# Liquid Phase TEM of Diffusing Emulsion Droplets

## TL;DR

This paper uses liquid phase TEM to study how emulsion droplets move in a liquid, revealing that their motion is influenced by a fractal energy landscape.

## Contribution

The study provides new insights into the anomalous diffusion of emulsion droplets using in situ liquid phase TEM.

## Key findings

- Droplet motion is anomalous and influenced by a fractal energy landscape.
- Larger droplets show superdiffusive motion due to spatial constraints.
- Smaller droplets exhibit random walks on fractals.

## Abstract

The origin of the viscoelastic behavior that many nanoparticles display during diffusive motion is unknown. Such dynamics are difficult to record without sophisticated methods that combine a suitable observation window of motion in time with high image resolution. Herein, we study and describe the diffusion of two types of particles in the form of emulsion droplets in situ via liquid phase TEM. For both, the observed particle motion in solution is anomalous (non‐Brownian) and is either sub‐ or super‐diffusive. Fractional Brownian motion (fBm) and random walks on fractals (RWF) are the two potential mechanisms. It can be challenging to differentiate these since they may have the same position or velocity autocorrelation function, but they diverge in the average number of sites visited, which is connected to the fractal dimension of the walk. We conclude that droplet‐surface interactions and electron beam fluence create a fractal energy landscape yielding peculiar dynamics.

Motion of emulsion droplets was observed via in situ liquid phase transmission electron microscopy. Analysis revealed that the motion is self‐affine and influenced by multiple stochastic processes, as well as a fractal landscape created by the electron beam. The largest droplets exhibited superdiffusional motion as a result of spatial constraints, while smaller droplets exhibited random walks on fractals.