Dielectric spectroscopy

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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. Dielectric responses.svg
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.

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.

Dielectric electrically poorly conducting or non-conducting, non-metallic substance of which charge carriers are generally not free to move

A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material as they do in an electrical conductor but only slightly shift from their average equilibrium positions causing dielectric polarization. Because of dielectric polarization, positive charges are displaced in the direction of the field and negative charges shift in the opposite direction. This creates an internal electric field that reduces the overall field within the dielectric itself. If a dielectric is composed of weakly bonded molecules, those molecules not only become polarized, but also reorient so that their symmetry axes align to the field.

Frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency. The period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example: if a newborn baby's heart beats at a frequency of 120 times a minute, its period—the time interval between beats—is half a second. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light.

Electric dipole moment vector physical quantity

The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity. The SI units for electric dipole moment are coulomb-meter (C⋅m); however, the most commonly used unit in atomic physics and chemistry is the debye (D).

Contents

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.

Electrical impedance intensive physical property

Electrical impedance is the measure of the opposition that a circuit presents to a current when a voltage is applied. The term complex impedance may be used interchangeably.

Spectroscopy study of the interaction between matter and electromagnetic radiation

Spectroscopy is the study of the interaction between matter and electromagnetic radiation. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, by a prism. Later the concept was expanded greatly to include any interaction with radiative energy as a function of its wavelength or frequency, predominantly in the electromagnetic spectrum, though matter waves and acoustic waves can also be considered forms of radiative energy; recently, with tremendous difficulty, even gravitational waves have been associated with a spectral signature in the context of LIGO and laser interferometry. Spectroscopic data are often represented by an emission spectrum, a plot of the response of interest as a function of wavelength or frequency.

Bode plot graph of the frequency response of a linear system presented in logarithmic scale

In electrical engineering and control theory, a Bode plot is a graph of the frequency response of a system. It is usually a combination of a Bode magnitude plot, expressing the magnitude of the frequency response, and a Bode phase plot, expressing the phase shift.

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. Materials or systems exhibiting multiple phases (such as composites or heterogeneous materials) commonly show a universal dielectric response, whereby dielectric spectroscopy reveals a power law relationship between the impedance (or the inverse term, admittance) and the frequency, ω, of the applied AC field.

Alternating current electric voltage which periodically reverses direction; form in which electric power is delivered to businesses and residences; form of electrical energy that consumers typically use when they plug electric appliances into a wall socket

Alternating current (AC) is an electric current which periodically reverses direction, in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in which electric power is delivered to businesses and residences, and it is the form of electrical energy that consumers typically use when they plug kitchen appliances, televisions, fans and electric lamps into a wall socket. A common source of DC power is a battery cell in a flashlight. The abbreviations AC and DC are often used to mean simply alternating and direct, as when they modify current or voltage.

Resistor Passive electrical component providing electrical resistance

A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active elements, and terminate transmission lines, among other uses. High-power resistors that can dissipate many watts of electrical power as heat, may be used as part of motor controls, in power distribution systems, or as test loads for generators. Fixed resistors have resistances that only change slightly with temperature, time or operating voltage. Variable resistors can be used to adjust circuit elements, or as sensing devices for heat, light, humidity, force, or chemical activity.

Capacitor electrical component used to store energy for a short period of time

A capacitor is a passive two-terminal electronic component that stores electrical energy in an electric field. The effect of a capacitor is known as capacitance. While some capacitance exists between any two electrical conductors in proximity in a circuit, a capacitor is a component designed to add capacitance to a circuit. The capacitor was originally known as a condenser or condensator. The original name is still widely used in many languages, but not commonly in English.

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.

Electrochemical cell device capable of either generating electrical energy from chemical reactions or facilitating chemical reactions through the introduction of electrical energy

An electrochemical cell is a device capable of either generating electrical energy from chemical reactions or using electrical energy to cause chemical reactions. The electrochemical cells which generate an electric current are called voltaic cells or galvanic cells and those that generate chemical reactions, via electrolysis for example, are called electrolytic cells. A common example of a galvanic cell is a standard 1.5 volt cell meant for consumer use. A battery consists of one or more cells, connected either in parallel, series or series-and-parallel pattern.

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.

Fuel cell device that converts the chemical energy from a fuel into electricity

A fuel cell is an electrochemical cell that converts the potential energy from a fuel into electricity through an electrochemical reaction of hydrogen fuel with oxygen or another oxidizing agent. Fuel cells are different from batteries in requiring a continuous source of fuel and oxygen to sustain the chemical reaction, whereas in a battery the chemical energy comes from chemicals already present in the battery. Fuel cells can produce electricity continuously for as long as fuel and oxygen are supplied.

Dielectric mechanisms

Dielectrics spectroscopy machine CSIRO ScienceImage 10377 Dielectrics.jpg
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:

The characteristic time is an estimate of the order of magnitude of the reaction time scale of a system. It can loosely be defined as the inverse of the reaction rate. In chemistry, the characteristic time is used to determine whether the problem needs to be solved as an equilibrium problem or a kinetic problem.

Resonance phenomenon in which a vibrating system or external force drives another system to oscillate with greater amplitude at specific frequencies

In mechanical systems, resonance is a phenomenon that occurs when the frequency at which a force is periodically applied is equal or nearly equal to one of the natural frequencies of the system on which it acts. This causes the system to oscillate with larger amplitude than when the force is applied at other frequencies.

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, [6] 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. [2]

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 O + e, without mass-transfer limitation, the relationship between the current density and the electrode overpotential is given by the Butler–Volmer equation: [7]

with

.
is the exchange current density and and are the symmetry factors.
Fig. 1: Steady-state current density vs. overpotential for a redox reaction ButlerVolmer1.png
Fig. 1: Steady-state current density vs. overpotential for a redox reaction

The curve 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:

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

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:

for .

Double layer capacitance

An electrode electrolyte interface behaves like a capacitance called electrochemical double-layer capacitance . The equivalent circuit for the redox reaction in Fig. 2 includes the double-layer capacitance as well as the charge transfer resistance. 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 CircuitRctCdlparallele.png
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:

where is the angular frequency of a sinusoidal signal (rad/s), and .

It is obtained:

Nyquist diagram of the impedance of the circuit shown in Fig. 3 is a semicircle with a diameter and an angular frequency at the apex equal to (Fig. 3). Other representations, Bode plots, or Black plans can be used. [9]

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

Ohmic resistance

The ohmic resistance 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. . [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 can be easily determined measuring the impedance of a redox reaction for .

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, [22] the analysis of milk composition, [23] the characterization and the determination of the freezing end-point of ice-cream mixes, [24] [25] the measure of meat ageing, [26] the investigation of ripeness and quality in fruits [27] [28] [29] and the determination of free acidity in olive oil. [30]

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. [34] [35]

Biomedical sensors working in the microwave range relies on dielectric spectroscopy to detect changes in the dielectric properties over a frequency range. The IFAC database can be used as a resource to get the dielectric properties for human body tissues. [36]

See also

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References

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