Effect of Surface Tension from MD Simulations on Size-Dependent Deliquescence of NaCl Nanoparticles

Abstract

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 ( δ ). 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 δ ^LV (water–air) is 0.15 nm, δ ^LV (soln–air) is 0.10 nm, δ ^SL (NaCl–soln:) is 0.13 nm, and δ ^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.

Acknowledgments

This material is based upon work supported by the National Science Foundation under Grant no. 0304213 and the James S. McDonnell Foundation. Any opinions, findings, and conclusions and recommendations are those of the authors and do not necessarily reflect the views of the National Science Foundation. We thank the San Diego Super Computing Institute (SDSC) for providing computational resources used in our calculations. We thank Saman Alavi for input and suggestions regarding this work.

Notes

^a Wang et al. 1998.

^b Adamson 1990.

^c Fujii et al. 2005; Gaonkar and Neuman 1987; Heller et al. 1966; Jasper 1972.

^d Abramzon and Gauberk 1993; Adamson 1990; Heller et al. 1966; Wu and Nancollas 1999.

^a mNm⁻¹.

^b nm.