Analyzing the Effects of Polymeric Dielectric Materials on Micro Capacitive Pressure Sensors: A Model Incorporating Displacement-Dependent Porosity

Abstract

Recently, the extensive utilization of porous polymeric materials to amplify the sensitivity of capacitive devices is noticeable. The absence of an effective mathematical model for studying these devices has spurred the development of a comprehensive mathematical model in the current work. This model is formulated to analyze the static and dynamic behavior of systems incorporating a porous polymer dielectric material within the gap between flexible and fixed microplates. The derived nonlinear governing equations encompass the effects of electrostatic force, von-Karman nonlinear strains, and displacement-dependent porosity. Employing spatial decomposition, the resulting nonlinear algebraic equations and ordinary differential equations are leveraged to study the static and transient dynamic behavior, as well as the frequency response of the sensor using a learning approach. Two scenarios are investigated to assess the impact of various geometrical and physical parameters on sensor sensitivity one with a polymeric material and another without, each with distinct parameter values. The results reveal that the inclusion of a polymeric dielectric material increases electrostatic force but concurrently elevates the equivalent stiffness of the structure. The effectiveness of using a polymeric dielectric material is contingent upon the specific geometrical and physical properties of the sensor. Moreover, the obtained results in simplified cases are compared to existing numerical and experimental data, demonstrating a high degree of agreement. This work significantly contributes to advancing the understanding of sensors incorporating porous polymer dielectric materials and underscores their potential for enhanced sensitivity across diverse applications.