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<title>Ring-opening polymerization</title>
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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Ring-opening polymerization</span></span>
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<div class="quotebox-title" style=""><a href="International_Union_of_Pure_and_Applied_Chemistry" title="International Union of Pure and Applied Chemistry">IUPAC</a> definition</div>
<blockquote class="quotebox-quote left-aligned" style="">
<p>A <a href="Polymerization" title="Polymerization">polymerization</a> in which a <a href="Cyclic_compound" title="Cyclic compound">cyclic</a> <a href="Monomer" title="Monomer">monomer</a> yields a monomeric unit which is <a href="Open-chain_compound" title="Open-chain compound">acyclic</a> or contains fewer cycles than the monomer.
Note:
If monomer is <a href="Polycyclic_compound" title="Polycyclic compound">polycyclic</a>, the opening of a single ring is sufficient to classify the <a href="Chemical_reaction" title="Chemical reaction">reaction</a> as ring-opening polymerization.
</p><p>Modified from the earlier definition.<sup id="cite_ref-Goldbook_1-0" class="reference"><a href="#cite_note-Goldbook-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-PAC1996_2-0" class="reference"><a href="#cite_note-PAC1996-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>
</p>
</blockquote>
<div style="padding-bottom: 0; padding-top: 0.5em"><cite class="left-aligned" style=""><a rel="nofollow" class="external text" href="http://www.iupac.org/publications/pac/80/10/2163/">Penczek S.; Moad, G. <i>Pure Appl. Chem.</i>, <b>2008</b>, 80(10), 2163-2193</a></cite></div>
</div>

<p>In <a href="Polymer_chemistry" title="Polymer chemistry">polymer chemistry</a>, <b>ring-opening polymerization</b> (<b>ROP</b>) is a form of <a href="Chain-growth_polymerization" title="Chain-growth polymerization">chain-growth polymerization</a> in which the <a href="End_group" title="End group">terminus</a> of a <a href="Polymer" title="Polymer">polymer</a> chain attacks <a href="Cyclic_compound" title="Cyclic compound">cyclic monomers</a> to form a longer polymer (see figure). The reactive center can be <a href="Radical_(chemistry)" title="Radical (chemistry)">radical</a>, <a href="Anion" class="mw-redirect" title="Anion">anionic</a> or <a href="Cation" class="mw-redirect" title="Cation">cationic</a>.
</p><p>Ring-opening of cyclic monomers is often driven by the relief of <a href="Ring_strain" title="Ring strain">bond-angle strain</a>. Thus, as is the case for other types of polymerization, the <a href="Enthalpy" title="Enthalpy">enthalpy</a> change in ring-opening is negative.<sup id="cite_ref-Young_3-0" class="reference"><a href="#cite_note-Young-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Many rings undergo ROP.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>
</p>
<meta property="mw:PageProp/toc">
<div class="mw-heading mw-heading2"><h2 id="Monomers">Monomers</h2></div>
<p>Many <a href="Cyclic_compound" title="Cyclic compound">cyclic monomers</a> are amenable to ROP.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> These include <a href="Epoxide" title="Epoxide">epoxides</a>,<sup id="cite_ref-Sarazin_6-0" class="reference"><a href="#cite_note-Sarazin-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Longo_7-0" class="reference"><a href="#cite_note-Longo-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> cyclic trisiloxanes, some lactones<sup id="cite_ref-Sarazin_6-1" class="reference"><a href="#cite_note-Sarazin-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Jerome_8-0" class="reference"><a href="#cite_note-Jerome-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> and <a href="Lactide" title="Lactide">lactides</a>,<sup id="cite_ref-Jerome_8-1" class="reference"><a href="#cite_note-Jerome-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> cyclic <a href="Anhydride" class="mw-redirect" title="Anhydride">anhydrides</a>,<sup id="cite_ref-Longo_7-1" class="reference"><a href="#cite_note-Longo-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> <a href="Cyclic_carbonate" class="mw-redirect" title="Cyclic carbonate">cyclic carbonates</a>,<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> and <a href="Amino_acid_N-carboxyanhydride" title="Amino acid N-carboxyanhydride">amino acid <i>N</i>-carboxyanhydrides</a>.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Many strained <a href="Cycloalkene" title="Cycloalkene">cycloalkenes</a>, e.g <a href="Norbornene" title="Norbornene">norbornene</a>, are suitable monomers via <a href="Ring-opening_metathesis_polymerization" title="Ring-opening metathesis polymerization">ring-opening metathesis polymerization</a>. Even highly strained <a href="Cycloalkane" title="Cycloalkane">cycloalkane</a> rings, such as <a href="Cyclopropane" title="Cyclopropane">cyclopropane</a><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> and <a href="Cyclobutane" title="Cyclobutane">cyclobutane</a><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> derivatives, can undergo ROP.
