# Elucidating fluctuating diffusivity in center-of-mass motion of polymer models with time-averaged mean-square-displacement tensor

## TL;DR

This paper introduces a tensor-based method to analyze fluctuating diffusivity in polymer models using trajectory data, revealing distinct fluctuation patterns across different models and applicable to experimental SPT data.

## Contribution

A novel tensor-based approach to extract and analyze fluctuating diffusivity from trajectory data, capturing both magnitude and orientation fluctuations.

## Key findings

- Different polymer models show unique fluctuation patterns.
- The method distinguishes between magnitude and orientational diffusivity fluctuations.
- Applicable to single-particle-tracking experimental data.

## Abstract

There have been increasing reports that the diffusion coefficient of macromolecules depends on time and fluctuates randomly. Here, a novel method to elucidate the fluctuating diffusivity from trajectory data is developed. The time-averaged mean square displacement (MSD), a common tool in single-particle-tracking (SPT) experiments, is generalized into a second order tensor, with which information on both magnitude fluctuations and orientational fluctuations of the diffusivity can be clearly detected. This new method is utilized to analyze the center-of-mass motion of four polymer models, the Rouse model, the Zimm model, a reptation model, and a rigid rodlike polymer, and it is found that these models exhibit distinctly different types of magnitude and orientational fluctuations of the diffusivity. This method of the time-averaged MSD tensor can be applied also to the trajectory data obtained in SPT experiments.