The temperature of water-ice crystallization initiation decreases (T) were determined in the binary water solutions of water soluble fullerenol: C₆₀(OH)₂₄ - H₂O at 272.85-273.15 K. Solution concentrations (in molar fractions) vary over a wide range x_nano-cluster = 5:0 10^-6 ÷ 1:6 10-4 a.un. Liquidus temperatures were determined with the help of Beckman thermometer with a linear resolution of the device scale 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.