Dielectric

In electromagnetism, a dielectric is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the material as they do in an electrical conductor, because they have no loosely bound, or free, electrons that may drift through the material, but instead they shift, only slightly, from their average equilibrium positions, causing dielectric polarisation. Because of dielectric polarisation, positive charges are displaced in the direction of the field and negative charges shift in the direction opposite to the field. 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 polarised, but also reorient so that their symmetry axes align to the field.
The study of dielectric properties concerns storage and dissipation of electric and magnetic energy in materials. Dielectrics are important for explaining various phenomena in electronics, optics, solid-state physics and cell biophysics.

Terminology

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. Insulator is generally used to indicate electrical obstruction while dielectric is used to indicate the energy storing capacity of the material. A common example of a dielectric is the electrically insulating material between the metallic plates of a capacitor. The polarisation of the dielectric by the applied electric field increases the capacitor's surface charge for the given electric field strength.
The term dielectric was coined by William Whewell in response to a request from Michael Faraday.
A perfect dielectric is a material with zero electrical conductivity, thus exhibiting only a displacement current; therefore it stores and returns electrical energy as if it were an ideal capacitor.

Electric susceptibility

The electric susceptibility of a dielectric material is a measure of how easily it polarises in response to an electric field. This, in turn, determines 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.
It is defined as the constant of proportionality relating an electric field to the induced dielectric polarisation density such that
where is the electric permittivity of free space.
The susceptibility of a medium is related to its relative permittivity by
So in the case of a classical vacuum,
The electric displacement is related to the polarisation density by

Dispersion and causality

In general, a material cannot polarise instantaneously in response to an applied field. The more general formulation as a function of time is
That is, the polarisation is a convolution of the electric field at previous times with time-dependent susceptibility given by. The upper limit of this integral can be extended to infinity as well if one defines for. An instantaneous response corresponds to Dirac delta function susceptibility .
It is more convenient in a linear system to take the Fourier transform and write this relationship as a function of frequency. Due to the convolution theorem, the integral becomes a simple product,
The susceptibility is frequency dependent. The change of susceptibility with respect to frequency characterises the dispersion properties of the material.
Moreover, the fact that the polarisation can only depend on the electric field at previous times, a consequence of causality, imposes Kramers–Kronig constraints on the real and imaginary parts of the susceptibility.

Dielectric polarisation

Basic atomic model

In the classical approach to the dielectric, the material is made up of atoms. Each atom consists of a cloud of negative charge 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 characterised 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 behaviour of the dielectric.
When the electric field is removed, the atom returns to its original state. The time required to do so is called relaxation time; an exponential decay.
This is the essence of the model in physics. The behaviour of the dielectric now depends on the situation. The more complicated the situation, the richer the model must be to accurately describe the behaviour. 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 ?
Is the response the same everywhere ?
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 behaviour of the dielectric, which, for a given material, can be characterised by the function F defined by the equation:
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 modelled include:

Refractive index
Group velocity dispersion
Birefringence
Self-focusing
Harmonic generation
Dipolar polarisation

Dipolar polarisation is a polarisation that is either inherent to polar molecules, or can be induced in any molecule in which the asymmetric distortion of the nuclei is possible. Orientation polarisation results from a permanent dipole, e.g., that arises from the 104.45° angle between the asymmetric bonds between oxygen and hydrogen atoms in the water molecule, which retains polarisation in the absence of an external electric field. The assembly of these dipoles forms a macroscopic polarisation.
When an external electric field is applied, the distance between charges within each permanent dipole, which is related to chemical bonding, remains constant in orientation polarisation; however, the direction of polarisation itself rotates. This rotation occurs on a timescale that depends on the torque and surrounding local viscosity of the molecules. Because the rotation is not instantaneous, dipolar polarisations lose the response to electric fields at the highest frequencies. A molecule rotates about 1 radian per picosecond in a fluid, thus this loss occurs at about 10¹¹ Hz. The delay of the response to the change of the electric field causes friction and heat.
When an external electric field is applied at infrared frequencies or less, the molecules are bent and stretched by the field and the molecular dipole moment changes. The molecular vibration frequency is roughly the inverse of the time it takes for the molecules to bend, and this distortion polarisation disappears above the infrared.

Ionic polarisation

Ionic polarisation is polarisation caused by relative displacements between positive and negative ions in ionic crystals.
If a crystal or molecule consists of atoms of more than one kind, the distribution of charges around an atom in the crystal or molecule leans to positive or negative. As a result, when lattice vibrations or molecular vibrations induce relative displacements of the atoms, the centers of positive and negative charges are also displaced. The locations of these centers are affected by the symmetry of the displacements. When the centers do not correspond, polarisation arises in molecules or crystals. This polarisation is called ionic polarisation.
Ionic polarisation causes the ferroelectric effect as well as dipolar polarisation. The ferroelectric transition, which is caused by the lining up of the orientations of permanent dipoles along a particular direction, is called an order-disorder phase transition. The transition caused by ionic polarisations in crystals is called a displacive phase transition.

In biological cells

Ionic polarisation enables the production of energy-rich compounds in cells and, at the plasma membrane, the establishment of the resting potential, energetically unfavourable transport of ions, and cell-to-cell communication.
All cells in animal body tissues are electrically polarised – in other words, they maintain a voltage difference across the cell's plasma membrane, known as the membrane potential. This electrical polarisation results from a complex interplay between ion transporters and ion channels.
In neurons, the types of ion channels in the membrane usually vary across different parts of the cell, giving the dendrites, axon, and cell body different electrical properties. As a result, some parts of the membrane of a neuron may be excitable, whereas others are not.

Dielectric dispersion

In physics, dielectric dispersion is the dependence of the permittivity of a dielectric material on the frequency of an applied electric field. Because there is a lag between changes in polarisation and changes in the electric field, the permittivity of the dielectric is a complex function of the frequency of the electric field. Dielectric dispersion is very important for the applications of dielectric materials and the analysis of polarisation systems.
This is one instance of a general phenomenon known as material dispersion: a frequency-dependent response of a medium for wave propagation.
When the frequency becomes higher:

The dipolar polarisation can no longer follow the oscillations of the electric field in the microwave region around 10¹⁰ Hz,
The ionic polarisation and molecular distortion polarisation can no longer track the electric field past the infrared or far-infrared region around 10¹³ Hz,
The electronic polarisation 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 polarisation, if a polarisation process loses its response, permittivity decreases.