Non-Gaussian subdiffusion of single-molecule tracers in a hydrated polymer network

Area of Science:

• Soft matter physics
• Polymer science
• Statistical mechanics

Background:

• Single molecule tracking in hydrated polymer networks reveals complex tracer dynamics.
• Tracer motion is characterized by subdiffusion, attributed to the viscoelastic nature of the gel-like environment.
• Observed subdiffusion correlates with negative autocorrelation of instantaneous displacements at short times.

Purpose of the Study:

• To analyze tracer trajectories and explain the observed subdiffusive and non-Gaussian behaviors.
• To model the complex dynamics using a generalized Langevin approach.
• To investigate the relationship between network heterogeneity and the degree of non-Gaussianity.

Main Methods:

• Analysis of numerous individual tracer trajectories from single molecule tracking experiments.
• Application of a generalized Langevin model for an overdamped particle with algebraically decaying correlations.
• Correlation of model parameters with experimentally observed distributions of motion parameters.

Main Results:

• Individual tracer displacements exhibit Gaussian statistics, but combined trajectories show non-Gaussian distributions.
• The central part of the non-Gaussian distribution is well-approximated by an exponential distribution spreading sublinearly with time.
• The degree of non-Gaussianity is shown to be dependent on the extent of heterogeneity within the polymer network.

Conclusions:

• The generalized Langevin model successfully explains the subdiffusive and non-Gaussian dynamics observed in polymer networks.
• Network heterogeneity, controlled by motion parameter distributions, directly influences the non-Gaussian nature of tracer displacements.
• This work provides a theoretical framework for understanding complex particle motion in viscoelastic media.