Dielectric

A dielectric is a material in which an applied electric field produces electrical polarization: a displacement or reorientation of positive and negative charges that creates electric dipole moments. Unlike an electrical conductor, an ideal dielectric does not support sustained transport of free charge through its bulk. Real dielectrics nevertheless have finite leakage and dissipate some electrical energy. Their behavior is central to capacitors, electrical insulation, and the propagation of electromagnetic waves. (ocw.mit.edu)

Polarization and microscopic mechanisms

Electrical polarization does not require a material to acquire a net electric charge. Instead, charges within its constituent atoms or molecules shift relative to one another, or existing dipoles become preferentially aligned. The macroscopic polarization vector, $\mathbf P$, is the electric dipole moment per unit volume. Polarization generally produces bound charges at surfaces and, when it varies spatially, within the material. These charges contribute to the total electric field. (web.mit.edu)

Several mechanisms can contribute to dielectric polarization:

• Electronic polarization: the electron distribution shifts relative to the atomic nucleus.
• Ionic polarization: positively and negatively charged ions undergo relative displacement.
• Orientational polarization: permanent molecular dipoles become partially aligned with the field; thermal motion opposes this alignment.
• Interfacial or space-charge polarization: mobile charges accumulate at boundaries, defects, or interfaces between regions with different electrical properties. (nvlpubs.nist.gov)

These mechanisms operate on different timescales. Interfacial and orientational responses commonly contribute at lower frequencies, whereas electronic polarization can persist into the optical range. Consequently, a dielectric’s response cannot generally be represented by one number valid at every frequency. (nvlpubs.nist.gov)

Permittivity and the macroscopic description

The electric displacement field, $\mathbf D$, separates the contribution of free charge from that of polarization:

where $\varepsilon_0$ is the vacuum permittivity. In a linear, isotropic dielectric,

where $\chi_e$ is the electric susceptibility and $\varepsilon$ is the material’s permittivity. Its relative permittivity is

The term dielectric constant commonly denotes the static or real-valued relative permittivity, although this quantity can depend on frequency, temperature, and other conditions. (ocw.mit.edu)

In anisotropic materials, permittivity is a tensor: polarization need not point in the same direction as the applied field. In nonlinear materials, polarization is not simply proportional to field strength. Thus, $\mathbf D=\varepsilon\mathbf E$ with a single scalar constant is a useful constitutive model, not a universal description. (ctcms.nist.gov)

The bound volume and surface charge densities are

where $\hat{\mathbf n}$ is the outward normal to the dielectric surface. Gauss’s law becomes

with $\rho_f$ denoting free charge density. At an interface, the jump in the normal component of $\mathbf D$ equals the free surface charge density; the tangential electric field is continuous under ordinary electrostatic conditions. These relations are part of the macroscopic formulation of Maxwell’s equations. (web.mit.edu)

Capacitors and stored energy

A dielectric between the electrodes of a capacitor changes the relation between electrode charge and voltage. For parallel plates of area $A$, separated by distance $d$, with the gap completely filled by a homogeneous linear dielectric and edge effects neglected,

where $C_0=\varepsilon_0A/d$ is the capacitance of the same geometry in vacuum. (ocw.mit.edu)

The consequences of inserting a dielectric depend on what remains fixed:

• Fixed free charge: in an isolated capacitor, capacitance increases while voltage and stored electrostatic energy decrease.
• Fixed voltage: with an ideal voltage source connected, capacitance, electrode charge, and stored electrostatic energy increase. The source supplies additional energy during insertion. (ocw.mit.edu)

For an ideal linear capacitor,

Correspondingly, the electric energy density in a linear, nondispersive, lossless dielectric is

In an isotropic medium this becomes $u=\tfrac12\varepsilon E^2$. Dispersive or dissipative media require a more careful treatment of stored and absorbed energy. (web.mit.edu)

