Monte Carlo simulations of fluids whose particles interact with a logarithmic potential

Area of Science:

• Statistical Mechanics
• Computational Physics
• Materials Science

Background:

• Previous work introduced a continuous potential with a logarithmic divergence at a specific particle separation.
• This potential, phi(r) = -epsilon ln(1-(sigma/r)^m), models inter-particle interactions in fluids.

Purpose of the Study:

• To verify predictions regarding the calculation of internal energy for this logarithmic potential fluid.
• To investigate the fluid's pressure, mean square force, and elastic moduli.
• To explore the fluid's phase behavior and its transition to hard sphere-like properties.

Main Methods:

• Monte Carlo simulations were employed to study the model fluid.
• Standard statistical mechanics formulas for continuous potentials were used for energy calculations.
• The virial expression was utilized for pressure calculations.

Main Results:

• Internal energy calculations were validated across all temperatures.
• Pressure calculations faced limitations at higher reduced temperatures due to the potential's divergence.
• Mean square force and elastic moduli were finite only below T*=1, indicating a transition to hard sphere-like behavior.

Conclusions:

• The logarithmic fluid transitions to hard sphere-like behavior with increasing temperature, marked by a sharp change at T*=1.
• The study confirms the solid-fluid phase transition in this model system.
• The findings provide insights into the behavior of fluids with diverging potentials.