Relaxation time glass-forming liquids

A common feature of the slow ( a ) structural relaxation in glass-forming liquids is an apparent universal analytic form for the long time decay, which is described by a stretched exponential. For example, for the intermediate scattering function, ISF,... 

The solidity of gel electrolytes results from chain entanglements. At high temperatures they flow like liquids, but on cooling they show a small increase in the shear modulus at temperatures well above T. This is the liquid-to-rubber transition. The values of shear modulus and viscosity for rubbery solids are considerably lower than those for glass forming liquids at an equivalent structural relaxation time. The local or microscopic viscosity relaxation time of the rubbery material, which is reflected in the 7], obeys a VTF equation with a pre-exponential factor equivalent to that for small-molecule liquids. Above the liquid-to-rubber transition, the VTF equation is also obeyed but the pre-exponential term for viscosity is much larger than is typical for small-molecule liquids and is dependent on the polymer molecular weight. 

The AG model [48] for the dynamics of glass-forming liquids essentially postulates that the drop in S upon lowering temperature is accompanied by collective motion and that the fluid s structural relaxation times r are activated with a barrier height that is proportional [80] to the number z of polymer... 

According to SS, the structural relaxation time of a glass-forming liquid is described by a generalized Arrhenius expression [39, 40],... 

It has been revealed that the relaxation time at the crossover temperature, i.e., —logx(Tx) is universal, namely, —1 1 for glass-forming liquids that spans a wide range of kinetic behavior [118]. 

Perhaps the most important distinction between classical solids and classical liquids is that the latter quickly shape themselves to the container in which they reside, while the former maintain their shape indefinitely. Many complex fluids are intermediate between solid and liquid in that while they maintain their shape for a time, they eventually flowr They are solids at short times and liquids at long times hence, they are viscoelastic. The characteristic time required for them to change from solid to liquid varies from fractions of a second to days, or even years, depending on the fluid. Examples of complex fluids with long structural or molecular relaxation times include glass-forming liquids, polymer melts and solutions, and micellar solutions. 

The a-relaxation behavior for many glass-forming liquids is also described by the KWW relaxation function that is obtained by a transform of the following time domain function to the frequency domain one [87] ... 

Relaxation functions for fractal random walks are fundamental in the kinetics of complex systems such as liquid crystals, amorphous semiconductors and polymers, glass forming liquids, and so on [73]. Relaxation in these systems may deviate considerably from the exponential (Debye) pattern. An important task in dielectric relaxation of complex systems is to extend [74,75] the Debye theory of relaxation of polar molecules to fractional dynamics, so that empirical decay functions for example, the stretched exponential of Williams and Watts [76] may be justified in terms of continuous-time random walks. 

The narrow transformation range commonly referred to as the glass transition is the temperature interval where the characteristic molecular relaxation time becomes of the order of 100 s (the laboratory time scale). The viscosities of several glass-forming liquids are shown in Fig. 3 as a... 

Fig. 12. Adam-Gibbs plots of the dielectric relaxation time of 2-methyltetrahydrofuran (2-MTHF) and 3-bromopentane (3-BP) versus (Tsconi) . The lines are VTF fits, 7 fus is the fusion temperature, and Tb is the temperature below which the VTF equation applies. /I ag and Avf are prefactors in the Adam-Gibbs and VTF equations, respectively. Tk is the calorimetri-cally determined Kauzmann temperature, and To is the VTF singular temperature, which were set equal in the VTF (line) fits. (Reprinted with permission from R. Richer and C. A. Angell. Dynamics of glass-forming liquids. V. On the link between molecular dynamics and configurational entropy. J. Chem. Phys. (1998) 108 9016. Copyright 1998, American Institute of Physics.)...

Novikov, V. N., and Sokolov, A. P. (2003) Universality of the dynamic crossover in glass-forming liquids A magic relaxation time, Phys. Rev. A 67, 031507. 

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