Linear viscoelasticity polymer materials

The initial elastic response in this case is o = fie. Similar to the creep compliance, a linear viscoelastic polymer has a relaxation modulus T(t), which is a characteristic material property. 

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. 

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... 

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. 

Our reason for stressing the concept of representative volume element is that it seems to provide a valuable dividing boundary between continuum theories and molecular or microscopic theories. For scales larger than the RVE we can use continuum mechanics (classical and large strain elasticity, linear and non-linear viscoelasticity) and derive from experiment useful and reproducible properties of the material as a whole and of the RVE in particular. Below the scale of the RVE we must consider the micromechanics if we can - which may still be analysable by continuum theories but which eventually must be studied by the consideration of the forces and displacements of polymer chains and their interactions. 

In spite of the apparent sensitivity to the material properties, the direct assignment of the phase contrast to variation in the chemical composition or a specific property of the surface is hardly possible. Considerable difficulties for theoretical examination of the tapping mode result from several factors (i) the abrupt transition from an attractive force regime to strong repulsion which acts for a short moment of the oscillation period, (ii) localisation of the tip-sample interaction in a nanoscopic contact area, (iii) the non-linear variation of both attractive forces and mechanical compliance in the repulsive regime, and (iv) the interdependence of the material properties (viscoelasticity, adhesion, friction) and scanning parameters (amplitude, frequency, cantilever position). The interpretation of the phase and amplitude images becomes especially intricate for viscoelastic polymers. 

Viscoelasticity has already been introduced in Chapter 1, based on linear viscoelasticity. However, in polymer processing large deformations are imposed on the material, requiring the use of non-linear viscoelastic models. There are two types of general non-linear viscoelastic flow models the differential type and the integral type. 

The analysis viscoelasticity performed by David Roylance [25] is a nice outline about the mechanical response of polymer materials. This author consider that viscoelastic response is often used as a probe in polymer science, since it is sensitive to the material s chemistry and microstructure [25], While not all polymers are viscoelastic to any practical extent, even fewer are linearly viscoelastic [24,25], this theory provide a usable engineering approximation for many applications in polymer and composites engineering. Even in instances requiring more elaborate treatments, the linear viscoelastic theory is a useful starting point. 

The slip of viscoelastic polymeric materials (and flow instabilities) was reviewed in detail by Denn (6). Apparent slip at the wall was observed with highly entangled linear polymers, but not with branched polymers or linear polymers with insufficient numbers of... 

Linear amorphous polymers can behave as either Hookian elastic (glassy) materials, or highly elastic (rubbery) substances or as viscous melts according to prevailing temperature and time scale of experiments. The different transitions as shown schematically in Figure 5.1 are manifestations of viscoelastic deformations, which are time dependent [1]. 

New heterocyclic polymers designed especially for service at elevated temperatures have intriguing properties, some of which are in contrast to properties usually associated with linear noncrystalline polymers. These polymers have sometimes been described as stiff chains because of the long inflexible repeat units of which they are comprised. Relatively few quantitative studies have yet appeared in the dilute solution properties or the viscoelastic behavior of the new heterocyclic polymers—partly because of the difficulties inherent in working with the poorly soluble materials. Some studies on the polyimide with the (idealized) structure ... 

On a global scale, the linear viscoelastic behavior of the polymer chains in the nanocomposites, as detected by conventional rheometry, is dramatically altered when the chains are tethered to the surface of the silicate or are in close proximity to the silicate layers as in intercalated nanocomposites. Some of these systems show close analogies to other intrinsically anisotropic materials such as block copolymers and smectic liquid crystalline polymers and provide model systems to understand the dynamics of polymer brushes. Finally, the polymer melt-brushes exhibit intriguing non-linear viscoelastic behavior, which shows strainhardening with a characteric critical strain amplitude that is only a function of the interlayer distance. These results provide complementary information to that obtained for solution brushes using the SFA, and are attributed to chain stretching associated with the space-filling requirements of a melt brush. 

