# Surface tension of supercooled water nanodroplets from computer simulations

## TL;DR

This study uses computer simulations to analyze the surface tension of supercooled water nanodroplets, revealing temperature-dependent behavior linked to structural changes and a potential liquid-liquid phase transition.

## Contribution

It provides a detailed comparison of mechanical and thermodynamic methods for calculating surface tension and introduces the use of surface tension as a probe for phase transition behavior in supercooled water.

## Key findings

- Different results from the two calculation routes for surface tension and Tolman length.
- Surface tension increases more rapidly below 230 K, indicating structural changes.
- Surface tension correlates with the formation of a tetrahedral network, suggesting a liquid-liquid phase transition.

## Abstract

We estimate the liquid-vapour surface tension from simulations of TIP4P/2005 water nanodroplets of size $N$=100 to 2880 molecules over a temperature $T$ range of 180 K to 300 K. We compute the planar surface tension $\gamma_p$, the curvature-dependent surface tension $\gamma_s$, and the Tolman length $\delta$, via two approaches, one based on the pressure tensor (the "mechanical route") and the other on the Laplace pressure (the "thermodynamic route"). We find that these two routes give different results for $\gamma_p$, $\gamma_s$ and $\delta$, although in all cases we find that $\delta\ge 0$ and is independent of $T$. Nonetheless, the $T$ dependence of $\gamma_p$ is consistent between the two routes and with that of Vega and de Miguel [J. Chem. Phys. 126, 154707 (2007)] down to the crossing of the Widom line at 230 K for ambient pressure. Below 230 K, $\gamma_p$ rises more rapidly on cooling than predicted from behavior for $T\ge 300$ K. We show that the increase in $\gamma_p$ at low $T$ is correlated to the emergence of a well-structured random tetrahedral network in our nanodroplet cores, and thus that the surface tension can be used as a probe to detect behavior associated with the proposed liquid-liquid phase transition in supercooled water.