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The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A
dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the ma ...
is an insulating material, and the dielectric constant of an insulator measures the ability of the insulator to store electric energy in an electrical field. Permittivity is a material's property that affects the Coulomb force between two point charges in the material. Relative permittivity is the factor by which the electric field between the charges is decreased relative to vacuum. Likewise, relative permittivity is the ratio of the
capacitance Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are ...
of a
capacitor A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals. The effect of ...
using that material as a
dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the ma ...
, compared with a similar capacitor that has vacuum as its dielectric. Relative permittivity is also commonly known as the dielectric constant, a term still used but deprecated by standards organizations in engineering as well as in chemistry.


Definition

Relative permittivity is typically denoted as (sometimes , lowercase kappa) and is defined as :\varepsilon_(\omega) = \frac, where ''ε''(''ω'') is the complex frequency-dependent permittivity of the material, and ''ε''0 is the vacuum permittivity. Relative permittivity is a dimensionless number that is in general
complex-valued In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form ...
; its real and imaginary parts are denoted as: : \varepsilon_r(\omega) = \varepsilon_'(\omega) - i \varepsilon_''(\omega). The relative permittivity of a medium is related to its electric susceptibility, , as . In anisotropic media (such as non cubic crystals) the relative permittivity is a second rank tensor. The relative permittivity of a material for a
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
of zero is known as its static relative permittivity.


Terminology

The historical term for the relative permittivity is ''dielectric constant''. It is still commonly used, but has been deprecated by standards organizations, because of its ambiguity, as some older reports used it for the absolute permittivity ε. The permittivity may be quoted either as a static property or as a frequency-dependent variant, in which case it is also known as the ''dielectric function''. It has also been used to refer to only the real component ε'r of the complex-valued relative permittivity.


Physics

In the causal theory of waves, permittivity is a complex quantity. The imaginary part corresponds to a phase shift of the polarization relative to and leads to the attenuation of electromagnetic waves passing through the medium. By definition, the linear relative permittivity of vacuum is equal to 1, that is ε = ε0, although there are theoretical nonlinear quantum effects in vacuum that become non-negligible at high field strengths. The following table gives some typical values. The relative permittivity of ice is ~3.15.


Measurement

The relative static permittivity, ''εr'', can be measured for static electric fields as follows: first the
capacitance Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are ...
of a test
capacitor A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals. The effect of ...
, ''C''0, is measured with vacuum between its plates. Then, using the same capacitor and distance between its plates, the capacitance ''C'' with a
dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the ma ...
between the plates is measured. The relative permittivity can be then calculated as :\varepsilon_ = \frac. For time-variant electromagnetic fields, this quantity becomes
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
-dependent. An indirect technique to calculate ''εr'' is conversion of radio frequency S-parameter measurement results. A description of frequently used S-parameter conversions for determination of the frequency-dependent ''εr'' of dielectrics can be found in this bibliographic source. Alternatively, resonance based effects may be employed at fixed frequencies.


Applications


Energy

The relative permittivity is an essential piece of information when designing
capacitor A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals. The effect of ...
s, and in other circumstances where a material might be expected to introduce
capacitance Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are ...
into a circuit. If a material with a high relative permittivity is placed in an electric field, the magnitude of that field will be measurably reduced within the volume of the dielectric. This fact is commonly used to increase the capacitance of a particular capacitor design. The layers beneath etched conductors in printed circuit boards ( PCBs) also act as dielectrics.


Communication

Dielectrics are used in
radio frequency Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the up ...
(RF) transmission lines. In a coaxial cable, polyethylene can be used between the center conductor and outside shield. It can also be placed inside waveguides to form
filters Filter, filtering or filters may refer to: Science and technology Computing * Filter (higher-order function), in functional programming * Filter (software), a computer program to process a data stream * Filter (video), a software component that ...
.
Optical fibers An optical fiber, or optical fibre in Commonwealth English, is a flexible, transparent fiber made by drawing glass ( silica) or plastic to a diameter slightly thicker than that of a human hair. Optical fibers are used most often as a mea ...
are examples of ''dielectric waveguides''. They consist of dielectric materials that are purposely doped with impurities so as to control the precise value of ''εr'' within the cross-section. This controls the
refractive index In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, ...
of the material and therefore also the optical modes of transmission. However, in these cases it is technically the relative permittivity that matters, as they are not operated in the electrostatic limit.


