Dielectric spectroscopy

A dielectric permittivity spectrum over a wide range of frequencies. The real and imaginary parts of permittivity are shown, and various processes are depicted: ionic and dipolar relaxation, and atomic and electronic resonances at higher energies. From the Dielectric spectroscopy page of the research group of Dr. Kenneth A. Mauritz.

Dielectric spectroscopy (which falls in a subcategory of impedance spectroscopy) measures the dielectric properties of a medium as a function of frequency.^[1][2][3][4] It is based on the interaction of an external field with the electric dipole moment of the sample, often expressed by permittivity.

It is also an experimental method of characterizing electrochemical systems. This technique measures the impedance 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 electrochemical impedance spectroscopy (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 resistance.

Almost any physico-chemical system, such as electrochemical cells, mass-beam 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.

Dielectric mechanisms

CSIRO Dielectrics spectroscopy machine

There 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 relaxation 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 nucleus 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 nucleus of the atom reorients in response to the electric field. This is a resonant process. Atomic polarization is intrinsic to the nature of the atom and is a consequence of an applied field. Electronic polarization refers to the electron density and is a consequence of an applied field. Atomic polarization is usually small compared to electronic polarization.

Dipole relaxation

This originates from permanent and induced dipoles aligning to an electric field. Their orientation polarisation is disturbed by thermal noise (which mis-aligns 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, pressure^[5] 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 Maxwell-Wagner-Sillars 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.^[1]

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 10²-10¹⁰ Hz. Relaxation mechanisms are relatively slow compared to resonant electronic transitions or molecular vibrations, which usually have frequencies above 10¹² Hz.

Principles

Steady-state

For a redox reaction R $\leftrightarrow$ O + e, without mass-transfer limitation, the relationship between the current density and the electrode overpotential is given by the Butler-Volmer equation:

$j_{\text{t}}=j_0\left(\exp(\alpha_{\text{o}}\,f\, \eta)-\exp(-\alpha_{\text{r}}\,f\,\eta)\right)$

with

$\eta=E-E_{\text{eq}} ,\;f=F/(R\,T),\;\alpha_{\text{o}}+\alpha_{\text{r}}=1$. $j_{0}$ is the exchange current density and $\alpha_{\text{o}}$ and $\alpha_{\text{r}}$ are the symmetry factors.

Fig. 1 : Steady-state current density vs. overpotential for a redox reaction.

The curve $j_{\text{t}}\; vs.\; E$ is not a straight line (Fig. 1), therefore a redox reaction is not a linear system.^[6]

Dynamic behavior

Faradaic impedance

In an electrochemical cell the faradaic impedance of an electrolyte-electrode interface is the joint electrical resistance and capacitance at that interface.

Let us suppose that the Butler-Volmer relationship correctly describes the dynamic behavior of the redox reaction  :

$j_{\text{t}}(t)=j_{\text{t}}(\eta(t))=j_0\,\left(\exp(\alpha_{\text{o}}\,f\, \eta(t))-\exp(-\alpha_{\text{r}}\,f\,\eta(t))\right)$

Dynamic behavior of the redox reaction is characterized by the so-called charge transfer resistance defined by :

$R_{\text{ct}}=\frac{1}{\partial j_{\text{t}}/\partial \eta }= \frac{1}{f\,j_0\,\left(\alpha_{\text{o}}\,\exp(\alpha_{\text{o}}\,f\, \eta)+\alpha_{\text{r}}\,\exp(-\alpha_{\text{r}}\,f\, \eta) \right)}$

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:

$R_{\text{ct}} = \frac{1}{f\,j_0}$

for $\eta = 0$ .

Double layer capacitance

An electrode $|$ electrolyte interface behaves like a capacitance called electrochemical double-layer capacitance $C_{\text{dl}}$. The equivalent electrical circuit for the redox reaction taking account of the double-layer capacitance is shown in Fig. 2. Another analog circuit commonly used to model the electrochemical double-layer is called a constant phase element.

Fig. 2 : Equivalent circuit for a redox reaction without mass-transfer limitation.

The electrical impedance of this circuit is easily obtained remembering the impedance of a capacitance which is given by :

$Z_{\text{dl}}(\omega) =\frac{1}{\text{i}\,\omega\, C_{\text{dl}}}$

where $\omega$ is the angular frequency of a sinusoidal signal (rd/s), and $\scriptstyle{ \text{i}=\sqrt{-1}}$. It is obtained:

$Z(\omega)=\frac{R_{\text{t}}}{1+R_{\text{t}}\,C_{\text{dl}}\,\text{i} \,\omega}$

Nyquist diagram of the impedance of the circuit shown in Fig. 3 is a semicircle with a diameter $\scriptstyle{R_{\text{t}}}$ and an angular frequency at the apex equal to $\scriptstyle{1/(R_{\text{t}}\,C_{\text{dc}})}$ (Fig. 3). Others representations, Bode or Black plans can be used.^[7]

Fig. 3 : Electrochemists Nyquist diagram of a RC parallel circuit. The arrow indicates increasing angular frequencies.

