127.44

6.5433927.88051741.0223-0.681190.774-0.24830.60868426350.95169.3870.09281-3.861560.8778858604-156-1626.370369127.447

6.5122428.03231761.1741-0.712340.881-0.29310.766816671.13169.5670.16866-4.3641541.4451544936-154-1626.369465127.457

6.4715628.18471781.3265-0.753020.994-0.33250.84902042111.305169.7420.24098-4.8781522.146082661-152-1626.368348127.463

6.481928.18561801.3274-0.742680.992-0.33540.90549628061.305169.7420.24932-5.1271502.999495649-150-1626.366988127.471

polarized indicates the coulomb energy when point charges are determined for each quantum geometry at each dihedral value

C6F14 charges areB3LYP 631G* Mulliken with constrained torsion for three middle dihedrals and free terminal CF3

1502.999495649

1522.146082661

1541.4451544936

1560.8778858604

158

1600.2114707183

1620.0527108022

1640

1660.0257278916

1680.107304133

1700.2648090301

1720.4480418187

1740.6086842635

1760.76681667

1780.8490204211

1800.9054962806

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Polarized

Point Charges: Coulomb from QM Polarized Charges

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

QM B3LYP

Dihedral angle

Energy (Kcal/mol)


000000

000000

000000

000000

000000

000000

000000

000000

000000

000000

000000

000000

000000

000000

000000

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Polarized

vanderWaals

FixedCharge

Total FF

QM B3LYP

vdw+fixedQ

Dihedral Angle (degrees)

Relative Energy (wrt 162deg Kcal/mol)

C6F14 Dihedral Helicity

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

00000

FixedCharge

Total FF

QM B3LYP

Fixed-Polarized

Polarized

Dihedral Angle (degrees)

Relative Energy (wrt 162deg Kcal/mol)

C6F14 Dihedral Helicity

Van der Waals parameters of exponential-6Density (g/cm3) cDsubH (kcal/mol) dR1.98726cal/deg-mol

zDvdWRvdWK

Cb120.08443.88370.0735286242.4705373227

F120.044533.49852.2247 0.04754.0622.4077372865

130.04723.4482.2252 0.04134.0723.751295754

140.049353.41122.2244 0.03894.0624.8331874038

150.050923.38252.2243 0.03604.0625.6232199108

160.052463.35892.2253 0.03494.0626.3981562553

PredictionsThe simulated monoclinic (M phase) structure of C20F42, looking through the crystal along the C direction on the left and along the B-direction on the right. (A = 9.65 ; B = 5.70 ; C = 28.3 , = 97.2o; = = 90 o)

High Pressure forms of C20F42 The figure shows predicted stable helical conformations for C20F42. From left to right t+, t-, g+, g-, h+, and h- enantiomeric pair conformations. The atoms are colored to facilitate the viewing of their helical nature. The tighter the dihedral angle (from 164 to 60) the shorter the molecule gets. Fluorine atoms of each color would be located on the same side if the molecule were prepared in the all-trans conformation.

MD simulation of Uniaxial Tension in Crystalline Cu nano-wire(Tahir, Strachan, Goddard, 2000N=1370 atomsstrain rate = 0.5% / 10 ps= 5x109 1/sT = 300 KFailure at ~ 100%up to 25 %

Failure: Impact Spallation(Strachan & Goddard)N=10,000 Ta atomsVelocity= 6 km/sMD allows the study of spallation of metals vs. TAnd impact speeds

Deformation: dislocation mobility from MD simulation in TaMD @ T = 0.001 K5670 atomsScrew Dislocations Dipole annihilation (PBC)MD simulations using First Principles Force Fields:Core energy and structure of dislocationsDislocation mobility (Peierls stress, kink energies, etc.)Provides an accurate atomistic description of the fundamental unit mechanisms that control plasticity

Transport properties:gas diffusion in polymers High-frequency short-wave-length modes of the polymer are not critical for diffusion

The penetrant molecule does not affect the polymer dynamics The model captures the correct:

Thermal fluctuations

Time correlations of the polymerWe developed the Multiple Time Step MD method to study gas diffusion in polymer.

Features: New FF termsVan der Waals CoulombBonds Angles DihedralsCos harmonic angleDreiding DihedralUmbrella InversionExponential-6Exocyclic bonds

Sandia Lammpsparallelism via a spatial-decomposition algorithmlong-range Coulombic interactions Ewald or PPPM (particle-mesh Ewald): Smeared of charges on 3d grid followed by FFT transform of charge density, solution of Poisson Equation, Differentiation (forces),remapping to atomsForce Fields:harmonic molecular potentials (bond, angle, torsion, improper) class II (cross-term) molecular potentials NVE, NVT, NPT dynamics constraints on atoms or groups of atoms rRESPA long-timescale integrator energy minimizer (Hessian-free truncated Newton method)

MSC-Lammps Added FeaturesExtended Force Field Energy FunctionsSmooth Cubic Spline switch functions for non-bondPreprocessing of input files for automatic FF and EEXP generationTrajectory File GenerationPostProcessing of Thermodynamic Functions by VAC Wilsons MethodAtomistic Energy Partitioning and Visualization

MSC-Lammps Programming Paradigm

Periodic Boundary Conditions1x1x12x2x2

Ewald Trick

Ewald Equation

Charge Density

Ewald Forces

Basic PPPM Parallel Algorithm

Interpolate smeared charges to gridSum charge from grid ghost pointsSend charge values from spatial-to FFT-decompositionSolve Poissons equation on grid via FFTs.Send field values from FFT-to spatial-decomposition.Acquire fields for grid ghost points.Interpolate field values on grid to atoms.

