Modeling velocity autocorrelation functions for confined fluids using gamma distributions

Area of Science:

• Physics
• Physical Chemistry
• Materials Science

Background:

• Understanding fluid dynamics in confined geometries is crucial for various applications.
• Existing models often struggle to accurately capture the short-time dynamics of confined fluids.
• The instantaneous normal mode (INM) density of states (DOS) provides insights but has limitations.

Purpose of the Study:

• To propose a novel model for the short-time dynamics of fluids confined in slit-shaped pores.
• To develop an analytical expression for the velocity autocorrelation function (VACF) and relaxation times.
• To validate the model against molecular dynamics simulations and INM analysis.

Main Methods:

• The model is based on the observation that the real lobe of the INM DOS follows a gamma distribution.
• The density of states of the confined fluid is represented by a gamma distribution.
• The resulting VACF is constructed to be accurate up to the fourth frequency moment.

Main Results:

• The proposed model provides an analytical expression for the VACF and relaxation times.
• The model accurately captures the short-time behavior of the VACF for confined fluids.
• The model's predictions for relaxation times show better agreement with molecular dynamics than INM theory, despite predicting zero self-diffusivity.

Conclusions:

• The developed model offers a superior description of short-time dynamics for confined fluids compared to INM DOS.
• The analytical nature of the model simplifies calculations of VACF and relaxation times.
• This model advances the understanding of fluid behavior in nanoporous materials.