Strain dependence

Kigure 27 Stress response varies with strain amplitude for the anhydrolated zeolite, Linda 3A (molecular structure, K9Na3[(AI02)i2(Si02)i2], dispersed in paraffin oil. A) the strain amplitude is 3.0 B) the strain amplitude is 9.0 C) the strain amplitude is 27.0. For all three curves the applied electric field is 1.0 kV/mm. Reproduced with permission from D.R. Gamota and F.E. Filisko, J. Rheol., 35(1991)399. 

(54) indicates that the energy dissipated by the viscous damping is proportional to the square of shear strain amplitude, the dynamic viscosity and the frequency of the dynamic field. Substituting Eq. (53) into Eq.(52) one may obtain  

(56) indicates that an ellipse will be obtained if x is plotted against y. In other words, in viscous damping an elliptic hysteresis loop will be obtained. The energy dissipated per volume per cycle due to Coulomb damping in an oscillatory motion is given  

Not all ER suspensions have a linear viscoelasticity region and G and G don t always decrease with the strain amplitude. Such examples can be found in two similar aluminosilicate particulate materials dispersed in silicone oil systems [83]. Those two particulates have a common molecular formula that can be expressed as (A120j) (67O2), where 

5 Hz and zero electric field. For the PS suspension, G, G , and initially show a slightly decrease with the increase of strain amplitude, and then increase with it Whereas for the MS suspension, G, G , and j 7 j decrease 

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The choice of the strain of microorganism is one of the important variables in the process. The strains to be used in manufacture are mutants of the original producer, which are chosen as the result of a planned program of mutant selection. Sometimes a spontaneous mutation occurs usually, it is induced by mutagenic agents or irradiation of various sorts. The choice of the best strain depends on its abiUty to produce large amounts of the proper antibiotic in a reasonable time from ingredients that are economically feasible (73). 

The transition obtained under stress can be in some cases reversible, as found, for instance, for PBT. In that case, careful studies of the stress and strain dependence of the molar fractions of the two forms have been reported [83]. The observed stress-strain curves (Fig. 16) have been interpreted as due to the elastic deformation of the a form, followed by a plateau region corresponding to the a toward [t transition and then followed by the elastic deformation of the P form. On the basis of the changes with the temperature of the critical stresses (associated to the plateau region) also the enthalpy and the entropy of the transition have been evaluated [83]. 

FIGURE 22.2 Flocculation behavior of the smaU-strain modulus at 160°C of uncross-linked solution-based styrene-butadiene rubber (S-SBR) composites of various molar mass with 50 phr N234, as indicated (left) and strain dependence of the annealed samples after 60 min (right). (From Kliippel, M. and Heinrich, G., Kautschuk, Gummi, Kunststoffe, 58, 217, 2005. With permission.)... 

Above a critical hller concentration, the percolation threshold, the properties of the reinforced rubber material change drastically, because a hller-hUer network is estabhshed. This results, for example, in an overproportional increase of electrical conductivity of a carbon black-hUed compound. The continuous disruption and restorahon of this hller network upon deformation is well visible in the so-called Payne effect [20,21], as represented in Figure 29.5. It illustrates the strain-dependence of the modulus and the strain-independent contributions to the complex shear or tensUe moduli for carbon black-hlled compounds and sUica-hUed compounds. 

FIGURE 30.9 Modeling the strain dependence of complex modulus. 

Lines in Figure 30.12 were drawn with parameters obtained when fitting data with Equation 30.3. It is fairly obvious that, outside the experimental window, data would not necessarily conform to such a simple model, which in addition cannot meet the inflection at 100% strain. All results were nevertheless fitted with the model essentially because correlation coefficient were excellent, thus meaning that the essential features of G versus strain dependence are conveniently captured through fit parameters. Furthermore any data can be recalculated with confidence within the experimental strain range with an implicit correction for experimental scatter. Results are given in Table 30.1 note that 1/A values are given instead of A. 

FIGURE 30.12 Ethylene-propylene-diene monomer (EPDM) compounding complex modulus strain dependence samples TR, EM, and AG. 

FIGURE 30.20 Mixing siUca-fiUed compound Complex modulus strain dependence at selected position along the mixing hue. 

FIGURE 33.8 Strain dependence of G for oil extended solution SBR (OESSBR)/BR and natural rubber (NR) filled with a variety of fillers. 

FIGURE 33.10 Strain dependence of G for vulcanizates filled with a variety of fillers. 

Caughey B, Raymond GJ, Bessen RA. Strain-dependent differences in beta-sheet conformations of abnormal prion protein. J Biol Chem 1998 273 32230-32235. 

