
March 26, 2016 

Dielectric spectroscopy (sometimes called Electrical impedanceimpedance spectroscopy), and also known as Electrochemical Impedance Spectroscopy, measures the dielectric properties of a medium as a function of frequency. It is based on the interaction of an external field with the electric Electric dipole momentdipole moment of the sample, often expressed by permittivity. It is also an experimental method of characterizing electrochemical systems. This technique measures the Electrical impedanceimpedance of a system over a range of frequencies, and therefore the frequency response of the system, including the energy storage and dissipation properties, is revealed. Often, data obtained by EIS is expressed graphically in a Bode plot or a Nyquist plot. Impedance is the opposition to the flow of alternating current (AC) in a complex system. A passive complex electrical system comprises both energy dissipater (resistor) and energy storage (capacitor) elements. If the system is purely resistive, then the opposition to AC or direct current (DC) is simply Electrical resistanceresistance. Almost any physicochemical system, such as electrochemical cells, massbeam oscillators, and even biological tissue possesses energy storage and dissipation properties. EIS examines them. This technique has grown tremendously in stature over the past few years and is now being widely employed in a wide variety of scientific fields such as fuel cell testing, biomolecular interaction, and microstructural characterization. Often, EIS reveals information about the reaction mechanism of an electrochemical process: different reaction steps will dominate at certain frequencies, and the frequency response shown by EIS can help identify the rate limiting step. Text books on this subject are only beginning to emerge on a larger scale, perhaps the most popular text book on EIS is . A more recent text is . French text books are available ,. Dielectric mechanismsThere are a number of different dielectric mechanisms, connected to the way a studied medium reacts to the applied field (see the figure illustration). Each dielectric mechanism is centered around its characteristic frequency, which is the reciprocal of the characteristic time of the process. In general, dielectric mechanisms can be divided into dielectric relaxationrelaxation and resonance processes. The most common, starting from high frequencies, are: Electronic polarization This resonant process occurs in a neutral atom when the electric field displaces the electron density relative to the Atomic nucleusnucleus it surrounds. This displacement occurs due to the equilibrium between restoration and electric forces. Electronic polarization may be understood by assuming an atom as a point nucleus surrounded by spherical electron cloud of uniform charge density. Atomic polarization Atomic polarization is observed when the electronic cloud is deformed under the force of the applied field, so that the negative and positive charge are formed. This is a resonant process. Dipole relaxation This originates from permanent and induced dipoles aligning to an electric field. Their orientation polarisation is disturbed by thermal noise (which misaligns the dipole vectors from the direction of the field), and the time needed for dipoles to relax is determined by the local viscosity. These two facts make dipole relaxation heavily dependent on temperature and chemical surrounding. Ionic relaxation Ionic relaxation comprises ionic conductivity and interfacial and space charge relaxation. Ionic conductivity predominates at low frequencies and introduces only losses to the system. Interfacial relaxation occurs when charge carriers are trapped at interfaces of heterogeneous systems. A related effect is MaxwellWagnerSillars polarization, where charge carriers blocked at inner dielectric boundary layers (on the mesoscopic scale) or external electrodes (on a macroscopic scale) lead to a separation of charges. The charges may be separated by a considerable distance and therefore make contributions to the dielectric loss that are orders of magnitude larger than the response due to molecular fluctuations. Dielectric relaxation Dielectric relaxation as a whole is the result of the movement of dipoles (dipole relaxation) and electric