Editing Tacticity (section)

==Definition==
[[Image:Meso diad.PNG|thumb|right|200px|An example of ''{{nobr|m diads}}'' in a polypropylene molecule.]]
[[Image:Racemo diad.PNG|thumb|right|200px|An example of ''{{nobr|r diads}}'' 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 adjacent 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 adjacent {{nobr|r diads}}, and a '''heterotactic triad''' (''rm'') is composed of an {{nobr|r diad}} adjacent to 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}}