View source for Tacticity

{{Short description|Relative conformational uniformity of repeating units in a macromolecule}}
{{TopicTOC-Polymer}}
[[Image:Syndiotactic polypropene.png|thumb|right|A ball-and-stick model of syndiotactic [[polypropylene]].]]
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'''Tacticity''' (from {{langx|el|τακτικός|taktikos}}, "relating to arrangement or order") is the relative [[stereochemistry]] of adjacent [[chirality (chemistry)|chiral]] centers within a [[macromolecule]].<ref>''Introduction to polymers'' R.J. Young {{ISBN|0-412-22170-5}}{{page needed|date = December 2024}}{{full|date = December 2024}}</ref>{{better source|date = December 2024}} The practical significance of tacticity rests on the effects on the physical properties of the [[polymer]]. The regularity of the macromolecular structure influences the degree to which it has rigid, [[Crystallinity|crystalline]] long range order or flexible, [[amorphous]] long range disorder. Precise knowledge of tacticity of a polymer also helps understanding at what temperature a polymer [[melting|melts]], how [[soluble]] it is in a [[solvent]], as well as its mechanical properties.

A '''tactic macromolecule''' in the [[IUPAC]] definition is a macromolecule in which essentially all the configurational (repeating) units are identical. In a hydrocarbon macromolecule with all carbon atoms making up the backbone in a [[tetrahedral molecular geometry]], the zigzag backbone is in the paper plane with the substituents either sticking out of the paper or retreating into the paper;{{Overly detailed inline|date = December 2024}}, this projection is called the [[Natta projection|Natta projection after Giulio]] [[Giulio Natta|Natta]].{{citation needed lead|date = December 2024}} Tacticity is particularly significant in [[vinyl polymer]]s of the type -{{chem|H|2|C-CH(R)-}}, where each [[repeating unit]] contains a [[substituent]] R attached to one side of the polymer [[Backbone chain|backbone]]. The arrangement of these substituents can follow a regular pattern- appearing on the same side as the previous one, on the opposite side, or in a random configuration relative to the preceding unit. '''Monotactic''' macromolecules have one [[Stereoisomerism|stereoisomeric]] atom per repeat unit,{{citation needed lead|date = December 2024}} '''ditactic''' to '''n-tactic''' macromolecules have more than one stereoisomeric atom per unit.{{citation needed lead|date = December 2024}}

{{Quote box
 |title =[[International Union of Pure and Applied Chemistry|IUPAC]] definition
 |quote = The orderliness of the succession of configurational repeating units in<br/>the main chain of a regular [[macromolecule]], a regular oligomer molecule,<br/>a regular block, or a regular chain.<ref>{{cite journal |title=Glossary of basic terms in polymer science (IUPAC Recommendations 1996) |journal=[[Pure and Applied Chemistry]] |year=1996 |volume=68 |issue=12 |pages=2287–2311 |doi=10.1351/pac199668122287 |url=http://pac.iupac.org/publications/pac/pdf/1996/pdf/6812x2287.pdf |last1=Jenkins |first1=A. D. |last2=Kratochvíl |first2=P. |last3=Stepto |first3=R. F. T. |last4=Suter |first4=U. W. |s2cid=98774337 |access-date=2013-07-25 |archive-date=2016-03-04 |archive-url=https://web.archive.org/web/20160304041907/http://pac.iupac.org/publications/pac/pdf/1996/pdf/6812x2287.pdf |url-status=dead }}</ref> 
}}

==Definition==
[[Image:Meso diad.PNG|thumb|right|200px|Examples of ''{{nobr|m diads}}'' in a polypropylene molecule.]]
[[Image:Racemo diad.PNG|thumb|right|200px|Examples of ''{{nobr|r diads}}'' in a polypropylene molecule.]]
[[File:Mm triad.png|thumb|right|200px|An isotactic (''mm'') triad in a polypropylene molecule.]]
[[Image:Rr triad.PNG|thumb|right|200px|A syndiotactic (''rr'') triad in a polypropylene molecule.]]
[[Image:Rm triad.PNG|thumb|right|200px|A heterotactic (''rm'') triad in a polypropylene molecule.]]

