Excluded-Volume Effects in Star Polymer Solutions:  Six-Arm Star Polystyrene in Cyclohexane near the ϑ Temperature

Abstract

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-...

Radius of Gyration of Polystyrene Combs and Centipedes in a ϑ Solvent

“…1 This model reproduced R g almost quantitatively for 3-, 4-, and 6-arm star polymers with the molecular weight of each side chain being more than 10 000. [2][3][4] However, R g for star polymers with more arms and comb polymers were found to be systematically larger than the calculated values. 2,[5][6][7][8][9] This was explained by considering that such branched polymers expand due to the high segment densities.…”

Dilute-Solution Properties of Polystyrene Polymacromonomer Having Side Chains of over 100 Monomeric Units

“…In the calculation of the solid curves, we have used the following parameters: h (the monomeric contour length of the main chain) = 0.27 nm, b (the effective bond length of each side chain, i.e., of linear PS) = 0.74 nm, 2 (the binary cluster integral) = 0.034 nm 3 in toluene, 32 and 3 (the ternary cluster integral) = 4 Â 10 À3 nm 6 in cyclohexane, [33][34][35] and 0 À1 ¼ 12 and 8 nm in toluene and cyclohexane, 31 respectively. The dashed lines representing b À1 in Figure 6 are fairly close to the data points for the respective solvents at n s > 50, but their slope of 2 predicted by eqs 6 and 7 are much higher than those of the experimental relations even in this large n s region.…”

Light Scattering and Phase Separation Studies on Cyclohexane Solutions of Six-Arm Star Polystyrene†

“…13,14 These samples, synthesized by a coupling reaction of anionically polymerized living polystyrene, were well fractionated and their weight to number-average molecular weight ratios were less than 1.04. The ratio of M w of each sample to that for its arm was 6 AE 0:3, ensuring that each molecule has almost exactly six arms with very narrow length distribution.…”

“…The ratio of M w of each sample to that for its arm was 6 AE 0:3, ensuring that each molecule has almost exactly six arms with very narrow length distribution. 13,14 The chosen samples were dried for more than 24 h in vacuo and dissolved into cyclohexane, which had been dried over sodium metal, refluxed for 4 h, and fractionally distilled. Solutions for light scattering measurements were optically clarified with a Teflon filter of 0.5 mm pore size.…”