Orientational ordering and correlations in a quasi-one-dimensional hard-dumbbell fluid

Area of Science:

• Physics
• Statistical Mechanics
• Soft Matter Physics

Background:

• Understanding the thermodynamic properties and ordering in low-dimensional fluids is crucial.
• Hard dumbbell models capture essential features of molecular shape and interactions.

Purpose of the Study:

• To analytically characterize thermodynamic properties, orientational ordering, and correlation functions of a quasi-one-dimensional hard dumbbell fluid.
• To investigate the crossover behavior and high-pressure limits.

Main Methods:

• Exact transfer-matrix formulation for a quasi-one-dimensional hard dumbbell fluid.
• Analytical derivation of equation of state, orientational distribution, and radial distribution functions.
• Numerical solutions of the discretized transfer operator and scaling arguments.

Main Results:

• Derived exact expressions for thermodynamic and correlation functions, governed by spectral properties of an integral operator.
• Identified a continuous crossover from weak to strong orientational ordering (unimodal to bimodal) with increasing density.
• Observed nonmonotonic pressure behavior relative to the Tonks gas and a universal pressure ratio at high pressures.

Conclusions:

• The transfer-matrix method provides a complete analytical framework for hard dumbbell fluids.
• Density drives a significant change in orientational order and correlation decay.
• High-pressure behavior exhibits universal characteristics related to orientational and positional fluctuations.