Radius of gyration of polystyrene combs and centipedes in solution

The method of Iatrou et al. (Macromolecules 1998, 31, 6697) was applied to synthesize a normal comb polystyrene sample with uniform side chains equally spaced along the main chain but with the most probable distribution in the main chain length. The molecular weights of the side chain and the connector (the part of the main chain between the neighboring side Chains) were 3.5 x 10(4) and 2.3 x 104, respectively. The sample was analyzed using a gel-permeation chromatography system with a multiangle light scattering and refractive index detector to determine the relationship between the z-average mean square radius of gyration [S-2] and the weight-average molecular weight M-W. Tetrahydrofuran (THF) was chosen as the solvent. The relation fell considerably below that for linear polystyrene. The slope of the plot of log [S2](1/2) vs log M-w for the comb polymer was 0.46, a value much smaller than the Flory exponent 0.6 for linear chains in good solvents. Similar measurements were also made on polystyrene centipedes prepared by Iatrou et al., which have two side chains at each junction point. As the ratio r of the molecular weight of the side chain to that of the connector increased, the [S-2] VS M-w relation was lowered. Comparison of the experimental relationship with theoretical predictions for flexible discrete chains suggested that the main chains of the two types of polymer are stiffened by the crowding of the side chains. To estimate the backbone stiffness, [S-2] was calculated on the basis of the wormlike comb model whose main and side chains have different Kuhn lengths lambda (-1) and lambda (-1)(s), respectively. With lambda (-1)(s) = 2 nm and the linear mass density = 390 nm(-1) (for both main chain and side chains), lambda (-1) was estimated so as to give the closest agreement between the calculated and measured [S-2]. It was found that the calculated values for the comb polymer with lambda (-1) = 5.5 nm agree closely with the experimental data. The data for the centipedes were also explained by the theory, which showed the backbone stiffness to increase with increasing r.