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 ) hase I: All TransPhase II TGTG’ Phase III T 3 GT 3 G’ Angle (degree) Angle (degree) Torsional angle (degree) Torsional angle (degree) C C C 0 +2 -1 -2 Restraint is applied to bond 0 Perpendicular to the chains strain rate (10 10 1/s) Shear Stress (GPa) xy Strain rate 3.85 x 10 10 (1/s) yz xz Perpendicular to the chains xy yz Along the chains Perpendicular to the chains Along the chains D b /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 (polariza Phase transformation from non-polar to polar (polariza driven by applied strain for a driven by applied strain for a single nucleation single nucleation site site ab initio QM EoS of various phases Torsional barriers Vibrational frequencies Force Fields and MD Elastic, dielectric constants Nucleation Barrier Domain wall and interface mobility Phase transitions Anisotropic Viscosity Meso- Macro-scale Nanostructure- properties relationships Constitutive Laws Multi-Scale-Modeling Roadmap Initial condition Non-polar Load Mechanically driven non- polar (T 3 G) to polar (all-trans) transformation ALLOWS FOR ARBITRARY SHAPES AND GENERAL ELECTROMECHANICAL BC IN 2D and 3D Complex nucleation of polar phase Undeformed Deformed (T 3 G) (all-trans) Nucleation of a G bond in an all-T Configuration PVDF P(VDF-TrFE) Energy ( kcal / mol ) Torsional angle (degree) +1 C C C •Torsions of bonds +1 and -1 remain ~180° •Intrinsic Conservation of Torsion Angles Stress (Gpa) Mobility ( m/s ) Polar (all trans) Non-Polar (T 3 G) 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 10 Time (ps) 15 20 25 30 0.4 0.3 0.2 0.1 0 0.5 Shear Stress (GPa) -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 Viscosity (Pa.s) 2.0 3.0 4.0 5.0 6.0 7.0 0.000 50 0.00055 0.00060 0.00065 0.0020 0.0025 0.0030 0.0035 0.0040 S xx e S yy S xy y x x y c b a Represents ferroelectric phase y x S train ( ) Energy (J ) 0 0.02 0.04 0.06 0 5E+06 1E+07 1.5E+07 30% polarized 20% Strain () strain rate (10 10 1/s) • Eulerian code • Coupled electromechanical response • Long-range interaction • Hierarchical Multiscale: Parameters obtained from atomistics • Interface tracking – level set • Nucleating mechanism with G 0 Energy Barrier • Propagation mechanism driven by global minimization of Gibbs free energy – G m (Energy Barrier for motion)