Beyond the single-file fluid limit using transfer matrix method: Exact results for confined parallel hard squares

Area of Science:

• Physics
• Physical Chemistry
• Materials Science

Background:

• Confined fluids exhibit unique properties compared to bulk systems.
• Understanding particle behavior in quasi-one-dimensional systems is crucial for nanotechnology.

Purpose of the Study:

• To extend the transfer matrix method for hard core fluids between confining walls.
• To investigate the structural behavior of hard squares in quasi-one-dimensional pores.

Main Methods:

• Developed an eigenvalue equation for hard squares confined between parallel walls (pore width σ to 3σ).
• Utilized the transfer matrix method, extending it for inter-particle passage and multilayer formation.

Main Results:

• Identified three distinct structures: single-layer fluid, double-layer fluid, and a solid-like phase with correlated layers.
• Observed continuous structural transitions with increasing density, lacking sharp thermodynamic phase transitions.
• Characterized the high-density structure as broken two-layer clusters with particles in the pore center.

Conclusions:

• The system exhibits rich structural polymorphism under confinement.
• Density-driven continuous transitions, rather than abrupt phase transitions, govern fluid ordering in these quasi-1D systems.