Departures from perfect isomorph behavior in Lennard-Jones fluids and solids

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Chemistry

Background:

• Isomorphs represent lines of invariant microstructure under density scaling in phase diagrams.
• Perfect isomorphicity is limited to inverse power and hard sphere potentials.
• Understanding deviations is crucial for accurately modeling real systems.

Purpose of the Study:

• Develop theoretical tools to quantify isomorphicity deviations for general potentials.
• Test these tools using the Lennard-Jones (LJ) system.
• Investigate the physical significance of isomorph correlations.

Main Methods:

• Utilized theoretical criteria to assess isomorphicity deviations.
• Employed the Lennard-Jones system as a model.
• Calculated shear viscosity and self-diffusion coefficients.
• Analyzed virial-potential energy fluctuations and effective inverse power law (IPL) systems.

Main Results:

• A simple method accurately predicts isomorphs in the fluid range for the LJ system.
• Shear viscosity and self-diffusion coefficients exhibit good scaling along predicted isomorphs.
• The effective IPL exponent (n') converges to 12 at high temperatures as ~T^-1/2.
• Derived analytic expressions for radial distribution function derivatives along isomorphs.

Conclusions:

• The developed methods provide accurate predictions for isomorph behavior in systems beyond simple potentials.
• Isomorph invariance extends to the variance of the radial distribution and fluctuation functions.
• This work offers valuable tools for molecular simulations and understanding fluid behavior.