Ring-opening polymerization: Difference between revisions

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{{short description|Chain polymerization involving cyclic monomers}}
{{Quote box
|title = [[International Union of Pure and Applied Chemistry|IUPAC]] definition for '''ring-opening polymerization'''
|quote = A [[polymerization]] in which a [[Cyclic compound|cyclic]] [[monomer]] yields a monomeric unit which is [[Open-chain compound|acyclic]] or contains fewer cycles than the monomer.
 
Note:
If the monomer is [[Polycyclic compound|polycyclic]], the opening of a single ring is sufficient to classify the [[Chemical reaction|reaction]] as ring-opening polymerization.
 
Modified from the earlier definition.<ref name="Goldbook">{{GoldBookRef|title=Ring-opening polymerization|file=R05396|accessdate=Mar 10, 2014}}</ref><ref name=PAC1996>{{cite journal
.<ref name=PAC1996>{{cite journal
|url= http://iupac.org/publications/pac/68/12/2287/
|doi = 10.1351/pac199668122287
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|last1= Jenkins |first1= A. D. |last2= Kratochvíl |first2= P. |last3= Stepto |first3= R. F. T. |last4= Suter |first4= U. W.
|journal= Pure and Applied Chemistry |volume=68 |year=1996 |pages=2287–2311
|issue= 12|doi-access= free }}</ref>
|source = [http://www.iupac.org/publications/pac/80/10/2163/ Penczek S.; Moad, G. ''Pure Appl. Chem.'', '''2008''', 80(10), 2163-2193]
|align = right
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[[File:General scheme ionic prop.png|thumb|600px|General scheme ionic propagation. Propagating center can be radical, cationic or anionic.]]
In [[polymer chemistry]], '''ring-opening polymerization''' ('''ROP''') is a form of [[chain-growth polymerization]], in which the terminus of a [[polymer]] chain attacks [[cyclic compound|cyclic monomers]] to form a longer polymer (see figure). The reactive center can be [[Radical (chemistry)|radical]], [[anion]]ic or [[cation]]ic. Some cyclic monomers such as [[norbornene]] or [[cyclooctadiene]] can be [[polymerization|polymerized]] to high [[molecular mass|molecular weight]] polymers by using metal [[Catalysis|catalysts]]. ROP is a versatile method for the synthesis of [[biopolymer]]s.
 
In [[polymer chemistry]], '''ring-opening polymerization''' ('''ROP''') is a form of [[chain-growth polymerization]], in which the [[End group|terminus]] of a [[polymer]] chain attacks [[cyclic compound|cyclic monomers]] to form a longer polymer (see figure). The reactive center can be [[Radical (chemistry)|radical]], [[anion]]ic or [[cation]]ic. Some cyclic monomers such as [[norbornene]] or [[cyclooctadiene]] can be [[polymerization|polymerized]] to high [[molecular mass|molecular weight]] polymers by using metal [[Catalysis|catalysts]]. ROP is a versatile method for the synthesis of [[biopolymer]]s.
Ring-opening of cyclic monomers is often driven by the relief of [[ring strain|bond-angle strain]]. Thus, as is the case for other types of polymerization, the [[enthalpy]] change in ring-opening is negative.<ref name=Young>{{cite book|last=Young|first=Robert J.|title=Introduction to Polymers|year=2011|publisher=CRC Press|location=Boca Raton|isbn=978-0-8493-3929-5}}</ref>
 
Ring-opening of cyclic monomers is often driven by the relief of [[ring strain|bond-angle strain]]. Thus, as is the case for other types of polymerization, the [[enthalpy]] change in ring-opening is negative.<ref name=Young>{{cite book|last=Young|first=Robert J.|title=Introduction to Polymers|year=2011|publisher=CRC Press|location=Boca Raton|isbn=978-0-8493-3929-5}}</ref> Many rings undergo ROP.<ref>{{cite journal |doi=10.1007/s00726-006-0432-9}}</ref>
 