Particle Mesh

Mesh Forces

Benchmarks (7,000 atoms)

Procs 1 2 4 8 16 32 64 128 256 512 N 7K 7K 7K 7K 7K 7K 7K 7K 7K 7K CPU 4.42 2.20 1.13 0.602 0.324 0.17 0.106 0.066 0.0465 0.0453 || Eff 100.0 100.5 97.8 91.9 85.3 81.3 65.2 52.3 37.2 19.1

Chart1

4.42

2.2

1.13

0.602

0.324

0.17

0.106

0.0661

0.0465

0.0453

CPU

Number of Processors N

CPU Time (Secs)

Lammps 7000 Atom case

Sheet1

Procs1248163264128256512

CPU4.422.21.130.6020.3240.170.1060.06610.04650.0453

Parallelism100100.597.891.985.381.365.252.337.219.1

Procs1248163264128256512

N7K14K29K57K114K228K457K913K1.83M3.65M

CPU4.424.374.364.414.444.464.534.54.564.57

||Eff100101.3101.4100.299.799.197.898.397.196.8

N7K7K7K7K7K7K7K7K7K7K

Procs1248163264128256512


CPU4.422.21.130.6020.3240.170.1060.06610.04650.0453

||Eff100100.597.891.985.381.365.252.337.219.1

Procs1248163264128256512

N7K14K29K57K114K228K457K913K1.83M3.65M

CPU4.424.374.364.414.444.464.534.54.564.57

||Eff100101.3101.4100.299.799.197.898.397.196.8

Sheet1

CPU


CPU Time (Secs)


MPSIM

CPU

Parallelism

timings

MPSIM-ORIGIN1-EWALDTotal Time(s)NprocstepsAtomsTime (ms)/step/atomAccuracy

big.origin1.1.out257.1411467502721.090.675

big.origin1.2.out257.1421467502721.090.675

big.origin1.4.out257.1441467502721.090.675

small.origin1.1.out12.721283250179.800.025

small.origin1.2.out11.252320250140.630.025

small.origin1.4.out12.504288250173.610.025

Ewald Accuracy0.00010

LIQUID-CRYSTAL CaseTime (S)Machine-Proc-MethodNprocstepsAtomstime/step/atom msParallel

big.shortcut.tflop.16:2.66TFLOP-16ShortCut1610067503.94

big.longcut.tflop.16:7.11TFLOP-16LongCut16100675010.54

small.periodic.tflop.8:2.76TFLOP-8-SMALL8100025011.03

small.nonperiodic.tflop.8:3.18TFLOP-8NP-SMALL8100025012.70

big.pppm.t3e.16:13.61T3E-16PPPM16100675020.17

big.longcut.t3e.16:14.16T3E-16LongCut16100675020.97

big.pppm.tflop.16:16.96TFLOP-16PPM16100675025.13

small.nonperiodic.sgi.1:7.40SGI-1-SMALL1100025029.60

small.periodic.sgi.1:8.84SGI-1NP-SMALL1100025035.36

big.pppm.origin824.38ORIGIN-8PPPM8100675036.12120%

big.pppm.origin440.80ORIGIN-4PPPM4100675060.44

small.origin1.1.out12.72MPSIM-ORIGIN1-EWALD-SMALL1283250179.80

big.ewald.tflop.16:153.60TFLOP-8Ewald161006750227.56

big.ewald.origin8202.00ORIGIN-8Ewald81006750299.2694%



big.ewald.origin3590.90ORIGIN-3Ewald31006750875.41

big.origin1.1.out257.14MPSIM-ORIGIN1-EWALD11467502721.09

MPSIMTime(s)ProcessorsstepsAtomsAccuracy

big.origin1.1.out257.14ORIGIN1-MPSIM-EWALD11467502721.090.675



small.origin1.1.out12.72ORIGIN1-MPSIM-EWALD1283250179.800.025



time/step/atom ms

Machine-Proc-Meth

Timing (ms per step/atom)

LAMMPS99/MPSIM Timings

Chart3

100

100.5

97.8

91.9

85.3

81.3

65.2

52.3

37.2

19.1

Parallelism

Number of Processors

% Efficiency

Parallelism (7,000 Atoms)

Sheet1

Procs1248163264128256512

CPU4.422.21.130.6020.3240.170.1060.06610.04650.0453

Parallelism100100.597.891.985.381.365.252.337.219.1

Procs1248163264128256512

N7K14K29K57K114K228K457K913K1.83M3.65M

CPU4.424.374.364.414.444.464.534.54.564.57

||Eff100101.3101.4100.299.799.197.898.397.196.8


Procs1248163264128256512


CPU4.422.21.130.6020.3240.170.1060.06610.04650.0453

||Eff100100.597.891.985.381.365.252.337.219.1

Procs1248163264128256512

N7K14K29K57K114K228K457K913K1.83M3.65M

CPU4.424.374.364.414.444.464.534.54.564.57

||Eff100101.3101.4100.299.799.197.898.397.196.8

Sheet1

CPU


CPU Time (Secs)


