Entanglement molecular weight modulus

Note that p is independent of molecular weight, since for Gaussian chains M/ [R )q is a constant. At 140°C, the entanglement molecular weight Mg, plateau modulus G, and the tube diameter a (defined below in Section 3.7.1) are related to p by (Fetters et al. 1994)... 

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... 

M/Me- Thus, the line shape of the relaxation modulus G t) changes with concentration. As showm below, the viscoelastic behavior of the entangled component in the concentrated blend solution is well described by Eq. (9.19) with the entanglement molecular weight Me replaced by M, which is given by Eq. (11.4). This means that G t) is universal among monodisperse melt systems and blend solution systems, as all the G t) curves are described by... 

The entanglement molecular weight Mg has been predetermined from the plateau modulus — a static property. An error in the Mg value will lead to an error in the obtained K value as both Mg and K appear in the equations for the relaxation times ta, tx, tb and rc as pointed out... 

We return now to the difference in behavior between the two types of PMMA with molecular weights of 1.5 x 10 and 3.6 x 10 . We note that the rubbery modulus of the type with the higher molecular weight reaches a plateau at /iR = 3.4 MPa. As we discuss in Chapter 6 on rubber elasticity, the entanglement molecular weight Me can be determined from this modulus through the statistical theory of rubber elasticity (Ferry, 1980) as... 

In the earlier discussion of the plateau modulus, it was remarked that a liquid of long chains acts, at intermediate times or frequencies, like a network. The theory of rubber elasticity predicts a relationship between the shear modulus and the concentration of network strands (Chapter 1). This relationship is used to evaluate Me, the equivalent molecular weight of a strand in the entanglement network, which is called the entanglement molecular weight [1] ... 

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