Relative permittivity

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Relative permittivities of some materials at room temperature under 1 kHz
Materialεr
Vacuum 1 (by definition)
Air 1.00058986±0.00000050
(at STP, for 0.9 MHz), [1]
PTFE/Teflon2.1
Polyethylene/XLPE2.25
Polyimide 3.4
Polypropylene 2.2–2.36
Polystyrene 2.4–2.7
Carbon disulfide 2.6
Mylar 3.1 [2]
Paper, printing, 200 kHz,1.4 [3]
Electroactive polymers 2–12
Mica 3–6 [2]
Silicon dioxide 3.9 [4]
Sapphire 8.9–11.1 (anisotropic) [5]
Concrete 4.5
Pyrex (glass)4.7 (3.7–10)
Neoprene 6.7 [2]
Rubber 7
Diamond 5.5–10
Salt 3–15
Graphite 10–15
Silicon 11.68
Silicon nitride 7–8 (polycrystalline, 1 MHz) [6] [7]
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 87.9, 80.2, 55.5
(0, 20, 100 °C) [8]
for visible light: 1.77
Hydrofluoric acid 175, 134, 111, 83.6
−73 °C, −42 °C, −27 °C, 0 °C),
Hydrazine 52.0 (20 °C),
Formamide 84.0 (20 °C)
Sulfuric acid 84–100 (20–25 °C)
Hydrogen peroxide 128 aqueous–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 [9] 1200–10,000 (20–120 °C)
Lead zirconate titanate 500–6000
Conjugated polymers 1.8–6 up to 100,000 [10]
Calcium copper titanate >250,000 [11]
Temperature dependence of the relative static permittivity of water Water relative static permittivity.svg
Temperature dependence of the relative static permittivity of water

The relative permittivity of a material is its (absolute) permittivity expressed as a ratio relative to the vacuum permittivity.

Permittivity physical quantity, measure of the resistance to the electric field

In electromagnetism, absolute permittivity, often simply called permittivity, usually denoted by the Greek letter ε (epsilon), is the measure of capacitance that is encountered when forming an electric field in a particular medium. More specifically, permittivity describes the amount of charge needed to generate one unit of electric flux in a given medium. A charge will yield more electric flux in a medium with low permittivity than in a medium with high permittivity. Permittivity is the measure of a material's ability to store an electric field in the polarization of the medium.

The physical constant ε0, commonly called the vacuum permittivity, permittivity of free space or electric constant or the distributed capacitance of the vacuum, is an ideal, (baseline) physical constant, which is the value of the absolute dielectric permittivity of classical vacuum. It has the CODATA value

Contents

Permittivity is a material property that affects the Coulomb 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 the capacitance of a capacitor using that material as a dielectric, 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 [12] as well as in chemistry. [13]

Capacitance Ability of a body to store an electrical charge

Capacitance is the ratio of the change in an electric charge in a system to the corresponding change in its electric potential. There are two closely related notions of capacitance: self capacitance and mutual capacitance. Any object that can be electrically charged exhibits self capacitance. A material with a large self capacitance holds more electric charge at a given voltage than one with low capacitance. The notion of mutual capacitance is particularly important for understanding the operations of the capacitor, one of the three elementary linear electronic components.

Capacitor Passive two-terminal electronic component that stores electrical energy in an electric field

A capacitor is a device that stores electrical energy in an electric field. It is a passive electronic component with two terminals.

Dielectric electrically poorly conducting or non-conducting, non-metallic substance of which charge carriers are generally not free to move

A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material as they do in an electrical conductor but only slightly shift from their average equilibrium positions causing dielectric polarization. Because of dielectric polarization, positive charges are displaced in the direction of the field and negative charges shift in the opposite direction. This creates an internal electric field that reduces the overall field within the dielectric itself. If a dielectric is composed of weakly bonded molecules, those molecules not only become polarized, but also reorient so that their symmetry axes align to the field.

Definition

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

where ε(ω) is the complex frequency-dependent permittivity of the material, and ε0 is the vacuum permittivity.

