The Vogel-Fulcher-Tammann equation is exposed as a particular example of the mean field theory. It is generalized by taking into account an arbitrary critical exponent of susceptibility, discriminating between different classes of universality. The Bell-Evans-Polanyi principle is employed to estimate the difference between the activation energies of flows in crystals and glasses, which appears to coincide with the excess Gibbs energy of the glass compared to the crystal.

In this study, we report a novel synthesis of hydrophobic silica aerogel powder composites, functionalized and binary-doped with [Tb(phen)₂](NO₃)₃ and [Eu(phen)₂](NO₃)₃ nanocrystals, employing a two-step sol-gel methodology. The investigation delves into the structural elucidation, optical properties and thermal conductivity of these functionalized Tb(III)-Eu(III) composites. Our analysis encompasses diffuse reflectance spectra, along with excitation and luminescence spectra, highlighting the quantum yields of composites with varying chemical composition. Remarkably, these samples exhibit a strong luminescence, with distinct hues of red or green color upon the specific doping type and level. The detailed examination of excitation spectra and quantum yields unequivocally establishes robust energy transfer mechanisms from the 1,10-phenanthroline molecule to the lanthanide ions. Notably, our study uncovers a Tb³⁺→Eu³⁺ energy transfer phenomenon within the binary functionalized samples, providing compelling evidence for a structural formation process occurring within the mesoporous framework of the aerogel powders.