# Is water a good dielectric

Physical size
Surname dielectric conductivity or permittivity
Size type Tensor
Formula symbol of size
Size and
System of units
unit dimension
SI

The Permittivityε (from Latin: permitter = allow, leave, let through), too dielectric conductivity called, indicates the permeability of a material to electric fields. A permittivity is also assigned to the vacuum, since electrical fields can also develop or electromagnetic fields can propagate in the vacuum. The permittivity is the product of the Vacuum permittivityε0 and the relative permittivityεr:

εε0 · εr

This is where the relative permittivity the quantification of (mostly) field-weakening superposition effects of electrical fields within electrically insulating materials.

The designation Dielectric constant For Permittivity is considered obsolete and should no longer be used.

### Explanation of the permittivity using the example of insulating materials

Permittivity is a material property of electrically insulating, polar or non-polar substances, which are also called dielectrics. This property manifests itself when the substances are exposed to electrical fields, for example in a capacitor. When an electric field is applied to a capacitor filled with material, the charge carriers of the insulation material orient themselves on the electric field vector and form a polarization field that counteracts and weakens the external field. Assuming a given electrical excitation field, this phenomenon of field weakening can be described by adding a factor ε to the insulating materialr to the electric field constant ε0 (Permittivity of the vacuum). From the external electrical excitationD., also known as the electric flux density, is the result of the electric fieldE. with the permittivity ε to:

You can see that with the same electrical excitation D. and increasing values ​​of εr the electric field strength E. decreases. In this way, the field-weakening effect is detected with the same electrical excitation, i. H. for a given electrical flux density or a given electrical charge. Under the influence of a fixed voltage applied to the capacitor plates U and the electric field E.=U/d (Plate spacing d) results in the electrical excitation D. with the permittivity ε to:

In electrodynamics and also in electrostatics, the permittivity is used to describe the above. Phenomena used as a proportionality factor in the relationship between electrical excitation and electrical field strength

In matter, this equation only represents the lowest order of a generally non-linear relationship: In the case of large field strengths, one either understands the permittivity as dependent on the field strength and writes it down ε (E), or one leads alongside ε = ε(1) further Taylor coefficients, ε(2) etc., which the field strength dependence of D. describes:

In a vacuum, the reference material for an insulating material is the relative permittivity

### Vacuum permittivity

The permittivity of the vacuum ε0 is based on the current German-language draft of the international size system as electric field constant designated. Further designations are:

• electrical constant (mainly from the translation of the term commonly used in English-speaking countries electric constant)
• Dielectric constant of the vacuum (no longer recommended)
• Influence constant (outdated)

In a vacuum there is between the magnetic field constantμ0, the electric field constant ε0 and the speed of light in vacuum c0 the following relationship predicted by Maxwell and confirmed experimentally in 1857 by Wilhelm Eduard Weber and Rudolf Kohlrausch:

.

With the (by definition) exactly known constants of nature and as well as the circle number Pi with π = 3.141592654 ..., the permittivity of the vacuum can be calculated from this with any precision:

In addition to Coulomb's law, Ampère's law and Faraday's law of induction, this relationship represents a further link between electromagnetic and mechanical units that must be taken into account when choosing an electromagnetic system of units.

In systems of units that explicitly trace the electromagnetic variables back to mechanical basic variables, namely the various variants of the CGS system of units ε0 chosen as a dimensionless number:

(Heaviside-Lorentz system of units),

(electrostatic, electromagnetic or Gaussian system of units; in this system the 4π based on Coulomb's law).

In the SI system, the electromagnetic values ​​are traced back to the mechanical values ​​in the definition of the current strength (ampere), which amounts to the magnetic permeability of the vacuum as

is defined, from which it follows

### Relative permittivity

In addition to the designation relative permittivity For εr the following terms are still in use:

• Permittivity number
• Dielectric constant (no longer recommended)
• Dielectric constant (should be avoided because εr a dimensionless one number and no dimensional constant represents)

Only for isotropic media at constant temperature and constant frequency of the electric field is εr a static, scalar quantity. In this simplest case, it indicates the factor by which the voltage on a capacitor drops if not only a vacuum (or, with little error, simply air), but a dielectric, non-conductive material is placed between the capacitor plates.

