Rotational Brownian motion is the random change in the orientation of a

polar molecule In chemistry, polarity is a separation of electric charge leading to a molecule or its chemical groups having an electric dipole moment, with a negatively charged end and a positively charged end. Polar molecules must contain one or more polar ...

due to collisions with other molecules. It is an important element of theories of

dielectric In electromagnetism, a dielectric (or dielectric medium) 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 ma ...

materials. The polarization of a dielectric material is a competition between

torque In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment of force (also abbreviated to moment). It represents the capability of a force to produce change in the rotational motion of th ...

s due to the imposed

electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical 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 In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' (epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more in ...

of a dielectric material depends on the strength and frequency of the imposed electric field. Rotational Brownian motion was first discussed by

Peter Debye Peter Joseph William Debye (; ; March 24, 1884 – November 2, 1966) was a Dutch-American physicist and physical chemist, and Nobel laureate in Chemistry. Biography Early life Born Petrus Josephus Wilhelmus Debije in Maastricht, Netherland ...

,Debye, P., ''Berichte der deutschen Physikalischen Gesellschaft'', 15, 777 (1913) who applied

Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theor ...

's theory of translational

Brownian motion Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas). This pattern of motion typically consists of random fluctuations in a particle's position insi ...

to the rotation of molecules having permanent

electric dipole The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity. The SI unit for electric dipole moment is the coulomb- meter (C⋅m). T ...

s. 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

. 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. 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.

References

External links

Random Walks of Ellipsoids
Research carried out at the

University of Pennsylvania The University of Pennsylvania (also known as Penn or UPenn) is a Private university, private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest- ...

in which the rotational Brownian motion of an isolated ellipsoidal particle was definitively measured. Dielectrics Wiener process Rotation {{Physics-stub

See also

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References

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