Relative permittivity

Relative static permittivities of some materials at room temperature under 1 kHz^[1]

Material	εr
Vacuum	1 (by definition)
Air	1.00058986 ± 0.00000050 (at STP, for 0.9 MHz),[2]
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 [3]
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)
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 zirconate titanate	500–6000
Conjugated polymers	1.8-6 up to 100,000[4]
Calcium Copper Titanate	>250,000[5]

Temperature dependence of the relative static permittivity of water

The relative permittivity of a material under given conditions reflects the extent to which it concentrates electrostatic lines of flux. Technically, 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. Similarly, it is also the ratio of the capacitance of a capacitor using that material as a dielectric, compared to a similar capacitor which has a vacuum as its dielectric.

Terminology

The relative permittivity of a material for a frequency of zero is known as its static relative permittivity or as its dielectric constant. Other terms used for the zero frequency relative permittivity include relative dielectric constant and static dielectric constant. While they remain very common, these terms are ambiguous and have been deprecated by some standards organizations.^[6][7] The reason for the potential ambiguity is twofold. First, some older authors used "dielectric constant" or "absolute dielectric constant" for the absolute permittivity ε rather than the relative permittivity.^[8] Second, while in most modern usage "dielectric constant" refers to a relative permittivity,^[7][9] it may be either the static or the frequency-dependent relative permittivity depending on context.

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

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

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. 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,^[9] that is ε = ε₀, although there are theoretical nonlinear quantum effects in vacuum that have been predicted at high field strengths (but not yet observed).^[10]

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

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_x with a dielectric between the plates is measured. The relative dielectric constant can be then calculated as

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

For time-variant electromagnetic fields, this quantity becomes frequency-dependent and in general is called relative permittivity.

Practical relevance

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.

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 ε_r 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.

Chemical applications

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.^[11] This information is of great value when designing separation, sample preparation and chromatography techniques in analytical chemistry.

Complex permittivity

Similar as for absolute permittivity, relative permittivity can be decomposed into real and imaginary parts:^[12]

ε_r(ω) = ε_r'(ω) + iε_r''(ω).

Lossy medium

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

$\varepsilon_{r} = \varepsilon_{r}' + i \frac{\sigma}{\omega \varepsilon_0},$

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]" (,^[12] p. 8). Expanding the angular frequency ω = 2πc/λ and the electric constant ε₀ = 1/(µ₀c²), it reduces to:

ε_r = ε_r' + iσλκ,

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 = ε_r" 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 (,^[13] 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 (,^[13] eq.(4.8)-(4.9), p. 122).

See also

• Curie temperature
• Dielectric spectroscopy
• Dielectric strength
• Electret
• Ferroelectricity
• Green–Kubo relations
• High-k dielectric
• Kramers–Kronig relation
• Linear response function
• Low-k dielectric
• Loss tangent
• Permittivity
• Refractive index

References

1. ^ Dielectric Constants of Materials (2007). Clipper Controls.
2. ^ L. G. Hector and H. L. Schultz (1936). The Dielectric Constant of Air at Radiofrequencies. 7. 133–136. doi:10.1063/1.1745374. 
3. ^ Paul R. Gray, Paul J. Hurst, Stephen H. Lewis, Robert G. Meyer (2009). Analysis and Design of Analog Integrated Circuits (Fifth ed.). New York: Wiley. p. 40. ISBN 978-0-470-24599-6. 
4. ^ Pohl, Herbert A. (1986). "Giant polarization in high polymers". Journal of Electronic Materials 15: 201. Bibcode 1986JEMat..15..201P. doi:10.1007/BF02659632. 
5. ^ http://www.shef.ac.uk/ccl/research/ccto.html
6. ^ Braslavsky, S.E. (2007). "Glossary of terms used in photochemistry (IUPAC recommendations 2006)". Pure and Applied Chemistry 79: 293–465. doi:10.1351/pac200779030293. http://iupac.org/publications/pac/2007/pdf/7903x0293.pdf. 
7. ^ ^{a b} IEEE Standards Board (1997). "IEEE Standard Definitions of Terms for Radio Wave Propagation". p. 6. http://ieeexplore.ieee.org/servlet/opac?punumber=5697. 
8. ^ King, Ronold W. P. (1963). Fundamental Electromagnetic Theory. New York: Dover. p. 139. 
9. ^ ^{a b} John David Jackson (1998). Classical Electrodynamics (Third ed.). New York: Wiley. p. 154. ISBN 047130932X. 
10. ^ Mourou, Gerard A. (2006). "Optics in the relativistic regime". Reviews of Modern Physics 78: 309. Bibcode 2006RvMP...78..309M. doi:10.1103/RevModPhys.78.309. 
11. ^ Lide, D. R., ed (2005). CRC Handbook of Chemistry and Physics (86th ed.). Boca Raton (FL): CRC Press. ISBN 0-8493-0486-5. 
12. ^ ^{a b} Linfeng Chen and Vijay K. Varadan (2004). Microwave electronics: measurement and materials characterization. John Wiley and Sons. p. 8, eq.(1.15). doi:10.1002/0470020466. ISBN 0470844922. http://books.google.co.jp/books?id=2oA3po4coUoC&pg=PA8. 
13. ^ ^{a b} Lourtioz, J.-M. et al. (2005). Photonic Crystals: Towards Nanoscale Photonic Devices. Springer. ISBN 354024431X. http://books.google.com/books?id=vSszZ2WuG_IC&pg=PA121.