Shift factors, temperature dependence

Scalco, Huseby, and Blyler (8), Zosel (9), and Bergen and Morris (10). Prest and Porter (23) applied the same principle to homopolymer blends [poly (2,6-dimethylphenylene oxide)-polystyrene]. Recently some papers were published on triblock copolymers of styrene-butadiene-styrene and on their blends with polybutadiene (24, 25). Triblock copolymers can be considered heterophase material as the different constituent blocks are thermodynamically incompatible with each other, and, consequently, polystyrene domains are enclosed in polybutadiene (continuous matrix). The findings indicate that these systems are in general thermorheologically complex, so that the shift factor ar depends not only on temperature but also on time. These conclusions have been extrapolated to other two-phase systems. 

There is also the issue whether the temperature shift factor ax depends on the technique used or is it a property of the material independent of the kind of experiments performed. In derivation of equation 28 it was assumed that ax is a material property (2,3). This is confirmed by experiments. The continuous line seen in Figure 16 agrees with the experimental shift factors obtained from creep (shown as circles) equally well as with ax values obtained from stress relaxation results (64). 

The Knauss-Emri Model. There have been several works in the literature in which volume- or ee-ooZume-dependent clocks were used to describe the nonlinear viscoelastic response of polymeric glasses. The chief success among these is the ICnauss-Emri model (163) in which the reduced time was defined in terms of a shift factor that depended on temperature, stress, and concentration of small molecules in such a way that the responses depended on the free volume induced by each of these parameters. For an isothermal single phase and homogeneous material, the equations are... 

From the data in Fig. 4.8b, estimate the shift factors required to displace the data at 0 = 0.5 (consider only this point) so that all runs superimpose on the experiment conducted at 128 C at 0 = 0.5. Either a ruler or proportional dividers can be used to measure displacements. Criticize or defend the following proposition Whether a buffered aqueous solution of H2O2 and 1. containing small amounts of S2O3 and starch, appears blue or colorless depends on both the time and the temperature. This standard general chemistry experiment could be used to demonstrate the equivalency of time and temperature. The pertinent reactions for the iodine clock are... 

For most purposes only the Stokes-shifted Raman spectmm, which results from molecules in the ground electronic and vibrational states being excited, is measured and reported. Anti-Stokes spectra arise from molecules in vibrational excited states returning to the ground state. The relative intensities of the Stokes and anti-Stokes bands are proportional to the relative populations of the ground and excited vibrational states. These proportions are temperature-dependent and foUow a Boltzmann distribution. At room temperature, the anti-Stokes Stokes intensity ratio decreases by a factor of 10 with each 480 cm from the exciting frequency. Because of the weakness of the anti-Stokes spectmm (except at low frequency shift), the most important use of this spectmm is for optical temperature measurement (qv) using the Boltzmann distribution function. 

Master curves can also be constmcted for crystalline polymers, but the shift factor is usually not the same as the one calculated from the WLF equation. An additional vertical shift factor is usually required. This factor is a function of temperature, partly because the modulus changes as the degree of crystaHiuity changes with temperature. Because crystaHiuity is dependent on aging and thermal history, vertical factors and crystalline polymer master curves tend to have poor reproducibiUty. 

The measurement of correlation times in molten salts and ionic liquids has recently been reviewed [11] (for more recent references refer to Carper et al. [12]). We have measured the spin-lattice relaxation rates l/Tj and nuclear Overhauser factors p in temperature ranges in and outside the extreme narrowing region for the neat ionic liquid [BMIM][PFg], in order to observe the temperature dependence of the spectral density. Subsequently, the models for the description of the reorientation-al dynamics introduced in the theoretical section (Section 4.5.3) were fitted to the experimental relaxation data. The nuclei of the aliphatic chains can be assumed to relax only through the dipolar mechanism. This is in contrast to the aromatic nuclei, which can also relax to some extent through the chemical-shift anisotropy mechanism. The latter mechanism has to be taken into account to fit the models to the experimental relaxation data (cf [1] or [3] for more details). Preliminary results are shown in Figures 4.5-1 and 4.5-2, together with the curves for the fitted functions. 

Dynamic mechanical measurements for elastomers that cover wide ranges of frequency and temperature are rather scarce. Payne and Scott [12] carried out extensive measurements of /a and /x" for unvulcanized natural mbber as a function of test frequency (Figure 1.8). He showed that the experimental relations at different temperatures could be superposed to yield master curves, as shown in Figure 1.9, using the WLF frequency-temperature equivalence, Equation 1.11. The same shift factors, log Ox. were used for both experimental quantities, /x and /x". Successful superposition in both cases confirms that the dependence of the viscoelastic properties of rubber on frequency and temperature arises from changes in the rate of Brownian motion of molecular segments with temperature. 

Investigation of the linear viscoelastic properties of SDIBS with branch MWs exceeding the critical entanglement MW of PIB (about -7000 g/mol ) revealed that both the viscosity and the length of the entanglement plateau scaled with B rather than with the length of the branches, a distinctively different behavior than that of star-branched PIBs. However, the magnitude of the plateau modulus and the temperature dependence of the terminal zone shift factors were found to... 

This behavior is in between that of a liquid and a solid. As an example, PDMS properties obey an Arrhenius-type temperature dependence because PDMS is far above its glass transition temperature (about — 125°C). The temperature shift factors are... 

Master curves can often be made for crystalline as well as for amorphous polymers (33-38). The horizontal shift factor, however, will generally not correspond to a WLF shift factor. In addition, a vertical shift factor is generally required which, has a strong dependence on temperature (36-38). At least part of the vertical shift factor results from the change in... 

For capacity measurements, several techniques are applicable. Impedance spectroscopy, lock-in technique or pulse measurements can be used, and the advantages and disadvantages of the various techniques are the same as for room temperature measurements. An important factor is the temperature dependent time constant of the system which shifts e.g. the capacitive branch in an impedance-frequency diagram with decreasing temperature to lower frequencies. Comparable changes with temperature are also observed in the potential transients due to galvanostatic pulses. 

It can be seen in the plot in Figure 11 that EA . shows a clear temperature dependence. For rising temperatures the mass transport limitation can be observed, which leads to a lowering of EAs by a factor of V2 in the pore diffusion regime down to 0, owing to the shift of the reaction from the interior of the pore system of the catalytic particle to the outer surface. In the final state, the diffusion through the boundary layer becomes the rate-limiting step of the reaction. 

In all cases, an increase in temperature shifts the equilibrium towards the keto form by disrupting the internal H-bond which is the main stabilization factor of the enol or enamine. The tautomerism is more temperature dependant for keto-quinaldines than for... 

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