The interface between two condensed phases is associated with a free energy density, within which valuable mechanistic information is hidden. Conversely, control over this quantity by adjustment of various physicochemical parameters is a key requirement in the design of functional materials with high surface-area-to-volume ratios, i.e. nanostructures. Where the work of interface formation is small or negative, a thermodynamically stable dispersion (colloid) is possible given an appropriate dependence of this energy density on interface curvature. This phenomenon has been proposed to operate in systems of solid colloidal nanoparticles, providing a tantalizing avenue to realize highly stable and targetable nanoparticle ensembles based on thermodynamic considerations rather than on reaction kinetics. We adapt classical nucleation theory (CNT) to the thermodynamic analysis of such proposed stable nanoparticle solutions as a means to derive parameters related to the curvature dependence of the interfacial free energy and apply this analysis to two previously reported experiments on spherical inorganic nanoparticles: gold nanoparticles stabilized with thiols in organic solvent and iron oxide nanoparticles in highly basic solution. Size-dependent interfacial free energies depending on particle radius as a power law provide good descriptions of the entire observed size distribution. In particular, size distributions of gold nanoparticles are completely consistent with a previously proposed mechanism of stabilization by electrostatic charging. The CNT-based analysis also serves as a check on the validity of the assertion of absolute thermodynamic stability; we find that, in contrast to the assumptions of earlier models, it is much more likely that the nanoparticle systems we consider here are only metastable dispersions in a supersaturated solution. This emphasizes the need for more careful experimental tests of the stability of such dispersions relative to the bulk solid.

Size-dependent interface thermodynamics and the absolute stability of colloidal solids

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