Vogel-Tammann-Fulcher expression

The Tg may also increase as a result of increased interactions between ion pairs and the formation of ion clusters. The increase in Tg is nearly linear with the ratio Li /EO, even up to a ratio of 0.5 for LiCF3S03 solubilized in PM MS-8 or in the identical poly(methacrylate) comb polymer (Figure 3). The rise in Tg is much more rapid for the poly(methacrylate) comb polymer than for the polysiloxane. The free-volume mechanism of ion conduction is confirmed in our system by the linearity of temperature-dependent conductivity plots when the Vogel-Tammann-Fulcher (VTF) expression a = exp [-K T - rj] (in which is the ideal Tg and and K are constants) (i, 2, 9) is applied. 

Most viscosity-temperature relationships for glasses take the form of an Arrhenius expression, as was the case for binary metal alloys. The Vogel-Fulcher-Tammann (VFT) equation is one such relationship. 

Parmi les expressions empiriques proposees, c est celle de Vogel (1921), reprise plus tard par Fulcher (1925), et Tammann et Hesse (1926), qui represente le mieux la variation thermique de la viscosite des liquides surfondus, dans un domaine de temperature relativement etendu au dessus de Tr Elle s ecrit... 

The polymer dynamics involves several relaxation processes, some of which start within the vitreous region and cross into high-temperature melts. For example, the fast relaxations of the backbone chain or side groups start near the Vogel-Fulcher-Tammann-Hesse (VFTH) temperature and extend io T>Tc. The linearized VFTH expression is... 

The WLF expression has been shown [12] to be related to the Vogel-Fulcher-Tammann-Hesse equation [14—16],... 

The Vogel-Fulcher-Tammann (VFT) equation is an empirical expression relating q to T and can be interpreted in terms of the different models. The VLT expression is accurate over a wide range of temperatures and is widely used in many practical applications. 

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