Excluded-Volume Effects in Dilute Polymer Solutions. I. Equilibrium Properties

Abstract

Data of the statistical radius ${\mathrm{〈\hspace{0.17em}S}}^2{\mathrm{\hspace{0.17em}〉}}^{\text{1\hspace{0.17em}/\hspace{0.17em}2}}$ and the second virial coefficient $A_2$ were obtained for sharp fractions of polychloroprene (PCP) in methyl ethyl ketone (MEK), n‐butyl acetate, and carbon tetrachloride at 25°C and in trans‐decalin at temperatures ranging from 1° to 50°C. MEK at 25°C and trans‐decalin at 2°C were found to be theta solvents for PCP. From these data two dimensionless quantities defined by ${\alpha }_s^2{\mathrm{\hspace{0.17em}=\hspace{0.17em}〈\hspace{0.17em}S}}^2{\mathrm{\hspace{0.17em}〉\hspace{0.17em}/\hspace{0.17em}〈\hspace{0.17em}S}}^2{〉}_0\mathrm{and}{\mathrm{\Psi \hspace{0.17em}=\hspace{0.17em}A}}_2{M}^{\text{1/2}}{\text{[4π}}^{\text{3/2}}{N}_A{\mathrm{(\hspace{0.17em}〈\hspace{0.17em}S}}^2{\mathrm{\hspace{0.17em}〉\hspace{0.17em}/\hspace{0.17em}M}}^{\text{3\hspace{0.17em}/\hspace{0.17em}2}}{]}^{\text{−1}}$ were calculated for all combinations of molecular weight $M$ , solvent species, and temperature, where ${\mathrm{〈\hspace{0.17em}S}}^2{\mathrm{\hspace{0.17em}〉}}_0$ is the value of ${\mathrm{〈\hspace{0.17em}S}}^2\mathrm{\hspace{0.17em}〉}$ under $\theta$ conditions and $N_A$ is Avogadro's number. These two quantities should be functions of a single parameter $z$ , usually known as the interaction parameter, which is proportional to $M^{\text{1/2}}$ . With the data for these quantities from the present experiments on PCP as well as from Berry's experiments on polystyrene, comparative tests of typical theories for the excluded‐volume effects on dilute polymer solutions were attempted. The criteria used for this purpose were (a) linearity between $M^{\text{1/2}}$ and $z$ calculated from ${\alpha }_s$ determined under fixed solvent conditions and (b) agreement between calculated and observed curves for $\Psi$ against ${\alpha }_s$ . It was found that, though not perfectly, the modified Flory equation for ${\alpha }_s\mathrm{(z)}$ combined with the modified Flory–Krigbaum–Orofino equation for $\mathrm{\Psi (z)}$ or Yamakawa's recent theories for these quantities were best consistent with the experimental data chosen. The Fixman equation and the Ptitysn equation failed to obey criterion (a).