High polymer solutions. Part II.—The osmotic pressures of polystyrene solutions

Bawn, C. E. H.; Freeman, R. F. J.; Kamaliddin, A. R.

doi:10.1039/tf9504600862

Cited by 96 publications

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“…These features are quite similar to what was observed previously for polystyrene in cyclohexane. 1 The positive A 3 at e and its increase with a decrease in T below e demonstrate that the twoparameter theory does not hold for PIB in IAIV; we note again that the theory predicts A 3 to vanish ate and to be negative below e.…”

Section: Molecular Weight and Virial Coefficientsmentioning

confidence: 94%

“…1 This implies that the binary cluster approximation is no longer valid for A 3 of these typical flexible polymers near the' theta point.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%

“…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.…”

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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: Molecular Weight and Virial Coefficientsmentioning

confidence: 94%

Section: Third Virial Coefficientmentioning

confidence: 99%

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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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“…These Kc=R 0 data were analyzed in terms of the Bawn plot 24 of Sðc 1 ; c 2 Þ against ðc 1 þ c 2 Þ, where Sðc 1 ; c 2 Þ is defined by 25 Figure 2 shows the Bawn plots for four-arm star polystyrene samples in cyclohexane at 34.5 C, where pairs of data for neighboring c 1 and c 2 in a series of polymer concentrations are omitted since they were less accurate. The intercept and slope of each line give A 2 and A 3 , respectively, which are summarized in Table I.…”

Section: Resultsmentioning

confidence: 99%

Effects of Chain Ends and Three-Segment Interactions on Second and Third Virial Coefficients of Four-Arm Star Polystyrenes

2009

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Second and third virial coefficients (A 2 and A 3 , respectively) for cyclohexane solutions (34.5 C) of three four-arm star polystyrene (PS) samples with a benzyl group at each arm end (4SPS-Bz) and two four-arm star PS samples with a sec-butyl group at each arm end (4SPS-Bu) were determined as functions of weight-average molecular weight M w lower than 1:5 Â 10 4 . As in the case for linear PS with benzyl ends, A 2 for 4SPS-Bz at the theta temperature (34.5 C), where A 2 vanishes for sufficiently high M w , was negative and decreased with lowering M w in contrast to the increase of positive A 2 for 4SPS-Bu. The negative A 2 for 4SPS-Bz was ascribed to the effects of three-segment interactions and binary interactions between middle and junction point segments, while the positive A 2 for 4SPS-Bu was explained as due to the effects from arm ends. These findings reveal that the previously observed lowering in apparent theta temperature (with decreasing M w ), where A 2 ¼ 0 for a given M w , for four-arm star polystyrene is attributed to the arm-end effect. The values of A 3 for both 4SPS-Bz and 4SPS-Bu were positive and increased with decreasing M w at the theta temperature, showing significant three-segment interactions among two middle and one junction point or one arm-end segment. 1 found from light scattering measurements that the second virial coefficient A 2 of linear polystyrene (PS) with benzyl ends (benzyl-PS) in cyclohexane at the theta point Â (34.5 C) becomes negative and decreases with decreasing weight-average molecular weight M w in contrast to positive and increasing A 2 for linear PS with a butyl group at one of the chain ends (butyl-PS), 2,3 where Â is defined as the temperature at which A 2 vanishes for sufficiently high molecular weight M. They explained the negative A 2 for benzyl-PS as due to the effects from three-segment interactions with negligibly small chain-end effects. On the other hand, for butyl-PS the end effects 4 on A 2 were predominant, demonstrating that the chain-end groups strongly affect A 2 of low M polystyrene (M w < 3 Â 10 4 ) at Â. It is well-known for star polymers that the apparent theta temperature Â app , where A 2 ¼ 0 for a given M, decreases with lowering M.5-11 This is equivalent to an increase in A 2 with decreasing M at a fixed temperature Â. Such molecular weight dependence of Â app (or opposite dependence of A 2 at Â) for star polymers has been interpreted as due to effects of threesegment interactions by theories based on the smootheddensity model. 12,13 However, a more rigorous perturbation calculation 14 predicts a decrease in A 2 at Â with deceasing M for f (the number of arms) less than five. 15 This prediction, contradictory to the behavior of experimental A 2 for star polymers, at least, with f 4, prompted us to examine the end effects on A 2 of four-arm star PS as was done for linear PS. We note that the previously investigated star polystyrene samples, anionically synthesized with butyllithium, [16][17][18][19][20] had a butyl group at each arm end.In t...