==Monomers==
Many [[cyclic compound|Cycliccyclic monomers]] that are amenable to ROP include [[epoxide]]s, cyclic trisiloxanes, some lactones, [[lactide]]s, [[cyclic carbonate]]s, and [[amino acid N-carboxyanhydride]]s.<ref>{{Citecite journal |lastdoi=JEROME10.3390/polym5020361|firstdoi-access=Cfree |last2title=LECOMTE|first2=P|date=2008Ring-06-10|title=RecentOpening advancesPolymerization—An inIntroductory theReview synthesis|date=2013 of|last1=Nuyken aliphatic|first1=Oskar polyesters|last2=Pask by|first2=Stephen ring-opening polymerization☆|journal=AdvancedPolymers Drug Delivery Reviews|volume=605 |issue=92 |pages=1056–1076|doi=10.1016/j.addr.2008.02.008|pmid=18403043|issn=0169-409X361–403 }}</ref> These include [[epoxide]]s,<ref name=Sarazin>{{cite journal|title=Discrete Cationic Complexes for Ring-Opening Polymerization Catalysis of Cyclic Esters and Epoxides|authorsauthor=Yann Sarazin, |author2=Jean-François Carpentier |journal=Chemical Reviews|year=2015|volume=115|issue=9|pages=3564–3614|doi=10.1021/acs.chemrev.5b00033|pmid=25897976}}</ref><ref name=Longo>{{cite journal|title=Ring-Opening Copolymerization of Epoxides and Cyclic Anhydrides with Discrete Metal Complexes: Structure–Property Relationships|first1=Julie M.|last1=Longo|first2=Maria J.|last2= Sanford|first3=Geoffrey W.|last3=Coates|journal=Chemical Reviews|year=2016|volume=116|issue=24|pages=15167–15197|doi=10.1021/acs.chemrev.6b00553|pmid=27936619}}</ref>. cyclic trisiloxanes,{{cn|date=December 2023}} some lactones<ref name=Sarazin/><ref name=Jerome>{{citeCite journal|authorlast1=Kricheldorf, H. R. JEROME|yearfirst1=2006 C|last2=LECOMTE|first2=P|date=2008-06-10|title=PolypeptidesRecent andadvances 100in Yearsthe of Chemistrysynthesis of Α-Aminoaliphatic Acidpolyesters Nby ring-Carboxyanhydridesopening polymerization☆|journal=AngewandteAdvanced ChemieDrug International EditionDelivery Reviews|volume=4560|issue=359|pages=5752–57841056–1076|doi= 10.10021016/aniej.200600693addr.2008.02.008|pmid=16948174 18403043|hdl=2268/3723|issn=0169-409X|url=http://orbi.ulg.ac.be/handle/2268/3723|hdl-access=free}}</ref> Manyand strained[[lactide]]s,<ref cycloalkenesname=Jerome/> cyclic [[anhydride]]s,<ref e.gname=Longo/> [[norbornenecyclic carbonate]]s,<ref>{{cite arejournal|last=Matsumura|first=Shuichi|author2=Tsukada, suitableKeisuke monomers|author3=Toshima, viaKazunobu [[ring|title=Enzyme-openingCatalyzed metathesisRing-Opening polymerization]]Polymerization of 1,3-Dioxan-2-one to Poly(trimethylene carbonate)|journal=Macromolecules|date=May 1997|volume=30|issue=10|pages=3122–3124|doi=10.1021/ma961862g|bibcode=1997MaMol..30.3122M}}
</ref> and [[amino acid N-carboxyanhydride|amino acid ''N''-carboxyanhydride]]s.<ref>{{cite journal|author=Kricheldorf, H. R. |year=2006 |title=Polypeptides and 100 Years of Chemistry of α-Amino Acid ''N''-Carboxyanhydrides|journal=Angewandte Chemie International Edition |volume=45|issue=35|pages=5752–5784|doi= 10.1002/anie.200600693|pmid=16948174 }}</ref><ref>{{cite journal|title=Synthesis of Well-Defined Polypeptide-Based Materials via the Ring-Opening Polymerization of α-Amino Acid N-Carboxyanhydrides|author=Nikos Hadjichristidis |author2=Hermis Iatrou |author3=Marinos Pitsikalis |author4=Georgios Sakellariou |journal=Chemical Reviews|year=2009|volume=109|issue=11|pages= 5528–5578|doi=10.1021/cr900049t|pmid=19691359}}</ref> Many strained [[cycloalkene]]s, e.g [[norbornene]], are suitable monomers via [[ring-opening metathesis polymerization]]. Even highly strained [[cycloalkane]] rings, such as [[cyclopropane]]<ref>{{cite journal |title= The Polymerization of Cyclopropane |first1= R. J. |last1= Scott |first2= H. E. |last2= Gunning |journal= J. Phys. Chem. |year= 1952 |volume= 56 |issue= 1 |pages= 156–160 |doi= 10.1021/j150493a031 }}</ref> and [[cyclobutane]]<ref>{{cite journal |title= Ring-Opening Polymerization of the Cyclobutane Adduct of Methyl Tricyanoethylenecarboxylate and Ethyl Vinyl Ether |first1= Tsutomu |last1= Yokozawa |first2= Ei-ichi |last2= Tsuruta |journal= Macromolecules |year= 1996 |volume= 29 |issue= 25 |pages= 8053–8056 |doi= 10.1021/ma9608535 }}</ref> derivatives, can undergo ROP.
 
