Dynamic moduli variation with temperature

Figure 6 Typical plots from dynamic mechanical thermal analysis showing storage modulus and tan6 variation with temperature [27]. SO (---), S2 (--).

Dynamic thermal mechanical analysis indicates significant broadening of glass transition temperature at or around PU/EP composition of 70/30. This is true for all three groups studied. At this composition, storage modulus showed much less steep variations with temperature during the transition from glassy to rubbery state. 

Fig. 42. Variation of elastic modulus, E, with temperature and radiation dose (dynamic values) [428].

Fig. 38 Variations of dynamic storage modulus G/ with temperature during the isochronal dynamic temperature sweep experiments at co = O.lrad/s for (open circle) SI-2, open triangle) IS-t-COONa, open square) (IS-t-COONa)/Cloisite SOB nanocomposite, and open inverted triangle) (IS-t-COONa)/Cloisite 20A nanocomposite, (Reprinted from Zha et al. [55], Copyright 2005, with permission from the American Chemical Society)...

Figure 10. The variation of the dynamic storage modulus (G ) of UHMWPE pseudo-gels of different concentration (w/w) with temperature at =50 sec"l.

The variation of the damping factor (tan 5) with temperature was measured using a Polymer Laboratories Dynamic Mechanical Thermal Analyzer (DMTA). The measurements were performed on the siloxanfe-modified epoxies over a temperature range of — 150° to 200 °C at a heating rate of 5 °C per minute and a frequency of 1 Hz. The sample dimensions were the same as those used for flexural modulus test specimens. 

Figure 7.5 Dynamic mechanical spectra showing the variation of storage modulus (.S, 9) and loss modulus (E",0) with temperature for emulsion polymers prepared from styrene (50 wt%) and ethyl acrylate (50 wt%) using different processes (adapted from ref. 65).

The dependence of the relaxation temperatures on the level of absorbed water is known from dynamic mechanical studies (82,87,89) as well as dielectric studies (90). The temperature variations with sorbed moisture of the loss modulus peaks for the three relaxations are shown in Figure 38 (82). The test frequency for the three relaxations varies slightly but is around 1 Hz. The data indicate that the temperature of the a relaxation at a given frequency decreases by about 100°C between dryness and saturation. The relaxation is also shifted to lower temperatures and higher frequencies by absorbed water, while the temperature of the y relaxation is only slightly affected, shifting somewhat to lower temperatures and higher frequencies. 

Rheological models have been described for steady shear viscosity function, normal stress difference function, complex viscosity function, dynamic modulus function and the extensional viscosity function. The variation of viscosity with temperature and pressure is also discussed. 

To understand this variation, one can look for the answer with variations of bulk properties with M. For this purpose the Fox and Flory law (58, 59) which gives a equivalence between and glass transition temperature as given in Figure 8a can be used and applied to the variation of PS mechanical dynamic modulus with temperature determined by Perez (60) (Figure 8b), supposing that this M -temperature equivalence doesn t affect the variation of the dynamic modulus. The maximal variation of the dynamical modulus with Mw is about 15% from the smallest to the highest Mw samples. It is thus insufficient to explain a variation of the friction coefficient of about a factor of two. 

Figure 8b Variation of the dynamic modulus values of one PS sample with temperature as adapted from (59). Using Fox and Flory equivalence between temperature and weight given in figure 9a, circles are pointed corresponding to the sample used for those studies.

The dynamic properties of filled rubbers are widely studied by many researchers in this field of which the contribution made by Payne is the most significant. The dependence of strain amplitude on the storage modulus in filled mbbers is known as the Payne effect [27]. At a strain more than 0.1 %, the storage modulus of filled rubber collapses from a plateau value of G O to a minimum value Goo and this decrease is accompanied by a maximum of the loss modulus, G". The variation in this storage modulus value with respect to the minimum value is called amplitude of the Payne effect, and this increases with the filler content, specific surface and properties of the filler and its dispersion within the matrix. The amplitude inversely changes with temperature. A lot of investigations were performed in order to explain the Payne effect and reasons behind it. Payne neglected the contribution... 

Dynamic mechanical spectroscopy of these copolymers showed that the batch latexes comprised a two-peaked distribution of copolymer compositions and the semi-continuous latexes, a single-peaked distribution. Figure 6 shows the variation of log modulus with temperature for the 49 51 vinyl acetate-butyl acrylate molar ratio, which is typical of the difference between the batch and... 

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