Editing Polymer (section)

====Chain length====
A common means of expressing the length of a chain is the [[degree of polymerization]], which quantifies the number of monomers incorporated into the chain.<ref>McCrum, p. 30</ref><ref name="PP33">Rubinstein, p. 3</ref> As with other molecules, a polymer's size may also be expressed in terms of [[molecular weight]]. Since synthetic polymerization techniques typically yield a statistical distribution of chain lengths, the molecular weight is expressed in terms of weighted averages. The [[number-average molecular weight]] (''M''<sub>n</sub>) and [[weight-average molecular weight]] (''M''<sub>w</sub>) are most commonly reported.<ref>McCrum, p. 33</ref><ref name="PP233">Rubinstein, pp. 23–24</ref> The ratio of these two values (''M''<sub>w</sub> / ''M''<sub>n</sub>) is the [[dispersity]] (''Đ''), which is commonly used to express the width of the molecular weight distribution.<ref>Painter, p. 22</ref>

The physical properties<ref>{{cite book |last1= De Gennes |first1= Pierre Gilles |title= Scaling concepts in polymer physics |year= 1979 |publisher= Cornell University Press |location= Ithaca, N.Y. |isbn= 978-0-8014-1203-5}}</ref> of polymer strongly depend on the length (or equivalently, the molecular weight) of the polymer chain.<ref name="PP5">Rubinstein, p. 5</ref> One important example of the physical consequences of the molecular weight is the scaling of the [[viscosity]] (resistance to flow) in the melt.<ref>McCrum, p. 37</ref> The influence of the weight-average molecular weight (<math>M_w</math>) on the melt viscosity (<math>\eta</math>) depends on whether the polymer is above or below the onset of [[reptation|entanglements]]. Below the entanglement molecular weight{{clarify|date=December 2018}}, <math>\eta \sim {M_w}^{1}</math>, whereas above the entanglement molecular weight, <math>\eta \sim {M_w}^{3.4}</math>. In the latter case, increasing the polymer chain length 10-fold would increase the viscosity over 1000 times.<ref>Introduction to Polymer Science and Chemistry: A Problem-Solving Approach By Manas Chanda</ref>{{page needed|date=December 2018}} Increasing chain length furthermore tends to decrease chain mobility, increase strength and toughness, and increase the glass-transition temperature (T<sub>g</sub>).<ref>{{cite journal |last1=O'Driscoll |first1=K. |last2=Amin Sanayei |first2=R. |date=July 1991 |title=Chain-length dependence of the glass transition temperature |journal=Macromolecules |volume=24 |issue=15 |pages=4479–4480 |doi= 10.1021/ma00015a038|bibcode=1991MaMol..24.4479O}}</ref> This is a result of the increase in chain interactions such as [[Van der Waals force|van der Waals attractions]] and [[reptation|entanglements]] that come with increased chain length.<ref>{{cite book|last1=Pokrovskii|first1=V. N.|year=2010|title=The Mesoscopic Theory of Polymer Dynamics|series=Springer Series in Chemical Physics|volume=95|doi=10.1007/978-90-481-2231-8|isbn=978-90-481-2230-1|bibcode=2010mtpd.book.....P|url=https://cds.cern.ch/record/1315698}}</ref><ref>{{cite journal|last1=Edwards|first1=S. F.|year=1967|title=The statistical mechanics of polymerized material|journal=Proceedings of the Physical Society|volume=92|issue=1|pages=9–16|bibcode=1967PPS....92....9E|doi=10.1088/0370-1328/92/1/303}}</ref> These interactions tend to fix the individual chains more strongly in position and resist deformations and matrix breakup, both at higher stresses and higher temperatures.