Conventional wisdom in the synthesis of dispersed or solvated inorganic nanomaterials (especially colloidal nanoparticles) holds that, due to the positive work required to form interfaces between particles and their surrounding environment, dispersed systems are inherently unstable and will inevitably coarsen to lower their free energy in a more bulk-like state. Experimental and theoretical work has shown, however, that dispersions of solids that appear to meet the criteria of thermodynamic stability can be obtained when the solid-solution interface energy is sufficiently reduced through adsorption or other mechanisms. Thus inorganic nanoparticle solutions appear to exist analogously to liquid-liquid microemulsions in spite of the higher interfacial energy density of solids. Generalized methods for the preparation of nanoparticle dispersions based purely on thermodynamic considerations would have attractive features for experimenters, such as insensitivity to preparation conditions and indefinite system lifetime. We provide a statistical thermodynamic approach based on classical nucleation theory that indicates from completely general considerations that, if the excess free energy associated with interface formation increases sufficiently rapidly with decreasing particle size, sharply peaked particle size distributions in the nanometer range can indeed be made thermodynamically stable. The size distribution is given by a simple analytical expression which is the exponent of the work of nanoparticle formation times a polynomial factor having a degree dependent on the statistical model used. Conversely, given an experimental size distribution for a thermodynamically stable dispersed system, the dependence of the interfacial energy on particle radius can be determined. We examine previous experimental data and discuss its implications for the stabilization mechanism of nanoparticles at equilibrium. We also outline molecular simulation approaches to evaluating the important free energy parameters and emphasize the need for more rigorous testing of thermodynamic stability in suspected stable dispersed systems. The thermodynamic analysis, finally, provides clear experimental directions for optimizing the perfection of stable nanostructures by identifying the limiting polydispersity, the narrowest size distribution achievable.

Thermodynamically stable dispersed solids: Interfacial free energy-particle size distribution correspondence and the limiting polydispersity

ACS Spring Meeting 2021

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