Polarizability usually refers to the tendency of matter, when subjected to an electric field, to acquire an electric dipole moment in proportion to that applied field. It is a property of particles with an electric charge. When subject to an electric field, the negatively charged electrons and positively charged atomic nuclei are subject to opposite forces and undergo charge separation. Polarizability is responsible for a material's dielectric constant and, at high (optical) frequencies, its refractive index.
\chi=\varepsilonr-1
\alpha
Magnetic polarizability likewise refers to the tendency for a magnetic dipole moment to appear in proportion to an external magnetic field. Electric and magnetic polarizabilities determine the dynamical response of a bound system (such as a molecule or crystal) to external fields, and provide insight into a molecule's internal structure.[2] "Polarizability" should not be confused with the intrinsic magnetic or electric dipole moment of an atom, molecule, or bulk substance; these do not depend on the presence of an external field.
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
\alpha
p
E
\alpha=
| |p| | |
| |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 (
\alpha
\alpha'
\alpha'(cm3)=
| 106 | |
| 4\pi\varepsilon0 |
\alpha(C{ ⋅ m2{ ⋅ }V-1
\alpha(F{ ⋅ m2})
where
\varepsilon0
\alpha'
\alpha=4\pi\varepsilon0\alpha'
The polarizability of individual particles is related to the average electric susceptibility of the medium by the Clausius–Mossotti relation:
R={\displaystyle\left({
| 4\pi | |
| 3 |
NA
\alphac
\varepsilonr=\epsilon/\epsilon0
Polarizability for anisotropic or non-spherical media cannot in general be represented as a scalar quantity. Defining
\alpha
x,y
z
x
x
p
y
y
p
To describe anisotropic media a polarizability rank two tensor or
3 x 3
\alpha
\alpha=\begin{bmatrix} \alphaxx&\alphaxy&\alphaxz\\ \alphayx&\alphayy&\alphayz\\ \alphazx&\alphazy&\alphazz\\ \end{bmatrix}
so that:
p=\alphaE
The elements describing the response parallel to the applied electric field are those along the diagonal. A large value of
\alphayx
x
y
\alpha
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.
Polarizability and molecular property are related to refractive index and bulk property. In crystalline structures, the interactions between molecules are considered by comparing a local field to the macroscopic field. Analyzing a cubic crystal lattice, we can imagine an isotropic spherical region to represent the entire sample. Giving the region the radius
a
P.
p
| 4\pia3 | |
| 3 |
P.
We can call our local field
F
E
Ein=\tfrac{-P
F=E-Ein=E+
| P | |
| 3\varepsilon0 |
The polarization is proportional to the macroscopic field by
P=\varepsilon0(\varepsilonr-1)E=\chie\varepsilon0E
\varepsilon0
\chie
F=\tfrac{1}{3}(\varepsilonr+2)E
| P= | N\alpha | F= |
| V |
| N\alpha | |
| 3V |
(\varepsilonr+2)E
and simplified with
\varepsilonr=1+\tfrac{N\alpha}{\varepsilon0V}
P=\varepsilon0(\varepsilonr-1)E
E
| \varepsilonr-1 | = | |
| \varepsilonr+2 |
| N\alpha | |
| 3\varepsilon0V |
We can replace the relative permittivity
\varepsilonr
n
\varepsilonr=n2
M
\rho
\tfrac{N}{V}=\tfrac{NA\rho}{M}
RM=
| NA\alpha | |
| 3\varepsilon0 |
=\left(
| M | |
| \rho |
\right)
| n2-1 | |
| n2+2 |
This equation allows us to relate bulk property (refractive index) to the molecular property (polarizability) as a function of frequency.[8]
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.[9] 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.
Ground state electron configuration models are often inadequate in studying the polarizability of bonds because dramatic changes in molecular structure occur in a reaction.[10]
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.[11]
The method of spin amplitudes uses quantum mechanics formalism to more easily describe spin dynamics. Vector and tensor polarization of particle/nuclei with spin are specified by the unit polarization vector
p