MPSIM

Parallelism

Number of Processors

% Efficiency

Parallelism (7,000 Atoms)

timings

MPSIM-ORIGIN1-EWALDTotal Time(s)NprocstepsAtomsTime (ms)/step/atomAccuracy

big.origin1.1.out257.1411467502721.090.675

big.origin1.2.out257.1421467502721.090.675

big.origin1.4.out257.1441467502721.090.675

small.origin1.1.out12.721283250179.800.025

small.origin1.2.out11.252320250140.630.025

small.origin1.4.out12.504288250173.610.025

Ewald Accuracy0.00010

LIQUID-CRYSTAL CaseTime (S)Machine-Proc-MethodNprocstepsAtomstime/step/atom msParallel

big.shortcut.tflop.16:2.66TFLOP-16ShortCut1610067503.94

big.longcut.tflop.16:7.11TFLOP-16LongCut16100675010.54

small.periodic.tflop.8:2.76TFLOP-8-SMALL8100025011.03

small.nonperiodic.tflop.8:3.18TFLOP-8NP-SMALL8100025012.70

big.pppm.t3e.16:13.61T3E-16PPPM16100675020.17

big.longcut.t3e.16:14.16T3E-16LongCut16100675020.97

big.pppm.tflop.16:16.96TFLOP-16PPM16100675025.13

small.nonperiodic.sgi.1:7.40SGI-1-SMALL1100025029.60

small.periodic.sgi.1:8.84SGI-1NP-SMALL1100025035.36

big.pppm.origin824.38ORIGIN-8PPPM8100675036.12120%

big.pppm.origin440.80ORIGIN-4PPPM4100675060.44

small.origin1.1.out12.72MPSIM-ORIGIN1-EWALD-SMALL1283250179.80

big.ewald.tflop.16:153.60TFLOP-8Ewald161006750227.56




big.ewald.origin3590.90ORIGIN-3Ewald31006750875.41

big.origin1.1.out257.14MPSIM-ORIGIN1-EWALD11467502721.09

MPSIMTime(s)ProcessorsstepsAtomsAccuracy







time/step/atom ms

Machine-Proc-Meth

Timing (ms per step/atom)

LAMMPS99/MPSIM Timings

Design of a Nanomechanical Fluid Control Valve Based on the Deflection of a Functionalized Silicon CantileverCoupling of Molecular Mechanics and Mechanical Engineering Methods Santiago Solares, Mario Blanco, and William A. Goddard IIIMaterials and Process Simulation Center, CaltechJuly, 2002

SOME EARLY DESIGN LEARNINGSMOLDING Vs. CRIMPINGUSE OF SPLINES AND CUTOFFSTWISTING OF Si(111) CANTILEVER

Si(100) CANTILEVER STRAIN ENERGY ANALYSIS

STRAIN ENERGY FOR A DEFLECTED FLAT SLAB = YwLoH3/24Rc2AVERAGE CALCULATED YOUNGS MODULUS: 76.7 Gpa (EXPERIMENTAL, BULK 47 GPa)

CALCULATION SHEET

Cantilever Deflection Study - Si100 and Si111

(Calculation sheet)

Calculation of the deflection coordinates

Cantilever length = 100 Ang.

Radius of

Curvature, Ang.Polar angleX-displacementY-displacement

601.6666666667-40.27552-65.74341(minimum radius - one cuadrant)

651.5384615385-35.03398-62.89860

701.4285714286-30.70678-60.07779

751.3333333333-27.10466-57.35718

801.25-24.08123-54.77421

851.1764705882-21.52326-52.34421


10000.15-0.56187-11.22892

9500.1578947368-0.62249-11.81752

9000.1666666667-0.69348-12.47109

8500.1764705882-0.77734-13.20098

8000.1875-0.87736-14.02135

ENERGY CURVES DRAFT

Energy Curves for Cantilevers and Nanotubes

(NOTE: The plane of zero stress is not the same for all pieces)

Piece length = 150 Ang. (cantilevers and nanotubes)

Plane of zero stress bisects the piece

Radius ofInverse RadiusPolar angleX-displacementY-displacementForce Field Energy

Curvature, Ang.of Curv., Ang^-1Polar angleX-displacementSi100 cantileverSi111 cantilever10_10 nanotube17_17_nanotube

