Relative permittivity

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 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

Likewise, relative permittivity is the ratio of the capacitance of a capacitor using that material as a dielectric, 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^[15] as well as in chemistry.^[16]

Definition

Relative permittivity is typically denoted as ε_r(ω) (sometimes κ, lowercase kappa) and is defined as

${\displaystyle \varepsilon _{\text{r}}(\omega )={\frac {\varepsilon (\omega )}{\varepsilon _{0}}},}$

where ε(ω) is the complex frequency-dependent permittivity of the material, and ε₀ is the vacuum permittivity.

Relative permittivity is a dimensionless number that is in general complex-valued; its real and imaginary parts are denoted as:^[17]

${\displaystyle \varepsilon _{\text{r}}(\omega )=\varepsilon _{\text{r}}'(\omega )-i\varepsilon _{\text{r}}''(\omega ).}$

The relative permittivity of a medium is related to its electric susceptibility, χ_e, as ε_r(ω) = 1 + χ_e.

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 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,^[15][16] because of its ambiguity, as some older reports used it for the absolute permittivity ε.^[15][18][19] 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.^{[citation needed]}

Physics

In the causal theory of waves, permittivity is a complex quantity. The imaginary part corresponds to a phase shift of the polarization P relative to E and leads to the attenuation of electromagnetic waves passing through the medium. By definition, the linear relative permittivity of vacuum is equal to 1,^[19] that is ε = ε₀, although there are theoretical nonlinear quantum effects in vacuum that become non-negligible at high field strengths.^[20]

The following table gives some typical values.

The relative low frequency permittivity of ice is ~96 at −10.8 °C, falling to 3.15 at high frequency, which is independent of temperature.^[21] It remains in the range 3.12–3.19 for frequencies between about 1 MHz and the far infrared region.^[22]

Measurement

The relative static permittivity, ε_r, can be measured for static electric fields as follows: first the capacitance of a test capacitor, C₀, is measured with vacuum between its plates. Then, using the same capacitor and distance between its plates, the capacitance C with a dielectric between the plates is measured. The relative permittivity can be then calculated as

${\displaystyle \varepsilon _{\text{r}}={\frac {C}{C_{0}}}.}$

For time-variant

The relative permittivity is an essential piece of information when designing capacitors, and in other circumstances where a material might be expected to introduce capacitance 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

The relative permittivity of air changes with temperature, humidity, and barometric pressure.[25] 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

The correlation should, however, be treated with caution. For instance, dichloromethane has a value of ε_r of 9.08 (20 °C) and is rather poorly soluble in water (13 g/L or 9.8 mL/L at 20 °C); at the same time, tetrahydrofuran has its ε_r = 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 ε_r values of

where λ is the wavelength, c is the speed of light in vacuum and κ = µ₀c / 2π = 59.95849 Ω ≈ 60.0 Ω is a newly introduced constant (units ohms, or reciprocal siemens, such that σλκ = ε_r remains unitless).

Metals

Permittivity is typically associated with

References