Deciphering the intricate dielectric relaxation processes of cellulose paper: Extraction of distribution of relaxation time and analysis of degradation characteristics

Cellulose material is a dielectric with intricate microscopic relaxation processes due to its complex structure. However, conventional models and curve fitting methods used for tracing and analyzing these processes often fail to capture crucial dielectric information. This paper aimed to extract the Distribution of Relaxation Time (DRT), the most fundamental and effective dielectric information providing the time scale and relative contribution of all microscopic relaxation processes. First, a distributed extended Debye model with infinite branches was constructed based on the microscopic nature of dielectric relaxation. Then, an implicit equation of the DRT function was established, inspired by the mathematical principles of infinite subdivision and summation. To obtain the numeral solution of the DRT function, a regularization method was proposed and validated. Finally, the approach was applied to cellulose insulating paper with varying degradation degrees. The relaxation process with a long time constant played a significant role, and variations during the degradation process were attributed to reduced activation energy. With clear physical interpretation and robust mathematical foundation, our method sheds light on the intricate dielectric relaxation processes in cellulose. This not only enhances the theoretical understanding and practical application of cellulose materials but also provides valuable insights for the analysis and application of other materials.