what are the parameters that i need to consider. also what is the difference between the activation energy calculated from log(sigma) vs 1000/T and from vogel fulcher relation. do i need to consider both the activation energies?
You can use relation log(sigma)=f(1000/T), which should be the linear dependence. When you fit a linear equation to log(sigma)=f(1000/T), you should obtain two parameters, a and b, to equation y=ax+b, where:
y=log(sigma)
x=1000/T
a=-Ea/R
b=y0
Above consideration is about Arrhenius equation, in general form:
y=y0exp(-Ea/RT)
After taking the natural logarithm, a new equation is obtained:
lny=y0+(-Ea/RT)
While VFT equation has the following form:
y=y0exp(Ea/(T-T0))
After taking the natural logarithm:
lny=y0+(Ea/(T-T0))
When you plot lny=f(T), it should exhibit linear dependence.
After this treatment it ought to be easy to fit an equation lny=y0+(Ea/(T-T0)) to lny=f(T) (for example by using excel's solver or any other software).
If you read publications including VFT and Arrhenius equations, you would find out that these both activation energies are not equal to each other (in practice).
Hope it helps you in some way.
The VFT-equation should only be considered as a semi-empirical ansatz to describe the temperature-dependence of e.g. the ion conductivity of several systems like ionic liquids or liquid battery electrolytes. However, using this equation for evaluating your data results in values for 3 empirical parameters. One of them (B, see below) seems to be similar to the activation energy, as described by Mr. Oster. Please note, that its unit is Kelvin and not e.g. eV. Thus, you cannot easily extract an activation energy from a VFT-fit.
What you could e.g. do is to set
-B/(T-T0) = Ea/kT
and solve for Ea. Then, you could calculate a kind of temperature-dependent, apparent activation energy which accounts for the curvature of the Arrhenius-plot. (Please note: If Arrhenius behavior is observed instead of VFT behavior, the Arrhenius-plot is linear due to a more or less temperature-independent activation energy within the chosen temperature range).
For VTF fit we require graph between ln(sigma) vs 1/T or ln(sigma) vs 1000/T
What is T0 here? Is it the value of initial temoerature or room temperature?
"To" is a free fit parameter and often called the "Vogel-temperature" which is usually related to the glass transition temperature for fragile systems showing a glass transition. For more information, you could have e.g. a look at publications in the ionic liquid community: see for instance Tokuda et al., J. Phys. Chem. B 2006, 110, 2833-2839. For deeper insights into the VFT theory, I recommend the following papers: K. Trachenko, Journal of Non-Crystalline Solids 354 (2008) 3903–3906 or Garcia-Colin et al. Phys. Rev. B 40 (1989) 7040-7044.
Those interested at the topic addressed by this query may possibly want to check also this somewhat related RG discussion: https://www.researchgate.net/post/How_to_fit_viscosity_data_using_Vogel-Tamman-Fulcher_VTF_equation
We cannot use the plot of log(Y)=f(1000/T), because it's the Arrhenius behavior, not the VFT one.
Method Vogel-Fulcher-Tammann behavior for Viscosity
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