# Polarization (electricity)

Physical size
Surname polarization
Formula symbol ${\ displaystyle {\ vec {P}}}$
Size and
unit system
unit dimension
SI A · s · m -2 I · L −2 · T

Polarization (or dielectric polarization ) is a physical quantity from electrodynamics that characterizes the strength of the dipole moment in a dielectric material .

Even with non-conductive materials, the application of an external electric field shifts electric charges over short distances in the order of magnitude of an atomic distance. In electrical conductors, this shift can be carried out for significantly longer distances and induction called. In both cases, a macroscopic charge distribution (polarization charges or bound charges) can be measured on the surfaces.

## Mechanisms

Exemplary curve of the complex relative permittivity over a wide frequency range (assumption: the material contains movable dipole molecules). The real part (red) used to be called the relative dielectric constant , although it is strongly frequency-dependent. The imaginary part (blue) is a measure of the energy loss in the dielectric. The prominent points are called resonances , in the vicinity of which dispersion is observed.

All matter is made up of charged building blocks of very different mass. In non-conductors, these building blocks are bound to their environment, but can still move in different ways:

• Dipole molecules can be permanently oriented with direct voltage . Use in the electret microphone .
• At very low frequencies (<10 3  Hz) ions can occasionally change places and remain there even after the external field has been switched off ( dielectric absorption ). Energy is consumed in the process, which is why it assumes high values. Because of the high mass of the ions, these rapid field changes cannot follow and the effect disappears above 10 5  Hz.${\ displaystyle {\ varepsilon _ {r} ''}}$
• As the frequency increases, dipole molecules are stimulated to periodically flip over at around 10 10  Hz - provided they are present and not held in place by a crystal lattice such as ice. In the microwave oven, for example, there is enormous friction between neighboring water molecules.
• Molecules without a dipole moment cannot be heated in this way and are therefore suitable as insulating material in high-frequency capacitors. In these materials no resonance  can be measured at 10 10 Hz.
• At 10 12  Hz the ions oscillate around their positions of rest in the molecule. Because the deflections are limited to fractions of an atomic diameter, the maximum possible polarization is quite small. The curved course is a characteristic sign of resonance and the accompanying phase shift. Resonance is invariably associated with absorption.${\ displaystyle {\ varepsilon _ {r} '}}$
• In the vicinity of visible light at 10 15  Hz one observes resonances of the electrons in the electric field of the atomic nucleus. This leads to changes in the direction of light waves in glass ( refractive index ) and to color filters.
• In the UV region at frequencies above 10 16  Hz, electrical polarization effects are no longer observed.

### Displacement polarization

The atomic nucleus (positive center of charge) is drawn by an external field to the left of the negative center of charge (electron shell).

Electronic polarization: For non-polar molecules, the electron cloud , which the atomic nucleus , surrounded by the applied external electric field against the atomic core moved. This creates a macroscopic, inhomogeneous charge distribution inside the body. As soon as the external field disappears, the locations of the centers of gravity are identical again. If it is an alternating electric field (see microwave oven ), no heat energy is generated by the swinging back and forth of the core .

### Orientation polarization

Dipole moment of an H 2 O molecule.
red: negative partial charge
blue: positive partial charge
green: directional dipole

In some types of molecules, such as water , the focal points of the positive and negative electrical charges are clearly separated from one another. One then speaks of dipole molecules or permanent dipoles, the directions of which are statistically distributed in the ground state. A technically significant exception are the electrets , which contain permanently aligned electrical dipoles.

Due to the action of an external electric field, these dipoles are increasingly rectified, the stronger this field is. This type of polarization takes place slowly because of the large masses to be moved; it is also temperature-dependent. An increase in temperature disturbs the same alignment more and more. As the frequency of the electric field increases, this polarization is the first to disappear. In contrast, the shift polarization is only weakly dependent on the temperature.

### Ion polarization

The electrostatic field shifts the positive and negative ions of a previously neutral molecule against each other within the ion lattice, so that a dipole is created. Examples are inorganic insulating materials or capacitor ceramics.

### Piezoelectricity

In some dielectrics, mechanical stress can generate electrical polarization. Applications are piezo lighter , force sensors and - because the effect is reversible - quartz oscillators .

### Space charge polarization / interface polarization

It is assumed here that free charge carriers (positive + negative ions, electrons) are present in a dielectric. Without an external field, the individual charges cancel each other out and the dielectric has an electrically neutral effect on the outside. After applying the external field, charge carriers move to the electrode of opposite polarity. A “macroscopic dipole” forms. Cross interfaces can hinder this migration. The charge separation within a layer has the same effect on the outside. Example: oil-paper insulation, inclusions in the dielectric

## Quantitative consideration

Polarization refers to the vector field that results from a permanent or induced dipole moment in a dielectric material . The polarization vector is defined as the dipole moment per volume. ${\ displaystyle {\ vec {P}}}$

The dependence of polarization on the electric field is generally non-linear and anisotropic: ${\ displaystyle {\ vec {P}}}$${\ displaystyle {\ vec {E}}}$

${\ displaystyle P_ {i} / \ varepsilon _ {0} = \ sum _ {j} \ chi _ {ij} ^ {(1)} E_ {j} + \ sum _ {jk} \ chi _ {ijk} ^ {(2)} E_ {j} E_ {k} + \ sum _ {jk \ ell} \ chi _ {ijk \ ell} ^ {(3)} E_ {j} E_ {k} E _ {\ ell} + \ cdots \!}$

They are tensors -th level, is the vacuum dielectric constant . describes the linear susceptibility , is responsible for the Pockels effect and for the Kerr effect . ${\ displaystyle \ chi ^ {(i)}}$ ${\ displaystyle (i + 1)}$${\ displaystyle \ varepsilon _ {0}}$${\ displaystyle \ chi ^ {(1)}}$${\ displaystyle \ chi ^ {(2)}}$${\ displaystyle \ chi ^ {(3)}}$

In a homogeneous linear isotropic dielectric medium , the polarization is parallel and proportional to the electric field : ${\ displaystyle {\ vec {E}}}$

${\ displaystyle {\ vec {P}} = \ varepsilon _ {0} \ chi {\ vec {E}}}$

where is the electrical susceptibility of the medium, d. H. and for . ${\ displaystyle \ chi}$${\ displaystyle \ chi _ {ij} ^ {(1)} = \ chi \, \ delta _ {ij}}$${\ displaystyle \ chi ^ {(i)} = 0}$${\ displaystyle i \ geq 2}$

If the polarization is not proportional to the electric field , then the medium is called nonlinear (see also: nonlinear optics ). If the direction of from is not parallel to that of from , as is the case in many crystals, the medium is anisotropic (see also: crystal optics ). ${\ displaystyle {\ vec {P}}}$${\ displaystyle {\ vec {E}}}$${\ displaystyle {\ vec {P}}}$${\ displaystyle {\ vec {E}}}$

The above-mentioned types of polarization add up to a total polarization or total susceptibility:

${\ displaystyle \, \ chi = \ chi _ {\ text {electron}} + \ chi _ {\ text {ion}} + \ chi _ {\ text {orientation}}}$

The individual susceptibilities are frequency-dependent. For low frequencies, all parts contribute. At higher frequencies, the orientation polarization disappears first (the molecules can no longer rotate with the rapidly changing E-field, e.g. from the microwave range), then the ionic polarization (the ions can no longer follow the field due to their inertia, e.g. from the infrared range) and finally the electronic polarization (approximately from the UV range), so that the overall susceptibility in the maximum frequency range drops to zero.