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“…Except PS600 and PS700, they were analyzed using the Bawn plot, 8 that is, S(c 1 ,c 2 ), as defined by the following equation plotted against c 1 +c 2 : 7…”

Section: Discussionmentioning

confidence: 99%

Second and third virial coefficients of low-molecular-weight polystyrene with a benzyl end in toluene

Okada

Matsumoto

Nakamura

2010

Polym J

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Light-scattering measurements were taken on six samples of polystyrene (PS) with a benzyl group at one end of the chain (benzyl-PS) in toluene at 15 1C. The second and third virial coefficients (A 2 and A 3 , respectively) were determined as functions of weight-average molecular weight, M w , which ranges from 6.0Â10 2 to 1.2Â10 4 . It was found that values of A 2 for benzyl-PS were systematically smaller than those for PS with a butyl group at one end of the chain (butyl-PS) and that the difference becomes larger with decreasing M w . From the A 2 data obtained, the excess binary-cluster integral between the butyl end and the middle segments was estimated to be about three times larger than the binary-cluster integral between the benzyl end and the middle segments, where 'excess' means the difference from the binary-cluster integral between middle segments. The A 3 values for benzyl-PS for M w o10 4 were also smaller than those for butyl-PS. If we assume a term independent of molecular weight in A 3 , the excess ternary-cluster integral among one butyl end and two middle segments was estimated to be about five times larger than that among one benzyl end and two middle segments. Polymer Journal (2010) 42, 386-390; doi:10.1038/pj.2010.11; published online 10 March 2010Keywords: chain-end effect; good solvent; light scattering; polystyrene; second virial coefficient; third virial coefficient INTRODUCTION Solution properties of long flexible polymers are discussed on the basis of the two-parameter theory. 1,2 However, this theory cannot describe properties in low-molecular-weight regions, in which effects from stiffness and/or local conformations of the chain, chain-end groups and three-segment interactions become essential. 3 The importance of the effects of chain stiffness on A 2 was discussed by Yamakawa. 4 Einaga et al. 5 later showed that the effects of chain ends, as well as chain stiffness, must be considered to obtain a quantitative agreement between the theoretical and observed values of A 2 for polystyrene (PS) in toluene (a good solvent) for M w o10 4 , where M w denotes the weight-average molecular weight. The PS samples used by Einaga et al. 5 had a butyl group at one end of the chain. If we perform a similar study on PS samples with different chain ends, different results may be obtained.It is known that data for A 2 in cyclohexane solutions of PS with a butyl group (butyl-PS) versus PS with a benzyl group (benzyl-PS) at one end of the chain show very different tendencies for M w o10 4 at the theta point (34.5 1C), where A 2 for sufficiently large M w vanishes. The positive A 2 of butyl-PS increasing with decreasing M w is attributed to effects from the chain ends. 4 On the other hand, values of A 2 for benzyl-PS became negative and decreased with decreasing M w . 6 It was considered that the negative values of A 2 occurred because of the effects of the three-segment interactions and that effects from chain ends were negligibly small. From these results on the theta solvent system, we may expect to re...

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High polymer solutions. Part II.—The osmotic pressures of polystyrene solutions

Cited by 96 publications

References 0 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

Effects of Chain Ends and Three-Segment Interactions on Second and Third Virial Coefficients of Four-Arm Star Polystyrenes

Second and third virial coefficients of low-molecular-weight polystyrene with a benzyl end in toluene

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