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

Abstract

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...

Self-Assembly and Critical Solubility Temperature of Supramolecular Polystyrene Bottle-Brushes in Cyclohexane

“…corresponding to ~ 11 arms), the critical temperature Tc was only slightly lower than that of a linear polystyrene of the same molecular weight as that of S34U3S34 aggregates. This result confirms both the theory and previous experimental evidences reporting only a very small reduction of Tc (by 2-3°C) for star-shaped polystyrenes with a relatively small number of arms (< 12), 41,[58][59][60][61][62][63] Moreover, the temperature hardly affected the self-assembly of S34U3S34: Nagg remained almost constant until precipitation occurred. Details are given in Figure S12 of the Supporting Information for this polymer.…”

Coexistence and Phase Behavior of Solvent–Polystyrene-Grafted Gold Nanoparticle Systems

“…Consistent with previous reports for linear and architected polystyrene in cyclohexane, PS-AuNPs also exhibit an upper critical solution temperature (UCST) and an immiscibility gap that shifts to higher temperatures as macromolecular size increases, i.e., as graft molecular weight for PGNs increases (Figure ). The concentration dependence at ϕ PGN > ϕ C * also increases with graft molecular weight, as observed with linear chains and branched macromolecular architectures, , and predicted by prior theoretical reports on stars. , Finally, the coexistence curves for PS53-Au10 in the various solvents (cyclohexane, cyclopentane, and ethyl acetate) are within ∼10 °C of that reported for linear high-MW polystyrene in that solvent. − …”

“…Examples of these constructions are summarized in SI7.0. Figure 6 compares experimental PS-AuNP coexistence curves (panels a and b) and T C * (panels c and d) to prior reports of linear, 58−63 4-arm star, 64 and 6-arm star 51 PS in cyclohexane. The qualitative effects of architecture on the general shape of coexistence behavior are seen in Figure 6a,b as the number and size of branches (grafts) increase.…”

“…As the number of branches of a given molecular weight increases (linear (blue) → stars (red) → PGNs (black)), the solvent-rich side of the two-phase region likewise widens (Figure a). At a constant molecular weight, however (Figure b), increased branching, where the increase in the number of branches is proportional to the reduction in branch molecular weight, results in a decreased T C * and an increased ϕ C *. − For example, Terao and co-workers experimentally demonstrated such a shift for linear, 4-arm, and 6-arm polystyrene of similar molecular weights in cyclohexane. , Chain conformation and associated excluded volume depend on the local density of branch points (or the nanoparticle radius and graft area for a PGN). These constraints determine the balance of solvent–(polymer) segment and segment–segment interactions throughout the canopy.…”

“…Lines are drawn as a guide. (c) T C * as a function of arm molecular weight for cyclohexane solutions of linear chains, − 4-arm stars, and 6-arm stars compared to extrapolated values for PS-AuNPs with r = 10 nm (black triangles) and r = 6 nm (black circles). (d) T C * as a function of the total PS molecular weight for the cyclohexane solutions shown in (c).…”