Beiträge zur Thermodynamik von Polymerlösungen 7. Untersuchungen an Lösungen von Oligomeren des Methacrylsäuremethylesters

Springer, Jürgen; Ueberreiter, Kurt; Moeller, Elvira

doi:10.1002/bbpc.19650690610

Cited by 16 publications

(4 citation statements)

References 22 publications

(1 reference statement)

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“…It is seen that A2 in acetone at 25.0 0C also exhibits an upswing with decreasing Aiw for small Mw. This result is consistent with the literature data obtained by Springer et al 26 from vapor pressure osmometry for methyl methacrylate oligomers in the same solvent, although their data exhibit a sharp decrease with decreasing Mw for Mw < 300. However, its direct comparison with our data may be inappropriate since the terminal groups of their samples are unknown.…”

Section: Resultssupporting

confidence: 93%

“…Appendix. Analysis of Literature Data for Oligomers Following the procedure described in the text, we have analyzed the literature data obtained by Springer et al 26 for A2 from vapor pressure osmometry for methyl methacrylate oligomers in acetone at 25.0 °C. (We note that the chemical structures of the end groups of their samples are unknown, as already mentioned.)…”

Section: Discussionmentioning

confidence: 99%

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Second Virial Coefficient of Oligo- and Poly(methyl methacrylate)s. Effects of Chain Stiffness and Chain Ends

Abe¹,

Einaga²,

Yamakawa³

1994

Macromolecules

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Section: Resultssupporting

confidence: 93%

Section: Discussionmentioning

confidence: 99%

Second Virial Coefficient of Oligo- and Poly(methyl methacrylate)s. Effects of Chain Stiffness and Chain Ends

Abe¹,

Einaga²,

Yamakawa³

1994

Macromolecules

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“…This can be done in such a way that in the coil limit the values of h(2) as a function of z with as given by eq 10 (with 2-z) are as close as possible to those of the Barrett function15 h(z) at any z, i.e. h(2) ^(1 + 14.3z + 57.3z2)"02 (17) The result thus obtained reads h(2) = (1 + 7.742 + 52.3227/10)"10/27 (18) We note that in the coil limit the difference between the values of calculated from eq 14 with eq 18 and with the Barrett equation for h does not exceed 3%.…”

Section: Effects Of Chain Stiffnesssupporting

confidence: 61%

On the theory of the second virial coefficient for polymer chains

Yamakawa¹

1992

Macromolecules

100

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The theory of the second virial coefficient A2 for flexible polymers is reconsidered in order to explain two observations inconsistent with the two-parameter theory prediction. One is the decrease in the interpenetration function with increasing molecular weight M in good solvents even in the ordinary range of M in which the unperturbed mean-square radius of gyration is proportional to M. The other is the nonvanishing of A2 for small M at the temperature. It is shown that the first observation may be explained by considering effects of chain stiffness on and also on the expansion factor as, which remain rather large even in the range of M above, although vanishingly small for very large M, according to the Yamakawa-Stockmayer-Shimada theory for the wormlike and helical wormlike chains. Therefore the theory also predicts that the increase in with increasing solvent power depends in general on M. The second may be explained by considering possible effects of chain ends. Both effects are then analyzed by a comparison with experiment. Thus it is emphasized that the two-parameter theory should be considered a limiting law for extremely large M.

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“…According to the theory,7 A2 in general may be written in the form A2 = A2HW) + Af1 (14) where A2HW) is the part of A2 without the effect of chain ends, i.e., that part of A2 which vanishes at 0, and A® represents the contribution of the effect of chain ends to A2. The first term A^0 may be written as A2hw> = (NAcJ/2L2B/2M2)h (15) where NA is Avogadro's number, and c» and B are given by 4 + (X_Ir0)2 C" 4 + (X-V + (X"V and B = 0/a2c"3/2 (17) The h function is given by h(lt) = (1 + 7.742 + 52.3227/1V0/27 (18) with 2 = I/ass (19) In eq 19,2 is the intermolecular scaled excluded-volume parameter defined by16…”

Section: Discussionmentioning

confidence: 99%

Second virial coefficients of oligo- and polystyrenes. Effects of chain ends

Einaga¹,

Abe²,

Yamakawa³

1993

Macromolecules

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The second virial coefficient Az was determined from light scattering measurements for atactic polystyrene in cyclohexane at 34.5 "C (e) and in toluene at 15.0 OC down to the oligomer region, including the monomer, in order to clarify the effect of chain ends on Az. The observed dependence of AZ on weightaverage molecular weight M, may well be explained by the Yamakawa theory that takes into account both the effects of chain ends and chain stiffness. It is shown that the observed nonvanishing of Az at 8 arises from the former effect. The excess effective binary-cluster integrals 81 and 82 associated with the chain end beads are estimated to be 16 and 260 A3 in cyclohexane and 220 and 270 Aa in toluene, respectively, taking the repeat unit as a single bead. These values are of reasonable order of magnitude compared to those for small molecules. It is then striking to find that the effect of chain ends exists even at relatively large M, ( N 103 in the good solvent toluene. For this system, however, the previous conclusion for the interpenetration function 9 still remains valid, since the contribution AiE) of the effect of chain ends to A2 is not very large in the ordinary range of M,. As the cubed radius expansion factor a,+ (or M,) is decreased, the (true) 9 including no effect of AiE) in toluene first increases gradually, then passes through a maximum and a minimum, and finally increases steeply, deviating significantly upward from the two-parameter theory values but being consistent with the Yamakawa theory. This is due to the effect of chain stiffness. As a,+ (or M,)is further decreased, the contribution of AiE) to Az or to the apparent interpenetration function 9ap as usually defined from the whole Az including AiE) becomes progressively large. It is shown that the rapid increase of 9'ap there with decreasing M, arises mainly from the effect of chain ends but not from that of chain stiffness, in contrast to the prevailing notion.

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Beiträge zur Thermodynamik von Polymerlösungen 7. Untersuchungen an Lösungen von Oligomeren des Methacrylsäuremethylesters

Cited by 16 publications

References 22 publications

Second Virial Coefficient of Oligo- and Poly(methyl methacrylate)s. Effects of Chain Stiffness and Chain Ends

Second Virial Coefficient of Oligo- and Poly(methyl methacrylate)s. Effects of Chain Stiffness and Chain Ends

On the theory of the second virial coefficient for polymer chains

Second virial coefficients of oligo- and polystyrenes. Effects of chain ends

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