Polymer rheology linear strain

The viscoelastic response of polymer melts, that is, Eq. 3.1-19 or 3.1-20, become nonlinear beyond a level of strain y0, specific to their macromolecular structure and the temperature used. Beyond this strain limit of linear viscoelastic response, if, if, and rj become functions of the applied strain. In other words, although the applied deformations are cyclic, large amplitudes take the macromolecular, coiled, and entangled structure far away from equilibrium. In the linear viscoelastic range, on the other hand, the frequency (and temperature) dependence of if, rf, and rj is indicative of the specific macromolecular structure, responding to only small perturbations away from equilibrium. Thus, these dynamic rheological properties, as well as the commonly used dynamic moduli... 

The linear viscoelastic models (LVE), which are widely used to describe the dynamic rheological response of polymer melts below the strain limit of the linear viscoelastic response of polymers. The results obtained are characteristic of and depend on the macromolecular structure. These are widely used as rheology-based structure characterization tools. 

Measurement of the linear viscoelastic properties is the basic rheological characterization of polymer melts. These properties may he evaluated in the time domain (mainly creep and relaxation experiments) or in the frequency domain in this case we will talk about mechanical spectroscopy, where the sample experiences a harmonic stimulus (either stress or strain). 

The investigation of non-linear behaviour is an active field for many other polymer systems. For example Payne (1962) interpreted a maximum in G" (with respect to strain) in the non-linear behaviour of filled suspensions, which has been denoted the Payne effect. Maier and Goritz (1996) and Wilhelm et al. (2000) examined the use of Fourier-transform analysis of non-sinusoidal waveforms produced by materials exhibiting non-linear behaviour. This concept of using Fourier-transform rheology to characterize the non-linear... 

The complex viscosity as a function of frequency, maximum strain and temperature is generally determined with one rheometer. Standard ASTM 4440-84/90 defines the measurement of rheological parameters of polymer samples using dynamic oscillation. This standard reiterates the importance of determining the linear viscoelastic region prior to performing dynamic frequency sweeps. 

This chapter is devoted to the molecular rheology of transient networks made up of associating polymers in which the network junctions break and recombine. After an introduction to theoretical description of the model networks, the linear response of the network to oscillatory deformations is studied in detail. The analysis is then developed to the nonlinear regime. Stationary nonhnear viscosity, and first and second normal stresses, are calculated and compared with the experiments. The criterion for thickening and thinning of the flows is presented in terms of the molecular parameters. Transient flows such as nonhnear relaxation, start-up flow, etc., are studied within the same theoretical framework. Macroscopic properties such as strain hardening and stress overshoot are related to the tension-elongation curve of the constituent network polymers. 

The rheological properties of polymer blends - and especially of thermosetting polymer blends - share a close relationship to the morphology and reactions involved. Moreover, these properties can cause changes in shear or strain conditions that may lead to dramatic variations in the phase structure and other properties of polymer blends. The time-temperature superposition principle (WLF-type equations) and power laws have been widely applied to the linear viscoelastic behavior of both neat polymers and blends, despite the fact that they may reflect different types of structure transitions for either thermoplastic or thermosetting resins. 

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