Describing nonequilibrium soft matter with mean field game theory

Area of Science:

• Soft Matter Physics
• Polymer Science
• Statistical Mechanics

Background:

• Diblock copolymers exhibit complex phase behavior crucial for materials science.
• Understanding polymer phase evolution, especially order-order transformations, is experimentally and theoretically challenging.

Purpose of the Study:

• To develop a novel theoretical framework for simulating diblock copolymer phase evolution.
• To investigate order-order phase transformations, including hexagonal cylinders, lamellae, and gyroid structures, under temperature changes.

Main Methods:

• Combining self-consistent mean field theory with an emerging game theory approach.
• Analyzing phase transformations upon quenched temperature changes.

Main Results:

• Game theoretical dynamics accurately predict local composition evolution.
• Simulated small-angle scattering patterns align with experimental observations.
• Nucleation and growth mechanisms are active when quenched far from the critical point.
• Epitaxial growth phenomena were observed.

Conclusions:

• The presented methodology offers a new approach to studying polymer dynamics.
• This is the first integration of mean field game theory and statistical mechanics for soft matter systems.
• The model provides realistic treatments of diblock copolymer phase evolution.