View source for Gel point

{{Short description|Abrupt change in the viscosity of a solution of polymerizable materials}}
{{distinguish|Gel point (petroleum)}}

In [[polymer chemistry]], the '''gel point''' is an abrupt change in the [[viscosity]] of a solution containing polymerizable components. At the gel point, a solution undergoes [[gelation]], as reflected in a loss in fluidity. After the monomer/polymer solution has passed the gel point, internal stress builds up in the gel phase, which can lead to volume shrinkage. Gelation is characteristic of polymerizations that include [[crosslinker]]s that can form 2- or 3-dimensional networks. For example, the condensation of a [[dicarboxylic acid]] and a [[triol]] will give rise to a gel whereas the same dicarboxylic acid and a [[diol]] will not. The gel is often a small percentage of the mixture, even though it greatly influences the properties of the bulk.<ref>{{cite book |author=R.J. Young |author2=P. A. Lovell |title=Introduction to Polymers, 2nd Edition|publisher=Chapman & Hall|place=London|year=1991|isbn=0-412-30640-9}}</ref>

==Mathematical definition==
An infinite [[polymer network]] appears at the gel point. Assuming that it is possible to measure the extent of reaction, <math>p</math>, defined as the fraction of [[monomer]]s that appear in [[cross-link]]s, the gel point can be determined.<ref>Paul, Hiemenz C., and Lodge P. Timothy. Polymer Chemistry. Second ed. Boca Raton: CRC P, 2007. 381-389</ref>
The critical extent of reaction  <math>p_c</math> for the gel point to be formed is given by:

:<math>p_c = \frac{1}{N-1} \approx \frac{1}{N} </math>
For example, a polymer with N≈200 is able to reach the gel point with only 0.5% of monomers reacting. This shows the ease at which polymers are able to form infinite networks.
The critical extent of reaction for [[gelation]] can be determined as a function of the properties of the monomer mixture, <math>r</math>, <math>p</math>, and <math>f</math>:<ref>{{cite journal
  | last = Pinner
  | first = S.H. 
  | title = Functionality of non-equivalent mixtures
  | journal = Journal of Polymer Science
  | year = 1956 
 | volume = XXI
  | issue = 97
  | pages = 153–157
  | doi = 10.1002/pol.1956.120219718
  | bibcode = 1956JPoSc..21..153P 
  }}</ref>

:<math>p_c = \frac{1}{\sqrt{r+rp(f-2)}}  </math>

==See also==
*[[Pour point]]
*[[Cold filter plugging point]]
*[[Petroleum]]

==References==
{{Reflist}}

==Further reading==
*{{cite book|author1=Rudin, Alfred |author2=Choi, Phillip |title=The Elements of Polymer Science and Engineering, 3rd Edition|year=2012|publisher=Elsevier Science|page=410|isbn=978-0-12-382178-2}}

[[Category:Polymer physics]]
[[Category:Chemical properties]]