An Analytical Model for Porous Polymer-Ceramic Capacitive Pressure Sensors

An analytical model for pressure sensors is constructed, predicting the capacitive response of a porous, polymer-ceramic composite under an applied pressure. Consisting of mechanical and dielectric counterparts, the iterative model is constructed in detail. The elastic modulus of the three-phase material is approximated by first considering only the polymer-ceramic composite mixture, and then incorporating porosity into the solid composite model. A new model has been developed for approximating the changing elastic modulus of porous polymers undergoing quasi-static compression, which induces the collapsing pores. Necessary material constants were obtained from experimental data published in literature. The permittivity of the paraelectric polymer matrix is modeled, accounting for piezodielectric effects imposed by external pressure and thermally induced stresses caused by substrate pinning. Similarly, the ferroelectric ceramic filler is modeled, considering changes in polarization caused by thermally induced phase transformations in the crystal structure. The final model is evaluated against experimental data, providing insight into composition and microstructure effects on the sensor response.