# Rotational Brownian motion

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Rotational Brownian motion is the random change in the orientation of a polar molecule due to collisions with other molecules. It is an important element of theories of dielectric materials.

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.

## Contents

The polarization of a dielectric material is a competition between torques due to the imposed electric field, which tend to align the molecules, and collisions, which tend to destroy the alignment. The theory of rotational Brownian motion allows one to calculate the net result of these two competing effects, and to predict how the permittivity of a dielectric material depends on the strength and frequency of the imposed electric field.

In classical electromagnetism, polarization density is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material. When a dielectric is placed in an external electric field, its molecules gain electric dipole moment and the dielectric is said to be polarized. The electric dipole moment induced per unit volume of the dielectric material is called the electric polarization of the dielectric.

Torque, moment, or moment of force is the rotational equivalent of linear force. The concept originated with the studies of Archimedes on the usage of levers. Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object. The symbol for torque is typically , the lowercase Greek letter tau. When being referred to as moment of force, it is commonly denoted by M.

An electric field is a vector field surrounding an electric charge that exerts force on other charges, attracting or repelling them. Mathematically the electric field is a vector field that associates to each point in space the force, called the Coulomb force, that would be experienced per unit of charge by an infinitesimal test charge at that point. The units of the electric field in the SI system are newtons per coulomb (N/C), or volts per meter (V/m). Electric fields are created by electric charges, or by time-varying magnetic fields. Electric fields are important in many areas of physics, and are exploited practically in electrical technology. On an atomic scale, the electric field is responsible for the attractive force between the atomic nucleus and electrons that holds atoms together, and the forces between atoms that cause chemical bonding. Electric fields and magnetic fields are both manifestations of the electromagnetic force, one of the four fundamental forces of nature.

Rotational Brownian motion was first discussed by Peter Debye, [1] who applied Einstein's theory of translational Brownian motion to the rotation of molecules having permanent electric dipoles. Debye ignored inertial effects and assumed that the molecules were spherical, with an intrinsic, fixed dipole moment. He derived expressions for the dielectric relaxation time and for the permittivity. These formulae have been successfully applied to many materials. However, Debye's expression for the permittivity predicts that the absorption tends toward a constant value when the frequency of the applied electric field becomes very large—the "Debye plateau". This is not observed; instead, the absorption tends toward a maximum and then declines with increasing frequency.

Peter Joseph William Debye was a Dutch-American physicist and physical chemist, and Nobel laureate in Chemistry.

Brownian motion or pedesis is the random motion of particles suspended in a fluid resulting from their collision with the fast-moving molecules in the fluid.

The breakdown in Debye's theory in these regimes can be corrected by including inertial effects; allowing the molecules to be non-spherical; including dipole-dipole interactions between molecules; etc. These are computationally very difficult problems and rotational Brownian motion is a topic of much current research interest.

James Robert C. McConnell was an Irish Catholic priest and theoretical physicist. Fr. McConnell entered University College Dublin (UCD) in 1932 and graduated in 1936 with a first-class honours master's degree in mathematics. After leaving UCD, McConnell began his study for the priesthood, entering Clonliffe College. He moved to Rome after a year and earned a B.D., B.C.L., and S.T.L. and was ordained in 1939. He was made a Doctor of Mathematical Sciences by the Royal University of Rome in 1941.

The International Standard Book Number (ISBN) is a numeric commercial book identifier which is intended to be unique. Publishers purchase ISBNs from an affiliate of the International ISBN Agency.

## Related Research Articles

Dispersion may refer to:

Intermolecular forces (IMF) are the forces which mediate interaction between molecules, including forces of attraction or repulsion which act between molecules and other types of neighboring particles, e.g., atoms or ions. Intermolecular forces are weak relative to intramolecular forces – the forces which hold a molecule together. For example, the covalent bond, involving sharing electron pairs between atoms, is much stronger than the forces present between neighboring molecules. Both sets of forces are essential parts of force fields frequently used in molecular mechanics.

In physics, the term dielectric strength has the following meanings:

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

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 particular medium. Accordingly, 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.

In molecular physics, the van der Waals force, named after Dutch scientist Johannes Diderik van der Waals, is a distance-dependent interaction between atoms or molecules. Unlike ionic or covalent bonds, these attractions do not result from a chemical electronic bond; they are comparatively weak and therefore more susceptible to disturbance. The Van der Waals force quickly vanishes at longer distances between interacting molecules.

Electrophoresis is the motion of dispersed particles relative to a fluid under the influence of a spatially uniform electric field. Electrophoresis of positively charged particles (cations) is sometimes called cataphoresis, while electrophoresis of negatively charged particles (anions) is sometimes called anaphoresis.

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 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 SI, it is expressed in units of coulomb per metre squared (C⋅m−2).

