A dielectric (or dielectric material) 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.[1] 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.[1] The study of dielectric properties concerns storage and dissipation of electric and magnetic energy in materials.[2][3][4] Dielectrics are important for explaining various phenomena in electronics, optics, solid-state physics, and cell biophysics. Contents 1 Terminology 2 Electric susceptibility 2.1 Dispersion and causality 3
3.1 Basic atomic model 3.2 Dipolar polarization 3.3 Ionic polarization 3.3.1 Ionic polarization of cells 4
5.1 Debye relaxation 5.2 Variants of the Debye equation 6 Paraelectricity 7 Tunability 8 Applications 8.1 Capacitors
8.2
9 Some practical dielectrics 10 See also 11 References 12 Further reading 13 External links Terminology[edit]
Although the term insulator implies low electrical conduction,
dielectric typically means materials with a high polarizability. The
latter is expressed by a number called the relative permittivity. The
term insulator is generally used to indicate electrical obstruction
while the term dielectric is used to indicate the energy storing
capacity of the material (by means of polarization). A common example
of a dielectric is the electrically insulating material between the
metallic plates of a capacitor. The polarization of the dielectric by
the applied electric field increases the capacitor's surface charge
for the given electric field strength.[1]
The term "dielectric" was coined by
P = ε 0 χ e E , displaystyle mathbf P =varepsilon _ 0 chi _ e mathbf E , where ε0 is the electric permittivity of free space. The susceptibility of a medium is related to its relative permittivity εr by χ e = ε r − 1. displaystyle chi _ e =varepsilon _ r -1. So in the case of a vacuum, χ e = 0. displaystyle chi _ e =0. The electric displacement D is related to the polarization density P by D = ε 0 E + P = ε 0 ( 1 + χ e ) E = ε r ε 0 E . displaystyle mathbf D = varepsilon _ 0 mathbf E +mathbf P = varepsilon _ 0 (1+chi _ e )mathbf E = varepsilon _ r varepsilon _ 0 mathbf E . Dispersion and causality[edit] In general, a material cannot polarize instantaneously in response to an applied field. The more general formulation as a function of time is P ( t ) = ε 0 ∫ − ∞ t χ e ( t − t ′ ) E ( t ′ ) d t ′ . displaystyle mathbf P (t)=varepsilon _ 0 int _ -infty ^ t chi _ e (t-t')mathbf E (t'),dt'. That is, the polarization is a convolution of the electric field at
previous times with time-dependent susceptibility given by χe(Δt).
The upper limit of this integral can be extended to infinity as well
if one defines χe(Δt) = 0 for Δt < 0. An instantaneous response
corresponds to
P ( ω ) = ε 0 χ e ( ω ) E ( ω ) . displaystyle mathbf P (omega )=varepsilon _ 0 chi _ e (omega )mathbf E (omega ). Note the simple frequency dependence of the susceptibility, or
equivalently the permittivity. The shape of the susceptibility with
respect to frequency characterizes the dispersion properties of the
material.
Moreover, the fact that the polarization can only depend on the
electric field at previous times (i.e., χe(Δt) = 0 for Δt < 0),
a consequence of causality, imposes Kramers–Kronig constraints on
the real and imaginary parts of the susceptibility χe(ω).
In the classical approach to the dielectric model, a material is made up of atoms. Each atom consists of a cloud of negative charge (electrons) bound to and surrounding a positive point charge at its center. In the presence of an electric field the charge cloud is distorted, as shown in the top right of the figure. This can be reduced to a simple dipole using the superposition principle. A dipole is characterized by its dipole moment, a vector quantity shown in the figure as the blue arrow labeled M. It is the relationship between the electric field and the dipole moment that gives rise to the behavior of the dielectric. (Note that the dipole moment points in the same direction as the electric field in the figure. This isn't always the case, and is a major simplification, but is true for many materials.) When the electric field is removed the atom returns to its original state. The time required to do so is the so-called relaxation time; an exponential decay. This is the essence of the model in physics. The behavior of the dielectric now depends on the situation. The more complicated the situation, the richer the model must be to accurately describe the behavior. Important questions are: Is the electric field constant or does it vary with time? At what rate? Does the response depend on the direction of the applied field (isotropy of the material)? Is the response the same everywhere (homogeneity of the material)? Do any boundaries or interfaces have to be taken into account? Is the response linear with respect to the field, or are there nonlinearities? The relationship between the electric field E and the dipole moment M gives rise to the behavior of the dielectric, which, for a given material, can be characterized by the function F defined by the equation: M = F ( E ) displaystyle mathbf M =mathbf F (mathbf E ) . When both the type of electric field and the type of material have been defined, one then chooses the simplest function F that correctly predicts the phenomena of interest. Examples of phenomena that can be so modeled include: Refractive index Group velocity dispersion Birefringence Self-focusing Harmonic generation Dipolar polarization[edit]
dipolar polarization can no longer follow the oscillations of the electric field in the microwave region around 1010 Hz; ionic polarization and molecular distortion polarization can no longer track the electric field past the infrared or far-infrared region around 1013 Hz, ; electronic polarization loses its response in the ultraviolet region around 1015 Hz. In the frequency region above ultraviolet, permittivity approaches the
constant ε0 in every substance, where ε0 is the permittivity of the
free space. Because permittivity indicates the strength of the
relation between an electric field and polarization, if a polarization
process loses its response, permittivity decreases.
