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| The '''degree of polymerization''', or DP, is usually defined as the number of [[structural unit|monomeric unit]]s in a [[macromolecule]] or [[polymer]] or [[oligomer]] molecule.<ref>[http://goldbook.iupac.org/D01569.html IUPAC Definition] in [[Compendium of Chemical Terminology]] (IUPAC Gold Book)</ref><ref>Cowie J.M.G. "Polymers: Chemistry and Physics of Modern Materials" (2nd edn Blackie 1991), p.10</ref><ref>Allcock H.R., Lampe F.W. and Mark J.P. "Contemporary Polymer Chemistry" (3d edn Pearson Prentice-Hall 2003), p.316</ref>
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| For a homopolymer, there is only one type of monomeric unit and the ''number-average'' degree of polymerization is given by <math>DP_n\equiv X_n=\frac{M_n}{M_0}</math>,
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| where M<sub>n</sub> is the [[Molar mass distribution#Number average molecular weight|number-average molecular weight]] and M<sub>0</sub> is the molecular weight of the monomer unit. For most industrial purposes, degrees of polymerization in the thousands or tens of thousands are desired. | |
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| Some authors, however, define DP as the number of [[repeat unit]]s, where for [[copolymer]]s the repeat unit may not be identical to the monomeric unit.<ref>Fried J.R. "Polymer Science and Technology" (Pearson Prentice-Hall, 2nd edn 2003), p.27</ref><ref>Rudin A. "Elements of Polymer Science and Engineering" (Academic Press 1982), p.7</ref> For example, in [[nylon-6,6]], the repeat unit contains the two monomeric units —NH(CH<sub>2</sub>)<sub>6</sub>NH— and —OC(CH<sub>2</sub>)<sub>4</sub>CO—, so that a chain of 1000 monomeric units corresponds to 500 repeat units. The degree of polymerization or chain length is then 1000 by the first (IUPAC) definition, but 500 by the second.
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| In [[step-growth polymerization]], in order to achieve a high degree of polymerization (and hence molecular weight), ''X''<sub>n</sub>, a high fractional monomer conversion, ''p'', is required, as per [[Carothers' equation]]: ''X''<sub>n</sub> = 1/(1−''p''). A monomer conversion of ''p'' = 99% would be required to achieve ''X''<sub>n</sub> = 100. For [[chain-growth polymerization]], however, this is not generally true and long chains are formed for much lower monomer conversions.
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| {{Quote box
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| |title = IUPAC definition
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| |quote = The number of monomeric units in a macromolecule an oligomer molecule, a block, or a 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}}</ref>
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| ==Correlation with physical properties==
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| [[File:Degree of polymerization.png|thumb|right|200px|Relationship between degree of polymerization and melting temperature for polyethylene. Data from Flory (1963).]]
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| Polymers with identical composition but different total molecular weights may exhibit different physical properties. In general, increasing degree of polymerization correlates with higher melting temperature <ref>Flory, P.J. and Vrij, A. J. Am. Chem. Soc.; 1963; 85(22) pp3548-3553</ref> and higher mechanical strength.
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| == Kinds of degree of polymerization ==
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| Mainly, there are two types used to measure the degree of polymerization, number average degree of polymerization and weight average degree of polymerization.
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| Number Average degree of polymerization is found by finding the [[Weighted mean]] of mole fraction o. While the weight average degree of polymerization is found by finding the weighted mean of weight fraction .<ref>{{cite book|first=Paul Painter & Michael Coleman|title=Fundamentals of Polymer Science}}</ref>
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| ==See also==
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| * [[Carothers equation]]
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| * [[Kinetic chain length]]
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| ==References==
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| {{reflist}}
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| [[Category:Polymer chemistry]]
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