High Plateau modulus

PROPERTIES OF SPECIAL INTEREST High plateau modulus (1.6 MPa) permits high filler... 

Ethylene/propylene copolymerization is of significant commercial importance. Elastomers formed from random ethylene/propylene copolymers (EP) possess a number of valuable properties including a high plateau modulus ( 1.6 MPa), which permits a higher filler loading and more cost-effective compounding. Furthermore, of the major hydrocarbon-based rubbers, EP is by far the least reactive with oxygen and ozone. 

This article presents uniaxial extension measurements on cis-1,4-polybutadiene networks of known junction functionality. The observed values of the reduced force from uniaxial extension measurements conform to the constrained junction theory of Flory. The reduced force intercept at 1/cX = 0 is fully comprehensible in terms of the cycle rank of the network, and can be calculated from chemical considerations. This holds even though the polybutadiene melt has a high plateau modulus. Therefore, discrete topological entanglements do not contribute perceptibly to the equilibrium modulus of polybutadiene networks. 

Polysulfone and polycarbonate, for example, are high plateau modulus materials, often referred to as engineering plastics. These are listed in Table 11, which, in the main, is based on a collection of data given by Roovers, Toporowski and Ethier [254]. As can be seen in Fig. 7, generally good agreement is found with the predicted behavior, which is based on the data given in Table 11. This demonstrates that the behavior reported is independent of polymer type. 

The different forms of the modulus are still widely disputed and different opinions are expressed in the literature. Hsu and Mark " " prepared networks of polybutadiene by endlinking. According to dynamic measurements polybutadiene has a high plateau modulus in viscoelasticity and one can expect a strong contribution to the modulus from entanglements. In this study experiments have been fitted to the stress-strain relations with the Flory constraint-fluctuation model as in ref. 245. The authors concluded that there is no contribution from entanglements to the modulus. The same conclusion was drawn in refs. 245-248. 

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. 

For highly concentrated solutions, Eq. (20) can be simplified, due to the fact that in such a case the plateau modulus G p is Mw independent. Under these conditions it is clear that E is solely a function of... 

Comments on Calculated Data. In several studies (13,18,19), G ax has been found to equal, or possibly be somewhat less than, the plateau modulus, G j, of a high molecular weight polymer whose chemical composition is the same as that of the network chains. Although G j for amorphous PPO has not been reported, it can be estimated from Zc, the number of chain atoms per molecule above which the viscosity increases approximately with the 3.4 power of Z. This quantity has been reported (25,26) to be about 400. As the chain atoms between entanglements is commonly about Zc/2, it follows that the molecular weight between entanglement loci is about 3900, and thus G j [ = (p/Me)RT] is about 0.65 MPa at 30°C. 

Since the excellent work of Moore and Watson (6, who cross-linked natural rubber with t-butylperoxide, most workers have assumed that physical cross-links contribute to the equilibrium elastic properties of cross-linked elastomers. This idea seems to be fully confirmed in work by Graessley and co-workers who used the Langley method on radiation cross-linked polybutadiene (.7) and ethylene-propylene copolymer (8) to study trapped entanglements. Two-network results on 1,2-polybutadiene (9.10) also indicate that the equilibrium elastic contribution from chain entangling at high degrees of cross-linking is quantitatively equal to the pseudoequilibrium rubber plateau modulus (1 1.) of the uncross-linked polymer. 

The viscosity scales, from Eq. (1), as Tj-GoTi-gp since and are the characteristic modus and relaxation times appearing respectively in the integral. The plateau modulus is independent of molecular weight for highly entangled polymers [1] but inversely proportional to so... 

Highly entangled systems, especially those of narrow molecular weight distribution, are characterized by a set of relaxations at long times (terminal relaxations) which are more or less isolated from the more rapid processes. The modulus associated with the terminal processes is called the plateau modulus G°,. Because t]0 and depend on weighted averages over H(x), their values are controlled almost completely by the terminal processes. These experimental... 

The use of monomers bearing more than two associating groups is a straightforward way to introduce a controlled amount of branches or crosshnks in a supramolecular polymer structure [6,58,121,123-127]. The improvement of the mechanical properties can be spectacular. For instance, trifunctional monomer 17 (Fig. 21) forms highly viscous solutions in chloroform, and is a viscoelastic material in the absence of solvent [124]. The reversibly cross-linked network displays a higher plateau modulus than a comparable covalently cross-linked model. This is explained by the fact that the reversibly cross-hnked network can reach the thermodynamically most stable conformation, whereas the covalent model, which has been cross-linked in solution and then dried, is kinetically trapped. 

In a large range of concentrations (< )S0.05) where the high component is assumed to behave as an entangled melt, the variations of the terminal relaxation time (Oni in the iso-free volume state (Fig. 29) confirms relation (6-8). As the steady-state compUance J l scales as ( )" (Fig. 30), the zero-shear viscosity tiol varies as expected and the plateau modulus Gn which reveals the entanglement network is proportional to 0 . ... 

For high concentrations the dynamics of the chains are the same as in melts. Excluded volume effects and the hydrodynamic interaction are not important. However, both the radius of the tube and the friction coefficient strongly depend on the concentration. Because the depedence of on G is nontrivial, there are no scaling laws relating x ax nnd r o lo the concentration. For the plateau modulus, it was found experimentally that (8)... 

The storage modulus of HI 8 dispersions in VE resin with low styrene content exhibits high plateau values in the linear viscoelastic regime with G > G" (G omitted for clarity). This is indicative of a viscoelastic solid with percolating gel structure [9]. However, addition of styrene results in a pronounced decrease of the storage modulus. 

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