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 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:
≃ 8.988×1015 ×
where , the vacuum permittivity, is ~8.854 × 10−12 (F/m). If the polarizability volume is denoted the relation can also be expressed generally (in SI) as .
Polarizability for anisotropic or non-spherical media cannot in general be represented as a scalar quantity. Defining as a scalar implies both that applied electric fields can only induce polarization components parallel to the field and that the and directions respond in the same way to the applied electric field. For example, an electric field in the -direction can only produce an component in and if that same electric field were applied in the -direction the induced polarization would be the same in magnitude but appear in the component of . 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.
The elements describing the response parallel to the applied electric field are those along the diagonal. A large value of here means that an electric-field applied in the -direction would strongly polarize the material in the -direction. Explicit expressions for have been given for homogeneous anisotropic ellipsoidal bodies.
Application in crystallography
The matrix above can be used with the molar refractivity equation and other data to produce density data for crystallography. Each polarizability measurement along with the refractive index associated with its direction will yield a direction specific density that can be used to develop an accurate three dimensional assessment of molecular stacking in the crystal. This relationship was first observed by Linus Pauling.
Generally, polarizability increases as the volume occupied by electrons increases. In atoms, this occurs because larger atoms have more loosely held electrons in contrast to smaller atoms with tightly bound electrons. On rows of the periodic table, polarizability therefore decreases from left to right. Polarizability increases down on columns of the periodic table. Likewise, larger molecules are generally more polarizable than smaller ones.
Water is a very polar molecule, but alkanes and other hydrophobic molecules are more polarizable. Water with its permanent dipole is less likely to change shape due to an external electric field. Alkanes are the most polarizable molecules. Although alkenes and arenes are expected to have larger polarizability than alkanes because of their higher reactivity compared to alkanes, alkanes are in fact more polarizable. This results because of alkene's and arene's more electronegative sp2 carbons to the alkane's less electronegative sp3 carbons.
Magnetic polarizability defined by spin interactions of nucleons is an important parameter of deuterons and hadrons. In particular, measurement of tensor polarizabilities of nucleons yields important information about spin-dependent nuclear forces.
The method of spin amplitudes uses quantum mechanics formalism to more easily describe spin dynamics. Vector and tensor polarization of particle/nuclei with spin S ≥ 1 are specified by the unit polarization vector and the polarization tensor P`. Additional tensors composed of products of three or more spin matrices are needed only for the exhaustive description of polarization of particles/nuclei with spin S ≥ 3⁄2 .
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