Complex number Element of a number system in which –1 has a square root

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. Because no real number satisfies this equation, i is called an imaginary number. For the complex number a + bi, a is called the real part, and b is called the imaginary part. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers, and are fundamental in many aspects of the scientific description of the natural world.

Relative permittivity is a dimensionless number that is in general complex-valued; its real and imaginary parts are denoted as: [14]

In dimensional analysis, a dimensionless quantity is a quantity to which no physical dimension is assigned, also known as a bare, pure, or scalar quantity or a quantity of dimension one, with a corresponding unit of measurement in the SI of one unit that is not explicitly shown. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Examples of quantities to which dimensions are regularly assigned are length, time, and speed, which are measured in dimensional units, such as metre, second and metre per second. This is considered to aid intuitive understanding. However, especially in mathematical physics, it is often more convenient to drop the assignment of explicit dimensions and express the quantities without dimensions, e.g., addressing the speed of light simply by the dimensionless number 1.

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

In electricity (electromagnetism), the electric susceptibility is a dimensionless proportionality constant that indicates the degree of polarization of a dielectric material in response to an applied electric field. The greater the electric susceptibility, the greater the ability of a material to polarize in response to the field, and thereby reduce the total electric field inside the material. It is in this way that the electric susceptibility influences the electric permittivity of the material and thus influences many other phenomena in that medium, from the capacitance of capacitors to the speed of light.

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

The relative permittivity of a material for a frequency of zero is known as its static relative permittivity.

Terminology

The historical term for the relative permittivity is dielectric constant. It is still commonly used, but has been deprecated by standards organizations, [12] [13] because of its ambiguity, as some older authors used it for the absolute permittivity ε. [12] [15] [16] The permittivity may be quoted either as a static property or as a frequency-dependent variant. It has also been used to refer to only the real component ε'r of the complex-valued relative permittivity.[ citation needed ]

Physics

In the causal theory of waves, permittivity is a complex quantity. The imaginary part 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, [16] that is ε = ε0, although there are theoretical nonlinear quantum effects in vacuum that become non-negligible at high field strengths. [17]

The following table gives some typical values.

Low-frequency dielectric constants of some common solvents
SolventDielectric constantTemperature (K)
benzene 2.3298
diethyl ether 4.3293
tetrahydrofuran (THF)7.6298
dichloromethane 9.1293
liquid ammonia 17273
ethanol 24.3298
methanol 32.7298
nitromethane 35.9303
dimethyl formamide (DMF)36.7298
acetonitrile 37.5293
water 78.4298
formamide 109293

Measurement

The relative static permittivity, εr, 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 with a dielectric between the plates is measured. The relative permittivity can be then calculated as

For time-variant electromagnetic fields, this quantity becomes frequency-dependent. An indirect technique to calculate εr is conversion of radio frequency S-parameter measurement results. A description of frequently used S-parameter conversions for determination of the frequency-dependent εr of dielectrics can be found in this bibliographic source. [18] Alternatively, resonance based effects may be employed at fixed frequencies. [19]

Applications

Energy

The relative permittivity 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 relative permittivity 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.

Communication

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 εr 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.

Environment

The relative permittivity of air changes with temperature, humidity, and barometric pressure. [20] 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

The relative static permittivity of a solvent is a relative measure of its chemical polarity. For example, water is very polar, and has a relative static permittivity of 80.10 at 20 °C while n-hexane is non-polar, and has a relative static permittivity of 1.89 at 20 °C. [21] This information is important when designing separation, sample preparation and chromatography techniques in analytical chemistry.

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

This is even more apparent when comparing the εr values of acetic acid (6.2528) [22] and that of iodoethane (7.6177). [22] The large numerical value of εr 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 over the orientational one in this case).

Lossy medium

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

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

where λ is the wavelength, c is the speed of light in vacuum and κ = µ0c/2π = 59.95849 Ω ≈ 60.0 Ω is a newly introduced constant (units ohms, or reciprocal siemens, such that σλκ = εr remains unitless).

