Plateau modulus polymers

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. 

Increasing the amount of crosslinker extends the plateau modulus to higher and higher temperatures, eventually eliminating the flow of the polymer. The effect on the glass transition is minimal. 

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. 

So far, the existence of a well-defined entanglement length in dense polymer systems has been inferred indirectly from macroscopic experiments like measurements of the plateau modulus. However, its direct microscopic observation remained impossible. The difficulty in directly evaluating the entanglement... 

The Gge contribution of the form given Eq.(2) represents the simplest form of permanent interchain interactions. The value of Gee at Teg=1 and w =1, i.e. the Gge contribution of a perfect network, has been assumed equal to the plateau modulus of the corresponding linear polymer (10,15,23). This assumption has not always been confirmed and, therefore, for the purpose of this work we prefer to consider g of g" as proportionality constants. 

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... 

Portions of the literature on viscoelasticity in concentrated polymer systems of narrow distribution have been reviewed recently (15, 16, 152, 153). The following discussion concerns three principal characteristics, the viscosity-molecular weight relation, the plateau modulus, and the steady-state compliance. 

Aharoni SM (1986) Correlation between chain parameters and the plateau modulus of polymers. Macromolecules 19(2) 426-434... 

Figure 45a-c shows an adaptation of the developed model to uniaxial stress-strain data of a pre-conditioned S-SBR-sample filled with 40 phr N220. The fits are obtained for the third stretching cycles at various prestrains by referring to Eqs. (38), (44), and (47) with different but constant strain amplification factors X=Xmax for every pre-strain. For illustrating the fitting procedure, the adaptation is performed in three steps. Since the evaluation of the nominal stress contribution of the strained filler clusters by the integral in Eq. (47) requires the nominal stress aR>1 of the rubber matrix, this quantity is developed in the first step shown in Fig. 45a. It is obtained by demanding an intersection of the simulated curves according to Eqs. (38) and (44) with the measured ones at maximum strain of each strain cycle, where all fragile filler clusters are broken and hence the stress contribution of the strained filler clusters vanishes. The adapted polymer parameters are Gc=0.176 MPa and neITe= 100, independent of pre-strain. According to the considerations at the end of Sect. 5.2.2, the tube constraint modulus is kept fixed at the value Ge=0.2 MPa, which is determined by the plateau modulus Gn° 0.4 MPa [174, 175] of the uncross-linked S-SBR-melt (Ge=l/2GN°). The adapted amplification factors Xmax for the different pre-strains ( max=l> 1-5, 2, 2.5, 3) are listed in the insert of Fig. 45a.

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. 

It is not clear why this transition should occur at such a higher level of arm entanglement for polystyrene stars than for other star polymers. This observation is in direct conflict with the standard assumption that through a proper scaling of plateau modulus (Go) and monomeric friction coefficient (0 that rheological behavior should be dependent only on molecular topology and be independent of molecular chemical structure. This standard assumption was demonstrated to hold fairly well for the linear viscoelastic response of well-entangled monodisperse linear polyisoprene, polybutadiene, and polystyrene melts by McLeish and Milner [24]. 

One convenient strategy to interpret these results is to review the molecular characteristics of binary blends as extracted from polymer melt rheology [40]. The influence of short chains (M < Me) is to effectively decrease the plateau modulus and the terminal relaxation times as compared to the pure polymer. Consequently, the molecular weight between entanglements... 

Apart from a reduction in the width of the plateau region and a lower plateau modulus, (G blend = 0.5 g pure polymer), the blend exhibits a shift... 

In section 3.1.3. we proposed a simple model to calculate the anisotropic form factor of the chains in a uniaxially deformed polymer melt. The only parameters are the deformation ratio X of the entanglement network (which was assumed to be identical to the macroscopic recoverable strain) and the number n, of entanglements per chain. For a chain with dangling end submolecules the mean square dimension in a principal direction of orientation is then given by Eq. 19. As seen in section 3.1.3. for low stress levels n can be estimated from the plateau modulus and the molecular weight of the chain (n 5 por polymer SI). 

At intermediate fi equendes, monodisperse polymers exhibit a well-defined "plateau region" where G = constant Gn (Figure 2). For a given macromolecular species, the value of the plateau modulus is a characteristic feature that does not depend on molecular weight. The only way to lower the plateau modulus is to add small compatible molecules, either of the same species or not this is, for example, what is done for Hot-Melt Adhesives (HMAs) when adding a "tackifying resin" which softens the polymer and improves the "tack". 

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