Relative static permittivity

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 relative static permittivity is represented as "ε_r" or sometimes $kappa$ or "K" or Dk. It is defined as

:$varepsilon\_\{r\}\; =\; frac\{varepsilon\_\{s\{varepsilon\_\{0,$

where "ε_s" is the static permittivity of the material, and "ε₀" is the electric constant. (The relative permittivity is the complex frequency-dependent $varepsilon(omega)\; /\; varepsilon\_0$, which gives the static relative permittivity for $omega=0$.)

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.citation |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=p. 293-465; see p. 32] [cite web |author=IEEE Standards Board|url=http://ieeexplore.ieee.org/iel4/5697/15269/00705931.pdf?arnumber=705931|title=IEEE Standard Definitions of Terms for Radio Wave Propagation|year=1997 |pages=p. 6] The reason for the potential ambiguity is twofold. First, some older authors used "dielectric constant" or "absolute dielectric constant" for the absolute permittivity $varepsilon$ rather than the relative permittivity. [cite book
last = King
first = Ronold W. P.
title = Fundamental Electromagnetic Theory
publisher = Dover
year = 1963
location = New York
pages = p. 139] Second, while in most modern usage "dielectric constant" refers to a relative permittivity [cite book|last=Jackson|first=John David|title=Classical Electrodynamics, 3rd edition|publisher=Wiley|year=1998|location=New York|pages=p. 154] , it may be either the static or the frequency-dependent relative permittivity depending on context.

By definition, the linear relative permittivity of vacuum, where $varepsilon\; =\; varepsilon\_0$, is equal to 1,cite book
author=John David Jackson
title=Classical Electrodynamics
edition=Third Edition
page=p. 154
publisher= Wiley
location=New York
year=1998
isbn=047130932X
url=http://worldcat.org/isbn/047130932X] although there are theoretical nonlinear quantum effects in vacuum that have been predicted at high field strengths (but not yet observed).Mourou, G. A., T. Tajima, and S. V. Bulanov, "Optics in the relativistic regime," "Reviews of Modern Physics" vol. 78 (no. 2), 309-371 (2006).]

The static relative permittivity of a medium is related to its static electric susceptibility, $chi\_e$ by

:$varepsilon\_r\; =\; 1\; +\; chi\_e,$

in SI units.

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 dielectric constant 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. [D.R. Lide, Ed. "CRC Handbook of Chemistry and Physics, 85th Ed." (2004). CRC Press. Boca Raton. p.8–141.] This information is of great value when designing separation, sample preparation and chromatography techniques in analytical chemistry.

ee also

*Permittivity
*Refractive index
*Ferroelectricity
*Dielectric strength
*Low-k
*High-k
*Linear response function
*Kramers–Kronig relation
*Green–Kubo relations
*Dielectric spectroscopy
*Curie point
*Electret

References