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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Light scattering and phase separation experiments were performed for four six-arm star polystyrene (6SPS) samples with weight-average molecular weights M w of 9:62  10 4 to 1:16  10 6 in cyclohexane below the theta temperature (34.5 C). From the former experiment, the apparent second virial coefficient J was obtained as functions of the polymer volume fraction and temperature T, along with the spinodals. In the latter experiment, the concentrations of coexisting two phases were determined as functions of T. The critical point T c determined from the coexisting curve was lower than that for fourarm star polystyrene (4SPS) when compared at the same M w . As was the case for 4SPS and linear polystyrene in cyclohexane, J for 6SPS at each T in a region of large was represented by a universal function of =P 0:1 regardless of P (the volume of the polymer chain relative to that of the solvent molecule), although it differed from the common function previously found for the other two types of polystyrene. It was concluded that the solubility of 6SPS higher than that of 4SPS in cyclohexane as indicated by the lower critical point is attributable to the chain-end effect.KEY WORDS: Star Polymer / Phase Separation / Chemical Potential / Binodal / Spinodal / Critical Point / Polystyrene / It is known that the phase separation temperature for star polymers in poor solvents are lower than that for the corresponding linear polymer with the same molecular weight and the same chemical structure. [1][2][3][4][5][6] This cannot be explained by theories invoking the Flory-Huggins type 7 mean-field approximation, but at present, there exists no molecular theory that explains the phase behavior of branched molecules. Recent Monte Carlo simulation results also fail to describe the experimental data. 8,9 In this situation, a phenomenological approach to the problem may be useful as an alternate. [10][11][12] In our previous work, Terao et al.4 carried out light scattering and phase separation experiments on four-arm star polystyrene (PS) in cyclohexane below the theta point  (34.5 C). Their light scattering data showed that the apparent second virial coefficient J at a fixed temperature T in a region of high polymer volume fraction can be represented by a universal function of =P 0:1 regardless of molecular weight and that the same function is also applicable to linear PS in cyclohexane, where P is the relative chain length (the volume of the polymer chain relative to that of the solvent molecule). The difference in J between four-arm star and linear PS's appeared only at low . Thus, it was concluded that the difference in the chemical potential of the solvent in the low region is responsible for the difference in phase separation behavior between the two polymers.The present study was undertaken as an extension of the previous work to six-arm star PS in cyclohexane below  to examine the J function behavior and the phase diagrams in relation to four-arm star and linear PS's. Light scattering and phase separation data obtained as func...