Linear viscoelastic region determination

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

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 . 

Figure 4.2. Dynamic properties as functions of strain in a dynamic step-strain test to determine the linear viscoelastic region for a highly filled epoxy-novolac moulding sample used for computer-chip encapsulation.

Dynamic-shear measurements are of the complex viscosity rj ) as a function of the dynamic oscillation rate (o), at constant temperature. These tests are defined as isothermal dynamic frequency sweeps. Since the dynamic frequency sweeps are conducted at a given amplitude of motion, or strain, it is necessary to ensure that the sweeps are conducted in the region where the response is strain-independent, which is defined as the linear viscoelastic region. This region of strain independence is determined by an isothermal strain sweep, which measures the complex viscosity as a function of applied strain at a given frequency. This ensures that a strain at which the dynamic frequency sweep may be conducted in the linear viscoelastic region is selected. 

The complex viscosity as a function of frequency, maximum strain and temperature is generally determined with one rheometer. Standard ASTM 4440-84/90 defines the measurement of rheological parameters of polymer samples using dynamic oscillation. This standard reiterates the importance of determining the linear viscoelastic region prior to performing dynamic frequency sweeps. 

The complex shear modulus is an indicator of the stiffness or resistance of the bituminous binder to deformation under load. The complex shear modulus and the phase angle define the resistance to shear deformation of the bituminous binder in the linear viscoelastic region. Finally, the complex modulus and the phase angle are used to determine or calculate performance-related criteria in accordance to specifications. 

Dynamic shear flow within the linear viscoelastic region was used to determine binodal and spinodal temperatures (Tb and T, respectively) in LCST-type... 

The equilibrium modulus and the memory function m(t-t ) can be obtained from measurements in the linear viscoelastic region. Oscillatory shear data are most appropriate to determine the linear viscoelastic functions We will not go further into this matter here, since the present article is concerned with the comparison of the shape of the nonlinear tensor functionals of different materials. 

In the case of gel-like samples (G > G" in the viscoelastic linear region), this test is frequently used to determine the yield point (yield stress) and flow point (flow stress). The yield point corresponds to the limiting value of the linear viscoelastic region. The flow point corresponds to the stress where G = G". 

For gel samples, these parameters are often measured as a function of time, strain and frequency. Observation of the gelation process can be achieved by monitoring the temporal evolution of G and G". The linear viscoelastic region within which G and G" are independent of shear strain can be determined by monitoring the moduli of the material as a function of the strain. 

Recent advances in dynamic rotational rheometers are of growing importance in food analyses for several reasons. (1) The measurement minimizes the destruction of the material. (2) The time required for a measurement is reasonably short in comparison with chemical or physical changes in the material. (3) The viscoelasticity of gels is characterized by determining G and G" in the linear viscoelastic (LVE) region no other method gives dynamic moduli values. 

Comparison with experimental data demonstrates that the bead-spring model allows one to describe correctly linear viscoelastic behaviour of dilute polymer solutions in wide range of frequencies (see Section 6.2.2), if the effects of excluded volume, hydrodynamic interaction, and internal viscosity are taken into account. The validity of the theory for non-linear region is restricted by the terms of the second power with respect to velocity gradient for non-steady-state flow and by the terms of the third order for steady-state flow due to approximations taken in Chapter 2, when relaxation modes of macromolecule were being determined. 

The four variables in dynamic oscillatory tests are strain amplitude (or stress amplitude in the case of controlled stress dynamic rheometers), frequency, temperature and time (Gunasekaran and Ak, 2002). Dynamic oscillatory tests can thus take the form of a strain (or stress) amplitude sweep (frequency and temperature held constant), a frequency sweep (strain or stress amplitude and temperature held constant), a temperature sweep (strain or stress amplitude and frequency held constant), or a time sweep (strain or stress amplitude, temperature and frequency held constant). A strain or stress amplitude sweep is normally carried out first to determine the limit of linear viscoelastic behavior. In processing data from both static and dynamic tests it is always necessary to check that measurements were made in the linear region. This is done by calculating viscoelastic properties from the experimental data and determining whether or not they are independent of the magnitude of applied stresses and strains. 

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