==History==
Ring-opening polymerization has been used since the beginning of the 1900s to produce [[polymer]]s. Synthesis of [[polypeptides]] which has the oldest history of ROP, dates back to the work in 1906 by Leuchs.<ref>{{cite journal|title=Glycine-carbonic acid|last=Leuchs|first=H.|journal=Berichte der deutschenDeutschen chemischenChemischen Gesellschaft|year=1906|volume=39|page=857|doi=10.1002/cber.190603901133|url=https://zenodo.org/record/1426172}}</ref> Subsequently, the ROP of anhydro [[sugars]] provided [[polysaccharides]], including synthetic [[dextran]], [[xanthan gum]], [[welan gum]], [[gellan gum]], diutan gum, and [[pullulan]]. Mechanisms and thermodynamics of ring-opening polymerization were established in the 1950s.<ref>{{cite journal|last=Dainton|first=F. S.|author2=Devlin, T. R. E. |author3=Small, P. A. |title=The thermodynamics of polymerization of cyclic compounds by ring opening|journal=Transactions of the Faraday Society|year=1955|volume=51|pagespage=1710|doi=10.1039/TF9555101710}}</ref><ref>{{cite journal|last=Conix|first=André|author2=Smets, G. |title=Ring opening in lactam polymers|journal=Journal of Polymer Science|date=January 1955|volume=15|issue=79|pages=221–229|doi=10.1002/pol.1955.120157918|bibcode=1955JPoSc..15..221C}}</ref> The first high-molecular weight polymers (M<sub>n</sub> up to 10<sup>5</sup>) with a [[repeat unit|repeating unit]] were prepared by ROP as early as in 1976.<ref>{{cite journal|last1= Kałuz̀ynski|first1=Krzysztof|last2=Libiszowski|first2=Jan|last3=Penczek|first3=Stanisław|title=Poly(2-hydro-2-oxo-1,3,2-dioxaphosphorinane). Preparation and NMR spectra|journal=Die Makromolekulare Chemie|volume=178|issue=10|year=1977|pages=2943–2947|issn=0025-116X|doi=10.1002/macp.1977.021781017}}</ref><ref>{{cite journal|last=Libiszowski|first=Jan|author2=Kałużynski, Krzysztof |author3=Penczek, Stanisław |title=Polymerization of cyclic esters of phosphoric acid. VI. Poly(alkyl ethylene phosphates). Polymerization of 2-alkoxy-2-oxo-1,3,2-dioxaphospholans and structure of polymers|journal=Journal of Polymer Science: Polymer Chemistry Edition|date=June 1978|volume=16|issue=6|pages=1275–1283|doi=10.1002/pol.1978.170160610|bibcode=1978JPoSA..16.1275L}}</ref>
 
An industrial application is the production of [[nylon-6]] from [[caprolactam]].
 
==Mechanisms==
Ring-opening polymerization can proceed via [[Radical (chemistry)|radical]], anionic, or cationic polymerization as described below.<ref name=nuyken>{{cite journal|last=Nuyken|first=Oskar|author2=Stephen D. Pask |title=Ring-Opening Polymerization—An Introductory Review|journal=Polymers|date=25 April 2013|volume=5|issue=2|pages=361–403|doi=10.3390/polym5020361|doi-access=free}}</ref> Additionally, radical ROP is useful in producing polymers with [[functional group]]s incorporated in the backbone chain that cannot otherwise be synthesized via conventional [[chain-growth polymerization]] of [[Vinyl group|vinyl]] monomers. For instance, radical ROP can produce polymers with [[ethers]], [[esters]], [[amide]]s, and [[carbonates]] as functional groups along the main chain.<ref name=nuyken /><ref name=dubois>{{cite book|last=Dubois|first=Philippe|title=Handbook of ring-opening polymerization|year=2008|publisher=Wiley-VCH|location=Weinheim|isbn=978-3-527-31953-4|edition=1. Aufl.}}</ref>
 
