Loss tangent network

However, because measurements are kinetically determined, this is a less accurate form of the equation. Very often it is observed that the measured shift factors, defined for different properties, are independent of the measured property. In addition, if for every polymer system, a different reference temperature is chosen, and ap is expressed as a function of T — rj, then ap turns out to be nearly universal for all polymers. Williams, Landel and Ferry believed that the universality of the shift factor was due to a dependence of relaxation rates on free volume. Although the relationship has no free volume basis, the constants and may be given significance in terms of free volume theory (Ratner, 1987). Measurements of shift factors have been carried out on crosslinked polymer electrolyte networks by measuring mechanical loss tangents (Cheradame and Le Nest, 1987). Fig. 6.3 shows values of log ap for... 

All the above observations seem to justify Porter s approach (Eq. 11.11)), according to which the Poisson s ratio should depend only on the cumulative loss tangent. It was found that the unrelaxed Poisson s ratio determined from ultrasound (5 MHz) propagation rate, for 12 of amine-crosslinked epoxy stoichiometric networks, displays only small variations (Av < 0.01), in spite of the relatively large variations of the cohesive energy density (0.59 < CED <0.66 GPa) and the crosslink density (2.0 5.9 mol kg 1)-... 

A more selective approach consists in trying to influence the kinetics of formation of at least one network in this case, the two networks are formed more or less simultaneously, and the resulting morphology and properties can be expected to vary to some extent without changing the overall composition. The same system as previously studied, PUR/PAc, has been utilized in order to prepare a series of in situ simultaneous IPNs (SIM IPNs), by acting essentially on two synthesis parameters the temperature of the reaction medium and the amount of the polyurethane catalyst. Note that the term simultaneous refers to the onset of the reactions and not necessarily to the process. The kinetics of the two reactions are followed by Fourier transform infra-red (FTIR) spectroscopy as described earlier (7,8). In this contribution, the dynamic mechanical properties, especially the loss tangent behavior, have been examined with the aim to correlate the preceding synthesis parameters to the shape and temperature of the transitions of the IPNs. 

While G >G" for the imperfect network, the storage modulus (filled squares) has a weak frequency dependence and the loss modulus (open squares) is significantly larger than for the perfect network. Both of these observations are caused by the gradual relaxation of dangling structures in the imperfect network (see Problem 9.43). The loss tangent tan 8 — G"jG is nearly perfect networks made by much larger for the imperfect network than for the nearly perfect one. 

The evolution of visco-elastic properties in non-Newtonian fluids exhibiting time-dependent rheological changes is a matter of wide scientific interest, particiflarly so in systems undergoing gelation. The gel-point, where a three-dimensional network structure is established, may be identified rheologically by the establishment of a eharacteristic frequency dependence of the dynamic moduli, and an associated frequency independent loss tangent [Winter and Chambon, 1986]. 

Figure 3.15 Plot of loss tangent versus temperature plots of epoxy networks cured with polyetheramine (Jeffemine) of various chain lengths SD-1 (Jeff-300), SD-2 (Jeff-500) and SD-3 (Jeff-800). Reprinted with permission from D. Ratna, N.R. Manoj, L. Chandrasekhar and B.C. Chakraborty, Polymers for Advanced Technologies, 2004, 15, 10,583 2003, John Wiley and Sons Publishers...

Thermal conductivity and flexural strength and volume resistivity are as good as conventional LTCC material. Because fine leak rate by helium gas through this material is less than 1 x 10 Pam /s, it is possible to measure the hermeticity of the package by fine leak method. Dielectric constant and loss tangent were determined by dielectric resonator method using an HP 8757C network... 

Several power functions were foimd between various physical quantities in relation to polymer gel. Of these power laws, the discovery of the relations for frequency and dynamic viscoelasticity of G (co) and G"(cb) has attracted much interest, and many research workers followed the frequency power law of the gelation. The application of the frequency power law to the gel point was first proposed by Winter et al. (Winter and Mour, 1997) Their experimental results suggested, at first, new methods for localising the gel point by the detection of a loss tangent independent of the frequency. Moreover, they discussed that the topological self similarity in the polymer network can be related to the straight line in G (o))... 

Figure 7.23. Temperature dependence ofme-chanical loss tangent in IPITs without filler (1-3), with 20% (4-6) and 40% (7-9) at various initiator concentrations a-0.74.10, b-2.96.10, c-5.4.10 mol/1. [Adapted by permission from Y. S. Lipatov, T. T. Alekseeva, V. F. Rosovitsky, and N. V. Babkina, Polym. Networks Blends, 4, 9 (1994)]...

The data on the temperature dependence of the elastic modulus and of the mechanical loss tangent are given in Fig. 38. It is seen that semi-IPNs are typical two-phase polymeric systems, exhibiting two relaxation transitions (determined from the positions of loss tangent maximiun). The shape of the temperature dependence of elastic modulus is also typical of two-phase systems. At the same time, a substantial shift in Tg of the hnear polymer from 343 to 308 K (samples 8-3) and a less marked shift in Tg of the PU network indicate the formation in the system of two phases with dissimilar compositions. The concurrent processes of PU network formation and microphase separation caused by thermodynamic immiscibihty of components result in the formation of phases enriched in one of the components. 

Fig. 43 Temperature dependencies of mechanical loss tangent for epoxy-diene networks. Numbers of curves correspond to (1) 19.6% of epoxy blocks, (2) 31.4%, (3) 46.6% [243]...

---