Two-dimensional colloidal fluids exhibiting pattern formation.

Area of Science:

• Statistical mechanics
• Soft matter physics
• Computational fluid dynamics

Background:

• Fluids with competing short-range attraction and long-range repulsion exhibit complex microphase separated structures.
• Understanding these structures is crucial for materials science and fluid dynamics.

Purpose of the Study:

• To develop and analyze a lattice-gas model for fluids with competing interactions.
• To compare predictions from density functional theory (DFT) with Monte Carlo simulations.
• To investigate the relationship between heat capacity and morphological transitions.

Main Methods:

• Development of a lattice-gas (generalized Ising) model.
• Analysis of the phase diagram using Monte Carlo computer simulations.
• Application of density functional theory (DFT) for structure prediction and stability analysis.

Main Results:

• DFT predictions for microphase separated structures align well with simulation results.
• Simulations reveal transitions analogous to micelle formation, which mean-field DFT does not fully capture.
• Peaks in heat capacity correlate with observed morphology changes.

Conclusions:

• The lattice-gas model, analyzed by DFT and simulations, effectively describes microphase separation in fluids with competing interactions.
• While DFT predicts structures accurately, it requires refinement to capture transition dynamics.
• Heat capacity analysis provides a valuable tool for identifying morphology transitions in such systems.