Linear viscoelasticity loss modulus

Stress relaxation for step squeezing of polystyrene at 180°C. (a) Stress versus time for increasing strain steps. Stress increases at short times, 2-10 ms because the plates take a finite time to close. The horizontal stress response signifies transducer overload. The rapid drop for strains e > 1 indicates loss of lubricant, (b) Stress relaxation data plotted as relaxation modulis. Solid line is the linear viscoelastic relaxation modulus calculated from shear dynamic data. Adapted from Soskey and Winter (1985). 

Other types of linear viscoelastic experiments may be used. Dynamic shear compliance measurements provide the storage and loss compliances J (co) and J"(co). An equation analogous to Eq.(3.12) is available for determining the initial modulus from J"(co) ... 

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

It is necessary to state more precisely and to clarify the use of the term nonlinear dynamical behavior of filled rubbers. This property should not be confused with the fact that rubbers are highly non-linear elastic materials under static conditions as seen in the typical stress-strain curves. The use of linear viscoelastic parameters, G and G", to describe the behavior of dynamic amplitude dependent rubbers maybe considered paradoxical in itself, because storage and loss modulus are defined only in terms of linear behavior. 

For deformation within the linear viscoelastic range. Equation 3.76 expresses the generated stress (ao) in terms of an elastic or storage modulus G and a viscous or loss modulus G". 

Accordingly, the phenomenological theory of linear viscoelasticity predicts the same frequency dependence for the loss relaxation modulus of solids and liquids in the terminal region. 

The viscoelastic responses of two polymer networks are shown in Fig. 7.29. One is a nearly perfect network (circles) made by end-linking linear chains with two reactive ends. The storage modulus for this network (filled circles) is independent of frequency and much larger than the loss modulus (open circles). For comparison, an imperfect network made by linking a mixture of chains with one and two reactive ends is also shown. 

An advanced rheometric expansion system (ARES) is used to determine Tg of samples. Strain sweep experiments from 0.01 to 1% strain are conducted to ensure that experiments are carried out in the linear viscoelastic region. All experiments are done at a frequency of IHz and a strain level of 0.05%, which is in the linear region. Temperature sweeps are conducted at a heating rate of 5°C/min over a temperature range which covers the glassy and rubbery regions of the soy flour samples at different water activities. The temperature at which the loss modulus (G") was at a maximum is used to estimate the T . 

Since the Gross frequency relaxation spectrum can be computed from r , i.e., from the loss modulus, G = T co, the agreement between the computed and measured G values provides good means of verifying both the computational and experimental procedures. It has been found that Eqs 7.83 and 7.84 are useful to evaluate the rheological performance of systems that obey the linear viscoelastic principles. 

These linear viscoelastic dynamic moduli are functions of frequency. For a suspension or an emulsitm material at low frequency, elastic stresses relax and viscous stresses dominate with the result that the loss modulus, G", is higher than the storage modulus, G. For a dilute solution, G" is larger than G over the entire frequency range, but they approach each other at higher frequencies as shown in Fig. 3. 

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