</p>
<div class="mw-heading mw-heading2"><h2 id="History">History</h2></div>
<p>Ring-opening polymerization has been used since the beginning of the 1900s to produce <a href="Polymer" title="Polymer">polymers</a>. Synthesis of <a href="Polypeptides" class="mw-redirect" title="Polypeptides">polypeptides</a> which has the oldest history of ROP, dates back to the work in 1906 by Leuchs.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Subsequently, the ROP of anhydro <a href="Sugars" class="mw-redirect" title="Sugars">sugars</a> provided <a href="Polysaccharides" class="mw-redirect" title="Polysaccharides">polysaccharides</a>, including synthetic <a href="Dextran" title="Dextran">dextran</a>, <a href="Xanthan_gum" title="Xanthan gum">xanthan gum</a>, <a href="Welan_gum" title="Welan gum">welan gum</a>, <a href="Gellan_gum" title="Gellan gum">gellan gum</a>, diutan gum, and <a href="Pullulan" title="Pullulan">pullulan</a>. Mechanisms and thermodynamics of ring-opening polymerization were established in the 1950s.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> The first high-molecular weight polymers (M<sub>n</sub> up to 10<sup>5</sup>) with a <a href="Repeat_unit" title="Repeat unit">repeating unit</a> were prepared by ROP as early as in 1976.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup>
</p><p>New research shows that ROP can be completed with cyclic esters with minimal to no use of solvents by using resonant acoustic mixing.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup>
</p><p>An industrial application is the production of <a href="Nylon-6" class="mw-redirect" title="Nylon-6">nylon-6</a> from <a href="Caprolactam" title="Caprolactam">caprolactam</a>.
</p>
<div class="mw-heading mw-heading2"><h2 id="Mechanisms">Mechanisms</h2></div>
<p>Ring-opening polymerization can proceed via <a href="Radical_(chemistry)" title="Radical (chemistry)">radical</a>, anionic, or cationic polymerization as described below.<sup id="cite_ref-nuyken_20-0" class="reference"><a href="#cite_note-nuyken-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> Additionally, radical ROP is useful in producing polymers with <a href="Functional_group" title="Functional group">functional groups</a> incorporated in the backbone chain that cannot otherwise be synthesized via conventional <a href="Chain-growth_polymerization" title="Chain-growth polymerization">chain-growth polymerization</a> of <a href="Vinyl_group" title="Vinyl group">vinyl</a> monomers. For instance, radical ROP can produce polymers with <a href="Ethers" class="mw-redirect" title="Ethers">ethers</a>, <a href="Esters" class="mw-redirect" title="Esters">esters</a>, <a href="Amide" title="Amide">amides</a>, and <a href="Carbonates" class="mw-redirect" title="Carbonates">carbonates</a> as functional groups along the main chain.<sup id="cite_ref-nuyken_20-1" class="reference"><a href="#cite_note-nuyken-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-dubois_21-0" class="reference"><a href="#cite_note-dubois-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Anionic_ring-opening_polymerization_(AROP)">Anionic ring-opening polymerization (AROP)</h3></div>
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</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Anionic_polymerization" class="mw-redirect" title="Anionic polymerization">Anionic polymerization</a></div>

<p>Anionic ring-opening polymerizations (AROP) involve <a href="Nucleophile" title="Nucleophile">nucleophilic reagents</a> as initiators. Monomers with a three-member ring structure - such as <a href="Epoxides" class="mw-redirect" title="Epoxides">epoxides</a>, <a href="Aziridines" title="Aziridines">aziridines</a>, and episulfides - undergo anionic ROP.<sup id="cite_ref-dubois_21-2" class="reference"><a href="#cite_note-dubois-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup>