===Diads===
Two adjacent structural units in a polymer molecule constitute a '''diad'''. Diads overlap: each structural unit is considered part of two diads, one diad with each neighbor. If a diad consists of two identically oriented units, the diad is called an '''{{nobr|m diad}}''' (formerly ''meso diad'', as in a [[meso compound]], now proscribed<ref name="danrotp">{{cite journal|title=Definitions and notations relating to tactic polymers (IUPAC Recommendations 2020)|journal=[[Pure and Applied Chemistry]]|year=2020|volume=92|issue=11|pages=1769–1779|doi=10.1515/pac-2019-0409|url=https://www.degruyter.com/document/doi/10.1515/pac-2019-0409/html|last1=Fellows|first1=Christopher M.|last2=Hellwich|first2=Karl-Heinz|last3=Meille|first3=Stefano V.|last4=Moad|first4=Graeme|last5=Nakano|first5=Tamaki|last6=Vert|first6=Michel|hdl=11311/1163218|hdl-access=free}}</ref>).  If a diad consists of units oriented in opposition, the diad is called an '''{{nobr|r diad}}''' (formerly ''racemo diad'', as in a racemic compound, now proscribed<ref name="danrotp" />).  In the case of vinyl polymer molecules, an {{nobr|m diad}} is one in which the substituents are oriented on the same side of the polymer backbone; in the Natta projection, they both point into the plane or both point out of the plane.

===Triads===

The stereochemistry of macromolecules can be defined even more precisely with the introduction of triads.  An '''isotactic triad''' (''mm'') is made up of two overlapping m diads, a '''syndiotactic triad'''  (also spelled '''syndyotactic'''<ref>Webster's Third New International Dictionary of the English Language, Unabridged; Oxford English Dictionary.</ref>) (''rr'') consists of two overlapping {{nobr|r diads}}, and a '''heterotactic triad''' (''rm'') is composed of an {{nobr|r diad}} overlapping an {{nobr|m diad}}.  The mass fraction of isotactic (''mm'') triads is a common quantitative measure of tacticity.

When the stereochemistry of a macromolecule is considered to be a [[Bernoulli process]], the triad composition can be calculated from the probability ''P''<sub>m</sub> of a diad being {{nobr|m type}}. For example, when this probability is 0.25 then the probability of finding:
*an isotactic triad is ''P''<sub>m</sub><sup>2</sup>, or 0.0625
*an heterotactic triad is 2''P''<sub>m</sub>(1–''P''<sub>m</sub>), or 0.375
*a syndiotactic triad is (1–''P''<sub>m</sub>)<sup>2</sup>, or 0.5625
with a total probability of 1. Similar relationships with diads exist for tetrads.<ref>{{cite journal|title = Configurational Sequence Studies by N.M.R. And the Mechanism of Vinyl Polymerisation|first = F. A.|last = Bovey|authorlink = Frank Alden Bovey|url = http://publications.iupac.org/pac/pdf/1967/pdf/1503x0349.pdf|year = 1967|journal = [[Pure and Applied Chemistry]]|pages = 349–368|volume = 15|issue = 3–4|doi = 10.1351/pac196715030349| s2cid=59059402 }}</ref>{{rp|357}}

===Tetrads, pentads, etc.===
The definition of tetrads and pentads introduce further sophistication and precision to defining tacticity, especially when information on long-range ordering is desirable.{{fact|date = December 2024}} Tacticity measurements obtained by [[carbon-13 NMR]] are typically expressed in terms of the relative abundance of various pentads within the polymer molecule, e.g. ''mmmm'', ''mrrm''.{{says who|date = December 2024}}

===Other conventions for quantifying tacticity===
The primary convention for expressing tacticity is in terms of the relative weight fraction of triad or higher-order components, as described above.  An alternative expression for tacticity is the average length of ''m'' and ''r'' sequences within the polymer molecule.  The average m-sequence length may be approximated from the relative abundance of pentads as follows:<ref>{{cite journal|doi=10.1016/0032-3861(93)90577-W|title=Microstructural analysis of polypropylenes produced with heterogeneous Ziegler–Natta catalysts|year=1993|last1=Paukkeri|first1=R|last2=Vaananen|first2=T|last3=Lehtinen|first3=A|journal=Polymer|volume=34|pages=2488|issue=12}}</ref>

<math>MSL = \frac{mmmm + \tfrac{3}{2} mrrr + 2 rmmr + \tfrac{1}{2} rmrm + \tfrac{1}{2} rmrr}{\tfrac{1}{2} mmmr + rmmr + \tfrac{1}{2}rmrm + \tfrac{1}{2}rmrr}</math>

{{clear}}

==Polymers==

[[File:IUPAC definition for a tactic block in a polymer.png|thumb|right|550px|link=https://doi.org/10.1351/goldbook.T06242|IUPAC definition for a tactic block in a polymer]]