### Relative permittivity in crystalline structures

Generally is εr however, a second order tensor, which reflects the crystalline (or differently ordered) structure of matter and thus the directional dependence of the factors. The tensor property of permittivity is the basis for crystal optics.

The relative permittivity εr is a second level tensor (and thus as a function of the direction of light propagation relative to marked crystal axes), which is dependent on the frequency (i.e. when considering light on its wavelength) as well as on the external electric field and magnetic fields, and will also be dielectric function called. Especially in English, the size symbol is also used κ used (see low-k dielectric or high-k dielectric).

### Frequency dependence of the relative permittivity

The permittivity in matter is frequency-dependent and can, for example, be modeled quite well using the simple model of the Lorentz oscillator. This frequency dependence is called dispersion. Tables usually give the numerical value at low frequencies (order of magnitude Hz – kHz, depending on the measurement method, possibly MHz) at which the molecular dipoles (and a forteriori the atomic electron orbitals) can follow the external field. The way in which the molecules remain in relation to the high-frequency electric field is described macroscopically with a complex relative permittivity.

### Complex-valued relative permittivity

The relative permittivity εr is generally complex valued. Just as with constant fields, polarization fields also form in dielectrics with alternating fields, but these may lag behind the applied external field size by a certain phase angle. The orientation of the charge carriers in the dielectric remains in the phase (in time) behind the polarization of the applied alternating field. This effect becomes stronger with increasing frequency. It is easy to imagine that alternating fields of high frequency generate heat losses through rapid, recurring repolarization in insulating materials. At even higher frequencies, with which charge carriers in the ribbon model of a crystal can be excited, energy is also absorbed. These phenomena are taken into account in that the relative permittivity has a complex value with:

is described, whereby the dielectric losses are recorded via the imaginary part of the permittivity. A widespread application that takes advantage of the dielectric loss phenomenon is in the microwave oven. The power loss density with dielectric heating is, based on the material volume:

The dielectric heating associated with the power loss, when integrated over the heating period, corresponds exactly to the internal energy of a material supplied to a material volume with electromagnetic waves, as described in thermodynamics. The imaginary part of the complex-valued, relative permittivity is a measure of the ability of a substance to convert electromagnetic field energy into heat energy at high frequencies.

### Temperature dependence

Temperature-dependent, for example, is the complex-valued relative permittivity of water, the real part of which assumes a value of about eighty at room temperature and about fifty-five at 95 ° C. The decrease in permittivity with increasing temperature is related to the degree of disorder of the charge carriers when the internal energy increases. From a molecular point of view, the polarizability decreases due to the increasing intrinsic movement of the charge carriers with higher internal energy; From a macroscopic point of view, the relative permittivity therefore decreases with an increase in temperature.

### Relative permittivity of selected materials

medium εr medium εr
vacuum 1,0 air 1,00059
Acrylic butadiene styrene (ABS) (30 ° C) 4,3 Aluminum oxide (clay) 7
Ammonia (0 ° C) 1,007 Barium titanate 103–104
benzene 2,28 Dry earth 3,9
Damp earth 29 Glass 6–8
Glycerin 42,5 rubber 2,5–3
dry wood 2–3,5 Potassium chloride 4,94
special ceramics up to 10,000 Methanol 32,6
petroleum 2 Polyethylene (PE) (90 ° C) 2,4
Polypropylene (PP) (90 ° C) 2,1 porcelain 2–6
Propanol 18,3 paraffin 2,2
paper 1–4 Polytetrafluoroethylene
(PTFE or also Teflon)
2
Pertinax FR4 (epoxy resin) 4,3–5,4 Polystyrene foam
(Styropor ® BASF)
1,03
Tantalum pentoxide 27 water 80,1
Water (f = 2.54 GHz) 77 Water (visible area) 1,77
Ice (−20 ° C) ≈ 100 Ice (−20 ° C, f> 100 kHz) 3,2

