# Relative permittivity

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Relative permittivities of some materials at room temperature under 1 kHz
Materialεr
Vacuum 1 (by definition)
Air 1.00058986±0.00000050
(at STP, for 0.9 MHz), [1]
PTFE/Teflon2.1
Polyethylene/XLPE2.25
Polyimide 3.4
Polypropylene
Polystyrene
Carbon disulfide 2.6
Mylar 3.1 [2]
Paper, printing, 200 kHz,1.4 [3]
Electroactive polymers
Mica
Silicon dioxide 3.9 [4]
Sapphire
Concrete 4.5
Pyrex (glass)4.7 (3.7–10)
Neoprene 6.7 [2]
Rubber 7
Diamond
Salt
Graphite
Silicon 11.68
Silicon nitride
Ammonia
Methanol 30
Ethylene glycol 37
Furfural 42.0
Glycerol
Water
Hydrofluoric acid
Hydrazine 52.0 (20 °C),
Formamide 84.0 (20 °C)
Sulfuric acid
Hydrogen peroxide
Hydrocyanic acid
Titanium dioxide
Strontium titanate 310
Barium strontium titanate 500
Barium titanate [9]
Conjugated polymers
Calcium copper titanate

The relative permittivity of a material is its (absolute) permittivity expressed as a ratio relative to the vacuum permittivity.

In electromagnetism, absolute permittivity, often simply called permittivity, usually denoted by the Greek letter ε (epsilon), is the measure of capacitance that is encountered when forming an electric field in a particular medium. More specifically, permittivity describes the amount of charge needed to generate one unit of electric flux in a given medium. A charge will yield more electric flux in a medium with low permittivity than in a medium with high permittivity. Permittivity is the measure of a material's ability to store an electric field in the polarization of the medium.

The physical constant ε0, commonly called the vacuum permittivity, permittivity of free space or electric constant or the distributed capacitance of the vacuum, is an ideal, (baseline) physical constant, which is the value of the absolute dielectric permittivity of classical vacuum. It has the CODATA value

## Contents

Permittivity is a material 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 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 [12] as well as in chemistry. [13]

Capacitance is the ratio of the change in an electric charge in a system to the corresponding change in its electric potential. There are two closely related notions of capacitance: self capacitance and mutual capacitance. Any object that can be electrically charged exhibits self capacitance. A material with a large self capacitance holds more electric charge at a given voltage than one with low capacitance. The notion of mutual capacitance is particularly important for understanding the operations of the capacitor, one of the three elementary linear electronic components.

A capacitor is a device that stores electrical energy in an electric field. It is a passive electronic component with two terminals.

A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material as they do in an electrical conductor but only slightly shift from their average equilibrium positions causing dielectric polarization. Because of dielectric polarization, positive charges are displaced in the direction of the field and negative charges shift in the opposite direction. This creates an internal electric field that reduces the overall field within the dielectric itself. If a dielectric is composed of weakly bonded molecules, those molecules not only become polarized, but also reorient so that their symmetry axes align to the field.

## Definition

Relative permittivity is typically denoted as εr(ω) (sometimes κ or K) and is defined as

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

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

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. Because no real number satisfies this equation, i is called an imaginary number. For the complex number a + bi, a is called the real part, and b is called the imaginary part. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers, and are fundamental in many aspects of the scientific description of the natural world.

Relative permittivity is a dimensionless number that is in general complex-valued; its real and imaginary parts are denoted as: [14]

In dimensional analysis, a dimensionless quantity is a quantity to which no physical dimension is assigned, also known as a bare, pure, or scalar quantity or a quantity of dimension one, with a corresponding unit of measurement in the SI of one unit that is not explicitly shown. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Examples of quantities to which dimensions are regularly assigned are length, time, and speed, which are measured in dimensional units, such as metre, second and metre per second. This is considered to aid intuitive understanding. However, especially in mathematical physics, it is often more convenient to drop the assignment of explicit dimensions and express the quantities without dimensions, e.g., addressing the speed of light simply by the dimensionless number 1.

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

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

In electricity (electromagnetism), the electric susceptibility is a dimensionless proportionality constant that indicates the degree of polarization of a dielectric material in response to an applied electric field. The greater the electric susceptibility, the greater the ability of a material to polarize in response to the field, and thereby reduce the total electric field inside the material. It is in this way that the electric susceptibility influences the electric permittivity of the material and thus influences many other phenomena in that medium, from the capacitance of capacitors to the speed of light.

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, [12] [13] because of its ambiguity, as some older authors used it for the absolute permittivity ε. [12] [15] [16] The permittivity may be quoted either as a static property or as a frequency-dependent variant. 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, [16] that is ε = ε0, although there are theoretical nonlinear quantum effects in vacuum that become non-negligible at high field strengths. [17]

The following table gives some typical values.

Low-frequency dielectric constants of some common solvents
SolventDielectric constantTemperature (K)
benzene 2.3298
diethyl ether 4.3293
tetrahydrofuran (THF)7.6298
dichloromethane 9.1293
liquid ammonia 17273
ethanol 24.3298
methanol 32.7298
nitromethane 35.9303
dimethyl formamide (DMF)36.7298
acetonitrile 37.5293
water 78.4298
formamide 109293

## Measurement

The relative static permittivity, εr, 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

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

For time-variant electromagnetic fields, this quantity becomes frequency-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. [18] Alternatively, resonance based effects may be employed at fixed frequencies. [19]

## Applications

### Energy

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 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. Optical fibers 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 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. [20] 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 is very polar, and has a relative static permittivity of 80.10 at 20 °C while n-hexane is non-polar, and has a relative static permittivity of 1.89 at 20 °C. [21] 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 (13 g/L or 9.8 mL/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 tetrahydrofuran, the oxygen atom can act as a hydrogen bond acceptor; where as dichloromethane cannot form hydrogen bonds with water.

This is even more apparent when comparing the εr values of acetic acid (6.2528) [22] and that of iodoethane (7.6177). [22] 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:

${\displaystyle \varepsilon _{r}=\varepsilon _{r}'-{\frac {i\sigma }{\omega \varepsilon _{0}}},}$

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 [electrical] conductivity caused by migrating charge carriers and it may also refer to an energy loss associated with the dispersion of ε′ [the real-valued permittivity]" ( [14] p. 8). Expanding the angular frequency ω = 2πc/λ and the electric constant ε0 = 1/µ0c2, which reduces to:

${\displaystyle \varepsilon _{r}=\varepsilon _{r}'-i\sigma \lambda \kappa ,}$

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 = εr remains unitless).

## Metals

Permittivity is typically associated with dielectric materials, however metals are described as having an effective permittivity, with real relative permittivity equal to one. [23] In the low-frequency region, which extends from radio frequencies to the far infrared 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. [24]

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