Material | εr |
---|---|
Vacuum | 1 (by definition) |
Air | 1.00058986±0.00000050 (at STP, 900 kHz), [1] |
PTFE/Teflon | 2.1 |
Polyethylene/XLPE | 2.25 |
Polyimide | 3.4 |
Polypropylene | 2.2–2.36 |
Polystyrene | 2.4–2.7 |
Carbon disulfide | 2.6 |
BoPET | 3.1 [2] |
Paper, printing | 1.4 [3] (200 kHz) |
Electroactive polymers | 2–12 |
Mica | 3–6 [2] |
Silicon dioxide | 3.9 [4] |
Sapphire | 8.9–11.1 (anisotropic) [5] |
Concrete | 4.5 |
Pyrex (glass) | 4.7 (3.7–10) |
Neoprene | 6.7 [2] |
Natural rubber | 7 |
Diamond | 5.5–10 |
Salt | 3–15 |
Melamine resin | 7.2–8.4 [6] |
Graphite | 10–15 |
Silicone rubber | 2.9–4 [7] |
Silicon | 11.68 |
GaAs | 12.4 [8] |
Silicon nitride | 7–8 (polycrystalline, 1 MHz) [9] [10] |
Ammonia | 26, 22, 20, 17 (−80, −40, 0, +20 °C) |
Methanol | 30 |
Ethylene glycol | 37 |
Furfural | 42.0 |
Glycerol | 41.2, 47, 42.5 (0, 20, 25 °C) |
Water | 87.9, 80.2, 55.5 (0, 20, 100 °C) [11] for visible light: 1.77 |
Hydrofluoric acid | 175, 134, 111, 83.6 (−73, −42, −27, 0 °C), |
Hydrazine | 52.0 (20 °C), |
Formamide | 84.0 (20 °C) |
Sulfuric acid | 84–100 (20–25 °C) |
Hydrogen peroxide | 128 aqueous–60 (−30–25 °C) |
Hydrocyanic acid | 158.0–2.3 (0–21 °C) |
Titanium dioxide | 86–173 |
Strontium titanate | 310 |
Barium strontium titanate | 500 |
Barium titanate [12] | 1200–10,000 (20–120 °C) |
Lead zirconate titanate | 500–6000 |
Conjugated polymers | 1.8–6 up to 100,000 [13] |
Calcium copper titanate | >250,000 [14] |
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 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 [15] as well as in chemistry. [16]
Relative permittivity is typically denoted as εr(ω) (sometimes κ, lowercase kappa) and is defined as
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]
The relative permittivity of a medium is related to its electric susceptibility, χe, as εr(ω) = 1 + χe.
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.
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 ]
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.
Solvent | Relative permittivity | Temperature | |
---|---|---|---|
C6H6 | benzene | 2.3 | 298 K (25 °C) |
Et2O | diethyl ether | 4.3 | 293 K (20 °C) |
(CH2)4O | tetrahydrofuran (THF) | 7.6 | 298 K (25 °C) |
CH2Cl2 | dichloromethane | 9.1 | 293 K (20 °C) |
NH3(liq) | liquid ammonia | 17 | 273 K (0 °C) |
C2H5OH | ethanol | 24.3 | 298 K (25 °C) |
CH3OH | methanol | 32.7 | 298 K (25 °C) |
CH3NO2 | nitromethane | 35.9 | 303 K (30 °C) |
HCONMe2 | dimethyl formamide (DMF) | 36.7 | 298 K (25 °C) |
CH3CN | acetonitrile | 37.5 | 293 K (20 °C) |
H2O | water | 78.4 | 298 K (25 °C) |
HCONH2 | formamide | 109 | 293 K (20 °C) |
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]
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
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. [23] Alternatively, resonance based effects may be employed at fixed frequencies. [24]
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.
Dielectrics are used in radio frequency (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.
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.
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. [26] 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 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) [27] and that of iodoethane (7.6177). [27] 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).
Again, similar as for absolute permittivity, relative permittivity for lossy materials can be formulated as:
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]" ( [17] p. 8). Expanding the angular frequency ω = 2πc / λ and the electric constant ε0 = 1 / μ0c2, which reduces to:
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).
Permittivity is typically associated with dielectric materials, however metals are described as having an effective permittivity, with real relative permittivity equal to one. [28] In the high-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. [29]
In optics, the refractive index of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
In electromagnetism, a dielectric 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 material as they do in an electrical conductor, because they have no loosely bound, or free, electrons that may drift through the material, but instead they shift, only slightly, from their average equilibrium positions, causing dielectric polarisation. Because of dielectric polarisation, positive charges are displaced in the direction of the field and negative charges shift in the direction opposite to the field. 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 polarised, but also reorient so that their symmetry axes align to the field.
In electrical engineering, electrical length is a dimensionless parameter equal to the physical length of an electrical conductor such as a cable or wire, divided by the wavelength of alternating current at a given frequency traveling through the conductor. In other words, it is the length of the conductor measured in wavelengths. It can alternately be expressed as an angle, in radians or degrees, equal to the phase shift the alternating current experiences traveling through the conductor.