Ohmic resistance

The ohmic resistance $R_\Omega$ appears in series with the electrode impedance of the reaction and the Nyquist diagram is translated to the right.

Measurement of the impedance parameters

Plotting the Nyquist diagram with a potentiostat^[8] 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 $\eta =0$.

Nyquist diagrams are made of several arcs for reactions more complex than redox reactions and with mass-transfer limitations.

Applications

Electrochemical Impedance Spectroscopy is used in a wide range of applications.^[9]
In the paint industry it is a useful tool to investigate the quality of coatings^[10][11] and to detect the presence of corrosion.^[12][13]
It is used in many biosensor systems as a label free technique to measure bacterial concentration^[14] and to detect dangerous pathogens such as Escherichia Coli O157:H7^[15] and Salmonella^[16] as well as yeast cells.^[17][18]
Electrochemical Impedance Spectroscopy is also used to analyze and characterize different food products. Some examples are the assessment of food/package interactions,^[19] the analysis of milk composition,^[20] the characterization^[21] and the determination of the freezing end-point^[22] of ice-cream mixes, the measure of meat ageing,^[23] the investigation of ripeness and quality in fruits^[24][25][26] and the determination of free acidity in olive oil.^[27][28]
In the field of human health monitoring is better known as Bioelectrical Impedance Analysis (BIA)^[29] and is used to estimate body composition^[30] as well as different parameters such as total body water and free fat mass.^[31]

See also

• Loss tangent
• Debye relaxation
• Ellipsometry
• Linear response function
• Kramers–Kronig relation
• Green–Kubo relations
• Electrochemistry
• Potentiostat

