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López-García JJ, Horno J, Grosse C. Impedance-Frequency Response of Closed Electrolytic Cells. MICROMACHINES 2023; 14:368. [PMID: 36838068 PMCID: PMC9963336 DOI: 10.3390/mi14020368] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/22/2022] [Revised: 01/26/2023] [Accepted: 01/27/2023] [Indexed: 06/18/2023]
Abstract
The electric AC response of electrolytic cells with DC bias is analyzed solving numerically the Poisson-Nernst-Planck equations and avoiding the commonly used infinite solution approximation. The results show the presence of an additional low-frequency dispersion process associated with the finite spacing of the electrodes. Moreover, we find that the condition of fixed ionic content inside the electrolytic cell has a strong bearing on both the steady-state and the frequency response. For example: the characteristic frequency of the high-frequency dispersion decreases when the DC potential increases and/or the electrode spacing decreases in the closed cell case, while it remains essentially insensitive on these changes for open cells. Finally, approximate analytic expressions for the dependences of the main parameters of both dispersion processes are also presented.
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Affiliation(s)
- José Juan López-García
- Departamento de Física, Universidad de Jaén, Campus Las Lagunillas, Ed. A-3, 23071 Jaén, Spain
| | - José Horno
- Departamento de Física, Universidad de Jaén, Campus Las Lagunillas, Ed. A-3, 23071 Jaén, Spain
| | - Constantino Grosse
- Departamento de Física, Universidad Nacional de Tucumán, Av. Independencia 1800, San Miguel de Tucumán 4000, Argentina
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2
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Chassagne C, Dubois E, Jiménez ML, van der Ploeg JPM, van Turnhout J. Compensating for Electrode Polarization in Dielectric Spectroscopy Studies of Colloidal Suspensions: Theoretical Assessment of Existing Methods. Front Chem 2016; 4:30. [PMID: 27486575 PMCID: PMC4949231 DOI: 10.3389/fchem.2016.00030] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2015] [Accepted: 06/17/2016] [Indexed: 11/13/2022] Open
Abstract
Dielectric spectroscopy can be used to determine the dipole moment of colloidal particles from which important interfacial electrokinetic properties, for instance their zeta potential, can be deduced. Unfortunately, dielectric spectroscopy measurements are hampered by electrode polarization (EP). In this article, we review several procedures to compensate for this effect. First EP in electrolyte solutions is described: the complex conductivity is derived as function of frequency, for two cell geometries (planar and cylindrical) with blocking electrodes. The corresponding equivalent circuit for the electrolyte solution is given for each geometry. This equivalent circuit model is extended to suspensions. The complex conductivity of a suspension, in the presence of EP, is then calculated from the impedance. Different methods for compensating for EP are critically assessed, with the help of the theoretical findings. Their limit of validity is given in terms of characteristic frequencies. We can identify with one of these frequencies the frequency range within which data uncorrected for EP may be used to assess the dipole moment of colloidal particles. In order to extract this dipole moment from the measured data, two methods are reviewed: one is based on the use of existing models for the complex conductivity of suspensions, the other is the logarithmic derivative method. An extension to multiple relaxations of the logarithmic derivative method is proposed.
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Affiliation(s)
- Claire Chassagne
- Environmental Fluid Mechanics, Faculty of Civil Engineering and Geosciences, Delft University of Technology Delft, Netherlands
| | - Emmanuelle Dubois
- Laboratoire PHENIX, Centre National de la Recherche Scientifique, Sorbonne Universités, UPMC Université Paris 06 Paris, France
| | - María L Jiménez
- Departamento de Física Aplicada, Universidad de Granada Granada, Spain
| | - J P M van der Ploeg
- Formerly affiliated with Leiden Institute of Chemistry, Leiden University RA Leiden, Netherlands
| | - Jan van Turnhout
- Department of Chemical Engineering, Delft University of Technology Delft, Netherlands
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Barbero G, Freire FCM, Scalerandi M, Alexe-Ionescu AL. Role of the Adsorption Phenomenon on the Ionic Equilibrium Distribution and on the Transient Effects in Electrolytic Cells. J Phys Chem B 2006; 110:17889-97. [PMID: 16956278 DOI: 10.1021/jp062271n] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We analyze the influence of the adsorption of ions at the interfaces on the transient phenomena occurring in an electrolytic cell submitted to a steplike external voltage. In the limit of small amplitude of the applied voltage, where the equation of the problem can be linearized, we obtain an analytical solution for the bulk and surface densities of ions and for the electrical potential. We also obtain, in this limit, the relaxation time for the transient phenomena.