Infinite0000-16795.5-22429.616773.325270.1

2249.1640.0004450.0666914462-0.11117-5.00000-16781.8-22381.416772.125300

1123.32890.0008900.1335316843-0.44537-10.00000-16775.5-22343.816780.325386.4

747.48650.0013380.2006725205-1.00471-15.00000-16762.2-22283.216798.725528.6

559.13450.0017880.2682717665-1.79278-20.00000-16741.3-22146.616829.125727.2

445.76980.0022430.3364965505-2.81477-25.00000-16712.5-21983.316873.925982.2

369.8890.0027040.4055270635-4.07763-30.00000-16674.6-21960.316935.326291.8

315.41620.0031700.4755621303-5.59039-35.0000017015.726445.117_17 buckled

274.31130.0036450.5468239916-7.36444-40.0000017117.326642.317_17 buckled

242.104480.0041300.6195672216-9.41407-45.0000017241.426826.917_17 buckled

2140.0046730.7009345794-11.98451-50.4526917407.126950.117_17 buckled

NOTE: INCLUDE THE FOLLOWING STATISTICS FOR EACH PIECE

Number of atoms

Number of layers

Dimensions

Electrostatic energy

Plane of zero stress is the bottom face of the cantilever

Radius ofInverse RadiusForce FieldForce Field

Curvature, Ang.of Curv., Ang^-1Energy Si_100Energy Si_111

Infinite0156282223174

2000.00000.000500156300223384

1052.63160.000950154521220841

714.28570.001400152786218361

540.54050.001850151092215941

434.78260.002300149440213579

363.63640.002750147827211173

312.50000.003200146252209022

273.97260.003650144714206824

243.90240.004100143211204677

219.78020.004550141744202580

FINAL ENERGY CURVES

Strain Energy Results for Nanomechanical Valve Components

Cantilevers and Nanotubes

Piece length = 150 Ang.


Inverse RadiusEnergyEnergyEnergy_2Energy_2EnergyEnergyEnergy

of Curv., Ang^-1Si100_cantSi111_cantSi100_cant**Si111_cant**10_10_NT17_17_NT17_17_NT

00.00.00.00.00.00.0

0.00044513.7048.2054.80192.80-1.2029.90

0.00089020.0085.8080.00343.207.00116.30

0.00133833.30146.40133.20585.6025.40258.50

0.00178854.20283.00216.801132.0055.80457.10

0.00224383.00446.30332.001785.20100.60712.10

0.002704120.90469.30483.601877.20162.001021.701021.70

0.003170242.401175.00BUCKLED

0.003645344.001372.20BUCKLED

0.004130468.101556.80BUCKLED

0.004673633.801680.00BUCKLED

**NOTE: These values have been corrected to represent the strain energy for the given curvature

when the plane of zero stress is the bottom of the cantilever, as it happens in electrostatically-induced deflection

Charged Monolayer - 50% Coverage



Inverse RadiusEnergyEnergy

of Curv., Ang^-1Si100_cantSi111_cant

00.00.0

0.00050018.0210.0

0.000950-1761.0-2333.0

0.001400-3496.0-4813.0

0.001850-5190.0-7233.0

0.002300-6842.0-9595.0

0.002750-8455.0-12001.0

0.003200-10030.0-14152.0

0.003650-11568.0-16350.0

0.004100-13071.0-18497.0

0.004550-14538.0-20594.0

Si100_CANT_CHART

0

54.8

80

133.2

216.8

332

483.6

Curvature, 1/Ang.

Energy, kcal/mol

Si100 CANTILEVER - Strain Energy Vs. Curvature (corrected to have the plane of zero stress on the bottom face)

Si111_CANT_CHART

0

192.8

343.2

585.6

1132

1785.2

1877.2

Curvature, 1/Ang.

Energy, kcal/mol

Si111 CANTILEVER - Strain Energy Vs. Curvature (Plane of zero stress is the bottom face)

10_10_CNT_CHART

0

-1.2

7

25.4

55.8

100.6

162

242.4

344

468.1

633.8

Curvature, 1/Ang.

Energy, kcal/mol

10,10 CARBON NANOTUBE - Strain Energy Vs. Curvature (plane of zero stress bisects the tube)

17_17_NT_CHART

00

29.90.0004446096

116.30.0008902112

258.50.0013378168

457.10.0017884784

712.10.0022433103

1021.71021.7

0.00317041421175

0.00364549331372.2

0.00413044811556.8

0.00467289721680

SMOOTH BENDING

BUCKLED

Curvature, 1/Ang

Energy, kcal/mol

17,17 NANOTUBE - Strain Energy Vs. Curvature (plane of zero stress bisects the tube)

Si100_CHARGED_CANT_CHART

0

18

-1761

-3496

-5190

-6842

-8455

-10030

-11568

-13071

-14538

Curvature, 1/Ang.

Energy, kcal/mol

Si100_C3_CHARGED CANTILEVER - Electrostatic Energy Vs. Curvature (plane of zero stress is the bottom face)


0

210

-2333

-4813

-7233

-9595

-12001

-14152

-16350

-18497

-20594

Curvature, 1/Ang.

Energy, kcal/mol


ENERGY_CONTRIB_TABLE

Strain Energy Results for Assembled Valve

17_17 nanotube, Si100 cantilever, and 10% - 25% of electrostatic energy

(Using regression functions)


Plane of zero stress at the bottom of the cantilever bisecting the nanotube

10% OF ELECTROSTATIC ENERGY:

