Micellization as a connectivity transition: a topological Ising model with a hydrophobic constraint

Area of Science:

• Computational physics and chemistry
• Soft matter physics
• Statistical mechanics

Background:

• Micellization is traditionally explained by the hydrophobic effect, a collective phenomenon.
• Existing models often focus on explicit molecular interactions and solvent properties.

Purpose of the Study:

• To propose and investigate a novel topological Ising model for micellization.
• To abstract the hydrophobic effect as a solvent-exclusion constraint based on local connectivity.
• To explore the role of topology and local interactions in amphiphile self-assembly.

Main Methods:

• Developed a topological Ising model on a square lattice with binary occupancy (amphiphiles/water).
• Defined neighborhood using a topological kernel with radius R and Chebyshev or Manhattan metrics.
• Simulated system dynamics using Metropolis updates at varying temperatures (T) and amphiphile densities (ρ).

Main Results:

• Observed the emergence of a giant amphiphilic component for more connective kernels (e.g., Chebyshev, R ≥ 3).
• Found that less connective configurations (e.g., Manhattan, R = 1) did not lead to aggregation in similar parameter ranges.
• Demonstrated that micellization is a connectivity transition governed by interaction topology.

Conclusions:

• The study supports a framework where micellization is a topological connectivity transition.
• Local interaction topology, rather than explicit metric scales, governs amphiphile self-assembly.
• The model provides a basis for quantitative comparisons with experimental and simulation data.