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Title: Describing nonequilibrium soft matter with mean field game theory

Abstract

We demonstrate that combining an emerging approach to game theory with self-consistent mean field theory provides realistic treatments of diblock copolymer phase evolution. We especially examine order-order phase transformations upon quenched temperature change involving hexagonal cylinders, lamellae, and the gyroid. Our findings demonstrate that (i) the game theoretical dynamics produce realistic trajectories for the evolution of the local compositions, (ii) the predicted small-angle scattering follows experimentally observed trends, (iii) nucleation and growth is active when the system is quenched far from the critical point, and (iv) epitaxial growth is manifest. Lastly, to our knowledge, the methodology presented provides the first merger of mean field game theory and statistical mechanics for soft matter systems, giving a new inroad to studying polymer dynamics.

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1532707
Alternate Identifier(s):
OSTI ID: 1511079
Report Number(s):
LA-UR-18-30104
Journal ID: ISSN 0021-9606
Grant/Contract Number:  
89233218CNA000001
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 150; Journal Issue: 17; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Material Science

Citation Formats

Welch, Paul Michael Jr., Rasmussen, Kim Orskov, and Welch, Cynthia F. Describing nonequilibrium soft matter with mean field game theory. United States: N. p., 2019. Web. doi:10.1063/1.5081829.
Welch, Paul Michael Jr., Rasmussen, Kim Orskov, & Welch, Cynthia F. Describing nonequilibrium soft matter with mean field game theory. United States. doi:10.1063/1.5081829.
Welch, Paul Michael Jr., Rasmussen, Kim Orskov, and Welch, Cynthia F. Tue . "Describing nonequilibrium soft matter with mean field game theory". United States. doi:10.1063/1.5081829. https://www.osti.gov/servlets/purl/1532707.
@article{osti_1532707,
title = {Describing nonequilibrium soft matter with mean field game theory},
author = {Welch, Paul Michael Jr. and Rasmussen, Kim Orskov and Welch, Cynthia F.},
abstractNote = {We demonstrate that combining an emerging approach to game theory with self-consistent mean field theory provides realistic treatments of diblock copolymer phase evolution. We especially examine order-order phase transformations upon quenched temperature change involving hexagonal cylinders, lamellae, and the gyroid. Our findings demonstrate that (i) the game theoretical dynamics produce realistic trajectories for the evolution of the local compositions, (ii) the predicted small-angle scattering follows experimentally observed trends, (iii) nucleation and growth is active when the system is quenched far from the critical point, and (iv) epitaxial growth is manifest. Lastly, to our knowledge, the methodology presented provides the first merger of mean field game theory and statistical mechanics for soft matter systems, giving a new inroad to studying polymer dynamics.},
doi = {10.1063/1.5081829},
journal = {Journal of Chemical Physics},
number = 17,
volume = 150,
place = {United States},
year = {2019},
month = {5}
}

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