Plateau elastic modulus

The problem of concentration dependence of yield stress will be discussed in detail below. Here we only note that (as is shown in Figs 9 and 10) yield stress may change by a few decimal orders while elastic modulus changes only by several in the field of rubbery plateau and, moreover, mainly in the range of high concentrations of a filler. 

Figure 3.3 Variation of elastic modulus of a polymer with temperature. As the degree of crystallinity increases, the extent of rubbery plateau region decreases.

Emulsions with a high volume fraction of droplets (0 > 0.64) and foams show solidlike properties such as a yield stress and a low-frequency plateau value of G. The magnitudes of the yield stress and elastic modulus can be estimated using simple cellular foam models. These and related models show that at low shear rates where the shear stress is close to the yield value, the flow occurs by way of intermittent bubble-reorganization events. The dissipative processes that occur during foam and emulsion flows are still under active investigation. 

For glassy polymer systems without crystallites or other cross-links, a glass-liquid transition occurs. For systems with permanent, i.e., covalent, cross-links, the elastic modulus keeps decreasing with increasing temperature until a plateau value is reached. 

Adsorbed gelatine molecules alone do not show a frequency dependence of surface elasticity (Fig. 6.19), which corresponds to a behaviour of an insoluble monolayers. The presence of surfactants changes the elastic and relaxation behaviour dramatically. With increasing SDS concentration the elasticity modulus (frequency independent plateau value of the elasticity) first increases and then decreases. The dynamic behaviour of the mixed adsorption layer changes from one completely formed by gelatine molecules to an adsorption layer completely controlled by surfactant molecules (Fig. 6.20). A similar behaviour can be observed for CTAB and a perfluorinated surfactant (Hempt et al. 1985). 

Another example of network formation is found in PEO (poly(ethylene oxide))-silica systems [58, 59]. At relatively small-particle concentrations, the elastic modulus increases at low frequencies, suggesting that stress relaxation of these hybrids is effectively arrested by the presence of silica nanoparticles. This is indicative of a transition from liquidlike to solidlike behavior. At high frequencies, the effect of particles is weak, indicating that the influence of particles on stress relaxation dynamics is much stronger than their influence on the plateau modulus. 

Rubbery flow After the rubbery plateau the modulus again decreases from lO to 10 Nm in the section D to E. The effect of applied stress to a polymer in states (3) and (5) is shown in Figure 13.1(c), where there is instantaneous elastic response followed by a region of flow. 

Dynamic spectroscopy (this method is more sensitive to Tg modifications) characterized cured MTI as polymer networks. The existence of the high-elasticity plateau typical for cross-linked organic polymers makes it possible to determine values of high elastic modulus in the pseudoequilibrium zone. Systems based on oligoethers and mixtures with oligoesters are characterized by E values of 5.0 and 8.5 MPa, respectively, which comply with adhesion strength data. 

Elastic modidus temperature dependences obtained for all specimens thus studied (see Fig. 3.31) have the typical appearance of pely-mer compesites based on linear binders. A sharp fall of elastic modulus for all composites studied above the glass-transition temperature and the absence of a viscoelasticity plateau indicate that the composite polymer binder is not a network piolymer. 

These transverse entanglements, separated by a typical length ta govern the elastic response of solutions, in a way first outlined by Isambert and Maggs. A more complete discussion of the rheology of such solutions can be found in Morse and Hiimer et al.The basic result for the mbber-like plateau shear modulus for such solutions can be obtained by noting that the mrmber density of entropic constraints (entanglements) is thus where n = fl[a ) is... 

The resulting time-dependent post-fire elastic modulus distributions through the cross section depths, obtained from Eq. 8.2, were shown in Figure 8.19a,b for the noncooled and water-cooled cases [14]. The steps in the curves at 17 and 179 mm distance from the hot face, at time t = 0, resulted from the different elastic modules of face sheets and webs (see material description in Section 8.4.1). The water-cooled case showed a modulus reduction in the outer part of the fire-exposed face sheet only, where a plateau was reached at 88% of the initial value (corresponding to the recovery modulus) at a depth of 8-14 mm from the hot face. In the noncooled case, however, a progressive change of post-fire elastic modulus through the entire depth of the inner face sheet, webs, and some parts of the outer face sheet was... 

In homopolymers, physical properties are to some extent dependent on molar mass. Class transition temperature and various mechanical properties will increase with molar mass and eventually reach some sort of plateau value. The same is of course tme for a (statistical) copolymer, but in the case of a copolymer there is an additional degree of freedom. The copolymer composition may have a significant influence on maaoscopic properties. If the homopolymers of the two monomers in a copolymer have different Tg values, the Tg value of a statistical copolymer will fie in between the two homopolymer values. More or less, the same holds tme for other properties, such as hardness and elasticity modulus. All of this is tme if the copolymer has a narrow CCD. If the CCD is broader or even bimodal, phase separation may occur. This will lead to a much more complex situation, where the properties are a function not just of the overall chemical composition, but also of the phase morphology as was indicated in Section 6.12.3.1. An additional complication can be introduced if the copolymer chains contain a gradient as explained in Section 6.12.7. 

A plasticiser is a material incorporated in a plastic to increase its workability and flexibility or distensibility. The melt viscosity, elastic modulus and Tg of a plastic are lowered by a plasticiser addition. There are several theories to explain plasticiser effects such as the lubricity, gel, and free volume. Plasticisers are essentially nonvolatile solvents and therefore, polymer and plasticiser compatibility is very important and the solubility parameter difference (A8) should be less than 1.8. When present in small amounts plasticisers generally act as antiplasticisers, (i.e., they increase the hardness and decrease the elongation of polymers). Figure 6.12 illustrates the effect of plasticiser on modulus. Increasing concentration of the plasticiser shifts the transition from the high modulus (glassy) plateau region to the low, i.e., to occur at lower temperature [9]. 

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