No abstract

Effects of chain stiffness and three-segment interactions on the reduced third virial coefficient g (= / • 2 ) for linear flexible chains in good solvents are theoretically investigated to explain the recent experimental finding that, in contrast to the two-parameter theory prediction, g remains positive when the radius expansion factor as approaches unity by lowering the polymer molecular weight M in a given good solvent. Here, A¡ and A3 are the second and third virial coefficients, respectively. The stiffness effect on g is evaluated in the binary cluster approximation first by applying perturbatively Yamakawa and Stockmayer's wormlike bead model and then by combining the first-order result with the Stockmayer-Casassa theory of g for flexible chains. The excluded-volume parameter is transformed to as3 using the combination of the Yamakawa-Stockmayer-Shimada theory and the Domb-Barrett equation for as. Finally, the effect of threesegment interactions is incorporated in a first-order perturbation approximation. The theoretical g thus calculated as a function of as3 is found to agree satisfactorily with the published data for polystyrene and polyisobutylene in good solvents for as down to near unity.

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.

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 ( =