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| {| class="sortable wikitable" style="float:right; margin-left:10px; text-align:center"
| | Contract, Project or Program Administrator Jamey from Ladner, likes listening to music, health and fitness and autographs. Intends to retire and take the family to many of the noteworthy heritage listed places on the globe like Old Village of Hollóko and its Surroundings.<br><br>Here is my website ... [http://vccbay.com/item.php?id=26437&mode=1 the best Weight gainer in the world] |
| |+ <small>Relative permittivities of some materials at [[room temperature]] under [[radio wave|1 kHz]] <ref>[http://www.clippercontrols.com/pages/Dielectric-Constant-Values.html Dielectric Constants of Materials] (2007). Clipper Controls.</ref> (corresponds to an [[electromagnetic wave]] with wavelength of 300 km)</small>
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| | '''Material''' || '''ε<sub>r</sub>'''
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| |-
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| | [[Vacuum]] || 1 (by definition)
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| |-
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| | [[Air]] || {{val|1.00058986}} ± 0.00000050 <br>(at [[Standard conditions for temperature and pressure|STP]], for 0.9 MHz),<ref>{{cite book|author=L. G. Hector and H. L. Schultz|year=1936|title= The Dielectric Constant of Air at Radiofrequencies|journal=Physics|volume=7|issue=4|pages=133–136|doi=10.1063/1.1745374}}</ref>
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| |-
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| | [[PTFE]]/Teflon || 2.1
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| |-
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| | [[Polyethylene]] || 2.25
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| |-
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| | [[Polyimide]] || 3.4
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| |-
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| | [[Polypropylene]] || 2.2–2.36
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| |-
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| | [[Polystyrene]] || 2.4–2.7
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| |-
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| | [[Carbon disulfide]] || 2.6
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| |-
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| | [[Paper]] || 3.85
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| |-
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| | [[Electroactive polymers]] || 2–12
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| |-
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| | [[Silicon dioxide]] || 3.9 <ref name=Gray&Meyer>
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| {{cite book
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| |author=Paul R. Gray, Paul J. Hurst, Stephen H. Lewis, Robert G. Meyer
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| |title=Analysis and Design of Analog Integrated Circuits
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| |edition=Fifth
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| |publisher= Wiley
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| |location=New York
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| |year=2009
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| |isbn=978-0-470-24599-6
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| |page=40}}
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| </ref>
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| |-
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| | [[Concrete]] || 4.5
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| |-
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| | [[Pyrex]] ([[Glass]]) || 4.7 (3.7–10)
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| |-
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| | [[Rubber]] || 7
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| |-
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| | [[Diamond]] || 5.5–10
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| |-
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| | [[Salt]] || 3–15
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| |-
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| | [[Graphite]] || 10–15
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| |-
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| | [[Silicon]] || 11.68
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| |-
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| | [[Ammonia]] || 26, 22, 20, 17<br>(−80, −40, 0, 20 °C)
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| |-
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| | [[Methanol]] || 30
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| |-
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| | [[Ethylene Glycol]] || 37
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| |-
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| | [[Furfural]] || 42.0
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| |-
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| | [[Glycerol]] || 41.2, 47, 42.5<br>(0, 20, 25 °C)
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| |-
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| | [[Water]] || 88, 80.1, 55.3, 34.5<br>(0, 20, 100, 200 °C)<br> for visible light: 1.77
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| |-
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| | [[Hydrofluoric acid]] || 83.6 (0 °C)
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| |-
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| | [[Formamide]] || 84.0 (20 °C)
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| |-
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| | [[Sulfuric acid]] || 84–100<br>(20–25 °C)
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| |-
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| | [[Hydrogen peroxide]] || 128 [[aqueous|aq]]–60<br>(−30–25 °C)
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| |-
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| | [[Hydrocyanic acid]] || 158.0–2.3<br>(0–21 °C)
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| |-
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| | [[Titanium dioxide]] || 86–173
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| |-
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| | [[Strontium titanate]] || 310
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| |-
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| | [[Barium]] [[strontium titanate]] || 500
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| |-
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| | [[Barium titanate]] || 1250–10,000<br>(20–120 °C)
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| |-
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| | [[Lead zirconium titanate]] || 500–6000
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| |-
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| | [[conjugated system|Conjugated polymers]] || 1.8–6 up to 100,000<ref>{{cite journal|doi=10.1007/BF02659632|title=Giant polarization in high polymers|year=1986|last1=Pohl|first1=Herbert A.|journal=Journal of Electronic Materials|volume=15|page=201|bibcode = 1986JEMat..15..201P }}</ref>
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| |-
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| | [[Calcium copper titanate]] || >250,000<ref>http://oatao.univ-toulouse.fr/698/1/boulos_698.pdf</ref>
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| |}
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| [[File:Water relative static permittivity.svg|thumb|right|Temperature dependence of the relative static permittivity of water]]
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| 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.
