The proton transport properties of Nafion membranes were studied in a wide range of temperature by using an air-tight sample holder able to maintain the sample hydrated at high relative humidity. The proton conductivity of hydrated Nafion membranes continuously increased in the temperature range of 40–180 °C with relative humidity kept at RH = 100%. In the temperature range of 40–90 °C, the proton conductivity followed the Arrhenius-like thermal dependence. The calculated apparent activation energy Ea values are in good agreement with proton transport via the structural diffusion in absorbed water. However, at higher measuring temperatures an upturn of the electrical conductivity was observed to be dependent on the thermal history of the sample.

No abstract

The Dyson index, β, plays an essential role in random matrix theory, as it labels the so-called “three-fold way” that refers to the symmetries satisfied by ensembles under unitary transformations. As is known, its 1, 2, and 4 values denote the orthogonal, unitary, and symplectic classes, whose matrix elements are real, complex, and quaternion numbers, respectively. It functions, therefore, as a measure of the number of independent non-diagonal variables. On the other hand, in the case of β ensembles, which represent the tridiagonal form of the theory, it can assume any real positive value, thus losing that function. Our purpose, however, is to show that, when the Hermitian condition of the real matrices generated with a given value of β is removed, and, as a consequence, the number of non-diagonal independent variables doubles, non-Hermitian matrices exist that asymptotically behave as if they had been generated with a value 2β. Therefore, it is as if the β index were, in this way, again operative. It is shown that this effect happens for the three tridiagonal ensembles, namely, the β–Hermite, the β–Laguerre, and the β–Jacobi ensembles.