Polarizability
Encyclopedia
Polarizability is the measure of the change in a molecule's electron distribution in response to an applied electric field, which can also be induced by electric interactions with solvents or ionic reagents. 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.
or molecule
, to be distorted from its normal shape by an external electric field
, which is applied typically by inserting the molecule in a charged parallel-plate capacitor
, but may also be caused by the presence of a nearby ion
or dipole.
The electronic polarizability
is defined as the ratio of the induced dipole moment
of an atom to the electric field 
that produces this dipole moment.
Polarizability has the SI units of C·m2·V−1 = A2·s4·kg−1 but is more often expressed as polarizability volume with units of cm3 or in Å
3 = 10−24 cm3.
where 
is the vacuum permittivity
.
The polarizability of individual particles is related to the average electric susceptibility
of the medium by the Clausius-Mossotti relation
.
Note that the polarizability
as defined above is a scalar
quantity. This implies that the applied electric fields can only produce polarization components parallel to the field. For example, an electric field in the
-direction can only produce an 
component in 
. However, it can happen that an electric field in the 
-direction, produces a 
or 
component in the vector 
. In this case 
is described as a tensor
of rank 2, which is represented with respect to a given system of axes (frame of reference) by a
matrix
.
, 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.
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.
interactions of nucleon
s is an important parameter of deuterons and hadron
s. 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 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 .
Definition
Electric polarizability is the relative tendency of a charge distribution, like the electron cloud of an atomAtom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
or molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
, to be distorted from its normal shape by an external electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
, which is applied typically by inserting the molecule in a charged parallel-plate capacitor
Capacitor
A capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...
, but may also be caused by the presence of a nearby ion
Ion
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...
or dipole.
The electronic polarizability
is defined as the ratio of the induced dipole momentDipole moment
Dipole moment can be defined as the product of magnitude of charge & distance of separation between the charges.Dipole moment may refer to:*Electric dipole moment, the measure of the electrical polarity of a system of charges...
of an atom to the electric field that produces this dipole moment.Polarizability has the SI units of C·m2·V−1 = A2·s4·kg−1 but is more often expressed as polarizability volume with units of cm3 or in Å
Ångström
The angstrom or ångström, is a unit of length equal to 1/10,000,000,000 of a meter . Its symbol is the Swedish letter Å....
3 = 10−24 cm3.
where is the vacuum permittivityPermittivity
In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...
.
The polarizability of individual particles is related to the average electric susceptibility
Electric susceptibility
In electromagnetism, the electric susceptibility \chi_e is a dimensionless proportionality constant that indicates the degree of polarization of a dielectric material in response to an applied electric field...
of the medium by the Clausius-Mossotti relation
Clausius-Mossotti relation
The Clausius–Mossotti relation is named after the Italian physicist Ottaviano-Fabrizio Mossotti, whose 1850 book analyzed the relationship between the dielectric constants of two different media, and the German physicist Rudolf Clausius, who gave the formula explicitly in his 1879 book in the...
.
Note that the polarizability
as defined above is a scalarScalar (physics)
In physics, a scalar is a simple physical quantity that is not changed by coordinate system rotations or translations , or by Lorentz transformations or space-time translations . This is in contrast to a vector...
quantity. This implies that the applied electric fields can only produce polarization components parallel to the field. For example, an electric field in the
-direction can only produce an component in . However, it can happen that an electric field in the -direction, produces a or component in the vector . In this case is described as a tensorTensor
Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of...
of rank 2, which is represented with respect to a given system of axes (frame of reference) by a
matrixMatrix (mathematics)
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
.
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 tablePeriodic table
The periodic table of the chemical elements is a tabular display of the 118 known chemical elements organized by selected properties of their atomic structures. Elements are presented by increasing atomic number, the number of protons in an atom's atomic nucleus...
, 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.
Though water is a very polar
Polar
- Science, technology, and mathematics :*Polar , a satellite launched by NASA in 1996*Polar , a strongly magnetic cataclysmic variable star system...
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 spinSpin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
interactions of nucleon
Nucleon
In physics, a nucleon is a collective name for two particles: the neutron and the proton. These are the two constituents of the atomic nucleus. Until the 1960s, the nucleons were thought to be elementary particles...
s is an important parameter of deuterons and hadron
Hadron
In particle physics, a hadron is a composite particle made of quarks held together by the strong force...
s. In particular, measurement of tensor
Tensor
Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of...
polarizabilities of nucleons yields important information about spin-dependent nuclear forces.
The method of spin amplitudes uses quantum mechanics formalism
Mathematical formulation of quantum mechanics
The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. Such are distinguished from mathematical formalisms for theories developed prior to the early 1900s by the use of abstract mathematical structures, such as...
to more easily describe spin dynamics. Vector and tensor polarization of particle/nuclei with spin 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 .See also
- Polarization densityPolarization densityIn classical electromagnetism, polarization density is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material. When a dielectric is placed in an external electric field, its molecules gain electric dipole moment and the dielectric is...
- MOSCEDMOSCEDMOSCED is a thermodynamic model for the estimation of limiting activity coefficients . From a historical point of view MOSCED can be regarded as an improved modification of the Hansen method and the Hildebrand solubility model...
, an estimation method for activity coefficients; uses polarizability as parameter