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| ==Definition==
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| '''Relative permittivity''' is typically denoted as {{math|ε<sub>r</sub>(ω)}} (sometimes {{math|κ}} or {{math|K}}) and is defined as
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| :<math>\varepsilon_{r}(\omega) = \frac{\varepsilon(\omega)}{\varepsilon_{0}},</math>
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| where ''ε(ω)'' is the [[complex number|complex]] frequency-dependent [[Permittivity|absolute permittivity]] of the material, and ε<sub>0</sub> is the [[vacuum permittivity]].
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| Relative permittivity is a [[Dimensionless quantity|dimensionless]] number that is in general [[complex number|complex-valued]]; its real and imaginary parts are denoted as:<ref name=ChenVaradan2004>{{cite book|author=Linfeng Chen and Vijay K. Varadan|year=2004|title=Microwave electronics: measurement and materials characterization|url=http://books.google.co.jp/books?id=2oA3po4coUoC&pg=PA8|publisher=John Wiley and Sons|isbn=0-470-84492-2|doi=10.1002/0470020466|page=8, eq.(1.15)}}</ref>
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| :<math> \varepsilon_r(\omega) = \varepsilon_{r}'(\omega) + i \varepsilon_{r}''(\omega). </math>
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| The relative permittivity of a medium is related to its [[electric susceptibility]], {{math|χ<sub>e</sub>}}, as {{math|ε<sub>r</sub>(ω) {{=}} 1 + χ<sub>e</sub>}}.
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| In anisotropic media (such as non cubic crystals) the relative permittivity is a second rank [[tensor]].
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| The relative permittivity of a material for a [[frequency]] of zero is known as its '''static relative permittivity'''.
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| === Terminology ===
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| Dielectric constant is the historical term which, although still very common, has been deprecated by the relevant standards organizations.<ref name="IUPAC">{{cite journal |last=Braslavsky |first=S.E.|url=http://iupac.org/publications/pac/2007/pdf/7903x0293.pdf |title=Glossary of terms used in photochemistry (IUPAC recommendations 2006)|journal=Pure and Applied Chemistry|volume=79 |year=2007 |pages=293–465|doi=10.1351/pac200779030293}}</ref><ref name=IEEE1997>{{cite web |author=[[IEEE]] Standards Board|url=http://ieeexplore.ieee.org/servlet/opac?punumber=5697|title=IEEE Standard Definitions of Terms for Radio Wave Propagation|year=1997 |page=6}}</ref> There is potential ambiguity in this predecessor name, as some older authors used it for the absolute permittivity ε<ref>{{cite book
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| |last = King
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| |first = Ronold W. P.
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| |authorlink = Ronold W. P. King
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| |title = Fundamental Electromagnetic Theory
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| |publisher = Dover
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| |year = 1963
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| |location = New York
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| |page = 139}}</ref> while in most modern usage it refers to a relative permittivity ε<sub>r</sub>,<ref name=IEEE1997/><ref name=Jackson/> 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'<sub>r</sub> of the complex-valued relative permittivity.{{citation needed|date=September 2013}}
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| ===Physics===
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| The imaginary portion of the permittivity corresponds to a phase shift of the polarization {{math|'''P'''}} relative to {{math|'''E'''}} and leads to the attenuation of electromagnetic waves passing through the medium. By definition, the linear relative [[vacuum permittivity|permittivity of vacuum]] is equal to 1,<ref name=Jackson>
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| {{cite book
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| |author=John David Jackson
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| |title=Classical Electrodynamics
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| |edition=Third
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| |publisher= Wiley
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| |location=New York
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| |year=1998
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| |isbn=0-471-30932-X
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| |page=154}}
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| </ref> that is ε = ε<sub>0</sub>, although there are theoretical nonlinear [[quantum electrodynamics|quantum]] effects in vacuum that exist at high field strengths.<ref name=Mourou>{{cite journal|doi=10.1103/RevModPhys.78.309|title=Optics in the relativistic regime|year=2006|last1=Mourou|first1=Gerard A.|journal=Reviews of Modern Physics|volume=78|page=309|bibcode=2006RvMP...78..309M}}</ref>
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| ==Measurement==
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| The relative static permittivity, ''ε<sub>r</sub>'', can be measured for static [[electric field]]s as follows: first the [[capacitance]] of a test [[capacitor]], ''C<sub>0</sub>'', is measured with vacuum between its plates. Then, using the same capacitor and distance between its plates the capacitance ''C<sub>x</sub>'' with a [[dielectric]] between the plates is measured. The relative dielectric constant can be then calculated as
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| :<math>\varepsilon_{r} = \frac{C_{x}} {C_{0}}.</math>
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| For time-variant [[electromagnetic field]]s, this quantity becomes [[frequency]]-dependent. An indirect technique to calculate ''ε<sub>r</sub>'' is conversion of radio frequency [[S-parameter]] measurement results. A description of frequently used S-parameter conversions for determination of the frequency-dependent ''ε<sub>r</sub>'' of dielectrics can be found in this bibliographic source.<ref>{{cite web|url=http://www.rohde-schwarz.com/appnote/RAC-0607.0019.pdf|title= Measurement of Dielectric Material Properties|first1=CheeYaw|last1=Kuek|publisher=R&S}}</ref> Alternatively, resonance based effects may be employed at fixed frequencies.<ref>{{cite doi|10.1109/LMWC.2011.2122303}}</ref>
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| ==Applications==
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| ===Energy===
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| The dielectric constant is an essential piece of information when designing [[capacitor]]s, 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 ([[Printed circuit board|PCBs]]) also act as dielectrics.
