Bragg-Williams Theory for Particles with a Size-Modulating Internal Degree of Freedom

Area of Science:

• Soft Matter Physics
• Physical Chemistry
• Materials Science

Background:

• Soft matter systems exhibit molecules with internal degrees of freedom, leading to multiple size states.
• Particle size variations influence their pressure-sensitive behavior and accessible states.
• The Bragg-Williams model approximates phase diagrams based on inter-particle interactions.

Purpose of the Study:

• To extend the Bragg-Williams model for soft matter particles with two distinct sizes in a solvent.
• To incorporate particle-solvent interactions as effective surface tension.
• To analyze the impact of energetic preferences on phase diagrams.

Main Methods:

• Utilized a lattice-sublattice approximation to model particles in two size states.
• Extended the Bragg-Williams mean-field theory.
• Investigated particle-solvent interactions and their effect on phase behavior.

Main Results:

• Demonstrated a single phase-two phases-single phase sequence of phase transitions with increasing temperature.
• Showcased how energetic preferences for specific particle states alter phase diagrams.
• Validated the model's ability to predict pressure-sensitive behavior in soft matter.

Conclusions:

• The extended Bragg-Williams model accurately captures the complex phase behavior of size-varying soft matter.
• Particle-solvent interactions and internal state preferences are critical factors in determining soft matter phase transitions.
• The findings provide insights into the design and understanding of responsive soft materials.