Dynamical self-consistent field theory for kinetics of structure formation in dense polymeric

systemsDouglas J. Grzetic

CAP Congress 2014

Advisor: Robert A. Wickham

Introduction

particle-based simulation(MD, Brownian dynamics)

coarse-grained field theories(DFT, tdGL, etc)

• Interacting many-body problem

Introduction

particle-based simulation(MD, Brownian dynamics)

coarse-grained field theories(DFT, tdGL, etc)?

• Interacting many-body problem

First-principles microscopic dynamics

drag force spring force “Fspr” non-bondedinteraction force

random force

• Many-body interacting Langevin equation

Dynamical self-consistent field theory

• Dynamical mean-field approximation

• Derived from first-principles microscopic dynamicsD. J. Grzetic, R. A. Wickham and A.-C. Shi, Statistical dynamics of classical systems: A self-consistent field approach, J. Chem. Phys. (2014, in press)

Potential applications to dynamical problems

colloidal dynamics

active matter

entangled chain dynamics

phase separation kineticshttp://www.nonmet.mat.ethz.ch/research/Colloidal_Chemistry_Ceramic_Processing/Colloid_Chemistry.jpg

R. K. W. Spencer and R. A. Wickham, Soft Matter (2013)http://upload.wikimedia.org/wikipedia/commons/3/32/EscherichiaColi_NIAID.jpg

Potential applications to dynamical problems

colloidal dynamics

active matter

entangled chain dynamics

phase separation kineticshttp://www.nonmet.mat.ethz.ch/research/Colloidal_Chemistry_Ceramic_Processing/Colloid_Chemistry.jpg

R. K. W. Spencer and R. A. Wickham, Soft Matter (2013)http://upload.wikimedia.org/wikipedia/commons/3/32/EscherichiaColi_NIAID.jpg

D. J. Grzetic, R. A. Wickham and A.-C. Shi, Statistical dynamics of classical systems: A self-consistent field approach, J. Chem. Phys. (2014, in press)

Dynamical self-consistent field theory

density:

mean field:

functional Smoluchowski equation:

D. J. Grzetic, R. A. Wickham and A.-C. Shi, Statistical dynamics of classical systems: A self-consistent field approach, J. Chem. Phys. (2014, in press)

Dynamical self-consistent field theory

density:

mean field:

functional Smoluchowski equation:

• Equivalent Langevin simulation of chain dynamics (1.6 million chain ensemble)

• Parallelizable (~1 day run time, 32 cores)

Single-chain dynamics in a mean field

• Truncated Lennard-Jones interaction

Microscopic (non-bonded) bead-bead interaction

Symmetric polymer blend: spinodal decomposition

spinodal

BA

Onset of macro-phase separation:structure factor

Microphase separation in AB diblock copolymers

timescale ~102tR

BAasymmetric

Order-order transition: structure factor

rA - rB structure factor

Chain configuration statistics: Rg map

rA - rB radius of gyration, A block

more stretched

less stretched

Conclusions• Demonstrated ability to study kinetics of

macro/microphase separation in large, dense inhomogeneous polymer systems

• Truly non-equilibriummean field theory

• Connection to microscopicdynamics (Rg, tR)

• Retain chain conformationstatistics

D. J. Grzetic, R. A. Wickham and A.-C. Shi, Statistical dynamics of classical systems: A self-consistent field approach, J. Chem. Phys. (2014, in press)