Piezoresistive relaxation and creep model of porous polymer nanocomposite supported by experimental data

Porous piezoresistive nanocomposites (PPNs), a blend of conductive nanomaterials and a porous polymer matrix, have garnered significant attention in the realm of flexible pressure sensors. The porous microstructure offers exceptional sensitivity and lightweight characteristics of these sensors, but it also introduces challenges such as relaxation and creep behaviors. Grounded in viscoelastic theory, this paper introduces a mathematical model that provides a quantitative analysis of the resistance-strain relationship of PPN-based piezoresistive sensors, considering both bulk resistance and contact resistance. To elucidate the relaxation and creep behaviors, the model incorporates the conformational change and the slip motion of the polymer macromolecules during the deformation. Utilizing the Adam optimization algorithm, the model can accurately depict the piezoresistive behavior of various PPNs (with different porosities and conductive nanomaterial contents) with a fitting accuracy exceeding 99%. Furthermore, we explored some atypical characteristics of the PPN-based sensor, such as the negative resistance-strain behavior and the overshooting of bulk resistance. This study sets a theoretical basis for the development of sensitive and stable PPN-based sensors.