References

1. Kremer F., Schonhals A., Luck W. Broadband Dielectric Spectroscopy. – Springer-Verlag, 2002.
2. Sidorovich A. M., Dielectric Spectrum of Water. – Ukrainian Physical Journal, 1984, vol. 29, No 8, p. 1175-1181 (In Russian).
3. Hippel A. R. Dielectrics and Waves. – N. Y.: John Willey & Sons, 1954.
4. Volkov A. A., Prokhorov A. S., Broadband Dielectric Spectroscopy of Solids. – Radiophysics and Quantum Electronics, 2003, vol. 46, Issue 8, p. 657–665.
5. Floudas G., Paluch, M., Grzybowski A., Ngai K. L. Molecular Dynamics of Glass-Forming Systems - Effects of Pressure. Springer-Verlag, 2011.
6. Linear vs. non-linear systems in impedance measurements Archived December 5, 2008, at the Wayback Machine.
7. "Potentiostat stability mystery explained" (PDF). Retrieved 2011-11-08.
8. Impedance, admittance, Nyquist, Bode, Black, etc. Archived July 21, 2011, at the Wayback Machine.
9. Lasia, A. Electrochemical Impedance Spectroscopy and Its Applications. In "Modern aspects of electrochemistry", volume 32. pp. 143–248.
10. McIntyre, J.M.; Pham, H.Q. (1996). "Electrochemical impedance spectroscopy; a tool for organic coatings optimizations". Progress in Organic Coatings. 27 (1-4): 201–207. doi:10.1016/0300-9440(95)00532-3.
11. Amirudin, A.; Thieny, D. (1995). "Application of electrochemical impedance spectroscopy to study the degradation of polymer-coated metals". Progress in Organic Coatings. 26 (1): 1–28. doi:10.1016/0300-9440(95)00581-1.
12. Bonora, P.L.; Deflorian, F.; Fedrizzi, L. (1996). "Electrochemical impedance spectroscopy as a tool for investigating underpaint corrosion". Electrochimica Acta. 41 (7-8): 1073–1082. doi:10.1016/0013-4686(95)00440-8.
13. Rammelt, U.; Reinhard, G. (1992). "Application of electrochemical impedance spectroscopy (EIS) for characterizing the corrosion-protective performance of organic coatings on metals". Progress in Organic Coatings. 21 (2-3): 205–226. doi:10.1016/0033-0655(92)87005-U.
14. Maalouf, R.; Fournier-Wirth, C.; Coste, J.; Chebib, H.; Saikali, Y.; Vittori, O.; Errachid, A.; Cloarec, J.P.; Martelet, C.; Jaffrezic-Renault, N. (2007). "Label-Free Detection of Bacteria by Electrochemical Impedance Spectroscopy:  Comparison to Surface Plasmon Resonance". Analytical Chemistry. 79 (13): 4879–4886. doi:10.1021/ac070085n.
15. Ruan, C.; Yang, L.; Li, Y. (2002). "Immunobiosensor Chips for Detection of Escherichia coli O157:H7 Using Electrochemical Impedance Spectroscopy". Analytical Chemistry. 74 (18): 4814–4820. doi:10.1021/ac025647b.
16. Nandakumar, V.; La Belle, J.T.; Reed, J.; Shah, M.; Cochran, D.; Joshi, L.; Alford, T.L. (2008). "A methodology for rapid detection of Salmonella typhimurium using label-free electrochemical impedance spectroscopy". Biosensors & Bioelectronics. 24 (4): 1039–1042. doi:10.1016/j.bios.2008.06.036.
17. Soley, A.; Lecina, M.; Gamez, X.; Cairo, J.J.; Riu, P.; Rosell, X.; Bragos, R.; Godia, F. (2005). "On-line monitoring of yeast cell growth by impedance spectroscopy". Journal of Biotechnology. 118 (4): 398–405. doi:10.1016/j.jbiotec.2005.05.022.
18. Chen, H.; Heng, C.K.; Puiu, P.D.; Zhou, X.D.; Lee, A.C.; Lim, T.M.; Tan, S.N. (2005). "Detection of Saccharomyces cerevisiae immobilized on self-assembled monolayer (SAM) of alkanethiolate using electrochemical impedance spectroscopy". Analytica Chimica Acta. 554 (1-2): 52–59. doi:10.1016/j.aca.2005.08.086.
19. Hollaender, J. (2009). "Rapid assessment of food/package interactions by electrochemical impedance spectroscopy (EIS)". Food Additives & Contaminants. 14 (6-7): 617–626. doi:10.1080/02652039709374574.
20. Mabrook, M.F.; Petty, M.C. (2003). "Effect of composition on the electrical conductance of milk". Journal of Food Engineering. 60 (3): 321–325. doi:10.1016/S0260-8774(03)00054-2.
21. Grossi, M.; Lanzoni, M.; Lazzarini, R.; Riccò, B. (2012). "Automatic ice-cream characterization by impedance measurements for optimal machine setting". Measurement. 45: 1747–1754. doi:10.1016/j.measurement.2012.04.009.
22. Grossi, M.; Lazzarini, R.; Lanzoni, M.; Riccò, B. (2011). "A novel technique to control ice-cream freezing by electrical characteristics analysis". Journal of Food Engineering. 106: 347–354. doi:10.1016/j.jfoodeng.2011.05.035.
23. Damez, J.L.; Clerion, S.; Abouelkaram, S.; Lepetit, J. (2008). "Beef meat electrical impedance spectroscopy and anisotropy sensing for non-invasive early assessment of meat ageing". Journal of Food Engineering. 85 (1): 116–122. doi:10.1016/j.jfoodeng.2007.07.026.
24. Rehman, M.; Abu Izneid, J.A.; Abdullha, M.Z.; Arshad, M.R. (2011). "Assessment of quality of fruits using impedance spectroscopy". International Journal of Food Science & Technology. 46 (6): 1303–1309. doi:10.1111/j.1365-2621.2011.02636.x.
25. Harker, F.R.; Forbes, S.K. (1997). "Ripening and development of chilling injury in persimmon fruit: An electrical impedance study". New Zealand Journal of Crop and Horticultural Science. 25 (2): 149–157. doi:10.1080/01140671.1997.9514001.
26. Bauchot, A.D.; Harker, F.R.; Arnold, W.M. (2000). "). The use of electrical impedance spectroscopy to assess the physiological condition of kiwifruit". Postharvest Biology and Technology. 18 (1): 9–18. doi:10.1016/S0925-5214(99)00056-3.
27. Grossi, M.; Di Lecce, G.; Gallina Toschi, T.; Riccò, B. (2014). "Fast and accurate determination of olive oil acidity by electrochemical impedance spectroscopy". IEEE Sensors Journal. 14 (9): 2947–2954. doi:10.1109/JSEN.2014.2321323.
28. Grossi, M.; Di Lecce, G.; Gallina Toschi, T.; Riccò, B. (2014). "A novel electrochemical method for olive oil acidity determination". Microelectronics Journal. 45: 1701–1707. doi:10.1016/j.mejo.2014.07.006.
29. Kyle, U.G.; Bosaeus, I.; De Lorenzo, A.D.; Deurenberg, P.; Elia, M.; Gomez, J.M.; Heitmann, B.L.; Kent-Smith, L.; Melchior, J.C.; Pirlich, M.; Scharfetter, H.; Schols, A.; Pichard, C. (2004). "Bioelectrical impedance analysis—part I: review of principles and methods". Clinical Nutrition. 23 (5): 1226–1243. doi:10.1016/j.clnu.2004.06.004.
30. Tengvall, M.; Ellegard, L.; Malmros, V.; Bosaeus, N.; Lissner, L.; Bosaeus, I. (2009). "Body composition in the elderly: Reference values and bioelectrical impedance spectroscopy to predict total body skeletal muscle mass". Clinical Nutrition. 28 (1): 52–58. doi:10.1016/j.clnu.2008.10.005.
31. Van Loan, M.D.; Withers, P.; Matthie, J.; Mayclin, P.L. Use of Bioimpedance Spectroscopy to Determine Extracellular Fluid, Intracellular Fluid, Total Body Water, and Fat-Free Mass. Chapter in Human Body Composition, Volume 60 of the series Basic Life Sciences. pp. 67–70.

• Basics of Electrochemical Impedance Spectroscopy
• Electrochimica Acta