Describing nonequilibrium soft matter with mean field game theory

Welch, Paul Michael Jr.; Rasmussen, Kim Orskov; Welch, Cynthia F.

doi:10.1063/1.5081829

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:

^[1];

^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: Tue May 07 00:00:00 EDT 2019

Research Org.:: Los Alamos National Laboratory (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.

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                    Welch, Paul Michael Jr., Rasmussen, Kim Orskov, & Welch, Cynthia F. Describing nonequilibrium soft matter with mean field game theory.  United States.  https://doi.org/10.1063/1.5081829

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                    Welch, Paul Michael Jr., Rasmussen, Kim Orskov, and Welch, Cynthia F. Tue .  
"Describing nonequilibrium soft matter with mean field game theory".  United States.  https://doi.org/10.1063/1.5081829.  https://www.osti.gov/servlets/purl/1532707.

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@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         = {Tue May 07 00:00:00 EDT 2019},

  month        = {Tue May 07 00:00:00 EDT 2019}

}

Copy to clipboard

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Title: Describing nonequilibrium soft matter with mean field game theory

Abstract

Citation Formats

Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle journal, January 2006

Mean field games journal, March 2007

Schrödinger Approach to Mean Field Games journal, March 2016

Kinetic Pathways of Lamellae to Gyroid Transition in Weakly Segregated Diblock Copolymers journal, November 2015

Dynamic density functional theory for microphase separation kinetics of block copolymer melts journal, December 1993

Mesoscopic dynamics of copolymer melts: From density dynamics to external potential dynamics using nonlocal kinetic coupling journal, October 1997

The dynamic mean-field density functional method and its application to the mesoscopic dynamics of quenched block copolymer melts journal, March 1997

Model for Pattern Formation in Polymer Surfactant Nanodroplets journal, October 2003

Field-theoretic polymer simulations journal, September 2001

Dynamics and rheology of inhomogeneous polymeric fluids: A complex Langevin approach journal, October 2002

Field-Theoretic Computer Simulation Methods for Polymers and Complex Fluids journal, January 2002

Dynamical theory of polymer melt morphology journal, June 1987

Kinetics of metastable states in block copolymer melts journal, December 1989

Adsorption Dynamics. Extension of Self-Consistent Field Theory to Dynamical Problems journal, May 1997

Dynamics of surface directed mesophase formation in block copolymer melts journal, January 1999

Formation of Interfaces in Incompatible Polymer Blends: A Dynamical Mean Field Study journal, June 1999

Three-Dimensional Numerical Simulations of Viscoelastic Phase Separation: Morphological Characteristics journal, March 2001

Kinetics of morphological transitions between mesophases* journal, September 2001

Kinetics of Morphological Transitions in Microphase-Separated Diblock Copolymers journal, July 2004

Hexagonally Perforated Lamella-to-Cylinder Transition in a Diblock Copolymer Thin Film under an Electric Field journal, June 2008

Improved numerical algorithm for exploring block copolymer mesophases journal, July 2002

Unifying Weak- and Strong-Segregation Block Copolymer Theories journal, January 1996

Complex Phase Behavior of Polyisoprene-Polystyrene Diblock Copolymers Near the Order-Disorder Transition journal, November 1994

Transformations to and from the Gyroid Phase in a Diblock Copolymer journal, August 1998

Microphase separation in poly(isoprene- b -ethylene oxide) diblock copolymer melts. I. Phase state and kinetics of the order-to-order transitions journal, January 1999

Nucleation and growth in order-to-order transitions of a block copolymer journal, April 2000

Unexpected Intermediate State for the Cylinder-to-Gyroid Transition in a Block Copolymer Solution journal, January 2002

Kinetics and Mechanisms for the Cylinder-to-Gyroid Transition in a Block Copolymer Solution journal, August 2002

New Epitaxial Phase Transition between DG and HEX in PS- b -PI journal, January 2009

Transition Mechanisms for Complex Ordered Phases in Block Copolymer Melts journal, February 1998

Observation of a reversible thermotropic order-order transition in a diblock copolymer journal, March 1994

Phase Behaviour and Morphologies of Block Copolymers book, January 2005

Origin of epitaxies between ordered phases of block copolymers journal, January 2011

Hexagonal mesophases between lamellae and cylinders in a diblock copolymer melt journal, October 1993

Templated Crystallization from Oriented Gyroid and Hexagonal Melt Phases in a Diblock Copolymer journal, November 2002

Thermodynamic Stability and Anisotropic Fluctuations in the Cylinder-to-Sphere Transition of a Block Copolymer journal, October 1999