===Anionic ring-opening polymerization (AROP)===
{{main article|Anionic polymerization}}
[[File:Wiki566665.tif|thumb|400px|center|The general mechanism for anionic ring-opening polymerization. Polarized functional group is represented by X-Y, where the atom X (usually a carbon atom) becomes electron deficient due to the highly electron-withdrawing nature of Y (usually an oxygen, nitrogen, sulfur, etc.). The nucleophile will attack atom X, thus releasing Y-<sup>−</sup>. The newly formed nucleophile will then attack the atom X in another monomer molecule, and the sequence would repeat until the polymer is formed.<ref name=dubois />]]
Anionic ring-opening polymerizations (AROP) are involve [[nucleophile|nucleophilic reagents]] as initiators. Monomers with a three-member ring structure - such as [[epoxides]], [[aziridines]], and [[episulfides]] - undergo anionic ROP.<ref name=dubois />
 
A typical example of anionic ROP is that of [[caprolactone|ε-caprolactone]], initiated by an [[alkoxide]].<ref name=dubois />
Line 44 ⟶ 46:
 
Cationic initiators and intermediates characterize cationic ring-opening polymerization (CROP). Examples of [[cyclic compound|cyclic monomers]] that polymerize through this mechanism include [[lactone]]s, [[lactam]]s, [[amine]]s, and [[ether]]s.<ref name="cowie cation">{{cite book|last=Cowie|first=John McKenzie Grant|title=Polymers: Chemistry and Physics of Modern Materials|year=2008|publisher=CRC Press|location=Boca Raton, Florida|isbn=978-0-8493-9813-1|pages=105–107}}</ref> CROP proceeds through an [[SN1 reaction|S<sub>N</sub>1]] or [[SN2 reaction|S<sub>N</sub>2]] propagation, chain-growth process.<ref name=nuyken /> The mechanism is affected by the stability of the resulting [[ion|cationic]] species. For example, if the atom bearing the positive charge is stabilized by [[activating group|electron-donating groups]], polymerization will proceed by the S<sub>N</sub>1 mechanism.<ref name=dubois /> The cationic species is a [[heteroatom]] and the chain grows by the addition of cyclic monomers thereby opening the ring system.
[[ImageFile:PTMEG synthesis.PNGsvg|450px|center|thumb|Synthesis of [[Spandex]].<ref name="kirk">{{cite encyclopedia |year=1996 |title =Polyethers, Tetrahydrofuran and Oxetane Polymers |first1= Gerfried|last1= Pruckmayr|first2= P.|last2= Dreyfuss|first3= M. P.|last3= Dreyfuss |encyclopedia=Kirk‑Othmer Encyclopedia of Chemical Technology |publisher=John Wiley & Sons |location= |id= }}</ref>]]
The monomers can be activated by [[Brønsted–Lowry acid–base theory|Bronsted acids]], [[carbenium ion]]s, [[Onium compound|onium ions]], and metal cations.<ref name=nuyken />
 
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===Ring-opening metathesis polymerization===
{{main article|Ring-opening metathesis polymerization}}
[[Ring-opening metathesis polymerisation|Ring-opening metathesis polymerization]] (ROMP) produces [[Saturated and unsaturated compounds|unsaturated]] polymers from [[cycloalkene]]s or bicycloalkenes. It requires [[Organometallic chemistry|organometallic catalysts]].<ref name=nuyken />
 
