# Ring-opening polymerization

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{{short description|Chain polymerization involving cyclic monomers}}
{{Quote box
 |title = [IUPAC](/source/International_Union_of_Pure_and_Applied_Chemistry) definition
 |quote = A [polymerization](/source/polymerization) in which a [cyclic](/source/Cyclic_compound) [monomer](/source/monomer) yields a monomeric unit which is [acyclic](/source/Open-chain_compound) or contains fewer cycles than the monomer.
Note:
If monomer is [polycyclic](/source/Polycyclic_compound), the opening of a single ring is sufficient to classify the [reaction](/source/Chemical_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 
|url= http://iupac.org/publications/pac/68/12/2287/
|doi = 10.1351/pac199668122287
|title= Glossary of basic terms in polymer science (IUPAC Recommendations 1996)
|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
}}

thumb|600px|General scheme ionic propagation. Propagating center can be radical, cationic or anionic.

In [polymer chemistry](/source/polymer_chemistry), '''ring-opening polymerization''' ('''ROP''') is a form of [chain-growth polymerization](/source/chain-growth_polymerization) in which the [terminus](/source/End_group) of a [polymer](/source/polymer) chain attacks [cyclic monomers](/source/cyclic_compound) to form a longer polymer (see figure). The reactive center can be [radical](/source/Radical_(chemistry)), [anion](/source/anion)ic or [cation](/source/cation)ic.

Ring-opening of cyclic monomers is often driven by the relief of [bond-angle strain](/source/ring_strain). Thus, as is the case for other types of polymerization, the [enthalpy](/source/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 |title=Mechanisms of homocysteine toxicity in humans |date=2007 |last1=Perła-Kaján |first1=J. |last2=Twardowski |first2=T. |last3=Jakubowski |first3=H. |journal=Amino Acids |volume=32 |issue=4 |pages=561–572 |pmid=17285228 }}</ref> 

==Monomers==
Many [cyclic monomers](/source/cyclic_compound) are amenable to ROP.<ref>{{cite journal |doi=10.3390/polym5020361|doi-access=free |title=Ring-Opening Polymerization—An Introductory Review |date=2013 |last1=Nuyken |first1=Oskar |last2=Pask |first2=Stephen |journal=Polymers |volume=5 |issue=2 |pages=361–403 }}</ref> These include [epoxide](/source/epoxide)s,<ref name=Sarazin>{{cite journal|title=Discrete Cationic Complexes for Ring-Opening Polymerization Catalysis of Cyclic Esters and Epoxides|author=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>{{Cite journal|last1=JEROME|first1=C|last2=LECOMTE|first2=P|date=2008-06-10|title=Recent advances in the synthesis of aliphatic polyesters by ring-opening polymerization☆|journal=Advanced Drug Delivery Reviews|volume=60|issue=9|pages=1056–1076|doi=10.1016/j.addr.2008.02.008|pmid=18403043|hdl=2268/3723|issn=0169-409X|url=http://orbi.ulg.ac.be/handle/2268/3723|hdl-access=free}}</ref> and [lactide](/source/lactide)s,<ref name=Jerome/> cyclic [anhydride](/source/anhydride)s,<ref name=Longo/> [cyclic carbonate](/source/cyclic_carbonate)s,<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}}
</ref> and [amino acid ''N''-carboxyanhydride](/source/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](/source/cycloalkene)s, e.g [norbornene](/source/norbornene), are suitable monomers via [ring-opening metathesis polymerization](/source/ring-opening_metathesis_polymerization). Even highly strained [cycloalkane](/source/cycloalkane) rings, such as [cyclopropane](/source/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](/source/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 |bibcode= 1996MaMol..29.8053Y }}</ref> derivatives, can undergo ROP.

