Viscous Flow of Glass-forming Liquids: A Cluster Approach
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Viscous Flow of Glass-forming Liquids: A Cluster Approach G. J. Fana, E. J. Laverniaa, and H. J. Fechtb Department of Chemical Engineering and Materials Science, University of California, Davis, CA 95616, USA b University of Ulm, Center for Micro- and Nanomaterials, D-89081 Ulm, Germany also at Research Center Karlsruhe, Institute of Nanotechnology, D-76021 Karlsruhe, Germany a
ABSTRACT An accurate description of the structure of a glass-forming liquid has eluded investigators, partly due to the dynamic behaviour that is inherent to liquids. The free volume concept provides a useful descriptor of a structural parameter that can be applied to glass-forming liquids. In previous work, we developed a cluster model to account for the viscous flow of glass-forming liquids (G. J. Fan and H. J. Fecht, J. Chem. Phys. 116, 5002 (2002)). In this work, we found that the kinetic fragility of a glass-forming liquid is quantitatively connected with its entropy of fusion ∆Sf, the value of its melting point Tm, and the structures of interfaces between clusters. We will demonstrate that the proposed cluster model is consistent with an energy landscape model of the glass transition. On the basis of this suggestion, glassforming liquids, consisting of nanometer-sized clusters, may be responsible for the observed similarity in the mechanical properties between metallic glasses and nanostructured metals. INTRODUCTION When crystallization is kinetically avoided, the molecular motion in a supercooled liquid gradually slows down without interference of the obvious discontinuous phase transition. At a certain temperature, the time required for relaxing the system back to the equilibrium due to temperature changes will eventually exceed the experimental time scale (around 100 s), at which the system starts to deviate from the equilibrium state. This process is manifested by the glass transition. The viscosity of the glass-forming liquid at the glass transition temperature is on the order of 1012 Pas, indicating the solid state of the glass, though structurally disordered [1]. The viscous slow down of the glass-forming liquids over wide temperature ranges was described by a well-known empirical Vogel-Fulcher-Tammann (VFT) equation:
η = η 0 exp[DT0 (T − T0 )] (1) where η0, D, and T0 are the fitting parameters. η tends to diverge as T approaches T0. The VFT equation can be derived within the framework free volume model of the glass transition proposed by Cohen and Turnbull [2]. According to the free volume model theory, the free volume per atomic volume, vf, can be expressed by v f = C (T − T0 ) The viscous slow down due to annealing out of the free volume when temperature is decreased was mathematically linked by
( 2)
η = η 0 exp(γv * v f ) (3) where γ and v* are constants. Replacing vf by equation 2 yields the VFT equation with D = γv*/CT0. The VFT equation is a very useful equation in describing the viscous slow down of
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many glass-forming liquids. However, it fails to describe the viscosity changes for some glass-formi
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