crosslinkdensity

Crosslink density is the number of crosslinks connecting polymer chains in a network, typically denoted νe. It can be expressed per unit volume (mol/L or mol/m^3) or per unit mass, and applies to covalent networks as well as networks with physical crosslinks such as ionic bonds or hydrogen bonding.

A higher crosslink density restricts chain mobility, increasing stiffness and the glass transition temperature, reducing solvent uptake and swelling, and generally elevating modulus and thermal stability while reducing elongation at break.

In rubber elasticity, the shear modulus relates to crosslink density by G ≈ νe RT (νe in mol/m^3). Consequently E ≈ 3G for isotropic networks in small strain. The Flory–Rehner theory links swelling behavior to νe and the polymer–solvent interaction parameter χ.

Determination methods include equilibrium swelling analyzed with Flory–Rehner theory and dynamic mechanical analysis to obtain modulus and infer νe. Additional approaches use solvent uptake and diffusion measurements. All methods assume a reasonably homogeneous network and distinguish between elastic and non-elastic crosslinks.

Crosslink density is controlled by synthesis conditions (crosslinker functionality, initiator, temperature, curing time) and by network defects such as dangling ends or loops that reduce the fraction of elastic strands. Physical crosslinks may be reversible and environment-dependent.

Applications span hydrogels, vulcanized rubbers, dental resins, and ion-exchange materials, where νe governs swelling, diffusion, stiffness, and durability.