</p><p>A typical example of anionic ROP is that of <a href="Caprolactone" title="Caprolactone">ε-caprolactone</a>, initiated by an <a href="Alkoxide" title="Alkoxide">alkoxide</a>.<sup id="cite_ref-dubois_21-3" class="reference"><a href="#cite_note-dubois-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading3"><h3 id="Cationic_ring-opening_polymerization">Cationic ring-opening polymerization</h3></div>
<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Cationic_polymerization" title="Cationic polymerization">Cationic polymerization</a></div>
<p>Cationic initiators and intermediates characterize cationic ring-opening polymerization (CROP). Examples of <a href="Cyclic_compound" title="Cyclic compound">cyclic monomers</a> that polymerize through this mechanism include <a href="Lactone" title="Lactone">lactones</a>, <a href="Lactam" title="Lactam">lactams</a>, <a href="Amine" title="Amine">amines</a>, and <a href="Ether" title="Ether">ethers</a>.<sup id="cite_ref-cowie_cation_22-0" class="reference"><a href="#cite_note-cowie_cation-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> CROP proceeds through an <a href="SN1_reaction" title="SN1 reaction">S<sub>N</sub>1</a> or <a href="SN2_reaction" title="SN2 reaction">S<sub>N</sub>2</a> propagation, chain-growth process.<sup id="cite_ref-nuyken_20-2" class="reference"><a href="#cite_note-nuyken-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> The mechanism is affected by the stability of the resulting <a href="Ion" title="Ion">cationic</a> species. For example, if the atom bearing the positive charge is stabilized by <a href="Activating_group" class="mw-redirect" title="Activating group">electron-donating groups</a>, polymerization will proceed by the S<sub>N</sub>1 mechanism.<sup id="cite_ref-dubois_21-4" class="reference"><a href="#cite_note-dubois-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> The cationic species is a <a href="Heteroatom" title="Heteroatom">heteroatom</a> and the chain grows by the addition of cyclic monomers thereby opening the ring system.
</p>

<p>The monomers can be activated by <a href="Br%C3%B8nsted%E2%80%93Lowry_acid%E2%80%93base_theory" title="Brønsted–Lowry acid–base theory">Bronsted acids</a>, <a href="Carbenium_ion" title="Carbenium ion">carbenium ions</a>, <a href="Onium_compound" class="mw-redirect" title="Onium compound">onium ions</a>, and metal cations.<sup id="cite_ref-nuyken_20-3" class="reference"><a href="#cite_note-nuyken-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup>
</p><p>CROP can be a <a href="Living_polymerization" title="Living polymerization">living polymerization</a> and can be terminated by nucleophilic reagents such as <a href="Alkoxy_group" title="Alkoxy group">phenoxy anions</a>, <a href="Phosphine" title="Phosphine">phosphines</a>, or <a href="Polyelectrolyte" title="Polyelectrolyte">polyanions</a>.<sup id="cite_ref-nuyken_20-4" class="reference"><a href="#cite_note-nuyken-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> When the amount of monomers becomes depleted, termination can occur intra or intermolecularly. The active end can "backbite" the chain, forming a <a href="Macrocycle" title="Macrocycle">macrocycle</a>. <a href="Alkyl" class="mw-redirect" title="Alkyl">Alkyl</a> chain transfer is also possible, where the active end is quenched by transferring an alkyl chain to another polymer.