The mechanism for ROMP follows similar pathways as [[olefin metathesis]]. The initiation process involves the coordination of the cycloalkene monomer to the [[Transition metal carbene complex|metal alkylidene complex]], followed by a [2+2] type [[cycloaddition]] to form the metallacyclobutane intermediate that cycloreverts to form a new alkylidene species.<ref name=sutthasupa>{{cite journal|last=Sutthasupa|first=Sutthira|author2=Shiotsuki, Masashi |author3=Sanda, Fumio |title=Recent advances in ring-opening metathesis polymerization, and application to synthesis of functional materials|journal=Polymer Journal|date=13 October 2010|volume=42|issue=12|pages=905–915|doi=10.1038/pj.2010.94|doi-access=free}}</ref><ref name=hartwig>{{cite book|last=Hartwig|first=John F.| authorlinkauthor-link = John F. Hartwig | title=Organotransition metal chemistry : from bonding to catalysis|year=2010|publisher=University Science Books|location=Sausalito, California|isbn=9781891389535978-1-891389-53-5}}</ref>
[[File:Romp mechanism.png|thumb|center|850px|General scheme of the mechanism for ROMP.]] Commercially relevant [[Saturated and unsaturated compounds|unsaturated]] polymers synthesized by ROMP include Norsorex (poly[[Norbornene|polynorbornenenorbornene]]), Vestenamer (polycyclooctene)poly[[cyclooctene]], and Metton (polycyclopentadiene)poly[[cyclopentadiene]].<ref>{{Cite journal|last=Love|first=Jennifer A.|last2=Morgan|first2=John P.|last3=Trnka|first3=Tina M.|last4=Grubbs|first4=Robert H.|date=2002-11-04|title=A Practical and Highly Active Ruthenium-Based Catalyst that Effects the Cross Metathesis of Acrylonitrile|journal=Angewandte Chemie International Edition|volume=41|issue=21|pages=4035–4037|doi=10.1002/1521-3773(20021104)41:21<4035::aid-anie4035>3.0.co;2-i|issn=1433-7851}}</ref><ref>{{Cite journal|lastlast1=Walsh|firstfirst1=Dylan J.|last2=Lau|first2=Sii Hong|last3=Hyatt|first3=Michael G.|last4=Guironnet|first4=Damien|date=2017-09-25|title=Kinetic Study of Living Ring-Opening Metathesis Polymerization with Third-Generation Grubbs Catalysts|journal=Journal of the American Chemical Society|language=EN|volume=139|issue=39|pages=13644–13647|doi=10.1021/jacs.7b08010|pmid=28944665|issn=0002-7863}}</ref>
 
