Time-temperature superposition dynamic shear

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 maximum strain rate (e < Is1) for either extensional rheometer is often very slow compared with those of fabrication. Fortunately, time-temperature superposition approaches work well for SAN copolymers, and permit the elevation of the reduced strain rates kaj to those comparable to fabrication. Typical extensional rheology data for a SAN copolymer (h>an = 0.264, Mw = 7 kg/mol,Mw/Mn = 2.8) are illustrated in Figure 13.5 after time-temperature superposition to a reference temperature of 170°C [63]. The tensile stress growth coefficient rj (k, t) was measured at discrete times t during the startup of uniaxial extensional flow. Data points are marked with individual symbols (o) and terminate at the tensile break point at longest time t. Isothermal data points are connected by solid curves. Data were collected at selected k between 0.0167 and 0.0840 s-1 and at temperatures between 130 and 180 °C. Also illustrated in Figure 13.5 (dashed line) is a shear flow curve from a dynamic experiment displayed in a special format (3 versus or1) as suggested by Trouton [64]. The superposition of the low-strain rate data from two types (shear and extensional flow) of rheometers is an important validation of the reliability of both data sets. 

From dynamic experiments and applying the time temperature superposition principle, the complex shear modulus is measured over about five decades and the Rouse model can be checked extensively [37]. 

Figure 1. Linear dynamic oscillatory shear response of the 50K PBA based Si02 hybrid sample. The data collected at temperatures between 30 and 80 °C were reduced to a single master curve using the principle of time-temperature superpositioning. The horizontal frequency shift factors (af were similar to that for the pure PBA homopolymer.

Blends of atactic poly(methyl methacrylate) with poly(ethylene glycol), PMMA/PEG, were reported miscible [Colby, 1989]. Their rheology, PMMA/PEG = 50/50 and 80/20 at T = 160-210°C, was studied in a dynamic shear field [Booij and Palmen, 1992]. By contrast with homopolymers, the blends did not follow the time-temperature superposition. The deviation was particularly large at low temperatures. The reason for the deviation is most likely based on the different temperamre dependence of the relaxation functions. The authors concluded that in miscible blends, the temperature dependence of the relaxation times of individual macromolecules depends on composition. This leads to different degrees of mutual entanglement and hence the rubber plateau moduli. 

Rheological measurements were performed in a stress rheometer fixture with a 2-cm cone and plate having a 1° cone angle and gap of 27 pm. Dynamic shear moduli were measured at 0.5% strain between 0.1 and 100 rad/s. Creep compliance was measured with a constant applied stress in the range of 0.1 to 5 kPa. Both measurements were performed over a series of temperatures to obtain data for time-temperature superposition. 

Ye and Sridhar report dynamic moduli and shear thinning in solutions of three-arm star polystyrenes dissolved in di-n-butylphthalate(29). Unlike many other authors. Ye and Sridhar identified each point as to its measmement temperature, permitting testing of refinements to simple time-temperature superposition. Figure 13.19 shows G oo) oo and G" oo)joo. The G" co)lco accurately follows the ansatz forms. With increasing c the power-law exponent and the exponential prefactor a increase and the stretching exponent v decreases. The G [Pg.417]

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