Rotational Brownian motion

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
Dielectric
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 in a conductor, but only slightly shift from their average equilibrium positions causing dielectric...

 materials.

The polarization
Polarization density
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...

 of a dielectric material is a competition between torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....

s due to the imposed electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...

, 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
Permittivity
In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...

 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 Debye
Peter Joseph William Debye FRS was a Dutch physicist and physical chemist, and Nobel laureate in Chemistry.-Early life:...

, who applied Einstein's theory of translational Brownian motion
Brownian motion
Brownian motion or pedesis is the presumably random drifting of particles suspended in a fluid or the mathematical model used to describe such random movements, which is often called a particle theory.The mathematical model of Brownian motion has several real-world applications...

 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.

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.

External links

  • Random Walks of Ellipsoids Research carried out at the University of Pennsylvania
    University of Pennsylvania
    The University of Pennsylvania is a private, Ivy League university located in Philadelphia, Pennsylvania, United States. Penn is the fourth-oldest institution of higher education in the United States,Penn is the fourth-oldest using the founding dates claimed by each institution...

    in which the rotational Brownian motion of an isolated ellipsoidal particle was definitively measured.