Inverse RadiusEnergyEnergy10% ElectrostaticTotal

of Curv., Ang^-1Si100_cant17_17 nanotubeEnergyEnergy

015.0-1.6106.3119.7

0.00012017.751.5170.3189.57

0.00024022.227.5234.3164.05

0.00036028.4216.41-1.6943.14

0.00048036.3528.17-37.6926.83

0.00060046.0142.82-73.6915.14

0.00072057.3960.35-109.698.05

0.00084070.5080.76-145.695.57

0.00096085.34104.05-181.697.70

0.001080101.91130.21-217.6914.44

0.001200120.21159.26-253.6925.78




015.0-1.62265.8279.2

0.00030025.1011.6040.7877.48

0.00060046.0142.82-184.23-95.40

0.00090077.7192.04-409.23-239.48

0.001200120.21159.26-634.23-354.76

0.001500173.51244.48-859.23-441.23

0.001800237.61347.70-1084.23-498.91

0.002100312.51468.92-1309.23-527.79

0.002400398.21608.14-1534.23-527.87

0.002700494.711027.57-1759.23-236.94

0.003000602.021131.32-1984.23-250.89

25% OF ELECTROSTATIC ENERGY AND TWO CANTILEVERS 50% LONGER



030.0-1.62797.3825.7

0.00060092.0142.82-552.68-417.84

0.001200240.42159.26-1902.68-1503.00

0.001800475.22347.70-3252.68-2429.75

0.002400796.43608.14-4602.68-3198.11

0.0030001204.031131.32-5952.68-3617.32

0.0036001698.041338.82-7302.68-4265.82

0.0042002278.441546.31-8652.68-4827.92

0.0048002945.251753.81-10002.68-5303.62

0.0054003698.451961.31-11352.68-5692.92

0.0060004538.062168.80-12702.68-5995.81

ENERGY_CONTRIB_CHART_10%

15.003-1.6189106.31119.6941

17.747521.5091470.3189.56666

22.220047.5171834.3164.04722

28.4205616.40522-1.6943.13578

36.3490828.17326-37.6926.83234

46.005642.8213-73.6915.1369

57.3901260.34934-109.698.04946

70.5026480.75738-145.695.57002

85.34316104.04542-181.697.69858

101.91168130.21346-217.6914.43514

120.2082159.2615-253.6925.7797

Si_100 CANTILEVER

17_17 NANOTUBE

10% ELECTROSTATIC

TOTAL

CURVATURE, 1/Ang.

ENERGY, kcal/mol

PARTIAL ENERGY CONTRIBUTIONS OF ACTUATOR COMPONENTS AND TOTAL ENERGY Vs. CURVATURE, USING 10% OF THE AVAILABLE ELECTROSTATIC ENERGY


15.003-1.6189265.775279.1591

25.104311.601240.77577.4805

46.005642.8213-184.225-95.3981

77.706992.0414-409.225-239.4767

120.2082159.2615-634.225-354.7553

173.5095244.4816-859.225-441.2339

237.6108347.7017-1084.225-498.9125

312.5121468.9218-1309.225-527.7911

398.2134608.1419-1534.225-527.8697

494.71471027.5706-1759.225-236.9397

602.0161131.319-1984.225-250.89

SI_100_CANTILEVER

17_17 NANOTUBE

25% ELECTROSTATIC

TOTAL

CURVATURE, 1/Ang.

Energy, kcal/mol


ENERGY_CONTRIB_CHART_25%_2_CANT

30.006-1.6189797.325825.7121

92.011242.8213-552.675-417.8425

240.4164159.2615-1902.675-1502.9971

475.2216347.7017-3252.675-2429.7517

796.4268608.1419-4602.675-3198.1063

1204.0321131.319-5952.675-3617.324

1698.03721338.8158-7302.675-4265.822

2278.44241546.3126-8652.675-4827.92

2945.24761753.8094-10002.675-5303.618

3698.45281961.3062-11352.675-5692.916

4538.0582168.803-12702.675-5995.814

Si_100 CANTILEVER

17,17 NANOTUBE

25% ELEC. E. 2 CANT-50% LONGER

TOTAL ENERGY

CURVATURE, 1/Ang.

ENERGY, kcal/mol

PARTIAL ENERGY CONTRIBUTIONS OF ACTUATOR COMPONENTS AND TOTAL ENERGY Vs. CURVATURE, USING 25% OF THE AVAILABLE ELECTROSTATIC ENERGY USING TWO CANTILEVERS, 50% LONGER

CANTILEVER_SIZE_SCALE_UP

Scale-up of Cantilever Initial Electrostatic Energy Vs. Dimensions

Width

Length31.647.463.279

150156282313177505492726854

171.4187527377368611241881543

192.92198904440647214201043110

2142532465129878355431210810

2352874955839169532201384040

25732255665666910741301562310

27835836273109411980101745200

30039485580706513246301932360

NOTES:

1. Scale-up in the longitudinal direction corresponds directly to usable motion

2. Scale-up in the width direction does not directly correspond to longitudinal motion and should be done with

caution (relaxation includes lateral deflection which is not usable motion)

