Interface description of Milli-Q water cells: Temperature dependence of the CPE parameters T. de Andrade a,b , F.C.M. Freire b , G. Barbero a,c , A.L. Alexe–Ionescu a,d, ⁎ a Dipartimento di Scienza Applicata e Tecnologia, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy b Departamento di Física, Universidade Estadual de Maringá, Avenida Colombo 5790, 87020-900 Maringá, Paraná, Brazil c National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoye shosse 31, 115409 Moscow, Russian Federation d University Politehnica of Bucharest, Faculty of Applied Sciences, Splaiul Independentei 313, 060042 Bucharest, Romania abstract article info Article history: Received 26 May 2016 Received in revised form 23 June 2016 Accepted 26 June 2016 Available online 30 June 2016 We report on the temperature dependence of the Milli-Q water cell response, limited by surgical steel electrodes, to an external periodic excitation. Using the Electrochemical Impedance Spectroscopy technique (EIS), the spec- tra of the real and imaginary parts of the electrical impedance of the cell are experimentally obtained. Important deviations from the theoretical predictions of the Poisson–Nernst–Planck model, assuming blocking electrodes, are observed. Our experimental results indicate that the properties of the electrodes play an important role in the low frequency part of the spectra. In the absence of a simple physically based theoretical model, we fit our data utilizing three equivalent electric circuits containing a constant phase element (CPE) charged to describe the properties of the electrodes. From our analysis it follows that a “good” equivalent electric circuit for the anal- ysis of the response of an electrolytic cell to an external periodic voltage is formed by a parallel of a bulk capac- itance and resistance of ionic origin. The CPE is then charged to mimic the interface effects. From a mathematical point of view this is equivalent to assume that the phenomenological parameters describing the non-ideal blocking properties of the electrode, in the Chang-Jaffe, Ohmic or Langmuir models, are frequency dependent. © 2016 Published by Elsevier B.V. Keywords: Electrochemical impedance spectroscopy Interface CPE Milli-Q water 1. Introduction The response of an electrolytic cell to an external electric stimulus is usually investigated using the electrochemical impedance spectroscopy technique (EIS). When the external voltage is a simple harmonic func- tion of time, of circular frequency ω, from the analysis of the spectra of real, R, and imaginary, X, parts of the electric impedance, Z, of the cell it is possible to derive information on the effective dielectric and con- ductivity parameters. In the case of ionic conductivity, a description of the influence of the ions on the electric response of the cell to an exter- nal periodic voltage is done in terms of an equivalent electric circuit where each element, resistance, capacitance or inductance, is related to a specific process [1,2]. Our aim is the analysis of the response of a cell containing Milli-Q water with surgical steel electrodes to an external excitation, in the low frequency region where the ionic relaxation plays a fundamental role. In this frequency region the water can be considered not disper- sive, and the experimentally observed dispersion is due to the motion of the ions present in water. A similar research in the frequency domain from 1.1 GHz to 57 GHz has been published by Kaatze [3]. In the frequency range explored by Kattze [3] the ionic contribution to the electric response of the cell to the external periodic excitation is completely negligible, and the dispersion has molecular origin, related to the dipolar moments rotation. We show that, in the low frequency re- gion, an equivalent circuit of the cell able to reproduce our experimental data is formed by a parallel of a bulk capacitance, of the liquid free of ions, and a resistance of ionic origin, in series with a constant phase element (CPE). In this electric circuit the CPE is charged to take into account all interfacial effects related to the electrodes and to the ions confinement due to the presence of the external electric field. From a mathematical point of view this circuit is equivalent to impose bound- ary conditions on the dynamic variables characterizing the liquid con- taining ions localized on the limiting surfaces of the liquid, in contact with the electrodes. The phenomenological parameters entering the boundary conditions are expected to be frequency dependent. The paper is organized as follows. In Section 2, the models proposed for the theoretical analysis of the spectra of the real and imaginary parts of the electrical impedance of the cell are discussed, underlying their limits. The experimental setup is described in Section 3. A few consider- ations on the CPE are reported in Section 4, devoted to the analysis of the spectra, at impedance level. Using a fitting procedure based on an equivalent electric circuit containing a Debye element in series with a CPE and a parasite inductance due to the connecting cables, the expo- nent and amplitude of the CPE versus the temperature are determined. Journal of Electroanalytical Chemistry 777 (2016) 19–25 ⁎ Corresponding author at: University Politehnica of Bucharest, Faculty of Applied Physics, Splaiul Independentei 313, 060042 Bucharest, Romania. http://dx.doi.org/10.1016/j.jelechem.2016.06.036 1572-6657/© 2016 Published by Elsevier B.V. Contents lists available at ScienceDirect Journal of Electroanalytical Chemistry journal homepage: www.elsevier.com/locate/jelechem