Estimating Position-Dependent and Anisotropic Diffusivity Tensors from Molecular Dynamics Trajectories: Existing...

Area of Science:

• Materials Science
• Computational Physics
• Statistical Mechanics

Background:

• Confinement alters material properties, making them position-dependent.
• Molecular dynamics (MD) simulations reveal spatial heterogeneities.
• Calculating transport coefficients like diffusivity under confinement is complex.

Purpose of the Study:

• To review methods for estimating diffusivity profiles from MD simulations.
• To discuss challenges in applying bulk methods to confined systems.
• To explore various algorithms for calculating confined diffusivity.

Main Methods:

• Spatial binning for static properties.
• Addressing challenges in estimating transport coefficients.
• Overviewing heuristic extensions of bulk methods.
• Discussing rigorous algorithms: kernel-based, Bayesian, operator discretization.
• Exploring biasing potentials and constraints on tracer particles.
• Estimating diffusivity from mean first passage time and committor probability profiles.

Main Results:

• Diffusivity estimation under confinement requires specialized methods beyond simple binning.
• Various approximate and rigorous algorithms exist for calculating diffusivity profiles.
• Methods range from heuristic extensions to advanced computational techniques.
• Frameworks from computational chemistry aid diffusivity calculations.

Conclusions:

• Accurate diffusivity profiling in confined materials is crucial for understanding their behavior.
• A diverse toolkit of methods exists, each with strengths and limitations.
• Future work can refine existing methods and develop novel approaches.