Abstract

Cross-linked polyethylene (XLPE or PEX) is a major material for cable insulation. Antioxidant is usually used as a dopant added in XLPE to prevent the insulation from oxidation. However, the antioxidant diffuses out of an XLPE matrix during thermal ageing, which accelerates oxidation, causing the degradation of the insulation. Few models have been developed to represent the diffusion behavior of the antioxidant. One paper has reported that the antioxidant in XLPE migrates from low to high concentration but no explanation has been given. Starting with the theories of uphill diffusion and reaction-diffusion, this paper has developed a physics-based model explicating why the antioxidant migrates against the concentration gradient. In addition to the concentration, the activity coefficient (γ) of the antioxidant is also considered. With physical significance, this study mathematically proves the inhomogeneous distribution of the diffusing oxygen in XLPE makes γ a function of oxygen concentration. γ determines the driving force rendering the uphill diffusion of the antioxidant. Besides the γ function, the decomposition rate of the antioxidant has been modeled.

keywords Cable insulation; Thermal degradation; Aging; Cross-linked polyethylene; XLPE; PEX; Oxidation; Diffusion; Activity coefficient; Chemical potential; Antioxidant