Polymers linear viscoelasticity

PP bead foams of a range of densities were compressed using impact and creep loading in an Instron test machine. The stress-strain curves were analysed to determine the effective cell gas pressure as a function of time under load. Creep was controlled by the polymer linear viscoelastic response if the applied stress was low but, at stresses above the foam yield stress, the creep was more rapid until compressed cell gas took the majority of the load. Air was lost from the cells by diffusion through the cell faces, this creep mechanism being more rapid than in extruded foams, because of the small bead size and the open channels at the bead bonndaries. The foam permeability to air conld be related to the PP permeability and the foam density. 15 refs. 

The composite natm e of polyurethane elastomers strongly affects their linear viscoelastic properties. It is known that for most polymers, linear viscoelastic moduli (storage modulus, E u,T), and loss modulus, E" u,T)) are characterized by the so-called time-temperature superposition (TTS) (see, e.g. Ferry [74]). Such behavior can be understood if one assumes that E (and E") is always a function of the product ut T), where t(T) is effective relaxation time. 

Rubinstein, M., Colby, R. H. Self-consistent theory of polydisperse entangled polymers Linear viscoelasticity ofhinary hlends./ Chem. Phys. (1988) 89, pp. 5291-5306... 

At sufficiently low strain, most polymer materials exhibit a linear viscoelastic response and, once the appropriate strain amplitude has been determined through a preliminary strain sweep test, valid frequency sweep tests can be performed. Filled mbber compounds however hardly exhibit a linear viscoelastic response when submitted to harmonic strains and the current practice consists in testing such materials at the lowest permitted strain for satisfactory reproducibility an approach that obviously provides apparent material properties, at best. From a fundamental point of view, for instance in terms of material sciences, such measurements have a limited meaning because theoretical relationships that relate material structure to properties have so far been established only in the linear viscoelastic domain. Nevertheless, experience proves that apparent test results can be well reproducible and related to a number of other viscoelastic effects, including certain processing phenomena. 

C. Friedrich, K. Mattes, and D. Schulze, Non-linear Viscoelastic Properties of Polymer Melts as Analyzed by LAOS-FT Experiments, lUPAC Macro 2004, Paris, France, July 4—9, 2004, Paper 6.1.3. 

Here we describe the strain history with the Finger strain tensor C 1(t t ) as proposed by Lodge [55] in his rubber-like liquid theory. This equation was found to describe the stress in deforming polymer melts as long as the strains are small (second strain invariant below about 3 [56] ). The permanent contribution GcC 1 (r t0) has to be added for a linear viscoelastic solid only. C 1(t t0) is the strain between the stress free state t0 and the instantaneous state t. Other strain measures or a combination of strain tensors, as discussed in detail by Larson [57], might also be appropriate and will be considered in future studies. A combination of Finger C 1(t t ) and Cauchy C(t /. ) strain tensors is known to express the finite second normal stress difference in shear, for instance. 

Factorizability has also been found to apply to polymer solutions and melts in that both constant rate of shear and dynamic shear results can be analyzed in terms of the linear viscoelastic response and a strain function. The latter has been called a damping function (67,68). 

We have developed the idea that we can describe linear viscoelastic materials by a sum of Maxwell models. These models are the most appropriate for describing the response of a body to an applied strain. The same ideas apply to a sum of Kelvin models, which are more appropriately applied to stress controlled experiments. A combination of these models enables us to predict the results of different experiments. If we were able to predict the form of the model from the chemical constituents of the system we could predict all the viscoelastic responses in shear. We know that when a strain is applied to a viscoelastic material the molecules and particles that form the system gradual diffuse to relax the applied strain. For example, consider a solution of polymer... 

The term y(t,t ) is the shear strain at time t relative to the strain at time t. The use of a memory function has been adopted in polymer modelling. For example this approach is used by Doi and Edwards11 to describe linear responses of solution polymers which they extended to non-linear viscoelastic responses in both shear and extension. 

This section is primarily concerned with the behaviour of simple homo-polymers. The development of viscoelastic theory was intimately linked with the study of polymeric species. This area of activity has led the way in the development of rheological models and experimental design and so is a very important area for the proto-rheologist to understand. So far in this chapter we have taken the approach of developing phase diagrams from a rheological perspective in order to understand linear viscoelastic... 

The application of finite strains and stresses leads to a very wide range of responses. We have seen in Chapters 4 and 5 well-developed linear viscoelastic models, which were particularly important in the area of colloids and polymers, where unifying features are readily achievable in a manner not available to atomic fluids or solids. In Chapter 1 we introduced the Peclet number ... 

Contents Chain Configuration in Amorphous Polymer Systems. Material Properties of Viscoelastic Liquids. Molecular Models in Polymer Rheology. Experimental Results on Linear Viscoelastic Behavior. Molecular Entan-lement Theories of Linear iscoelastic Behavior. Entanglement in Cross-linked Systems. Non-linear Viscoelastic-Properties. 

When Zotefoam HDPE materials of density 98 kg m" were subjected to a single major compressive impact (419), after recovery at 50 °C for 1 hour, the performance, defined as the energy density absorbed before the compressive stress reached 2.5 MPa was back to 75% of the initial value. Further severe impacts caused a further deterioration of the performance of the recovered foam. Peak compressive strains of 80 to 90% caused some permanent buckling of the cell walls of HDPE foams. The recovery is much slower than the 0.1 second impact time, so is not a conventional linear viscoelastic response. It must be driven by the compressed air in internal cells in the gas, with some contribution from viscoelasticity of the polymer. Recovery of dimensions had slowed to a very low rate after 10 seconds at 20 °C or after 10 seconds at 50 °C. 

The effect of gas compression on the uniaxial compression stress-strain curve of closed-cell polymer foams was analysed. The elastic contribution of cell faces to the compressive stress-strain curve is predicted quantitatively, and the effect on the initial Young s modulus is said to be large. The polymer contribution was analysed using a tetrakaidecahedral cell model. It is demonstrated that the cell faces contribute linearly to the Young s modulus, but compressive yielding involves non-linear viscoelastic deformation. 3 refs. 

Only a few non-linear viscoelastic properties have been studied with polymers of well-characterized structure. The most prominent of these is the shear-rate dependence of viscosity. Considerable data have now been accumulated for several polymers, extending over a wide range of molecular weights and concen-... 

The Eyring analysis does not explicity take chain structures into account, so its molecular picture is not obviously applicable to polymer systems. It also does not appear to predict normal stress differences in shear flow. Consequently, the mechanism of shear-rate dependence and the physical interpretation of the characteristic time t0 are unclear, as are their relationships to molecular structure and to cooperative configurational relaxation as reflected by the linear viscoelastic behavior. At the present time it is uncertain whether the agreement with experiment is simply fortuitous, or whether it signifies some kind of underlying unity in the shear rate dependence of concentrated systems of identical particles, regardless of their structure and the mechanism of interaction. 

Rouse, P.E. A theory of the linear viscoelastic properties of dilute solutions of coiling polymers. J. Chem. Phys. 21,1272-1280 (1953). 

Graessley,W.W. Linear viscoelasticity in entangling polymer systems. J. Chem. Phys. 54, 5143-5157 (1971). 

Forsman,W.C., Grand, H.S. Theory of entanglement effects in linear viscoelastic behavior of polymer solutions and melts. I. Symmetry considerations. Macromolecules 5,289-293 (1972). 

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