==Thermodynamics==
The formal thermodynamic criterion of a given monomer polymerizability is related to a sign of the [[free enthalpy]] ([[Gibbs free energy]]) of polymerization:
:<math display=block>\Delta G_p(xy) = \Delta H_p(xy)-T\Delta S_p(xy)</math>
where:
where x and y indicate monomer and polymer states, respectively (x and/or y = l (liquid), g ([[gaseous]]), c ([[amorphous solid]]), c’ ([[crystalline solid]]), s ([[solution]])), ΔH<sub>p</sub>(xy) and ΔSp(xy) are the corresponding [[enthalpy]] (SI unit: joule per kelvin) and [[entropy]] (SI unit: joule) of polymerization, and T is the absolute temperature (SI unit: kelvin).
:{{mvar|x}} and {{mvar|y}} indicate monomer and polymer states, respectively ({{mvar|x}} and/or {{mvar|y}} = l (liquid), g ([[gaseous]]), c ([[amorphous solid]]), c' ([[crystalline solid]]), s ([[Solution (chemistry)|solution]]));
The free [[enthalpy]] of polymerization (ΔG<sub>p</sub>) may be expressed as a sum of standard [[enthalpy]] of polymerization (ΔG<sub>p</sub>°) and a term related to instantaneous monomer molecules and growing [[macromolecules]] concentrations:
:{{math|Δ''H<sub>p</sub>''(''xy'')}} is the [[enthalpy]] of polymerization (SI unit: joule per kelvin);
:<math>\Delta G_p = \Delta G^\circ_p + RT\ln\frac{[...-(m)_{i+1} m^\ast]}{[M][...-(m)_i m^\ast]}</math>
:{{math|Δ''S{{sub|p}}''(''xy'')}} is the [[entropy]] of polymerization (SI unit: joule);
where R is the [[gas constant]], M is the monomer, (m)<sub>i</sub> is the monomer in an initial state, and m<sup>*</sup> is the active monomer.
:{{mvar|T}} is the [[absolute temperature]] (SI unit: kelvin).
Following [[Flory–Huggins solution theory]] that the reactivity of an active center, located at a [[macromolecule]] of a sufficiently long macromolecular chain, does not depend on its [[degree of polymerization]] (DPi), and taking in to account that ΔG<sub>p</sub>° = ΔH<sub>p</sub>° - TΔS<sub>p</sub>° (where ΔH<sub>p</sub>° and ΔS<sub>p</sub>° indicate a standard polymerization [[enthalpy]] and [[entropy]], respectively), we obtain:
The free [[enthalpy]] of polymerization (ΔG{{math|Δ''G<sub>p</sub>''}}) may be expressed as a sum of standard [[enthalpy]] of polymerization (ΔG{{math|Δ''G<sub>p</sub>''°}}) and a term related to instantaneous monomer molecules and growing [[macromolecules]] concentrations:
:<math>\Delta G_p = \Delta H^\circ_p - T(\Delta S^\circ_p + R\ln[M])</math>
:<math chem display=block>\Delta G_p = \Delta G^\circ_p + RT\ln\frac{[...\ldots - (\ce{m})_{i+1} \ce{m}^\ast]}{[\ce{M}][...\ldots-(\ce{m})_i \ce{m}^\ast]}</math>
At [[Chemical equilibrium|equilibrium]] (ΔG<sub>p</sub> = 0), when polymerization is complete the monomer concentration ([M]<sub>eq</sub>) assumes a value determined by standard polymerization parameters (ΔH<sub>p</sub>° and ΔS<sub>p</sub>°) and polymerization temperature:
where:
:<math>[M]_{eq} = e^{\frac{\Delta H^\circ_p}{RT} - \frac{\Delta S^\circ_p}{R}}</math>
:{{mvar|R}} is the [[gas constant]];
:<math>\ln\frac{DP_n}{DP_n - 1}[M]_{eq} = \frac{\Delta H^\circ_p}{RT} - \frac{\Delta S^\circ_p}{R}</math>
:{{math|M}} is the monomer;
:<math>[M]_{eq} = \frac{DP_n - 1}{DP_n} e^{\frac{\Delta H^\circ_p}{RT} - \frac{\Delta S^\circ_p}{R}}</math>
:{{math|(m)<sub>''i''</sub>}} is the monomer in an initial state;
Polymerzation is possible only when [M]<sub>0</sub> > [M]<sub>eq</sub>. Eventually, at or above the so-called [[ceiling temperature]] (T<sub>c</sub>), at which [M]<sub>eq</sub> = [M]<sub>0</sub>, formation of the high polymer does not occur.
:{{math|m<sup>*</sup>}} is the active monomer.
:<math>T_c = \frac{\Delta H^\circ_p}{\Delta S^\circ_p + R\ln[M]_0} ; (\Delta H^\circ_p<0, \Delta S^\circ_p<0)</math>
Following [[Flory–Huggins solution theory]] that the reactivity of an active center, located at a [[macromolecule]] of a sufficiently long macromolecular chain, does not depend on its [[degree of polymerization]] (DPi{{math|''DP{{sub|i}}''}}), and taking in to account that ΔG{{math|1=Δ''G<sub>p</sub>''° = ΔHΔ''H<sub>p</sub>''° -&minus; TΔS''T''Δ''S<sub>p</sub>''°}} (where ΔH{{math|Δ''H<sub>p</sub>''°}} and ΔS{{math|Δ''S<sub>p</sub>''°}} indicate a standard polymerization [[enthalpy]] and [[entropy]], respectively), we obtain:
:<math>T_f = \frac{\Delta H^\circ_p}{\Delta S^\circ_p + R\ln[M]_0} ; (\Delta H^\circ_p>0, \Delta S^\circ_p>0)</math>
:<math>\Delta G_p = \Delta H^\circ_p - T(\Delta S^\circ_p + R\ln[M])</math>
For example, [[tetrahydrofuran]] (THF) cannot be polymerized above T<sub>c</sub> = 84&nbsp;°C, nor cyclo-octasulfur (S<sub>8</sub>) below T<sub>f</sub> = 159&nbsp;°C.<ref>{{cite journal|last=Tobolsky|first=A. V.|title=Equilibrium polymerization in the presence of an ionic initiator|journal=Journal of Polymer Science|date=July 1957|volume=25|issue=109|pages=220–221|doi=10.1002/pol.1957.1202510909|bibcode=1957JPoSc..25..220T}}</ref><ref>{{cite journal|last=Tobolsky|first=A. V.|title=Equilibrium polymerization in the presence of an ionic initiator|journal=Journal of Polymer Science|date=August 1958|volume=31|issue=122|pages=126|doi=10.1002/pol.1958.1203112214|bibcode=1958JPoSc..31..126T|doi-access=free}}</ref><ref>{{cite journal|last=Tobolsky|first=Arthur V.|author2=Eisenberg, Adi |title=Equilibrium Polymerization of Sulfur|journal=Journal of the American Chemical Society|date=May 1959|volume=81|issue=4|pages=780–782|doi=10.1021/ja01513a004}}</ref><ref>{{cite journal|last=Tobolsky|first=A. V.|author2=Eisenberg, A. |title=A General Treatment of Equilibrium Polymerization|journal=Journal of the American Chemical Society|date=January 1960|volume=82|issue=2|pages=289–293|doi=10.1021/ja01487a009}}</ref> However, for many monomers, T<sub>c</sub> and T<sub>f</sub>, for polymerization in the bulk, are well above or below the operable polymerization temperatures, respectively.
At [[Chemical equilibrium|equilibrium]] (ΔG{{math|1=Δ''G<sub>p</sub>'' = 0}}), when polymerization is complete the monomer concentration ({{math|[M]<sub>eq</sub>}}) assumes a value determined by standard polymerization parameters (ΔH{{math|Δ''H<sub>p</sub>''°}} and ΔS{{math|Δ''S<sub>p</sub>''°}}) and polymerization temperature:
The polymerization of a majority of monomers is accompanied by an [[entropy]] decrease, due mostly to the loss in the translational degrees of freedom. In this situation, polymerization is thermodynamically allowed only when the enthalpic contribution into ΔG<sub>p</sub> prevails (thus, when ΔH<sub>p</sub>° < 0 and ΔS<sub>p</sub>° < 0, the inequality |ΔH<sub>p</sub>| > -TΔS<sub>p</sub> is required). Therefore, the higher the ring strain, the lower the resulting monomer concentration at [[Chemical equilibrium|equilibrium]].
<math chem display=block>\begin{align}
 
