Dielectric Constant

 Material εr Vacuum 1 (by definition) Air 1.00058986 ± 0.00000050 (at STP, for 0.9 MHz), PTFE/Teflon 2.1 Polyethylene 2.25 Polyimide 3.4 Polypropylene 2.2–2.36 Polystyrene 2.4–2.7 Carbon disulfide 2.6 Paper 3.85 Electroactive polymers 2–12 Silicon dioxide 3.9  Concrete 4.5 Pyrex (Glass) 4.7 (3.7–10) Rubber 7 Diamond 5.5–10 Salt 3–15 Graphite 10–15 Silicon 11.68 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 88, 80.1, 55.3, 34.5(0, 20, 100, 200 °C) for visible light: 1.77 Hydrofluoric acid 83.6 (0 °C) Formamide 84.0 (20 °C) Sulfuric acid 84–100(20–25 °C) Hydrogen peroxide 128 aq–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 1250–10,000(20–120 °C) Lead zirconium titanate 500–6000 Conjugated polymers 1.8–6 up to 100,000 Calcium copper titanate >250,000

The relative permittivity of a material under given conditions reflects the extent to which it concentrates electrostatic lines of flux. In technical terms, it is the ratio of the amount of electrical energy stored in a material by an applied voltage, relative to that stored in a vacuum (see: vacuum permittivity). Likewise, it is also the ratio of the capacitance of a capacitor using that material as a dielectric, compared to a similar capacitor that has a vacuum as its dielectric.

Definition

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

$\varepsilon_\left\{r\right\}\left(\omega\right) = \frac\left\{\varepsilon\left(\omega\right)\right\}\left\{\varepsilon_\left\{0\right\}\right\},$

where ε(ω) is the complex frequency-dependent absolute 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:

$\varepsilon_r\left(\omega\right) = \varepsilon_\left\{r\right\}\text{'}\left(\omega\right) + i \varepsilon_\left\{r\right\}$(\omega).

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.

Terminology

Dielectric constant is the historical term which, although still very common, has been deprecated by the relevant standards organizations. There is potential ambiguity in this predecessor name, as some older authors used it for the absolute permittivity ε while in most modern usage it refers to a relative permittivity εr, which in its turn may be either its static or the frequency-dependent variant, depending on context. It has also been used to refer to only the real component ε'r of the complex-valued relative permittivity.

Physics

The imaginary portion of the permittivity 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, that is ε = ε0, although there are theoretical nonlinear quantum effects in vacuum that exist at high field strengths.

Measurement

Template:Merge section from 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 Cx with a dielectric between the plates is measured. The relative dielectric constant can be then calculated as

$\varepsilon_\left\{r\right\} = \frac\left\{C_\left\{x\right\}\right\} \left\{C_\left\{0\right\}\right\}.$

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. Alternatively, resonance based effects may be employed at fixed frequencies.

Applications

Energy

The dielectric constant 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 dielectric constant 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.

Environmental

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.

Chemical

The relative static permittivity of a solvent is a relative measure of its polarity. For example, water (very polar) has a dielectric constant of 80.10 at 20 °C while n-hexane (very non-polar) has a dielectric constant of 1.89 at 20 °C. This information is of great value 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.

Lossy medium

Again, similar as for absolute permittivity, relative permittivity for lossy materials can be formulated as:

$\varepsilon_\left\{r\right\} = \varepsilon_\left\{r\right\}\text{'} + \frac\left\{\sigma\right\}\left\{j\omega \varepsilon_0\right\},$

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]" (, p. 8). Expanding the angular frequency ω = 2πc/λ and the electric constant ε0 = 1/(µ0c2), it reduces to:

$\varepsilon_\left\{r\right\} = \varepsilon_\left\{r\right\}\text{'} - j \sigma \lambda \kappa,$

where λ is the wavelength, c is the speed of light in vacuum and κ = µ0c/2π ≈ 60.0 S−1 is a newly introduced constant (units reciprocal of siemens, such that σλκ = εr" remains unitless).

Metals

Although permittivity is typically associated with dielectric materials, we may still speak of an effective permittivity of a metal, with real relative permittivity equal to one ( eq.(4.6), p. 121). In the low-frequency region (which extends from radiofrequencies to the far infrared region), the plasma frequency of the electron gas is much greater than the electromagnetic propagation frequency, so the complex permittivity ε of a metal is practically a purely imaginary number, expressed in terms of the imaginary unit and a real-valued electrical conductivity ( eq.(4.8)–(4.9), p. 122).