Distribution of relaxation times from dielectric spectroscopy using Monte Carlo simulated annealing: Application toα−PVDF

Abstract

The existence of a distribution of relaxation times has been widely used to describe the relaxation function versus frequency in glass-forming liquids. Several empirical distributions have been proposed and the usual method is to fit the experimental data to a model that assumes one of these functions. Another alternative is to extract from the experimental data the discrete profile of the distribution function that best fits the experimental curve without any a priori assumption. To test this approach a Monte Carlo algorithm using the simulated annealing is used to best fit simulated dielectric loss data, Љ(), generated with Cole-Cole, Cole-Davidson, Havriliak-Negami, and Kohlrausch-Williams-Watts ͑KWW͒ functions. The relaxation times distribution, G"ln()…, is obtained as an histogram that follows very closely the analytical expression for the distributions that are known in these cases. Also, the temporal decay functions, (t), are evaluated and compared to a stretched exponential. The method is then applied to experimental data for ␣-polyvinylidene fluoride over a temperature range 233 KрTр278 K and frequencies varying from 3 MHz to 0.001 Hz. These data show the existence of two relaxation processes: the fast segmental ␣ a process associated with the glass transition and a ␣ c mode, which is slower and due to changes in conformation that can occur in the crystalline regions. The experimental curves are fitted by the simulated annealing direct signal analysis procedure, and the relaxation times distributions are calculated and found to vary with temperature. The decay function is also evaluated and it shows clearly its bimodal character and a good agreement with a KWW function with a temperature dependent ␤ for each mode. The relaxation plots are drawn for each mode and the Vogel-Tammann-Fulcher and Arrhenius parameters are found. The fragility parameter for polyvinylidene flouride ͑PVDF͒ is found to be 87, which characterizes this polymer as a relatively structurally strong material.

Dielectric relaxations in PVDF/BaTiO3 nanocomposites

“…The frequency and temperature limit of instrument constraints the full view of α a relaxation. Earlier literature work confirms peak at 10 +07 Hz to be related to the microBrownian cooperative motions of the main chain backbone and is dielectric manifestation of the glass transition temperature of PVDF [19]. The relaxation peak at about 10 +00 Hz is attributed to α a relaxation and is associated with the molecular motions in crystalline region of PVDF.…”

“…The frequency dependence of dielectric loss can be described by Havriliak-Negami (HN) function. Havriliak-Negami (HN) functional formalism [19] that can be phenomenologically described as a combination of the conductivity term with the HN functional form as Equation (1): (1) where σ dc is the direct current electrical conductivity, ω = 2πf is the angular frequency, ε 0 denotes the vacuum permittivity, N is an exponent (0<N<1), Δε k is the dielectric of the k th process, τ HN k is the most probable value of the central relaxation time distribution function, and a k and b k are shape parameters related to symmetric and asymmetric broadening of the relaxation peak, respectively. All HN fits reported here were performed using WinFit software program provided with the Novocontrol dielectric analyzer.…”

Multifunctional nanocomposites of poly(vinylidene fluoride) reinforced by carbon nanotubes and magnetite nanoparticles

“…The frequency limit of the instrument constrained the full view of this relaxation. However, earlier works have confirmed the peak around 1 MHz is related to the micro-Brownian cooperative motions of the main chain backbone and is essentially the dielectric manifestation of the glass transition temperature of the PVDF [46][47][48]. The second relaxation peak observed at lower than 10 Hz is the !…”

Dielectric properties of PVDF thin films doped with 3 wt.% of RCl3 (R = Gd or Er)

“…The ε of pure PVDF increases with temperature, and exhibits a shoulder around room temperature for these selected frequencies. This shoulder is associated with the glass transition temperature (T g ) of PVDF, 21 which and can be interpreted by considering the micro-Brownian motion in the amorphous region of the main polymer chain, 22,23 or what is called the α a -process. To show the difference between the ε values of pure PVDF and PVDF containing 3 wt.% ErCl 3 and GdCl 3 , the ε of pure PVDF is again plotted along with those of the doped samples (Figs.…”