Rubber-elastic plateau

The stress relaxation properties of a high molecular weight polybutadiene with a narrow molecular weight distribution are shown in Figure 1. The behavior is shown in terms of the apparent rubber elasticity stress relaxation modulus for three differrent extension ratios and the experiment is carried on until rupture in all three cases. A very wide rubber plateau extending over nearly 6 decades in time is observed for the smallest extension ratio. However, the plateau is observed to become narrower with increasing extension... 

Chain entanglements are the cause of rubber-elastic properties in the liquid. Below the "critical" molecular mass (Mc) there are no indications of a rubbery plateau. The length of the latter is strongly dependent on the length of the molecular chains, i.e. on the molar mass of the polymer. From the shear modulus of the pseudo rubber plateau the molecular weight between entanglements may be calculated ... 

Rigid rodcrystallisation, 706 Rod climbing effect, 526 Rod-like molecules, 252 Rod-like polymer molecules, 274 Rod-shaped particle, 276 Rubber elasticity, 401 Rubbery plateau, 400 Rudin equations, 272 Rudin-Strathdee equation, 602 Rules of thumb for substituting an H-atom by a group X, 182... 

In this work we used polystyrene-based ionomers.-Since there is no crystallinity in this type of ionomer, only the effect of ionic interactions has been observed. Eisenberg et al. reported that for styrene-methacrylic acid ionomers, the position of the high inflection point in the stress relaxation master curve could be approximately predicted from the classical theory of rubber elasticity, assuming that each ion pah-acts as a crosslink up to ca. 6 mol %. Above 6 mol %, the deviation of data points from the calculated curve is very large. For sulfonated polystyrene ionomers, the inflection point in stress relaxation master curves and the rubbery plateau region in dynamic mechanical data seemed to follow the classical rubber theory at low ion content. Therefore, it is generally concluded that polystyrene-based ionomers with low ion content show a crosslinking effect due to multiplet formation. More... 

Mechanical oscillation measurements could only be carried out on nonionic PAAm-BisAAm gels. Because of their high degree of swelling, the saponified swelled gels could not be cut into suitable samples without their being destroyed. Via the theory of rubber elasticity developed by Flory (32), the value of the plateau modulus (Gp ) obtained by mechanical oscillation measurements is directly related to the number of elastically effective chains per unit volume (v J. 

Glassy state, glass transition and rubber-elastic plateau can be clearly distinguished. The dynamic glass transition temperature Tg as an important engineering parameter can be determined by the maximum of E" and tan 5. 

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... 

Above the glass transition lies the rubbery plateau region, region 3. The equations of state for rubber elasticity (see Section 1.5.4) apply here if the material is crosslinked, these equations may apply up to the decomposition temperature (see dashed line. Figure 1.12). 

The data for a semicrystalline sample of polystyrene are also shown in the graph of Fig. 4.145. They show a much higher Ethan the rubbery plateau. Here the crystals form a dense network between the parts of the molecules that become liquid at the glass transition temperature. This network prohibits flow beyond the rubber elastic extension of the liquid parts of the molecules. Unimpeded flow is possible only after the crystals melt in the vicinity of 5(X) K. 

Classical rubber elasticity theory predicts that the plateau modulus,, for a diluted polymer, is proportional to the square of the volume fraction of the polymer. Scaling law interpretations for dilute solutions by P.G. 

The storage modulus of a 3wt% solution shows almost rubber elastic behaviour with a slope of approximately 0.035. The slope of the i] curve, i.e. 0.94, is in reasonable agreement with the slope of G. The rubber plateau decreases gradually (almost monotonically) with increasing temperature, although a weak transition is perceptible at about 40 °C, where the slope changes little. 

Estimation of the crosslink density of a thermoset network can be obtained from the storage modulus values in the rubbery plateau region. In principle, the crosslink density of a cured thermoset network could be calculated from the theory of rubber elasticity. The shear modulus G of a crosslinked rubbery network is given by [33] ... 

Vilgis and Erman that the constraint models and slip-link models have much in common, (iv) elucidating the effects of cross-link functionality and degree of cross linking, (v) exploring a variety of elastomeric polymers, particularly those having very different values of the plateau modulus, and (vi) generalizing rubber-elasticity models to include viscoelastic effects as well. 

In equation 76a the reptation time A,rep is the time for the chain to escape from the tube (orientation relaxation occurs from the end to the center of the chain). Gn is the entanglement plateau modulus (this value is slightly different from that implied from rubber elasticity of an entangled network) and f pit) is a normalized relaxation modulus for the reptation process. In this time regime, equation 76a implies that the modulus is separable into a time fimction and a modulus function. This becomes important in discussing the nonlinear response, which is done, in more detail, below. Some other viscoelastic functions from the DE tube model of reptation are... 

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