Capacitance Sensor Project Dielectric Properties

Transcription

1 Capacitance Sensor Project Dielectric Properties Introduction Most plastics are dielectrics or insulators (poor conductors of electricity) and resist the flow of a current. This is one of the most useful properties of plastics and makes much of our modern society possible through the use of plastics as wire coatings, switches and other electrical and electronic products. Despite this, dielectric breakdown can occur at sufficiently high voltages to give current transmission and possible mechanical damage to the plastic. Not all polymers behave the same when subjected to voltage and plastics can be classified as polar or non-polar to describe their variations in behavior. In polar plastics, dipoles are created by an imbalance in the distribution of electrons and in the presence of an electric field the dipoles will attempt to move to align with the field. This will create dipole polarization of the material and because movement of the dipoles is involved there is a time delay to the movement. Examples of polar plastics are PMMA (poly-methyl meth-acrylate), PVC (polyvinylchloride), PA (Polyamide, Nylon), PC (Polycarbonate), PVAC (polyvinylacetate). The dielectric constant is a measure of the influence of a particular dielectric on the capacitance sensor. It measures how well a material separates the charges in a capacitor and is defined as the ratio of the capacitance of a set of electrodes (with the dielectric material between them) to the capacitance of the same electrodes (with a vacuum or air between them). The dielectric constant for a vacuum is equals to 1 and for all other materials it is greater than 1. 1

2 For dielectric measurements on solid polymers, the material usually is taken in form of a disc or film and inserted between metal plates of the capacitance sensor where an AC voltage is applied. The capacitance C x of such a sensor capacitor is calculated by: C x = ε ε o r A d Where ε o = As/(Vm) is the permittivity of free space, ε r - is the relative permittivity of the polymer, A - is the area where the electric field is active (equal to that of the smaller of two plates) d - is the thickness of the sample. For non-polar plastics the dielectric constant is independent of the alternating current frequency because the electron polarization is effectively instantaneous. Non-polar plastics always have dielectric constants of less than 3. 2

3 - For polar plastics the alternating current frequency is an important factor because of the time taken to align the polar dipoles. - At very low frequencies the dipoles have sufficient time to align with the field before it changes direction and the dielectric constant is high. - At very high frequencies the dipoles do not have time to align before the field changes direction and the dielectric constant is lower. - At intermediate frequencies the dipoles move but have not completed their movement before the field changes direction. - The time needed for alignment is determined by the thermal motion of the molecules. - Roughly we can say that the time needed for alignment is the inverse of this thermal hopping frequency. - On the other hand, we know that the frequency of thermal motion depends on temperature, following the equation. f th = f o e E kt Where f 0 - is a constant, which is supposed to be in the order of magnitude of vibration frequencies of the molecules (10 12 to Hz) E - is the height of the energy barrier, which the dipoles have to overcome during their motion, K - is the Boltzmann constant, T - is the absolute temperature. Thus, by changing the temperature (for instance by cooling a polymer down from the melt), we can observe a transition from mobile to immobile molecules, if we measure at constant frequency. The dielectric constant epsilon, will be about 10 for polar polymers at high temperatures. However, at low temperatures, there is only a small elastic displacement of the atoms, and epsilon is about 3 (the same as for non-polar materials). At the transition temperature, the frequency of the electric field is exactly the same as the frequency of the thermal motion, and the imaginary part of epsilon (see below) shows a maximum. Therefore, we can use the shape of the imaginary part of the epsilon curve, in order to determine the transition frequency f max. After that, according to the equation (see above), it is widely used to plot log f max over (1/T), to obtain a diagram, where the slope of the line allows calculating the energy barrier E. Therefore such a plot is called activation energy diagram. 3

4 Method of measurement: The AC impedance of the sensor capacitor is: Z = 1 x jωcx Where w = 2πf J - represents the unit of the imaginary scale in the mathematics of complex numbers. Z x can be measured by measuring two voltages in a series connection of the unknown with a reference capacitor. This is realized in the experiment in the following circuit: We need to mention that an additional element, a resistor with high impedance, is connected in parallel to the reference capacitor, in order to avoid static charges between the two capacitors, which may arise from sources outside of the circuit. 4

5 Data Acquisition The data acquisition is implemented inside a small blue box. This box is connected to a USB port of a computer. The program which is installed on a computer controls this device, repeating data acquisitions, calculating the voltage ratio, the frequency as well as the real and imaginary part of the complex dielectric constant ε, and presenting the results in a diagram on the screen. At the same time, one of the channels in the small blue box is measuring the temperature of the sample holder by means of a thermocouple. Experimental Procedure 1- Before inserting your sample in the sample holder near the heating fan, please disconnect the generator and the blue box (analog/digital converter) because your hands may carry electrostatic charges. 2- It is recommended to cover the aluminum ground plate as well as the upper electrode plate with aluminum film, in order to facilitate cleaning afterwards. 3- Plug in the cables again and check the connections if consistent with the circuit diagram above. 4- Switch on the function generator and select a frequency f = 5 khz and 10 V output voltage. 5- Start the program on the computer and enter the parameters for your measurement. You have to give information to the computer program - which reference capacitor you have selected - which reference resistor you have selected - which is the thickness and the area of your sample, and this should be done, using C = ε o A d This is required for the calculation of ε 6- Start data acquisition and select the chart epsilon, and you should find a diagram of the dielectric constant plotted over the temperature. At room temperature, we are in the glassy state and the real part should be around 3, and the imaginary part should be much smaller. 7- Start heating the sample. Observe the temperature reading at the screen, and, after reaching a temperature well above the glass transition, for instance for PVAc about 140 o C, you can start cooling by switching the fan to position 1. 5

6 Project Evaluation and Results Write a report including the following points. 1- Introduction about the capacitive sensors, types and applications. 2- Capacitive sensor theory of operation. 3- Note any results which are coming not as expected, and try to indicate a reason for it. 4- You should observe a transition from a low level of ε at low temperatures to a higher level of ε at high temperatures by plotting a curve shows that transition. 6