Dimensions of branched and linear polymer chains in solution: Modifications of flory's theory

It is pointed out that a theory proposed by Vrij for the expansion of a linear polymer chain in solution beyond its unperturbed size is also applicable formally to branched chains. The theory predicts the temperature at which the chain obeys random-flight statistics to be lower for a branched chain than for a linear one (for a polymer–solvent system exhibiting the usual upper critical consolute point). Vrij's derivation follows a well-known procedure of Flory, but refines it to take account of the variation of the time-averaged segment density with distance from the center of mass of the chain. This modification in combination with a somewhat different derivation is shown to lead to a similar result. Yet another scheme for “correcting” Flory's theory is outlined. Some reasons are advanced for questioning the physical significance of these small modifications of Flory's theory, all of which depend on the retention of previously ignored terms in power series expansions.