Entanglement strain-dependent

It became clear in the early development of the tube model that it provided a means of calculating the response of entangled polymers to large deformations as well as small ones [2]. Some predictions, especially in steady shear flow, lead to strange anomaUes as we shall see, but others met with surprising success. In particular the same step-strain experiment used to determine G(t) directly in shear is straightforward to extend to large shear strains y. In many cases of such experiments on polymer melts both Hnear and branched, monodisperse and polydisperse,the experimental strain-dependent relaxation function G(t,Y) may be written... 

Another group of theories is based upon intermolecular strain dependent effects caused 1) by orientationally active short chains, 2) by excluded volume, and 3) by a structuring in the network, including entanglements. The first two do not yield a sufficiently large C2. For the third, several proposals have been made, but they are either qualitative or, as yet, incomplete. The structuring hypothesis needs special emphasis because we have seen that many networks may indeed exhibit much more structure than is implied by the normal picture of coiling-chain networks. 

The deformation dependence of the stress in the Edwards tube model is the same as in the classical models [Eqs (7.32) and (7.33)] because each entanglement effectively acts as another crosslink junction in the network. Therefore, the Edwards tube model is unable to explain the stress softening at intermediate deformations, demonstrated in Fig. 7.8. The reason for the classical functional form of the stress strain dependence is that the confining potential is assumed to be independent of deformation. 

Data for a 60 mole % PHB/PET system are shown in Figure 20, We observe at all strain levels that G continues to relax to zero rather than approach a plateau as would be the case when a yield stress exists. The relaxation modulus also seems to be highly stain dependent which is in contrast to the fact that dynamic and steady shear material functions agree so well. For flexible chain polymers the strain dependence of G is associated with the rate of loss of entanglements. For LCP it is not clear as to the significance of the strain dependence of G. 

Non-linear viscoelastic properties were observed for fumed silica-poly(vinyl acetate) (PVAc) composites, with varying PVAc molar mass and including a PVAc copolymer with vinyl alcohol. Dynamic mechanical moduli were measured at low strains and found to decrease with strain depending on surface treatment of the silica. The loss modulus decreased significantly with filler surface treatment and more so with lower molar mass polymer. Copolymers with vinyl alcohol presumably increased interactions with silica and decreased non-linearity. Percolation network formation or agglomeration by silica were less important than silica-polymer interactions. Silica-polymer interactions were proposed to form trapped entanglements. The reinforcement and nonlinear viscoelastic characteristics of PVAc and its vinyl alcohol copolymer were similar to observations of the Payne effect in filled elastomers, characteristic of conformations and constraints of macromolecules. ... 

Fig. 25. Reduced nonlinear stress relaxation modulus as a function of strain for a polymer solution. This plot illustrates the strongly nonlinear or strain-dependent behavior of entangled polymers. After Osaki et al. (80), with permission.

Initially, for characterisation by mechanical spectroscopy, the strain dependence of, for example, the complex shear modulus (G ) is established. Typical results are shown schematically in Figure 2.8. This experiment establishes the linear viscoelastic region of the system, within which the viscoelastic functions are independent of strain. In other words, the applied strain does not perturb the sample. For entanglement networks the linear viscoelastic region extends to approximately 25% strain. 

Figure 2.8 Strain dependence of an entanglement solution or strong gel ( ) and weak gel (o).

In the two classic viscometric deformations of simple shear and extension, the appropriate components of Q have very different behaviour. For small shear strains, the shear stress depends on the component Q which has the linear asymptotic form 47/15. This prefactor is the origin of tne constant v in the tube potential of Sect. 3.For large strains, however, Qxy 7 and therefore predicts strong shear-thinning. Physically this comes from the entanglement loss on re-... 

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