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| {{About||electromagnetic waves|Polarization (waves)|other uses|Polarization (disambiguation)}}
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| {{expert-subject|Chemistry|article|date=May 2010}}
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| '''Polarizability''' is the ability for a molecule to be polarized. 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.<ref name="CERN">{{cite web |author=L. Zhou |coauthors=F. X. Lee, W. Wilcox, J. Christensen |title=Magnetic polarizability of hadrons from lattice QCD |url=http://cdsweb.cern.ch/record/581347/files/0209128.pdf |publisher=European Organization for Nuclear Research ([[CERN]]) |year=2002 |format=[[PDF]] |accessdate=25 May 2010}}</ref>
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| =={{anchor|Electric polarizability|Electronic polarizability}}Electric polarizability==
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| ===Definition===
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| 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]], 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#Field_from_an_electric_dipole|dipole]].
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| The electronic polarizability <math>\alpha</math> is defined as the ratio of the induced [[Electric dipole moment|dipole moment]] <math>\boldsymbol{p}</math> of an atom to the electric field <math>\boldsymbol{E}</math> that produces this dipole moment.
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| <math>\boldsymbol{p} = \alpha \boldsymbol{E}</math>
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| Polarizability has the [[SI units]] of C·m<sup>2</sup>·V<sup>−1</sup> = A<sup>2</sup>·s<sup>4</sup>·kg<sup>−1</sup> while its cgs unit is cm<sup>^3</sup>. Usually it is expressed in cgs units as a so-called polarizability volume, instead of cm<sup>^3</sup> it is sometimes expressed in [[Angstrom|Å]]<sup>3</sup> = 10<sup>−24</sup> cm<sup>3</sup>. One can convert from SI units to cgs units as follows:
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| <math>\alpha (\mathrm{cm}^3) = \frac{10^{6}}{ 4 \pi \varepsilon_0 }\alpha (\mathrm{C} \cdot \mathrm{m}^2 \cdot \mathrm{V}^{-1})</math>
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| where <math>\varepsilon_0 </math> is the [[permittivity|vacuum permittivity]]. If the polarizability volume is denoted <math>\alpha'</math> the relation can also be expressed generally<ref name=Atkins>{{cite book|title=Atkins' Physical Chemistry|year=2010|publisher=Oxford University Press|isbn=978-0-19-954337-3|page=622-629|last1=Atkins|first1=Peter|last2=de Paula|first2=Julio|chapter=17}}</ref> (in SI) as <math>4\pi\varepsilon_0 \alpha' = \alpha</math>.
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| The polarizability of individual particles is related to the average [[electric susceptibility]] of the medium by the [[Clausius-Mossotti relation]].
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| Note that the polarizability <math>\alpha</math> as defined above is a [[scalar (physics)|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 <math>x</math>-direction can only produce an <math>x</math> component in <math>\boldsymbol{p}</math>. However, it can happen that an electric field in the <math>x</math>-direction, produces a <math>y</math> or <math>z</math> component in the vector <math>\boldsymbol{p}</math>. In this case <math>\alpha</math> is described as a [[tensor]] of rank 2, which is represented with respect to a given system of axes (frame of reference) by a <math>3 \times 3</math> [[Matrix (mathematics)|matrix]].
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| ===Tendencies===
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| Generally, polarizability increases as volume occupied by electrons increases.<ref name="anslyn"/> In atoms, this occurs because larger atoms have more loosely held electrons in contrast to smaller atoms with tightly bound electrons.<ref name="anslyn"/><ref name="Schwerdtfeger">{{cite book| last1 = Schwerdtfeger | first1 = Peter | title = Atomic Static Dipole Polarizabilities | editor = G. Maroulis | volumetitle = Computational Aspects of Electric Polarizability Calculations: Atoms, Molecules and Clusters | publisher = IOS Press | year = 2006 }}[http://www.worldscibooks.com/etextbook/p464/p464_chap01.pdf]</ref> On rows of the [[periodic table]], polarizability therefore increases from right to left.<ref name="anslyn"/> Polarizability increases down on columns of the periodic table.<ref name="anslyn"/> Likewise, larger molecules are generally more polarizable than smaller ones.
