What is the gel point?

It is the critical extent of reaction at which crosslinking first produces a single network spanning the whole sample. At that point the weight-average molar mass diverges and the material changes from a viscous liquid to an insoluble, elastic gel.

Why does a crosslinked polymer swell but not dissolve?

The covalent network holds all chains together as one giant molecule, so solvent can enter and expand the network but cannot separate individual chains. The degree of swelling decreases as crosslink density increases.

Polymer Network Formation and Crosslinking

Crosslinking joins polymer chains into a continuous network, transforming a soluble, fusible material into an insoluble elastomer, thermoset, or gel whose properties are governed by the density of crosslinks.

Definition

Crosslinking is the formation of covalent (or strong physical) bonds between separate polymer chains, and network formation is the process by which such crosslinks connect chains into a single macroscopic molecule that no longer dissolves or melts but swells and deforms elastically.

Scope

This topic covers the chemistry and statistics of network formation: crosslinking during step-growth with multifunctional monomers, vulcanization and chemical crosslinking of preformed chains, the gel point and the divergence of molar mass at gelation, the distinction between sol and gel fractions, swelling of crosslinked networks, and the relation between crosslink density and the modulus of elastomers and thermosets.

Core questions

At what extent of reaction does a branching system reach the gel point?
How does crosslink density determine modulus, swelling, and the sol/gel split?
How do vulcanization and thermoset cure differ from network formation during polymerization?
Why do crosslinked networks swell but not dissolve?

Key theories

Flory-Stockmayer gelation theory: Statistical treatment of bond formation among multifunctional units predicts a critical conversion—the gel point—at which the weight-average molar mass diverges and an infinite network first appears, and it gives the distribution between soluble sol and insoluble gel beyond that point.
Rubber elasticity and crosslink density: The equilibrium elastic modulus of a crosslinked network is proportional to the number of network chains per unit volume, so measuring modulus or equilibrium swelling reports the crosslink density and average molar mass between crosslinks.

Mechanisms

Networks form either during polymerization, when monomers with functionality greater than two create branch points that eventually connect into an infinite structure, or after polymerization, when preformed chains are joined—by sulfur bridges in vulcanized rubber, by curing agents in epoxies, or by radiation. As crosslinking proceeds the molar mass grows and branches multiply until, at the gel point, a single network spans the sample; beyond that point the material has an insoluble gel fraction coexisting with a shrinking soluble sol fraction, and the network swells in good solvents to an extent set by its crosslink density.

Clinical relevance

Crosslinking creates the elastomers, thermosets, and gels essential to modern materials: vulcanized rubber for tires and seals, epoxy and phenolic resins for adhesives and composites, and crosslinked hydrogels for contact lenses, superabsorbents, and tissue scaffolds. Because a thermoset cannot be remelted, network formation also defines whether a material is recyclable by melting.

History

Charles Goodyear's discovery of rubber vulcanization in 1839 was the first practical crosslinking process, and the statistical theory of gelation was developed by Flory and independently by Stockmayer around 1941-1944, predicting the gel point and connecting molecular branching to the sol-gel transition.

Key figures

Paul Flory
Walter Stockmayer
Charles Goodyear

Seminal works

flory1953
odian2004

Frequently asked questions

What is the gel point?: It is the critical extent of reaction at which crosslinking first produces a single network spanning the whole sample. At that point the weight-average molar mass diverges and the material changes from a viscous liquid to an insoluble, elastic gel.
Why does a crosslinked polymer swell but not dissolve?: The covalent network holds all chains together as one giant molecule, so solvent can enter and expand the network but cannot separate individual chains. The degree of swelling decreases as crosslink density increases.