Havriliak-Negami function

The complex dielectric permittivity data of a sample, obtained from DS measurements in a frequency and temperature interval can be organized into the matrix data massive = [s, ] of size M x N, where Eq = ( >, , 7 ), M is the number of measured frequency points, and N is the number of measured temperature points. Let us denote by / =/(co x) the fitting function of n parameters x = x, X2,..., xn. This function is assumed to be a linear superposition of the model descriptions (such as the Havriliak-Negami function or the Jonscher function, considered in Section II.B.l). The dependence of/on temperature T can be considered to be via parameters only / =/(co x(T )). Let us denote by X = [jc,-(7 )] the n x N matrix of n model parameters xt, computed at N different temperature points 7. ... 

Figure 1. Dielectric loss spectra of 5%wt. CNBz in trystyrene at different temperatures. Continuous lines are from fitting Havriliak-Negami functions, dotted line is a KWW function (n=0.55) fitted to the spectrum at T=221 K. Vertical arrow shows the location for the characteristic frequency of the JG process, VjQ=l/(2tiTjQ) as predicted by Eq.l.

In order to determine the structural relaxation times for the octa-O-acetyl-lactose we analyzed dielectric loss spectra of this carbohydrate with use of the Havriliak- Negami function. The temperature dependence of logioTa was fitted to the Vogel- Fulcher- Tammann (VFT) function... 

The temperature dependences of relaxation times of the p and y processes of lactose and the secondary mode of octa-O-acetyl-lactose are presented in Fig. 6. In order to determine relaxation times of P- and y- modes of lactose and octa-O-acetyl-lactose the Cole-Cole and Havriliak-Negami functions were used respectively. Activation energies of all secondary relaxations were estimated from the Arrhenius fits... 

Shn(Q.< ) derived from the Havriliak-Negami function (Eqs. 32 and 33) (-), 5-function... 

Construction and Analysis of Arrhenius Plots Complex permittivity data, like those shown in Fig. 6.18, are customarily analyzed by a superposition of several Havriliak-Negami functions and a conductivity term, that is... 

The imaginary part of the dielectric a-relaxation can be analyzed by using the phenomenological Havriliak-Negami function ... 

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