Linear polyethylene, relaxation

A similar continuity in the Tj s through the melting temperature was previously reported for linear polyethylene. (17) We have now investigated the temperature dependence of this quantity, for this polymer, in more detail and have also studied a low density (branched) polyethylene. The results for the poly-ethylenes are summarized in Fig. 8. The new data reported here substantiate the conclusion previously reached for linear polyethylene. A similar conclusion can now be reached for the baclc-bone carbons of low density (branched) polyethylene. The melting temperature for this particular sample, under the crystallization conditions studied, is less than 110°C. (33) Thus, the spin-lattice relaxation parameters for the bac)cbone carbons are the same for both the linear and branched polymers over the temperature range studied here. Changes that occur in Tq as the temperature is reduced below 0°C involve other considerations and will be discussed in detail elsewhere. (22)... 

The major results described could be partially anticipated from those previously reported for linear polyethylene (17) as well as those for cis polyisoprene. (] ) For the latter polymer, by taking advantage of its crystallization kinetic characteristics, it was possible to compare the relaxation parameters of the completely amorphous and partially crystalline polymer (31% crystallinity) at the same temperature, 0°C. This is a unique situation and allows for some unequivocal comparisons. It was definitively observed that for all the carbons of cis polyisoprene the T] s did not change with crystallization. 

Proton NMR relaxation parameters have also been determined for polyethylene ( ) and polyethylene oxide (39) in the melting region. The apparent contradiction between the proton spin-lattice relaxation parameter for a high molecular weight linear polyethylene sample at its melting point, with the relaxation measurements, has previously been pointed out. (17) This discrepancy is still maintained with the more detailed results reported here for both types of polyethylene. For the proton relaxation a small, but distinct, discontinuity is reported at the melting teirperature. (38)... 

Gray and McCrum735 used the Hashin-Shtrikman theory to explain the origin of the y relaxation in PE and PTFE, Maeda et al.745 have given exact analyses of several two phase models for semi-crystalline polymers and Buckley755 represented a biaxially oriented sheet of linear polyethylene by a two phase composite model. 

The extensional dynamic storage modulus E and the loss factor tan 8 for a series of linear polyethylene tapes of different draw ratios are shown in Fig. 30(a) and (b). There are two features worthy of particular note. First, the modulus at low temperatures is about 160 GPa, which is about one half of the theoretical modulus and the maximum value obtained from neutron diffraction and other measurements. Secondly, the a and y relaxations are both dearly visible even in the highest draw ratio material, although the magnitude of tan 5 for the y relaxation reduces with increasing draw ratio. 

The dynamic mechanical results of this study demonstrate that backbone crystallinity plays an important role in the properties of these materials. Moreover, it is observed that thermal history affects the properties of the materials investigated in a more complex manner than can be explained by simple changes in the degree of crystallinity. At low levels of sulfonation the materials generally behave very much like linear polyethylene, but this behavior is modified significantly as the level of sulfonation is increased. Evidence is clearly present for the existence of an ionic-phase relaxation that supports the proposed model for micro-phase-separated domains (5,6,7). However, owing to the effects of crystallinity the concentration at which the ionic-phase relaxation first... 

Shear compliance J(t) of linear polyethylene at different temperatures in the region of the o relaxation. Measurements are talsignificant differences in the shape of the curves at different temperatures (after McCrum and Morris). 

In order to fit isothermal data (for example the linear polyethylene data for 15°C, see Figure 4.4) it is necessary to fit to the data the three adjustable parameters of the Zener model, which are J, /r, and t. Since the Zener model is supposed equalfy valid for creep, stress relaxation, and dynamic response, these same parameters should then fit (for linear polyethylene at IS C) G(t), G (tu) and J ([Pg.146]

Non-linear, time-dependent characteristics of viscoelastic materials such as polyethylene have been mathematically modelled and the model compared with experimental results. Mechanical properties such as creep and stress relaxation are non-linear because they include time-dependent and irreversible components. The time-dependent component is non-linear when relaxation time is longer than the timeframe of the experiment. This becomes increasingly so at high stress. Low stress will act on faster responding deformation modes and as stress increases slower modes will respond. The slower modes will be non-linear relative to the timescale of the experiment. Some slower modes such as relative translation of molecules are irreversible. Stress relaxation is complementary to creep in that strain is applied creating a stress that may relax according to the relative times of the experiment and molecular processes. 

Information on the local structure of polymers is not limited to proton-proton spin diffusion experiments. Spin diffusion among the carbons can also be used [97], However, because of the low gyromagnetic ratio and natural abundance of the carbon-13 nuclei, it is less efficient than proton-proton spin diffusion. At natural abundance, the rate of spin diffusion is usually too low to compete with the rate of spin-lattice relaxation in most polymers. However, an interesting exception is that of semi-crystalline polymers such as linear polyethylene and cellulose which have very long longitudinal relaxation times and for which natural-abundance spin... 

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