charges (ionic relaxation) due to an applied alternating field, and is usually observed in the frequency range 10^{2}10^{10} Hz. Relaxation mechanisms are relatively slow compared to resonant electronic transitions or molecular vibrations, which usually have frequencies above 10^{12} Hz. PrinciplesSteadystate For a redox reaction R $\backslash leftrightarrow$ O + e, without masstransfer limitation, the relationship between the current density and the electrode overpotential is given by the ButlerVolmer equation: $$ j_\textt=j_0\left(\exp(\alpha_\texto\,f\, \eta)\exp(\alpha_\textr\,f\,\eta)\right) with $\backslash eta=EE\_\backslash texteq\; ,\backslash ;f=F/(R\backslash ,T),\backslash ;\backslash alpha\_\backslash texto+\backslash alpha\_\backslash textr=1$. $j\_0$ is the exchange current density and $\backslash alpha\_\backslash texto$ and $\backslash alpha\_\backslash textr$ are the symmetry factors. The curve $j\_\backslash textt\backslash ;\; vs.\backslash ;\; E$ is not a straight line (Fig. 1), therefore a redox reaction is not a linear system . Dynamic behavior Faradaic impedance Let us suppose that the ButlerVolmer relationship correctly describes the dynamic behavior of the redox reaction : $$ j_\textt(t)=j_\textt(\eta(t))=j_0\,\left(\exp(\alpha_\texto\,f\, \eta(t))\exp(\alpha_\textr\,f\,\eta(t))\right) Dynamic behavior of the redox reaction is characterized by the socalled charge transfer resistance defined by : $$ R_\textct=\frac1\partial j_\textt/\partial \eta = \frac1f\,j_0\,\left(\alpha_\texto\,\exp(\alpha_\texto\,f\, \eta)+\alpha_\textr\,\exp(\alpha_\textr\,f\, \eta) \right) The value of the charge transfer resistance changes with the overpotential. For this simplest example the Faradaic impedance is reduced to a resistance. It is worthwhile to notice that: $$ R_\textct = \frac1f\,j_0 for $\backslash eta\; =\; 0$ . Double layer capacitance An electrode $$ electrolyte interface behaves like a capacitance called Electrical double layerelectrochemical doublelayer capacitance $C\_\backslash textdl$. The equivalent electrical circuit for the redox reaction taking account of the doublelayer capacitance is shown in Fig. 2. Another analog circuit commonly used to model the electrochemical doublelayer is called a constant phase element. The electrical impedance of this circuit is easily obtained remembering the impedance of a capacitance which is given by : $$ Z_\textdl(\omega) =\frac1\texti\,\omega\, C_\textdl where $\backslash omega$ is the angular frequency of a sinusoidal signal (rd/s), and $\backslash scriptstyle\; \backslash texti=\backslash sqrt1$. It is obtained : $$ Z(\omega)=\fracR_\textt1+R_\textt\,C_\textdl\,\texti \,\omega Nyquist diagram of the impedance of the circuit shown in Fig. 2 is a semicircle with a diameter $\backslash scriptstyleR\_\backslash textt$ and an angular frequency at the apex equal to $\backslash scriptstyle1/(R\_\backslash textt\backslash ,C\_\backslash textdc)$ (Fig. 3). Others representations, Bode or Black plans can be used . Ohmic resistance The ohmic resistance $R\_\backslash Omega$ appears in series with the electrode impedance of the reaction and the Nyquist diagram is translated to the right. Measurement of the impedance parametersPlotting the Nyquist diagram with a potentiostat and an impedance analyzer, most often included in modern potentiostats, allows the user to determine charge transfer resistance, double layer capacitance and ohmic resistance. The exchange current density $j\_0$ can be easily determined measuring the impedance of a redox reaction for $\backslash eta=0$. Nyquist diagrams are made of several arcs for reaction more complex than redox reaction and with masstransfer limitation. See also
ReferencesSee also
Category:Spectroscopy Category:Electric and magnetic fields in matter Category:Physics Category:Electrochemistry ca:Espectrosc??pia d'imped??ncia electroqu??mica de:Dielektrische Spektroskopie es:Espectroscopia diel??ctrica fa:????????????????? ?????????????? ?????????????????????????? fr:Spectroscopie di??lectrique he:???????????? ???????? ???????????? pl:Spektroskopia dielektryczna pt:Espectroscopia diel??ctrica sl:dielektri??na spektroskopija This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "dielectric spectroscopy".



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