Power law mass dependence of diffusion: A mode coupling theory analysis

Area of Science:

• Physical Chemistry
• Theoretical Physics
• Computational Chemistry

Background:

• Solute diffusion exhibits weak mass dependence, often explained by hydrodynamic theories like Stokes-Einstein.
• Kinetic theories predict stronger mass dependence, yet neither fully explains observed power-law relationships.

Purpose of the Study:

• To investigate the weak mass dependence of the self-diffusion coefficient using mode coupling theory (MCT).
• To address the limitations of existing MCT in accurately predicting mass dependence.

Main Methods:

• Analysis of diffusion using a generalized mode coupling theory (MCT).
• Development of a new prescription for short-time dynamics of density and current terms.
• Implementation of full self-consistency between frequency-dependent friction and mean square displacement.

Main Results:

• Standard MCT inaccurately predicts an inverse mass dependence.
• Generalized MCT accurately reproduces the power-law mass dependence observed in simulations.
• The current mode was found to have negligible impact on diffusion.

Conclusions:

• Modified MCT provides an accurate description of diffusion's weak mass dependence.
• Hydrodynamic arguments for weak mass dependence are questionable for same-size solute-solvent systems.
• The study highlights the importance of short-time dynamics and self-consistency in diffusion theories.