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Relative permittivity

From Wikipedia, the free encyclopedia
Measure of the electric polarizability of a dielectric, compared with that of a vacuum
Relativepermittivities of some materials atroom temperature under1 kHz
Materialεr
Vacuum1 (by definition)
Air1.00058986±0.00000050
(atSTP, 900 kHz),[1]
PTFE/Teflon2.1
Polyethylene/XLPE2.25
Polyimide3.4
Polypropylene 2.2–2.36
Polystyrene 2.4–2.7
Carbon disulfide2.6
BoPET3.1[2]
Paper, printing1.4[3] (200 kHz)
Electroactive polymers 2–12
Mica 3–6[2]
Silicon dioxide3.9[4]
Sapphire 8.9–11.1 (anisotropic)[5]
Concrete4.5
Pyrex (glass)4.7 (3.7–10)
Neoprene6.7[2]
Natural rubber7
Diamond 5.5–10
Salt 3–15
Melamine resin 7.2–8.4[6]
Graphite 10–15
Silicone rubber 2.9–4[7]
Silicon11.68
GaAs12.4[8]
Silicon nitride 7–8 (polycrystalline, 1 MHz)[9][10]
Ammonia 26, 22, 20, 17 (−80, −40, 0, +20 °C)
Methanol30
Ethylene glycol37
Furfural42.0
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),
Hydrazine52.0 (20 °C),
Formamide84.0 (20 °C)
Sulfuric acid 84–100 (20–25 °C)
Hydrogen peroxide 128aqueous–60
(−30–25 °C)
Hydrocyanic acid 158.0–2.3 (0–21 °C)
Titanium dioxide 86–173
Strontium titanate310
Barium strontium titanate500
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]
Temperature dependence of the relative static permittivity of water

Therelative permittivity (in older texts,dielectric constant) is thepermittivity of a material expressed as a ratio with theelectric permittivity of a vacuum. Adielectric 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 theCoulomb 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 thecapacitance of acapacitor using that material as adielectric, 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]

Definition

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Relative permittivity is typically denoted asεr(ω) (sometimesκ, lowercasekappa) and is defined as

εr(ω)=ε(ω)ε0,{\displaystyle \varepsilon _{\text{r}}(\omega )={\frac {\varepsilon (\omega )}{\varepsilon _{0}}},}

whereε(ω) is thecomplex frequency-dependentpermittivity of the material, andε0 is thevacuum permittivity.

Relative permittivity is adimensionless number that is in generalcomplex-valued; its real and imaginary parts are denoted as:[17]

εr(ω)=εr′(ω)−iεr″(ω).{\displaystyle \varepsilon _{\text{r}}(\omega )=\varepsilon _{\text{r}}'(\omega )-i\varepsilon _{\text{r}}''(\omega ).}

The relative permittivity of a medium is related to itselectric susceptibility,χe, asεr(ω) = 1 +χe.

In anisotropic media (such as non cubic crystals) the relative permittivity is a second ranktensor.

The relative permittivity of a material for afrequency of zero is known as itsstatic relative permittivity.

Terminology

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The historical term for the relative permittivity isdielectric 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 permittivityε.[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 thedielectric function. It has also been used to refer to only the real componentε′r of the complex-valued relative permittivity.[citation needed]

Physics

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In the causal theory of waves, permittivity is a complex quantity. The imaginary part corresponds to a phase shift of the polarizationP relative toE and leads to the attenuation of electromagnetic waves passing through the medium. By definition, the linear relativepermittivity of vacuum is equal to 1,[19] that isε =ε0, although there are theoreticalnonlinear quantum effects in vacuum that become non-negligible at high field strengths.[20]

The following table gives some typical values.

Low-frequency relative permittivity of some common solvents
SolventRelative permittivityTemperature
C6H6benzene2.3298 K (25 °C)
Et2Odiethyl ether4.3293 K (20 °C)
(CH2)4Otetrahydrofuran (THF)7.6298 K (25 °C)
CH2Cl2dichloromethane9.1293 K (20 °C)
NH3(liq)liquid ammonia17273 K (0 °C)
C2H5OHethanol24.3298 K (25 °C)
CH3OHmethanol32.7298 K (25 °C)
CH3NO2nitromethane35.9303 K (30 °C)
HCONMe2dimethyl formamide (DMF)36.7298 K (25 °C)
CH3CNacetonitrile37.5293 K (20 °C)
H2Owater78.4298 K (25 °C)
HCONH2formamide109293 K (20 °C)

The relative low frequency permittivity ofice 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]

