Viscoelastic spectra

Characteristic maximum relaxation time determined from the terminal region of the viscoelastic spectrum. 

A series of modulus-time curves was also made for temperatures covering the entire viscoelastic spectrum. At higher temperatures, the instrument was first allowed to reach the desired temperature and was held there for half an hour. Samples were then quickly inserted. After 10 minutes moduli were measured as a function of time up to 1000 seconds. Total measuring time for each isotherm thus was kept to less than 30 minutes to minimize chemical decomposition and plasticizer evaporation. 

The addition of a monofunctional POSS epoxy did not alter the shape of the viscoelastic spectrum despite their ability to shift it to higher temperatures. This means that the POSS epoxy nano-reinforcement did not contribute... 

The narrowing of the viscoelastic spectrum as salinity increases is analogous to motional narrowing of line widths in NMR spectroscopy. The narrowing process occurs when the breakage time Tbr becomes smaller than the reptation time Trep. In the limit Tbr Trep, the Gates model predicts that G(t) is monoexponential, with a time constant t given by... 

In actual long term applications of polymers, however, it is well known that chemical reactions occur which actually change the viscoelastic properties of the material while it is in use. In addition, environmental factors such as exposure to solvents or even water, while not always chemically modifying a material, can have a profound influence on its viscoelastic properties in much the same way as a true chemical transformation. If predictions based exclusively on time-temperature correspondence were to be successful, the rates of all of these processes would have to vary with temperature in exactly the same m inner as does the viscoelastic spectrum. While this might be approximately true in certain special cases, it is usually not so. Thus, a more general theoretical framework is necessary to predict the properties of simultaneously chemically reacting and physically relaxing networks. 

A more realistic alternative to free-volume-derived models is to interpret relaxation and related properties of polymers in terms of the interactions among segments. Thus, in the softening regime of the viscoelastic spectrum, falling... 

Viscoelastic spectrum Quasi-elastic neutron scattering... 

The result expressed as a function of the oscillatory frequency w is often referred to as the viscoelastic spectrum. Because the polymeric liquid has both the viscous and elastic properties, the time dependence of the induced stress will not be totally either in phase or out of phase with the oscillatory rate-of-strain. Substituting Eq. (4.31) into Eq. (4.22), we obtain the stress... 

The measured G and G" (or equivalently rj and 77") values, as a function of the frequency w, can be displayed as a spectrum — the viscoelastic spectrum. Figures 4.9 and 4.10 show the storage modulus spectra G lo) and the loss modulus spectra G" oj), respectively, of a series of nearly monodisperse polystyrene samples. 

Furthermore, in the line-shape analyses of these viscoelastic spectra, the molecular-weight distributions of P7, FIO, F35, and F80 included in the calculations are identical, respectively, to those extracted from the line-shape analyses of the spectra of the pure melt systems, some of which have been shown in Chapter 10. Thus, the close agreements between theory and experiment in the line-shape analyses have been achieved under the consistency of maintaining the same molecular-weight distributions of the samples between the pure-melt and blend-solution systems. Thus, in a quantitative way, the universality of viscoelastic spectrum is shown extending over the melt and blend-solution systems in accordance with Eq. (11.5) with the molecular weight normalized with respect to Mg for the melt and Mg for the blend solution. 

The transformation of the viscoelastic spectrum with changing concentration is well explained in terms of Eq. (11.5) with M given by Eq. (11.4). 

As discussed in this section, the tube-dilation effect, i.e. M J/Me > 1, mainly occurs in the terminal-relaxation region of component two in a binary blend. This effect means that the basic mean-field assumption of the Doi-Edwards theory (Eq. (8.3)) has a dynamic aspect when the molecular-weight distribution of the polymer sample is not narrow. This additional dynamic effect causes the viscoelastic spectrum of a broadly polydisperse sample to be much more complicated to analyze in terms of the tube model, and is the main factor which prevents Eq. (9.19) from being applied... 

In the short-time or high-frequency region of the viscoelastic response (relaxation modulus G t), viscoelastic spectrum G (w) or creep compliance J(t)) of a polymer melt with modulus values in the range from lO to 10 °dynes/cm (or compliance values in the range from to... 

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