</p>
<div class="mw-heading mw-heading3"><h3 id="Ring-opening_metathesis_polymerization">Ring-opening metathesis polymerization</h3></div>
<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Ring-opening_metathesis_polymerization" title="Ring-opening metathesis polymerization">Ring-opening metathesis polymerization</a></div>
<p><a href="Ring-opening_metathesis_polymerisation" class="mw-redirect" title="Ring-opening metathesis polymerisation">Ring-opening metathesis polymerisation</a> (ROMP) produces <a href="Saturated_and_unsaturated_compounds" title="Saturated and unsaturated compounds">unsaturated</a> polymers from <a href="Cycloalkene" title="Cycloalkene">cycloalkenes</a> or bicycloalkenes. It requires <a href="Organometallic_chemistry" title="Organometallic chemistry">organometallic catalysts</a>.<sup id="cite_ref-nuyken_20-5" class="reference"><a href="#cite_note-nuyken-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup>
</p><p>The mechanism for ROMP follows similar pathways as <a href="Olefin_metathesis" title="Olefin metathesis">olefin metathesis</a>. The initiation process involves the coordination of the cycloalkene monomer to the <a href="Transition_metal_carbene_complex" title="Transition metal carbene complex">metal alkylidene complex</a>, followed by a [2+2] type <a href="Cycloaddition" title="Cycloaddition">cycloaddition</a> to form the metallacyclobutane intermediate that cycloreverts to form a new alkylidene species.<sup id="cite_ref-sutthasupa_24-0" class="reference"><a href="#cite_note-sutthasupa-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-hartwig_25-0" class="reference"><a href="#cite_note-hartwig-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup>
</p>
<p> Commercially relevant <a href="Saturated_and_unsaturated_compounds" title="Saturated and unsaturated compounds">unsaturated</a> polymers synthesized by ROMP include poly<a href="Norbornene" title="Norbornene">norbornene</a>, poly<a href="Cyclooctene" title="Cyclooctene">cyclooctene</a>, and poly<a href="Cyclopentadiene" title="Cyclopentadiene">cyclopentadiene</a>.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup>
</p><div class="mw-heading mw-heading2"><h2 id="Thermodynamics">Thermodynamics</h2></div>
<p>The formal thermodynamic criterion of a given monomer polymerizability is related to a sign of the <a href="Free_enthalpy" class="mw-redirect" title="Free enthalpy">free enthalpy</a> (<a href="Gibbs_free_energy" title="Gibbs free energy">Gibbs free energy</a>) of polymerization:
<span class="mwe-math-element mwe-math-element-block"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta G_{p}(xy)=\Delta H_{p}(xy)-T\Delta S_{p}(xy)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">Δ<!-- Δ --></mi>
<msub>
<mi>G</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>p</mi>
</mrow>
</msub>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mi>y</mi>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mi mathvariant="normal">Δ<!-- Δ --></mi>
<msub>
<mi>H</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>p</mi>
</mrow>
</msub>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mi>y</mi>
<mo stretchy="false">)</mo>
<mo>−<!-- − --></mo>
<mi>T</mi>
