The hard‐sphere model for linear and regular star polybutadienes

The dilute solution properties of linear, 18‐arm, and 270‐arm star polybutadienes have been studied in a theta solvent and in a good solvent. Values of the radius of gyration R G , the second virial coefficient A 2 , the intrinsic viscosity [η], and the diffusion coefficient D 0 have been measured for each polymer. The ratios R T / R G , R V / R G , and R H / R G for each type of polymer are used to compare the four dilute solution properties. R T is termed the “thermodynamic radius.” It is the radius of the hard sphere with the same excluded volume as the polymer coil. R T is calculated from A 2 by R T = (3 A 2 M 2 /16η N A ) 1/3 . R V and R H are equivalent hard spheres defined for the intrinsic viscosity and translational diffusion coefficient, respectively. R T / R G , R V / R G , and R H / R G increase from about 0.7 for linear polymer coils as the number of arms in the star increases. Values of the ratios for the 18‐arm stars are less than the value for the hard‐sphere, but the values of the ratios of the 270‐arm stars are equal to the hard‐sphere limit within experimental error.