1. Dynamical self-consistent field theory for kinetics of structure formation in dense polymeric systems Douglas J. Grzetic CAP Congress 2014 Advisor: Robert A. Wickham

2. Introduction particle-based simulation (MD, Brownian dynamics) coarse-grained field theories (DFT, tdGL, etc) Interacting many-body problem

3. Introduction particle-based simulation (MD, Brownian dynamics) coarse-grained field theories (DFT, tdGL, etc) ? Interacting many-body problem

4. First-principles microscopic dynamics drag force spring force “F spr ” non-bonded interaction force random force Many-body interacting Langevin equation

5. Dynamical self-consistent field theory Dynamical mean-field approximation Derived from first-principles microscopic dynamics 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)

6. Potential applications to dynamical problems colloidal dynamics active matter entangled chain dynamics phase separation kinetics http://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

7. Potential applications to dynamical problems colloidal dynamics active matter entangled chain dynamics phase separation kinetics http://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

8. 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:

9. 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:

10. 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

11. Truncated Lennard-Jones interaction Microscopic (non-bonded) bead-bead interaction

12. Symmetric polymer blend: spinodal decomposition spinodal BA

13. Onset of macro-phase separation: structure factor

14. Microphase separation in AB diblock copolymers timescale ~10 2  R B A asymmetric

15. Order-order transition: structure factor  A -  B structure factor

16. Chain configuration statistics: R g map  A -  B radius of gyration, A block more stretched less stretched

17. Conclusions Demonstrated ability to study kinetics of macro/microphase separation in large, dense inhomogeneous polymer systems Truly non-equilibrium mean field theory Connection to microscopic dynamics (R g,  R ) Retain chain conformation statistics 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)