The wave impedance of an electromagnetic wave is the ratio of the transverse components of the electric and magnetic fields. For a transverse-electric-magnetic (TEM) plane wave traveling through a homogeneous medium, the wave impedance is everywhere equal to the intrinsic impedance of the medium. In particular, for a plane wave travelling through empty space, the wave impedance is equal to the impedance of free space. The symbol Z is used to represent it and it is expressed in units of ohms. The symbol η (eta) may be used instead of Z for wave impedance to avoid confusion with electrical impedance.
In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ε (epsilon), is a measure of the electric polarizability of a dielectric material. A material with high permittivity polarizes more in response to an applied electric field than a material with low permittivity, thereby storing more energy in the material. In electrostatics, the permittivity plays an important role in determining the capacitance of a capacitor.
Capacitance is the capacity of a material object or device to store electric charge. It is measured by the charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are two closely related notions of capacitance: self capacitance and mutual capacitance. An object that can be electrically charged exhibits self capacitance, for which the electric potential is measured between the object and ground. Mutual capacitance is measured between two components, and is particularly important in the operation of the capacitor, an elementary linear electronic component designed to add capacitance to an electric circuit.
In electromagnetism, displacement current density is the quantity ∂D/∂t appearing in Maxwell's equations that is defined in terms of the rate of change of D, the electric displacement field. Displacement current density has the same units as electric current density, and it is a source of the magnetic field just as actual current is. However it is not an electric current of moving charges, but a time-varying electric field. In physical materials, there is also a contribution from the slight motion of charges bound in atoms, called dielectric polarization.
In physics, the dissipation factor (DF) is a measure of loss-rate of energy of a mode of oscillation in a dissipative system. It is the reciprocal of quality factor, which represents the "quality" or durability of oscillation.
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.
Gaussian units constitute a metric system of physical units. This system is the most common of the several electromagnetic unit systems based on cgs (centimetre–gram–second) units. It is also called the Gaussian unit system, Gaussian-cgs units, or often just cgs units. The term "cgs units" is ambiguous and therefore to be avoided if possible: there are several variants of cgs with conflicting definitions of electromagnetic quantities and units.
In physics, the electric displacement field or electric induction is a vector field that appears in Maxwell's equations. It accounts for the electromagnetic effects of polarization and that of an electric field, combining the two in an auxiliary field. It plays a major role in topics such as the capacitance of a material, as well as the response of dielectrics to an electric field, and how shapes can change due to electric fields in piezoelectricity or flexoelectricity as well as the creation of voltages and charge transfer due to elastic strains.
Dielectric heating, also known as electronic heating, radio frequency heating, and high-frequency heating, is the process in which a radio frequency (RF) alternating electric field, or radio wave or microwave electromagnetic radiation heats a dielectric material. At higher frequencies, this heating is caused by molecular dipole rotation within the dielectric.
Vacuum permittivity, commonly denoted ε0, is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric constant, or the distributed capacitance of the vacuum. It is an ideal (baseline) physical constant. Its CODATA value is:
In electrical engineering, a capacitor is a device that stores electrical energy by accumulating electric charges on two closely spaced surfaces that are insulated from each other. The capacitor was originally known as the condenser, a term still encountered in a few compound names, such as the condenser microphone. It is a passive electronic component with two terminals.
In electrical engineering, dielectric loss quantifies a dielectric material's inherent dissipation of electromagnetic energy. It can be parameterized in terms of either the loss angleδ or the corresponding loss tangenttan(δ). Both refer to the phasor in the complex plane whose real and imaginary parts are the resistive (lossy) component of an electromagnetic field and its reactive (lossless) counterpart.
When an electromagnetic wave travels through a medium in which it gets attenuated, it undergoes exponential decay as described by the Beer–Lambert law. However, there are many possible ways to characterize the wave and how quickly it is attenuated. This article describes the mathematical relationships among:
A MIS capacitor is a capacitor formed from a layer of metal, a layer of insulating material and a layer of semiconductor material. It gets its name from the initials of the metal-insulator-semiconductor (MIS) structure. As with the MOS field-effect transistor structure, for historical reasons, this layer is also often referred to as a MOS capacitor, but this specifically refers to an oxide insulator material.
Optical conductivity is the property of a material which gives the relationship between the induced current density in the material and the magnitude of the inducing electric field for arbitrary frequencies. This linear response function is a generalization of the electrical conductivity, which is usually considered in the static limit, i.e., for time-independent or slowly varying electric fields.
In condensed matter physics, the Lyddane–Sachs–Teller relation determines the ratio of the natural frequency of longitudinal optic lattice vibrations (phonons) of an ionic crystal to the natural frequency of the transverse optical lattice vibration for long wavelengths. The ratio is that of the static permittivity to the permittivity for frequencies in the visible range .
A loop-gap resonator (LGR) is an electromagnetic resonator that operates in the radio and microwave frequency ranges. The simplest LGRs are made from a conducting tube with a narrow slit cut along its length. The LGR dimensions are typically much smaller than the free-space wavelength of the electromagnetic fields at the resonant frequency. Therefore, relatively compact LGRs can be designed to operate at frequencies that are too low to be accessed using, for example, cavity resonators. These structures can have very sharp resonances making them useful for electron spin resonance (ESR) experiments, and precision measurements of electromagnetic material properties.