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

Abstract

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.

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

“…The solution temperature was kept within AE0:05 C. Neutral filters with known transmittance were used when the scattering intensity exceeded the limit of the detector. Since, considerable effects of absorption and multiple scattering on scattering intensity were observed in our previous study, 4 the measured (or apparent) reduced intensity R ;app at scattering angle was corrected for them according to the following procedure of Terao et al 4 The true reduced scattering intensity R is related to R ;app by…”

“…It took 5 h to 2 d for equilibration at a temperature kept within AE0:01 C. The solute concentration in each phase-separated solution was determined by differential refractometery as described previously. 4 The instrument was calibrated with cyclohexane solutions of sample 6S17 with different w's lower than 0.15 at temperatures between 25 and 35 C. Figure 1 shows K 0 =R 0 plotted against for six-arm star PS sample 6S17 at the indicated temperatures. All the curves fitting the data points at the respective T bend upward and have a common intercept 1=P at ¼ 0, where P is given by…”

“…The data points at each T (i.e., for a given symbol) follow a weakly sigmoidal curve as was observed for linear and four-arm star PS's. 4,11 The intercept (denoted below as J 0 ) and the initial slope of each curve are related to the second virial coefficient A 2 and the third virial coefficient, respectively, whose numerical data and some discussions are given in ref 13. The relation between J 0 and A 2 is represented by…”

“…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).…”

Star Polymers in Good Solvents From Dilute to Concentrated Regimes: Crossover Approach

“…This may be due to the vicinity of the theta temperature to the temperature at which the effective two-body interaction parameter v B in the effective Hamiltonian of the system is nearly equal to zero, or the same renormalized parameterū = v B L 4−d = 0 [118]. In addition, many theoretical [10,13,32], simulation [67,152] and experimental studies [15,67,69,153] have shown that for many model polymers, there is a depression of the theta temperature due to branching. For the hard-sphere star polymer model, θ conditions are not realized.…”