Viscoelasticity spectra

With this choice of j8, the theoretical picture presented in this section is consistent, for example, with the range in MJM (from about 2 to about 20) explored by the polyisoprene (PI) data set of Fetters et al. [5] using a single value of Mg of 5000 g mol" The viscosities of these melts cover five decades in magnitude yet the current theory, together with values for Gq and Tg consistent with data on linear PI predicts the entire range of viscoelastic spectra (see Fig. 9). 

The power laws for viscoelastic spectra near the gel point presumably arise from the fractal scaling properties of gel clusters. Adolf and Martin (1990) have attempted to derive a value for the scaling exponent n from the universal scaling properties of percolation fractal aggregates near the gel point. Using Rouse theory for the dependence of the relaxation time on cluster molecular weight, they obtain n = D/ 2- - Df ) = 2/3, where Df = 2.5 is the fractal dimensionality of the clusters (see Table 5-1), and D = 3 is the dimensionality of... 

Overall, the semi-quantitative agreement between the linear viscoelastic spectra and first-principles MCT calculations is very promising. Yet, crystallization effects in the data prevent a closer look, which will be given in Sect. 6.2, where data from a more polydisperse sample are discussed. 

Since the viscosity is the integration of G t) (Eq. (4.30)), the relaxation modulus G t) should contain more detailed information than the single viscosity value r/o. A wrong conclusion can be made if the conclusion is simply based on the viscosity result. On the basis of the viscosity data (Fig. 4.7), the onset of entanglement was traditionally believed to occm at Me 2.4Me. Shown in Chapters 10 and 11, detailed studies of the viscoelastic spectra in terms of the extended reptation theory as well as the Rouse theory have indicated that the onset occurs at Me-... 

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. 

This universality has also been illustrated by Watanabe et al. in another way. They compared the line shapes of the viscoelastic spectra of a nearly monodisperse polystyrene melt (sample L161 with = 1.72 x 10 and Myj/Mn = 1.07) and a blend solution (consisting of two nearly monodisperse polystyrene polymers L407 with Miu = 4.27 x 10 and M /Mn = 1.05 as component two and sample LIO with = 1.05 x 10 and Mw/Mn = 1.08 as component one the weight-fraction ratio of the blend is... 

Table 14.1 Characteristics M, M /Mn and Tg (based on DSC and defined at ts = 1,000sec) and parameters A, / and Z extracted by analyzing the creep-compliance J(t) curves or viscoelastic spectra G (ta) of the polystyrene samples, whose structural-relaxation times TS, structural-growth parameters s and frictional factors K are displayed, respectively, in Figs. 14.13, 14.14 and 14.15. Also shown are the K values at 127.5°C of samples A, B, C and F2 along with the average value of K shown in Table 10.1 and the Mw, MwjMn, and Tg (DCS) of F2. The reference theory used in each analysis is indicated. 

Fig. 14.10 The viscoelastic spectra G (cj) of LIO measured at different temperatures (V at 92°C A at 95°C O at 99°C at 105°C A at 110°C at 120°C and at 130° C) composed together by matching all the spectra over the glassy-relaxation region (using 105° C (AT = 15K) as the reference temperature) and superimposed on the corresponding calculated curves (the glassy-relaxation region solid line the entropic region solid line at 105°C (AT = 15K), long-dash line at 110°C (AT = 20K), medium-dash line at 120°C (AT = 30K), and short-dash line at 130°C (AT = 40K)).

I am grateful to Professors M. D. Ediger and T. Inoue for providing their data in digital form. The data from Professor Ediger are used in Fig. 15.1. The data from Professor Inoue allow the analyses of viscoelastic spectra to be a smooth process, as presented in Chapter 14. 

Figure 7.6 shows viscoelastic spectra at 35 C for different concentrations. This figure demonstrates that the crossing of the storage modulus (G ) and the loss modulus (G") is observed at the frequencies 20-100 rad s , which is much lower... 

Figure 7.7b shows the concentration dependence of the plateau modulus obtained from the fitting of the viscoelastic spectra. We have also calculated GL from Tls and 770 by using the relation... 

Figure 7.8 shows the phase diagram of the C16E7/D2O system reported previously [22, 29] where experimental points for the steady-state viscosity and viscoelastic spectra are shown by crosses and circles, respectively. The experimental points for the light-scattering and self-diffusion measurements are almost the same as those for the steady-state viscosity. 

Figure 7.6 Viscoelastic spectra at 35 °C and different concentrations for C16E7/D2O system. The closed and open symbols indicate the storage modulus (C ) and the...

Figure 7.8 Phase diagram of C16E7/D2O system [22, 29]. The circles and crosses indicate experimental points for the viscoelastic spectra and steady-state viscosity, respectively.

For probe tack, the newly measured debonding energies constitute a new dimension for short duration performance. In addition to the peak force, tack energy should be considered in many high speed applications. Since the peak force and tack energy appeared to have originated from different parts of the viscoelastic spectra, it offered an opportunity to adjust the formulation for optimum performance. 

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