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| Though water is a very [[chemical polarity|polar]] molecule, [[alkanes]] and other [[hydrophobic]] molecules are more polarizable. Alkanes are the most polarizable molecules.<ref name="anslyn"/> 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.<ref name="anslyn"/> This results because of alkene's and arene's more electronegative sp<sup>2</sup> carbons to the alkane's less electronegative sp<sup>3</sup> carbons.<ref name="anslyn"/>
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| 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.<ref name="anslyn">{{cite book| last1 = Anslyn| last2 = Dougherty| first1 = Eric| first2 = Dennis | authorlink2 = Dennis Dougherty | title = Modern Physical Organic Chemistry | publisher = University Science | year = 2006 | isbn = 978-1-891389-31-3}}[http://books.google.com/books?id=gY-Sxijk_tMC&pg=PA25&dq=organic+chemistry+polarizability&hl=en&ei=NasLToOwF8Ta0QG7kq2iAQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CC0Q6AEwAA#v=onepage&q=organic%20chemistry%20polarizability&f=false]</ref>
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| =={{anchor|Magnetic polarizability}}Magnetic polarizability==
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| Magnetic polarizability defined by [[Spin (physics)|spin]] interactions of [[nucleon]]s is an important parameter of [[deuteron]]s and [[hadron]]s. In particular, measurement of [[tensor]] polarizabilities of nucleons yields important information about spin-dependent nuclear forces.<ref name="Silenko">{{cite web |author=A. J. Silenko |title=Manifestation of tensor magnetic polarizability of the deuteron in storage ring experiments |url=http://www.springerlink.com/content/m2744373305l24m7/ |publisher=Springer Berlin / Heidelberg |date=18 Nov 2008 |doi=10.1140/epjst/e2008-00776-9 |accessdate=25 May 2010}}</ref>
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| The method of spin amplitudes uses [[Mathematical formulation of quantum mechanics|quantum mechanics formalism]] to more easily describe spin dynamics. Vector and tensor polarization of particle/nuclei with spin {{math|<big>S</big> ≥ 1}} are specified by the unit polarization vector <math>\boldsymbol{p}</math> and the polarization tensor ''P''<sub>`</sub>. 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 {{math|<big>S</big> ≥ {{frac|3|2}}}} .<ref name="Silenko"/>
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| ==See also==
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| * [[Polarization density]]
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| * [[MOSCED]], an estimation method for activity coefficients; uses polarizability as parameter
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| ==References==
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| {{reflist}}
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| ==External links==
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| * [http://books.google.com/books?id=bI-ZmZWeyhkC&pg=PA290&lpg=PA290&dq=Magnetic+polarizability&source=bl&ots=G5kn6PLhSr&sig=ZJKTzwW-YZhTKtOLjbEHcRzdVfA&hl=en&ei=13z8S8HGG8KBlAfbx-nGDw&sa=X&oi=book_result&ct=result&resnum=2&ved=0CBQQ6AEwATgK#v=onepage&q=Magnetic%20polarizability&f=false The theory of the electromagnetic field] by David M. Cook
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| * [http://arxiv.org/abs/hep-ph/9309211 Consistent Calculation of the Nucleon Electromagnetic Polarizabilities in Chiral Perturbation Theory Beyond Next-to-Leading Order]
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| * [http://bearspace.baylor.edu/Walter_Wilcox/www/LHPCPresentation-Dell.pdf Hadron polarizabilities and magnetic moments with background field methods] ([[PDF]])
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| {{particles}}
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| [[Category:Atomic physics]]
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| [[Category:Chemical physics]]
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| [[Category:Electric and magnetic fields in matter]]
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| [[Category:Polarization (waves)]]
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