Relaxation time loss mechanisms

As the relaxation times for mechanical losses are about 10 6 sec or greater, it is evident that the flow units, which will change their places, are connected with their neighbors by more than one chemical bond. Some chemical binding forces have to be overcome simultaneously otherwise coupled flip-flop-processes will play a dominant role. In phase with the external stress 0 = 0 expjut there is a purely elastic deformation so that... 

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. 

The slower rise and decay of normal stress transients compared to shear stress arises quite simply and directly from the polydispersity of relaxation times (78), and probably has no direct bearing on entanglement mechanisms per se. Likewise, the depression of the superimposed moduli at low frequencies follows from rather non-specific continuum models, the loss moduli by Eqs.(8.49) and (8.50) from the simple fluid model, and the storage moduli from the following properties of the more specific but still quite general BKZ model (366,372) ... 

Fig. 2.15 Illustration of three deformation mechanisms proposed for BCC spheres, depending on shear rate (Koppi et al. 1994) (a) slow shearing results in creep (b) at an intermediate shear rate, the generation of numerous defects leads to a loss of translational order (c) at high shear rates, the spheres, undergo an affine elastic deformation. The layers shown represent [110) planes of a BCC structure, y is the inverse relaxation time of the defects.

One can see that introduction of the reptation mechanism of conformational relaxation, instead of diffusive mechanism, does not affect the values of the terminal quantities, but, one can expect, improves the situation in the region of the minima of the loss modulus G" reptation branch fill the gap between the orientational and the second conformational branches of relaxation times. Thus, the description with help of two relaxation branches is valid in the terminal zone and for higher frequencies close to it. 

FIG. 13.29 Frequency-temperature correlation map for polystyrene, (o, ) mechanical loss peaks ( , ) dielectric loss peaks (A, ) NMR narrowing and T, (i.e. spin-lattice relaxation time) minima for (open symbols) atactic an (filled symbols) isotactic polystyrenes. From Yano and Wada (1971). Courtesy John Wiley Sons, Inc. 

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