Dielectric spectroscopy

Dielectric spectroscopy (which falls in a subcategory of impedance spectroscopy) measures the dielectric properties of a medium as a function of frequency.^[2][3][4][5] 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 is the opposition to the flow of

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

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

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,^[6] and chemical surrounding.

Ionic relaxation

Ionic relaxation comprises

For a redox reaction R ${\displaystyle \leftrightarrow }$ O + e, without mass-transfer limitation, the relationship between the current density and the electrode overpotential is given by the Butler–Volmer equation:^[7] $${\displaystyle j_{\text{t}}=j_{0}\left(\exp(\alpha _{\text{o}}\,f\,\eta )-\exp(-\alpha _{\text{r}}\,f\,\eta )\right)}$$ with $${\displaystyle \eta =E-E_{\text{eq}},\;f=F/(R\,T),\;\alpha _{\text{o}}+\alpha _{\text{r}}=1.}$$ ${\displaystyle j_{0}}$ is the exchange current density and ${\displaystyle \alpha _{\text{o}}}$ and ${\displaystyle \alpha _{\text{r}}}$ are the symmetry factors.

The curve ${\displaystyle j_{\text{t}}}$ vs. ${\displaystyle E}$ is not a straight line (Fig. 1), therefore a redox reaction is not a linear system.^[8]

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: $${\displaystyle j_{\text{t}}(t)=j_{\text{t}}(\eta (t))=j_{0}\left(\exp(\alpha _{\text{o}}\,f\,\eta (t))-\exp(-\alpha _{\text{r}}\,f\,\eta (t))\right)}$$

Dynamic behavior of the redox reaction is characterized by the so-called charge transfer resistance ${\displaystyle R_{\text{ct}}}$ defined by: $${\displaystyle R_{\text{ct}}={\frac {1}{\partial j_{\text{t}}/\partial \eta }}={\frac {1}{f\,j_{0}\,\left(\alpha _{\text{o}}\exp(\alpha _{\text{o}}\,f\,\eta )+\alpha _{\text{r}}\exp(-\alpha _{\text{r}}\,f\,\eta )\right)}}}$$

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: $${\displaystyle R_{\text{ct}}={\frac {1}{f\,j_{0}}}}$$ for ${\displaystyle \eta =0}$.

Double-layer capacitance

An electrode ${\displaystyle |}$ electrolyte interface behaves like a capacitance called

${\displaystyle C_{\text{dl}}}$

${\displaystyle C_{\text{dl}}}$

${\displaystyle R_{\text{ct}}}$

The electrical impedance of this circuit is easily obtained remembering the impedance of a capacitance which is given by: $${\displaystyle Z_{\text{dl}}(\omega )={\frac {1}{i\omega C_{\text{dl}}}}}$$ where ${\displaystyle \omega }$ is the angular frequency of a sinusoidal signal (rad/s), and ${\displaystyle i^{2}=-1}$.

It is obtained: $${\displaystyle Z(\omega )={\frac {R_{\text{t}}}{1+R_{\text{t}}C_{\text{dl}}i\omega }}}$$

Nyquist diagram of the impedance of the circuit shown in Fig. 3 is a semicircle with a diameter ${\displaystyle R_{\text{t}}}$ and an angular frequency at the apex equal to ${\displaystyle 1/(R_{\text{t}}\,C_{\text{dc}})}$ (Fig. 3). Other representations, Bode plots, or Black plans can be used.^[9]

Ohmic resistance

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

Universal dielectric response

Under AC conditions with varying frequency ω, heterogeneous systems and composite materials exhibit a universal dielectric response, in which overall admittance exhibits a region of power law scaling with frequency. ${\displaystyle Y\propto \omega ^{\alpha }}$.^[10]

Measurement of the impedance parameters

Plotting the Nyquist diagram with a potentiostat^[11] 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 ${\displaystyle j_{0}}$ can be easily determined measuring the impedance of a redox reaction for ${\displaystyle \eta =0}$.

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.^[12]

In the paint and coatings industry, it is a useful tool to investigate the quality of coatings^[13][14] and to detect the presence of corrosion.^[15][16]

It is used in many biosensor systems as a label-free technique to measure bacterial concentration^[17] and to detect dangerous pathogens such as Escherichia coli O157:H7^[18] and Salmonella,^[19] and yeast cells.^[20][21]

Electrochemical impedance spectroscopy is also used to analyze and characterize different food products. Some examples are the assessment of food–package interactions,

In the field of human health monitoring is better known as bioelectrical impedance analysis (BIA)^[31] and is used to estimate body composition^[32] as well as different parameters such as total body water and free fat mass.^[33]

Electrochemical impedance spectroscopy can be used to obtain the frequency response of batteries and electrocatalytic systems at relatively high temperatures.^[34][35][36]

Biomedical sensors working in the microwave range relies on dielectric spectroscopy to detect changes in the dielectric properties over a frequency range, such as non-invasive continuous blood glucose monitoring.^[37][38] The IFAC database can be used as a resource to get the dielectric properties for human body tissues.^[39]

For heterogenous mixtures like suspensions impedance spectroscopy can be used to monitor the particle sedimentation process.^[40]

See also

References