Relative static permittivity Information & Relative static permittivity Links at HealthHaven.com

Relative static permittivities of some materials at room temperature under 1 kHz^[1]
Material	ε_r
Aluminium (1 kHz)	−1300+i1.3×10¹⁴ ^[2]
Silver (1 kHz)	−85+i8×10¹² ^[2]
Vacuum	1 (by definition)
Air	1.00058986 ± 0.00000050 (at STP, for 0.9 MHz), ^[3]
Teflon	2.1
Polyethylene	2.25
Polystyrene	2.4–2.7
Carbon disulfide	2.6
Paper	3.5
Electroactive polymers	2–12
Silicon dioxide	4.5
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
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)
(La,Nb):(Zr,Ti)PbO₃	500–6000
Conjugated polymers	1.8-6 up to 100000^[4]

The relative static permittivity (or static relative permittivity) of a material under given conditions is a measure of the extent to which it concentrates electrostatic lines of flux. It is the ratio of the amount of stored electrical energy when a potential is applied, relative to the permittivity of a vacuum. The relative static permittivity is the same as the relative permittivity evaluated for a frequency of zero.

The static relative permittivity is a special case of the more general relative permittivity. The latter is denoted ε_r(ω) (sometimes $κ$ or K or Dk) 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 electric constant. The former is simply the latter evaluated at the limit ω → 0:

$\varepsilon_{r} = \lim_{\omega \rightarrow 0} \varepsilon_{r}(\omega) = \frac{\varepsilon_{s}}{\varepsilon_{0}},$

where ε_s is the static absolute permittivity.

Other terms for the relative static permittivity are the dielectric constant, or relative dielectric constant, or static dielectric constant. These terms, while they remain very common, are ambiguous and have been deprecated by some standards organizations.^[5]^[6] 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.^[7] Second, while in most modern usage "dielectric constant" refers to a relative permittivity^[8]^[6], it may be either the static or the frequency-dependent relative permittivity depending on context.

By definition, the linear relative permittivity of vacuum is equal to 1^[8], 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).^[9]

The static relative permittivity of a medium is related to its static electric susceptibility, χ_e by

$\varepsilon_r = 1 + \chi_e$

[edit] 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.

[edit] 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.

[edit] 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.^[10] This information is of great value when designing separation, sample preparation and chromatography techniques in analytical chemistry.

[edit] Complex permittivity

Similar as for absolute permittivity, relative permittivity can be decomposed into real and imaginary parts^[11]:

$\varepsilon_{r}(\omega) = \varepsilon_{r}'(\omega) + i \varepsilon_{r}''(\omega)$ .

[edit] Lossy medium

Again, similar as for absolute permittivity, relative permittivity for lossy materials can be formulated in terms of "optical conductivity" σ (units S/m, siemens per meter) as (^[11], eq.(11.61), p.479):

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

or, expanding the angular frequency ω = 2πc/λ and the electric constant ε₀ = 1/(µ₀c²), as:

$\varepsilon_{r} = \varepsilon_{r}' + i \sigma \lambda k,$

where λ is the wavelength, c is the speed of light in vacuum and k = µ₀c/2π ≈ 60.0 S^-1 is a constant (units reciprocal of siemens, such that σλk = ε_r" remains unitless).

[edit] See also

[edit] References

^ Dielectric Constants of Materials (2007). Clipper Controls.
^ ^a ^b Lourtioz, J.-M. et al. (2005). Photonic Crystals: Towards Nanoscale Photonic Devices. Springer. p. 121. ISBN 354024431X. http://books.google.com/books?id=vSszZ2WuG_IC&pg=PA121.
^ L. G. Hector and H. L. Schultz (1936). The Dielectric Constant of Air at Radiofrequencies. 7. 133–136. doi:10.1063/1.1745374.
^ Pohl, Herbert A. (1986). "Giant polarization in high polymers". Journal of Electronic Materials 15: 201. doi:10.1007/BF02659632.
^ 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.
^ ^a ^b IEEE Standards Board (1997). "IEEE Standard Definitions of Terms for Radio Wave Propagation". pp. p. 6. http://ieeexplore.ieee.org/servlet/opac?punumber=5697.
^ King, Ronold W. P. (1963). Fundamental Electromagnetic Theory. New York: Dover. pp. 139.
^ ^a ^b John David Jackson (1998). Classical Electrodynamics (Third ed.). New York: Wiley. pp. 154. ISBN 047130932X.
^ Mourou, Gerard A. (2006). "Optics in the relativistic regime". Reviews of Modern Physics 78: 309. doi:10.1103/RevModPhys.78.309.
^ Lide, D. R., ed. (2005), CRC Handbook of Chemistry and Physics (86th ed.), Boca Raton (FL): CRC Press, ISBN 0-8493-0486-5
^ ^a ^b Linfeng Chen and Vijay K. Varadan (2004). Microwave electronics: measurement and materials characterization. John Wiley and Sons. p. 8, eq.(1.15). ISBN 0470844922. http://books.google.co.jp/books?id=2oA3po4coUoC&pg=PA8.

[0] Dielectric Constants of Materials (2007). Clipper Controls.

[Drude-1] Lourtioz, J.-M. et al. (2005). Photonic Crystals: Towards Nanoscale Photonic Devices. Springer. p. 121. ISBN 354024431X. http://books.google.com/books?id=vSszZ2WuG_IC&pg=PA121.

[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] Pohl, Herbert A. (1986). "Giant polarization in high polymers". Journal of Electronic Materials 15: 201. doi:10.1007/BF02659632.

[IUPAC-4] 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.

[IEEE1997-5] IEEE Standards Board (1997). "IEEE Standard Definitions of Terms for Radio Wave Propagation". pp. p. 6. http://ieeexplore.ieee.org/servlet/opac?punumber=5697.

[6] King, Ronold W. P. (1963). Fundamental Electromagnetic Theory. New York: Dover. pp. 139.

[Jackson-7] John David Jackson (1998). Classical Electrodynamics (Third ed.). New York: Wiley. pp. 154. ISBN 047130932X.

[Mourou-8] Mourou, Gerard A. (2006). "Optics in the relativistic regime". Reviews of Modern Physics 78: 309. doi:10.1103/RevModPhys.78.309.

[9] Lide, D. R., ed. (2005), CRC Handbook of Chemistry and Physics (86th ed.), Boca Raton (FL): CRC Press, ISBN 0-8493-0486-5

[ChenVaradan2004-10] Linfeng Chen and Vijay K. Varadan (2004). Microwave electronics: measurement and materials characterization. John Wiley and Sons. p. 8, eq.(1.15). ISBN 0470844922. http://books.google.co.jp/books?id=2oA3po4coUoC&pg=PA8.

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