Viscoelastic loss moduli

Preliminary nanoindentation results on other teeth (premolars, incisors and canines) indicate variations in mechanical properties as large as those discussed for molars [unpubl. data]. In each case the exact distribution of mechanical properties within the enamel appears to correlate with the extent of mechanical loading experienced by the tooth during mastication. However, there appears to be an increase in the viscoelasticity (loss modulus) for the enamel of anterior teeth when compared to posterior teeth, again this may be related to their function. 

The radiation and temperature dependent mechanical properties of viscoelastic materials (modulus and loss) are of great interest throughout the plastics, polymer, and rubber from initial design to routine production. There are a number of laboratory research instruments are available to determine these properties. All these hardness tests conducted on polymeric materials involve the penetration of the sample under consideration by loaded spheres or other geometric shapes [1]. Most of these tests are to some extent arbitrary because the penetration of an indenter into viscoelastic material increases with time. For example, standard durometer test (the "Shore A") is widely used to measure the static "hardness" or resistance to indentation. However, it does not measure basic material properties, and its results depend on the specimen geometry (it is difficult to make available the identity of the initial position of the devices on cylinder or spherical surfaces while measuring) and test conditions, and some arbitrary time must be selected to compare different materials. 

A viscoelastic material also possesses a complex dynamic viscosity, rj = rj - - iv( and it can be shown that r = G jiuj-, rj = G juj and rj = G ju), where CO is the angular frequency. The parameter Tj is useful for many viscoelastic fluids in that a plot of its absolute value Tj vs angular frequency in radians/s is often numerically similar to a plot of shear viscosity Tj vs shear rate. This correspondence is known as the Cox-Merz empirical relationship. The parameter Tj is called the dynamic viscosity and is related to G the loss modulus the parameter Tj does not deal with viscosity, but is a measure of elasticity. 

Fig. 21. Dynamic viscoelastic properties of a low density polyethylene (LDPE) at 150°C complex dynamic viscosity Tj, storage modulus G and loss modulus G" vs angular velocity, CO. To convert Pa-s to P, multiply by 10 to convert Pa to dyn/cm, multiply by 10.

The extent of the solid-like character, i.e. the strength of the samples, can be directly described by the storage modulus G. As both moduli rised during gelation, it seemed to be more efficient to take the ratio of G to G , describing the dominant elastic character of the viscoelastic sample, as a second characteristic quantity than to use the loss modulus G" itself. 

For a viscoelastic solid, the loss modulus which reflects the viscous processes in the material is unaffected by the presence of a spring without a dashpot. The storage modulus includes the elastic component G(0) ... 

Lu et al. [7] extended the mass-spring model of the interface to include a dashpot, modeling the interface as viscoelastic, as shown in Fig. 3. The continuous boundary conditions for displacement and shear stress were replaced by the equations of motion of contacting molecules. The interaction forces between the contacting molecules are modeled as a viscoelastic fluid, which results in a complex shear modulus for the interface, G = G + mG", where G is the storage modulus and G" is the loss modulus. G is a continuum molecular interaction between liquid and surface particles, representing the force between particles for a unit shear displacement. The authors also determined a relationship for the slip parameter Eq. (18) in terms of bulk and molecular parameters [7, 43] ... 

Fig. 6 Variation of viscoelastic properties as a function of strain amplitude of uncrosslinked and dynamically vulcanized blends at 180°C (a) storage modulus, (b) loss modulus. CD2 TPV prepared by preblending, PD2 TPV prepared by phase mixing, SD2 TPV prepared by split addition...

Gels are viscoelastic bodies, the rheological properties of which can be described by two parameters, the storage modulus (G, which is a measure of its elasticity) and the loss modulus (G", which is a measure of its viscous nature). The combined viscoelastic modulus (G ) is a measure of the overall resistance of a gel to deformation. These moduli are often highly dependent on the time-scale of deformation. Another important parameter of a food gel is its yield stress. 

Figure H3.2.4 Linear viscoelastic region as determined by the strain dependence of G (storage modulus) and G (loss modulus).

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. 

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