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J. Phys. Chem. 1996, 100, 5118-5122
Random-Walk Approach to Dynamic and Thermodynamic Properties of Supercooled Melts. 2. Coupling of Structural Units and Susceptibility Spectra V. I. Arkhipov,† H. Ba1 ssler,* and D. V. Khramtchenkov† Fachbereich Physikalische Chemie und Zentrum fu¨ r Materialwissenschaften, Philipps-UniVersita¨ t, D-35032 Marburg, Germany ReceiVed: August 8, 1995; In Final Form: NoVember 22, 1995X
The random-walk model of structural dynamics in supercooled liquids is generalized to account for longrange cooperative phenomena. Coupling of structural units within ordered clusters is shown to cause narrowing of the distribution function for the energies of structural units. As the temperature approaches a critical value TK the ordered clusters expand, the distribution function approaches a δ-function, and the configurational entropy vanishes. This allows to identify the temperature TK as the Kauzmann temperature. The model is also applied to the calculation of susceptibility spectra. The results are in quantitative agreement with existing experimental data.
Introduction The random-walk model of structural dynamics describes inelastic excitations in supercooled liquids as a fast change of microtopology within the close neighborhood of a given particle (a molecule or a subunit thereof). This corresponds to a fast transition of the structural unit (the particle together with its surrounding) from one metastable state to another. In terms of energy it is equivalent to a jump of the structural unit within the energy landscape. To make a jump the structural unit must acquire an energy sufficient for its rearrangement without further thermal excitation. A state with a minimum energy allowing for such rearrangements is usually called the “fluid state”. Since many molecules contribute to the energy of a structural unit, each contribution varying randomly in disordered media, a broad distribution is typical for energies of possible metastable states. The basic ideas of the random-walk model for dynamic properties of supercooled liquids were laid down by Ba¨ssler1 and later on were used by Richert and Ba¨ssler2 to explain the non-Arrhenius temperature dependence of the viscosity and to prove occurrence of the kinetic freezing effect in systems with the energetic disorder. The freezing effect was also studied by Dyre within the framework of a multiple-trapping model.3 An elaborate version of the random walk model has meanwhile been given by Dyre.4 Recently5 (hereafter referred to as to paper 1), the random-walk model has been extended to describe the temperature dependencies of both the viscosity and characteristic relaxation times in strong and fragile liquids.6 In paper 1 it was shown that increasing fragility corresponds to increasing energetic disorder described by the parameter R in the distribution function g(E) of possible metastable states (DPMS)
g(E) )
( | |)
E R exp E0 2E0Γ(1/R)
R
, R
