Shear moduli factors that determine

Since hardness and the shear modulus are usually proportional, the factors that determine the shear moduli need to be understood. The shear moduli are functions of the local polarizability and this depends on the valence electron density, as well as the energy needed to promote a valence electron to its first excited state. The latter depends on the strength of the chemical bond between two atoms. This will be discussed in more detail in Chapter 3. 

The paper first considers the factors affecting intramolecular reaction, the importance of intramolecular reaction in non-linear random polymerisations, and the effects of intramolecular reaction on the gel point. The correlation of gel points through approximate theories of gelation is discussed, and reference is made to the determination of effective functionalities from gel-point data. Results are then presented showing that a close correlation exists between the amount of pre-gel intramolecular reaction that has occurred and the shear modulus of the network formed at complete reaction. Similarly, the Tg of a network is shown to be related to amount of pre-gel intramolecular reaction. In addition, materials formed from bulk reaction systems are compared to illustrate the inherent influences of molar masses, functionalities and chain structures of reactants on network properties. Finally, the non-Gaussian behaviour of networks in compression is discussed. 

In addition to knowing the temperature shift factors, it is also necessary to know the actual value of ( t ) at some temperature. Dielectric relaxation studies often have the advantage that a frequency of maximum loss can be determined for both the primary and secondary process at the same temperature because e" can be measured over at least 10 decades. For PEMA there is not enough dielectric relaxation strength associated with the a process and the fi process has a maximum too near in frequency to accurately resolve both processes. Only a very broad peak is observed near Tg. Studies of the frequency dependence of the shear modulus in the rubbery state could be carried out, but there... 

The number of resonant peaks that can be measured is dependent on the loss factor of the material, but, typically, there are three to five peaks. As expected, the resonant peaks appear at higher frequencies in the glassy state than in the rubbery state. From the amplitude and frequency of each measured resonant peak. Young s modulus and loss factor are determined at the corresponding frequency and temperature. By assuming Poisson s ratio of 0.5, Young s modulus is converted to shear modulus. The loss factor in extension is assumed to equal the loss factor in shear. 

Results obtained using the order parameter determined by SALS, as the value of the orientation efficiency factor, are always closer to the lower bound values of the Young s modulus of the composites. The order parameter is determined as a function of the angle of the fibers to the shear direction, meaning that its value will be more accurate for an in-plane distribution of the fibers. This would probably be the case if the fibers had higher aspect ratio. Nevertheless, SALS seems to be a promising... 

Firstly, it has been shown that there may be many experimental problems in a direct determination of the experimental fimction. In shear, damping functions obtained from step strain and from step strain rate experiments do not match each other. This poses an important question on the validity of the separability assumption in the short time rai e. Significant departures from this factorization have already been observed in the case of narrow polystyrene fractions by Takahashi et al. [54]. These authors found that time-strain superposition of the linear and nonlinear relaxation moduli was only possible above a cert2un characteristic time. It is interesting to note that this is predicted by the Doi-Edwards theory [10] and according to this theory, this phenomena is attributed to an additional decrease of the modulus connected to a tube contraction process and time-strain separability may hold after this equilibration process has been completed. Other examples of non-separability were also reported by Einaga et al. [55] and more recently by Venerus et al. [56] for solutions. 

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