==History==
Ring-opening polymerization has been used since the beginning of the 1900s to produce [polymer](/source/polymer)s. Synthesis of [polypeptides](/source/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 Deutschen Chemischen 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](/source/sugars) provided [polysaccharides](/source/polysaccharides), including synthetic [dextran](/source/dextran), [xanthan gum](/source/xanthan_gum), [welan gum](/source/welan_gum), [gellan gum](/source/gellan_gum), diutan gum, and [pullulan](/source/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|page=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 [repeating unit](/source/repeat_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>

New research shows that ROP can be completed with cyclic esters with minimal to no use of solvents by using resonant acoustic mixing.<ref>{{Cite journal |last1=Fowler |first1=Harriet R. |last2=O’Shea |first2=Riley |last3=Sefton |first3=Joseph |last4=Howard |first4=Shaun C. |last5=Muir |first5=Benjamin W. |last6=Stockman |first6=Robert A. |last7=Taresco |first7=Vincenzo |last8=Irvine |first8=Derek J. |date=2025-02-10 |title=Rapid, Highly Sustainable Ring-Opening Polymerization via Resonant Acoustic Mixing |journal=ACS Sustainable Chemistry & Engineering |volume=13 |issue=5 |pages=1916–1926 |doi=10.1021/acssuschemeng.4c06330 |pmc=11816011 |pmid=39950108}}</ref>

An industrial application is the production of [nylon-6](/source/nylon-6) from [caprolactam](/source/caprolactam).

==Mechanisms==
Ring-opening polymerization can proceed via [radical](/source/Radical_(chemistry)), 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](/source/functional_group)s incorporated in the backbone chain that cannot otherwise be synthesized via conventional [chain-growth polymerization](/source/chain-growth_polymerization) of [vinyl](/source/Vinyl_group) monomers. For instance, radical ROP can produce polymers with [ethers](/source/ethers), [esters](/source/esters), [amide](/source/amide)s, and [carbonates](/source/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}}
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) involve [nucleophilic reagents](/source/nucleophile) as initiators. Monomers with a three-member ring structure - such as [epoxides](/source/epoxides), [aziridines](/source/aziridines), and [episulfides](/source/episulfides) - undergo anionic ROP.<ref name=dubois />

A typical example of anionic ROP is that of [ε-caprolactone](/source/caprolactone), initiated by an [alkoxide](/source/alkoxide).<ref name=dubois />  [Silicone](/source/Silicone)s are produced by AROP starting with cyclic siloxanes.  A representative reaction is shown with hexamethyltrisiloxane:<ref name=West>{{cite book | last1=Mark | first1=James E. | last2=Allcock | first2=H. R. | last3=West | first3=Robert | title=Inorganic Polymers | publisher=Prentice Hall | publication-place=Englewood Cliffs (N.J.) | date=1992 | isbn=0-13-465881-7 | page=}}</ref>
: {{chem2| n[Si(CH3)2O]3 -> [Si(CH3)2O]_{3n}  }}

===Cationic ring-opening polymerization===
{{main article|Cationic polymerization}}

Cationic initiators and intermediates characterize cationic ring-opening polymerization (CROP).  Examples of [cyclic monomers](/source/cyclic_compound) that polymerize through this mechanism include [lactone](/source/lactone)s, [lactam](/source/lactam)s, [amine](/source/amine)s, and [ether](/source/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 [S<sub>N</sub>1](/source/SN1_reaction) or [S<sub>N</sub>2](/source/SN2_reaction) propagation, chain-growth process.<ref name=nuyken />  The mechanism is affected by the stability of the resulting [cationic](/source/ion) species.  For example, if the atom bearing the positive charge is stabilized by [electron-donating groups](/source/activating_group), polymerization will proceed by the S<sub>N</sub>1 mechanism.<ref name=dubois />   The cationic species is a [heteroatom](/source/heteroatom) and the chain grows by the addition of cyclic monomers thereby opening the ring system.
[[File:PTMEG synthesis.svg|450px|center|thumb|Synthesis of [Spandex](/source/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 }}</ref>]]
The monomers can be activated by [Bronsted acids](/source/Br%C3%B8nsted%E2%80%93Lowry_acid%E2%80%93base_theory), [carbenium ion](/source/carbenium_ion)s, [onium ions](/source/Onium_compound), and metal cations.<ref name=nuyken />