<mi mathvariant="normal">Δ<!-- Δ --></mi>
<msub>
<mi>S</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>p</mi>
</mrow>
</msub>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mi>y</mi>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \Delta G_{p}(xy)=\Delta H_{p}(xy)-T\Delta S_{p}(xy)}</annotation>
</semantics>
</math></span></span>
where:
</p>
<dl><dd><span class="texhtml mvar" style="font-style:italic;">x</span> and <span class="texhtml mvar" style="font-style:italic;">y</span> indicate monomer and polymer states, respectively (<span class="texhtml mvar" style="font-style:italic;">x</span> and/or <span class="texhtml mvar" style="font-style:italic;">y</span> = l (liquid), g (<a href="Gaseous" class="mw-redirect" title="Gaseous">gaseous</a>), c (<a href="Amorphous_solid" title="Amorphous solid">amorphous solid</a>), c' (<a href="Crystalline_solid" class="mw-redirect" title="Crystalline solid">crystalline solid</a>), s (<a href="Solution_(chemistry)" title="Solution (chemistry)">solution</a>));</dd>
<dd><span class="texhtml">Δ<i>H<sub>p</sub></i>(<i>xy</i>)</span> is the <a href="Enthalpy" title="Enthalpy">enthalpy</a> of polymerization (SI unit: joule per kelvin);</dd>
<dd><span class="texhtml">Δ<i>S<sub>p</sub></i>(<i>xy</i>)</span> is the <a href="Entropy" title="Entropy">entropy</a> of polymerization (SI unit: joule);</dd>
<dd><span class="texhtml mvar" style="font-style:italic;">T</span> is the <a href="Absolute_temperature" class="mw-redirect" title="Absolute temperature">absolute temperature</a> (SI unit: kelvin).</dd></dl>
<p>The free enthalpy of polymerization (<span class="texhtml">Δ<i>G<sub>p</sub></i></span>) may be expressed as a sum of standard enthalpy of polymerization (<span class="texhtml">Δ<i>G<sub>p</sub></i>°</span>) and a term related to instantaneous monomer molecules and growing <a href="Macromolecules" class="mw-redirect" title="Macromolecules">macromolecules</a> concentrations:
<span class="mwe-math-element mwe-math-element-block"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta G_{p}=\Delta G_{p}^{\circ }+RT\ln {\frac {[\ldots -({\ce {m}})_{i+1}{\ce {m}}^{\ast }]}{[{\ce {M}}][\ldots -({\ce {m}})_{i}{\ce {m}}^{\ast }]}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
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<mi mathvariant="normal">Δ<!-- Δ --></mi>
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<annotation encoding="application/x-tex">{\displaystyle \Delta G_{p}=\Delta G_{p}^{\circ }+RT\ln {\frac {[\ldots -({\ce {m}})_{i+1}{\ce {m}}^{\ast }]}{[{\ce {M}}][\ldots -({\ce {m}})_{i}{\ce {m}}^{\ast }]}}}</annotation>
</semantics>
</math></span></span>
where:
</p>
<dl><dd><span class="texhtml mvar" style="font-style:italic;">R</span> is the <a href="Gas_constant" title="Gas constant">gas constant</a>;</dd>
<dd><span class="texhtml">M</span> is the monomer;</dd>
<dd><span class="texhtml">(m)<sub><i>i</i></sub></span> is the monomer in an initial state;</dd>
<dd><span class="texhtml">m<sup>*</sup></span> is the active monomer.</dd></dl>
