Effect of surface tension from MD simulations on size-dependent deliquescence of NaCl nanoparticles

The deliquescence of sodium chloride is size dependent for particles smaller than 100 nm, with some discrepancies between measured and predicted deliquescence relative humidity as a function of size. Two sources of uncertainty in current models are the solid-liquid/solid-vapor surface tensions and the curvature dependence of surface tension. Molecular Dynamics simulations are used to calculate surface tensions and their corresponding upper bounds, which compare well with measured values of liquid-vapor (LV) interfaces and significantly reduce uncertainty compared to experimental estimates of solid-liquid (SL) and solid-vapor (SV) interfaces. Surface tensions calculated for nanoparticles in the 2-10 nm size range are related to the corresponding flat interface values using the first-order Tolman length (delta). At 1 atm and 300 K, the Tolman length determined from the test-area method is of the order of 0.1 nm with a precision between 5% and 10%. The delta(LV) (water-air) is 0.15 nm, delta(LV) (soln-air) is 0.10 nm, delta(SL) (NaCl-soln:) is 0.13 nm, and delta(SV) (NaCl-air) is 0.14 nm, with positive values corresponding to a decrease in surface tension for smaller particles. The size-dependent deliquescence relative humidity is calculated using a thermodynamic model of water uptake with these new surface tension estimates and with Tolman length corrections. The reduced uncertainties in surface tension significantly improve agreement with measured deliquescence relative humidity of sodium chloride nanoparticles with 5-150 nm diameters. The size-dependent corrections to surface tension produce a minor improvement in the comparison of predicted and measured deliquescence relative humidity of particles smaller than 3 nm.