Normalized storage modulus

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).

Fig. 7.10 The temperature dependence of the normalized storage modulus and loss modulus ofZr4i 2Tii3.8Cui2.5NiioBe22.5 bulk metallic glass (from Pelletier (2005) courtesy of Elsevier).

The influence of the draw ratio could further be explained by studying the normalized storage modulus with temperature at different draw ratios as depicted in Figure 15.9. 

Figure 15.9. Variation of normalized storage modulus of MFCs with draw ratio at temperatures 10°C, 25°C, 50°C and80°C...

Normalized storage modulus can be defined as the ratio of the storage modulus of the composite to the storage modulus of the matrix at the same temperature. It is evident from the plot that as the draw ratio increases the normalized storage modulus increases, reaches a maximum value and then decreases. Also at a particular draw ratio, the normalized storage modulus increases with increase in temperature. This indicates the restriction of the mobility of the PP molecules due to the presence of the PET microfibrils at elevated temperatures. 

Figure 7.3 Dependence ofthe normalized storage modulus/MLG[ B/CL/ ron reduced frequency ca < >...

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. 

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. 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,...

There may be other settings in the test method, such as timings for data collection, and these should normally be left at the default values. The time for the experiment should typically be set to 30 min. This is normally adequate, but if steady state occurs more quickly, it is not a problem, because most tests can be interrupted. The instrument should be set to display the following information in real time storage modulus (G ), loss modulus (G"), corrected phase angle (8), and the actual percent strain. If the instrument has the capability to display the waveforms visually, this should be switched on. 

C. D. Han and M. S. Jhon, Correlation of the first normal stress difference with shear stress and of the storage modulus with loss modulus for homopolymers, J. Appl. Polym. Sci. 32(3), 3809— 3840 (1986). 

Let us add here some remarks on the normal stress difference. According to the Rouse-Zimm model [132,133] the first normal stress difference may be related to the storage modulus G. Taking into account only the longest relaxation time x, one gets... 

Storage modulus measurements. All measurements were taken at temperatures near 45 °C above the network Tg s. Representative network true stress versus strain curves from the tensile experiments are shown in Fig. 2. The ordinate axis, true stress, is normalized by 3eRT to account for the different test temperatures employed. The resultant curves are thereby directly comparable for structural differences, since the instantaneous slopes are proportional to l/M, after Eq. (2). The curves of all five networks are linear and reversible up to strains of around 10 percent. The reversibility suggests that the measurements were performed under near-equilibrium conditions and that the networks were stable at the high test temperatures employed. 

DMA analysis substantiated the possible morphological features that could partially account for the trend in mechanical and fracture properties of the glass laminate composites [146]. The DMA, done at a frequency of 1 Hz, are given in Fig. 12, where the percentage retention of the room temperature storage modulus (E ) is plotted as a function of temperature to normalize the anomalies resulting from differences in resin content for different systems. EPOBAN-modified... 

The vast majority of concentrated dispersions, such as LADDs, exhibit both viscous and elastic properties. These systems are therefore referred to as viscoelastic. The flow properties discussed in the previous section are not sufficient for complete rheological characterization of viscoelastic fluids. Dynamic mechanical properties, characterized by the storage modulus (G ) and loss modulus (G"), are normally... 

As a crystalline polymer melts, a sharp reduction in NMR line width to values below 0.05 gauss occurs. There is also a decrease in the storage modulus of up to four decades ( 1010 to lO6 dynes/sq. cm.). The sharp reduction in NMR line width is readily seen in low molecular weight substances such as the normal paraffins 44) and vinyl stearate 5). 

Four measures of melt elasticity have been used the first normal stress difference, Nj, the storage modulus, G , and the two indirect ones, the entrance-exit pressure drop, P. (or Bagley correction), and the extrudate swell, B. In homogeneous melts, the four measures are in a... 

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