:<math> {}[\ce{M}]_{\rm eq} &= e^{\exp\left(\frac{\Delta H^\circ_p}{RT} - \frac{\Delta S^\circ_p}{R}}</math>\right) \\[4pt]
==See also==
:<math> \ln\frac{DP_n}{DP_n - 1}[\ce{M}]_{\rm eq} &= \frac{\Delta H^\circ_p}{RT} - \frac{\Delta S^\circ_p}{R}</math> \\[4pt]
* [[Ring opening metathesis polymerization]]
:<math> [\ce{M}]_{\rm eq} &= \frac{DP_n - 1}{DP_n} e^{\exp\left(\frac{\Delta H^\circ_p}{RT} - \frac{\Delta S^\circ_p}{R}}</math>\right)
* [http://www.pslc.ws/macrog/meta.htm Olefin Metathesis Polymerization]
\end{align}</math>
PolymerzationPolymerization is possible only when {{math|[M]<sub>0</sub> > [M]<sub>eq</sub>}}. Eventually, at or above the so-called [[ceiling temperature]] ({{mvar|T<sub>c</sub>}}), at which {{math|1=[M]<sub>eq</sub> = [M]<sub>0</sub>}}, formation of the high polymer does not occur.
<math chem display=block>\begin{align}
:<math> T_c &= \frac{\Delta H^\circ_p}{\Delta S^\circ_p + R\ln[\ce{M}]_0} ; \quad (\Delta H^\circ_p<0,\ \Delta S^\circ_p<0)</math> \\[4pt]
:<math> T_f &= \frac{\Delta H^\circ_p}{\Delta S^\circ_p + R\ln[\ce{M}]_0} ; \quad (\Delta H^\circ_p>0,\ \Delta S^\circ_p>0)</math>
\end{align}</math>
For example, [[tetrahydrofuran]] (THF) cannot be polymerized above {{mvar|T<sub>c</sub> }}&nbsp;= &nbsp;84&nbsp;°C, nor cyclo-octasulfur (S<sub>8</sub>) below {{mvar|T<sub>f</sub> }}&nbsp;= &nbsp;159&nbsp;°C.<ref>{{cite journal|last=Tobolsky|first=A. V.|title=Equilibrium polymerization in the presence of an ionic initiator|journal=Journal of Polymer Science|date=July 1957|volume=25|issue=109|pages=220–221|doi=10.1002/pol.1957.1202510909|bibcode=1957JPoSc..25..220T}}</ref><ref>{{cite journal|last=Tobolsky|first=A. V.|title=Equilibrium polymerization in the presence of an ionic initiator|journal=Journal of Polymer Science|date=August 1958|volume=31|issue=122|pagespage=126|doi=10.1002/pol.1958.1203112214|bibcode=1958JPoSc..31..126T|doi-access=free}}</ref><ref>{{cite journal|last=Tobolsky|first=Arthur V.|author2=Eisenberg, Adi |title=Equilibrium Polymerization of Sulfur|journal=Journal of the American Chemical Society|date=May 1959|volume=81|issue=4|pages=780–782|doi=10.1021/ja01513a004}}</ref><ref>{{cite journal|last=Tobolsky|first=A. V.|author2=Eisenberg, A. |title=A General Treatment of Equilibrium Polymerization|journal=Journal of the American Chemical Society|date=January 1960|volume=82|issue=2|pages=289–293|doi=10.1021/ja01487a009}}</ref> However, for many monomers, {{mvar|T<sub>c</sub>}} and {{mvar|T<sub>f</sub>}}, for polymerization in the bulk, are well above or below the operable polymerization temperatures, respectively.
The polymerization of a majority of monomers is accompanied by an [[entropy]] decrease, due mostly to the loss in the translational degrees of freedom. In this situation, polymerization is thermodynamically allowed only when the enthalpic contribution into ΔG{{math|Δ''G<sub>p</sub>''}} prevails (thus, when ΔH{{math|Δ''H<sub>p</sub>''° < 0}} and ΔS{{math|Δ''S<sub>p</sub>''° < 0}}, the inequality {{math|ΔH{{abs|Δ''H<sub>p</sub>|''}} > -TΔS&minus;''T''Δ''S<sub>p</sub>''}} is required). Therefore, the higher the ring strain, the lower the resulting monomer concentration at [[Chemical equilibrium|equilibrium]].
 