Environment

The relative permittivity of air changes with temperature, humidity, and barometric pressure. Sensors can be constructed to detect changes in capacitance caused by changes in the relative permittivity. Most of this change is due to effects of temperature and humidity as the barometric pressure is fairly stable. Using the capacitance change, along with the measured temperature, the relative humidity can be obtained using engineering formulas.


Chemistry

The relative static permittivity of a solvent is a relative measure of its chemical polarity. For example,
water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as ...
is very polar, and has a relative static permittivity of 80.10 at 20 °C while ''n''-
hexane Hexane () is an organic compound, a straight-chain alkane with six carbon atoms and has the molecular formula C6H14. It is a colorless liquid, odorless when pure, and with boiling points approximately . It is widely used as a cheap, relative ...
is non-polar, and has a relative static permittivity of 1.89 at 20 °C. This information is important when designing separation, sample preparation and chromatography techniques in analytical chemistry. The correlation should, however, be treated with caution. For instance, dichloromethane has a value of εr of 9.08 (20 °C) and is rather poorly soluble in water (13g/L or 9.8mL/L at 20 °C); at the same time, tetrahydrofuran has its εr = 7.52 at 22 °C, but it is completely miscible with water. In the case of tetrahydrofuran, the oxygen atom can act as a hydrogen bond acceptor; whereas dichloromethane cannot form hydrogen bonds with water. This is even more remarkable when comparing the εr values of acetic acid (6.2528)AE. Frisch, M. J. Frish, F. R. Clemente, G. W. Trucks. Gaussian 09 User's Reference. Gaussian, Inc.: Walligford, CT, 2009.- p. 257. and that of iodoethane (7.6177). The large numerical value of εr is not surprising in the second case, as the iodine atom is easily polarizable; nevertheless, this does not imply that it is polar, too (electronic polarizability prevails over the orientational one in this case).


Lossy medium

Again, similar as for absolute permittivity, relative permittivity for lossy materials can be formulated as: : \varepsilon_r = \varepsilon_r' - \frac, in terms of a "dielectric conductivity" ''σ'' (units S/m, siemens per meter), which "sums over all the dissipative effects of the material; it may represent an actual lectricalconductivity caused by migrating charge carriers and it may also refer to an energy loss associated with the dispersion of ''ε''′ he real-valued permittivity ( p. 8). Expanding the
angular frequency In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit ti ...
''ω'' = 2π''c/λ'' and the electric constant ''ε''0 = 1/''µ''0''c''2, which reduces to: : \varepsilon_r = \varepsilon_r' - i\sigma\lambda\kappa, where ''λ'' is the wavelength, ''c'' is the speed of light in vacuum and ''κ'' = ''µ''0''c''/2π = 59.95849 Ω ≈ 60.0 Ω is a newly introduced constant (units
ohm Ohm (symbol Ω) is a unit of electrical resistance named after Georg Ohm. Ohm or OHM may also refer to: People * Georg Ohm (1789–1854), German physicist and namesake of the term ''ohm'' * Germán Ohm (born 1936), Mexican boxer * Jörg Ohm (bor ...
s, or reciprocal siemens, such that ''σλκ'' = ''ε''r remains unitless).


Metals

Permittivity is typically associated with
dielectric materials In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mater ...
, however metals are described as having an effective permittivity, with real relative permittivity equal to one. equation (4.6), page 121 In the low-frequency region, which extends from radio frequencies to the far
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of Light, visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from ...
and terahertz region, the plasma frequency of the electron gas is much greater than the electromagnetic propagation frequency, so the refractive index ''n'' of a metal is very nearly a purely imaginary number. In the low frequency regime, the effective relative permittivity is also almost purely imaginary: It has a very large imaginary value related to the conductivity and a comparatively insignificant real-value.Lourtioz (2005), equations (4.8)–(4.9), page 122


See also

* Curie temperature * Dielectric spectroscopy * Dielectric strength * Electret * Ferroelectricity *
Green–Kubo relations The Green–Kubo relations (Melville S. Green 1954, Ryogo Kubo 1957) give the exact mathematical expression for transport coefficients \gamma in terms of integrals of time correlation functions: :\gamma = \int_0^\infty \left\langle \dot(t) \dot(0 ...
* High-κ dielectric * Kramers–Kronig relation * Linear response function * Low-κ dielectric * Loss tangent * Permittivity *
Refractive index In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, ...
* Permeability (electromagnetism)


References

{{DEFAULTSORT:Relative Permittivity Electricity Electric and magnetic fields in matter Colloidal chemistry