Elastic properties viscoelasticity

The elastic and viscoelastic properties of materials are less familiar in chemistry than many other physical properties hence it is necessary to spend a fair amount of time describing the experiments and the observed response of the polymer. There are a large number of possible modes of deformation that might be considered We shall consider only elongation and shear. For each of these we consider the stress associated with a unit strain and the strain associated with a unit stress the former is called the modulus, the latter the compliance. Experiments can be time independent (equilibrium), time dependent (transient), or periodic (dynamic). Just to define and describe these basic combinations takes us into a fair amount of detail and affords some possibilities for confusion. Pay close attention to the definitions of terms and symbols. 

The various elastic and viscoelastic phenomena we discuss in this chapter will be developed in stages. We begin with the simplest the case of a sample that displays a purely elastic response when deformed by simple elongation. On the basis of Hooke s law, we expect that the force of deformation—the stress—and the distortion that results-the strain-will be directly proportional, at least for small deformations. In addition, the energy spent to produce the deformation is recoverable The material snaps back when the force is released. We are interested in the molecular origin of this property for polymeric materials but, before we can get to that, we need to define the variables more quantitatively. 

Fluids without any sohdlike elastic behavior do not undergo any reverse deformation when shear stress is removed, and are called purely viscous fluids. The shear stress depends only on the rate of deformation, and not on the extent of derormation (strain). Those which exhibit both viscous and elastic properties are called viscoelastic fluids. 

The viscoelasticity is a combination of viscous and elastic properties in a plastic with... 

Viscoelasticity A combination of viscous and elastic properties in a plastic with the relative contribution of each being dependent on time, temperature, stress, and strain rate. It relates to the mechanical behavior of plastics in which there is a time and temperature dependent relationship between stress and strain. A material having this property is considered to combine the features of a perfectly elastic solid and a perfect fluid. 

Many materials of practical interest (such as polymer solutions and melts, foodstuffs, and biological fluids) exhibit viscoelastic characteristics they have some ability to store and recover shear energy and therefore show some of the properties of both a solid and a liquid. Thus a solid may be subject to creep and a fluid may exhibit elastic properties. Several phenomena ascribed to fluid elasticity including die swell, rod climbing (Weissenberg effect), the tubeless siphon, bouncing of a sphere, and the development of secondary flow patterns at low Reynolds numbers, have recently been illustrated in an excellent photographic study(18). Two common and easily observable examples of viscoelastic behaviour in a liquid are ... 

It is likely that most biomaterials possess non-linear elastic properties. However, in the absence of detailed measurements of the relevant properties it is not necessary to resort to complicated non-linear theories of viscoelasticity. A simple dashpot-and-spring Maxwell model of viscoelasticity will provide a good basis to consider the main features of the behaviour of the soft-solid walls of most biomaterials in the flow field of a typical bioprocess equipment. 

Equation (52) allows us to estimate the impact of viscoelastic braking on the capillary flow rate. As an example, we will consider that the liquid is tricresyl phosphate (TCP, 7 = 50 mN-m t = 0.07 Pa-s). The viscoelastic material is assumed to have elastic and viscoelastic properties similar to RTV 615 (General Electric, silicone rubber), i.e., a shear modulus of 0.7 MPa (E = 2.1 MPa), a cutoff length of 20 nm, and a characteristic speed, Uo, of 0.8 mm-s [30]. TCP has a contact angle at equilibrium of 47° on this rubber. 

Anseth et al. [20] have reviewed the literature dealing with the mechanical properties of hydrogels and have considered in detail the effects of gel molecular structure, e.g., cross-linking, on bulk mechanical properties using theories of rubber elasticity and viscoelasticity. 