ε ^ ( ω ) = ε ∞ + Δ ε 1 + i ω τ , displaystyle hat varepsilon (omega )=varepsilon _ infty + frac Delta varepsilon 1+iomega tau , where ε∞ is the permittivity at the high frequency limit, Δε = εs − ε∞ where εs is the static, low frequency permittivity, and τ is the characteristic relaxation time of the medium. Separating the real and imaginary parts of the complex dielectric permittivity yields:[8] ε ′ = ε ∞ + ( ε s − ε ∞ ) ( 1 + ω 2 τ 2 ) displaystyle varepsilon '=varepsilon _ infty + frac (varepsilon _ s -varepsilon _ infty ) (1+omega ^ 2 tau ^ 2 ) ε ″ = ( ε s − ε ∞ ) ω τ 1 + ω 2 τ 2 displaystyle varepsilon ''= frac (varepsilon _ s -varepsilon _ infty )omega tau 1+omega ^ 2 tau ^ 2 The dielectric loss is also represented by: tan δ = ε ″ ε ′ = ( ε s − ε ∞ ) ω τ ε s + ε ∞ ω 2 τ 2 displaystyle tan delta = frac varepsilon '' varepsilon ' = frac (varepsilon _ s -varepsilon _ infty )omega tau varepsilon _ s +varepsilon _ infty omega ^ 2 tau ^ 2 This relaxation model was introduced by and named after the physicist
Cole–Cole equation This equation is used when the dielectric loss peak shows symmetric broadening Cole–Davidson equation This equation is used when the dielectric loss peak shows asymmetric broadening Havriliak–Negami relaxation This equation considers both symmetric and asymmetric broadening Kohlrausch–Williams–Watts function (Fourier transform of stretched exponential function) Curie-von Schweidler law This shows the response of dielectrics to an applied DC field to
behave according to a power law, which can be expressed as an integral
over weighted exponential functions.
Paraelectricity[edit]
See also: Ferroelectricity
Charge separation in a parallel-plate capacitor causes an internal electric field. A dielectric (orange) reduces the field and increases the capacitance. Commercially manufactured capacitors typically use a solid dielectric material with high permittivity as the intervening medium between the stored positive and negative charges. This material is often referred to in technical contexts as the capacitor dielectric.[16] The most obvious advantage to using such a dielectric material is that it prevents the conducting plates, on which the charges are stored, from coming into direct electrical contact. More significantly, however, a high permittivity allows a greater stored charge at a given voltage. This can be seen by treating the case of a linear dielectric with permittivity ε and thickness d between two conducting plates with uniform charge density σε. In this case the charge density is given by σ ε = ε V d displaystyle sigma _ varepsilon =varepsilon frac V d and the capacitance per unit area by c = σ ε V = ε d displaystyle c= frac sigma _ varepsilon V = frac varepsilon d From this, it can easily be seen that a larger ε leads to greater
charge stored and thus greater capacitance.
Industrial coatings such as parylene provide a dielectric barrier
between the substrate and its environment.
See also[edit] Classification of materials based on permittivity
Paramagnetism
Clausius-Mossotti relation
References[edit] ^ a b c Dielectric. Encyclopædia Britannica: "Dielectric, insulating
material or a very poor conductor of electric current. When
dielectrics are placed in an electric field, practically no current
flows in them because, unlike metals, they have no loosely bound, or
free, electrons that may drift through the material."
^ Arthur R. von Hippel, in his seminal work,
Further reading[edit] Jackson, John David (August 10, 1998). Classical Electrodynamics (3 rd ed.). John Wiley & Sons. ISBN 978-0-471-30932-1. 808 or 832 pages. Scaife, Brendan (September 3, 1998). Principles of Dielectrics
(Monographs on the
External links[edit] Electromagnetism – A chapter from an online textbook
"Dielectric". Encyclopedia Americana. 1920.
"Dielectric".
v t e Polarization states dielectric paraelectricity ferroelectricity antiferroelectricity helielectricity ferrielectricity Authority control |