Non-destructive monitoring and quantitative analysis of moisture absorption in epoxy using THz time-domain spectroscopy and a three-phase effective medium model

Water uptake in epoxy resins significantly affects their mechanical and dielectric properties, leading to long-term reliability concerns. However, conventional gravimetric methods are limited in their ability to distinguish among absorbed water states and to provide non-destructive evaluation. In this study, we propose a non-contact, non-destructive method based on terahertz time-domain spectroscopy (THz-TDS) for the quantitative analysis of moisture absorption in epoxy. The complex permittivity of water-immersed DGEBA epoxy was extracted as a function of immersion time and analyzed using a coupled model that combines a three-phase Landau–Lifshitz–Looyenga (LLL) dielectric mixing model with a Kohlrausch–Williams–Watts (KWW) kinetic model. This approach enables model-based estimation of the effective volume fractions of bound water (BW) and free water (FW). Compared with the conventional two-phase model, which considers only BW, the proposed three-phase LLL-KWW model showed substantially improved agreement with both gravimetric measurements and terahertz-derived complex permittivity, particularly under high-uptake conditions and during prolonged immersion. The model maintained high accuracy, with mean errors of 0.41% and 4.21% for the real and imaginary parts of permittivity, respectively, and demonstrated robust performance across the full frequency range. The results further indicate that the contribution of FW becomes increasingly significant during long-term immersion, providing a physically consistent interpretation of non-Fickian moisture absorption behavior. These findings demonstrate that THz-TDS, combined with a three-phase dielectric mixing framework, offers a reliable, non-destructive method for analyzing water uptake in epoxy, with strong potential for condition monitoring and lifetime assessment of polymer-based materials.