Poly relaxation modulus

Figure 12.10 Temperature dependence of the tensile storage relaxation modulus for poly(vinyl chloride) at frequencies of (O) 0.1 Hz, ( ) 0.3 Hz, ( ) 1 Hz, ( ) 3 Hz, and (A) 10 Hz.

Figure 12,27 Variation of the complex relaxation modulus of poly(ethylene ter-ephthalate) with temperature, in the vicinity of the glass-rubber relaxation, for samples of various crystallinities obtained in isothermal crystallizations ( ) 46%, (<>) 40%, ( ), (V) 26%, ( ) 2-3%, and (O) 0%. (From Ref. 33.)...

Figure 12.28 Temperature dependence of the complex relaxation modulus of poly(ethylene terephthalate), in the glassy region, for the same samples of Figure 12.27.

Other highly crystallinity polymers such as polyisopropylene and poly-oxymethylene also exhibit in order of increasing temperature the y, P, and a relaxation processes. It is worth noting that while polyisopropylene exhibits a well-developed P absorption, polyoxymethylene, like HDPE, exhibits two prominent a and y relaxations and a small P relaxation whose intensity seems to increase as the degree of crystallinity decreases (43). This behavior is illustrated in Figure 12.33, where both the shear relaxation modulus and the logarithmic decrement of polyoxymethylene are plotted against temperature. 

Figure 12.33 Storage relaxation modulus and logarithmic decrement for poly-oxymethylene specimens of two crystallinities (O) 76% and ( ) 54%. Squares refer to the values of G and A of a specimen measured immediately after storage at room temperature ( ). (From Ref. 43.)...

FIGURE 3.19 Logarithm of tensile relaxation modulus versus logarithm of time for unfractionated poly(methyl methacrylate) of My = 3.6 X 10 . (After McLoughlin, J. R. and Tobolsky, A. V. 1952. /. Colloid Sci.y 7, 555.)... 

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).

Fig. 4.147 Tensile-creep and relaxation modulus of poly(oxymethylene) at various stress and strain levels for 22 °C [98Dom].

Fig. 4.170 Flexural-relaxation modulus of an unreinforced and a reinforced poly(oxymethylene) copolymer with 30 wt.-% of glass fibers at 23 °C and different strain levels [98Dom].

Fig. 4.179 Compression-relaxation modulus of a poly(oxymethylene) copolymer for various strain levels [12Els].

Tensile modnlns of poly-p-phenylene [83], relaxation modulus in LDPE [84], diglycidyl ether bisphenol A epoxy resins [85], and styrene-butadiene block copolymers with doped polyaniline [86]. 

Another simple adaptation of the Boltzmann superposition principle is that of Findlay and Lai [14], who worked with step stress histories applied to specimens of poly(vinylchloride). Their theory was reformulated by Pipkin and Rogers [15] for general stress and strain histories. Pipkin and Rogers took a non-linear stress relaxation modulus R t, e), defined somewhat differently from G in Equation (10.4) ... 

FIG. 12-16. Relaxation modulus of poly(vinyl alcohol) (PVA) poly(vinyl formate) (PVF) and partially formylated poly(vinyl alcohol)s with mole percentages of esterification as indicated, reduced to 80°C. (Nakatani, lijima, Suganuma, and Kawai. )... 

Above Ts. the properties of such partly crystalline systems have already been illustrated in Fig. 12-15. Here the relaxation modulus for poly(vinyl alcohol) resembles those of the polyethylenes in Fig. 16-8, although the slope is steeper probably the lack of tactidty leads to substantial imperfecticnis of crystallinity even without esteriHcation. With increasing esterification, the curves become steeper, and at 40% esterification the relaxation modulus falls by two and a half logarithmic decades in the range of reduced time investigated. 

Figure 15.28 Logarithm of relaxation modulus versus logarithm of time for poly(methyl methacrylate) between 40°C and 135°C.

Figure 3.16 Some experimental dynamic components, (a) Storage and loss compliance of crystalline polytetrafluoroethylene measured at different frequencies. [Data from E. R. Fitzgerald, J. Chem. Phys. 27 1 180 (1957).] (b) Storage modulus and loss tangent of poly(methyl acrylate) and poly(methyl methacrylate) measured at different temperatures. (Reprinted with permission from J. Heijboer in D. J. Meier (Ed.), Molecular Basis of Transitions and Relaxations, Gordon and Breach, New York, 1978.)...

The effect of the side chain bulkiness has been further studied on a series of chloro derivatives of poly(ethyl methacrylate)(PEMA). Though poly(2-chloroethyl methacrylate) exhibits69 a pronounced peak at Ty = 117 K, poly(2,2,2-trichloroethyl methacrylate), poly(2,2,2-trichloro-l-methoxyethyl methacrylate), and poly(2,2,2-trichloro-l-ethoxyethyl methacrylate) do not show (Fig. 6) any low-temperature loss maximum above the liquid nitrogen temperature157. However, these three polymers probably display a relaxation process below 77 K as indicated by the decrease in the loss modulus with rising temperature up to 100 K. Their relaxation behavior seems to be similar to that of PEMA rather than of poly(2-chloroethyl methacrylate) which is difficult to explain. 

For polymers containing branched side chains Fig. 2.67 show the variation of the modulus E , E and the loss tangent for PDIPI and PDIBI in the temperature range under study. Two relaxations can be observed where the most prominent is the a relaxation associated to the glass transition as in the systems previously reported. Tg increases as the volume of the side chain increases. This result is in good agreement with that observed for the corresponding family of poly(methacrylate)s [242],... 

Figure 10.2 The relaxation rate (1/T2s)max measured for a cured mixture of a poly(ethylene glycol) diacrylate (Mn = 700 g/mol) and 2-ethylhexyl acrylate as a function of the storage modulus at 273 K (-0.1 °C) [52]. The rubbery plateau was observed for all samples at 273 K (-0.1 °C). (1/T2s)max corresponds to the relaxation component with short decay time that was measured at 323 K (50 °C) for partially swollen in 1,1,2,2-C2D2C14 samples. This relaxation component corresponds to the relaxation of network chains. The line represents the result of a linear regression analysis intercept = 1.1 0.3 ms-1 slope = 0.34 0.02 ms MPa)"1. The correlation...

Figure 2. Mechanical loss tangent (tan 5) and elastic storage modulus at 102 c.p.s. and spin-lattice relaxation time (20) vs. temperature for poly (4-methyl-l-pentene) crystallized from dilute solution...

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