===Isotactic polymers===
Isotactic polymers are composed of isotactic macromolecules (IUPAC definition).<ref>[[IUPAC]] [http://www.iupac.org/reports/1996/6812jenkins/molecules.html macromolecular glossary] {{webarchive|url=https://web.archive.org/web/20080211121815/http://www.iupac.org/reports/1996/6812jenkins/molecules.html |date=2008-02-11 }}</ref> In isotactic macromolecules, all the substituents are located on the same side of the macromolecular backbone. An isotactic macromolecule consists of 100% {{nobr|m diads}}, though IUPAC also allows the term for macromolecules with at least 95% {{nobr|m diads}} if that looser usage is explained.<ref name="danrotp" /> [[Polypropylene]] formed by [[Ziegler–Natta catalyst|Ziegler–Natta catalysis]] is an example of an isotactic polymer.<ref>Stevens, P. S. Polymer Chemistry: An Introduction, 3rd ed.; Oxford Press: New York, 1999; pp 234–235</ref> Isotactic polymers are usually [[semicrystalline]]<ref name=":0" /> and generally (but not exclusively) crystallize in a helical configuration.<ref>{{Cite journal |last=Yashima |first=Eiji |last2=Maeda |first2=Katsuhiro |last3=Iida |first3=Hiroki |last4=Furusho |first4=Yoshio |last5=Nagai |first5=Kanji |date=2009-11-11 |title=Helical Polymers: Synthesis, Structures, and Functions |url=https://doi.org/10.1021/cr900162q |journal=Chemical Reviews |volume=109 |issue=11 |pages=6102–6211 |doi=10.1021/cr900162q |issn=0009-2665|url-access=subscription }}</ref><ref>{{Cite journal |last=Auriemma |first=Finizia |last2=De Rosa |first2=Claudio |last3=Corradini |first3=Paolo |date=2004 |title=Non-Helical Chain Conformations of Isotactic Polymers in the Crystalline State |url=https://onlinelibrary.wiley.com/doi/abs/10.1002/macp.200300126 |journal=Macromolecular Chemistry and Physics |language=en |volume=205 |issue=3 |pages=390–396 |doi=10.1002/macp.200300126 |issn=1521-3935|url-access=subscription }}</ref> 

:[[File:Isotactic-A-2D-skeletal.png|400px|isotactic polymers]]
:[[File:Isotactic-polypropylene-3D-balls.png|400px|isotactic polypropylene]]

===Syndiotactic polymers===
In syndiotactic or '''syntactic''' macromolecules the substituents have alternate positions along the chain. The macromolecule comprises 100% {{nobr|r diads}}, though IUPAC also allows the term for macromolecules with at least 95% {{nobr|r diads}} if that looser usage is explained. Syndiotactic [[polystyrene]], made by [[metallocene catalysis polymerization]], is crystalline with a [[melting point]] of 161&nbsp;°C. [[Gutta percha]] is also an example syndiotactic polymer.<ref>Brandrup, Immergut, Grulke (Editors), Polymer Handbook 4th edition, Wiley-Interscience, New York, 1999. VI/11</ref>

:[[File:Syndiotactic-2D-skeletal.png|400px|syndiotactic polymers]]
:[[File:Syndiotactic-polypropylene-3D-balls.png|400px|syndiotactic polypropylene]] 

===Atactic polymers===
{{refimprove section|date = December 2024}}
In atactic macromolecules the substituents are placed randomly along the chain. The percentage of {{nobr|m diads}} is understood to be between 45 and 55% unless otherwise specified, but it could be any value other than 0 or 100% if that usage is clarified.<ref name="danrotp" /> With the aid of spectroscopic techniques such as [[Nuclear magnetic resonance|NMR]], it is possible to pinpoint the composition of a polymer in terms of the percentages for each triad.<ref>{{Citation |last=Hatada |first=Koichi |title=Stereochemistry of Polymers |date=2004 |work=NMR Spectroscopy of Polymers |pages=73–93 |editor-last=Hatada |editor-first=Koichi |url=https://doi.org/10.1007/978-3-662-08982-8_3 |access-date=2025-06-30 |place=Berlin, Heidelberg |publisher=Springer |language=en |doi=10.1007/978-3-662-08982-8_3 |isbn=978-3-662-08982-8 |last2=Kitayama |first2=Tatsuki |editor2-last=Kitayama |editor2-first=Tatsuki|url-access=subscription }}</ref>
:[[File:Atactic-2D-skeletal.png|400px|atactic polymers]]

