Cryometry and excess thermodynamic functions in water soluble of the fullerenol C$_{60}$(OH)$_{24}$

The temperature of water-ice crystallization initiation decreases ($\Delta\mathrm{T}$) were determined in the binary water solutions of water soluble fullerenol: $\mathrm{C}_{60}\mathrm{(OH)}_{24}-\mathrm{H}_{2}\mathrm{O}$ at $272.85$-$273.15$ K. Solution concentrations (in molar fractions) vary over a wide range $x_{nano-cluster} = 5.0\cdot10^{-6}\div 1.6\cdot10^{-4}$ a.un. Liquidus temperatures were determined with the help of Beckman thermometer with a linear resolution of the device scale $\frac{\Delta T}{\Delta h}\approx 0.01$ K/mm ($h$ — height of Hg capillary raising). For the thermodynamic description of the discussed systems, we have elaborated an original semi-empirical model, the virial decomposition asymmetric model (VD-AS), with assistance from partial molar functions of nano-clusters (activities and activity coefficients) were calculated. The Gibbs energies for the solutions and miscibility gap concentration regions were calculated. VD-AS model excellently describes pre-delamination or micro-heterogeneous-structure formation in the considered solutions. These calculations are confirmed by the dynamic light scattering data.