Melting of crystallites in a solid porous matrix and the application limits of the Gibbs-Thomson equation.

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 surroundings on the melting point of the crystallites.

Some universality in subcritical behavior of real substances and model fluids.

On the basis of the latest advances in Mayer's cluster-based approach, the reduced forms of the well-known virial expansions are derived in terms of scaled reducible and irreducible cluster integrals. This transformation minimizes the dependence on temperature and the effect of parameters specific for each thermodynamic system, thus making the resulting reduced expansions indeed universal on the quantitative level. In particular, the scaling of isotherms and saturation curves for various systems (the Lennard-Jones model, different lattice gases, and real substances with simple nonpolar molecules as well as complex polar ones) confirms the approximate universality of the proposed reduced variables for temperature, pressure, and density at subcritical gaseous states up to the saturation point.

Construction of subcritical isotherms for model and real gases on the basis of Mayer's cluster expansion.

Existing rigorous statistical approaches still cannot quantitatively describe condensation phenomena in real fluids and even model systems with some simplified interaction potential. Here, we present a method to evaluate the unlimited subcritical set of Mayer's reducible cluster integrals (the power coefficients of virial expansions) by using the information on several virial coefficients and empirical value of saturation activity. As to the requirements on the initial number of known virial coefficients, the calculations for the Lennard-Jones model indicate that only the second virial coefficient is sufficient to reproduce gas isotherms (including the flat phase-transition region) with high accuracy at low temperatures.

Nanocrystallite-liquid phase transition in porous matrices with chemically functionalized surfaces.

Nanocrystallite-liquid phase transitions are studied for 1-octadecene confined in the pores of chemically functionalized silica gels. These silica gels possess similar fractal geometries of the pore system but differ in chemical termination of the surface, specific surface area (F) and pore volume (V). Linear dependencies of the melting temperature and specific melting heat on the F/V ratio are found for a series of silica gels with identical surface termination.

Divergence of activity expansions: Is it actually a problem?

For realistic interaction models, which include both molecular attraction and repulsion (e.g., Lennard-Jones, modified Lennard-Jones, Morse, and square-well potentials), the asymptotic behavior of the virial expansions for pressure and density in powers of activity has been studied taking power terms of high orders into account on the basis of the known finite-order irreducible integrals as well as the recent approximations of infinite irreducible series.