CROP can be a [living polymerization](/source/living_polymerization) and can be terminated by nucleophilic reagents such as [phenoxy anions](/source/Alkoxy_group), [phosphine](/source/phosphine)s, or [polyanions](/source/Polyelectrolyte).<ref name=nuyken /> When the amount of monomers becomes depleted, termination can occur intra or intermolecularly.  The active end can "backbite" the chain, forming a [macrocycle](/source/macrocycle).  [Alkyl](/source/Alkyl) chain transfer is also possible, where the active end is quenched by transferring an alkyl chain to another polymer.

===Ring-opening metathesis polymerization===
{{main article|Ring-opening metathesis polymerization}}
[Ring-opening metathesis polymerisation](/source/Ring-opening_metathesis_polymerisation) (ROMP) produces [unsaturated](/source/Saturated_and_unsaturated_compounds) polymers from [cycloalkene](/source/cycloalkene)s or bicycloalkenes.  It requires [organometallic catalysts](/source/Organometallic_chemistry).<ref name=nuyken />

The mechanism for ROMP follows similar pathways as [olefin metathesis](/source/olefin_metathesis).  The initiation process involves the coordination of the cycloalkene monomer to the [metal alkylidene complex](/source/Transition_metal_carbene_complex), followed by a [2+2] type [cycloaddition](/source/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.| author-link = John F. Hartwig | title=Organotransition metal chemistry: from bonding to catalysis|year=2010|publisher=University Science Books|location=Sausalito, California|isbn=978-1-891389-53-5}}</ref>  
thumb|center|850px|General scheme of the mechanism for ROMP. Commercially relevant [unsaturated](/source/Saturated_and_unsaturated_compounds) polymers synthesized by ROMP include poly[norbornene](/source/norbornene), poly[cyclooctene](/source/cyclooctene), and poly[cyclopentadiene](/source/cyclopentadiene).<ref>{{Cite journal|last1=Walsh|first1=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|bibcode=2017JAChS.13913644W |issn=0002-7863}}</ref>

