Adam-Gibbs-Vogel

Hodge model (Adam Gibbs Vogel parameters) ... 

Several well-known equations are available for interpreting the temperature dependence of viscosity, diffusion coefficient, and other relaxation rates for T > Tg. The Doolittle equation [18], the WLF equation [19], the Vogel-Fulcher equation [20], and the Adam-Gibbs equation [21] can be expressed in the same form. They are known to fit well with the relaxation data of liquids in equilibrium. The universal functional form is [20]... 

Link 8. Some Results We began our quest fully expecting to derive the Vogel-Fulcher (VF) equation (40) along the lines of the Adam-Gibbs (AG) approach (41) and then extend the results to frequencies other than zero. Instead, much to our surprise we found that our logical extension of the equilibrium theory (what we believe to be a logical extension) results in a much different functional form for the zero frequency viscosity. Whereas the VF equation... 

To incorporate polymers into the above scheme, we need to recognise that the special effects of polymer chain length on viscosity enter the problem in the pre-exponents of Vogel-Fulcher or Adam-Gibbs-like expressions (see equation (2)) and, accordingly, to scale them out. This is achieved by use of the WLF representation. To get the appropriate landscape ground state... 

Figure 11. Self-diffusion coefficient plotted vs. temperature, for several lattice sizes. The solid and the dotted line are fits to the Vogel-Fulcher and Adam-Gibbs equation, respectively. Prom (Binder, K. Baschnagel, J. Bdhmer, S. Paul, W. Phil Mag. 5, in press.).

Figure 11 also reproduces the Vogel-Fulcher fit of Figure 10 and additionally shows a fit to the Adam-Gibbs equation (48),... 

With T2 = To and Acp 1/T, the VFT equation is obtained. At the Vogel temperature the configurational entropy vanishes, z(T) diverges like z(T) (T — To) but no information about the absolute size of a CRR can be obtained. The approach of Adam and Gibbs was extended by Donth (1992,2001) to obtain the size of a CRR. Within a fluctuation model a formula was developed which allows to calculate a correlation length (or volume Vcrr) from the height of the step in Cp and the temperature fluctuation 8T of a CRR at Tg as... 

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