Universal sequence of ordered structures obtained from mesoscopic description of self-assembly.

Area of Science:

• Soft-matter physics
• Theoretical chemistry
• Materials science

Background:

• Understanding self-assembly in soft matter is crucial for designing materials.
• Existing theories often struggle to capture both microscopic and mesoscopic length scales.

Purpose of the Study:

• To develop a unified mesoscopic theory for soft-matter systems.
• To predict and explain the phase behavior of self-assembling materials.

Main Methods:

• Systematic coarse-graining procedure combining density functional theory and statistical field theory.
• Derivation of a grand-thermodynamic potential with microscopic and mesoscopic fluctuation terms.
• Obtained Ornstein-Zernicke-like equations for density fluctuations.

Main Results:

• The theory yields a universal sequence of phases: disordered, bcc, hexagonal, lamellar, inverted hexagonal, inverted bcc, disordered.
• Microscopic expressions for parameters in Landau-type theories (Landau-Ginzburg-Wilson and Landau-Brazovskii) were derived.
• The bicontinuous gyroid phase (Ia3d symmetry) was identified for specific interaction potentials.

Conclusions:

• The developed theory successfully unifies different theoretical approaches for soft matter.
• The predicted universal phase sequence aligns with experimental and simulation data.
• The theory provides a framework for understanding complex phase formation in self-assembling systems.