Approximative "one particle" bridge function B(1)(r) for the theory of simple fluids

Area of Science:

• Statistical Mechanics
• Thermodynamics
• Computational Physics

Background:

• Calculating the excess chemical potential (βμe) in hard sphere fluids is crucial for understanding their thermodynamic properties.
• The one-particle bridge function (B(1)(r)) is essential for these calculations but difficult to determine directly.
• Existing methods often require complex approximations or extensive simulations.

Purpose of the Study:

• To derive new properties of the one-particle bridge function (B(1)(r)) for hard sphere fluids.
• To develop a method for calculating the excess chemical potential (βμe) that relies on the two-particle bridge function (B(2)(r)).
• To investigate the relationship between correlation functions and the Kirkwood charging parameter.

Main Methods:

• The study utilizes an investigation of the correlation function's dependence on the Kirkwood charging parameter.
• It leverages the known two-particle bridge function (B(2)(r)) to infer properties of B(1)(r).
• Topological homotopy considerations are addressed within this framework.

Main Results:

• New, useful information on B(1)(r) is provided for well-defined dynamical regimes of the hard sphere fluid.
• Signatures of transitions between these dynamical regimes are identified through the trends of B(1)(r).
• The approach yields self-consistent results for the excess chemical potential (βμe).

Conclusions:

• The derived properties of B(1)(r) offer a more accessible route to calculating the excess chemical potential (βμe) in hard sphere systems.
• The results align excellently with existing simulation data, validating the proposed method.
• This work provides valuable insights into the behavior of B(1)(r) and its connection to fluid dynamics.