Linear viscoelasticity structure-property

Mechanical properties of plastics are invariably time-dependent. Rheology of plastics involves plastics in all possible states from the molten state to the glassy or crystalline state (Chapter 6). The rheology of solid plastics within a range of small strains, within the range of linear viscoelasticity, has shown that mechanical behavior has often been successfully related to molecular structure. Studies in this area can have two objectives (1) mechanical characterization of... 

Since these double-base proplnts consist essentially of a single phase which bears the total load in any application of force, their mechanical property behavior is significantly different from composite proplnts. In the latter formulations, the hydrocarbon binder comprises only about 14% of the composite structure, the remainder being solid particles. Under stress, the binder of these proplnts bears a proportionately higher load than that in the single phase double-base proplnts. At small strain levels, these proplnts behave in a linear viscoelastic manner where the solids reinforce the binder. As strain increases, the bond between the oxidizer and binder breaks down... 

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. 

The surface characteristics of these species are determined by the particulates and stress transfer across the membrane will tend to be low, reducing internal circulation within the drop. The structure of the interface surrounding the drop plays a significant role in determining the characteristics of the droplet behaviour. We can begin our consideration of emulsion systems by looking at the role of this layer in determining linear viscoelastic properties. This was undertaken by... 

Quantitative evidence regarding chain entanglements comes from three principal sources, each solidly based in continuum mechanics linear viscoelastic properties, the non-linear properties associated with steady shearing flows, and the equilibrium moduli of crosslinked networks. Data on the effects of molecular structure are most extensive in the case of linear viscoelasticity. The phenomena attributed to chain entanglement are very prominent here, and the linear viscoelastic properties lend themselves most readily to molecular modeling since the configuration of the system is displaced for equilibrium only slightly by the measurement. 

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 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... 

Linear viscoelasticity is the simplest type of viscoelastic behavior, in which viscoelastic properties are independent of the magnitude of applied stress or strain (Barnes et al., 1989 Gunasekaran and Ak, 2002). Linear viscoelasticity is usually exhibited by food materials at very small strains (Rao, 1992) that cause negligible damage to the food s structure the phenomenon must therefore be investigated experimentally using small deformation test methods. 

In addition, other measurement techniques in the linear viscoelastic range, such as stress relaxation, as well as static tests that determine the modulus are also useful to characterize gels. For food applications, tests that deal with failure, such as the dynamic stress/strain sweep to detect the critical properties at structure failure, the torsional gelometer, and the vane yield stress test that encompasses both small and large strains are very useful. 

The ability of a polymer to effectively dissipate energy as part of a structure can be related to its linear viscoelastic properties. These are measured by dynamic mechanical analysis. 

It is commonplace for rheologists to investigate the linear viscoelastic properties of materials and, indeed, this is certainly the case in the pharmaceutical and related sciences. Bird et al. (24) and Barnes et al. (2) have suggested several reasons for this, including the ability to derive speculative molecular structures of materials from their rheological response in the linear viscoelastic region and, additionally, the ability to relate the parameters derived from the linear viscoelastic response to quality control procedures and, in some instances, to clinical response (7,9,19,25-27). Furthermore, the mathematical principles associated with the linear viscoelastic response are less complex than those for nonlinear viscoelasticity, thus ensuring relatively simple interpretations of results. 

When we progress from the foregoing qualitative discussion of structure-property relationships to the quantitative specification of mechanical properties, we enter a jungle that has been only partially explored. The most convenient point of departure into this large and complex subject is provided by the topic of "linear viscoelasticity." Linear viscoelasticity represents a relatively simple extension of classical (small-strain) theory of elasticity. In situations where linear viscoelasticity applies, the mechanical properties can be determined from a few experiments and can be specified in any of several equivalent formulations (11). 

Overall, the regime of linear viscoelasticity is characterized by reasonable success in establishing structure-property relationships. The properties themselves are unambiguously and simply specifiable. The relevant structural features are largely recognizable aspects of molecular structure. Molecular theories exist that provide a bridge between the molecular structure and the macroscopic viscoelastic properties. 

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. 

Rheological studies of PET nanocomposites are not ample, but show very interesting features. In the low frequency range, the nanocomposites display a more elastic behavior than that of PET. It appears that there are some physical network structures formed due to filler interactions, collapsed by shear force, and after all the interactions have collapsed, the melt state becomes isotropic and homogeneous. Linear viscoelastic properties of polycaprolactone and Nylon-6 [51] with MMT display a pseudo-solidlike behavior in the low frequency range of... 

Linear viscoelasticity is valid only imder conditions where structural changes in the material do not induce strain-dependent modulus. This condition is fulfilled by amorphous polymers. On the other hand, the structural changes associated with the orientation of crystalline polymers and elastomers produce anisotropic mechanical properties. Such polymers, therefore, exhibit nonlinear viscoelastic behavior. 

Qualitatively, the stress created by imposing oscillatory strains will be a function of the amplitude of strain, its frequency, and the properties of the polymeric solution. By applying sufficiently small strains, we can minimize the strain dependency from the material response. Thus, the amplitude of strain is no longer an important consideration, resulting in a linear viscoelastic response. Small strain measurements can be important for certain application as they do not adversely affect the structure of the fluid. 

The coated material used on the pipe is usually a viscoelastic layer adhered on the pipe. The internal losses in the coated material are modeled according to the theory of linear viscoelasticity, which is also the model implemented in the software DISPERSE [17] used for the wave structure analysis. The shear velocity and shear attenuation of bitumen are obtained from the result of Simonetti measurement [16] for the software used to predict the attenuation of guided wave. The material properties of the other two coated materials are found from the data bank in the DISPERSE software. The theory of linear viscoelasticity for isotropic and homogenous media is modeled in the frequency domain, which leads to linear equation of motion [18]. Thus... 

The aim is to review the linear viscoelastic behaviour of NR and components that can be added to compositions to impart non-linear viscoelastic behaviour. Non-linear viscoelastic behaviour enhances mechanical damping properties. Damping can be bought about by use of alternate chemical structures to NR, however often it is convenient to enhance properties of existing materials. 

Entanglements of flexible polymer chains contribute to non-linear viscoelastic response. Motions hindered by entanglements are a contributor to dielectric and diffusion properties since they constrain chain dynamics. Macromolecular dynamics are theoretically described by the reptation model. Reptation includes fluctuations in chain contour length, entanglement release, tube dilation, and retraction of side chains as the molecules translate using segmental motions, through a theoretical tube. The reptation model shows favourable comparison with experimental data from viscoelastic and dielectric measurements. The model reveals much about chain dynamics, relaxation times and molecular structures of individual macromolecules. 

Chazeau L, Cavaille JY, Canova G et al (1999a) Viscoelastic properties of plasticized PVC reinforced with cellulose whiskers. J Appl Polym Sci 71 1797-1808 Chazeau L, Cavaille JY, Terech P (1999b) Mechanical behaviour above Tg of a plasticised PVC reinforced with cellulose whiskers a SANS structural study. Polymer 40 5333-5344 Chazeau L, Paillet M, Cavaille JY (1999c) Plasticized PVC reinforced with cellulose whiskers. I. Linear viscoelastic behavior analyzed through the quasi-point defect theory. J Polym Sci Part B Polym Phys 37 2151-2164... 

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