Universal Law for Diffusion in Continuous Potential Energy Landscapes

Area of Science:

• Soft Matter Physics
• Statistical Mechanics
• Complex Systems

Background:

• Colloidal particle diffusion is fundamental to many physical and biological processes.
• Understanding diffusion in complex potential energy landscapes is challenging.
• Existing models often lack quantitative predictive power for diverse environments.

Purpose of the Study:

• To investigate the diffusion dynamics of colloidal particles in quasi-two-dimensional potential energy landscapes.
• To establish a universal relationship between potential landscape characteristics and diffusion coefficients.
• To develop a quantitative tool for analyzing complex dynamical phenomena.

Main Methods:

• Utilized video microscopy to track colloidal particle movement.
• Employed scanning optical tweezers to construct potential energy landscapes.
• Performed computer simulations to complement experimental data.
• Extracted diffusion coefficients from long-time mean squared displacements.

Main Results:

• Discovered a universal relation predicting normalized long-time diffusion coefficient.
• Characterized potential landscapes using Shannon information entropy (S_N) and generalized packing fraction (ϕ).
• Validated the relation across various potential distributions and dynamic ranges.

Conclusions:

• The universal law provides a quantitative method to predict diffusion based on landscape shape.
• This finding simplifies complex potential distributions into two dimensionless numbers.
• Offers a powerful tool for studying dynamical phenomena in systems lacking general models.