Dynamic moduli molecular weight distribution

The mechanical properties of polypropylene (PP) mainly vary on degree of crystallinity, molecular weight, and molecular weight distribution. The degree of crystallinity is mainly responsible for mechanical properties in which small deformations are involved, such as dynamic elastic modulus, heat distortion temperature, and hardness. 

Let us look at typical behavior of these material functions. In Figure 3.3.5 we see that G versus o) looks similar to G versus 1/r from Figure 3.3.1. For rubber it becomes constant at low frequency (long times), and for concentrated polymeric liquids it shows the plateau modulus Ge and decreases with co in the limit of low frequency. The loss modulus is much lower than G for a crosslinked rubber and sometimes can show a local maximum. This maximum is more pronounced in polymeric liquids, especially for narrow molecular weight distribution. The same features are present in dilute suspensions of rodlike particles, but not for dilute random coil polymer solutions, as Figure 3.3.3b shows. These applications of the dynamic moduli to structural characterization are discussed in Chapters 10 and 11. 

We first consider the behavior of the dynamic storage modulus and the dynamic loss modulus. Colby, et a/. (15) report an extremely extensive series of measurements of the storage and loss moduli of a 925 kDa (M ) polybutadiene having a narrow molecular weight distribution (M /Mn < 1.1 M /Mw < 1-1). Solutions were made in the Theta solvent dioctylphthalate (DOP) at 12°C above the Theta temperature, and the good solvent phenyloctane (PO). Viscosities were reported at 15 volume fractions extending from extreme dilution 0.001) up to the melt full... 

These equations are often used in terms of complex variables such as the complex dynamic modulus, E = E + E", where E is called the storage modulus and is related to the amount of energy stored by the viscoelastic sample. E" is termed the loss modulus, which is a measure of the energy dissipated because of the internal friction of the polymer chains, commonly as heat due to the sinusoidal stress or strain applied to the material. The ratio between E lE" is called tan 5 and is a measure of the damping of the material. The Maxwell mechanical model provides a useful representation of the expected behavior of a polymer however, because of the large distribution of molecular weights in the polymer chains, it is necessary to combine several Maxwell elements in parallel to obtain a representation that better approximates the true polymer viscoelastic behavior. Thus, the combination of Maxwell elements in parallel at a fixed strain will produce a time-dependent stress that is the sum of all the elements ... 

As will be noted no molecular anisotropies and no effects due to size and size distribution of the particles of the discrete phase are recognized. Through E = 2(1 + p)G Eq. (2.5) can be used to predict also the complex tensile modulus. A good example for the applicability of Eq. (2.5) is furnished by the experimental data obtained by Dickie et al. [75]. For the dynamic tensile modulus of a physical mixture (polymer blend) of 75% by weight polymethylmethacrylate (PMMA, continuous phase) and 25% butylacrylate (PBA, discrete phase) within experimental error correspondence of calculated and measured data was obtained (Fig. 2.13,... 

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