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Affiliation(s)
- Giovanni Barbero
- Dipartimento di Fisica del Politecnico, Corso Duca degli Abruzzi 24, 10129 Torino, Italia
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Freire FCM, Barbero G, Scalerandi M. Electrical impedance for an electrolytic cell. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:051202. [PMID: 16802923 DOI: 10.1103/physreve.73.051202] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2005] [Indexed: 05/10/2023]
Abstract
We analyze in which experimental conditions the concept of electrical impedance is useful for an electrolytic cell. The analysis is performed by solving numerically the differential equations governing the phenomenon of the redistribution of the ions in the presence of an external electric field and comparing the results with the ones obtained by solving the linear approximation of these equations. The control parameter in our study is the amplitude of the applied voltage, assumed a simple harmonic function of the time. We show that the bulk distribution of ions close to the electrodes differs from the one obtained by means of the linear analysis already for small amplitudes of the applied voltage. Nevertheless, the concept of electrical impedance remains valid. For larger amplitudes, the current in the circuit is no longer harmonic at the same frequency of the applied voltage. Therefore the concept of electrical impedance is no longer meaningful.
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Affiliation(s)
- F C M Freire
- Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy.
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Zhou H, Preston MA, Tilton RD, White LR. Calculation of the dynamic impedance of the double layer on a planar electrode by the theory of electrokinetics. J Colloid Interface Sci 2005; 292:277-89. [PMID: 15996678 DOI: 10.1016/j.jcis.2005.05.037] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2005] [Revised: 05/16/2005] [Accepted: 05/16/2005] [Indexed: 10/25/2022]
Abstract
Applications of microelectromechanical systems in the biotechnological arena (bioMEMS) are a subject of great current interest. Accurate calculation of electric field distribution in these devices is essential to the understanding and design of processes such as dielectrophoresis and AC electroosmosis that drive MEMS-based devices. In this paper, we present the calculation of the electrical double-layer impedance (Z(el)) of an ideally polarizable plane electrode using the standard model of colloidal electrokinetics. The frequency variation of the electrical potential drop across the double layer above a planar electrode in a general electrolyte solution is discussed as a function of the electrode zeta potential zeta, the Debye length kappa(-1), the electrolyte composition and the bulk region thickness L.
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Affiliation(s)
- Hao Zhou
- Department of Chemical Engineering, Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
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6
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Becchi M, Avendaño C, Strigazzi A, Barbero G. Impedance Spectroscopy of Water Solutions: The Role of Ions at the Liquid−Electrode Interface. J Phys Chem B 2005; 109:23444-9. [PMID: 16375317 DOI: 10.1021/jp044443r] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We discuss the influence of the ions dissolved in a liquid on the impedance spectroscopy of a cell. Our analysis is performed in the small-voltage regime, where the actual bulk density of ions is only slightly perturbed by the external electric field. In this framework, we show that the presence of the ions can be taken into account by a surface density of charge. The agreement between the theoretical prediction, on the basis of the assumption that the ionic mobility is frequency independent, and the experimental data for the real and imaginary parts of the impedance is fairly good for frequencies larger than 100 Hz. In the low-frequency range, the agreement of the theory with the experiment is rather poor. In this region, the experimental data can be successfully fitted by introducing the impedance of the metal-electrolyte interface, which is accurately represented by Zi = w(i omega)(-nu), where w and nu are two constants, with 0 < nu < 1. From the analysis of the experimental data, we determine w and nu. The theoretical predictions of our model are in good agreement with the experimental data in the investigated frequency range.
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Affiliation(s)
- M Becchi
- Dipartimento di Fisica del Politecnico and I.N.F.M., Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
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7
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Barbero G. Influence of adsorption phenomenon on the impedance spectroscopy of a cell of liquid. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:062201. [PMID: 16089790 DOI: 10.1103/physreve.71.062201] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2004] [Indexed: 05/03/2023]
Abstract
We investigate the influence of the adsorption phenomenon on the impedance spectroscopy measurements. The analysis is performed by assuming that the ions have the same mobility and the electrodes are perfectly blocking. We find that in the low frequency range the presence of the adsorption phenomenon is responsible for an increasing of the real part of the impedance of the cell, similar to the one usually described by means of the impedance of the metal-electrolyte interface. The frequency dependencies theoretically predicted by our model for the real and imaginary parts of the complex dielectric constant are in qualitative agreement with the experimental data published by other groups.