Polymers that are formed by [[free-radical polymerization|free-radical mechanisms]], such as [[polyvinyl chloride]] are usually atactic.{{fact|date = December 2024}} Due to their random nature atactic polymers are usually [[amorphous]].{{fact|date = December 2024}} In ''hemi-isotactic macromolecules'' every other repeat unit has a random substituent.{{fact|date = December 2024}}

Atactic polymers such as [[polystyrene]] ([[Polystyrene|PS]]) are technologically very important.{{fact|date = December 2024}} It is possible to obtain syndiotactic polystyrene using a [[Kaminsky catalyst]],<ref>{{cite journal|doi=10.1021/ma00206a010 |title=Syndiotactic polymerization of styrene with supported Kaminsky-Sinn catalysts |date=1990 |last1=Soga |first1=Kazuo |last2=Nakatani |first2=Hisayuki |journal=Macromolecules |volume=23 |issue=4 |pages=957–959 |bibcode=1990MaMol..23..957S }}</ref> but most industrial polystyrene produced is atactic.{{fact|date = December 2024}} The two materials have very different properties because the irregular structure of the atactic version makes it impossible for the polymer chains to stack in a regular fashion: whereas syndiotactic PS is a semicrystalline material, the more common atactic version cannot crystallize and forms a ''glass'' instead.{{fact|date = December 2024}} This example is quite general in that many polymers of economic importance are atactic glass formers.{{fact|date = December 2024}}

===Eutactic polymers===
In eutactic macromolecules, substituents may occupy any specific (but potentially complex) sequence of positions along the chain.{{fact|date = December 2024}} Isotactic and syndiotactic polymers are instances of the more general class of eutactic polymers, which also includes heterogeneous macromolecules in which the sequence consists of substituents of different kinds (for example, the side-chains in proteins and the bases in nucleic acids).{{fact|date = December 2024}}

== Effect on polymer properties ==
Tacticity has a significant effect on [[Crystallization of polymers|polymer crystallinity]], and thus affects other properties that depend on crystallinity such as strength, melting point, and solubility. Isotactic and syndiotactic polymers have a more ordered structure and can form semicrystalline materials, while atactic polymers are generally amorphous (i.e. not crystalline) because their lack of order prevents them from packing into a crystal lattice.<ref name=":0">{{Cite book |last=Odian |first=George |title=Principles of polymerization |date=2004 |publisher=J. Wiley & sons |isbn=978-0-471-27400-1 |edition=4th |location=Hoboken (N.J.) |pages=633}}</ref> Crystallinity generally leads to better mechanical strength, solvent resistance, and barrier properties, but amorphous polymers do not necessarily have poor mechanical properties and can have other advantages such as optical clarity.<ref name=":0" /><ref>{{Cite book |last=Hiemenz |first=Paul C. |title=Polymer chemistry |last2=Lodge |first2=Timothy |date=2007 |publisher=CRC Press |isbn=978-1-57444-779-8 |edition=2nd |location=Boca Raton |pages=496,511}}</ref>  As an example, atactic polypropylene is an amorphous polymer with a [[Glass transition|glass-transition temperature]], ''T''<sub>g</sub>, of -27&nbsp;°C, while isotactic polypropylene is crystalline with a ''T''<sub>g</sub> of -26&nbsp;°C and a melting temperature, ''T''<sub>m</sub>, of 160&nbsp;°C and syndiotactic polypropylene is also crystalline with a higher ''T''<sub>g</sub> of -4.3&nbsp;°C and a lower ''T''<sub>m</sub> of 126&nbsp;°C.<ref>{{Citation |last=Woo |first=Eamor M. |title=Tacticity in Vinyl Polymers |date=2011 |work=Encyclopedia of Polymer Science and Technology |url=https://onlinelibrary.wiley.com/doi/abs/10.1002/0471440264.pst363 |access-date=2025-06-29 |publisher=John Wiley & Sons, Ltd |language=en |doi=10.1002/0471440264.pst363 |isbn=978-0-471-44026-0 |last2=Chang |first2=Ling|url-access=subscription }}</ref> Isotactic polypropylene is strong and high-melting and so is widely used in a range of applications, while atactic polypropylene is soft and waxy and sees only limited use in adhesives and as an asphalt additive.<ref name=":0" />