Determination

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The relative static permittivity,εr, can be determined for staticelectric fields as follows: first thecapacitance of a testcapacitor,C0, is measured with vacuum between its plates. Then, using the same capacitor and distance between its plates, the capacitanceC with adielectric between the plates is measured. The relative permittivity can be then calculated as

εr=CC0.{\displaystyle \varepsilon _{\text{r}}={\frac {C}{C_{0}}}.}

For time-variantelectromagnetic fields, this quantity becomesfrequency-dependent. An indirect technique to calculateεr is conversion of radio frequencyS-parameter measurement results. A description of frequently used S-parameter conversions for determination of the frequency-dependentεr of dielectrics can be found in this bibliographic source.[23] Alternatively, resonance based effects may be employed at fixed frequencies.[24]

Applications

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Energy

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The relative permittivity is an essential piece of information when designingcapacitors, and in other circumstances where a material might be expected to introducecapacitance into a circuit. If a material with a high relative permittivity is placed in anelectric 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

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Dielectrics are used inradio frequency (RF) transmission lines. In acoaxial cable,polyethylene can be used between the center conductor and outside shield. It can also be placed inside waveguides to formfilters.Optical fibers are examples ofdielectricwaveguides. They consist of dielectric materials that are purposely doped with impurities so as to control the precise value ofεr within the cross-section. This controls therefractive 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

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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.

Chemistry

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The relative static permittivity of a solvent is a relative measure of itschemical polarity. For example,water is very polar, and has a relative static permittivity of 80.10 at 20 °C whilen-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 andchromatography techniques inanalytical chemistry.

The correlation should, however, be treated with caution. For instance,dichloromethane has a value ofεr of9.08 (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 itsεr =7.52 at 22 °C, but it is completely miscible with water. In the case of tetrahydrofuran, the oxygen atom can act as ahydrogen bond acceptor; whereas dichloromethane cannot form hydrogen bonds with water.

This is even more remarkable when comparing theεr values ofacetic acid (6.2528)[27] and that ofiodoethane (7.6177).[27] The large numerical value ofεr is not surprising in the second case, as theiodine atom is easily polarizable; nevertheless, this does not imply that it is polar, too (electronicpolarizability prevails over the orientational one in this case).

Lossy medium

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

εr=εr′−iσωε0,{\displaystyle \varepsilon _{\text{r}}=\varepsilon _{\text{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 ofε′ [the real-valued permittivity]".[17]: 8  Expanding theangular frequencyω = 2πc / λ and theelectric constantε0 = 1 / μ0c2, which reduces to:

εr=εr′−iσλκ,{\displaystyle \varepsilon _{\text{r}}=\varepsilon _{\text{r}}'-i\sigma \lambda \kappa ,}

whereλ is the wavelength,c is the speed of light in vacuum andκ =μ0c / 2π = 59.95849 Ω ≈ 60.0 Ω is a newly introduced constant (unitsohms, or reciprocalsiemens, such thatσλκ =εr remains unitless).

Metals

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Permittivity is typically associated withdielectric 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 farinfrared andterahertz region, the plasma frequency of the electron gas is much greater than the electromagnetic propagation frequency, so the refractive indexn 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]

