Determination of interfacial parameters of a soluble particle in a nonideal solution from measured deliquescence and efflorescence humidities

In order to study the growth/shrinking of a hygroscopic nanoparticle during hydration/dehydration in an atmosphere of water vapour, we have employed a thermodynamic approach proposed by Shchekin et al. (2008). This approach uses the mechanic and thermodynamic concept of disjoining pressure of thin films and allows, among others, the prediction of the humidity growth factor of both (i) a homogeneous solution droplet with completely dissolved residual core and (ii) a heterogeneous solution droplet with partially dissolved residual core as a function of the ambient relative humidity. For application to a nanometric sodium chloride particle we have extended the original approach by (i) considering the nonideality of the solution through the dependence of molecular volumes of the solvent and solute molecules and the solute and solvent activities on the solution concentration, (ii) deriving an equation for the estimation of the efflorescence properties of a homogeneous solution droplet, and (iii) combining the empirical power law fittings for the size dependence of the deliquescence and efflorescence relative humidity values by Biskos et al. (2006a). It was demonstrated how the solution/solute interface energy and the correlation length of a thin solution film can be determined from a combination of experimentally determinable efflorescence and deliquescence humidities with the present calculus. The solution/solute interface energy was found to be in close agreement with some previous values reported in the literature, while it strongly differs from data of some other sources. The calculated deliquescence humidity shows a low sensitivity to the choice of the numerical value for the film correlation length. The estimated film correlation length of 1 nm for a nanometric sodium chloride particle with dry particle radius of 5 nm was found to be reconcilable with available a priori estimates of the correlation length from the literature when the measurement uncertainty of the deliquescence humidity is considered. Considering the combination of an extensive calculus, a comprehensive set of thermophysical constraints, and independent measurements of the deliquescence and efflorescence humidities as functions of dry particle radius, the obtained values of the solution/solute interface energy and the correlation length are in close agreement with previous estimations. The humidification of sodium chloride particles in the initial hydration stages was found to be very sensitive to the specification of the disjoining pressure. The enhancement of the wettability of the particle surface leads to an earlier onset of hygroscopic growth

Validity of Tolman’s equation: How large should a droplet be?

Surface tension and the length δ (distance between the Gibbs surface of tension Rs and the equimolar surface Re) of simple liquid droplet (Lennard-Jones and Yukawa) are computed over a wide range of droplet sizes up to about 4x106 molecules. The study is based on the Gibbs theory of capillarity combined with the density–functional approach to gas–liquid nucleation. Since this method provides behavior of the surface tension fully consistent with the tension of the planner surface, the constant in Tolman’s equation δx can be determined unequivocally from the asymptotic behavior of σ s . Comparison of the tension given by Tolman’s equation against the result of exact thermodynamic relations reveals that Tolman’s equation is valid only when the droplet holds more than 106 molecules for the simple fluid systems near their triple points, in contrast to the conventional wisdom that Tolman’s equation may be applicable down to droplets holding a few hundreds of molecules