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of atoms, ions, and molecules; the ability of these particles to acquire a dipole moment p in an electric field E. The appearance of p is due to the displacement of electric charges in atomic systems under the influence of E; the moment p thus induced vanishes when no electric field is present. The concept of polarizability is generally not applied to particles having a permanent dipole moment, such as polar molecules. In relatively weak fields, the dependence of p on E is linear:
p = αE
where α is a quantitative measure of polarizability and is sometimes itself called molecular polarizability. For some molecules the value of α may depend on the direction of E; this is known as anisotropic polarizability. In strong electric fields, the dependence of p upon E ceases to be linear.
In the equation above, E is the electric field at the location of the particle. For an isolated particle, such as a molecule of a rarefied gas, it coincides with the external field. In a liquid or crystal, the internal fields generated by other charged particles surrounding the given particle are added to the external field.
Under the force of an electric field, the moment p does not appear instantaneously. The transition time τ of moment p depends on the nature of the particles and surrounding medium. A static value of polarizability corresponds to an electrostatic field. In a variable field, such as a harmonically varying field, the polarizability is dependent on the frequency ω and transition time τ. For sufficiently low ω and sufficiently small τ, the moment p changes in phase with field variation, and the polarizability coincides with static polarizability. For very high ω or large τ, the moment p may not arise at all; the particle does not “sense” the presence of the field, so there is no polarizability. In intermediate cases, especially when ω approximates 1/τ, the phenomena of dispersion and absorption are observed.
A distinction is made between several types of polarizability. Electronic polarizability is due to the displacement in a field E of the electron shells with respect to atomic nuclei. Ionic polarizability (in ionic crystals) derives from the displacement of ions of opposite signs from the equilibrium process and in opposite directions. Atomic polarizability is due to the displacement in a field E of atoms of different types in a molecule and is related to the asymmetric distribution of electron density. The temperature dependence of these types of polarizability is slight; as the temperature rises, the polarizability decreases somewhat.
In the physics of solid and liquid dielectrics, polarizability is understood as mean polarizability. Here P represents the polarization per particle and per unit field: a = P/EN, where N the number of particles. The polarizability of polar dielectrics is called orientation polarizability. The polarization of dielectrics whose particles move alternately from one position to another under the influence of an electric field can be described by introducing relaxation polarizability. Extreme sensitivity to temperature is a characteristic feature of these types of polarizability.
In the literature on the physics of dielectrics, the proportionality factor Χ between P and E—P = ΧE—that is, the dielectric susceptibility, is sometimes called polarizability.
The concept of polarizability has found extensive application in the physics of dielectrics, molecular physics, and physical chemistry. For relatively simple systems the relation between polarizability and the macroscopic characteristics of a substance is described; for example, for electronic polarizability it is described by the Lorentz-Lorenz formula and Clausius-Mossotti equation, and for orientation polarizability, by the Langevin-Debye formula. Through these and similar formulas it is possible to experimentally determine the polarizability. The concept of polarizability is used to analyze and explain a number of optical effects such as the polarization and scattering of light, optical activity, and the Raman effect, particularly in systems consisting of extremely large molecules, such as proteins.
REFERENCESSkanavi, G. I. Fizika dielektrikov (oblast’ slabykh polei). Moscow-Leningrad, 1949.
Frö hlich, H. Teoriia dielektrikov. Moscow, 1960. (Translated from English.)
Vol’kenshtein, M. V. Stroenie i fizicheskie svoistva molekul. Moscow-Leningrad, 1955.
A. S. GUSEV