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

Abe, Fumiaki; Einaga, Yoshiyuki; Yamakawa, Hiromi

doi:10.1021/ma00090a019

Cited by 43 publications

(62 citation statements)

References 21 publications

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“…It is seen that there is rather good agreement between theory and experiment, and that remains appreciable up to Figure 12 shows similar plots for a-PMMA in acetonitrile at 44.oac (B) and in acetone at 25.0°C. 64 The curves have the same meaning as those in Figure 11. It is interesting to see that A 2 ,e for a-PMMA exhibits a minimum.…”

Section: Second Virial Coefficientmentioning

confidence: 97%

A New Framework of Polymer Solution Science. The Helical Wormlike Chain

Yamakawa

1999

Polym J

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ABSTRACT:The object of this review article is to introduce and digest Yamakawa's new book, "Helical Wormlike Chains in Polymer Solutions." A brief description is given of a new model for polymer chains, called the helical wormlike chain, and its applications to dilute solution behavior of polymers, that is, equilibrium, steady-state transport, and dynamical properties. The description follows most of the chapters of the book. It is shown that all theoretical and experimental investigations on the basis of this model provide a new framework of polymer solution science, which takes the place of the Flory-Kirkwood framework.KEY The object of this review article is to introduce and digest Yamakawa's new book 1 entitled" Helical Wormlike Chains in Polymer Solutions." As stated in its Preface, it is intended to give a comprehensive and systematic description of the statistical-mechanical, transport, and dynamic theories of dilute solution properties of both flexible and semiflexible polymers, including oligomers, developed on the basis of the "helical wormlike (HW) chain" model, along with an analysis of extensive experimental data. Much of the material in the book arises from his research reported since the year of publication of his earlier (1971) book. 2 The results of this research were already very often reviewed. 3 -7 Now the framework of polymer solution theory constructed by Flory 8 • 9 consists of three concepts: (I) the excluded-volume effect in long flexible (Gaussian) polymer chains, (2) the universality of the unperturbed ( EJ) state without that effect, and (3) the rotational isomeric state (RIS) model for (unperturbed) real chains of arbitrary length. The study of dilute solution behavior of flexible polymers based on the first two concepts was almost completed around 1970, leading to the so-called two-parameter (TP) theory. 2 It is at almost the same time that the statistical-mechanical method for treating the RIS model, which takes account of the details of the chemical structure and local conformations of the chain on the atomic level, was established by Flory and coworkers.9 However, for many equilibrium and steadystate transport problems on stiff or semiflexible polymers, such details are not amenable to mathematical treatments, and moreover are often unnecessary to consider. Some coarse-graining may then be introduced to replace this discrete model by continuous models. In 1976, for this purpose we proposed a general continuous model, called the HW chain. 10 This new model may describe equilibrium conformational and steady-state transport properties of all kinds of real chains, both flexible and stiff, on the bond length or somewhat longer scales, thus bridging a gap between the RIS model and the classical continuous model, that is, the KratkyPorod (KP) wormlike chain. 11 Specifically, the transport t Professor Emeritus.

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Section: Second Virial Coefficientmentioning

confidence: 97%

A New Framework of Polymer Solution Science. The Helical Wormlike Chain

Yamakawa

1999

Polym J

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“…3 As is well known, effects of chain ends on A 2 become remarkably large in the range of small M w , including oligomers. 9,[21][22][23][24][25][26] The slope of the plots in the range of M w . 10 4 , where the A 2 values for the L, T, and B samples agree with each other, is ca.…”

Section: Second Virial Coefficient In Methanol At 25 Cmentioning

confidence: 99%

“…We note that A (E) 2 rapidly decreases to 0 with increasing M and has been shown to be very small for M & 10 5 for all the vinyl polymers examined so far. 9,[22][23][24][25] It is seen from eqs 1-7 that the theoretical values of A 2 may be calculated for a given polymer by the use of proper values of À1 , M L , and B along with 1 and 2 . As in the cases of other vinyl polymers, we adopt the touched-bead model as a hydrodynamic model, 9 in which N identical spherical beads of diameter d b are arrayed with spacing d b between them along the KP chain of total contour length L ¼ Nd b , its [] (¼ ½ 0 ) without excluded volume may be written in the form, 9,29…”

