A general phenomenological relation for the subdiffusive exponent of anomalous diffusion in disordered media

Area of Science:

• Physics
• Materials Science
• Biophysics

Background:

• Diffusion in complex media like gels is crucial for transport phenomena.
• Understanding tracer particle dynamics in heterogeneous environments is challenging.
• Existing models often struggle to capture the transition to subdiffusive behavior.

Purpose of the Study:

• To numerically investigate tracer particle diffusion in fixed gels.
• To characterize the transition from diffusive to subdiffusive motion based on accessible volume fraction.
• To develop a predictive model for tracer dynamics in gels.

Main Methods:

• Numerical simulations of finite inert tracer particles in fixed gels.
• Analysis of mean square displacement (MSD) to identify subdiffusion.
• Cluster analysis of gel accessible volume.
• Separation of mobile and trapped tracer populations for analysis.

Main Results:

• Subdiffusive motion (MSD ∼ tα) observed as accessible volume fraction (p) decreases.
• Two tracer populations identified: mobile (subdiffusive) and trapped.
• A phenomenological law for mobile tracer subdiffusion exponent (αmob) derived: αmob(p) ≈ a ln(p) + c.
• A power law for trapping probability (ptrap) found: ptrap ∼ (p/pc)-γ, with γ ≃ 2.9.
• Predicted ensemble-averaged subdiffusion exponent: α = αmob(1 - ptrap).

Conclusions:

• The developed model accurately predicts tracer diffusion in various gels.
• The parameter 'a' (≈0.2) shows robustness across different gel types and experimental data.
• This work provides a unified framework for understanding subdiffusion in disordered media.