Alternative Explanation of the Difference between Translational Diffusion and Rotational Diffusion in Supercooled Liquids

Abstract

We offer an alternative explanation of the breakdown of Debye−Stokes−Einstein and Stokes−Einstein relations observed as enhanced translational diffusion compared with rotational diffusion of probe molecules in supercooled liquids and polymers close to the glass transition temperature. By showing that the breakdowns of Debye−Stokes−Einstein and Stokes−Einstein relations in glass-forming liquids are special cases of a more general phenomenon, it becomes clear that a more general explanation than spatially heterogeneous dynamics is needed. In the framework of the coupling model, the explanation is based on the fact that different dynamic variables μ weigh the intermolecular cooperativity differently and have different coupling parameters (i.e., degrees of intermolecular cooperativity), nμ, which enter into the stretch exponents of their correlation functions, 〈μ(0)μ(t)〉 = exp[−(t/τμ)1-nμ], represented in the Kohlrausch form. In some of the applications we made, the values of nμ's are known from experiment and the difference between them is absolutely clear. The explanation of the difference between the τμ's and their temperature dependencies then becomes quantitative, requiring no adjustable parameter (Ngai, K. L.; Mashimo, S.; Fytas, G. Macromolecules 1988, 21, 3030). An exception is the present explanation of the breakdown of Stokes−Einstein relation where experimental technique has not yet been developed to determine the microscopic correlation function and, hence, the coupling parameter of translational diffusion. The explanation from the coupling model is based on the assumption that the known coupling parameter of rotational diffusion is larger than that of translational diffusion, which has been justified on theoretical grounds and can be falsified experimentally when the latter becomes known in the future. The effect depends on the degree of probe participation in the cooperative dynamics with the host molecules characterized by the ratio, τc/τα, of the probe rotational relaxation time τc to the α-relaxation time of the neat host τα. The observed variation in the magnitude of the enhanced translation with the size of the probes in supercooled liquids and polymers is explained. In the process, we have established a correlation between the enhanced translation and τc/τα as well as a correlation between the Kohlrausch exponent β of the rotation correlation function and τc/τα. These two correlations when combined give rise to the correlation between enhanced translational diffusion and (1-β) established earlier by Ediger and co-workers. The present explanation of enhanced translational diffusion can also explain the recent findings of (a) a parallel enhancement of dielectric relaxation in supercooled liquids by Chang and Sillescu and (b) a breakdown of the Debye−Stokes−Einstein relation of deploarized light scattering data of diglycidyl ether of bisphenol A by Comez et al. On the other hand, the spatially heterogeneous dynamics explanation of enhanced translation no longer can explain these results.