Light scattering and viscosity measurements were made on anionically polymerized four-arm star polystyrene samples with weight-average molecular weights M w of 8.5 × 104 to 3.1 × 106 in cyclohexane at different temperatures to determine the mean-square radius of gyration 〈S 2〉, the second and third virial coefficients (A 2 and A 3), and the intrinsic viscosity. The values of A 3 at the ϑ point (34.5 °C), where A 2 for any sample was essentially zero, were about 5 × 10-4 cm6 mol g-3 and yielded a value of 4 × 10-45 cm6 for the ternary cluster integral. It was shown that although the binary cluster approximation breaks down for A 3 near ϑ, it holds for 〈S 2〉 and A 2, as is the case with linear chains, if the binary cluster integral is replaced by a linear combination of the binary and ternary cluster integrals. The expansion factor α S 2 for 〈S 2〉 and that for the intrinsic viscosity plotted against the excluded-volume parameter z in the coil limit for M w > 8 × 105 came close to the known relations for linear polystyrene of high molecular weight in cyclohexane. On the other hand, the relation between the interpenetration function Ψ and α S 3 for the star polymer appeared far above that for the linear chain at temperatures above ϑ. These experimental results for α S 2 and Ψ were quantitatively explained by the interpolation formulas constructed in this work.

Radii of gyration, second and third virial coefficients, and intrinsic viscosities have been determined by light scattering and viscometry for four-arm star polystyrene samples with weight-average molecular weights M w of 9.1 × 104 to 3.1 × 106 in benzene at 25 °C. They are compared with typical data for linear polystyrene in the same solvent to establish the ratios of the respective properties of the star chain to those of the linear chain at high M w. The relation between the radius expansion factor and the excluded-volume parameter z for M w > 3 × 105 comes close to the known relation for the linear polymer in the coil limit and is described by the previously proposed interpolation formula. On the other hand, the viscosity expansion factor vs z plot appears significantly below that for linear polystyrene, the difference remaining to be explained theoretically. The values obtained for the interpenetration function are in the range between 0.43 and 0.46 and about 1.8 times as large as those for the linear polymer. They agree closely with recent Monte Carlo simulation data, but their comparison with the previously constructed interpolation expression suggests that, as in the case for linear flexible polymers, the effect of chain stiffness on the second virial coefficient needs to be considered for M w below 106.

Light-scattering and phase-separation experiments were performed on cyclohexane solutions of four narrow-distribution samples of four-arm star polystyrene with molecular weights of 8.5 × 104 to 1.4 × 106, and the results were compared with literature data for linear polystyrene in cyclohexane. The upper critical solution temperatures T c for the star polymer were systematically lower than those for the linear polymer, showing a considerable effect of chain branching on phase separation. The apparent second virial coefficients J of light scattering for the two polymers, plotted against φ/P 0.1 at a fixed temperature below ϑ, happened to form a composite curve at high polymer concentrations, regardless of the relative degree of polymerization P (φ denotes the polymer volume fraction), whereas they appreciably differed at low concentrations, reflecting the finding that the (true) second virial coefficient for the star polymer is significantly larger than that for the linear polymer below ϑ. The chemical potentials of the solvent and solute components derived from the J data were shown to explain the phase diagrams of the two systems fairly well. Thus it was concluded that the difference in T c between four-arm star and linear polystyrenes arises primarily from the difference in J in dilute solution.

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-...

Seven narrow-distribution samples of six-arm star polystyrene ranging in weight-average molecular weight Mw from 6.1 x 10 4 to 3.4 x 10 6 in benzene at 25°C have been studied by light scattering and viscometry to determine their z-average radii of gyration, second and third virial coefficients, and intrinsic viscosities. The ratios of the respective properties to those of linear polystyrene in the same solvent are established for high Mw. Data analysis shows that the relation between the radius expansion factor and the conventional excluded-volume parameter z comes close to the known relations for four-arm star and linear polystyrenes of high molecular weight and is described fairly satisfactorily by the previously proposed interpolation formula. On the other hand, the viscosity expansion factor vs. z curve appears slightly below that for linear polystyrene though almost superimposed on that for the four-arm star polymer. Thus the difference in this expansion factor between the linear and star chains remains to be explained theoretically. The experimental interpenetration function for the six-arm star polymer gradually decreases to about 0.6, a value close to recent Monte Carlo data, with increasing Mw. Its comparison with the previously constructed interpolation expression suggests that, as was the case for linear flexible polymers, the effect of chain stiffness on the second virial coefficient needs to be considered for Mw below 10 6 •