Polystyrene entanglement molecular weight

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... 

Table 6.3 Parameters of Polystyrene within the Framework of the Reptation Theory [20]. The Entanglement Molecular Weight, M, and the Tube Diameter, dt, of Polystyrene is 13309 g/mol and 76.5 A, Respectively [21]...

The polymerization of styrene anionically produces an atactic block. The typical end block molecular weight for polymers used in pressure-sensitive adhesives is below the 18,000 Da entanglement molecular weight of polystyrene (see Table 15.3). Thus the softening point of these polymers is less than that of pure polystyrene. Like the tackifiers and oils discussed below, the polystyrene end blocks are in the oligomeric region where properties still depend on molecular weight (see O Fig. 15.18). 

Polystyrene is an important commercial thermoplastic that has been described by Priddy [121]. Its entanglement molecular weight is aroimd 18,000 and for both structure-rheology studies and commercial applications, molecular weights much higher than this are of primary interest. Nearly all commercial polystyrene is atactic and is thus a transparent glass at temperatures below its Tg, which is 100 °C. New catalyst systems are able to produce isotactic and syndiotactic versions, but these have not found practical applications to date due to their brittleness. 

Figure 11.2 Damping function h y> obtained from step-shear experiments on an entangled 20% solution of polystyrene of molecular weight 1.8 10 in chlorinated diphenyl (symbols) (data of Fukuda etal. [19]) compared to the predictions of the Doi-Edwards theory with (solid line) without (dashed line) the independent alignment approximation. From Doi and Edwards [131.

Figure 11.7 Measurements (symbols) versus predictions (lines) of the full MLD model for the shear stress crand first normal stress difference N, for a 10 wt% solution of polystyrene of molecular weight 2 million in tricresyl phosphate at 40 °C [36].The number of entanglements per chain is around Z = 16.7. = 11,500 dyn/cm and = 2.08 s were obtained by fitting the data.

Fig. 9.13. Breaking stress and crazing stress as a function of molecular weight of polystyrene at 25 °C (after (1461). M entanglement molecular weight.

The liquid-liquid transition has been shown to be a function of (see for example, ref. 4) at least until the critical entanglement molecular weight, is reached. Assuming for the moment that this holds true over the entire molecular weight range, a broad MWD polystyrene sample with the same M as PS-118, for example, should fall on the Tn line at the same point as PS-118 (see Fig. 4). PS-100 MWD = 2.5) was selected to test this assumption. 

Sulfonated polystyrene ionomers (alkali metal salts) with molecular weight below the entanglement molecular weight of polystyrene were prepared. The rheological behavior of the ionomers was characterized by dynamic and steady-state shear experiments. In general, the viscosity of the ionomers increased with sulfonation level and as the size of the cation decreased. Whereas, the starting polystyrenes were Newtonian fluids, the ionomers were non-Newtonian and viscoelastic. 

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