==Stereocontrolled polymerization==
Polymers with controlled tacticity (i.e. not atactic) must be produced via some type of stereocontrolled polymerization. Stereocontrolled polymerizations have been demonstrated with a variety of chain-growth polymerization mechanisms, although stereocontrolled [[Radical polymerization|radical]] and [[Cationic polymerization|cationic polymerizations]] are less common than stereocontrolled [[Coordination polymerization|coordination]] and [[Anionic addition polymerization|anionic polymerizations]] due to a lack of stereochemical definition at the propagating chain end.<ref>{{Cite journal |last=Teator |first=Aaron J. |last2=Varner |first2=Travis P. |last3=Knutson |first3=Phil C. |last4=Sorensen |first4=Cole C. |last5=Leibfarth |first5=Frank A. |date=2020-11-17 |title=100th Anniversary of Macromolecular Science Viewpoint: The Past, Present, and Future of Stereocontrolled Vinyl Polymerization |url=https://doi.org/10.1021/acsmacrolett.0c00664 |journal=ACS Macro Letters |volume=9 |issue=11 |pages=1638–1654 |doi=10.1021/acsmacrolett.0c00664|url-access=subscription }}</ref> Stereocontrolled polymerization of chiral monomers can also be enantioselective, meaning that one [[enantiomer]] of the monomer is selectively polymerized to give an isotactic polymer.<ref>{{Cite journal |last=Xie |first=Xiaoyu |last2=Huo |first2=Ziyu |last3=Jang |first3=Eungyo |last4=Tong |first4=Rong |date=2023-09-29 |title=Recent advances in enantioselective ring-opening polymerization and copolymerization |url=https://www.nature.com/articles/s42004-023-01007-z |journal=Communications Chemistry |language=en |volume=6 |issue=1 |pages=1–20 |doi=10.1038/s42004-023-01007-z |issn=2399-3669|pmc=10541874 }}</ref> Depending on the origin of stereoselectivity, stereocontrolled polymerizations can be classified as polymer chain-end control or enantiomorphic site control.

=== Polymer chain-end control ===
In polymer chain-end control, the stereochemistry of the most recent monomer added to the polymer chain determines the stereochemistry of the next monomer added. In an isoselective polymerization, the next monomer to be inserted will have the same stereochemistry as the previous monomer, while in a syndioselective polymerization it will be the opposite. The stereoselectivity of a polymerization with polymer chain-end control is quantified by ''P''<sub>m</sub> and ''P''<sub>r</sub>, the probabilities of forming an m and r diad, respectively. An isoselective polymerization has a ''P''<sub>m</sub> approaching 1, while a syndioselective polymerization has a ''P''<sub>r</sub> approaching 1.  When a stereoerror occurs (i.e. a monomer is added in the less favored orientation, such as the formation of a r diad in an isoselective polymerization), it is propagated, meaning that in an isoselective polymerization the substituents would switch from all being on one side of the polymer chain to all being on the other side.<ref name=":1">{{Cite journal |last=Coates |first=Geoffrey W. |date=2000-04-01 |title=Precise Control of Polyolefin Stereochemistry Using Single-Site Metal Catalysts |url=https://doi.org/10.1021/cr990286u |journal=Chemical Reviews |volume=100 |issue=4 |pages=1223–1252 |doi=10.1021/cr990286u |issn=0009-2665|url-access=subscription }}</ref>

=== Enantiomorphic site control ===
In enantiomorphic site control, the stereochemistry of the next monomer added is instead determined by the stereochemistry of the catalyst. The stereoselectivity of a polymerization with enantiomorphic site control is often quantified by the site control selectivity α, the probability of adding a monomer with a certain [[absolute configuration]]. For an isoselective polymerization, an α value of 0 or 1 indicates a fully isotactic polymer while an α value of 0.5 indicates an atactic polymer. When a stereoerror occurs, it is corrected, meaning that (in an isoselective polymerization) substituents will return to being on the same side of the polymer chain that they were on before the error.<ref name=":1" /> 

==Head/tail configuration==
{{More citations needed section|date = February 2025}}
[[Image:Tail head isomerism.svg|right]]
In [[vinyl polymer]]s, the complete configuration can be further described by defining polymer head/tail configuration. In a regular macromolecule, monomer units are normally linked in a head to tail configuration such that β-substituents are located on alternating carbon atoms. However, it is possible for defects to form where substituents are placed on adjacent carbon atoms, producing a head/head tail/tail configuration, such as by recombination of two growing [[free radical polymerization|radical chain]]s, or by direct head-head addition if [[steric]] effects are weak enough, such as in [[polyvinylidene fluoride]].<ref>{{cite journal|doi=10.1016/S0079-6700(99)00032-5 |title=Head to head polymers |date=1999 |last1=Vogl |first1=O. |last2=Qin |first2=M.F. |last3=Zilkha |first3=A. |journal=Progress in Polymer Science |volume=24 |issue=10 |pages=1481–1525 |doi-access=free }}</ref>

