The thermodynamics and structure of glass-forming liquids are considered within the framework of the heterophase fluctuation (HPF) model. The main goal of the theory developed is to fined for a description of the long-range correlations (LRC) of the density fluctuations known as the Fischer cluster. The van der Waals approximation of the HPF model shows that the liquid can have an isolated solid-fluid critical point analogous to the critical point of a gas-liquid system. Heterophase fluctuations in the form of solidlike noncrystalline and fluidlike clusters can have LRC in a narrow vicinity of the critical point. An analysis shows that the properties of the conventional critical fluctuations differ from those of the Fisher cluster. This forces one to look for another explanation of the observed LRC in glass-forming liquids. Large configurational entropy of liquids and glasses is a manifestation of multiplicity of the short-range ordering of molecules in the amorphous solidlike and fluidlike clusters. The multiplicity of short-range order results in structural heterogeneities. Random-field Ginzburg-Landau equations for the HPFs are deduced taking into account the structural heterogeneities. The random field is generated by these heterogeneities. It is found that at least three characteristic correlation scales are inherent to the HPF: the radius of local order, <$E r sub 0>, which is comparable with the radius of the first coordination sphere; the random-field-controlled radius of critical fluctuations, <$E R sub c>; the average correlation length of fractal aggregations formed by the correlate

d domains (the domains have size ~<$E R sub c>), <$E xi sub roman av>. The length <$E xi sub roman av> is the characteristic size of the Fischer cluster. The conditions for the appearance of the listed correlations are deduced by requiring that they provide minimization of the free energy of the system. The annealing kinetics and dynamics (the ultraslow modes) of the Fischer cluster are described.

• Бакай Олександр Степанович (1938–) (фізико-математичні науки)

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