Polystyrene plateau modulus

It is not clear why this transition should occur at such a higher level of arm entanglement for polystyrene stars than for other star polymers. This observation is in direct conflict with the standard assumption that through a proper scaling of plateau modulus (Go) and monomeric friction coefficient (0 that rheological behavior should be dependent only on molecular topology and be independent of molecular chemical structure. This standard assumption was demonstrated to hold fairly well for the linear viscoelastic response of well-entangled monodisperse linear polyisoprene, polybutadiene, and polystyrene melts by McLeish and Milner [24]. 

Dilution effect on the plateau modulus of linear polymers, Filled diamonds are polystyrene in cyclohexane at 34.5 °C (0-solvent), open squares are polystyrene in benzene at 25 °C (good solvent), filled circles are polybutadiene in dioctylphthalate at 25°C (near ... 

Consider a solution of polystyrene with molar mass M= 0°g moP in cyclohexane at 35 °C (0-solvent with viscosity ris = 7.6 x 10 Pa s). Estimate the relaxation time, plateau modulus, viscosity, and diffusion coefficient as functions of concentration in semidilute solution. 

Fig. 9 Loss angle as a function of the reduced modulus (ratio of complex modulus and plateau modulus) for polystyrene samples. (From RQfP )...

Shown in Fig. 4.6 are the curves of relaxation modulus, G t), of a series of nearly monodisperse polystyrene samples of different molecular weights. The higher the molecular weight, the slower the relaxation rate. In these measurements, the step deformation rise time is 0.04 s, which is much shorter than the relaxation times of interest in these curves. The most noteworthy is the appearance of a modulus plateau when the molecular weight is sufficiently large. As will be discussed in the later chapters, the entanglement molecular weight Mg can be calculated from the plateau modulus Gn- The analyses of these relaxation modulus curves in terms of the extended reptation theory developed in Chapter 9 will be detailed... 

The composition dependence of the relative molecular mass for entanglement has been studied in the context of viscoelasticity for example polystyrene (PS) and poly(xylenyl ether) (PXE) are fully miscible but have very different values of Me, 19100 for PS and 4300 for PXE. Measurements of the plateau modulus of mixtures suggested that a simple harmonic mean blending law was followed (Prest and Porter 1972). 

An examination of the same two resins in styrene-butadiene rubber shows a similar performance, but the compatibility is reversed. The aromatic polystyrene resin is mostly compatible with styrene-butadiene rubber as illustrated in Fig. 5, although the beginning of a small second peak in tan S is evident at about 80°C. The cycloaliphatic poly(vinyl cyclohexane) resin appears to be incompatible with styrene-butadiene rubber. The blend shows a significant second tan S peak at about 80 C and an elevation in the plateau modulus, as illustrated in Fig. 6. 

FIG. 17-15. Logarithmic plot of plateau modulus against concentration for solutions of polystyrene in benzyl n-butyl phthalate at 100°C. Different symbols correspond to calculations from various integration procedures and different molecular weights from 1.4 X 10 to 1.2 X 10 . Line n with slope between 2.2 and 2.3. (Nagasawa and collaborators. ) Reprinted with permission from iiacromolecules, 11, 888 (1978). Copyright by The American Chemical Society. 

Figure 11.7 compares the predictions of the MLD theory to steady-state shear data for a solution of nearly monodisperse polystyrene. In this comparison, the reptation time Tj and the plateau modulus have been taken as adjustable parameters. The theory used in this comparison is not the simplified toy model given by Eqs. 11.14 to 11.17, but a more complete theory with a contour variable, described in Mead et al [27]. The more complete version of the theory is able to include the effects of primitive path fluctuations as well as a more complete description of reptation and convective constraint release. Nevertheless, if the reptation time constant Tj is suitably adjusted to account phenomenologically for primitive path fluctuations (as discussed in Section 6.4.3 and 6.4-4.2), the predictions of Eqs. 11.14 to 11.17 are very similar to those of the full theory. 

The physical properties of the acid- and ion-containing polymers are quite interesting. The storage moduli vs. temperature behavior (Figure 8) was determined by dynamic mechanical thermal analysis (DMTA) for the PS-PIBMA diblock precursor, the polystyrene diblock ionomer and the poly(styrene)-b-poly(isobutyl methacrylate-co-methacrylic acid) diblock. The last two samples were obtained by the KC>2 hydrolysis approach. It is important to note that these three curves are offset for clarity, i.e. the modulus of the precursor is not necessarily higher than the ionomer. In particular, one should note the same Tg of the polystyrene block before and after ionomer formation, and the extension of the rubbery plateau past 200°C. In contrast, flow occurred in... 

Figure 8.19 Influence of molecular weight on the plateau length of narrow distribution polystyrene. The curves represent the storage relaxation modulus in the frequency domain reduced to 160°C. Viscosity-average molecular weights from left to right, xlO" 58, 51, 35, 27.5, 21.5, 16.7, 11.3, 5.9, and 4.7. (From Ref. 25.)...

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