==Additional reading==
*{{citeCite book|last=Luck|first=edited by Rajender K. Sadhir, Russell M.|title=Expanding Monomers: Synthesis, Characterization, and Applications |yeartitle-link=1992Expanding Monomers |publisher=CRC Press |locationyear=Boca1992 Raton, Florida|isbn=9780849351563978-0-8493-5156-3 |titleeditor-linklast=ExpandingLuck Monomers|editor-first=Russel M. |editor-last2=Sadhir |editor-first2=Rajender K. |location=Boca Raton, Florida}}
*{{cite journal|lasttitle=SugiyamaOrganocatalytic Ring-Opening Polymerization|firstauthor=JNahrain E. Kamber |author2=R.Wonhee NagahataJeong |author3=Robert M. GoyalWaymouth |author4=MRussell C. AsaiPratt |author5=MBas G. UedaG. Lohmeijer |author6=KJames L. TakeuchiHedrick |journal=ACSChemical Polymer PreprintsReviews|year=19982007|volume=40107|seriesissue=112|pagepages=905813–5840|doi=10.1021/cr068415b|pmid=17988157}}</ref>
*{{cite book |title= Handbook of Ring‐Opening Polymerization |editor1-first= Philippe |editor1-last= Dubois |editor2-first= Olivier |editor2-last= Coulembier |editor3-first= Jean-Marie |editor3-last= Raquez |publisher= Wiley |year= 2009 |isbn= 9783527628407 |doi= 10.1002/9783527628407 }}<!-- see especially chapter 13 "Polymerization of Cycloalkanes" lead-ref for expanding our article -->
*{{cite journal|title=Synthesis of Well-Defined Polypeptide-Based Materials via the Ring-Opening Polymerization of α-Amino Acid N-Carboxyanhydrides|authors=Nikos Hadjichristidis, Hermis Iatrou, Marinos Pitsikalis, Georgios Sakellariou|journal=Chemical Reviews|year=2009|volume=109|issue=11|pages= 5528–5578|doi=10.1021/cr900049t|pmid=19691359}}
*{{cite journal|title=Organocatalytic Ring-Opening Polymerization|authors=Nahrain E. Kamber, Wonhee Jeong, Robert M. Waymouth, Russell C. Pratt, Bas G. G. Lohmeijer, James L. Hedrick|journal=Chemical Reviews|year=2007|volume=107|issue=12|pages=5813–5840|doi=10.1021/cr068415b|pmid=17988157}}</ref>
*{{cite journal|last=Matsumura|first=Shuichi|author2=Tsukada, Keisuke |author3=Toshima, Kazunobu |title=Enzyme-Catalyzed Ring-Opening Polymerization of 1,3-Dioxan-2-one to Poly(trimethylene carbonate)|journal=Macromolecules|date=May 1997|volume=30|issue=10|pages=3122–3124|doi=10.1021/ma961862g|bibcode=1997MaMol..30.3122M}}
 
== References ==
<references />
 
{{DEFAULTSORT:Ring-Opening Polymerization}}
[[Category:Polymerization reactions]]