==Thermodynamics==
The formal thermodynamic criterion of a given monomer polymerizability is related to a sign of the [free enthalpy](/source/free_enthalpy) ([Gibbs free energy](/source/Gibbs_free_energy)) of polymerization:
<math display=block>\Delta G_p(xy) = \Delta H_p(xy)-T\Delta S_p(xy)</math>
where:
:{{mvar|x}} and {{mvar|y}} indicate monomer and polymer states, respectively ({{mvar|x}} and/or {{mvar|y}} = l (liquid), g ([gaseous](/source/gaseous)), c ([amorphous solid](/source/amorphous_solid)), c' ([crystalline solid](/source/crystalline_solid)), s ([solution](/source/Solution_(chemistry))));
:{{math|Δ''H<sub>p</sub>''(''xy'')}} is the [enthalpy](/source/enthalpy) of polymerization (SI unit: joule per kelvin); 
:{{math|Δ''S{{sub|p}}''(''xy'')}} is the [entropy](/source/entropy) of polymerization (SI unit: joule);
:{{mvar|T}} is the [absolute temperature](/source/absolute_temperature) (SI unit: kelvin).
The free enthalpy of polymerization ({{math|Δ''G<sub>p</sub>''}}) may be expressed as a sum of standard enthalpy of polymerization ({{math|Δ''G<sub>p</sub>''°}}) and a term related to instantaneous monomer molecules and growing [macromolecules](/source/macromolecules) concentrations: 
<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> 
where:
:{{mvar|R}} is the [gas constant](/source/gas_constant);
:{{math|M}} is the monomer;
:{{math|(m)<sub>''i''</sub>}} is the monomer in an initial state;
:{{math|m<sup>*</sup>}} is the active monomer.
Following [Flory–Huggins solution theory](/source/Flory%E2%80%93Huggins_solution_theory) that the reactivity of an active center, located at a [macromolecule](/source/macromolecule) of a sufficiently long macromolecular chain, does not depend on its [degree of polymerization](/source/degree_of_polymerization) ({{math|''DP{{sub|i}}''}}), and taking in to account that {{math|1=Δ''G<sub>p</sub>''° = Δ''H<sub>p</sub>''° &minus; ''T''Δ''S<sub>p</sub>''°}} (where {{math|Δ''H<sub>p</sub>''°}} and {{math|Δ''S<sub>p</sub>''°}} indicate a standard polymerization enthalpy and entropy, respectively), we obtain:  
:<math>\Delta G_p = \Delta H^\circ_p - T(\Delta S^\circ_p + R\ln[M])</math> 
At [equilibrium](/source/Chemical_equilibrium) ({{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 ({{math|Δ''H<sub>p</sub>''°}} and {{math|Δ''S<sub>p</sub>''°}}) and polymerization temperature:
<math chem display=block>\begin{align}
  {}[\ce{M}]_{\rm eq} &= \exp\left(\frac{\Delta H^\circ_p}{RT} - \frac{\Delta S^\circ_p}{R}\right) \\[4pt]
  \ln\frac{DP_n}{DP_n - 1}[\ce{M}]_{\rm eq} &= \frac{\Delta H^\circ_p}{RT} - \frac{\Delta S^\circ_p}{R} \\[4pt]
  [\ce{M}]_{\rm eq} &= \frac{DP_n - 1}{DP_n} \exp\left(\frac{\Delta H^\circ_p}{RT} - \frac{\Delta S^\circ_p}{R}\right)
\end{align}</math>
Polymerization is possible only when {{math|[M]<sub>0</sub> > [M]<sub>eq</sub>}}. Eventually, at or above the so-called [ceiling temperature](/source/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}
  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) \\[4pt]
  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)
\end{align}</math>
For example, [tetrahydrofuran](/source/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|page=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|bibcode=1959JAChS..81..780T }}</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|bibcode=1960JAChS..82..289T }}</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](/source/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 {{math|Δ''G<sub>p</sub>''}} prevails (thus, when {{math|Δ''H<sub>p</sub>''° < 0}} and {{math|Δ''S<sub>p</sub>''° < 0}}, the inequality {{math|{{abs|Δ''H<sub>p</sub>''}} > &minus;''T''Δ''S<sub>p</sub>''}} is required). Therefore, the higher the ring strain, the lower the resulting monomer concentration at [equilibrium](/source/Chemical_equilibrium).

==Additional reading==
*{{Cite book |title=Expanding Monomers: Synthesis, Characterization, and Applications |title-link=Expanding Monomers |publisher=CRC Press |year=1992 |isbn=978-0-8493-5156-3 |editor-last=Luck |editor-first=Russel M. |editor-last2=Sadhir |editor-first2=Rajender K. |location=Boca Raton, Florida}}
*{{cite journal|title=Organocatalytic Ring-Opening Polymerization|author=Nahrain E. Kamber |author2=Wonhee Jeong |author3=Robert M. Waymouth |author4=Russell C. Pratt |author5=Bas G. G. Lohmeijer |author6=James L. Hedrick |journal=Chemical Reviews|year=2007|volume=107|issue=12|pages=5813–5840|doi=10.1021/cr068415b|pmid=17988157}}
*{{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 -->

== References ==
<references />

Category:Polymerization reactions

---
Adapted from the Wikipedia article [Ring-opening polymerization](https://en.wikipedia.org/wiki/Ring-opening_polymerization) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Ring-opening_polymerization?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.