Dynamic Structure Factor of Polystyrene and Poly(methyl methacrylate) in ϑ Solvents

Sawatari, Nobuo; Yoshizaki, Takenao; Yamakawa, Hiromi

doi:10.1021/ma980354z

Cited by 19 publications

(31 citation statements)

References 25 publications

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“…Thus the so-called "universal" plot of Yf 0 Q(k)jkBTk 3 against k depends on the kind of polymer, and therefore is not universal. 15 r--r.,.------r-----.---------,------ .ooc (EJ) (e), 83 and DNA with L=2.24Jlm in 0.15moll-1 NaCl at 25.0°C ( () ). 85 The solid, dashed, and dot-dashed curves represent the respective HW or KP theoretical values.…”

Section: Dynamic Structure Factormentioning

confidence: 99%

“…85 The solid, dashed, and dot-dashed curves represent the respective HW or KP theoretical values. M = 4.86 x 10 6 and 1.31 x 10 7 ) in acetonitrile at 44.ooc (0), 83 and DNA with L=2.24{lm in 0.15moll-1 NaCl at 25.0oC. 85 The solid, dashed, and dot-dashed curves represent the respective HW or KP theoretical values, where the experimental values of p have been used in the theoretical calculation.…”

Section: Dynamic Structure Factormentioning

confidence: 99%

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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: Dynamic Structure Factormentioning

confidence: 99%

Section: Dynamic Structure Factormentioning

confidence: 99%

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

Yamakawa

1999

Polym J

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“…Fig. 18 shows plots of Z 0 OðkÞ=k B Tk 3 against hS [42]. It is seen that the values for a-PaMS are slightly but appreciably smaller than those for a-PS in the k 3 -region (the plateau region) for hS 2 i 1=2 k\2 where OðkÞ is proportional to k 3 .…”

Section: First Cumulant Of the Dynamic Structure Factormentioning

confidence: 98%

Fine characterization of oligomers and polymers in dilute solution

Osa

2006

Science and Technology of Advanced Materials

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A fine characterization was made of atactic poly(a-methylstyrene) and atactic polystyrene on the basis of the helical wormlike chain model. It is found that there is a remarkable difference in chain stiffness and local chain conformation between the two polymers. Such a difference is shown to be reflected clearly in behavior of equilibrium, transport, and dynamical properties and also in the excludedvolume effects. r

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“…20 As for ðkÞ, the CONTIN method 21 was employed as before. 1,2 For the determination of D for each sample, the normalized autocorrelation function g ð2Þ ðtÞ of the scattered light intensity was measured at five concentrations and at scattering angles ranging from 13 for AMS550 in cyclohexane. These measurements for each sample were carried out at the same concentrations as those in the case of the determination of D. The sampling times adopted for the determination of D were 120-180 ms for F850-a in toluene, 50-80 ms for Mr127 in acetone, 100 ms for AMS550 in toluene and PIB660 in nheptane, 60-150 ms for F850-a in cyclohexane, and 100 ms for AMS550 in cyclohexane.…”

Section: Dynamic Light Scatteringmentioning

confidence: 99%

“…[1][2][3] It has then been concluded that the universality predicted by the Gaussian chain theory [4][5][6] for the plot of 0 ðkÞ=k B Tk 3 against hS 2 i 1=2 k cannot be realized for flexible polymers even with very high molecular weights (' 10 6 {10 7 ), and that the height of the plateau in the k 3 -region depends on chain stiffness and local chain conformation, as predicted by the helical wormlike (HW) chain theory, 7,8 where 0 is the solvent viscosity, k B the Boltzmann constant, T the absolute temperature, and hS 2 i the mean-square radius of gyration. In this paper, we further proceed to make an experimental study of the excluded-volume effects on ðkÞ.…”

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confidence: 99%

First Cumulant of the Dynamic Structure Factor for Flexible Polymers. Excluded-Volume Effects

Osa

Sawatari²,

Yoshizaki

et al. 2006

Polym J

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ABSTRACT:The first cumulant ðkÞ of the dynamic structure factor as a function of the magnitude k of the scattering vector was determined from dynamic light scattering (DLS) measurements for an atactic polystyrene (a-PS) sample with the weight-average molecular weight M w ¼ 8:04 Â 10 6 in toluene at 15.0 C, an atactic poly(methyl methacrylate) (a-PMMA) sample with M w ¼ 1:31 Â 10 7 in acetone at 25.0 C, an atactic poly(-methylstyrene) (a-PMS) sample with M w ¼ 5:46 Â 10 6 in toluene at 25.0 C, and a polyisobutylene (PIB) sample with M w ¼ 6:63 Â 10 6 in n-heptane at 25.0 C. It was also determined for the a-PS and a-PMS samples in cyclohexane in the vicinity of the respective Â temperatures (34.5 and 30.5 C). The translational diffusion coefficient D was also determined from DLS measurements for the a-PS, a-PMMA, a-PMS, and PIB samples in the same solvent conditions mentioned above. From a comparison of the present data with the previous ones for all the samples in the respective Â temperatures, it is found that the observed dimensionless coefficient C of the k 4 -term in the expansion of ðkÞ does not almost depend on excluded volume, as predicted by the Tanaka-Stockmayer first-order perturbation theory of C, being in good agreement with the theoretical value for the Gaussian chain with nonpreaveraged hydrodynamic interaction. Further, it is found that the excluded-volume effect is very small on the quantity ½ðkÞ=Dk 2 À 1=hS 2 ik 2 over the whole range of k 2 examined, where hS 2 i is the mean-square radius of gyration. Their first-order perturbation theory of the height of the plateau in the k 3 -region, however, cannot explain the behavior of the present experimental data. The disagreement between theory and experiment may be regarded as arising from the fact that the theory based on the Gaussian chain model cannot take proper account of effects of chain stiffness and local chain conformation.

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Dynamic Structure Factor of Polystyrene and Poly(methyl methacrylate) in ϑ Solvents

Cited by 19 publications

References 25 publications

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

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

Fine characterization of oligomers and polymers in dilute solution

First Cumulant of the Dynamic Structure Factor for Flexible Polymers. Excluded-Volume Effects

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