==Techniques for measuring tacticity==

Tacticity may be measured directly using [[proton]] or [[carbon-13]] [[NMR]].  This technique enables quantification of the tacticity distribution by comparison of peak areas or integral ranges corresponding to known diads (r, m), triads (mm, rm+mr, rr) and/or higher order ''n''-ads, depending on spectral resolution.  In cases of limited resolution, stochastic methods such as [[Bernoulli process|Bernoullian]] or [[Markov chain|Markovian analysis]] may also be used to fit the distribution and predict higher ''n''-ads and calculate the isotacticity of the polymer to the desired level.<ref>{{cite journal|doi=10.1021/ma60057a006|title=Carbon-13 NMR Determination of Pentad Tacticity of Poly(vinyl alcohol)|year=1977|last1=Wu|first1=Ting Kai|last2=Sheer|first2=M. Lana|journal=Macromolecules|volume=10|pages=529|issue=3|bibcode = 1977MaMol..10..529W }}</ref>

Other techniques sensitive to tacticity include [[x-ray powder diffraction]], [[secondary ion mass spectrometry]] (SIMS),<ref>{{cite journal|doi=10.1002/(SICI)1096-9918(199701)25:1<41::AID-SIA211>3.0.CO;2-T|title=Influence of Tacticity on Polymer Surfaces Studiedby ToF-SIMS|year=1997|last1=Vanden Eynde|first1=X.|last2=Weng|first2=L. T.|last3=Bertrand|first3=P.|journal=Surface and Interface Analysis|volume=25|pages=41–45}}</ref> vibrational spectroscopy (FTIR)<ref>{{cite journal|doi=10.1021/ma00207a013|title=Normal-mode analysis of infrared and Raman spectra of crystalline isotactic poly(methyl methacrylate)|year=1990|last1=Dybal|first1=J.|last2=Krimm|first2=S.|journal=Macromolecules|volume=23|pages=1301|issue=5|bibcode = 1990MaMol..23.1301D }}</ref> and especially two-dimensional techniques.<ref>{{cite journal|doi=10.1021/ma00149a011|title=Observation of the stereochemical configuration of poly(methyl methacrylate) by proton two-dimensional J-correlated and NOE-correlated NMR spectroscopy|year=1985|last1=Schilling|first1=Frederic C.|last2=Bovey|first2=Frank A.|last3=Bruch|first3=Martha D.|last4=Kozlowski|first4=Sharon A.|journal=Macromolecules|volume=18|pages=1418|issue=7|bibcode = 1985MaMol..18.1418S }}</ref>  Tacticity may also be inferred by measuring another physical property, such as melting temperature, when the relationship between tacticity and that property is well-established.<ref>{{cite journal|doi=10.1021/ma8014992|title=Pressure Dependence of the Glass Transition in Atactic and Isotactic Polypropylene|year=2008|last1=Gitsas|first1=A.|last2=Floudas|first2=G.|journal=Macromolecules|volume=41|pages=9423|issue=23|bibcode = 2008MaMol..41.9423G }}</ref>

==References==
{{Reflist}}

==Further reading==
* {{cite web | author = Wandrey, Christine [Prof.] | date = 2004-04-19 | title = Molecular Basis of the Structure and Behavior of Polymers, Part II: Chemistry and Structure of Macromolecules—Design of Polymer Chains | type = polymer chemistry course materils | work = EPFL.ch | location = Lausanne, Switzerland | publisher =  Laboratory of Polymers and Biomaterials, Dept. of Chemistry, Ecole Polytechnique Federale de Lausanne (EPFL) | url = http://scgc.epfl.ch:80/load/cours_chim/cwandrey_part-2-1.pdf | url-status = dead | archive-url = https://web.archive.org/web/20040419014355/http://scgc.epfl.ch:80/load/cours_chim/cwandrey_part-2-1.pdf | archive-date = 2004-04-19}}

==External links==

*[https://web.archive.org/web/20040627210014/http://www.chemeng.ucla.edu/che112/Notes/polymer%20spectroscopy.pdf Application of spectroscopy in polymer characterisation] @ [[University of California, Los Angeles]]

[[Category:Polymer chemistry]]
[[Category:Stereochemistry]]