See also

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References

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  1. ^Hector, L. G.; Schultz, H. L. (1936). "The Dielectric Constant of Air at Radiofrequencies".Physics.7 (4):133–136.Bibcode:1936Physi...7..133H.doi:10.1063/1.1745374.
  2. ^abcYoung, H. D.; Freedman, R. A.; Lewis, A. L. (2012).University Physics with Modern Physics (13th ed.). Addison-Wesley. p. 801.ISBN 978-0-321-69686-1.
  3. ^Borch, Jens; Lyne, M. Bruce; Mark, Richard E. (2001).Handbook of Physical Testing of Paper Vol. 2 (2 ed.). CRC Press. p. 348.ISBN 0203910494.
  4. ^Gray, P. R.; Hurst, P. J.; Lewis, S. H.; Meyer, R. G. (2009).Analysis and Design of Analog Integrated Circuits (5th ed.). Wiley. p. 40.ISBN 978-0-470-24599-6.
  5. ^Harman, A. K.; Ninomiya, S.; Adachi, S. (1994). "Optical constants of sapphire (α‐Al2O3) single crystals".Journal of Applied Physics.76 (12):8032–8036.Bibcode:1994JAP....76.8032H.doi:10.1063/1.357922.
  6. ^"Dielectric Materials—The Dielectric Constant". RetrievedJune 17, 2023.
  7. ^"Properties of silicone rubber". Azo Materials.
  8. ^Fox, Mark (2010).Optical Properties of Solids (2 ed.).Oxford University Press. p. 283.ISBN 978-0199573370.
  9. ^"Fine Ceramics"(PDF).Toshiba Materials.
  10. ^"Material Properties Charts"(PDF).Ceramic Industry. 2013.
  11. ^Archer, G. G.; Wang, P. (1990). "The Dielectric Constant of Water and Debye-Hückel Limiting Law Slopes".Journal of Physical and Chemical Reference Data.19 (2):371–411.doi:10.1063/1.555853.
  12. ^"Permittivity".schools.matter.org.uk. Archived fromthe original on 2016-03-11.
  13. ^Pohl, H. A. (1986). "Giant polarization in high polymers".Journal of Electronic Materials.15 (4): 201.Bibcode:1986JEMat..15..201P.doi:10.1007/BF02659632.
  14. ^Guillemet-Fritsch, S.; Lebey, T.; Boulos, M.; Durand, B. (2006)."Dielectric properties of CaCu3Ti4O12 based multiphased ceramics"(PDF).Journal of the European Ceramic Society.26 (7): 1245.doi:10.1016/j.jeurceramsoc.2005.01.055.
  15. ^abcIEEE Standards Board (1997)."IEEE Standard Definitions of Terms for Radio Wave Propagation".IEEE STD 211-1997: 6.doi:10.1109/IEEESTD.1997.8638365 (inactive 1 July 2025).{{cite journal}}: CS1 maint: DOI inactive as of July 2025 (link)
  16. ^abBraslavsky, S.E. (2007)."Glossary of terms used in photochemistry (IUPAC recommendations 2006)"(PDF).Pure and Applied Chemistry.79 (3):293–465.doi:10.1351/pac200779030293.S2CID 96601716.
  17. ^abLinfeng Chen & Vijay K. Varadan (2004).Microwave electronics: measurement and materials characterization. John Wiley and Sons. p. 8, eq.(1.15).doi:10.1002/0470020466.ISBN 978-0-470-84492-2.
  18. ^King, Ronold W. P. (1963).Fundamental Electromagnetic Theory. New York: Dover. p. 139.
  19. ^abJohn David Jackson (1998).Classical Electrodynamics (Third ed.). New York: Wiley. p. 154.ISBN 978-0-471-30932-1.
  20. ^Mourou, Gerard A. (2006). "Optics in the relativistic regime".Reviews of Modern Physics.78 (2): 309.Bibcode:2006RvMP...78..309M.doi:10.1103/RevModPhys.78.309.
  21. ^Evans, S. (1965)."Dielectric Properties of Ice and Snow–a Review".Journal of Glaciology.5 (42):773–792.doi:10.3189/S0022143000018840.S2CID 227325642.
  22. ^Fujita, Shuji; Matsuoka, Takeshi; Ishida, Toshihiro; Matsuoka, Kenichi; Mae, Shinji,A summary of the complex dielectric permittivity of ice in the megahertz range and its applications for radar sounding of polar ice sheets(PDF)
  23. ^Kuek, CheeYaw."Measurement of Dielectric Material Properties"(PDF). R&S.
  24. ^Costa, F.; Amabile, C.; Monorchio, A.; Prati, E. (2011)."Waveguide Dielectric Permittivity Measurement Technique Based on Resonant FSS Filters".IEEE Microwave and Wireless Components Letters.21 (5): 273.Bibcode:2011IMWCL..21..273C.doi:10.1109/LMWC.2011.2122303.S2CID 34515302.
  25. ^5×10−6/°C, 1.4×10−6/%RH and 100×10−6/atm respectively. SeeA Low Cost Integrated Interface for Capacitive Sensors, Ali Heidary, 2010, Thesis, p. 12.ISBN 9789461130136.
  26. ^Lide, D. R., ed. (2005).CRC Handbook of Chemistry and Physics (86th ed.). Boca Raton, Florida: CRC Press.ISBN 0-8493-0486-5.
  27. ^abAE. Frisch, M. J. Frish, F. R. Clemente, G. W. Trucks. Gaussian 09 User's Reference. Gaussian, Inc.: Walligford, CT, 2009.- p. 257.
  28. ^Lourtioz, J.-M.; et al. (2005).Photonic Crystals: Towards Nanoscale Photonic Devices. Springer. pp. 121–122.ISBN 978-3-540-24431-8. equation (4.6), page 121
  29. ^Lourtioz (2005), equations (4.8)–(4.9), page 122
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