Order−Order Phase Transition between Spherical and Cylindrical Microdomain Structures of Block Copolymer. I. Mechanism of the Transition journal, February 2000

Small-Angle Neutron Scattering Study of a Cylinder-to-Sphere Order−Order Transition in Block Copolymers journal, May 2000

Is a time symmetric interpretation of quantum theory possible without retrocausality? journal, June 2017

ParaView: An End-User Tool for Large-Data Visualization book, January 2005

Fokker-Planck Equation journal, April 1963

Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle
journal, January 2006

Mean field games
journal, March 2007

Schrödinger Approach to Mean Field Games
journal, March 2016

Kinetic Pathways of Lamellae to Gyroid Transition in Weakly Segregated Diblock Copolymers
journal, November 2015

Dynamic density functional theory for microphase separation kinetics of block copolymer melts
journal, December 1993

Mesoscopic dynamics of copolymer melts: From density dynamics to external potential dynamics using nonlocal kinetic coupling
journal, October 1997

The dynamic mean-field density functional method and its application to the mesoscopic dynamics of quenched block copolymer melts
journal, March 1997

Model for Pattern Formation in Polymer Surfactant Nanodroplets
journal, October 2003

Field-theoretic polymer simulations
journal, September 2001

Dynamics and rheology of inhomogeneous polymeric fluids: A complex Langevin approach
journal, October 2002

Field-Theoretic Computer Simulation Methods for Polymers and Complex Fluids
journal, January 2002

Dynamical theory of polymer melt morphology
journal, June 1987

Kinetics of metastable states in block copolymer melts
journal, December 1989

Adsorption Dynamics. Extension of Self-Consistent Field Theory to Dynamical Problems
journal, May 1997

Dynamics of surface directed mesophase formation in block copolymer melts
journal, January 1999

Formation of Interfaces in Incompatible Polymer Blends: A Dynamical Mean Field Study
journal, June 1999

Three-Dimensional Numerical Simulations of Viscoelastic Phase Separation: Morphological Characteristics
journal, March 2001

Kinetics of morphological transitions between mesophases*
journal, September 2001

Kinetics of Morphological Transitions in Microphase-Separated Diblock Copolymers
journal, July 2004

Hexagonally Perforated Lamella-to-Cylinder Transition in a Diblock Copolymer Thin Film under an Electric Field
journal, June 2008

Improved numerical algorithm for exploring block copolymer mesophases
journal, July 2002

Unifying Weak- and Strong-Segregation Block Copolymer Theories
journal, January 1996

Complex Phase Behavior of Polyisoprene-Polystyrene Diblock Copolymers Near the Order-Disorder Transition
journal, November 1994

Transformations to and from the Gyroid Phase in a Diblock Copolymer
journal, August 1998

Microphase separation in poly(isoprene- b -ethylene oxide) diblock copolymer melts. I. Phase state and kinetics of the order-to-order transitions
journal, January 1999

Nucleation and growth in order-to-order transitions of a block copolymer
journal, April 2000

Unexpected Intermediate State for the Cylinder-to-Gyroid Transition in a Block Copolymer Solution
journal, January 2002

Kinetics and Mechanisms for the Cylinder-to-Gyroid Transition in a Block Copolymer Solution
journal, August 2002

New Epitaxial Phase Transition between DG and HEX in PS- b -PI
journal, January 2009

Transition Mechanisms for Complex Ordered Phases in Block Copolymer Melts
journal, February 1998

Observation of a reversible thermotropic order-order transition in a diblock copolymer
journal, March 1994

Phase Behaviour and Morphologies of Block Copolymers
book, January 2005

Origin of epitaxies between ordered phases of block copolymers
journal, January 2011

Hexagonal mesophases between lamellae and cylinders in a diblock copolymer melt
journal, October 1993

Templated Crystallization from Oriented Gyroid and Hexagonal Melt Phases in a Diblock Copolymer
journal, November 2002

Thermodynamic Stability and Anisotropic Fluctuations in the Cylinder-to-Sphere Transition of a Block Copolymer
journal, October 1999

Order−Order Phase Transition between Spherical and Cylindrical Microdomain Structures of Block Copolymer. I. Mechanism of the Transition
journal, February 2000

Small-Angle Neutron Scattering Study of a Cylinder-to-Sphere Order−Order Transition in Block Copolymers
journal, May 2000

Is a time symmetric interpretation of quantum theory possible without retrocausality?
journal, June 2017

ParaView: An End-User Tool for Large-Data Visualization
book, January 2005

Fokker-Planck Equation
journal, April 1963