3. These charts should only be used in the range used to create them

1.00001.00001.00001.00001.0000

1.14271.19991.20501.20921.2128

1.28601.40701.41791.42721.4351

1.42671.62041.63801.65291.6658

1.56671.83961.86451.88571.9042

1.71332.06392.09682.12492.1494

1.85332.29302.33442.37002.4010

2.00002.52662.57702.62052.6585

1.0001.5002.0002.500

1.00001.0002.0043.2344.651

1.14271.0002.0123.2594.701

1.28601.0002.0193.2814.744

1.42671.0002.0263.2994.781

1.56671.0002.0313.3164.814

1.71331.0002.0363.3304.844

1.85331.0002.0403.3434.870

2.00001.0002.0443.3554.894


0000

0000

0000

0000

0000

0000

0000

0000

1.0 WIDTH

1.5 WIDTH

2.0 WIDTH

2.5 WIDTH

DIMENSIONLESS LENGTH L/Lo

DIMENSIONLESS ENERGY E/Eo

SCALE-UP FACTORS IN THE LONGITUDINAL DIRECTION

1.0 WIDTHy = 1.5317x - 0.5515R2 = 0.9995

2.5 WIDTHy = 1.6645x - 0.691R2 = 0.9992

00000000

00000000

00000000

00000000

1.0 L

1.14 L

1.29 L

1.43 L

1.57 L

1.71 L

1.85 L

2.0 L

DIMENSIONLESS WIDTH, W/Wo

DIMENSIONLESS ENERGY, E/Eo

SCALE-UP FACTORS IN THE WIDTH DIRECTION

1.0 Ly = 0.4125x2 + 0.9929x - 0.4074R2 = 1

2.0 Ly = 0.4952x2 + 0.8654x - 0.3625R2 = 1

17,17 CARBON NANOTUBE STRAIN ENERGY ANALYSIS

STRAIN ENERGY FOR A DEFLECTED HOLLOW ROD = pYLo(Ro4 Ri4)/8Rc2AVERAGE CALCULATED YOUNGS MODULUS: 1719 Gpa, Experimental from vibrational frequencies 1250 GPa, graphite 630 Gpa, CNT tensile molecular simulations 640 673 GPa

CALCULATION SHEET

Cantilever Deflection Study - Si100 and Si111

(Calculation sheet)

Calculation of the deflection coordinates


Radius of

Curvature, Ang.Polar angleX-displacementY-displacement

601.6666666667-40.27552-65.74341(minimum radius - one cuadrant)

651.5384615385-35.03398-62.89860

701.4285714286-30.70678-60.07779

751.3333333333-27.10466-57.35718

801.25-24.08123-54.77421

851.1764705882-21.52326-52.34421


10000.15-0.56187-11.22892

9500.1578947368-0.62249-11.81752

9000.1666666667-0.69348-12.47109

8500.1764705882-0.77734-13.20098

8000.1875-0.87736-14.02135

ENERGY CURVES DRAFT

Energy Curves for Cantilevers and Nanotubes

(NOTE: The plane of zero stress is not the same for all pieces)

Piece length = 150 Ang. (cantilevers and nanotubes)


Radius ofInverse RadiusPolar angleX-displacementY-displacementForce Field Energy

Curvature, Ang.of Curv., Ang^-1Polar angleX-displacementSi100 cantileverSi111 cantilever10_10 nanotube17_17_nanotube

Infinite0000-16795.5-22429.616773.325270.1

2249.1640.0004450.0666914462-0.11117-5.00000-16781.8-22381.416772.125300

1123.32890.0008900.1335316843-0.44537-10.00000-16775.5-22343.816780.325386.4

747.48650.0013380.2006725205-1.00471-15.00000-16762.2-22283.216798.725528.6

559.13450.0017880.2682717665-1.79278-20.00000-16741.3-22146.616829.125727.2

445.76980.0022430.3364965505-2.81477-25.00000-16712.5-21983.316873.925982.2

369.8890.0027040.4055270635-4.07763-30.00000-16674.6-21960.316935.326291.8

315.41620.0031700.4755621303-5.59039-35.0000017015.726445.117_17 buckled

274.31130.0036450.5468239916-7.36444-40.0000017117.326642.317_17 buckled

242.104480.0041300.6195672216-9.41407-45.0000017241.426826.917_17 buckled

2140.0046730.7009345794-11.98451-50.4526917407.126950.117_17 buckled

NOTE: INCLUDE THE FOLLOWING STATISTICS FOR EACH PIECE

Number of atoms

Number of layers

Dimensions



Radius ofInverse RadiusForce FieldForce Field

Curvature, Ang.of Curv., Ang^-1Energy Si_100Energy Si_111

Infinite0156282223174

2000.00000.000500156300223384

1052.63160.000950154521220841

714.28570.001400152786218361

540.54050.001850151092215941

434.78260.002300149440213579

363.63640.002750147827211173

312.50000.003200146252209022

273.97260.003650144714206824

243.90240.004100143211204677

219.78020.004550141744202580

FINAL ENERGY CURVES

Strain Energy Results for Nanomechanical Valve Components

Cantilevers and Nanotubes



Inverse RadiusEnergyEnergyEnergy_2Energy_2EnergyEnergyEnergy

of Curv., Ang^-1Si100_cantSi111_cantSi100_cant**Si111_cant**10_10_NT17_17_NT17_17_NT

00.00.00.00.00.00.0

0.00044513.7048.2054.80192.80-1.2029.90

0.00089020.0085.8080.00343.207.00116.30

0.00133833.30146.40133.20585.6025.40258.50

0.00178854.20283.00216.801132.0055.80457.10

0.00224383.00446.30332.001785.20100.60712.10

0.002704120.90469.30483.601877.20162.001021.701021.70

0.003170242.401175.00BUCKLED

0.003645344.001372.20BUCKLED

0.004130468.101556.80BUCKLED

0.004673633.801680.00BUCKLED

**NOTE: These values have been corrected to represent the strain energy for the given curvature

when the plane of zero stress is the bottom of the cantilever, as it happens in electrostatically-induced deflection

Charged Monolayer - 50% Coverage



Inverse RadiusEnergyEnergy

of Curv., Ang^-1Si100_cantSi111_cant

00.00.0

0.00050018.0210.0

0.000950-1761.0-2333.0

0.001400-3496.0-4813.0

0.001850-5190.0-7233.0

0.002300-6842.0-9595.0

0.002750-8455.0-12001.0

0.003200-10030.0-14152.0

0.003650-11568.0-16350.0

0.004100-13071.0-18497.0

0.004550-14538.0-20594.0

Si100_CANT_CHART

0

54.8

80

133.2

216.8

332

483.6

Curvature, 1/Ang.

