Mechanical property measurement superpositioning

The isothermal curves of mechanical properties in Chap. 3 are actually master curves constructed on the basis of the principles described here. Note that the manipulations are formally similar to the superpositioning of isotherms for crystallization in Fig. 4.8b, except that the objective here is to connect rather than superimpose the segments. Figure 4.17 shows a set of stress relaxation moduli measured on polystyrene of molecular weight 1.83 X 10 . These moduli were measured over a relatively narrow range of readily accessible times and over the range of temperatures shown in Fig. 4.17. We shall leave as an assignment the construction of a master curve from these data (Problem 10). 

The time-temperature superpositioning principle was applied f to the maximum in dielectric loss factors measured on poly(vinyl acetate). Data collected at different temperatures were shifted to match at Tg = 28 C. The shift factors for the frequency (in hertz) at the maximum were found to obey the WLF equation in the following form log co + 6.9 = [ 19.6(T -28)]/[42 (T - 28)]. Estimate the fractional free volume at Tg and a. for the free volume from these data. Recalling from Chap. 3 that the loss factor for the mechanical properties occurs at cor = 1, estimate the relaxation time for poly(vinyl acetate) at 40 and 28.5 C. 

A final comment seems to be pertinent. In most cases actual measurements are not made at the frequencies of interest. However, one can estimate the corresponding property at the desired frequency by using the time (fre-quency)-temperature superposition techniques of extrapolation. When different apparatuses are used to measure dynamic mechanical properties, we note that the final comparison depends not only on the instrument but also on how the data are analyzed. This implies that shifting procedures must be carried out in a consistent manner to avoid inaccuracies in the master curves. In particular, the shape of the adjacent curves at different frequencies must match exactly, and the shift factor must be the same for all the viscoelastic functions. Kramers-Kronig relationships provide a useful tool for checking the consistency of the results obtained. 

Non-linear mechanical properties were observed for rubber eomposites and referred to as the Payne effect. The Payne effeet was interpreted as due to filler agglomeration where the filler clusters formed eontained adsorbed rubber. The occluded rubber molecules within filler elusters eould not eontribute to overall elastic properties. The composites behaved similarly to rubber composites with higher filler loading. Uniform and stable filler dispersion is required for rubber composites to exhibit linear viscoelastic behaviour. Payne performed dielectric measurements on SBR vulcanizates containing silica or carbon black. The dielectric data were used to construct time-temperature superposition master curves. The reference temperature increased with crosslinking but not significantly with filler. Comparison of dynamic mechanical and dielectric results for the SBR blended with NR was made and interpreted. ... 

Differential scanning calorimetry (DSC), DMA and TG were used by Tabaddor and co-workersl l to investigate the cure kinetics and the development of mechanical properties of a commercial thermoplastic/ thermoset adhesive, which is part of a reinforced tape system for industrial applications. From the results, the authors concluded that thermal studies indicate that the adhesive was composed of a thermoplastic elastomeric copolymer of acrylonitrile and butadiene phase and a phenolic thermosetting resin phase. From the DSC phase transition studies, they were able to determine the composition of the blend. The kinetics of conversion of the thermosetting can be monitored by TG. Dynamic mechanical analysis measurements and time-temperature superposition can be utilized to... 

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. 

Ferry went to Harvard University in 1937 and worked there in a variety of posts, including as a Junior Fellow, until he joined the University of Wisconsin in 1946. He was promoted to Full Professor in 1947 His extensive measurements of the temperature dependence of the dynamic mechanical properties of polymers led to the concept of reduced variables in rheology. His demonstration that time-temperature superposition applied to many systems is the basis for the rational description of polymer rheology. He measured the dynamic response over a very wide range of frequency. One of the fruits of this work is the Williams-Landel-Ferry (WLF) equation for time-temperature shift factors. 

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. 

If it is meaningless to conceive a direct measurement of a property of a quantum object, we must conclude that, as said above, we can only reach such information in an indirect way. The measurements we perform concern the way the quantum system communicates with the surrounding environment. Basically this means that our measurements retrieve the information conveyed by the quantum object to the environment. In this interaction much information about the perfectly coherent quantum system is destroyed by decoherence and we can measure only that associated with the so-called pointer states, which are those less affected by decoherence processes. In other words decoherence destroys the most part of superpositions. This is believed to occur through a super-selection mechanism induced by the environment itself. For this reason the reliability of the information and its inherent objectivity are defined by the degree of redundancy of the information conveyed by the quantum system. Only the states that survive this destruction process can be observed. Thus in contrast to the classical world, all the information about a physical system is objective at the quantum level the objectivity concerns only a part, and in a certain sense becomes synonymous with classical which means predictable. However, it is important to stress that they are always related to a... 

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