Reduced frequency relaxational

The molecular weight dependence enters Equation 29 through tiq For this reason It Is convenient to define the reduced frequency relaxation spectrum as ... 

Figure 28. Reduced frequency relaxation spectrum for LLDPE/PP System 1 (top) and System 2.

Figure 4. Plot of the difference between experimental G (uaT) and its relaxational contribution versus the reduced frequency for six representative networks.

Both Figs. 13-14 and 13-15 indicate that there is a critical reduced frequency coc above which the storage moduli are similar in the ordered and disordered states (see also Fig. 13-13). Hence, for co > cOc, the modulus is controlled by molecular relaxations, while... 

Figure 8. Reduced Gross frequency relaxation spectrum for Serles-I and II. The arrows Indicate computed coordinates of the maximum (Hg niax>Hiiax) ...

Using techniques of extraordinary resolution, it is possible to measure efficiently peak sphtting (E.COSY pattern) associated with intemuclear couplings [79]. By increasing maximum evolution times one can reach peak width determined practically only by relaxation rate. However, ultra-narrow peaks require enhanced digital resolution (number of points per Hertz) to be properly visualized. This often causes the need to use another procedure employing reduced frequency space. 

A typical master curve is shown in Figure 6.2 (Santangelo and Roland, 1998) for dynamic shear data of a high molecular weight 1,4-polyisoprene measured over about a 160 range, yielding 15 decades of reduced frequency (the actual data spanned less than 5 decades). A tensile stress relaxation master curve for a polyurea rubber that spans 13 decades is displayed in Figure 6.6 (Knauss and Zhao, 2007). 

The pores form a DC current path. The sum of their conductances is so large that the capacitive effect of the membrane as a dielectric is small at low frequencies. If there are not too many pores, most of the potential difference is over the membrane pores, and the E-field strength in the pores will be high. The counter-ions of the double layer on the pore walls will migrate synchronous with the E-field, and the solution inside the pore will be pumped back and forth by electroosmosis. At higher frequencies, the membrane susceptance will shunt the pores, and voltage across the pore will be reduced. Counterion relaxation will also occur, as shown in Figure 3.11. 

Here, Cg and Cj f are capacities in the low- and high-frequency limits, respectively. Incidentally, a CPE is an empirical admittance function of the type A(i ) , which reduces to a pure conductance, A = 1/2 , when a = 0 and to a pure capacity when a = 1 its use is justified if the relaxation time of the process under study is not single valued, but is distributed continuously around a mean [27]. In Eq. (1), a p value <1 was ascribed to a certain roughness at the interphase, while an a value <1 was ascribed to a continuous distribution of low-frequency relaxation phenomena. The physical significance of these two CPEs is not entirely clear. At any rate, over the potential range of the capacity minimum (i.e. between —0.4 and —0.7 V/SCE) both a and P were found to be very close to unity, thus denoting that the behavior of the SAM approaches that of a simple series RC network closely. Nelson and... 

Fig. 7 Reduced storage modulus [G ( )1 plotted on double logarithmic scales versus the reduced frequency cotq for a 3-D topologically-regular cubic (40 x 40 x 40) network cross-linked from Rouse chains of 20 beads each (solid line). Also shown are the contributions to the [G (ffl)] that come from intrachain relaxation (solid line with circles) and interchain relaxation (solid line with stars)...

Fig. 30 Reduced storage modulus [G (

To verify this model for low molecular weight liquid crystals, it is important to increase the viscosity of the respective liquids. To avoid crystallization it is also useful to make mixtures [12, 14,15]. In this way one is able to reduce the relaxation frequencies... 

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