Viscoelastic properties definition

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. 

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. 

To compile the definitions, a number of sources have been used. A number of the definitions were adapted from an International Organization for Standardization (ISO) manuscript on Plastics Vocabulary [1]. Where possible, the names for properties, their definitions and the symbols for linear viscoelastic properties were checked against past compilations of terminology [2-6]. Other documents consulted include ASTM publications [7-13]. 

Note 7 There are definitions of linear viscoelasticity which use integral equations instead of the differential equation in Definition 5.2. (See, for example, [11].) Such definitions have certain advantages regarding their mathematical generality. However, the approach in the present document, in terms of differential equations, has the advantage that the definitions and descriptions of various viscoelastic properties can be made in terms of commonly used mechano-mathematical models (e.g. the Maxwell and Voigt-Kelvin models). 

Before we discuss the viscoelastic properties of nonuniform fractal structures we shall give some basic definitions from the theory of elasticity. 

A definitive advance was made with the introduction of viscoelastic substances in anterior segment surgery (Balazs, 1983 Balazs, 1984 Balazs, 1986). Viscoelastic substances (ophthalmic viscosurgical devices, OVD), a class of nonactive surgical implants with viscous and/or viscoelastic properties were intended for use during surgery in the anterior segment of the eye. 

The anisotropic viscoelastic properties in shear of the meniscus have been determined by subjecting discs of meniscal tissue to sinusoidal torsional loading [35](Table B2.8). The specimens were cut in the three directions of orthotropic symmetry, i.e. circumferential, axial and radial. A definite correlation is seen with the orientation of the fibers and both the magnitude of the dynamic modulus IG I and the phase angle 8. 

Definition of terms relating to the non-ultimate mechanical properties of polymers. " This document defines mechanical terms of significance prior to failure of polymers. It deals in particular with bulk polymers and concentrated polymer solutions and their respective viscoelastic properties. It contains the basic definitions of experimentally observed stress, strain, deformations, viscoelastic properties, and the corresponding quantities that are commonly met in conventional mechanical characterization of polymeric materials. Definitions from ISO and ASTM publications are adapted. Only isotropic polymeric materials are considered. 

Gelation is defined as the point during polymerization when the polymer transforms from a hquid to a rubbery state [97]. At the molecular level, this correlates to the moment at which the molecular weight approaches infinity upon incipient formation of a cross-linked network. Macroscopically, gelation is defined as an abrupt increase in viscosity after which the polymer loses its ability to flow and develops viscoelastic properties. The macroscopic definition of gelation does not necessarily correlate to gelation at the molecular level, since hnear polymers... 

There was clearly a distinction in the viscosity and viscoelastic properties between the virgin copolymer and the other three materials. The natural PCR material behaved in a similar fashion to the virgin homopolymer, but with less definition in the changes from 0 to 4 passes. 

In the theories for dilute solutions of flexible molecules based on the bead-spring model, the contribution of the solute to the storage shear modulus, loss modulus, or relaxation modulus is given by a series of terms the magnitude of each of which is proportional to nkT, i.e., to cRTjM, as in equation 18 of Chapter 9 alternatively, the definition of [C ]y as the zero-concentration limit of G M/cRT (equations 1 and 6 of Chapter 9) implies that all contributions are proportional to nkT. Each contribution is associated with a relaxation time which is proportional to [ri Ti)sM/RT-, the proportionality constant (= for r i) depends on which theory applies (Rouse, Zimm, etc.) but is independent of temperature, as is evident, for example, in equation 27 of Chapter 9. Thus the temperature dependence of viscoelastic properties enters in four variables [r ], t/j, T explicitly, and c (which decreases slightly with increasing temperature because of thermal expansion). 

It is also clear that activity of a filler should be related to any definite property of material. It was proposed to introduce the concept of structural, kinetic, and thermod3uiamic activity of fillers. Structural activity of a filler is its abihty to change the polymer structure on molecular and submolecular level (crystallinity degree, size and shape of submolecular domains, and their distribution, crosslink density for network pol3rmers, etc.). Kinetic activity of a filler means the ability to change molecular mobility of macromolecides in contact with a solid surface and affect in such a way the relaxation and viscoelastic properties. Finally, thermodynamic activity is a filler s ability to influence the state of thermodynamic equilibrium, phase state, and thermodynamic parameters of filled polymers — especially important for filled poljmier blends (see Chapter 7). 

The presence of a low-viscosity interfacial layer makes the determination of the boundary condition even more difficult because the location of a slip plane becomes blurred. Transitional layers have been discussed in the previous section, but this is an approximate picture, since it stiU requires the definition of boundary conditions between the interfacial layers. A more accurate picture, at least from a mesoscopic standpoint, would include a continuous gradient of material properties, in the form of a viscoelastic transition from the sohd surface to the purely viscous liquid. Due to limitations of time and space, models of transitional gradient layers will be left for a future article. 

Several researchers reported viscoelastic behavior of yeast suspensions. Labuza et al. [9] reported shear-thinning behavior of baker s yeast (S. cerevisiae) in the range of 1 to 100 reciprocal seconds at yeast concentrations above 10.5% (w/w). The power law model was successfully applied. More recently, Mancini and Moresi [10] also measured the rheological properties of baker s yeast using different rheometers in the concentration range of 25 to 200 g dm. While the Haake rotational viscometer confirmed Labuza s results on the pseudoplastic character of yeast suspension, the dynamic stress rheometer revealed definitive Newtonian behavior. This discrepancy was attributed to the lower sensitivity of Haake viscometer in the range of viscosity tested (1.5 to 12 mPa s). Speers et al. [11] used a controlled shear-rate rheometer with a cone-and-plate system to measure viscosity of... 

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