Rubbery plateau

Above To, the material remains in a rubbery state, and at this point — 0 due to W T 1 that is, the applied oscillatory deformation is far slower than the cooperative segmental movements, and thus the internal reorganizations elastically absorb the solicitation. Thus, shows a constant value that may be related to the molecular weight between entanglements or crosslinks [42]. The influence of physical fillers may play a role in the -values during the rubbery plateau, as will be shown later. 

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At still longer times a more or less pronounced plateau is encountered. The value of the plateau modulus is on the order of 10 N m", comparable to the effect predicted for cross-linked elastomers in Sec. 3.4. This region is called the rubbery plateau and the sample appears elastic when observed in this time frame. 

In the rubbery plateau, a new impediment to movement must be overcome entanglements along the polymer chain. In discussing the effects of entanglements in Chap. 2, we compared them to crosslinks. Is it any surprise, then, that rubbery behavior similar to that shown by cross-linked elastomers characterizes this region ... 

The upswing in compliance from the rubbery plateau marks the onset of viscous flow. In this final stage the slope of the lines (the broken lines in Fig. 3.12) is unity, which means that the compliance increases linearly with time. 

Since pc 1/2, we observe that Me 2Mg, as commonly observed. Mg is determined from the onset of the rubbery plateau by dynamic mechanical spectroscopy and Me is determined at the onset of the highly entangled zero-shear viscosity law, T) M. This provides a new interpretation of the critical entanglement molecular weight Mg, as the molecular weight at which entanglement percolation occurs while the dynamics changes from Rouse to reptation. It also represents the... 

Crosslinking the PSA will increase the solvent resistance of the material and it will also have a significant effect on the rubbery plateau modulus of the polymer. Fig. 8 shows the effect of increasing amounts of a multifunctional az.iridine crosslinker, such as CX-100 (available from Avecia, Blackley, Manchester, UK) on the rheology of an acrylic polymer containing 10% acrylic acid. The amounts of crosslinker are based by weight on the dry weight of the PSA polymer. 

Lowering of the rubbery plateau modulus increases the compliance of the polymer making faster wet-out of a substrate possible. As a result, the PSAs show more aggressive tack properties. Provided the surface energy of the substrate allows for complete polymer wetting, a PSA with improved quick-stick and faster adhesion build will be obtained. 

Similar to the tackifiers discussed earlier, plasticizers have a very dramatic softening effect on the rubbery plateau modulus of the PSA. For this reason, high levels of plasticizers have to be avoided to maintain good cohesive strength in the adhesive, especially at elevated temperatures. Indeed, if high cohesive strength is desired, the amount of plasticizer used in a PSA is typically kept to a minimum, if used at all. 

As one example, in thin films of Na or K salts of PS-based ionomers cast from a nonpolar solvent, THF, shear deformation is only present when the ion content is near to or above the critical ion content of about 6 mol% and the TEM scan of Fig. 3, for a sample of 8.2 mol% demonstrates this but, for a THF-cast sample of a divalent Ca-salt of an SPS ionomer, having only an ion content of 4.1 mol%, both shear deformation zones and crazes are developed upon tensile straining in contrast to only crazing for the monovalent K-salt. This is evident from the TEM scans of Fig. 5. For the Ca-salt, one sees both an unfibrillated shear deformation zone, and, within this zone, a typical fibrillated craze. The Ca-salt also develops a much more extended rubbery plateau region than Na or K salts in storage modulus versus temperature curves and this is another indication that a stronger and more stable ionic network is present when divalent ions replace monovalent ones. Still another indication that the presence of divalent counterions can enhance mechanical properties comes from... 

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. 

The physical properties of the acid- and ion-containing polymers are quite interesting. The storage moduli vs. temperature behavior (Figure 8) was determined by dynamic mechanical thermal analysis (DMTA) for the PS-PIBMA diblock precursor, the polystyrene diblock ionomer and the poly(styrene)-b-poly(isobutyl methacrylate-co-methacrylic acid) diblock. The last two samples were obtained by the KC>2 hydrolysis approach. It is important to note that these three curves are offset for clarity, i.e. the modulus of the precursor is not necessarily higher than the ionomer. In particular, one should note the same Tg of the polystyrene block before and after ionomer formation, and the extension of the rubbery plateau past 200°C. In contrast, flow occurred in... 

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Moreover, real polymers are thought to have five regions that relate the stress relaxation modulus of fluid and solid models to temperature as shown in Fig. 3.13. In a stress relaxation test the polymer is strained instantaneously to a strain e, and the resulting stress is measured as it relaxes with time. Below the a solid model should be used. Above the Tg but near the 7/, a rubbery viscoelastic model should be used, and at high temperatures well above the rubbery plateau a fluid model may be used. These regions of stress relaxation modulus relate to the specific volume as a function of temperature and can be related to the Williams-Landel-Ferry (WLF) equation [10]. 

It is possible that either Me has increased by degradation of the network structure or the resin is internally plasticized by free chain ends. If Me has increased, then the modulus in the rubbery plateau region for irradiated specimens should be less than that of a control. As discussed above, E (Tg+40) decreases up to a dose of 5000 Mrads. Between 5000 and 10,000 Mrads, E (Tg+40) increases but remains 6% below the control. For the 73/27 and 80/20 samples (10,000 Mrads) which have been sorbed/desorbed, E (Tg+40) is 18.5% greater than the control. 

The molecular weight between crosslinks (Me) was determined for each epoxy/amine ratio of the neat resin from the rubbery plateau region of the modulus curve following the Tg region. This can be seen in Figure 13 for several epoxy/amine ratios. The Me values were calculated from the following equation ... 

While in the temperature range called the rubbery plateau, the soft polymer responds instantaneously and reversibly to applied stress and tends to be Hookean. In the rubber state, the polymer approaches Hooke s law for... 

As the temperature is increased above the rubbery plateau, the linear amorphous polymer assumes a viscous state and may undergo irreversible flow, i.e., flows such that the original shape is lost. The flow of the viscous liquid may approach a Newtonian flow, i.e., its flow properties may be estimated from Newton s law for ideal liquids. 

The viscosity of the polymer increases rapidly as the temperature is lowered toward Tg, and the polymer chains exist in many conformations as compact coils. The polymer undergoes reversible stretching when subjected to instantaneous stress in the rubbery plateau as it goes from a low to a high entropy value. 

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