Correlations between the Excluded Volumes and the Second Virial Coefficients of Linear Polymer Chains

By a hierarchy approach, it is shown that the Kurata theory of the second virial coefficient $A_2$ for linear polymer chains is the one to be combined with the theory of the expansion factor ${\alpha }_S$ developed in the previous paper. However, the equation for the expansion factor $ᾱ$ of a chain in contact with another is assumed to be of the same type as the equation for ${\alpha }_S$ . A comparison of theory and experiment is made using the following two properties as criteria of validity for the theory: (1) the consistency in the values of the excluded‐volume parameter $z$ determined from the theory of ${\alpha }_S$ and from the theory of $A_2$ with observed values for them; (2) the proportionality of $z$ so determined to the square root of the molecular weight. For this purpose, light‐scattering data obtained by Berry for polystyrene in decalin and toluene are used. It is shown that the present theories of ${\alpha }_S$ and $A_2$ do not violate the two criteria. Evidently his estimates of $z$ are too large, and the binary‐cluster integral is not proportional to $\text{1\hspace{0.17em}–\hspace{0.17em}Θ\hspace{0.17em}/\hspace{0.17em}T}$ , except near the Θ temperature.