Tabulated, comprehensive overviews of frequency- and temperature-dependent, complex relative permittivities of many materials can be found in [1] and especially in [2]

### Generalizations about dispersion, directional dependence and magnetic field

A relationship between the refractive index, the electrical permittivity and the magnetic permeability follows from Maxwell's equations,

Here are ε and μ at the relevant optical frequency (in the range of 1015 Hz). For gaseous, liquid and solid matter it is εr greater one. However, in other states of matter, e.g. B. in plasma (so-called "fourth aggregate state"), also values ​​that can be less than one.

In dispersive materials one has to do with the reaction of the material to electromagnetic fields with the frequency of light, i.e. very high frequencies over a wide frequency range. Here, the relationship between the refractive index and that measured at low frequencies must be ε formulated in a much more general way and take into account the frequency dependency (see Lorentz oscillator). In this way, absorption and reflection spectra of materials can be displayed well.

The dielectric constant is used as a complex variable, with a real part ε1 (also ε ’or εr, not to be confused with r For relative) and an imaginary part ε2 (also ε ’’ or εi). The contributions of various mechanisms in the material (e.g. band transitions) can be specified directly in these two components and their frequency dependency can be added - a more detailed representation can be found under electrical susceptibility. The (dispersive) relationship between the complex dielectric constant and the optical parameters, refractive index, can then be determined via the Kramers-Kronig relation n and absorption coefficientk being represented. This leads to the theoretical spectra of absorption and reflection, which can be compared and adapted with measured spectra.

For the calculation of such Spectra (from reflection or absorption) can in the case of (non-magnetic material) the sizes n and k the complex refractive index can be determined directly from the real and imaginary parts of the permittivity:

or.

vice versa:

or.

Likewise, i.a. the reflectance R. be calculated:

Due to their crystal structure, the properties of some materials are directional, e.g. B. birefringent materials. These materials find i.a. Application with retardation plates. Mathematically, this property can be captured by representation in tensor form, with components for the individual directions. These, in turn, are to be assessed as frequency-dependent and even to different degrees depending on the direction. In addition to the “natural” directional dependence, the properties can also cause a similar directional dependency through external influences such as a magnetic field (see magneto-optics) or pressure.

### Individual evidence

1. A. C. Metaxas, R. J. Meredith: "Industrial Microwave Heating (IEE Power Engineering Series)" Institution of Engineering and Technology, 1983, ISBN 0-90604-889-3.
2. Arthur von Hippel, Editor: "Dielectric Materials and Applications" Artech House, London, 1954, ISBN 0-89006-805-4.

### literature

• H. Frohne: Introduction to Electrical Engineering, Volume 2: Electric and Magnetic Fields. 4th edition. Teubner, Stuttgart, 1983, ISBN 3-519-30002-8.
• Károly Simonyi: Theoretical electrical engineering. 10th edition. Barth Publishing Company, 1993, ISBN 3-335-00375-6.
• Arthur von Hippel, editor: Dielectric Materials and Applications. Artech House, London, 1954, ISBN 0-89006-805-4.
• Arthur von Hippel: Dielectrics and Waves. Artech House, London, 1954, ISBN 0-89006-803-8.
• A. C. Metaxas, R. J. Meredith: Industrial Microwave Heating (IEE Power Engineering Series). Institution of Engineering and Technology, 1983, ISBN 0-90604-889-3.
• A. C. Metaxas: Foundations of Electroheat, A Unified Approach. John Wiley and Sons, 1996, ISBN 0-471-95644-9.
• Feynman, Leighton, Sands: The Feynman Lectures on Physics, Volume II. 6. Unchanged edition. Addison Wesley, 1977, ISBN 0-201-02117-X.

Categories: Electrodynamics | Vacuum technology