Influence of Predilution on Cross-Link Density: Consequences for the Front Factor and the Flory-Huggins Relation

Abstract

Abstract The influence of predilution before formation of a polymer network is considered. From theoretical and experimental considerations it is deduced that γ = γ °V0 and γ = γ g °V0 2 where γ y is the network segment density of the polymer phase, γg is the network segment density of the gel portion, Vo is the volume fraction of gel in the diluted stock, and the superscript zeros refer to the undiluted condition. As a result, it is concluded that the “front factor” for the elastic equation of state cannot vary with dilution of the network before cure as some have proposed. The reasons for the supposed variation are examined and a probable weakness found in the determination of cross-link density by chemical methods. The existence of the front factor is doubted. Use is made of the extended Flory-Huggins relation, whereby during differentiation the polymer-solvent interaction parameter is assumed to vary linearly with concentration, to equate network segment densities of prediluted and undiluted polymers through the relationγ g = γ g °V0. It is found that the slope of the curve X vs V2 calculates to be 0.33 where is the customary polymer-solvent interaction parameter and V2 is the volume fraction of polymer in a solvent swollen gel. A number of actual slopes are computed and found to be in the range 0.26 to 0.43 with some exceptions. In agreement with the work of Koningsveld, Staverman, Flory, and Tatara, it is shown that the first and second partial derivatives of the extended Flory-Huggins equation for soluble polymers may be used to calculate conditions at phase separations, which should be closer to experimental fact than those calculated from the original relation. Derivatives were obtained for cross-linked polymers but are not presented.