Cross-linking refers to the joining of polymer chains with covalent bonds. Cross-linking can occur during polymer synthesis or later with the addition of atoms or molecules which will share electrons with a part of the polymer chain.
The degree of cross-linking affects many properties of the resulting polymer. For example in most cases it is directly proportional to the viscosity, and inversely proportional to the degradation rate. The amount of cross-link sites can be tailored to achieve desired properties in the resulting polymer.
In one example, a cross-linking process called vulcanization is used to increase the tensile strength and decrease the degradation rate of elastomeric polymers. Vulcanization is the process of adding sulfur atoms to elastic polymer chains at high temperatures. The resulting connections allow the amorphous polymer chains to stretch to a limited extent, while restricting the slippage which would otherwise result in plastic deformation. This increases the modulus of elasticity.
Callister, William D., "Materials Science and Engineering an Introduction," John Wiley & Sons, Inc., New York (2003).