Size Dependence of the Integral Melting Enthalpy and Entropy of Nanoparticles

Precise thermodynamic relations to describe the size-dependent integral melting enthalpy and entropy of nanoparticles were deduced by virtue of designing a thermochemical cycle. The differences between integral and differential melting enthalpy and integral and differential melting entropy of nanoparticles were discussed. Nano-Sn of different sizes was prepared by means of chemical reduction, and differential scanning calorimetry (DSC) was utilized to obtain the melting temperature, melting enthalpy, and melting entropy. The experimental results agree with the theoretical predictions and literature results, demonstrating that the melting temperature, enthalpy, and entropy decrease with decreasing particle size and linearly vary with the reciprocal of particle size within the experimental size range. The variations of melting enthalpy and entropy with particle size mainly depend on the molar surface area, the interfacial tension, and the temperature coefficient of interfacial tension. These findings offer a better understanding of the effect of particle size on the melting thermodynamic behaviors of nanoparticles at different melting stages.