High relative permittivity alone does not ensure high usable energy storage. Breakdown strength also matters: in the ideal linear approximation, the energy density attainable near breakdown scales with $\varepsilon E_{\mathrm{bd}}^2$. Dielectric polymers therefore involve a balance between polarizability and resistance to high electric fields. (nist.gov)

Frequency dependence and dielectric loss

Under an alternating field, polarization may lag behind the driving field. A frequency-domain description uses complex permittivity. With the time convention $e^{i\omega t}$,

The real part characterizes the in-phase response, while the imaginary part describes loss. For a passive material under this convention, $\varepsilon''$ is nonnegative. The loss tangent is

A dielectric relaxation commonly produces a decrease in $\varepsilon'$ over a frequency interval and a peak in dielectric loss. A material can exhibit several such processes. (tsapps.nist.gov)

Conductivity can also contribute to measured loss. If a frequency-independent conductivity $\sigma$ is incorporated into the effective complex permittivity, it adds $\sigma/\omega$ to the absolute loss component $\varepsilon''$. Separating conduction, polarization loss, and electrode effects is therefore important when interpreting measurements, especially at low frequencies. (nvlpubs.nist.gov)

Dielectric response also governs light propagation. In a homogeneous, isotropic, approximately nonmagnetic medium, the complex refractive index satisfies approximately

In a transparent frequency range this reduces to $n^2\approx\varepsilon_r$. The relevant permittivity is the value at the light’s frequency, not the static dielectric constant. Its frequency dependence underlies optical dispersion and absorption. (ocw.mit.edu)

Materials and specialized behavior

Dielectrics include solids, liquids, and gases. Their properties reflect molecular structure, defects, interfaces, and measurement conditions; compilations of dielectric data therefore specify frequency and temperature rather than treating permittivity as an unconditional material constant. (nvlpubs.nist.gov)

Some dielectrics exhibit behavior beyond simple field-induced polarization:

• Ferroelectric materials possess spontaneous polarization that can be reversed by an applied electric field. Their polarization–field relation can show hysteresis and retain polarization after the field is removed.
• Piezoelectric materials couple electrical and mechanical responses: stress can generate an electrical response, while an electric field can produce strain. (ocw.mit.edu)

These effects support applications such as ferroelectric memory and electromechanical actuators, but also require constitutive descriptions that include polarization history or mechanical variables. (ocw.mit.edu)

Breakdown, insulation, and measurement

An insulating dielectric can become conductive when subjected to a sufficiently strong electric field. This dielectric breakdown limits operating voltage and may damage the material. Dielectrics consequently serve two related but distinct roles: controlling polarization and electric-field energy, and preventing unwanted electrical conduction. Transformer oil, for example, functions as an insulating dielectric, while capacitor films are evaluated for both permittivity and breakdown strength. (math.nist.gov)

Dielectric characterization uses different techniques for different frequency ranges and sample forms. Methods include capacitance measurements, transmission-line and waveguide measurements, resonant techniques, and free-space electromagnetic measurements. Reliable results require attention to sample geometry, calibration, losses, and measurement uncertainty. A reported permittivity or loss tangent is meaningful only together with its measurement conditions and the model used to extract it. (nist.gov)

References

1. 013 Electromagnetics and Applications, Lecture 2ocw.mit.edu
2. Dielectric characterization and reference materialsnvlpubs.nist.gov
3. Polarization Densityweb.mit.edu
4. Laws and Continuity Conditions with Polarizationweb.mit.edu
5. Electromagnetism II Formula Sheetlive.ocw.mit.edu
6. Compilation of the Static Dielectric Constant of Inorganic Solidssrd.nist.gov
7. Measurement of Dielectric Materials Propertiestsapps.nist.gov
8. Material Constants: Electric: Dielectric Permittivity epsilonctcms.nist.gov
9. Dielectric and electro-mechanic nonlinearities in perovskite oxide ferroelectrics, relaxors and relaxor ferroelectricsarxiv.org
10. Capacitorsocw.mit.edu
11. Energy Storageweb.mit.edu
12. Classical Electromagnetism and Opticsocw.mit.edu