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Metal nanoparticles electrodes present great difference in electrochemical thermodynamics compared with corresponding bulk electrodes, which depends on the size of nanoparticles that construct the electrodes. However, it remains unclear about the influences of particle size on electrochemical thermodynamics of the electrodes. Herein, the size-dependence of electrochemical thermodynamic functions of metal nanoparticles electrodes was deduced theoretically. Experimentally, taking copper nanoparticles electrode as an example, the standard electrode potentials, the temperature coefficients, and the thermodynamic functions of electrode reaction were obtained by determining the electrode potentials of the electrodes constructed by copper nanoparticles with different sizes at different temperatures. Both the theoretical and the experimental results indicate that with the particle size of metal nanoparticles decreasing, the standard electrode potential and surface tension decreases, while the temperature coefficient, the molar reaction Gibbs energy, enthalpy and entropy increase. Moreover, all these physical quantities are linearly related with the reciprocal of particle radius when the radius exceeds 10 nm. Meanwhile, we also found that the influence regularities of particle size on electrochemical thermodynamic functions of metal nanoparticles electrodes are quite opposite to those of oxide nanoparticles electrodes, which is attributed to the nanoparticles being reactant or product in an electrode reaction.

Melting phase transitions of nanoparticles are often involved in the preparations, research studies, and applications of nanomaterials. However, because of the changing melting temperature of nanoparticles during the melting process, the current relations of melting thermodynamic properties fail to accurately describe their actual melting behaviors. In this study, accurate thermodynamic relations between integral melting enthalpy and entropy and the size of nanoparticles with different shapes (sphere, rod, wire, and regular polyhedrons) were derived for the first time through designing a thermochemical cycle. In the experiment, Ag nanospheres, nanowires, and nanocubes with different sizes were prepared by chemical reduction methods, and differential scanning calorimetry was employed to determine the melting temperature, the melting enthalpy and the melting entropy. The experimental results agree with the theoretical predictions, indicating that the melting thermodynamic properties decrease with the particle size decrease and present linear variations with the inverse particle size within the experimental size range. Moreover, the melting enthalpy and entropy of nanoparticles in identical equivalent diameters take the same sequence as that of melting temperature as T o (wire) > T o (sphere) > T o (cube). The derived relations of melting thermodynamic properties can quantitatively describe the actual melting behaviors of nanoparticles, and the findings herein provide us a comprehensive understanding of the melting thermodynamic properties of nanomaterials in the whole melting process.

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