The Gel point in polymer chemistry

Polymer chemistry

Polymer chemistry or macromolecular chemistry is a multidisciplinary science that deals with the chemical synthesis and chemical properties of polymers or macromolecules. According to IUPAC recommendations, macromolecules refer to the individual molecular chains and are the domain of chemistry...

 is the point at which an infinite polymer network first appears. Assuming that it is possible to measure the extent of reaction, p, defined as the fraction of monomer

Monomer

A monomer is an atom or a small molecule that may bind chemically to other monomers to form a polymer; the term "monomeric protein" may also be used to describe one of the proteins making up a multiprotein complex...

s that appear in cross-link

Cross-link

Cross-links are bonds that link one polymer chain to another. They can be covalent bonds or ionic bonds. "Polymer chains" can refer to synthetic polymers or natural polymers . When the term "cross-linking" is used in the synthetic polymer science field, it usually refers to the use of...

s, the gel point can be determined.
The critical extent of reaction for the gel point to be formed is given by:

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, r, ρ, and f: