Energy distribution in an ensemble of nanoparticles and its consequences

In general, considerations about isothermal ensembles of nanoparticles assume that each one of the particles is at the same temperature. However, there are experimental indications that such an isothermal ensemble does not exist. Therefore, it is advised to analyze phenomena connected to the temperature distribution within such an ensemble. The detailed analysis presented in this work led to the assumption of a normal distribution of the energy within an ensemble of nanoparticles where basic properties of such an “isothermal” ensemble can be predicted. The width of the energy distribution decreases with increasing particle size. This particle size dependence of the energy per particle controls phase fluctuations in the vicinity of the transformation temperature. Additionally, applying the temperature profile of a phase transformation, it is possible to calculate the particle size distribution of the ensemble with a precision within the scattering range of the experimental data. This is the most important application of this analysis and coincidently a proof of the basic premise. The basic quantity determining the width of the energy distribution is the heat capacity of the particles. For these calculations, bulk data for the heat capacity were successfully applied. This leads to the conclusion that the data for heat capacity of nanoparticles are very close to the bulk values.