Elastically Effective Strand Density in Polymer Networks
Abstract A new expression is derived which relates the density of elastically effective strands in a polymer network to the densities of random cross-links, main-chain scissions, and entanglements and to the molecular weight distribution of the initial linear polymer. Methods are recommended for characterizing the cross-link and scission densities from measurable sol fractions and for determining the entanglement density empirically. The strand density can be evaluated quite easily for the random and uniform initial molecular weight distributions. The new expression differs appreciably from that of Mullins and Bueche, owing principally to a new criterion for effectively trapping network entanglements. The statistical approach used to derive the strand density is also used in a new derivation of an existing implicit expression for the gel fraction.