Polarizability

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. 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. Electric polarizability is the relative tendency of a charge distribution, like the electron cloud of an atom or molecule, to be distorted from its normal shape by an external electric field. The polarizability α {displaystyle alpha } in isotropic media is defined as the ratio of the induced dipole moment p {displaystyle {oldsymbol {p}}} of an atom to the electric field E {displaystyle {oldsymbol {E}}} that produces this dipole moment. α = p E {displaystyle alpha ={frac {oldsymbol {p}}{oldsymbol {E}}}} Polarizability has the SI units of C·m2·V−1 = A2·s4·kg−1 while its cgs unit is cm3. Usually it is expressed in cgs units as a so-called polarizability volume, sometimes expressed in Å3 = 10−24 cm3. One can convert from SI units to cgs units as follows: α ( c m 3 ) = 10 6 4 π ε 0 α ( C ⋅ m 2 ⋅ V − 1 ) = 10 6 4 π ε 0 α ( F ⋅ m 2 ) {displaystyle alpha (mathrm {cm} ^{3})={frac {10^{6}}{4pi varepsilon _{0}}}alpha (mathrm {C} cdot mathrm {m} ^{2}cdot mathrm {V} ^{-1})={frac {10^{6}}{4pi varepsilon _{0}}}alpha (mathrm {F} cdot mathrm {m} ^{2})} ≃ 8.988×1015 × α ( F ⋅ m 2 ) {displaystyle alpha (mathrm {F} cdot mathrm {m} ^{2})} where ε 0 {displaystyle varepsilon _{0}} , the vacuum permittivity, is ~8.854 × 10−12 (F/m). If the polarizability volume is denoted α ′ {displaystyle alpha '} the relation can also be expressed generally (in SI) as 4 π ε 0 α ′ = α {displaystyle 4pi varepsilon _{0}alpha '=alpha } . The polarizability of individual particles is related to the average electric susceptibility of the medium by the Clausius-Mossotti relation. Polarizability for anisotropic or non-spherical media cannot in general be represented as a scalar quantity. Defining α {displaystyle alpha } as a scalar implies both that applied electric fields can only induce polarization components parallel to the field and that the x , y {displaystyle x,y} and z {displaystyle z} directions respond in the same way to the applied electric field. For example, an electric field in the x {displaystyle x} -direction can only produce an x {displaystyle x} component in p {displaystyle {oldsymbol {p}}} and if that same electric field were applied in the y {displaystyle y} -direction the induced polarization would be the same in magnitude but appear in the y {displaystyle y} component of p {displaystyle {oldsymbol {p}}} . Many crystalline materials have directions that are easier to polarize than others and some even become polarized in directions perpendicular to the applied electric field, and the same thing happens with non-spherical bodies. Some molecules and materials with this sort of anisotropic behavior are often optically active, exhibiting effects such as birefringence of light.