Metals

Permittivity is typically associated with dielectric materials, however metals are described as having an effective permittivity, with real relative permittivity equal to one. [23] In the low-frequency region, which extends from radio frequencies to the far infrared and terahertz region, the plasma frequency of the electron gas is much greater than the electromagnetic propagation frequency, so the refractive index n 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. [24]

See also

Related Research Articles

The wave impedance of an electromagnetic wave is the ratio of the transverse components of the electric and magnetic fields. For a transverse-electric-magnetic (TEM) plane wave traveling through a homogeneous medium, the wave impedance is everywhere equal to the intrinsic impedance of the medium. In particular, for a plane wave travelling through empty space, the wave impedance is equal to the impedance of free space. The symbol Z is used to represent it and it is expressed in units of ohms. The symbol η (eta) may be used instead of Z for wave impedance to avoid confusion with electrical impedance.

Poynting vector

In physics, the Poynting vector represents the directional energy flux of an electromagnetic field. The SI unit of the Poynting vector is the watt per square metre (W/m2). It is named after its discoverer John Henry Poynting who first derived it in 1884. Oliver Heaviside also discovered it independently.

Displacement current Physical quantity in electromagnetism

In electromagnetism, displacement current density is the quantity D/∂t appearing in Maxwell's equations that is defined in terms of the rate of change of D, the electric displacement field. Displacement current density has the same units as electric current density, and it is a source of the magnetic field just as actual current is. However it is not an electric current of moving charges, but a time-varying electric field. In physical materials, there is also a contribution from the slight motion of charges bound in atoms, called dielectric polarization.

In physics, the dissipation factor (DF) is a measure of loss-rate of energy of a mode of oscillation in a dissipative system. It is the reciprocal of quality factor, which represents the "quality" or durability of oscillation.

In physics, the electric displacement field, denoted by D, is a vector field that appears in Maxwell's equations. It accounts for the effects of free and bound charge within materials. "D" stands for "displacement", as in the related concept of displacement current in dielectrics. In free space, the electric displacement field is equivalent to flux density, a concept that lends understanding to Gauss's law. In the International System of Units (SI), it is expressed in units of coulomb per meter square (C⋅m−2).

The Havriliak–Negami relaxation is an empirical modification of the Debye relaxation model in electromagnetism. Unlike the Debye model, the Havriliak–Negami relaxation accounts for the asymmetry and broadness of the dielectric dispersion curve. The model was first used to describe the dielectric relaxation of some polymers, by adding two exponential parameters to the Debye equation:

Dielectric heating

Dielectric heating, also known as electronic heating, radio frequency heating, and high-frequency heating, is the process in which a radio frequency (RF) alternating electric field, or radio wave or microwave electromagnetic radiation heats a dielectric material. At higher frequencies, this heating is caused by molecular dipole rotation within the dielectric.

Dielectric loss quantifies a dielectric material's inherent dissipation of electromagnetic energy. It can be parameterized in terms of either the loss angleδ or the corresponding loss tangent tan δ. Both refer to the phasor in the complex plane whose real and imaginary parts are the resistive (lossy) component of an electromagnetic field and its reactive (lossless) counterpart.

When an electromagnetic wave travels through a medium in which it gets attenuated, it undergoes exponential decay as described by the Beer–Lambert law. However, there are many possible ways to characterize the wave and how quickly it is attenuated. This article describes the mathematical relationships among:

MIS capacitor

A MIS capacitor is a capacitor formed from a layer of metal, a layer of insulating material and a layer of semiconductor material. It gets its name from the initials of the metal-insulator-semiconductor structure. As with the MOS field-effect transistor structure, for historical reasons, this layer is also often referred to as a MOS capacitor, but this specifically refers to an oxide insulator material.

