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 2 ( , , , ) = 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 Ω.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 10P 5 P Ω.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.

An Integrated Nanocomposite Proximity Sensor: Machine Learning-Based Optimization, Simulation, and Experiment

“…The nanocomposite sensor has a nanostructure simpler than that of previous studies [18,21,[35][36][37][38][39], but in our previous studies [40], there was an intricate microstructure in which CNTs were utilized as a reinforcement in the mold substrate thermoplastic polyurethane (TPU). Our primary results captured the initial testing validation of a capacitive-based sensor (experiment), and later this sensor was simulated by solving the partial differential Laplace equation [41]. Specifically, it was shown that the behavior becomes very sensitive in the specific range of the active materials (CNTs) used as reinforcements in the TPU matrix.…”

“…Experimental measurements show this behavior of the system clearly [40]. In addition to experimental observations, an analysis was accomplished with a couple of goals by the authors [41]. Firstly, an analytical solution (simulation) helps to achieve a higher level of understanding regarding what happens in the system, and secondly, quantization of the changes of capacitance with respect to the distance of the object not only helps in calibration of the sensor but also is beneficial for the design of different sensors for various applications.…”

“…The real part of derived impedance signified the equivalent resistance owing to the finite resistivity of the nanocomposite substrate while its imaginary part characterized the equivalent capacitance between the electrodes and object. Therefore, the following expression was used for calculation of the equivalent capacitance of the system [41]:…”

“…Our proposed geometrical sensing system was modeled in MATLAB as a Fourier series that uses the key parameters as inputs [41]. One of the main requirements for optimization process is a low runtime.…”

“…Absolute percentage change of capacitance to the initial capacitance at the different distance to the object was calculated and addressed as sensitivity. Moheimani et al [41] demonstrated earlier that resistivity of the film sensor originating from CNTs amount can affect its sensitivity.…”