Effects of Force Fields in Simulating Nano-to Subnano- level Geo-materials

Chung R SongChung R. SongSudarshan Adhikari

Weidong Wu, Ahmed Al-Ostaz

Department of Civil EngineeringThe University of MississippiThe University of Mississippi

University, MS 38677

Contents

MotivationForce FieldsResultsConcluding Remarks

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Motivation 1Motivation 1

Nanomechanics provides valuable information regardingNanomechanics provides valuable information regarding material properties in nano- to subnano- level.Can investigate the interaction of clay minerals and chemicals, t l i t t f hi h l h i bito supply input parameters for higher scale mechanics, bio degradation of environmental materials and so on.Force field is most important.Force field is based on non deterministic mechanics so called Heiderberg’s principle of uncertainty.

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Motivation 2Motivation 2

Each force field has its own assumptions or approximationsEach force field has its own assumptions or approximations.Without selecting the correct field molecular mechanics simulation may be a black box.Rational force fields for soils are not researched extensively.

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Force FieldFundamental Molecular MechanicsFundamental Molecular Mechanics

PPPPPP ++++ TorsionBendAngleStretchBondVDWCoulTotal PPPPPP ++++=

∑= jiqqeP2

∑≠

=ji ijo

Coul rP

πε4

⎥⎤

⎢⎡ ⎤⎡⎤⎡ RRo

612

∑≠ ⎥

⎥

⎦⎢⎢

⎣ ⎥⎥⎦

⎤

⎢⎢⎣

⎡−

⎥⎥⎦

⎤

⎢⎢⎣

⎡=

ji ij

o

ijoVDW r

RrRoDP 2

Well developed Cauchy-Born rule.

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d op d au y o u

Well developed input parameters.

Force FieldCoupled Molecular MechanicsCoupled Molecular Mechanics

43

φθ bbbbbondcoupluncoupl StretchBond PPPPPPP +++=+=

∑ −−+

∑ −+−+−=

'bb'bb

b

)'b'b)(bb(F

)bb(K)bb(K)bb(K

00

404

30302

2

[ ]∑ −+−+−−+

∑ −−+

φφφ

θθ

φφφ

θθ

)(b

)(b

)(b

,bb

bb

)cos(F)cos(F)cos(F)bb(

))(bb(F

31211 3210

00

Well developed input parameters?

[ ]∑ +++φ

φφφ φφφ,b

,b,b,b )cos(F)cos(F)cos(F)bb( 312110

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d op d pu pa a

How do we know them?

Force FieldCoupled Molecular MechanicsCoupled Molecular Mechanics

•From experiments

•From theoryy

•From empricism

•Combination

Typically a proper force field is determined from the crystal structure of molecules.structure of molecules.

Soils with impurities have very complicated structures, and selection of the proper force field is difficult.

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Several force fields are tried in this study.

Force FieldCoupled Molecular MechanicsCoupled Molecular Mechanics

•COMPASS (Condensed-phase Optimized Molecular Potentials for Atomistic simulation Studies) – theoretical, quantumn

h i b d b i i i (S l 1998)mechanics based, ab-initio, (Sun et al. 1998)

•PCFF (Polymer-Consistent Force Field) – ab-initio + experimental Warshel Lifson and coworkers (1973 1974)experimental, Warshel, Lifson and coworkers (1973, 1974)

•CVFF (Consistent Valence Force Field) – small organics, experimental experimental (Maple et al 1988)experimental, experimental, (Maple et al. 1988)

•Universal – most conventional, experimentally determined

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Results

Discover/ Discover/ Discover/ Forcite/ PublishedForce Field Discover/ COMPASS

Discover/ PCFF

Discover/ CVFF

Forcite/ Universal

Published Results**

El ti M d l 98 7 181 2 146 3 214105a

113 2bElastic Modulus (GPa)

98.7 181.2 146.3 214 113.2b

95.6c

Poisson's Ratio 0.11 0.06 0.07 0.1 0.06b

0 079c0.079c

Lame Constant λ (GPa) 12.56 12.23 11.14 23.4 15.7c

Lame ConstantLame Constant µ (GPa) 44.46 85.26 68.37 97.54 31.2c

* Other conditions: Temperature=25oC, Dynamic Time=50 pico seconds,

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Time Step=1 femto second, constant volume & constant temperature conditon.a Dutta and Penumadu (2007), bWang et al. (2007), cBase (1995)

Cell Size EffectsMolecular Level Jennite in Cement

Jennite

Molecular Level – Jennite in Cement

Jennite

Supercell/1a×1b×1c 2a×2b×2c

Ref

Properties1a×1b×1c 2a×2b×2c

Results 

MD Tools FC DC FC DC

E 44.1 82.2 66.9 ‐ 66

ν 0.28 0.33 0.34 ‐ 0.24

κ 33.3 78.4 69 ‐ 43

G 17.2 31.0 25 ‐ 26

Page 10

Concluding Remarks

COMPASS, the one which has a capability to obtain constants fromCOMPASS, the one which has a capability to obtain constants fromab-initio quantum mechanics, generally shows the most reasonableresults for quartz sands.

PCFF and CVFF es lted in m ch highe mod l s and inco ectPCFF and CVFF resulted in much higher modulus and incorrectresults for sands.

Universal, the one which is based on conventional molecularUniversal, the one which is based on conventional molecularmechanics, also showed unrealistic results for sands.

However, Discover COMPASS did not show reasonable results forJenniteJennite

From the study, the importance of selecting the proper force field isdemonstrated.demonstrated.

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Thank you for your attention.y f y

Q sti s?Questions?

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