Anionically polymerized six-arm star polystyrene samples with weight-average molecular weights Mw of 5.6 × 10 4 -3.2 × 10 6 were studied by light scattering and viscometry in cyclohexane at different temperatures to determine their z-average mean-square radii of gyration (〈S 2 〉z), second and third virial coefficients (A2 and A3), and intrinsic viscosities ([η]). The values of A3 at the Θ point (34.5°C ), where those of A2 were essentially zero for Mw > 10 6 , were about 5 × 10 -4 cm 6 mol g -3 and yielded 4 × 10 -45 cm 6 for the ternary cluster integral. The data for 〈S 2 〉z and A2 at Θ were in line with previous perturbation calculations taking into account ternary cluster interactions, but the (residual) ternary effects on these properties were not very significant, at least, for Mw > 10 6 . The expansion factor RS 2 for 〈S 2 〉 and that for [η] plotted against the conventional excluded-volume parameter for Mw > 1 × 10 6 came close to the known relations for both linear and four-arm star polystyrenes of high molecular weight in cyclohexane. On the other hand, the relation between Ψ (the interpenetration function) and RS 3 for the six-arm star polymer appeared far above that for the linear chain and appreciably above that for the four-arm star chain at temperatures above Θ. These experimental results for RS 2 and Ψ were quantitatively described by the interpolation formulas constructed in previous work. IntroductionThe present work is concerned with excluded-volume effects on the mean-square radius of gyration 〈S 2 〉, second virial coefficient A 2 , third virial coefficient A 3 , and intrinsic viscosity [η] of six-arm star polystyrene in cyclohexane near the Θ point. It is an extension of our previous light scattering and viscometric studies 1 on cyclohexane solutions of four-arm star polystyrene, for which the following conclusions were derived from data analysis and some theoretical calculations (see ref 2 for a good solvent system).(1) The binary cluster approximation breaks down for A 3 at and near the Θ point, but it holds for 〈S 2 〉 and A 2 , as is the case with linear chains, 3 if the binary cluster integral is replaced by a linear combination of the binary and ternary cluster integrals. (2) The relation between R S 2 (the expansion factor for 〈S 2 〉) and z (the conventional excluded-volume parameter) and that between R η 3 (the expansion factor for [η]) and z for molecular weights higher than 8 × 10 5 are almost the same as those 4,5 known for linear polystyrene in cyclohexane near the Θ point. On the other hand, the interpenetration function Ψ plotted against R S 3 (>1) appears significantly above that for the linear chain, reflecting the difference in molecular architecture. (3) These R S 2 vs z and Ψ vs R S 3 relations are satisfactorily described by the interpolation formulas constructed.The present study was undertaken to see whether the above conclusions apply to six-arm star polystyrene in cyclohexane. To this end, we prepared seven narrowdistribution samples of the star polymer ranging in weight-...
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