Multi-Scale Modeling of Electro-Active Polymers: Towards Computational Materials Design Haibin Su, Alejandro Strachan (LANL), Tahir Cagin, Albert Cuitino (Rutgers) & William A. Goddard III

Materials and Process Simulation Center, Beckman Institute, California Institute of Technology, Pasadena, California 91125

Quantum Mechanics and Molecular Mechanics Studies on Energetics and Nucleation Meso-Macro-Scale Modeling on Phase Transformation

SeqQuest code (P. Schultz, SNL), DFT, GGA-PBE, pseudopotentials, Gaussian basis set

( Energy in kcal / mole per carbon )

Phase I: All Trans Phase II TGTG’ Phase III T3GT3G’

An

gle

(deg

ree)

An

gle

(deg

ree)

Torsional angle (degree) Torsional angle (degree)

C C C0 +2-1-2

Restraint is applied to bond 0

Perpendicular to the chains

strain rate (1010 1/s)

Sh

ear

Str

ess

(GP

a)

xy

Strain rate 3.85 x 1010 (1/s)

yz

xz

Perpendicular to the chains

xy

yz

Along the chains

Perpendicular to the chains

Along the chains

Db

/E

-0.05 0 0.05 0.1

-0.08

-0.04

0

0.04

0.08

0.12

0.16

1

1

2

2

3

3

Phase transformation from non-polar to polar (polarization) Phase transformation from non-polar to polar (polarization) driven by applied strain for a driven by applied strain for a single nucleationsingle nucleation site site

ab initio QMEoS of various phasesTorsional barriersVibrational frequencies

Force Fields and MDElastic, dielectric constantsNucleation BarrierDomain wall and interface mobilityPhase transitionsAnisotropic Viscosity

Meso- Macro-scaleNanostructure-properties relationshipsConstitutive Laws

Multi-Scale-Modeling Roadmap

Initial conditionNon-polar

Load

Mechanically driven non-polar (T3G) to polar (all-trans) transformation

ALLOWS FOR ARBITRARY SHAPES AND GENERAL

ELECTROMECHANICAL BC IN 2D and 3D

Complex nucleation of polar phase

Undeformed Deformed

(T3G)

(all-trans)

Nucleation of a G bond in an all-T Configuration

PVDF

P(VDF-TrFE)

En

ergy

( k

cal /

mol

)

Torsional angle (degree)

+1C C C

•Torsions of bonds +1 and -1 remain ~180° •Intrinsic Conservation of Torsion Angles

Stress (Gpa)

Mob

ilit

y (

m/s

)

Polar (all trans) Non-Polar (T3G)

time = 0 ps time = 3 ps

time = 6 ps

Almost completely polar

time = 9 ps

Molecular Dynamics Studies on Interface Mobility and Chain Sliding

0 5 10Time (ps)

15 20 25 30

0.4

0.3

0.2

0.1

0

0.5

Sh

ear

Str

ess

(GP

a)

-0.2

-0.1

0.16

0.14

0.12

0.10

0.08

0.009

0.029

1.8 2.8 3.8 4.8 5.8 6.8

Along the chains

Perpendicular to the chains

Vis

cosi

ty (

Pa.

s)

2.0 3.0 4.0 5.0 6.0 7.0

0.00050

0.00055

0.00060

0.00065

0.0020

0.0025

0.0030

0.0035

0.0040

Sxxe

Syy Sxy

y

x

x

y

cb

a

Represents ferroelectric phase

yx

Strain ()

Energ

y(J)

0 0.02 0.04 0.060

5E+06

1E+07

1.5E+07

30% polarized

20%

Strain ()

strain rate (1010 1/s)

• Eulerian code

• Coupled electromechanical response

• Long-range interaction

• Hierarchical Multiscale: Parameters obtained from atomistics

• Interface tracking – level set

• Nucleating mechanism with G0 Energy Barrier

• Propagation mechanism driven by global minimization of

Gibbs free energy – Gm (Energy Barrier for motion)