Thermodynamic and structural anomalies of water
\nnanodroplets from computer simulations

Liquid water nanodroplets are valuable for studying supercooled water because they \nresist nucleation well below the bulk freezing temperature and conveniently selfpressurize \nin the interior. These features make nanodroplets good candidates for \nstudying the properties of liquid water and for probing the liquid-liquid critical point \n(LLCP) in water hypothesized to exist in the deeply supercooled state at high pressure, \nat which a distinct low density liquid (LDL) phase becomes distinct from a high \ndensity liquid (HDL) phase. \nWe conduct extensive molecular dynamics computer simulations to study the \nproperties of water nanodroplets using the TIP4P/2005 potential over a wide range \nof size and temperature. In order to improve the sampling of independent microstates, \nwe conduct “swarms” of independent simulations, in which we monitor the approach \nto equilibrium from the potential energy autocorrelation function. After a swarm \nof this size attains equilibrium, the ensemble of final microstates from each run is \nsufficient to evaluate equilibrium properties and their uncertainties in the shortest \nreal time. \nIn order to study the possibility of recovering bulk properties using nanodroplets, \nwe evaluate the Laplace pressure inside the nanodroplets from direct evaluation of \nthe local pressure tensor. We use a modification of a coarse-graining pressure tensor \nmethod that calculates the components of the microscopic pressure tensor as a function of radial distance r from the centre of a spherical water droplet. The pressure \ntensor beneath the surface region becomes approximately isotropic and constant \nwith r. From this region where the components of the pressure tensor are equal, we \ndetermine the Laplace pressure of the droplets. \nDefining the pressure and the density inside the nanodroplets enables us to probe \nthe properties of liquid water nanodroplet cores. We find that the bulk properties \nand related anomalies are present in the nanodroplets, such as the appearance of a \ndensity maximum. We simulate water nanodroplets under extremly low temperature \nconditions that have not been investigated thoroughly before. At such low temperatures, \nthe nanodroplets show interesting emergence of structural complexity in the \ninterior which may be linked to the LLCP and may indicate a HDL-like to LDL-like \ntransformation in the nanodroplets. \nWe also study the surface tension of water nanodroplets using different approaches. \nWhen employing the thermodynamic route to calculating surface tension, we find that \nthe Tolman correction is small and can be neglected. Therefore, the surface tension \nof nanodroplets can be approximated by the planar surface tension. We also observe \na sudden increase in the planar surface tension at low temperature on crossing the \nWidom line, which may signal the emergence of a LDL-like network in the interior of \nwater nanodroplets.

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