Surface tension of supercooled water nanodroplets from computer simulations

We estimate the liquid-vapor surface tension from simulations of TIP4P/2005 water nanodroplets of size N = 100 to 2880 molecules over a temperature T range of 180 K-300 K. We compute the planar surface tension γ_p, the curvature-dependent surface tension γ_s, and the Tolman length δ, 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 γ_p, γ_s, and δ although in all cases, we find that δ ≥ 0 and is independent of T. Nonetheless, the T dependence of γ_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, γ_p rises more rapidly on cooling than predicted from behavior for T ≥ 300 K. We show that the increase in γ_p at low T is correlated with 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.