Energy, kcal/mol

Si100 CANTILEVER - Strain Energy Vs. Curvature (plane of zero stress is the bottom face)

Si111_CANT_CHART

0

192.8

343.2

585.6

1132

1785.2

1877.2

Curvature, 1/Ang.

Energy, kcal/mol

Si111 CANTILEVER - Strain Energy Vs. Curvature (Plane of zero stress is the bottom face)

10_10_CNT_CHART

0

-1.2

7

25.4

55.8

100.6

162

242.4

344

468.1

633.8

Curvature, 1/Ang.

Energy, kcal/mol

10,10 CARBON NANOTUBE - Strain Energy Vs. Curvature (plane of zero stress bisects the tube)

17_17_NT_CHART

00

29.90.0004446096

116.30.0008902112

258.50.0013378168

457.10.0017884784

712.10.0022433103

1021.71021.7

0.00317041421175

0.00364549331372.2

0.00413044811556.8

0.00467289721680

y = 1E+08x2 + 14067x - 1.6189R2 = 1

y = 345828x + 93.835R2 = 0.9908

BUCKLING POINT

SMOOTH BENDING

BUCKLED

Curvature, 1/Ang

Energy, kcal/mol

17,17 NANOTUBE - Strain Energy Vs. Curvature (plane of zero stress bisects the tube)


0

18

-1761

-3496

-5190

-6842

-8455

-10030

-11568

-13071

-14538

Curvature, 1/Ang.

Energy, kcal/mol



0

210

-2333

-4813

-7233

-9595

-12001

-14152

-16350

-18497

-20594

Curvature, 1/Ang.

Energy, kcal/mol


ENERGY_CONTRIB_TABLE

Strain Energy Results for Assembled Valve

17_17 nanotube, Si100 cantilever, and 10% - 25% of electrostatic energy

(Using regression functions)


Plane of zero stress at the bottom of the cantilever bisecting the nanotube




015.0-1.6106.3119.7

0.00012017.751.5170.3189.57

0.00024022.227.5234.3164.05

0.00036028.4216.41-1.6943.14

0.00048036.3528.17-37.6926.83

0.00060046.0142.82-73.6915.14

0.00072057.3960.35-109.698.05

0.00084070.5080.76-145.695.57

0.00096085.34104.05-181.697.70

0.001080101.91130.21-217.6914.44

0.001200120.21159.26-253.6925.78




015.0-1.62265.8279.2

0.00030025.1011.6040.7877.48

0.00060046.0142.82-184.23-95.40

0.00090077.7192.04-409.23-239.48

0.001200120.21159.26-634.23-354.76

0.001500173.51244.48-859.23-441.23

0.001800237.61347.70-1084.23-498.91

0.002100312.51468.92-1309.23-527.79

0.002400398.21608.14-1534.23-527.87

0.002700494.711027.57-1759.23-236.94

0.003000602.021131.32-1984.23-250.89

25% OF ELECTROSTATIC ENERGY AND TWO CANTILEVERS 50% LONGER



030.0-1.62797.3825.7

0.00060092.0142.82-552.68-417.84

0.001200240.42159.26-1902.68-1503.00

0.001800475.22347.70-3252.68-2429.75

0.002400796.43608.14-4602.68-3198.11

0.0030001204.031131.32-5952.68-3617.32

0.0036001698.041338.82-7302.68-4265.82

0.0042002278.441546.31-8652.68-4827.92

0.0048002945.251753.81-10002.68-5303.62

0.0054003698.451961.31-11352.68-5692.92

0.0060004538.062168.80-12702.68-5995.81


15.003-1.6189106.31119.6941

17.747521.5091470.3189.56666

22.220047.5171834.3164.04722

28.4205616.40522-1.6943.13578

36.3490828.17326-37.6926.83234

46.005642.8213-73.6915.1369

57.3901260.34934-109.698.04946

70.5026480.75738-145.695.57002

85.34316104.04542-181.697.69858

101.91168130.21346-217.6914.43514

120.2082159.2615-253.6925.7797

Si_100 CANTILEVER

17_17 NANOTUBE

10% ELECTROSTATIC

TOTAL

CURVATURE, 1/Ang.

ENERGY, kcal/mol



15.003-1.6189265.775279.1591

25.104311.601240.77577.4805

46.005642.8213-184.225-95.3981

77.706992.0414-409.225-239.4767

120.2082159.2615-634.225-354.7553

173.5095244.4816-859.225-441.2339

237.6108347.7017-1084.225-498.9125

312.5121468.9218-1309.225-527.7911

398.2134608.1419-1534.225-527.8697

494.71471027.5706-1759.225-236.9397

602.0161131.319-1984.225-250.89

SI_100_CANTILEVER

17_17 NANOTUBE

25% ELECTROSTATIC

TOTAL

CURVATURE, 1/Ang.

