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A thermodynamics-based approach to determining stability conditions for metallic nano-ensembles is proposed. It is related to that [ultra-]dispersing the substance leads to changes in thermodynamic potentials (TPs) compared to those of a massive crystal of the same nature. This dimensional phenomenon consists of two components. Among those are a reduction of TPs due to vacancy-related effects and an increase of TPs due to the surface tension effect. Even linear, exponential, and normal distributions of particles on their size in the ensemble have been considered. The resulting equations have been applied to the nano-ensembles of either In or Au particles. The presence of ultra-small particles in an ensemble makes the vacancy-related effect more apparent than the surface tension effect, promoting system stability. With the decrease in the number of ultra-small particles, the vacancy-related effect drastically diminishes and can yield to the surface tension effect, thereby leading to the loss of stability.

This study expands the mathematical theory of the Temkin adsorption model and demonstrates the way experimental data are to be additionally treated. A functional complement property of the Temkin isotherm has been studied as a particular case of the common theory of asymptotic complement. This property is shown to give rise to various analytical strategies to be employed for processing or interpretation of the experimental results, e.g. to perform mapping of data obtained in experiments onto a conjugated part of the true isotherm, to judge if presupposed energetic heterogeneity type of the surface really takes place, etc. Experimental data for adsorption of carbon monoxide on gold and of sodium oleate on steel with and without a magnetite coating have been extensively analysed.