Polarizability is the ability to form instantaneous dipoles. It is a property of matter. Polarizabilities determine the dynamical response of a bound system to external fields, and provide insight into a molecule's internal structure. In a solid, polarizability is defined as dipole moment per unit volume of the crystal cell.

According to quantum mechanics, atoms and molecules can only hold certain defined quantities of energy, or exist in specific states. When such quanta of electromagnetic radiation are emitted or absorbed by an atom or molecule, the energy of the radiation changes the state of the atom or molecule from an initial state to a final state. An absorption band is a range of wavelengths, frequencies or energies in the electromagnetic spectrum which are characteristic of a particular transition from initial to final state in a substance.

Dielectric heating, also known as electronic heating, RF heating, and high-frequency heating, is the process in which a radio frequency 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.

Electroacoustic phenomena arise when ultrasound propagates through a fluid containing ions. The associated particle motion generates electric signals because ions have electric charge. This coupling between ultrasound and electric field is called electroacoustic phenomena. The fluid might be a simple Newtonian liquid, or complex heterogeneous dispersion, emulsion or even a porous body. There are several different electroacoustic effects depending on the nature of the fluid.

In dielectric spectroscopy, large frequency dependent contributions to the dielectric response, especially at low frequencies, may come from build-ups of charge. This Maxwell–Wagner–Sillars polarization, occurs either at inner dielectric boundary layers on a mesoscopic scale, or at the external electrode-sample interface on a macroscopic scale. In both cases this leads to a separation of charges. The charges are often separated over a considerable distance, and the contribution to dielectric loss can therefore be orders of magnitude larger than the dielectric response due to molecular fluctuations.

Brendan Kevin Patrick Scaife FTCD, MRIA, Boyle Laureate, is an Irish academic engineer and physicist who carried out pioneering work on the theory of dielectrics. Scaife founded the Dielectrics Group in Trinity College Dublin where he is Fellow Emeritus and formerly Professor of Electromagnetism, and previously to that a Professor of Engineering Science. Scaife showed that in a linear system the decay function is directly proportional to the autocorrelation function of the corresponding fluctuating macroscopic variable, and proved how the spectral density of the dipole moment fluctuations of a dielectric body could be calculated from the frequency dependence of the complex permittivity, ε(ω) = ε'(ω) – iε"(ω). It was independent of Ryogo Kubo who in 1957 developed the corresponding theory for magnetic materials. The work was published prior to the work of Robert Cole in 1965 which is often cited.

Plasmonic nanoparticles are particles whose electron density can couple with electromagnetic radiation of wavelengths that are far larger than the particle due to the nature of the dielectric-metal interface between the medium and the particles: unlike in a pure metal where there is a maximum limit on what size wavelength can be effectively coupled based on the material size.

Dielectric absorption is the name given to the effect by which a capacitor, that has been charged for a long time, discharges only incompletely when briefly discharged. Although an ideal capacitor would remain at zero volts after being discharged, real capacitors will develop a small voltage from time-delayed dipole discharging, a phenomenon that is also called dielectric relaxation, "soakage", or "battery action". For some dielectrics, such as many polymer films, the resulting voltage may be less than 1–2% of the original voltage, but it can be as much as 15% for electrolytic capacitors. The voltage at the terminals generated by the dielectric absorption may possibly cause problems in the function of an electronic circuit or can be a safety risk to personnel. In order to prevent shocks, most very large capacitors are shipped with shorting wires that need to be removed before they are used and/or permanently connected bleeder resistors. When disconnected at one or both ends, DC high-voltage cables can also "recharge themselves" to dangerous voltages.

Radio frequency welding, also known as dielectric welding and high frequency welding, is a plastics joining process that utilizes high-frequency radio waves to heat plastic parts to the point they form a melt layer. After the development of the melt layer, the parts are pressed together and then allowed to cool causing fusion. This process is capable of producing high quality joints in a range of plastics. Advantages of this process are fast cycle times, easily automated, repeatable, and good weld appearance. While this process has some great advantages, there are some limitations. Only plastics which have dipoles can be heated using radio waves and therefore not all plastics are able to be welded using this process. Also, this process is not well suited for thick or overly complex joints. The most common use of this process is lap joints or seals on thin plastic sheets or parts.

## References

1. Debye, P., Berichte der deutschen Physikalischen Gesellschaft, 15, 777 (1913)

The University of Pennsylvania is a private Ivy League research university located in the University City neighborhood of Philadelphia, Pennsylvania. Chartered in 1755, Penn is the sixth-oldest institution of higher education in the United States. It is one of the nine colonial colleges founded prior to the Declaration of Independence. Benjamin Franklin, Penn's founder and first president, advocated an educational program that trained leaders in commerce, government, and public service, similar to a modern liberal arts curriculum. The university's coat of arms features a dolphin on its red chief, adopted from Benjamin Franklin's own coat of arms.