A thermodynamic model is proposed to describe the melting of lamellar crystallite in a solid medium. This model includes a modification of the Gibbs-Thomson equation to make it applicable to the above-mentioned crystallites. The need for such modification is supported experimentally by studying the impact of the surrounding on the melting point of the crystallites. In particular, the application of the model to nanocrystals in open-porous systems makes it possible to determine the analytical relations for the melting point, the heat of melting, and the inverse effective size of the pores. The fitting of the experimental data with these functional relations then allows for the calculation of the nanocrystalline density, pressure in the nanocrystal, difference in the surface tension coefficients at the nanocrystal-matrix interface and melt-matrix interface, as well as the difference in the surface entropies per unit area at the nanocrystal-matrix and melt-matrix interfaces.
The study explores a scale effect inherent to the dielectric relaxation in nanocrystals: the dependence of dielectric relaxation parameters on the size of a nanocrystal. We offer a model of the scale effect for the dielectric relaxation caused by thermally activated motion. In this model, a nanocrystal is considered as a physical infinitesimal volume: a region where a local equilibrium exists. We conclude that the thermally activated motion causes the energy fluctuations in a nanocrystal as a whole. A relation between the intensity of these fluctuations and the size of nanocrystals is derived. According to this relation, the intensity of the fluctuations decreases with the decrease of the nanocrystal sizes. Using the relation, a characteristic of a thermally activated motion−the size of the activation zone−can be determined experimentally. We verify the model using experimental data for the complex dielectric permittivity of the composites (silica gel matrix with undecylenic acid nanocrystalline inclusions of various sizes) in the temperature range from −190 to 50 °C at frequencies 5, 10, 20, and 50 kHz. The results of the experiment agree with the predictions of the model.
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