The strain in electric field-associated bending of a PVA-PAA gel is given by the equation g = 6DY/L2 (see Eq. 21). The strain depends on the electric power applied to the gel. Thus, the deflection increases as the thickness becomes small even if the electric power remains constant. The PVA-PAA gel rod of 1 mm diameter bends semicircularly within 1 s under both dc and ac excitation. An artificial fish with a PVA-PAA gel tail 0.7 mm thick has been designed, and it has been demonstrated that the fish swims forward at a velocity of 2 cm/sec as the gel flaps back and forth under sinusoidally varied electric fields (Fig. 13b). This prototype of a biomimetic actuator shows that translational motion may be produced using bending deformation [74],... 

Their crystallization behavior compares with natural rubber, as follows (1) their rate of crystallization is more rapid and (2) their amount of crystallinity is temperature dependent, but considerably less strain dependent. These experimental rubbers have excellent green strength and building tack. 

Figure 18 shows the percent crystallinity obtained by birefringence measurements for NR at various elongations as a function of temperature. The relative shapes of the curves in this Figure show the pronounced temperature and strain dependence on the strain induced crystallization of NR. Of particular importance is the relatively high amounts of crystallinity that develop at room temperature. 

Our results tend to approach the affine theory with increasing z. That means, that the fluctuationsof crosslinks are more and more restricted, the reason for this being the change in microstructure. (This is quite different from the strain dependent restriction of fluctuations as predicted by Flory s recent theory.)... 

Comparison with Statistical Theory at Moderate Strains. So far we have shown, that a transition between the two limiting classical theories, i.e. affine theory and phantom theory, is possible by a suitable choice of the network microstructure. This argument goes beyond the revised theory by Ronca and Allegra and by Flory, which predicts such a transition as a result of increasing strain, thus explaining the experimentally observed strain dependence of the reduced stress. 

Figure 8. Mooney-Rivlin plots for strain dependent measurements at 298 K. Key A, PDMS-BI , PDMS-B2 X, PDMS-B3 O, PDMS-B5 , PDMS-B6 , PDMS-B7 V, PDMS-B8 A, PDMS-B9 PDMS-B10.

Mooney-Rivlin constants obtained from strain dependent measurements at 298 K... 

Concluding, we can state that the absolute values of the small-strain moduli, which are greater for networks having comblike crosslinks, than for those with tetrafunctional junctions, are understandable, if we assume that the fluctuations of junctions are restricted by the very short chains. The strain dependent measurements do not agree quantitatively with the recent theory, although the trends are in accordance. An exact correspondence... 

Equilibrium stress-strain dependences were determined in extension using a stress relaxation arrangement described earlier (21). Dry non-extracted samples were measured at 150 C in nitrogen atmosphere and extracted samples swollen in dimethylformamide were measured at 25 C. The equilibrium value of stress 6 e was reached within 2-4 min except of a few dry samples with the lowest tig, for which the equilibrium stress was determined using an extrapolation procedure described earlier (21). 

Polyurethane networks were prepared from polyoxypropylene (POP) triols(Union Carbide Niax Polyols) after removal of water by azeotropic distillation with benzene. For Niax LHT 240, the number-average molecular weight determined by VPO was 710 and the number-average functionality fn, calculated from Mjj and the content of OH groupSj determined by using excess phenyl isocyanate and titration of unreacted phenyl isocyanate with dibutylamine, was 2.78 the content of residual water was 0.02 wt.-%. For the Niax LG-56, 1 =2630, fn=2.78, and the content of H2O was 0.02wt.-%. The triols were reacted with recrystallized 4,4"-diphenylmethane diisocyanate in the presence of 0.002 wt.-% dibutyltin dilaurate under exclusion of moisture at 80 C for 7 days. The molar ratio r0H = [OH]/ [NCO] varied between 1.0 and 1.8. For dry samples, the stress-strain dependences were measured at 60 C in nitrogen atmosphere. The relaxation was sufficiently fast and no extrapolation to infinite time was necessary. 

A8. The Helmholtz elastic free energy relation of the composite network contains a separate term for each of the two networks as in eq. 5. However, the precise mathematical form of the strain dependence is not critical at small deformations. Although all the assumptions seem to be reasonably fulfilled, a simpler method, which would require fewer assumptions, would obviously be desirable. A simpler method can be used if we just want to compare the equilibrium contribution from chain engangling in the cross-linked polymer to the stress-relaxation modulus of the uncross-linked polymer. The new method is described in Part 3. 

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