Storage Time-temperature superposition

Fig. 21. Storage modulus (G ) for PCL based silicate nanocomposites. Silicate loadings are indicated by percentual values in the figure. Master-curves were obtained by application of time-temperature superposition and shifted to T0=55 °C. From Ref. [54].

While this paper reports only preliminary findings. It does Illustrate the usefulness of photocalorimetry to define optimum cure conditions for UV curable adhesives. In addition, once the mechanical spectrum of fully cured adhesive has been mapped, mechanical spectroscopy can be used to monitor cure efficiency. In this paper we have not explored the molecular weight Implications of Incomplete polymerization. Preliminary evaluation of loss and storage modulus data would suggest that time-temperature superposition may be necessary to evaluate molecular welght/degree of cure relationships and terminal, plateau, and transition zones (4). 

Fig. 6.12 Illustration of (a) the storage modulus, the loss modulus and the loss factor as a function of frequency across the glass transition temperature of amorphous polymers (b) the loss factor as a function of temperature according to the time-temperature superposition principle. Below the a peak for glass transition, there are secondary relaxation peaks...

The investigation of the Han plots, which is the log-log plot of storage modulus versus loss modulus, is another effective method to determine the onset of phase separation. This method is more sensitive to concentration fluctuations than data obtained from time-temperature superposition. The Han plot of homogeneous phases shows two main features temperature independence and terminal slope of two (Han et al. 1990, 1995). Deviations from these two criteria were reported only for Han plots above the LCST and below the UCST (Kim et al. 1998 Sharma and Clarke 2004). Therefore, it has been suggested to use this method to infer the phase-separation (binodal) temperature rheologicaUy. 

Yu et al. (2011) studied rheology and phase separation of polymer blends with weak dynamic asymmetry ((poly(Me methacrylate)/poly(styrene-co-maleic anhydride)). They showed that the failure of methods, such as the time-temperature superposition principle in isothermal experiments or the deviation of the storage modulus from the apparent extrapolation of modulus in the miscible regime in non-isothermal tests, to predict the binodal temperature is not always applicable in systems with weak dynamic asymmetry. Therefore, they proposed a rheological model, which is an integration of the double reptation model and the selfconcentration model to describe the linear viscoelasticity of miscible blends. Then, the deviatirMi of experimental data from the model predictions for miscible... 

Figure 10. Partial master curves of shear storage and loss moduli for 10 g dL l xylene solutions of a, u) -Be, Mg, Ca and Ba dicarboxylato PBD (Hycar CTB), respectively. Reference temperature 297°K. Six isotherms have been reported between 297 and 342°K and obey time-temperature superposition.

The composite natm e of polyurethane elastomers strongly affects their linear viscoelastic properties. It is known that for most polymers, linear viscoelastic moduli (storage modulus, E u,T), and loss modulus, E" u,T)) are characterized by the so-called time-temperature superposition (TTS) (see, e.g. Ferry [74]). Such behavior can be understood if one assumes that E (and E") is always a function of the product ut T), where t(T) is effective relaxation time. 

This chapter covers some of the methods and instruments used to determine the mechanical properties of polymers. Examples of instrument designs and typical data generated in these measurements will be introduced. In particular, automated axial tensiometers (to find elastic modulus, yield stress, and ultimate stress), dynamic mechanical analyzers (to determine storage and loss moduli), and rheometers (to measure flow viscosity) will be introduced. This chapter considers the principles behind the devices used to establish and measure the properties of viscometric flows. One of the common techniques used to determine viscous flow properties, PoisueiUe (laminar) flow in cylindrical tubes, is also important in technical applications, as polymer melts and solutions are often transported and processed in this manner. The time-temperature superposition principle is also covered as a way to predict polymer behavior over long timescales by testing materials across a range of temperatures. 

Figure 13.5 (O) Storage and (0) loss moduli of 49 g/1 5.48 MDa polystyrene in tricresylphosphate over a wide range of nominal frequencies, data being generated using a time-temperature superposition process, and functional fits to the data, beginning with measurements of Inoue, et fl/.(17).

Figure 13.15 Storage (O) and loss ( ) moduli of 10 wt% 1.24 MDa polybutadiene in 1 or 1.5 kDa phenyl-terminated polybutadiene as measured with a dynamic mechanical spectrometer, using time-temperature superposition with a 100 K temperature range, based on data of Tapadia and Wang(26). Solid lines are stretched exponentials and sums of two power-law decays.

The time-temperature superposition principle has been applied to the loss and storage moduli. For the homogeneous blend (one phase at temperature equal to 115 C), the superposition method works very well. Typical low frequency behaviours of G and G are shown by the lines in Figure 10. For temperatures close to (125, 135 and 140 C), a shoulder develops in the low frequency region for the storage modulus and becomes more important as the temperature is closer to T. This behaviour is similar to that observed by Bates et al. [19] for block copolymers near in the homogeneous region (disordered zone). In fact, these temperatures are well below as determined... 

Figure 46. Storage modulus, C/, of gluten - water mixtures in a time sweep test 10% strain, I Hz frequency). The master curve has been obtained by applying the time-temperature superposition principle. Temperatures considered 40 ( ), 50 ( ), 60 (0), 70 (O), 80 (A), and 90 ( ) °C (modified from [263])...

---