# Surface Excess Energy as a Unifying Thermodynamic Framework for Active Diffusion

## TL;DR

This paper introduces a new thermodynamic framework to explain how chemical reactions can enhance particle diffusion without external gradients.

## Contribution

The study proposes surface excess energy as a unifying concept for active diffusion in catalytic Janus particles.

## Key findings

- Interfacial reactions generate excess surface energy and sustained stresses that enhance diffusion.
- The framework explains nonmonotonic diffusivity trends observed in experiments with Janus particles and vesicles.
- The model aligns with data from nanometric particles and ATP-driven vesicles.

## Abstract

Directed motion of particles is typically explained by
phoretic
mechanisms arising under externally imposed chemical, electric, or
thermal gradients. In contrast, chemical reactions can enhance particle
diffusion even in the absence of such external gradients. We refer
to this increase as active diffusivity, often attributed to self-diffusiophoresis
or self-electrophoresis, although these mechanisms alone do not fully
account for experimental observations. Here, we investigate active
diffusivity in catalytic Janus particles immersed in reactive media
without imposed gradients. We show that interfacial reactions generate
excess surface energy and sustained interfacial stresses that supplement
thermal energy, enabling diffusion beyond the classical thermal limit.
We consistently quantify this contribution using both dissipative
and nondissipative approaches, assuming that the aqueous bath remains
near equilibrium. Our framework reproduces experimentally observed
trends in diffusivity versus activity, including the nonmonotonic
behaviors reported in some systems, and agrees with data for nanometric
Janus particles catalyzing charged substrates as well as vesicles
with membrane-embedded enzymes driven by ATP hydrolysis. These results
demonstrate that chemical reactions can induce and sustain surface-tension
gradients and surface excess energy, providing design principles for
tuning mobility in synthetic active matter.