Actually, some fluids and solids have both elastic (solid) properties and viscous (fluid) properties. These are said to be viscoelastic and are most notably materials composed of high polymers. The complete description of the rheological properties of these materials may involve a function relating the stress and strain as well as derivatives or integrals of these with respect to time. Because the elastic properties of these materials (both fluids and solids) impart memory to the material (as described previously), which results in a tendency to recover to a preferred state upon the removal of the force (stress), they are often termed memory materials and exhibit time-dependent properties. 

This document gives definitions of terms related to the non-ultimate mechanical behaviour or mechanical behaviour prior to failure of polymeric materials, in particular of bulk polymers and concentrated solutions and their elastic and viscoelastic properties. 

Silicone oils have very desirable visco-elastic properties, and are very stable. They have been used for many years for breast implants, as a cosmetic to improve appearance. There are many lawsuits charging that silicone oil can leak out of the containing sacks and cause adverse physiological reactions. The current customers either abandon the breast implant or use salt water implants, which do not have the same desirable viscoelastic properties. 

Elastic properties usually have a negligible effect on resistance to flow in straight pipes, but examples have been noted that the resistances of fittings may be as much as 10 times as great for viscoelastic liquids as for Newtonian ones. 

Thus, the problem of flow of a viscoelastic fluid between two flat parallel plates one of which is moving in a direction transverse to the main flow is reduced to a solution of simplified system (7) at boundary conditions (1). Analysis of relationships (7) for specific boundary conditions indicates that the problem is reduced to the case of a non-Newtonian viscous fluid. In other words, the velocity profile v(y) is determined only by viscous characteristics of the media and the effect of high-elasticity properties of the melt upon velocity (flow rate) characteristics of the flow can be neglected. 

Laws and McLaughlin30 discuss viscoelastic creep compliances of composite materials using another approach to the problem of the elastic properties of heterogeneous materials - the self-consistent method. 

The human erythrocyte possesses a characteristic biconcave shape and remarkable viscoelastic properties. Electron microscopy studies performed on red blood cells (RBC), ghosts, and skeletons revealed a two-dimensional lattice of cytoskeletal proteins. This meshwork of proteins was thought to determine the elastic properties of the RBC. This... 

Fibrin is a viscoelastic polymer, which means that it has both elastic and viscous properties (Ferry, 1988). Thus, the properties of fibrin may be characterized by stiffness or storage modulus (representing its elastic properties) and creep compliance or loss modulus/loss tangent (representing its inelastic properties). These parameters will determine how the clot responds to the forces applied to it in flowing blood. For example, a stiff clot will not deform as much as a less stiff one with applied stress. 

The physical properties of barrier dressings were evaluated using the Seiko Model DMS 210 Dynamic Mechanical Analyzer Instrument (see Fig. 2.45). Referring to Fig. 2.46, dynamic mechanical analysis consists of oscillating (1 Hz) tensile force of a material in an environmentally (37°C) controlled chamber (see Fig. 2.47) to measure loss modulus (E") and stored modulus (E ). Many materials including polymers and tissue are viscoelastic, meaning that they deform (stretch or pull) with applied force and return to their original shape with time. The effect is a function of the viscous property (E") within the material that resists deformation and the elastic property (E )... 

Effect of Crosslink Density on Elastic and Viscoelastic Properties... 

The effect (or lack of effect) of crosslinks on basic physical properties of thermosetting polymers is discussed in Chapter 10, while the effect on elastic and viscoelastic properties is analyzed in Chapter 11. Yielding and fracture of neat and modified thermosetting polymers are discussed in Chapters 12 and 13. Finally, the very important problem of the durability of polymer networks is presented in Chapter 14. 

These new variables are necessary to take into account viscoelastic effects linked to molecular motions. These effects are non-negligible in the glassy domain between boundaries a and (3 in the map of Fig. 11.2, and they are very important in the glass transition region (around boundary a). Here, we need relationships that express the effects of s, d (the stress rate may be used instead of the strain rate), and T on the previously defined elastic properties. Also numerical boundary values of elastic properties are required, characterizing unrelaxed and relaxed states (see Chapter 10). 

---