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| ===Communication===
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| 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 [[Dielectric resonator filter|filters]]. [[Optical fibers]] are examples of ''dielectric [[waveguide]]s''. They consist of dielectric materials that are purposely doped with impurities so as to control the precise value of ''ε<sub>r</sub>'' 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.
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| ===Environmental===
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| The relative permittivity of air changes with temperature, humidity, and barometric pressure.<ref>A Low Cost Integrated Interface for Capacitive Sensors, Ali Heidary, Thesis, p. 22</ref> 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.
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| ===Chemical===
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| The relative static permittivity of a solvent is a relative measure of its [[Chemical polarity|polarity]]. For example, [[water (molecule)|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.<ref>{{RubberBible86th}}</ref> This information is of great value when designing separation, [[sample preparation]] and [[chromatography]] techniques in [[analytical chemistry]].
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| The correlation should, however, be treated with caution. For instance, [[dichloromethane]] has a value of ε<sub>r</sub> of [[Dichloromethane (data page)|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 ε<sub>r</sub> = [[Tetrahydrofuran (data page)|7.52]] at 22 °C, but it is completely miscible with water. <!-- The commonly known "like-dissolves-like" principle could be useful here, as the probable reason for the discrepancy is the specific interaction between the oxygen atoms, as the THF could be treated as a homologue of water. -->
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| Even more apparent this is when considering the ε<sub>r</sub> of [[acetic acid]] (6.2528)<ref name="gaussian">AE. Frisch, M. J. Frish, F. R. Clemente, G. W. Trucks. Gaussian 09 User's Reference. Gaussian, Inc.: Walligford, CT, 2009.- p. 257.</ref> and that of [[iodoethane]] (7.6177)<ref name="gaussian" />. The large numerical value of ε<sub>r</sub> 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 the orientational one in this case).
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| ==Lossy medium==
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| Again, similar as for [[Lossy medium|absolute permittivity]], relative permittivity for lossy materials can be formulated as:
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| :<math> \varepsilon_{r} = \varepsilon_{r}' + \frac{i\sigma}{\omega \varepsilon_0}, </math>
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| in terms of a "dielectric conductivity" σ (units S/m, [[Siemens (unit)|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]" (,<ref name=ChenVaradan2004/> p. 8). Expanding the [[angular frequency]] ω = 2πc/λ and the [[electric constant]] ε<sub>0</sub> = 1/(µ<sub>0</sub>c<sup>2</sup>), it reduces to:
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| :<math> \varepsilon_{r} = \varepsilon_{r}' + i \sigma \lambda \kappa, </math>
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| where λ is the wavelength, ''c'' is the speed of light in vacuum and ''κ = µ<sub>0</sub>c/2π'' ≈ 60.0 S<sup>−1</sup> is a newly introduced constant (units reciprocal of [[Siemens (unit)|siemens]], such that σλκ = ε<sub>r</sub>" remains unitless).
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| ==Metals==
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| 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 (<ref name=Lourtioz>{{cite book|author=Lourtioz, J.-M. et al.|url=http://books.google.com/books?id=vSszZ2WuG_IC&pg=PA121|title=Photonic Crystals: Towards Nanoscale Photonic Devices|year=2005|publisher=Springer|isbn=3-540-24431-X}}</ref> 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 (<ref name=Lourtioz/> eq.(4.8)–(4.9), p. 122).
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| ==See also==
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| {{colbegin|3}}
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| *[[Curie temperature]]
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| *[[Dielectric spectroscopy]]
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| *[[Dielectric strength]]
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| *[[Electret]]
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| *[[Ferroelectricity]]
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| *[[Green–Kubo relations]]
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| *[[High-k dielectric]]
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| *[[Kramers–Kronig relation]]
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| *[[Linear response function]]
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| *[[Low-k dielectric]]
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| *[[Loss tangent]]
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| *[[Permittivity]]
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| *[[Refractive index]]
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| {{colend}}
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| ==References==
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| {{reflist|2}}
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| {{DEFAULTSORT:Relative Permittivity}}
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| [[Category:Electricity]]
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| [[Category:Electric and magnetic fields in matter]]
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| [[Category:Colloidal chemistry]]
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| [[de:Dielektrizitätszahl]]
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| [[eo:Dielektra permeableco]]
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| [[fa:ثابت گذردهی خلأ]]
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| [[fr:Permittivité]]
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| [[it:Costante dielettrica]]
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| [[pt:Constante dieléctrica]]
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| [[vi:Hằng số điện môi]]
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