Second and Third Virial Coefficients for Polyisobutylene in the Vicinity of the Theta Point

Akasaka, Kazutomo; Nakamura, Yo; Norisuye, Takashi; Teŕamoto, Akio

doi:10.1295/polymj.26.363

Cited by 16 publications

(11 citation statements)

References 19 publications

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“…The curve for each sample is parabolic with a broad positive minimum around ϑ and the minimum becomes shallower as M w decreases. These features are similar to what was observed for linear flexible polymers in ϑ solvents. ,, We note that those features for the latter class of polymers have been explained theoretically as due to remarkable ternary cluster effects . The molecular weight dependence of A 3 for four-arm star polystyrene at 34.5 °C is shown in Figure (unfilled circles), along with that for linear polystyrene in the same solvent (filled circles) .…”

Section: Resultssupporting

confidence: 81%

“…Radius of Gyration. Values of ( Kc / R θ ) c =0 were obtained by extrapolation of ( Kc / R θ − 2 A 2 c − 3 A 3 c 2 ) at fixed θ to c = 0, and radii of gyration were evaluated from the initial slopes of ( Kc / R θ ) c =0 1/2 vs sin 2 (θ/2) plots. Figure depicts the temperature dependence of 〈 S 2 〉 z 1/2 thus obtained for the three highest molecular weight samples 4S184‘, 4S384, and 4S662‘.…”

Section: Resultsmentioning

confidence: 99%

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

et al. 1997

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Light scattering and viscosity measurements were made on anionically polymerized four-arm star polystyrene samples with weight-average molecular weights M w of 8.5 × 104 to 3.1 × 106 in cyclohexane at different temperatures to determine the mean-square radius of gyration 〈S 2〉, the second and third virial coefficients (A 2 and A 3), and the intrinsic viscosity. The values of A 3 at the ϑ point (34.5 °C), where A 2 for any sample was essentially zero, were about 5 × 10-4 cm6 mol g-3 and yielded a value of 4 × 10-45 cm6 for the ternary cluster integral. It was shown that although the binary cluster approximation breaks down for A 3 near ϑ, it holds for 〈S 2〉 and A 2, as is the case with linear chains, if the binary cluster integral is replaced by a linear combination of the binary and ternary cluster integrals. The expansion factor α S 2 for 〈S 2〉 and that for the intrinsic viscosity plotted against the excluded-volume parameter z in the coil limit for M w > 8 × 105 came close to the known relations for linear polystyrene of high molecular weight in cyclohexane. On the other hand, the relation between the interpenetration function Ψ and α S 3 for the star polymer appeared far above that for the linear chain at temperatures above ϑ. These experimental results for α S 2 and Ψ were quantitatively explained by the interpolation formulas constructed in this work.

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Section: Resultssupporting

confidence: 81%

Section: Resultsmentioning

confidence: 99%

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

et al. 1997

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“…[18] for an extensive discussion). However, for some different quantities they are relevant: for instance, they determine the deviations from the ideal behavior of the equation of state at the θ point in the semidilute regime and the peculiar behavior of the third virial coefficient [32,67,68]. Unfortunately, it is not possible to use CG models to account also for these logarithmic corrections.…”

Section: B Coarse-graining Homopolymer Solutionsmentioning

confidence: 99%

Coarse-graining polymer solutions: A critical appraisal of single- and multi-site models

D’Adamo

Menichetti

Pelissetto

et al. 2015

Eur. Phys. J. Spec. Top.

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We critically discuss and review the general ideas behind single-and multi-site coarse-grained (CG) models as applied to macromolecular solutions in the dilute and semi-dilute regime. We first consider single-site models with zero-density and density-dependent pair potentials. We highlight advantages and limitations of each option in reproducing the thermodynamic behavior and the large-scale structure of the underlying reference model. As a case study we consider solutions of linear homopolymers in a solvent of variable quality. Secondly, we extend the discussion to multi-component systems presenting, as a test case, results for mixtures of colloids and polymers. Specifically, we found the CG model with zero-density potentials to be unable to predict fluidfluid demixing in a reasonable range of densities for mixtures of colloids and polymers of equal size. For larger colloids, the polymer volume fractions at which phase separation occurs are largely overestimated. CG models with density-dependent potentials are somewhat less accurate than models with zero-density potentials in reproducing the thermodynamics of the system and, although they presents a phase separation, they significantly underestimate the polymer volume fractions along the binodal. Finally, we discuss a general multi-site strategy, which is thermodynamically consistent and fully transferable with the number of sites, and that allows us to overcome most of the limitations discussed for single-site models.

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“…16 (the inverted triangles) in Figure 7, in which our previous data in CH (the squares)3 and in isoamyl isovalerate (IAIV) 4 at the theta temperature (the filled circles) are included.…”

Section: Radius Of Gyrationmentioning

confidence: 99%

Second and Third Virial Coefficients for Polyisobutylene in Heptane, an Intermediate Solvent

Akasaka

Nakamura

Norisuye

et al. 1994

Polym J

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ABSTRACT:Light scattering measurements have been made on nine polyisobutylene (PIB) fractions in heptane, an intermediate solvent, at 25°C to determine the second virial coefficient A 2 and the third virial coefficient A 3 as functions of weight-average molecular weight Mw ranging from '2.7 x 10 4 to 7.8 x 10 6 . For six of the fractions, z-average mean-square radii of gyration have also been determined. In the molecular weight range studied, A 2 and A 3 vary as Mw -0 -21 and M w o.ss, respectively, and the factor g defined by A 3 / A ,2 M w is about 0.33 almost independent of molecular weight. The data of g and 'l' (the interpenetration function) as functions of the cube of the radius expansion factor Cls, combined with previous data in cyclohexane, a good solvent, show that the two-parameter theory breaks down unless Cl/ is larger than about 2 for g and about 5 for 'l'. It is concluded from the comparison of these g data with the recent theory of Norisuye et al. that the failure of the two-parameter theory for g at small Cls 3 is due primarily to the neglect of three-segment interactions and that the effect of chain stiffness on g in heptane is of minor importance in the M w range studied. On the other hand, the stiffness effect on 'l' for PIB is found to be remarkable even at large Cls 3 • In fact, the different dependences of 'l' on Cls' observed for heptane and cyclohexane solutions are explained semiquantitatively by the Yamakawa theory which takes account of the stiffness effect within the binary cluster approximation.KEY WORDS Second Virial Coefficient / Third Virial Coefficient / Polyisobutylene / Excluded-Volume Effect / Expansion Factor / ThreeSegment Interaction / Light Scattering / Recently, we investigated the third virial coefficient A 3 for polystyrene 1 • 2 and polyisobutylene (PIB) 3 • 4 in both good and theta solvents by light scattering, and drew the following conclusions from experimental findings together with some theoretical calculations. 5 • 6 (1) The effect of three-segment interactions on A 3 is remarkable at and near the theta point e at which the second virial coefficient A 2 for high molecular weight M vanishes, so that the binary cluster approximation to A 3 or the two-parameter theory for it at and near e completely breaks down. (2) In good solvents, the ternary cluster effect on the reduced third virial coefficient g is appreciable only for relatively low M, and thus the binary cluster approximation holds for g unless the radius expansion factor a8 ( =

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Second and Third Virial Coefficients for Polyisobutylene in the Vicinity of the Theta Point

Cited by 16 publications

References 19 publications

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

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

Coarse-graining polymer solutions: A critical appraisal of single- and multi-site models

Second and Third Virial Coefficients for Polyisobutylene in Heptane, an Intermediate Solvent

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