Fractional Zener Modeling of the Viscoelastic Behavior of PET/rGO Composites

Poly(ethylene terephthalate) (PET) composites reinforced with reduced graphene oxide (rGO) were investigated in order to elucidate the influence of nanofiller concentration and compatibilization on the viscoelastic relaxation behavior across the glass transition. Composites containing 0.1 and 0.5 wt% rGO were prepared by melt blending, and selected systems incorporated 5 wt% of an ionomeric polyester (PETi) as compatibilizer to enhance interfacial adhesion. The thermomechanical response was characterized using dynamic mechanical analysis (DMA) as a function of temperature. Experimental results revealed a strong dependence of stiffness, damping, and glass transition behavior on filler concentration and interfacial interactions. While low rGO loading produced minor changes, the incorporation of 0.5 wt% rGO significantly increased the glassy modulus and shifted the glass transition temperature, indicating restricted segmental mobility. Compatibilized systems exhibited further stiffness enhancement and modified relaxation dynamics due to improved stress transfer and interphase development. To capture the distributed nature of the relaxation processes, the glass transition region was modeled using a fractional Zener model (FZM) with two spring-pot elements within a cooperative relaxation framework. The model successfully reproduced the experimental E′ and tanδ curves and revealed systematic variations in the fractional exponents and cooperative parameters. The results demonstrate that the introduction of rGO and compatibilizer progressively transforms the relaxation spectrum of PET from a relatively uniform segmental process into a heterogeneous, interfacially mediated viscoelastic response that is naturally described by fractional rheology.