Compliance loss

Figure 3.16 Some experimental dynamic components, (a) Storage and loss compliance of crystalline polytetrafluoroethylene measured at different frequencies. [Data from E. R. Fitzgerald, J. Chem. Phys. 27 1 180 (1957).] (b) Storage modulus and loss tangent of poly(methyl acrylate) and poly(methyl methacrylate) measured at different temperatures. (Reprinted with permission from J. Heijboer in D. J. Meier (Ed.), Molecular Basis of Transitions and Relaxations, Gordon and Breach, New York, 1978.)...

The parallel between the loss compliance spectrum—or those of the loss... 

Dynamic mechanical measurements were made on PTEE samples saturated with various halocarbons (88). The peaks in loss modulus associated with the amorphous relaxation near —90°C and the crystalline relaxation near room temperature were not affected by these additives. An additional loss peak appeared near —30° C, and the modulus was reduced at all higher temperatures. The amorphous relaxation that appears as a peak in the loss compliance at 134°C is shifted to 45—70°C in the swollen samples. 

The elastic and viscous modulus properties of mechanical strength are used to calculate the complex modulus and the loss compliance of compounds. These two parameters are used to assess dry traction and handling. Higher values relate directiy to dry traction and handling (cornering) within limits. 

These expressions show that, for example, any value of the storage modulus depends upon the values of both the storage and loss compliance. This is true for these dynamic properties, only the ratios interrelate simply ... 

Figure 5.29 The storage and loss compliance for a Mooney39 model...

Note 2 The absolute compliance is related to the storage compliance (5.16) and the loss compliance (Definition 5.17) by the relationship... 

Note 4 The eomplex complianee is related to the storage and loss compliances through the relationships... 

Where D" is the loss compliance or the out-of-phase component of the dynamic compliance. The rate is given by... 

Other types of linear viscoelastic experiments may be used. Dynamic shear compliance measurements provide the storage and loss compliances J (co) and J"(co). An equation analogous to Eq.(3.12) is available for determining the initial modulus from J"(co) ... 

Fig. 2. Reduced loss compliance or analogous dissipative dielectric permittivity for the linear array as a function of molecular weight...

Dynamic storage and loss compliance function for the cubic array are presented in Eqs. (T 11) and (T 12), respectively. 

Comparison of the reduced loss compliance of the one- and three-dimensional arrays is made in Figs. 7 and 8 where Eqs. (T 6) and (T 12) are plotted on reduced frequency scales for a number of molecular weights. The dispersion behavior in the linear case becomes progressively broader with increasing molecular weight. In contrast, the three-dimensional loss profile remains quite sharp even for large molecular weights. 

From the behaviour of the BXT copolymers, the authors concluded that j3 blocks of seven to nine units are required for a BPA-PC-like j3 transition. Such a conclusion can be questioned since the tan 8 curves for B3T and B5T copolymers show a clear shoulder in the - 100 °C region, suggesting that in these copolymers the motions involved in the ft transition of BPA-PC can occur within the B blocks. The larger tan 8 peak around - 25 to 0 °C reflects the motions encountered in the alternate BT copolymer. However, it is worth noting that a deeper analysis of the whole set of results would require consideration of the dynamic mechanical loss compliance, /", as done in Sects. 6, 7 and 8. 

Furthermore, a quantitative analysis [60] performed on the loss compliance, J", shows that the intensity of the y transition is mostly determined by the amount of lactam-12 units and does not depend on the nature, iso- or fere-, of the phthalic acid. 

The dynamic mechanical response of a material can be characterised through the loss modulus, the loss tangent, tan S, or the loss compliance, However, as already mentioned for Ar-Al-PA (Sect. 6), the loss compliance can be considered the most relevant parameter for quantitatively comparing different materials, at least for additive purposes. For this reason, the semi-quantitative analysis and the comparison of viscoelastic data determined for different systems have been performed [63] in terms of /", whereas the determination of activation energies and entropies are based on loss modulus data. 

Fig. 95 Temperature dependencies of the loss compliances, /", determined at 1 Hz for the HMDA, HA60 and HA95 systems (from [63])...

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