Section: Chain Stiffness In Methanol At 25 Cmentioning

confidence: 99%

Characterization of Linear Poly(N-isopropylacrylamide) and Cloud Points in its Aqueous Solutions

et al. 2009

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The second virial coefficient A 2 and intrinsic viscosity [] were determined in methanol at 25.0 C for poly(Nisopropylacrylamide) (PNIPA) samples synthesized by living anionic polymerization in the range of weight-average molecular weight M w from 4:91 Â 10 3 to 7:23 Â 10 4 , which are called L samples, and also for those by radical polymerization in tert-butanol and benzene by the use of azobis(isobutyronitrile) as an initiator in the range of M w from 1:23 Â 10 4 to 7:83 Â 10 4 , which are called T and B samples, respectively. It is found for both A 2 and [] that their values for the three kinds of samples agree well with each other in the range of M w. 3 Â 10 4 but deviate from each other as M w is increased from 3 Â 10 4 , the value for the L sample being the largest and that for the B sample the smallest. The result is consistent with the fact that the average chain dimension is the largest for the L sample having no branch point and the smallest for the B sample having the largest number of branch points. From a simultaneous analysis of A 2 and [] for the L samples on the basis of the Kratky-Porod wormlike chain with excluded volume, the stiffness parameter À1 is estimated to be 18 Å , which is almost the same as those determined for typical flexible polymers. For the L samples, the cloud point was also determined in their aqueous solutions in the range of the weight fraction w of PNIPA from ca. 0.5 to ca. 10%. It is found that the cloud point in the range of w & 2% decreases from ca. 32 C to ca. 18 C as M w is decreased from 7:23 Â 10 4 to 5:47 Â 10 3. Such behavior may be regarded as arising from effects of hydrophobic chain end groups of the L samples.

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“…PS in cyclohexane at 34.5°C ͑⌰͒,8,31 a-PS in transdecalin at 21.0°C ͑⌰͒,28 and a-PMMA in acetonitrile at 44.0°C ͑⌰͒,32,33 respectively. The solid, dashed, and dotted curves represent the theoretical values for a-PS in cyclohexane, a-PS in trans-decalin, and a-PMMA in acetonitrile, respectively, calculated from Eq.…”

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confidence: 99%

A Monte Carlo study of effects of chain stiffness and chain ends on dilute solution behavior of polymers. II. Second virial coefficient

Yamakawa

Yoshizaki

2003

The Journal of Chemical Physics

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A Monte Carlo ͑MC͒ study is made of the second virial coefficient A 2 for polymers using two freely rotating chains, each of bond angle 109°, with the Lennard-Jones 6-12 intramolecular and intermolecular potentials between beads in a cutoff version for the number of bonds in the chain ranging from 6 to 1000 in the ⌰ and good-solvent conditions. It is found that effects of chain ends on A 2 are appreciable for small molecular weight M , as was expected, and that the second virial coefficient A 2,⌰ at the ⌰ temperature, at which the ratio ͗S 2 ͘/M of the mean-square radius of gyration ͗S 2 ͘ to M becomes a constant independent of M for very large M , remains slightly negative even for such large ͑but finite͒ M where the effects of chain ends disappear. Such behavior of A 2,⌰ , which cannot be explained within the framework of the binary cluster theory, is shown to be understandable if possible effects of three-segment interactions are considered. The present MC data for A 2 ͑along with the previous ones for ͗S 2 ͘) may then be consistently explained by the existent theory based on the helical wormlike chain model only if a minor correction is made to the theoretical A 2,⌰ in almost the same range where the effects of chain ends are appeciable. The present MC data are also compared with experimental data, and it is shown that the latter may also be similarly explained.

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

Cited by 43 publications

References 21 publications

A New Framework of Polymer Solution Science. The Helical Wormlike Chain

A New Framework of Polymer Solution Science. The Helical Wormlike Chain

Characterization of Linear Poly(N-isopropylacrylamide) and Cloud Points in its Aqueous Solutions

A Monte Carlo study of effects of chain stiffness and chain ends on dilute solution behavior of polymers. II. Second virial coefficient

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