Loss modulus definition

Note that VTD-variance of Loss Tangent, and that SDTD is the standard deviation of Loss Tangent with similar definitions for GSP (G or real modulus) and GDP (G or loss modulus). 

Eqs. (1.16) are, of course, very well-known. G is known as the storage modulus in shear. It describes that part of the shear stress, which is in phase with the deformation. G" is the loss modulus in shear. It describes that part of shear stress which is 90 degrees out of phase. 6 is the loss angle. These definitions will be used occasionally in this review. 

According to the present author the applicability of this definition depends on the patience of the experimentalist if he allows himself more time, then he might conclude that a relaxation process starts at low frequ cies (as depicted by the presence of a minimum in the loss modulus at low fiequencies) or after a long time in creep experiments. Another, more philosophical definition (or a complaint) could be ... 

The quantities E and G refer to quasi-static measurements. When cyclic motions of stress and strain are involved, it is more convenient to use dynamical mechanical moduli. The complex Young s modulus is then defined as = " + iE", where E is the storage modulus and " the loss modulus. The storage modulus is a measure of the energy stored elastically during deformation the loss modulus is a measure of the energy converted to heat. Similar definitions hold for G, J, and other mechanical properties. 

The loss modulus G" vs. frequency can be easily predicted from the above equations by using the definition ... 

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). 

More definitive evidence of enzymatic attack was obtained with 1 1 copolymers of e-caprolactone and 6-valerolactone crosslinked with varying amounts of a dilactone (98,99). The use of a 1 1 mixture of comonomers suppressed crystallization and, together with the crosslinks, resulted in a low-modulus elastomer. Under in vitro conditions, random hydrolytic chain cleavage, measured by the change in tensile properties, occurred throughout the bulk of the samples at a rate comparable to that experienced by the other polyesters no weight loss was observed. However, when these elastomers were implanted in rabbits, the bulk hydrolytic process was accompanied by very rapid surface erosion. Weight loss was continuous, confined to the... 

Here t is the resulting shear stress, 6 is the phase shift often represented as tan(d), and (O is the frequency. The term 6 is often referred to as the loss angle. The in-phase elastic portion of the stress is To(cosd)sin(wt), and the out-of-phase viscous portion of the stress is To(sind)cos(complex modulus and viscosity, which can be used to extend the range of the data using the cone and plate rheometer [6] ... 

However, in contrast to the cases of complex elastic modulus G and dielectric constant e, the imaginary part of the piezoelectric constant, e", does not necessarily imply an energy loss (Holland, 1967). In the former two, G"/G and e"/e express the ratio of energy dissipation per cycle to the total stored energy, but e"/e does not have such a meaning because the piezoelectric effect is a cross-coupling effect between elastic and electric freedoms. As a consequence, e" is not a positive definite quantity in contrast to G" and e". In a similar way to e, however, the Kramers-Kronig relations (Landau and Lifshitz, 1958) hold for e ... 

A toughened material, by definition, features improvements in fracture resistance without substantial loss of mechanical strength or modulus. Figures 9 a and 9 b... 

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