Interrelation between shear modulus and the molecular parameters of viscous flow for glass forming liquids

The relationship between the free energy of viscous flow activation, the instantaneous modulus and the molar volume of kinetic units overcoming the barrier was derived by the author in the simplest form, ΔG^≠ = F_∞V¹, thirty-eight years ago. It was the result of the common solution for most general equations for the viscosity coefficient, the rate constant for shear relaxation in accordance with Maxwell’s relation. Here it is shown that this equation may be derived in the framework of the theory of elasticity and/or hydrodynamics. In this equation, V¹ = 8(r₀)³N_A, where V¹/N_A in the theory corresponds to the cube volume containing an inscribed molecule (atom) of radius r₀. The experimental proof of the equation shows that the atomic radii found from the viscous and elastic parameters match those obtained from direct structural investigations (X-ray and neutron scattering) with an average accuracy not worse than ∼5% (oxide, fluoride and chalcogenide glass melts). The theory needs development for molecular liquids with more complex structure. It is obvious that Maxwell’s relation is valid for modeling of viscous flow at the molecular level in supercooled liquids.