A simple model of entropy relaxation for explaining effective activation energy behavior below the glass transition temperature

Abstract

Strong changes in relaxation rates observed at the glass transition region are frequently explained in terms of a physical singularity of the molecular motions. We show that the unexpected trends and values for activation energy and preexponential factor of the relaxation time tau, obtained at the glass transition from the analysis of the thermally stimulated current signal, result from the use of the Arrhenius law for treating the experimental data obtained in nonstationary experimental conditions. We then demonstrate that a simple model of structural relaxation based on a time dependent configurational entropy and Adam-Gibbs relaxation time is sufficient to explain the experimental behavior, without invoking a kinetic singularity at the glass transition region. The pronounced variation of the effective activation energy appears as a dynamic signature of entropy relaxation that governs the change of relaxation time in nonstationary conditions. A connection is demonstrated between the peak of apparent activation energy measured in nonequilibrium dielectric techniques, with the overshoot of the dynamic specific heat that is obtained in calorimetry techniques.

Thermally stimulated depolarization current and dielectric spectroscopy used to study dipolar relaxations and trap level distribution in PMMA polymer

“…The obtained parameters don't converge in all cases and sometimes unrealistic values were found. Thermally stimulated depolarization currents (TSDC), were often used in complementarity with Dielectric relaxation spectroscopy (DRS), to reach a most complete knowledge of the relaxation mechanisms in various materials [29][30][31].…”

An explanation of the peculiar behavior of TSDC peaks at Tg: a simple model of entropy relaxation

“…We then demonstrate that a simple model based on a time dependent configurational entropy, originally proposed by some of us [1] and others [2], is sufficient to explain the experimental behavior, without invoking a kinetic singularity around T g . The pronounced variation of the effective activation energy then appears as a dynamic signature of entropy relaxation that governs the change of Adam-Gibbs relaxation time in non-stationary conditions.…”

“…This increase is too large to be interpreted as an activated process. Besides, the pre-exponential factor 0 τ takes unphysical values in the order of the difference of configurational entropy between the nonequilibrium and equilibrium situation, it is demonstrated [1,2] that the effective activation energy, act E , in nonequilibrium conditions can be expressed as:…”

“…In order to avoid this artifact due to the misuse of Arrehnius law in nonequilibrium conditions, a model that determines the variation of dT dS c / under a heating scan was proposed [1]. It is based on the assumption that S c obeys a first order relaxation.…”

Influence of TiO<SUB>2</SUB> Film/Substrate Contact on Photovoltaic Performance and Improved Efficiency in Dye-Sensitized Solar Cells

“…[36][37][38] The high concentration electrons can diffuse into the TiO 2 particles around the Al 2 O 3 particles as shown in Figure 8(c). Effective electron transportation pathways are completely cut by the Al 2 O 3 particles at film/substrate interface, which consequently cut the electron collection of cells through this Al 2 [54][55][56] It can be inferred that the electron concentration in the TiO 2 particles around the Al 2 O 3 particles is higher than that without Al 2 O 3 particles, increasing electrical potential of the surrounding film of Al 2 O 3 particles. As a result, the cell regions surrounding the Al 2 O 3 particles would work at a condition deviating from the short-circuit, although the cells are at the apparent short-circuit condition.…”