On the contraction factors of long-chain branched macromolecules

For several decades, the relation between the contraction factor of radius of gyration for branched macromolecules, g, and that of intrinsic viscosity, g′, has been presented as g′ = gε. The value of ε was assumed to be constant for branched macromolecules of a certain type, such as stars, or combs, or statistically branched macromolecules. Experimentally determined values of ε, however, turn out in the majority of cases to be molecular-weight dependent. The present study shows that molecular-weight-independent values of ε can be expected only for a plurality of molecules with identical architecture. By branched molecules with identical architecture we mean molecules in which with varying degree of polymerization the ratios of the degrees of polymerization of all sub-chains remain constant, irrespective of the integral degree of polymerization of individual molecules. Also, it has been demonstrated that the ratio of intrinsic viscosities of a linear and a branched polymer molecule having the same hydrodynamic volume, [η]l,V/[η]b,V < 1, is a measure of the relative increase of the volume fraction of polymer segments within the domain of a macromolecule due to branching.