Small-deformation dynamic measurement

Although creep-compliance (Kawabata, 1977 Dahme, 1985) and stress-relaxation techniques (Comby et al., 1986) have been used to study the viscoelestic properties of pectin solutions and gels, the most common technique is small-deformation dynamic measurement, in which the sample is subjected to a low-amplitude, sinusoidal shear deformation. The resultant stress response may be resolved into an in-phase and 90° out-of-phase components the ratio of these stress components to applied strain gives the storage and loss moduli (G and G"), which can be related by the following expression ... 

The interaction between two fillers particles can be investigated by measuring the Payne effect of a filled rubber compounds. In this measurement, dynamic properties are measured with strain sweep from a very small deformation to a high deformation. With the increased strain, the filler-filler network breaks and results in a lower storage modulus. This behavior is commonly known as the Payne effect... 

Static and dynamic linear viscoelastic measurements are used to gain insights into the relationships between cheese structure and rheological behavior. Non-linear viscoelastic measurements have been used to a relatively small degree to measure the response of cheese to large deformations. 

In 1949, Deuel and Neukom [131] sug sted that the origin of cro links in aqueous poly(vinyl alcohol)/borate gels is the complexation shown in Fig. 48. This concept of didiol type complexation was adopted by authors in more recent times [130,184-193]. Schultz and Myers [185] measured the dynamic moduli G and G" of polyfvinyl alcohol)/borate gels (at small deformation amplitudes in order not to disturb the gel [185]). At low frequendes, the gels showed Uquidlike behaviour this means that the borate crosslinks are dynamic in nature. Such results were also reported by Beltman [7]. He measu the dynamic moduli of a gel formed in a 4 wt% PVA98.5 solution with 2.5 wt% of borax (=0.0069 mol/1, which is equivalent to 0.0276 mol/1 of borate) at various temperatures (15-75 °C). Results are shown in Fig. 49. 

Differential dynamic measurements have also been made with other kinds of oscillating deformations. In studies by Painter of small dynamic shear deformations superimposed on large static shear strains in the same direction, the dynamic storage modulus G of cross-linked natural rubber and poly(dimethyl sil-oxane) at 24 Hz was found to increase with increasing static strains in excess of 721 = 0.2. Here 721 is defined as u jxt in the notation of Chapter 1. After a history of large static strain, however, the change in G with static strain in a second (and subsequent) sequence of experiments was much smaller. These history-dependent effects are no doubt related to the behavior in repeated stress-strain cycles in extension mentioned in Section 3 above. Some experiments on torsional deformations of stretched rubber strips have been reported. " ... 

Traditionally, polymer relaxation is characterized by a spectnun of multiple relaxation times corresponding to various modes of relaxation a polymer chain can undergo. The longest relaxation time corresponds to the relaxation of a whole chain, while the shorter ones correspond to the relaxation of short parts of the macromolecules. In this paper, we are particularly interested in the relaxation behavior at molecular chain level. Dynamic rheometers are the most used means for providing relaxation time spectrum of polymer melts [4-6]. However, since they only generate small scale melt deformation dming measurements, the relaxation time at macromolecular level... 

First. The problem of a limit of linearity has assumed a certain importance for investigating dynamic properties of filled polymers [4, 5], Even for very small (from the point of view of measuring rheological properties of pure polymer melts) amplitudes of deformation, the values of a modulus depend on the amplitude. 

It turns out that stress relaxation following a simple shear deformation is seldom employed experimentally. A more common technique is to measure the steady state response to small sinusoidal deformations as a function of angular frequency to. The dynamic storage modulus G (to) and loss modulus G"(to) in small sinusoidal deformations are related to G(t) ... 

The most common dynamic method is oscillatory testing, in which the sample is subjected to a sinusoidal oscillatory strain, and the resulting oscillatory stress measured. The more sophisticated rotational viscometers have the additional capability of dynamically testing liquid-like materials using small angle oscillatory shear. A parallel disc viscometer can be set up for testing solid-like materials (e.g., butter), in oscillatory shear. Some UTM-type solids rheometers, in which the moving crosshead can be made to reciprocate sinusoidally, can be used to test solid-like materials in oscillatory deformation in compression, tension or shear. 

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