Mathematical Model and Experimental Design of Nanocomposite Proximity Sensors

Abstract

A mathematical model of fringe capacitance for a nano-based proximity sensor, which takes the presence of different resistivities into account, is developed. An analytical solution obtained for a rectangular-shape sensor with applying of Gauss, Conversation of Charge and Ohm laws into Laplace's equation $abla ^{2}V\left ({x,y,z,t }\right)=0$ gives the electric potential distribution by which the fringe capacitance in a 2D domain area can be calculated. The calculated capacitance evidently decreases drastically due to the fringe phenomena while object moves toward the polymeric sensor. The model also asserts that the change of capacitance is under a noticeable influence of sensor resistivity, particularly in the range of $10^{3}$ - $10^{5} \Omega $.m, the initial capacitance varies from 0.045pF to 0.024 pF. The fabricated flexible nanocomposite sensors, Thermoplastic Polyurethane (TPU) reinforced by 1wt.% Carbon Nanotubes (CNTs) having resistivity $10^{5} \Omega $.m, are capable of detecting presence of an external object in a wide range of distance and indicating remarkable correlation with the mathematical solution. Our proximity sensor fabrication is straightforward and relatively simple. An unprecedented detection range of measurement reveals promising ability of this proximity sensor in applications of motion analysis and healthcare systems.