Light-Scattering and Phase-Separation Studies on CyclohexaneSolutions of Four-Arm Star PolystyreneKen Terao, Mitsuhiro Okumoto, Yo Nakamura,*,†Takashi Norisuye, andAkio Teramoto‡Department of Macromolecular Science, Osaka University, Machikaneyama-cho 1-1,Toyonaka, Osaka 560-0043, JapanReceived May 27, 1998; Revised Manuscript Received July 14, 1998ABSTRACT: Light-scattering andphase-separation experimentswere performedon cyclohexanesolutionsof four narrow-distribution samples of four-arm star polystyrene with molecular weights of 8.5 × 104to1.4 × 106, and the results were compared with literature data for linear polystyrene in cyclohexane. Theupper critical solution temperatures Tcfor the star polymer were systematically lower than those for thelinear polymer, showing a considerable effect of chain branching on phase separation. The apparentsecond virial coefficients J of light scattering for the two polymers, plotted against φ/P0.1at a fixedtemperature below Θ, happened to form a composite curve at high polymer concentrations, regardless ofthe relative degree of polymerization P (φ denotes the polymer volume fraction), whereas they appreciablydiffered at low concentrations, reflecting the finding that the (true) second virial coefficient for the starpolymer is significantly larger than that for the linear polymer below Θ. The chemical potentials of thesolvent and solute components derived from the J data were shown to explain the phase diagrams of thetwo systems fairly well. Thus it was concluded that the difference in Tcbetween four-arm star and linearpolystyrenes arises primarily from the difference in J in dilute solution.IntroductionPrediction of phase relationships of polymer solutionshas long been the subject of polymer thermodynamics,1,2but some fundamental problems are still left almostunexplored. An example is the effect of chain branchingon the phase diagram. Cowie et al.3found from cloudpoint measurements on cyclohexane solutions of starpolystyrenes that when compared atthe same molecularweight, upper critical solution temperatures for themare systematically lower than those for linear polysty-rene. Similar findings were also reported for random-and star-branched polystyrenes in cyclohexane by Satoet al.4and Yokoyama et al.,5respectively. It is naturalto discuss such differences in phase behavior in termsof the chemical potentials of the solvent and solutecomponents, which may be determined either experi-mentally or theoretically. For an experimental ap-proach, light-scattering measurements in the dilutethrough semidilute regimes may be appropriate, be-cause they give the differential chemical potential of thesolvent with high precision.6-9Although osmotic-pres-sure10and light-scattering11data are available forsemidilute solutions of star polymers in good solvents,no such data for poor solvent systems are as yetreported.In this work, we made light-scattering measurementson cyclohexane solutions of four-arm star polystyrenesamples with weight-average molecular weights Mwof8.5 × 104to 1.4 × 106and determined the chemicalpotential of the solvent as a function of temperature T,polymer concentration, andMw, following essentially thesame approach as that taken by Einaga et al.9for linearpolystyrene in cyclohexane. Phase equilibrium experi-ments on the star polymer + solvent system were alsocarried out to see the difference in phase separationbehavior between the star and linear polystyrenes andto analyze the data in terms of the chemical potentials.Experimental SectionPolymer Samples. Four-arm star polystyrene samples4S22, 4S39, 4S77′, and 4S384 were chosen from those used inprevious studies.12,13These samples had been prepared byanionic polymerization and well-fractionated; they are suf-ficiently narrow in molecular weight distribution and haveexactly four arms.Light Scattering. Scattered intensities were measured ona Fica-50light-scattering photometerin an angular range from30 to 150° using vertically polarized light of 436 and 546 nmwavelengths. Benzene at 25 °C was used as the referenceliquid, whose Rayleigh ratio was taken to be 46.5 × 10-6cm-1for 436 nm and 16.1 × 10-6cm-1for 546 nm.14Its depolar-ization ratio was determined to be 0.41 and 0.40 for 436 and546 nm, respectively, by the method of Rubingh and Yu.15Polymer solutions were optically clarified by filtration througha Teflon membrane.Values of the specific refractive index increment ∂n/∂c forfour-arm star polystyrene in cyclohexane at 546 nm wereevaluated from the relationdetermined in this work and those at 436 nm from thepreviously determined relation.13Correction of Scattering Intensities. (1) Absorbance.Absorbances A of cyclohexane solutions of 4S39, 4S384, andone linear low-molecular weight polystyrene sample (Mw)3300) were measured on a double-beam ultraviolet spectrom-eter (Shimadzu UV-200) using a quartz cell of 1 cm thickness.Measurements were also made on benzene solutions of 4S22,4S39, 4S384, and some linear polystyrene samples (Toso’sstandard samples) of different molecular weights.Figure 1 shows the concentration dependence of A for 4S39in cyclohexane at 436 nm and the indicated temperatures,where c represents the polymer mass concentration. Maxima†Current address: The University of Alabama at Birmingham,Birmingham, AL 35294.‡Current address: Research Organization of Science andEngineering, Ritsumeikan University, Noji-higashi, Kusatsu,Shiga 525-8577, Japan.∂n/∂c ) 0.1535 + 4.5 × 10-4(T/°C) + 87Mw-1(cm3g-1)6885Macromolecules 1998, 31, 6885-6890S0024-9297(98)00839-0 CCC: $15.00 © 1998 American Chemical SocietyPublished on Web 09/10/1998due to critical opalescence can be seen at c ∼ 0.09 g cm-3. Suchpronounced attenuation of light suggested substantial effectsof absorption,turbidity, andmultiple scattering on the reducedexcess scattering intensity Rθat scattering angle θ. In fact,plots of K/R0vs k2for the incident beams of 436 and 546 nmdid not accord with each other near the critical point, and theybent considerably upward at both low and high angles. Here,K is the optical constant and k the magnitude of the scatteringvector.The dashed line at each T in Figure 1 represents thecontribution from the absorption of light by the polymer,estimated from the absorption coefficient γ for four-arm starpolystyrene in benzene; this estimation is based on our findingthat the difference in γ between cyclohexane and benzenesolutions of linear low-molecular weight
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