<p>Following <a href="Flory%E2%80%93Huggins_solution_theory" title="Flory–Huggins solution theory">Flory–Huggins solution theory</a> that the reactivity of an active center, located at a <a href="Macromolecule" title="Macromolecule">macromolecule</a> of a sufficiently long macromolecular chain, does not depend on its <a href="Degree_of_polymerization" title="Degree of polymerization">degree of polymerization</a> (<span class="texhtml"><i>DP<sub>i</sub></i></span>), and taking in to account that <span class="texhtml">Δ<i>G<sub>p</sub></i>° = Δ<i>H<sub>p</sub></i>° − <i>T</i>Δ<i>S<sub>p</sub></i>°</span> (where <span class="texhtml">Δ<i>H<sub>p</sub></i>°</span> and <span class="texhtml">Δ<i>S<sub>p</sub></i>°</span> indicate a standard polymerization enthalpy and entropy, respectively), we obtain:
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta G_{p}=\Delta H_{p}^{\circ }-T(\Delta S_{p}^{\circ }+R\ln[M])}">
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<annotation encoding="application/x-tex">{\displaystyle \Delta G_{p}=\Delta H_{p}^{\circ }-T(\Delta S_{p}^{\circ }+R\ln[M])}</annotation>
</semantics>
</math></span><img src="./220a922430e9e4f58818db0e2be969135dd4db24.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:34.478ex; height:3.009ex;" alt="{\displaystyle \Delta G_{p}=\Delta H_{p}^{\circ }-T(\Delta S_{p}^{\circ }+R\ln[M])}" loading="lazy"></span></dd></dl>
<p>At <a href="Chemical_equilibrium" title="Chemical equilibrium">equilibrium</a> (<span class="texhtml">Δ<i>G<sub>p</sub></i> = 0</span>), when polymerization is complete the monomer concentration (<span class="texhtml">[M]<sub>eq</sub></span>) assumes a value determined by standard polymerization parameters (<span class="texhtml">Δ<i>H<sub>p</sub></i>°</span> and <span class="texhtml">Δ<i>S<sub>p</sub></i>°</span>) and polymerization temperature:
<span class="mwe-math-element mwe-math-element-block"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}{}[{\ce {M}}]_{\rm {eq}}&amp;=\exp \left({\frac {\Delta H_{p}^{\circ }}{RT}}-{\frac {\Delta S_{p}^{\circ }}{R}}\right)\\[4pt]\ln {\frac {DP_{n}}{DP_{n}-1}}[{\ce {M}}]_{\rm {eq}}&amp;={\frac {\Delta H_{p}^{\circ }}{RT}}-{\frac {\Delta S_{p}^{\circ }}{R}}\\[4pt][{\ce {M}}]_{\rm {eq}}&amp;={\frac {DP_{n}-1}{DP_{n}}}\exp \left({\frac {\Delta H_{p}^{\circ }}{RT}}-{\frac {\Delta S_{p}^{\circ }}{R}}\right)\end{aligned}}}">
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<annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}{}[{\ce {M}}]_{\rm {eq}}&amp;=\exp \left({\frac {\Delta H_{p}^{\circ }}{RT}}-{\frac {\Delta S_{p}^{\circ }}{R}}\right)\\[4pt]\ln {\frac {DP_{n}}{DP_{n}-1}}[{\ce {M}}]_{\rm {eq}}&amp;={\frac {\Delta H_{p}^{\circ }}{RT}}-{\frac {\Delta S_{p}^{\circ }}{R}}\\[4pt][{\ce {M}}]_{\rm {eq}}&amp;={\frac {DP_{n}-1}{DP_{n}}}\exp \left({\frac {\Delta H_{p}^{\circ }}{RT}}-{\frac {\Delta S_{p}^{\circ }}{R}}\right)\end{aligned}}}</annotation>
</semantics>
</math></span></span>
Polymerization is possible only when <span class="texhtml">[M]<sub>0</sub> &gt; [M]<sub>eq</sub></span>. Eventually, at or above the so-called <a href="Ceiling_temperature" title="Ceiling temperature">ceiling temperature</a> (<span class="texhtml mvar" style="font-style:italic;">T<sub>c</sub></span>), at which <span class="texhtml">[M]<sub>eq</sub> = [M]<sub>0</sub></span>, formation of the high polymer does not occur.
