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 the dipole moment per unit volume of the crystal cell.
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Definition
Electric polarizability is the relative tendency of a charge distribution, like the electron cloud of an atom or molecule, and consequently of any material body, to have its charges displaced by any external electric field, which in the uniform case is applied typically by a charged parallel-plate capacitor.
The polarizability
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:
where
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
To describe anisotropic media a polarizability rank two tensor or
The elements describing the response parallel to the applied electric field are those along the diagonal. A large value of
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.
R = Molar refractivity ,
Tendencies
Generally, polarizability increases as 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 increases from right to left. Polarizability increases down on columns of the periodic table. Likewise, larger molecules are generally more polarizable than smaller ones.
Though water is a very polar molecule, alkanes and other hydrophobic molecules are more polarizable. 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.
It is important to note that ground state electron configuration models are often inadequate in studying the polarizability of bonds because dramatic changes in molecular structure occur in a reaction.
Magnetic polarizability
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