For simple electrode geometries such as parallel plate and http://www.selleckchem.com/products/Tipifarnib(R115777).html cylindrical electrodes, the relationship between complex permittivity, capacitance and complex impedance vs. frequency is analytically obtained. Expressions for the capacitance of parallel plate and cylindrical capacitors are shown in Table 1. Using the concept of complex relative permittivity, Figure 1, the complex impedance of a capacitor with losses (C*) can be determined using Equation (1):Z=1j��?C*(1)Figure 1.Definition of complex relative permittivity [26].Table 1.Capacitance for different electrode geometries.The complex capacitance depends on the electrodes geometry and it corresponds to the same expressions shown in Table 1 using the complex permittivity.
The final complex impedance expression is a function of the sensing electrodes geometry, excitation frequency and the condition of the oil which is related to complex permittivity. For the cylindrical geometry the procedure for the impedance determination is shown in Figure 2.Figure 2.Equivalent circuit for cylindrical electrodesLubricating oil is a dielectric material with low losses (it is a good electrical insulator as it has low conductivity). Therefore, the dissipation factor for oil can be considered much lower than unity and hence, the real part of the complex permittivity is higher than the imaginary part. The complex impedance expression suggests a simple circuit for the cylindrical electrode system as shown in Figure 2. This equivalent circuit consists of one capacitor and one resistor connected in series (equivalent series resistor, ESR).
The equivalent circuit helps to understand the influence of the real and imaginary parts of the complex permittivity in the final impedance expression. The real part of the permittivity is related to the energy storage and the imaginary part to dielectric losses.As a result, any measurement AV-951 of complex impedance of the sensing electrodes is an indicator of the degradation of the oils. In analytical chemistry the measurement technique of electrode impedance as a function of frequency is commonly referred to as Electrochemical Impedance Spectroscopy (EIS). The underlying idea of Impedance Spectroscopy (IS) is the measurement and characterization of a material-electrode system. A complete impedance spectroscopy analysis involves more than a single set of measurements of impedance vs. frequency.
Frequently, full characterization requires that such sets of measurements are carried out over a range of temperatures and/or other externally controlled experimental phase 3 variables [28].During the last decade, several research studies considering the application of electrochemical impedance spectroscopy in lubrication have appeared [29�C34]. Important conclusions are drawn from these studies; the impedance response is dependent on the electrode��s geometry and its contact with the medium.