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Affiliation(s)
- G Barbero
- Dipartimento di Fisica del Politecnico and INFM, Corso Duca degli Abruzzi, 24-10129 Torino, Italy
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Bazant MZ, Thornton K, Ajdari A. Diffuse-charge dynamics in electrochemical systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:021506. [PMID: 15447495 DOI: 10.1103/physreve.70.021506] [Citation(s) in RCA: 424] [Impact Index Per Article: 21.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2004] [Indexed: 05/03/2023]
Abstract
The response of a model microelectrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem consists of a symmetric binary electrolyte between parallel-plate blocking electrodes, which suddenly apply a voltage. Compact Stern layers on the electrodes are also taken into account. The Nernst-Planck-Poisson equations are first linearized and solved by Laplace transforms for small voltages, and numerical solutions are obtained for large voltages. The "weakly nonlinear" limit of thin double layers is then analyzed by matched asymptotic expansions in the small parameter epsilon= lambdaD/L, where lambdaD is the screening length and L the electrode separation. At leading order, the system initially behaves like an RC circuit with a response time of lambdaDL/D (not lambdaD2/D), where D is the ionic diffusivity, but nonlinearity violates this common picture and introduces multiple time scales. The charging process slows down, and neutral-salt adsorption by the diffuse part of the double layer couples to bulk diffusion at the time scale, L2/D. In the "strongly nonlinear" regime (controlled by a dimensionless parameter resembling the Dukhin number), this effect produces bulk concentration gradients, and, at very large voltages, transient space charge. The article concludes with an overview of more general situations involving surface conduction, multicomponent electrolytes, and Faradaic processes.
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Affiliation(s)
- Martin Z Bazant
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Roldán-Toro R, Solier JD. Wide-frequency-range dielectric response of polystyrene latex dispersions. J Colloid Interface Sci 2004; 274:76-88. [PMID: 15120280 DOI: 10.1016/j.jcis.2004.02.068] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2003] [Accepted: 02/25/2004] [Indexed: 12/01/2022]
Abstract
In this work we analyze the dielectric properties of dilute colloidal suspensions of nonconducting spherical particles with a thin electrical double layer from experimental data obtained by performing impedance spectroscopy experiments over a broad frequency range, from 20 Hz to 1 GHz. The electrode polarization correction was made by fitting a circuit model in the complex impedance plane (impedance spectrum) using a constant phase angle (CPA) element to fit the electrode polarization in series with the sample impedance. This simple procedure is found to be effective in eliminating the electrode contribution. The dielectric response shows two different dispersions, the alpha relaxation (counterion relaxation) that occurs at low kilohertz frequencies, and the delta relaxation (Maxwell-Wagner effect) found in the MHz range. These are reasonably well fitted over a broad frequency range by the theoretical expressions given by a simplified standard model (not including anomalous conduction) and a generalized model (including anomalous conduction) for the low-frequency dispersion, plus Maxwell-Wagner-O'Konski theory for the delta relaxation in the mid-frequency range. An analysis was also made of the need to include, for these latices, the effects of ion mobility in the Stern layer in order for the values of the zeta-potential obtained from electrophoretic and dielectric data to be compatible with each other.
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Affiliation(s)
- R Roldán-Toro
- Department of Physics, University of Extremadura, Avda. de Elvas s/n, 06071 Badajoz, Spain
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Hollingsworth AD, Saville DA. A broad frequency range dielectric spectrometer for colloidal suspensions: cell design, calibration, and validation. J Colloid Interface Sci 2003; 257:65-76. [PMID: 16256457 DOI: 10.1016/s0021-9797(02)00029-2] [Citation(s) in RCA: 55] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2002] [Accepted: 10/04/2002] [Indexed: 10/27/2022]
Abstract
Electrode polarization complicates low-frequency measurements of the dielectric response of electrolyte solutions and colloidal suspensions. To deal with this longstanding problem, a new dielectric cell was developed along with a model based on the standard electrokinetic theory. The parallel plate cell utilizes a thin chamber that is easily filled and emptied; different chamber thicknesses are readily accommodated. The analytical form of the theoretical impedance model makes data analysis straightforward. Using standard electrolytes, the device and the theoretical model were tested over a wide range of frequencies for several electrolyte concentrations. Excellent agreement was found between the theory and the experimental data. The methodology developed to account for polarization effects exhibits a significant improvement over the conventional approaches and points up a deficiency in often-used equivalent circuit models.
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Affiliation(s)
- A D Hollingsworth
- Department of Chemical Engineering, Princeton University, Princeton, NJ 08544, USA
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