Analytical Model for Transient Space Charge in Low-Density Polyethylene

Despite being an experimentally well-studied phenomena, a consistent lacuna has always persisted in the theoretical and mathematical understanding of space charge dynamics in low-density polyethylene (LDPE). The macroscopic models reported so far in the literature seem to be insufficient and fail to predict the formation of homo- and hetero-charges near the electrodes and transport of charge packets. On the other hand, while microscopic models such as bipolar charge transport (BCT) model were able to explain homo-charge accumulation and movement of charge packets to a limited success, they are often fraught with assumptions such as neglection of diffusion phenomena and are structurally complicated when compared to macroscopic models. In this work, the authors have derived analytical solutions for space charge dynamics based on Maxwell’s equations and transient space charge limited current (TSLC)-based volumetric current models, which take into consideration the measured absorption (slow polarization) and steady-state volumetric currents. The proposed analytical (macroscopic) model can thus predict the homo- and hetero-charge accumulation in LDPE, which is validated through comparisons with the experimentally measured space charge, wherein a remarkable agreement was observed. Furthermore, the relation between the transient volumetric current and space charge dynamics is reaffirmed.