Small amplitude oscillatory shear

Small amplitude oscillatory shear is the method of choice for materials with very broad distributions of relaxation modes, such as materials near LST, and for materials which undergo change during the measurement. The dynamic moduli in Eq. 4-10 are defined by [10]... 

Using model concentrated suspensions of polyvinyl chloride and titanium dioxide particles in a Newtonian polybutene fluid, small amplitude oscillatory shear and creep experiments were described [2]. It was shown that the gel-like behaviour at very small strain, and strain hardening at a critical strain, are caused by particle interactions and the state of particle dispersion. 

This is the dynamic viscosity in small amplitude oscillatory shear which is the real component of the complex shear viscosity which is a function of the angular frequency of oscillation. 

For a small amplitude oscillatory shearing flow, the strain is defined as,... 

Recently, focus has been placed on small amplitude oscillatory shear technique to measure the dynamic moduli during the gelation process to identify the gel point. By this method, the continuous evolution of the viscoelastic properties throughout the... 

Figure 3.15 The frequency-dependent in-phase and out-of-phase components of the dynamic viscosity, rj and rj in small-amplitude oscillatory shear, along with the shear-rate dependence of the first normal stress coefficient hi (y) for a 0.05 wt% solution of polystyrene of molecular weight 2.25 X 10 in a solvent of oligomeric styrene. The lines through the data show the predictions of the Zimm theory for r and 2r)"f(o and the Zimm theory for hi(y) modified to account for finite extensibility, as discussed in Section 3.6.2.2.I. The dashed lines are the contributions of the individual Zimm relaxation modes to 2rj"((o) /

Bates 1984 Fredrickson and Larson 1987 Fredrickson andFIelfand 1988). The relaxation of these fluctuations involves collective motion of many molecules, and thus it is slower than the relaxation time of individual molecules. In small-amplitude oscillatory shearing, the fluctuation waveform is deformed, producing a slowly relaxing stress. Presumably, this accounts for (a) the anomalous contribution to G and (b) a similar, but smaller, contribution to G" (Rosedale and Bates 1990 Jin and Lodge 1997). (Similar anomalies are observed in polymer blends.) An asymmetric version of this PEP-PEE polymer that forms cylindrical domains shows an even larger low-frequency anomaly (Almdal et al. 1992). 

All the above theories are derived for rigid rod nematic liquid crystal systems. The rheological behavior of chiral nematic liquid crystals is more complex and less understood than that of nematic systems. Rey introduced a model based on rigid rod chiral nematic liquid crystals to describe permeation shear flow and small amplitude oscillatory shear flow. The model can predict some common phenomena of chiral nematic liquid crystals, e.g., the three-region... 

The loss and storage moduli of small amplitude oscillatory shear measurements [1, 3] follow from (5b) in the linear response case at y = 0 ... 

Having discussed steady-state shear flow in 6 and small-amplitude oscillatory shearing motion in 7, we now consider a superposition of these two types of flow this type of superposed flow has only recently been studied. 

In a dynamic experiment, a small-amplitude oscillatory shear is imposed to a molten polymer confined in the rheometer. The shear stress response of the polymeric system can be expressed as in Equation 22.14. In this equation, G and G" are dynamic moduli related to the elastic storage energy and dissipated energy of the system, respectively. For a viscoelastic fluid, two independent normal stress differences, namely, first and second normal stress differences can be defined. These quantities are calculated in terms of the differences of the components of the stress tensor, as indicated in Equation 22.15a and 22.15b, and can be obtained, for instance, from the radial pressure distribution in a cone-and-plate rheometer [5]. Some other experiments used in the determination of the normal stress differences can be found elsewhere [9, 22] ... 

RHEOLOGY OF POLYMERS WITH NANOFILLERS 16.2.3 Small-Amplitude Oscillatory Shear Flow... 

Prigogine, Trappeniers, and Mathot pressure-volume-temperature measurements lead zirconate titanate quaternary ammonium salts quasi-two-parameter theory rigid amorphous fraction Rheometrics extensional rheometer Rheometrics elongational rheometer for melts room temperature small-angle neutron scattering small-amplitude oscillatory shear flow small-angle x-ray scattering side-chain LCP... 

In marked contrast to measurements of shear rheological properties, such as apparent viscosity in steady shear, or of complex viscosity in small amplitude oscillatory shear, extensional viscosity measurements are far from straightforward. This is particularly so in the case of mobile elastic liquids whose rheology can mitigate against the generation of well-defined extensional flow fields. 

So, the mixtures show a viscoelastic behavior which is very different from neat PPS. Strong solid-like responses in the small amplitude oscillatory shear flow are observed. After quiescent annealing, a strainscaling transient stress behavior is observed in the mixtures in the reverse flow [61]. 

With dynamic rheometry, the measurement of the dynamic moduli G and G" in small amplitude oscillatory shear is exploited. The gelation point is reported to be the intersection point of the curves of storage and loss moduli, i.e. the moment at which tan 8 equals one [49]. However, the crossover is observed to correspond to the gel point only for stoichiometrically balanced network polymers and networks with excess crosslinking agent at temperatures much above Tg [50]. 

In the linear viscoelastic region G is constant. By application of a small amplitude oscillatory shear, the storage and loss modulus can be obtained ... 

Some of the manifestations of viscoelasticity are delayed relaxation of stress after cessation of flow phase shift between stress and strain rate in oscillatory shear flow shear thinning (decrease of viscosity) at shear rates exceeding the reciprocal of the longest relaxation time and normal stress differences in shear flow, whose magnitudes are related to the relaxation time spectrum. A very convenient observation for experimentalists is that there is a close similarity between the shear viscosity and first normal stress difference as functions of shear rate and the corresponding parameters, complex viscosity and storage modulus, as functions of frequency in a small amplitude oscillatory shear. 

It is especially simple to detect the instant of gelation of a material whose critical relaxation exponent c is known. For any frequency (within the power law region) and any temperature, in a small amplitude oscillatory shear experiment at constant a>o, GP is reached at the instant at which fimctions G (o, t)l in ncnl2) intersect (see eq. 3). 

To measure rheological percolation of composites under small-amplitude oscillatory shear... 

Fig. 3.10. The steady-state response of stress to a small-amplitude, oscillatory shear deformation.

For a small amplitude oscillatory shear in which the ER suspensions are in the linear response region, the rheological behavior was simulated on the basis of the point-dipole approximation [100, 101]. With the increase of... 

Fig. 4 a Low shear viscosity ii determined at y = 0.01 s b parameter t from a fit of MCT equations to small amplitude oscillatory shear data and c structural relaxation time ta from DLS as a function of polymer concentration cp for microgel suspensions Ml with N = 11 closed triangles) and M2 with N = 2.5 open triangles) at <() 0.63 as well as for M2 at <() 0.66 open... 

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