<span class="mwe-math-element mwe-math-element-block"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}T_{c}&amp;={\frac {\Delta H_{p}^{\circ }}{\Delta S_{p}^{\circ }+R\ln[{\ce {M}}]_{0}}};\quad (\Delta H_{p}^{\circ }<0,\ \Delta S_{p}^{\circ }<0)\\[4pt]T_{f}&amp;={\frac {\Delta H_{p}^{\circ }}{\Delta S_{p}^{\circ }+R\ln[{\ce {M}}]_{0}}};\quad (\Delta H_{p}^{\circ }>0,\ \Delta S_{p}^{\circ }>0)\end{aligned}}}">
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<annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}T_{c}&amp;={\frac {\Delta H_{p}^{\circ }}{\Delta S_{p}^{\circ }+R\ln[{\ce {M}}]_{0}}};\quad (\Delta H_{p}^{\circ }&lt;0,\ \Delta S_{p}^{\circ }&lt;0)\\[4pt]T_{f}&amp;={\frac {\Delta H_{p}^{\circ }}{\Delta S_{p}^{\circ }+R\ln[{\ce {M}}]_{0}}};\quad (\Delta H_{p}^{\circ }&gt;0,\ \Delta S_{p}^{\circ }&gt;0)\end{aligned}}}</annotation>
</semantics>
</math></span></span>
For example, <a href="Tetrahydrofuran" title="Tetrahydrofuran">tetrahydrofuran</a> (THF) cannot be polymerized above <span class="texhtml mvar" style="font-style:italic;">T<sub>c</sub></span>&nbsp;=&nbsp;84&nbsp;°C, nor cyclo-octasulfur (S<sub>8</sub>) below <span class="texhtml mvar" style="font-style:italic;">T<sub>f</sub></span>&nbsp;=&nbsp;159&nbsp;°C.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> However, for many monomers, <span class="texhtml mvar" style="font-style:italic;">T<sub>c</sub></span> and <span class="texhtml mvar" style="font-style:italic;">T<sub>f</sub></span>, 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 <a href="Entropy" title="Entropy">entropy</a> 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 <span class="texhtml">Δ<i>G<sub>p</sub></i></span> prevails (thus, when <span class="texhtml">Δ<i>H<sub>p</sub></i>° &lt; 0</span> and <span class="texhtml">Δ<i>S<sub>p</sub></i>° &lt; 0</span>, the inequality <span class="texhtml">|<span class="nowrap" style="padding-left:0.1em; padding-right:0.1em;">Δ<i>H<sub>p</sub></i></span>| &gt; −<i>T</i>Δ<i>S<sub>p</sub></i></span> is required). Therefore, the higher the ring strain, the lower the resulting monomer concentration at <a href="Chemical_equilibrium" title="Chemical equilibrium">equilibrium</a>.
</p>
<div class="mw-heading mw-heading2"><h2 id="Additional_reading">Additional reading</h2></div>
<ul><li><style data-mw-deduplicate="TemplateStyles:r1238218222">
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</style><cite id="CITEREFLuckSadhir1992" class="citation book cs1">Luck, Russel M.; Sadhir, Rajender K., eds. (1992). <a href="Expanding_Monomers" class="mw-redirect" title="Expanding Monomers"><i>Expanding Monomers: Synthesis, Characterization, and Applications</i></a>. Boca Raton, Florida: CRC Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a>&nbsp;<bdi>978-0-8493-5156-3</bdi>.</cite></li>
<li><cite id="CITEREFNahrain_E._KamberWonhee_JeongRobert_M._WaymouthRussell_C._Pratt2007" class="citation journal cs1">Nahrain E. Kamber; Wonhee Jeong; Robert M. Waymouth; Russell C. Pratt; Bas G. G. Lohmeijer; James L. Hedrick (2007). "Organocatalytic Ring-Opening Polymerization". <i>Chemical Reviews</i>. <b>107</b> (12): <span class="nowrap">5813–</span>5840. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fcr068415b">10.1021/cr068415b</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a>&nbsp;<a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/17988157">17988157</a>.</cite></li>
<li><cite id="CITEREFDuboisCoulembierRaquez2009" class="citation book cs1">Dubois, Philippe; Coulembier, Olivier; Raquez, Jean-Marie, eds. (2009). <i>Handbook of Ring-Opening Polymerization</i>. Wiley. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2F9783527628407">10.1002/9783527628407</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a>&nbsp;<bdi>9783527628407</bdi>.</cite></li></ul>
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