Energy, kcal/mol


ENERGY_CONTRIB_CHART_25%_2_CANT

30.006-1.6189797.325825.7121

92.011242.8213-552.675-417.8425

240.4164159.2615-1902.675-1502.9971

475.2216347.7017-3252.675-2429.7517

796.4268608.1419-4602.675-3198.1063

1204.0321131.319-5952.675-3617.324

1698.03721338.8158-7302.675-4265.822

2278.44241546.3126-8652.675-4827.92

2945.24761753.8094-10002.675-5303.618

3698.45281961.3062-11352.675-5692.916

4538.0582168.803-12702.675-5995.814

Si_100 CANTILEVER

17,17 NANOTUBE

25% ELEC. E. 2 CANT-50% LONGER

TOTAL ENERGY

CURVATURE, 1/Ang.

ENERGY, kcal/mol

PARTIAL ENERGY CONTRIBUTIONS OF ACTUATOR COMPONENTS AND TOTAL ENERGY Vs. CURVATURE, USING 25% OF THE AVAILABLE ELECTROSTATIC ENERGY USING TWO CANTILEVERS, 50% LONGER


Scale-up of Cantilever Initial Electrostatic Energy Vs. Dimensions

Width

Length31.647.463.279

150156282313177505492726854

171.4187527377368611241881543

192.92198904440647214201043110

2142532465129878355431210810

2352874955839169532201384040

25732255665666910741301562310

27835836273109411980101745200

30039485580706513246301932360

NOTES:

1. Scale-up in the longitudinal direction corresponds directly to usable motion

2. Scale-up in the width direction does not directly correspond to longitudinal motion and should be done with

caution (relaxation includes lateral deflection which is not usable motion)

3. These charts should only be used in the range used to create them

1.00001.00001.00001.00001.0000

1.14271.19991.20501.20921.2128

1.28601.40701.41791.42721.4351

1.42671.62041.63801.65291.6658

1.56671.83961.86451.88571.9042

1.71332.06392.09682.12492.1494

1.85332.29302.33442.37002.4010

2.00002.52662.57702.62052.6585

1.0001.5002.0002.500

1.00001.0002.0043.2344.651

1.14271.0002.0123.2594.701

1.28601.0002.0193.2814.744

1.42671.0002.0263.2994.781

1.56671.0002.0313.3164.814

1.71331.0002.0363.3304.844

1.85331.0002.0403.3434.870

2.00001.0002.0443.3554.894


0000

0000

0000

0000

0000

0000

0000

0000

1.0 WIDTH

1.5 WIDTH

2.0 WIDTH

2.5 WIDTH

DIMENSIONLESS LENGTH L/Lo

DIMENSIONLESS ENERGY E/Eo

SCALE-UP FACTORS IN THE LONGITUDINAL DIRECTION

1.0 WIDTHy = 1.5317x - 0.5515R2 = 0.9995

2.5 WIDTHy = 1.6645x - 0.691R2 = 0.9992

00000000

00000000

00000000

00000000

1.0 L

1.14 L

1.29 L

1.43 L

1.57 L

1.71 L

1.85 L

2.0 L

DIMENSIONLESS WIDTH, W/Wo

DIMENSIONLESS ENERGY, E/Eo

SCALE-UP FACTORS IN THE WIDTH DIRECTION

1.0 Ly = 0.4125x2 + 0.9929x - 0.4074R2 = 1

2.0 Ly = 0.4952x2 + 0.8654x - 0.3625R2 = 1

CARBON NANOTUBE CRIMPING STRAIN ENERGY ANALYSIS

NEW DESIGN76,500 ATOMS

Measuring Muscle Strengthwith an AFM TipCantilever deflection proportional to pull of molecular muscleAtomic Force Microscopy (AFM) tip can be attached to a surface-bound molecule

Dimerization vs. Complexation Not Necessarily the SameDifferentiate by NMR and mass spectrometry

Free Energy AnalysisDensity of Vibration State (Berens and Wilson,1981)Partition Function: Harmonic approximationclassical limitTotal energy from MDThermodynamics

Relative Stability Between Chain and Loop1o1l2c2lDA(l-o) = 23 kcal/mol+FSM = 29 kcal/mol DA(l-c) = -53 kcal/mol+FSM = -50 kcal/mol A E-TS

Free Energy of Concatenated Rotaxanes

Opto-mechanical MusclesAzobenzene monomer response to light365 nm trans cis420 nm cis transTension of a single strand ~ 205 pNLength change per monomer ~ 0.25 nmNot to exceed 50 nm in length for good efficiency in Quantum yieldDetermination of mechanical propertiesIntegration into NEMSextendedcontractedhn (420 nm)hn (365 nm)

One designed example:ABCDA B C D groups key design issue

ChallengesMulti-scale algorithmsParticle-Continuum AlgorithmsEnergy/Mass/Flux conservationMore General embedding algorithmsAtoms to beadsAtoms to stringsAtoms to complex topological objectsSpace fillingGrain boundary propertiesEmbedding mechanical (elastic) Viscoelastic, Thermal, and Chemical Properties

ChallengesLong-Range InteractionsBeyond particle mesh methods ? 18,482 atomsNafion Fuel Cell80 C100 ps MD148 hours 2 procNon-bond=127 hours

AcknowledgementsGoddard GroupTahir Cagin, Alejandro StrachanShiang-Tai LinSantiago SolaresStoddard GroupAndres Jaramillo

fundamentals of molecular dynamics for nano-technology applications mario blanco materials and...

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