PyOECP: A flexible open-source software library for estimating and modeling the complex permittivity based on the open-ended coaxial probe (OECP) technique

Abstract

We present PyOECP, a Python-based flexible open-source software for estimating and modeling the complex permittivity obtained from the open-ended coaxial probe (OECP) technique. The transformation of the measured reflection coefficient to complex permittivity is performed based on three different methods. The software library contains the dielectric spectra of common reference liquids, which can be used to transform the reflection coefficient into the dielectric spectra. Several Python routines that are commonly employed (e.g., SciPy and NumPy) in the field of science and engineering are required only so that the users can alter the software structure depending on their needs. The modeling algorithm exploits the Markov Chain Monte Carlo method for the data regression. The discrete relaxation models can be built by a proper combination of well-known relaxation models. In addition to these models, electrode polarization, a typical measurement artifact for interpreting dielectric spectra, can be incorporated into the modeling algorithm. A continuous relaxation model, which solves the Fredholm integral equation of the first kind (a mathematically ill-posed problem), is also included. This open-source software enables users to freely adjust the physical parameters to obtain physical insight into their materials under test and will be consistently updated for more accurate measurement and interpretation of dielectric spectra in an automated manner. This work describes the theoretical and mathematical background of the software, lays out the workflow, and validates the software functionality based on both synthetic and empirical data included in the software. Program summaryProgram title: PyOECP 0.5CPC Library link to program files:https://doi.org/10.17632/vsh6vb9cbv.1Developer's repository link:https://github.com/tyoon124Code Ocean capsule:https://codeocean.com/capsule/89645681Licensing provisions: BSD-3 Clause LicenseProgramming language: Python3External routines: Numpy, Scipy, and MatplotlibNature of problem: Estimate and interpret the frequency-dependent (complex) permittivity in fluid(s) and their mixtures based on the reflection coefficients obtained from the open-ended coaxial probe (OECP) technique. The obtained dielectric spectra can be useful for understanding the relaxation processes in an arbitrary fluid.Solution method: The reflection coefficient data is obtained as a text format from a Vector Network Analyzer (VNA). This text data is parsed into a Numpy array. Three different modules (Stuchly, Marsland, and Komarov) can be used to transform the parsed reflection coefficient data into complex permittivity as a function of the measurement frequency. The resultant dielectric spectra can be dissected and interpreted by fitting either discrete relaxation model(s) based on the Markov Chain Monte Carlo algorithm or a continuous relaxation model by applying the Zasetsky-Buchner method.