Analysis of two-dimensional energy and relaxation-time distributions from temperature-dependent broadband dielectric spectroscopy

Abstract

We present a method to determine the two-dimensional 2D distribution G(W,ln o ) of the relaxation time ϭ o exp(W/k B T) using an inversion of temperature-dependent broadband dielectric data. In contrast to the usual evaluation of 1D distributions g(), the 2D analysis reveals whether the broadening of a relaxation peak has its physical origins in a variation of the activation energy W, or the preexponential factor o , or both. A study of the ␤ relaxation of a polymer blend demonstrates the validity of the analysis. We compare the distribution obtained from dielectric ac data ͑5 Hz-300 MHz, 100 K-300 K͒ with the results of a thermally stimulated depolarization currents sampling technique. The contour line of G(W,ln o ) is shown to follow the compensation law. ͓S0163-1829͑98͒05815-9͔

TSDC spectroscopy of relaxational and interfacial phenomena

“…High frequency behaviour in dielectric relaxation corresponds to a low temperature in TSDC; in these domains the self-scaling property of the system becomes manifest as a power law in frequency in dielectric relaxation and a power law in heating rate in TSDC [50]. According to Pelster et al [54,55], the superposition of Debye-like relaxation processes with different relaxation times (see Eq. (13)) has a 2D distribution G(E,lnτ 0 ) of activation energy E and pre-exponential factor τ 0 .…”

“…(13)) has a 2D distribution G(E,lnτ 0 ) of activation energy E and pre-exponential factor τ 0 . The authors [54,55] evaluated G via inversion of temperature dependent broadband dielectric data. Simulations as well as experimental data demonstrate the validity of the analysis shown below.…”

Phase Transitions in Layered Semiconductor - Ferroelectrics

“…A detailed description can be found in (Banys et al, 2002). We assume that the complex dielectric spectrum * (ν) can be represented as a superposition of independent individual Debye-type relaxation processes (Schafer et al, 1996;Kim et al, 2000;Pelster et al, 1998) …”

Comparative dielectric studies of segmental mobility in novel polyurethanes

“…The relationships between TSDC and DRS have been studied by several investigators [17][18][19][20][21][22][23][24]. However, there are still some controversial points with respect to quantitative comparisons, e.g., of activation parameters of secondary relaxations [25][26][27].…”

“…This technique consists of 'sampling' the relaxation processes within a narrow temperature range by polarizing at a temperature T p and depolarizing at T d , a few degrees lower than T p , and by spanning the entire temperature range of the global TSDC peak with a series of TS measurements [16][17][18][19][20][21][23][24][25][26]. While this thermal cycling is not expected to have any influence on the form of the distribution in the case of secondary, local relaxations (parallel elementary processes) [20,26], this may not be the case for the cooperative α relaxation associated to the glass transition [19][20][21]23].…”