Storage moduli angular frequency

The relative viscosity rj and storage modulus G were determined by Cirkel and Okada in experiments using a rheometer in oscillatory rotational mode and Couette sample geometry as a function of Nafion volume fraction, cp, and angular frequency, a>, for the acid and sodium forms at 25 °C. Parallel experiments... 

Fig. 5 Master curve of storage modulus G, loss modulus G", and tan S as a function of the reduced angular frequency coa at the reference temperature of 150°C...

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) ... 

Fig. 2.1. First normal stress difference (pu—p22) as a function of shear rate q and doubled storage modulus 2 G as a function of angular frequency for a poly-dimethyl siloxane (M = 536,000) at a measurement temperature of 20° C. (o) (A n/C) cos 2y,...

The evolution of the dynamic viscosity rp (co, x) or of the dynamic shear complex modulus G (co.x) as a function of conversion, x, can be followed by dynamic mechanical measurements using oscillatory shear deformation between two parallel plates at constant angular frequency, co = 2irf (f = frequency in Hz). In addition, the frequency sweep at certain time intervals during a slow reaction (x constant) allows determination of the frequency dependence of elastic quantities at the particular conversion. During such experiments, storage G (co), and loss G"(co) shear moduli and their ratio, the loss factor tan8(co), are obtained ... 

Figure 2. The Storage Modulus G and the Loss Modulus G" as a Function of the Angular Frequency (CPySal, T 20°C, c = 50 mM).

The Influence of Temperature on the Viscoelastic Properties. The viscoelastic properties of the dilute surfactant systems depend on the temperature of the solutions strongly. Figure 8 shows the values for the storage modulus G as a function of the angular frequency at different temperatures for a 20 mM solution of CPySal. The elastic properties of the surfactant solutions decrease with increasing temperature. The solution equilibrated at 35 C shows only little elasticity in the frequency range below 1 Hz and at temperatures of 50 C the solutions behave as Newtonian fluids. The supermolecular structures which are present in these solutions and which are responsible for the viscoelastic properties seem to be completely destroyed under these experimental conditions. 

Aqueous viscoelastic surfactant solutions for hair and skin care are disclosed in U.S. Patent 5,965,502. Rheology conditions are specified for optimum flow behavior, in terms of the shear modulus as a function of temperature and pH. A representative graph of the storage and loss modulus as a function of angular frequency is presented in the patent and this is shown in Figure 4.8. Cited compositions contain anionic, betainic, and nonionic surfactants, electrolytes, and a water-soluble polymer. A nonionic gel personal cleanser is specified in U.S. Patent... 

Figure 14.21 Results of dynamic ( ) viscosity t), storage modulus G, versus angular frequency oj, of the dynamically crossUnked EPDM/PP blend samples of different compositions 20/80 ( ) 40/60 ( ) 60/40 ( ) w w. (From Reference 49 with permission from Wiley Interscience.)...

Dynamic viscoelasticity. From the oscillatory rotation of the plate dynamic viscoelasticity was estimated with the same equipment. The maximum shear was 0.250, and the angular frequencies employed ranged from 5.82x10" to 5.82x10" rad/sec. The rotation angle of the plate and the twist of the cone were recorded with an X-Y plotter. From the hysteresis loop obtained the storage modulus or dynamic elasticity (G ) and the loss... 

Figure 8. Effect of Streptomyces hyaluronidase on the dynamic viscoelasticity of proteoglycan. Concentrations proteoglycan, 4% enzyme, 1 TRU. Angular frequency 0.349 rad/s (O, 9) monomer CA, aggregate (9, A) storage modulus (O, loss modulus.

Fig. 3. Influence of silane coupling agent on dynamic viscoelastic properties of GF/PP composites (a) storage modulus as a function of angular frequency, (b) loss modulus as a function of angular frequency...

In Fig. 14(a), the storage modulus G is plotted against the angular frequency a> for various silane coupling agents treated GFL/PP composites. G of all treated GFL/PP is higher than... 

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