Network Structure in Terms of Prepolymer and Curative Parameters. II

In previously reported work, an equation was developed relating the cross-link density of a network formed from telechelic polymers with properties of the prepolymer mix. The absolute value of the network cross-link density in moles/gram was found to be 2q (1−1/fa−1/fp)(CDF)Wgwhere q=equivalents of functional groups per gram of pre-polymer, fp=functionality of prepolymer, fa=functionality of cross-linking agent, CDF=cross-link decrease factor, a nearly constant number now believed to have a value between 0.20 and 0.38, and Wg=weight fraction of gel. The CDF term is the factor by which the cross-link density in the gel is decreased because of failure of the reaction to go to completion at the maximum degree of cure. A mistake made in the derivation of the equation is now corrected and the CDF term is shown to be in a different and simpler form than previously given. In additional work the reactant ratio, r, has been introduced into the relation which becomes: Xd=2q (BF)(CDF)Wg where (CDF) is (e−ec)/(1−ec), (BF) or branching function is (r−r/fa−1/fp) when r > 1 and (1−r/fa−1/fp) when r < 1, e is the final extent of reaction of the prepolymer functional groups, and ec is their extent of reaction at the gel point. For the case where r=1, values of the branching function, the cross-link decrease factor, and the cross-link density per reactant equivalent were computed. The degree to which the equation is followed by real stocks was examined. Young's modulus, the reciprocal of the elongation-at-break, the hardness, and solvent swelling data (V2 5/3 X percent gel) were found to vary linearly with q(BF). When the crosslink decrease factor was given the value 0.25, agreement between the first equation above and crosslink density calculated from equilibrium modulus of elasticity and from the solvent swollen compression modulus was within a factor of 1.5 in three cases.