We will begin with a brief survey of linear viscoelasticity (section 2.1) we will define the various material functions and the mathematical theory of linear viscoelasticity will give us the mathematical bridges which relate these functions. We will then describe the main features of the linear viscoelastic behaviour of polymer melts and concentrated solutions in a purely rational and phenomenological way (section 2.2) the simple and important conclusions drawn from this analysis will give us the support for the molecular models described below (sections 3 to 6). 

It consists in developing numerical and analytical methods to invert a linear viscoelastic material fimction to determine the molecular weight distribution. There are several reasons to pursue such an objective many commercial polymers are slightly or not at aU soluble in usual solvents, thus techniques like gel permeation chromatography or light scattering are inapplicable. Rheological characterization can be performed on-line and in real time and it is also a less cots-effective technique. 

Polymeric fluids are the most studied of all complex fluids. Their rich rheological behavior is deservedly the topic of numerous books and is much too vast a subject to be covered in detail here. We must therefore limit ourselves to an overview. The interested reader can obtain more thorough presentations in the following references a book by Ferry (1980), which concentrates on the linear viscoelasticity of polymeric fluids, a pair of books by Bird et al. (1987a,b), which cover polymer constitutive equations, molecular models, and elementary fluid mechanics, books by Tanner (1985), by Dealy and Wissbrun (1990), and by Baird and Dimitris (1995), which emphasize kinematics and polymer processing flows, a book by Macosko (1994) focusing on measurement methods and a book by Larson (1988) on polymer constitutive equations. Parts of this present chapter are condensed versions of material from Larson (1988). The static properties of flexible polymer molecules are discussed in Section 2.2.3 their chemistry is described in Flory (1953). 

All the analysis so far described has assumed that the material is linearly elastic. Almost all polymers, however, show some evidence of time dependence and are viscoelastic. Since we are generally concerned with small strain behaviour for brittle cracks, it is reasonable to suppose that the materials are linearly viscoelastic so that, for example, when computing a strain from a stress, we caimot write ... 

Ageing plays a key role in the non-linear viscoelastic behaviour of polymers. When left at rest and at constant temperature, there is continuous stiffening. However, when the aged material is slightly heated or mechanically deformed, it is deaged and softened (Struik, 1978, 1983). 

Linear mechanical properties of the networks and gels discussed in this chapter are measured with the same methods of linear viscoelasticity as the polymer liquids (melts and solutions) discussed in Chapters 8 and 9. The various methods are described here, with examples pertaining to each class of materials. 

Keywords Elastohydrodynamic interactions Glass transition Linear viscoelasticity Nonlinear rheology Polymer-colloid materials Shear-thinning Wall slip... 

The accurate applicability of linear viscoelasticity is limited to certain restricted situations amorphous polymers, temperatures near or above the glass temperature, homogeneous, isotropic materials, small strains, and absence of mechanical failure phenomena. Thus, the theory of linear viscoelasticity is of limited direct applicability to the problems encounted in the fabrication and end use of polymeric materials (since most of these problems involve either large strains, crystalline polymers, amorphous polymers in a glass state failure phenomena, or some combination of these disqualifying features). Even so, linear viscoelasticity is a most important subject in polymer materials science—directly applicable in a minority of practical problems, but indirectly useful (as a point of reference) in a much wider range of problems. 

The linear viscoelastic properties in the melt state of highly grafted polymers on spherical silica nanoparticles are probed using linear dynamic oscillatory measurements and linear stress relaxation measurements. While the pure silica tethered polymer nanocomposite exhibits solid-like response, the addition of a matched molecular weight free matrix homopolymer chains to this hybrid material, initially lowers the modulus and later changes the viscoelastic response to that of a liquid. These results are consistent with the breakdown of the ordered mesoscale structure, characteristic of the pure hybrid and the high hybrid concentration blends, by the addition of homopolymers with matched molecular weights. 

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