Three-Parameter Theory of Dilute Polymer Solutions

Abstract

Three‐parameter theories of the expansion factor α and the second virial coefficient A₂ for chain polymers are presented to interpret primarily the experimental fact that the dimensionless ratio A₂M/[η] is not always a universal function of α, where M is the polymer molecular weight and [η] is the intrinsic viscosity. There are two effects to be considered, which are related to a third new parameter: one is the effect of a ternary‐cluster integral, and the other the effect of short‐range interactions. First, the Orofino—Flory theory is revised with respect to inclusion of the ternary‐cluster integral using the random‐flight model, and it is shown that this effect is rather of minor importance, though not completely negligible. As for the second effect, a discrete nature of real polymer chains is considered primarily, and a simple analysis is made on suitable model chains. It is shown that the discrete‐chain effect becomes significant when an effective bond of the chain is long compared to the range of average force between segments. Thus the most important third parameter is closely related to a degree of chain stiffness. With this parameter defined well, the theory agrees semiquantitatively with experiment for both flexible and stiff‐chain polymers.