Viscoelasticity storage modulus

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.

Adsorption of rubber over the nanosilica particles alters the viscoelastic responses. Analysis of dynamic mechanical properties therefore provides a direct clue of the mbber-silica interaction. Figure 3.22 shows the variation in storage modulus (log scale) and tan 8 against temperature for ACM-silica, ENR-silica, and in situ acrylic copolymer and terpolymer-silica hybrid nanocomposites. 

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] ... 

The static modulus and dynamic storage modulus were investigated for some open-celled PE foams by static compression tests and dynamic viscoelastic measurements in compression mode. Experimental data were compared with theoretical predictions. 8 refs. 

The dynamic storage modulus of closed-cell PE foams was investigated by dynamic viscoelastic measurement in the compression mode. It was found that dynamic modulus correlated with compression hardness and that the resistance against pressure inside the cells had no effect upon static modulus or dynamic storage modulus. 8 refs. 

The dynamic mechanical thermal analyzer (DMTA) is an important tool for studying the structure-property relationships in polymer nanocomposites. DMTA essentially probes the relaxations in polymers, thereby providing a method to understand the mechanical behavior and the molecular structure of these materials under various conditions of stress and temperature. The dynamics of polymer chain relaxation or molecular mobility of polymer main chains and side chains is one of the factors that determine the viscoelastic properties of polymeric macromolecules. The temperature dependence of molecular mobility is characterized by different transitions in which a certain mode of chain motion occurs. A reduction of the tan 8 peak height, a shift of the peak position to higher temperatures, an extra hump or peak in the tan 8 curve above the glass transition temperature (Tg), and a relatively high value of the storage modulus often are reported in support of the dispersion process of the layered silicate. 

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. 

In a rheomety experiment the two plates or cylinders are moved back and forth relative to one another in an oscillating fashion. The elastic storage modulus (G - The contribution of elastic, i.e. solid-like behaviour to the complex dynamic modulus) and elastic loss modulus (G" - The contribution of viscous, i.e. liquid-like behaviour to the complex modulus) which have units of Pascals are measured as a function of applied stress or oscillation frequency. For purely elastic materials the stress and strain are in phase and hence there is an immediate stress response to the applied strain. In contrast, for purely viscous materials, the strain follows stress by a 90 degree phase lag. For viscoelastic materials the behaviour is somewhere in between and the strain lag is not zero but less than 90 degrees. The complex dynamic modulus ( ) is used to describe the stress-strain relationship (equation 14.1 i is the imaginary number square root of-1). 

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