2.6. Positron Annihilation Lifetime Spectroscopy (PALS)

Positron Annihilation Lifetime Spectroscopy (PALS) measurements were performed using a fast-fast coincidence spectrometer with a time resolution of 230 ps [27,28,29,30,31,32]. A positron source (22 µCi ²²Na), wrapped in a 7 µm thick Kapton foil, was sandwiched between two identical samples of either dried or hydrolytically (physically) aged specimens. The samples were measured at room temperature or i–n the temperature range −50 to 100 °C. In each positron lifetime spectrum, 5 × 10⁶ counts were recorded. A silicon reference sample (218 ps) was measured for the source contribution, which was determined to be 14.7%. The software tool (LT 9) [33] was used to analyze the lifetime spectra, after the source and background corrections.

PALS spectra are decomposed into three lifetimes, which are extracted using a nonlinear least-squares fit of a weighted sum of exponentials:

where τ_i denotes the lifetime of the positron state i and I_i is its relative intensity.

The first component (~0.15–0.17 ns) is due to the annihilation of Para-Positronium (P-Ps), the second (0.35–0.4 ns) is ascribed to the annihilation of free positrons, and the third (1.5–2.8 ns) is due to the pick-off annihilation of Ortho-Positronium (O-Ps). However, PALS is a well-established technique to be used for determining the free volume (FV) of holes (or cavities) in molecular materials [34,35], which is related to the lifetime of the O-Ps pick-off (τ₃) by the Tao-Eldrup model [36]:

Here, R is the radius of the hole (potential well) and ∆R = 1.656 Å is the penetration depth of the O-Ps wave function into the material surrounding the potential well and represents the thickness of the electron layer. Specifically, FV = (4/3) πR³, in which R values are calculated from Equation (5).