Second and third virial coefficients for polyisobutylene in cyclohexane

Nakamura, Yo; Akasaka, Kazutomo; Katayama, Ken‐ichi; Norisuye, Takashi; Teŕamoto, Akio

doi:10.1021/ma00029a020

Cited by 30 publications

(26 citation statements)

References 10 publications

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“…5 The ratios of the weight-average to number-average molecular weight estimated from gel permeation chromatography (GPC) in chloroform were in the range 1.08-1.10. 5 The solvent IAIV (Tokyo Kasei Kogyo Co.) was washed twice with 2N aqueous sodium carbonate and three times with water, dehydrated with anhydrous potassium carbonate, and fractionally distilled twice under reduced nitrogen atmosphere. Each polymer sample was mixed with the solvent in a dry bag filled with nitrogen.…”

Section: Preparation Of Solutionsmentioning

confidence: 99%

“…We note that these values are one or two orders of magnitude smaller than those in the good solvent cyclohexane. 5 …”

Section: Molecular Weight and Virial Coefficientsmentioning

confidence: 99%

“…1 This implies that the binary cluster approximation is no longer valid for A 3 of these typical flexible polymers near the' theta point. If the ternary cluster integral /3 3 representing the interaction among three segments is incorporated into theory, A 3 near e is expressed by 16 • 17 (4) or (5) where (6) In these equations, NA is the Avogadro constant, n the number of segments in one chain, /3 2 the binary cluster integral, and b the segment length.…”

Section: Third Virial Coefficientmentioning

confidence: 99%

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

Akasaka

Nakamura

Norisuye

et al. 1994

Polym J

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ABSTRACT:The second virial coefficient A 2 and the third virial eoefficient A 3 have been determined for five polyisobutylene fractions ranging in weight-average molecular weight Mw from 8 x 10 4 to 1.6 x ·10 6 in isoamyl isovalerate at different temperatures Tbetween 21 and 37°C by light scattering. The theta temperature e where A 2 vanishes is found to be 27°C independent of Mw. The curve of A 3 vs. Tobtained for each fraction has a broad minimum around e, and the minimum becomes very shallow as M w decreases. These features are very similar to those observed previously for polystyrene in cyclohexane. The values of A 3 at e are in the range between 3 x 10-4 and 7x 10-4 molg-3 cm 6 , and thus demonstrate the breakdown of the binary cluster approximation to A 3 for polyisobutylene near e. It is shown that existing theories of A 2 and A 3 are incapable of explaining consistently the positive A3 at e and the molecular weight independence of 19 in the range of Mw studied, as found to be the case for polystyrene.KEY WORDS Second Virial Coefficient / Third Virial Coefficient / Polyisobutylene/ Theta Point/ Three-Segment Interaction/ Two-Parameter Theory / Light Scattering / In previous work, 1 we found from light scattering measurements that the third virial coefficient A 3 for polystyrene in cyclohexane remains positive at the theta temperature B where the second virial coefficient A 2 equals zero. This reveals the breakdown of the two-parameter theory 2 for A 3 near the theta point, since the theory predicts that A 2 and A 3 simultaneously vanish at B. Another important finding in the previous study was that A 3 increases with a decrease in temperature below B. This is also contrasted to the twoparameter theory prediction that A 3 should become negative below B.because it brings the polymer to the tht:ta state at room temperature and gives a refractive index increment large enough for light scattering experiment. 3 • 4 Data were obtained not only for A 2 and A 3 but also for the zaverage mean-square radius of gyration (S 2 )z as functions of molecular weight and temperature. The virial coefficient data at B are discussed below in relation to three-segment interactions.

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Section: Preparation Of Solutionsmentioning

confidence: 99%

“…We note that these values are one or two orders of magnitude smaller than those in the good solvent cyclohexane. 5 …”

Section: Molecular Weight and Virial Coefficientsmentioning

confidence: 99%

Section: Third Virial Coefficientmentioning

confidence: 99%

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

Akasaka

Nakamura

Norisuye

et al. 1994

Polym J

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“…The absence of electrolyte behavior was also confirmed. Nakamura and coworkers [4] have reported on the dependence of the second (A2) and third (A3) virial coefficients on molecular weight for poly(isobutylene) in cyclohexane solution. This is an extension of the work previously reported for polystyrene in benzene, in which A3 scaled with the molecular weight to the power of 0.6, and the reduced third virial coefficient, A3/(A2 2 Mw), was proportional to Mw.…”

Section: Dilute Solution Properties Of Homopolymersmentioning

confidence: 99%

Review of Light Scattering Literature

Potts¹

1994

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“…(3) The effect of chain stiffness on gin good solvents is rather small differing from the case of A 2 , 7 • 8 though it affects the relation between g and a/ for small a/ owing to the stiffness effect on a 8 . 9 -11 For a deeper understanding of the ternary cluster effect on A 3 we deemed it significant to explore the behavior of g in a solvent intermediate between good and theta solvents, and undertook a light scattering study, with PIB in heptane at 25°C chosen as the system. According to Matsumoto et al, 12 heptane is such a solvent for PIB.…”

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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 cyclohexane

Cited by 30 publications

References 10 publications

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

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

Review of Light Scattering Literature

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

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