Storage modulus function

Figure 15 Storage modulus, (E ), loss tangent (tanS), and loss modulus, (E ), as a function of temperature for P7MB and P8MB at 3 Hz.

FIGURE 28.11 Storage modulus as a function of temperature for the ENR stocks containing various fillers in 10 h. (From Siby Varghese, J. and Karger-Kocsis, J., J. Appl. Polym. Sci., 91, 813, 2004.)... 

Fig. 11. Effect of dielectric constant of dispersed particle on the ER effect in a polymer gel. The increment in shear storage modulus induced by an ac electric field of 0.4 kV/mm is plotted as a function of the real part of the dielectric constant of the particle...

Figure 34 Left (a) equilibrium storage modulus G as a function of y-irradiation dose determined from DMA experiments on exposed PU samples (b) 1/T2ave as a function of G. Right BC CPMAS NMR measurements on non-irradiated PU sample (a) 3 ms, (b) 0.5 ms, and (c) 100 pis. SS denotes soft segment HS denotes hard segment. Reprinted from Maxwell [87], Copyright 2003, with permission from Elsevier.

Figure 2.11 Schematic of the storage modulus as a function of the frequency of the applied strain for a polymer melt. The plateau gives the network modulus, GN. The plateau extends down to lower frequencies as the molecular weight is increased because the relaxation time is proportional to M3... 

Now these expressions describe the frequency dependence of the stress with respect to the strain. It is normal to represent these as two moduli which determine the component of stress in phase with the applied strain (storage modulus) and the component out of phase by 90°. The functions have some identifying features. As the frequency increases, the loss modulus at first increases from zero to G/2 and then reduces to zero giving the bell-shaped curve in Figure 4.7. The maximum in the curve and crossover point between storage and loss moduli occurs at im. 

Bauer, Denneler, and Wilert-Porada also studied the influence of temperature (30-120°C) and humidity (0 - 100%) on the mechanical properties of Nation 117 membrane via dynamic mechanical analysis (DMA). The mechanical behavior of Nation membranes in a humid atmosphere was observed to differ significantly from that in dry atmosphere, and the influence of water on the mechanical properties of the acid form of Nation was found to be complex. The maximum of the storage modulus ( ) as a function of humidity was shifted to higher humidity values with increasing temperature. 

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... 

Rgure 4.4. The plateau storage modulus (small solid symbols) and the minimum of the loss modulus G (small open symbols) as a function of the effective oil volume fraction. a = 0.25 um (circles), a = 0.37 j,m (triangles), a = 0.53 um (squares), and a = 0.74 qm (diamonds). The large circles are the measured values for the osmotic pressure. All data are normalized by yint/a (Adapted from [10].)... 

Fig. 4 DMTA analysis of a PPC with a Mn of 46 kDa, showing storage modulus G, loss modulus G", and tan d as a function of temperature (Borchardt and Luinstra, unpublished data)...

Figure 3.7 (a) Storage modulus versus frequency for the networks 5 PVP and (b) the same storage modulus scaled by of model complexes 1 2a versus the frequency of oscillation scaled by the same diss- Each of the networks consists of 5% (by metal functional group per pyridine residue) of ( ) 5a, (A) 5b, ( ) 5c, and ( ) 5d and PVP at 10% by total weight of the network in DMSO at 20°C. Data taken from Loveless et al. (2005). 

Figure 9.7 Profile of normalized storage modulus, E jE of Russet Burbank potato disc as a function of heating time at 60°C E is the storage modulus of the raw sample = 1.87 MPa. (Source Bu-Contreras, 2001).

Figure 19a, b compares the storage modulus as well as tan 8 for various nanocomposites prepared from EVA rubber having 50% vinyl acetate content and loaded with MWCNT, as a function of temperature [162]. Throughout the experimental temperature range of —35 to 20°C, the storage moduli show steady increase from the virgin rubber with the increase in MWCNT level (see Fig. 19a). For example, there is...

Dynamic mechanical analysis (DMA) has been carried out to understand the dynamic response of the blend after the addition of clay. The dependency of the storage modulus obtained from oscillatory tension deformation as a function of temperature is given in Fig. 44. All samples show a steep decrease of E over the temperature range T = 50 to 20°C followed by a rubbery plateau (Fig. 44a). The most exciting information, observed in this figure, is the increase of modulus values at room temperature by the addition of clay. The storage modulus increases from 2 MPa to 54 MPa with the addition of only 10 phr clay in the 25 EPDM/75 CR... 

Fig. 6 Variation of viscoelastic properties as a function of strain amplitude of uncrosslinked and dynamically vulcanized blends at 180°C (a) storage modulus, (b) loss modulus. CD2 TPV prepared by preblending, PD2 TPV prepared by phase mixing, SD2 TPV prepared by split addition...

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