The optical conductivity is a material property, which links the current density to the electric field for general frequencies. In this sense, this linear response function is a generalization of the electrical conductivity, which is usually considered in the static limit, i.e., for a time-independent electric field. While the static electrical conductivity is vanishingly small in insulators, the optical conductivity always remains finite in some frequency intervals ; the total optical weight can be inferred from sum rules. The optical conductivity is closely related to the dielectric function, the generalization of the dielectric constant to arbitrary frequencies.

Surface plasmon polariton

Surface plasmon polaritons (SPPs) are electromagnetic waves that travel along a metal–dielectric or metal–air interface, practically in the infrared or visible-frequency. The term "surface plasmon polariton" explains that the wave involves both charge motion in the metal and electromagnetic waves in the air or dielectric ("polariton").

Lyddane–Sachs–Teller relation determines the ratio of the natural frequency of longitudinal optic lattice vibrations (phonons) of an ion crystal to the natural frequency of the transverse optical lattice vibration for long wavelengths (zero wavevector)

In condensed matter physics, the Lyddane–Sachs–Teller relation determines the ratio of the natural frequency of longitudinal optic lattice vibrations (phonons) of an ionic crystal to the natural frequency of the transverse optical lattice vibration for long wavelengths. The ratio is that of the static permittivity to the permittivity for frequencies in the visible range .

Loop-gap resonator

A loop-gap resonator (LGR) is an electromagnetic resonator that operates in the radio and microwave frequency ranges. The simplest LGRs are made from a conducting tube with a narrow slit cut along its length. The LGR dimensions are typically much smaller than the free-space wavelength of the electromagnetic fields at the resonant frequency. Therefore, relatively compact LGRs can be designed to operate at frequencies that are too low to be accessed using, for example, cavity resonators. These structures can have very sharp resonances making them useful for electron spin resonance (ESR) experiments and precision measurements of electromagnetic material properties.

References

  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. 1 2 3 Young, 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. "Fine Ceramics" (PDF). Toshiba Materials.
  7. "Material Properties Charts" (PDF). Ceramic Industry. 2013.
  8. 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.
  9. "Permittivity". schools.matter.org.uk. Archived from the original on 2016-03-11.
  10. Pohl, H. A. (1986). "Giant polarization in high polymers". Journal of Electronic Materials . 15 (4): 201. Bibcode:1986JEMat..15..201P. doi:10.1007/BF02659632.
  11. 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.
  12. 1 2 3 IEEE Standards Board (1997). "IEEE Standard Definitions of Terms for Radio Wave Propagation". p. 6.
  13. 1 2 Braslavsky, 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.
  14. 1 2 Linfeng 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.
  15. King, Ronold W. P. (1963). Fundamental Electromagnetic Theory. New York: Dover. p. 139.
  16. 1 2 John David Jackson (1998). Classical Electrodynamics (Third ed.). New York: Wiley. p. 154. ISBN   978-0-471-30932-1.
  17. 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.
  18. Kuek, CheeYaw. "Measurement of Dielectric Material Properties" (PDF). R&S.
  19. Costa, F.; Amabile, C.; Monorchio, A.; Prati, E. (2011). "Waveguide Dielectric Permittivity Measurement Technique Based on Resonant FSS Filters" (PDF). IEEE Microwave and Wireless Components Letters. 21 (5): 273. doi:10.1109/LMWC.2011.2122303.
  20. 5×10−6/°C, 1.4×10−6/%RH and 100×10−6/atm respectively. See A Low Cost Integrated Interface for Capacitive Sensors, Ali Heidary, 2010, Thesis, p. 12. ISBN   9789461130136.
  21. Lide, D. R., ed. (2005). CRC Handbook of Chemistry and Physics (86th ed.). Boca Raton (FL): CRC Press. ISBN   0-8493-0486-5.
  22. 1 2 AE. Frisch, M. J. Frish, F. R. Clemente, G. W. Trucks. Gaussian 09 User's Reference. Gaussian, Inc.: Walligford, CT, 2009.- p. 257.
  23. 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
  24. Lourtioz (2005), equations (4.8)–(4.9), page 122