Poly stress relaxation

Master curves are important since they give directly the response to be expected at other times at that temperature. In addition, such curves are required to calculate the distribution of relaxation times as discussed earlier. Master curves can be made from stress relaxation data, dynamic mechanical data, or creep data (and, though less straightforwardly, from constant-strain-rate data and from dielectric response data). Figure 9 shows master curves for the compliance of poly(n. v-isoprene) of different molecular weights. The master curves were constructed from creep curves such as those shown in Figure 10 (32). The reference temperature 7, for the... 

Below Tx, stress relaxes out faster in quenched specimens than in slowly cooled ones for amorphous polymerysuch as poly(methyl methacrylate) (109). Quenched specimens of the same polymer have a creep rate at high... 

Figure 14 Stress-relaxation data on poly(a-methylstyrcne) at various temperatures. Molecular weight is 460,000. (F-tem Ref. 160.)...

Figure 15 Stress-relaxation master curves for poly(a-methylstyrene) of various molecular weights. Reference temperature = 459 K. (From Ref. 160.)...

Crystallinity—about.i to 15% (213,232). The creep of plasticized poly(vinyl chloride) polymers as a function of temperature, concentration, and kind of plasticizer has been studied by many workers, including Aiken et ai. (232), Neilscn ct ai. (234), and Sabia and Eirich (243). These last workers also studied stress relaxation (244). In the case of crystalline polymers, plasticizers and Copolymerization reduce the melting point and the degree of Crystallinity. These factors tend to increase the creep and stress relaxation, especially at temperatures approaching the melting point. 

Several attempts have been made to superimpose creep and stress-relaxation data obtained at different temperatures on styrcne-butadiene-styrene block polymers. Shen and Kaelble (258) found that Williams-Landel-Ferry (WLF) (27) shift factors held around each of the glass transition temperatures of the polystyrene and the poly butadiene, but at intermediate temperatures a different type of shift factor had to be used to make a master curve. However, on very similar block polymers, Lim et ai. (25 )) found that a WLF shift factor held only below 15°C in the region between the glass transitions, and at higher temperatures an Arrhenius type of shift factor held. The reason for this difference in the shift factors is not known. Master curves have been made from creep and stress-relaxation data on partially miscible graft polymers of poly(ethyl acrylate) and poly(mcthyl methacrylate) (260). WLF shift factors held approximately, but the master curves covered 20 to 25 decades of time rather than the 10 to 15 decades for normal one-phase polymers. 

Fujimoto,T., Ozaki.N., Nagasawa,M. Stress relaxation of monodisperse poly-a-methylstyrene. J. Polymer Sci. Pt. A-2 6,129-140 (1968). 

Stress relaxation master curve. For the poly-a-methylstyrene stress relaxation data in Fig. 1.33 [8], create a master creep curve at Tg (204°C). Identify the glassy, rubbery, viscous and viscoelastic regions of the master curve. Identify each region with a spring-dashpot diagram. Develop a plot of the shift factor, log (ax) versus T, used to create your master curve log (ot) is the horizontal distance that the curve at temperature T was slid to coincide with the master curve. What is the relaxation time of the polymer at the glass transition temperature ... 

Comparison of the dielectric and viscoelastic relaxation times, which, according to the above speculations, obey a simple relation rn = 3r, has attracted special attention of scholars (Watanabe et al. 1996 Ren et al. 2003). According to Watanabe et al. (1996), the ratio of the two longest relaxation times from alternative measurements is 2-3 for dilute solutions of polyisobu-tilene, while it is close to unity for undiluted (M 10Me) solutions. For undiluted polyisoprene and poly(d,/-lactic acid), it was found (Ren et al. 2003) that the relaxation time for the dielectric normal mode coincides approximately with the terminal viscoelastic relaxation time. This evidence is consistent with the above speculations and confirms that both dielectric and stress relaxation are closely related to motion of separate Kuhn s segments. However, there is a need in a more detailed theory experiment shows the existence of many relaxation times for both dielectric and viscoelastic relaxation, while the relaxation spectrum for the latter is much broader that for the former. 

The equilibrium 20 is important not only in the synthesis of linear polysiloxanes but also in their applications. The effects of water vapor on inducing chain cleavage at high temperature are not only reduced molecular weights but also a dramatic increase in the rates of chemically induced stress relaxation at 250 °C in cross-linked poly(dimethylsiloxane) networks under load (70). Slow hydrolytic bond cleavage in cross-linked networks is seen even in studies of stress relaxation in air at room temperature, and appreciable rates of stress relaxation in the loaded networks are measured at temperatures as low as 70 (7i). The stress relaxation is greatly accelerated... 

Stress Relaxation in Crosslinked Poly(Ethylene Tetrasulfide). J. Coll. Sqi. 19. 40-49 (1964). 

Equation 20 is similar to Equation 5. Its slope, however, is 3.0 instead of 4.4. The cause of this discrepancy is unknown. However, it should be remembered that a factor of 3.4 was found in stress relaxation experiments with polystyrene and poly ( -methylstyrene) (25). 

Another example of network formation is found in PEO (poly(ethylene oxide))-silica systems [58, 59]. At relatively small-particle concentrations, the elastic modulus increases at low frequencies, suggesting that stress relaxation of these hybrids is effectively arrested by the presence of silica nanoparticles. This is indicative of a transition from liquidlike to solidlike behavior. At high frequencies, the effect of particles is weak, indicating that the influence of particles on stress relaxation dynamics is much stronger than their influence on the plateau modulus. 

Figure 7.10. The effect of light on the dynamic properties of physical cross-links between azobenzene-modified poly(acrylate) and poly(cyclodextrin). The relaxation modulus in stress relaxation experiments is plotted after application at time zero of a fixed strain to a 0.7% polymer solution in water (polymer structure, cf. Fig. 7.1, with n = 11 and x=3) with polycyclodextrin at 0.25% (lower curves) or 0.5% (higher moduli). The sample was either incubated for 24h in the dark (dark-adapted, closed symbols) or continuously exposed to UV before and after loading in the rheometer (open symbols). Details on the samples composition are given in Pouliquen et al. (2007).

Cowie, J. M. G., McEwen, 1. J., and Matsuda, S., Stress relaxation and physical ageing in a blend of poly(styrene-co-acrylonitrile) and poly(methyl methacrylate), J. Chem. Soc. Faraday Trans., 94, 3481-3486 (1998a). 

Mijovic, J., Devine, S. T., and Ho, T., Physical ageing in polyfmethyl methacrylate)/ poly (styrene-co-acrylonitrile) blends. I. Stress relaxation, J. Appl. Polym. Sci., 39,1133-1151 (1990). 

A similar relaxation of orientation for PP-based CPNCs with PP-MA was reported by Lele et al. [2002], The authors presheared the system and then followed the disorientation with XRD. Again, the relaxation time was faster than expected from the theory of Brownian motion. Ren et al. [2000, 2003] studied polystyrene (PS) and poly(isobutylene-co-p-methyl styrene)-based CPNCs. The interlayer spacing in the system was dooi = 2.1 to 2.5 nm thus, it was intercalated only. The authors assumed that the disorientation observed was not governed by Brownian motion but by the stress relaxation of macromolecules. 

McLoughlin J. R. and Tobolsky, A. V. (1951) Effect of rate of cooling on stress relaxation of poly-methyl-methacrylate, /. Polymer ScL, 7, 658. 

Figure 1.22. Stress relaxation of a crosslinked poly(styrene-co-butadiene) rubber (at 1.7°C) at elongations from 350 to 525 %. Solid points indicate rupture, the dashed-line gives the ultimate stress. (Scott, 1967.)...

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