Modulus transform molecular

Fig. 3.22 Frequency-dependent dynamic modulus G"(co) from a PE chain of M =800 kg/mol at 509 K. The solid line gives the reptation prediction of G co)-cor . The peak here may not be confused with the a-relaxation of the glass dynamics. It immediately follows from the Fourier transform of strongly depends on molecular weight. The glass relaxation...

The theory is not limited in its application to the transient properties of amorphous polymers it can be used to make molecular interpretation and prediction of the dynamic viscoelastic properties of crosslinked polymers [24] as well. According to the Fourier-Laplace transformation, the complex tensile modulus can be separated into the real and imaginary parts... 

Although the (Simplex shear modulus is not the most appropriate function to use in all c ses, we wUl describe the linear viscoelastic behaviour in terms of this last function, which is tiie most referred to experimentally furthermore, molecular models are mostly linked to the relaxation modulus, which is the inverse Fourier transform of the complex shear modulus. 

Fig. 17 shows that the single filament tenacity (Instron) of the precursor may be considered as a suitable, simple indicator for molecular orientation. For a wide variety of precursor compositions, comonomer concentrations and spinning conditions, there is a relatively good linear relationship between sonic modulus and tenacity of the precursor fiber. The identification of the data points is given in Table 11. (Not all of the fibers used for Fig. 17 have been actually transformed to carbon fibers some of the AN/VBr carbon fiber data are taken from Sect. 5.)... 

The potential of Eq. (1) with parameters determined in Refs. [10, 11] was thoroughly tested in computer simulations of silica polymorphs. In Ref. [10], the structural parameters and bulk modulus of cc-quartz, a-cristobalite, coesite, and stishovite obtained from molecular dynamics computer simulations were found to be in good agreement with the experimental data. The a to / structural phase transition of quartz at 850 K ha.s also been successfully reproduced [12]. The vibrational properties computed with the same potential for these four polymorphs of crystalline silica only approximately reproduce the experimental data [9]. Even better results were reported in Ref. [5] where parameters of the two-body potential Eq. (1) were taken from Ref. [11]. It was found that the calculated static structures of silica polymorphs are in excellent agreement with experiments. In particular, with the pressure - volume equation of state for a -quartz, cristobalite, and stishovite, the pressure-induced amorphization transformation in a -quartz and the thermally induced a — j3 transformation in cristobalite are well reproduced by the model. However, the calculated vibrational spectra were only in fair agreement with experiments. 

The pH-value and Si02 content of this hydrosol are determined by the concentration of the raw materials and their mixing ratio. Typically acid excess is preferred, as under these conditions the intermediate sol is more stable and the process is less sensitive to feed fluctuations. During the sol-forming step an unstable intermediate-monomeric orthosilicic acid — is formed which then rapidly undergoes an acid-catalysed condensation reaction to form oligomers. When the molecular weight reaches ca. 6000, a sudden increase of both the viscosity and the modulus of elasticity is observed. This increase marks the transformation of the sol to a gel that will then further develop its internal structure. 

Equation (9.19) accurately describes the observed characteristics associated with the transformation of the G t) line shape with changing molecular weight. To illustrate the capability of the theory in describing these characteristics, the relaxation modulus curves calculated from Eq. (9.19) at Mw/Me = 10, 20 and 40, all with the polydispersity of Mm/M = 1.05, are shown in Fig. 9.4 for comparison with the experimental results, as shown in Fig. 4.6. In Chapter 10, in terms of the theory, quantitative analyses of the relaxation modulus curves of a series of nearly monodisperse polystyrene samples will be described in detail. 

A change of the order parameter modulus S (r) can also create polarization, for example due to transformation of the ellipsoidal shape of Q tensor in space. In this case we deal with the so-called ordoelectric polarization [14]. Indeed, decreasing S value results in less extended (less prolate) ellipsoid form without reorientation of its principal axes. Such a transformation may be caused by a scatter of the rigid molecular quadrupoles with respect to the director axis the stronger the scatter, the lower is the quadmpole order S and the less prolate ellipsoid Q. This is illustrated by Fig. 10.12 in sketch (a) the order parameter is stronger at the surface and... 

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