Dielectric spectroscopy

Dielectric spectroscopy ( also impedance spectroscopy) detects the dielectric properties of a medium as a function of frequency .. It is based on the interaction of an external electric field and the dipole moment of the medium investigated, which is given by the dielectric constant of the medium.

For the purposes of electrochemical impedance spectroscopy, the impedance of an electrochemical system, an electrolyte mainly investigated as a function of the frequency of an AC voltage.

• 2.1 Electrical

• 3.1 frequency domain spectroscopy (FDS )
• 3.2 Polarization and Depolarisationsstrommessung (PDC )
• 3.3 Schematic test

• 4.1 Evaluation using adaptation of model parameters
• 4.2 Analysis of electrochemical impedance spectroscopy

Dielectric mechanisms

There are different dielectric mechanisms according to the type, in which the examined medium reacts to the applied field, a distinction. Each of these mechanisms is connected to a frequency characteristic which is the inverse of the characteristic time of the process. Starting at high frequencies, the most important mechanisms are the following:

Electronic polarization

→ Main article: Polarization

Also referred to as electronic shifting polarization. This reaction takes place at neutral atoms when the applied electric field, the electron density is changed by the atomic nucleus. Figure 2 schematically shows a nuclear core including the electron shell in the absence of a field. In Figure 3, the state is seen in which a balance between the core and those of the binding forces the electric field prevails.

Atomic polarization

Atomic polarization occurs when the electron clouds can be deformed under the action of the forces of the electric field applied so that positive and negative charge regions formed. It is a resonance process.

Orientation polarization

→ Main article: orientation polarization

This effect originates in the permanent and induced dipoles, which are aligned in the electric field. Your orientation polarization is disturbed by thermal noise, which is not aligned with the electric field. The time required for relaxation, the dipoles determined by the local viscosity of the media. These two features make the dipole relaxation heavily dependent on the temperature and the chemical properties of the medium. Figure 4 shows dipoles in the absence of an electric field. In Figure 5 are shown aligned dipoles in the presence of an electric field.

Ionic Polarization

The ionic displacement polarization involves the ion conductivity and interfacial and space charge polarization. The ionic conductivity dominates at low frequencies, and due to system losses. Interfacial polarization occurs when charge carriers at interfaces meet in heterogeneous systems. Figure 6 shows an ion gate in the absence of an electric field. Figure 7 illustrates the ionic displacement polarization in the presence of an electric field

Dielectric relaxation

The dielectric relaxation as a whole is the result of movement of the dipole ( dipole relaxation ) and the carrier (ionic relaxation) caused by an applied alternating field. Is observed usually in the frequency ranges from 100 Hz to 10 GHz. Relaxation mechanisms are compared to resonance electronic transitions and molecular motion, which usually occur at frequencies above 1 THz, relatively slow.

Areas of application

In many areas where the inspection and assessment of material properties or system plays a role is the dielectric spectroscopy of importance. Application areas may include:

• Energy storage battery, double layer capacitor and fuel cell
• Biological and biomedical systems
• Geophysics ( Spectral Induced Polarization, SIP)
• Semiconductor
• Corrosion
• Surface Technology
• Kinetics

Electrical Engineering

From technical relevance, the dielectric spectroscopy is particularly important in the evaluation of insulation materials. These can be, for example cable insulation in the high-frequency or high-voltage technology, or even the oil-paper insulation in transformers and other high voltage equipment.

Measurement of the dielectric response

The dielectric in the dielectric spectroscopy response of a system in the frequency domain by use of two different methods can be determined. A combination of these methods described in the following is possible. This can be useful to outweigh the advantages and disadvantages of each method.

Frequency domain spectroscopy (FDS )

In the frequency domain spectroscopy (English and frequency-domain spectroscopy, FDS ) is exposed to an alternating field the system under investigation. The system response is recognized directly in the frequency domain. This method is particularly suitable for high frequencies.

Polarization and Depolarisationsstrommessung (PDC )

The polarization and Depolarisationsstrommessung (English Polarization Depolarization Current PDC) is exposed to a constant field to the system under investigation. The system response is determined from the measured polarization flows. These are transformed to the frequency domain. In particular at low frequencies, this method is advantageous.

Schematic test

For both methods, the same basic test setup is used. Here, a field is generated in a dielectric with a voltage source. With an ammeter, the current flowing through this medium flow is measured. A guard electrode is used, surface currents bypassing the measurement, so that only the volume flow is measured. This arrangement is shown in Figure 8. The investigation object ( dielectric) is application dependent.

Presentation and interpretation of measurement results

The impedance spectrum describes the transfer function of the system and can be represented as a Bode plot, or as a Nyquist diagram. Since in this case mainly occur capacities and rare inductors, the negative imaginary axis is usually applied to the top. Are typical curves for specific states in a system known as is often already a graphical analysis of the diagrams.

Evaluation by means of adjustment of model parameters

Is not sufficient, the graphical interpretation of the impedance spectrum (eg, in the Nyquist diagram ), it can be created for further analysis an equivalent circuit diagram of the system under investigation. The equivalent circuit diagram maps relevant to the investigation suspected chemical and physical processes. For example, a capacitor representing any existing electrochemical double layer. Besides the usual in electrical impedances (resistors, capacitors and inductors ) are other electrochemical phenomena may occur, caused for example by diffusion processes. To represent these phenomena in the model, additional elements such as the Warburg impedance or the Nernst impedance can be used.

The parameters of the equivalent circuit can be adjusted by using a curve fitting to the measured values ​​. Specifically tailored to the issues of impedance spectroscopy software that adapts the parameters with methods of nonlinear optimization exists for this calculation. The parameters of the fitted model or its change between various operating modes permit an interpretation about states and processes in the system.

Evaluation of an electrochemical impedance spectroscopy

As an example, an aqueous solution of iron (III) is - and iron ( II) ions are examined. In this solution emerges a working and counter electrode. Is applied to the electrodes to an AC voltage, several processes take place, which can be described by an equivalent circuit:

• In a double layer on the electrodes, the ions accumulate on or off. This layer will be described by means of a plate capacitor having the capacitance C.
• The AC voltage at the electrodes causes reversible redox reactions. Iron (III ) ions by electron micrograph to iron ( II ) ions and iron ( II) ions are oxidized by the electron emission. The absorption of electrons or electron donation to the electrodes requires an activation energy and is described by a charge transfer resistance Rd.
• Ions from the solution are transported to the electrodes and transported away from the electrodes. Here, the resistance of the solution plays a role, which is described by a resistor R.
• Due to the change of voltage change at the electrodes, the concentrations of the ions, which are reduced or oxidized. If the positive half sine wave at the working electrode, the oxidation takes place. Electrons are absorbed by the electrode. Is at the negative half cycle, then the reduction. Electrons are emitted from the electrode. The variations in concentration of the iron ( III) - and iron ( II ) ions cause a damped wave, which partially propagating in the solution. These can be described with a Warburg impedance element, which is a series circuit of a capacitor and a frequency-dependent loss of resistance in the ground.

The four impedance elements apply to the working electrode, but also on behalf of the counter electrode, since there run the same operations.

In the next step of evaluating the frequency-dependent behavior is calculated from assumed initial values ​​and compared with the measured data for each impedance element. Good agreement with a physical-chemical model is developed which describes the electrochemical system in detail, including the pressure and temperature. You can create, for comparison, a DC voltage to obtain even more information.