Time-temperature superimposed moduli

Fig. Z4 (a) Temperature ramp at a frequency a> = lOrads (strain amplitude A = 2%) for a nearly symmetric PEP-PEE diblock with Mn = 8.1 X 104gmol l, heating from the lamellar phase into the disordered phase. The order-disorder transition occurs at 291 1 °C, the grey band indicates the experimental uncertainty on the ODT (Rosedale and Bates 1990). (b) Dynamic elastic shear modulus as a function of reduced frequency (here aT is the time-temperature superposition shift factor) for a nearly symmetric PEP-PEE diblock with Mn = 5.0 X 1O g mol A Shift factors were determined by concurrently superimposing G and G"for w > and w > " respectively. The filled and open symbols correspond to the ordered and disordered states respectively. The temperature dependence of G (m < oi c) for 96 < T/°C 135 derives from the effects of composition fluctuations in the disordered state (Rosedale and Bates 1990). (c) G vs. G"for a PS-PI diblock with /PS = 0.83 (forming a BCC phase) (O) 110°C (A) 115°C ( ) 120°C (V) 125°C ( ) 130°C (A) 135°C ( ) 140°C ( ) 145°C. The ODT occurs at about 130°C (Han et at. 1995).

The Time-Temperature Superposition Principle. For viscoelastic materials, the time-temperature superposition principle states that time and temperature are equivalent to the extent that data at one temperature can be superimposed upon data at another temperature by shifting the curves horizontally along the log time or log frequency axis. This is illustrated in Figure 8. While the relaxation modulus is illustrated (Young s modulus determined in the relaxation mode), any modulus or compliance measure may be substituted. 

The second important consequence of the relaxation times of all modes having the same temperature dependence is the expectation that it should -bp possible to superimpose linear viscoelastic data taken at different temperatures. This is commonly known as the time-temperature superposition principle. Stress relaxation modulus data at any given temperature Tcan be superimposed on data at a reference temperature Tq using a time scale multiplicative shift factor uj- and a much smaller modulus scale multiplicative shift factor hf. 

Demonstration of the time-temperature superposition principle, using oscillatory shear data (G, filled circles and G", open diamonds) on a PVME melt with M — 124000 gmol. The right-hand plot shows the data that were acquired at the six temperatures indicated, with Tg = - 24°C chosen as the reference temperature. All data were shifted empirically on the modulus and frequency scales to superimpose, constructing master curves for G and G" in the left-hand plot. Data and... 

Within this regime it is found that the modulus E at one temperature can be related to that at another by a change in the time scale only, that is, there is an equivalenee between time and temperature. This means that the curve describing the modulus at one temperature can be superimposed on that for another by a constant horizontal displacement log (aj) along the log (t) axis, as shown in Fig. 23.5. 

Figure 15.8 shows the creep data obtained for PC in the temperature range 130-155 C. The logarithm of creep compliance (S) is shown as a function of the logarithm of decay time. One of the curves is selected as the reference (in this case, T = 145 °C), then the other curves are shifted along the log time axis and superimposed upon the reference curve. The final master curve based on creep data is shown in Figure 15.9. The curve shows that at small time intervals the material exhibits relatively low compliance (or high modulus). At longer times, viscous flow occurs and the material exhibits a high compliance (or modulus). Thus this master curve clearly demonstrates the effects of time on the mechanical properties of PC.

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