Strain and orientation

Cross-linked elastomers (the other main class of polymers studied by ESR) can be pre-strained above Tg to any desired extent (up to fracture) and their orientation stabilised by cooling below Tg before testing. At high pre-strains, strain-induced crystallization may occur providing a morphology essentially similar to that of synthetic fibres Cross-linked polymers may therefore be used to explore in a systematic manner, the role of strain and orientation in rmlecular fracture. 

A tensorial NMR parameter suitable for stress and strain imaging is the strain- and orientation-dependent quadrupole splitting of deuterons. Deuter-ated butadiene oligomers have been incorporated into household rub-berbands by swelling in order to apply spectroscopic imaging and doublequantum imaging of deuterons to detect stress and strain distributions under applied strain [82, 83]. 

Mobility of the reactants and reaction products of the oxidative kinetic chain reaction, of stabilisers and of the polymer molecules themselves affects the kinetics of the radical reactions. Morphology of a polymer material and its physical state, e g. stress, strain and orientation, has an effect on the mobility and therefore on the process of oxidative degradation. Fibres or slit films of polyethylene or pol ropylene are cold-drawn in the production. The orientation of the cold-drawn polymer material produced here has a particularly strong repercussion on oxidation stability. 

Stress-strain and orientation-strain measurements have been carried out on polyisoprene networks and have been compared with predictions of elasticity theories of real networks 29 ome illustrative results are reported hereafter. 

Terephthahc acid (TA) or dimethyl terephthalate [120-61 -6] (DMT) reacts with ethyleae glycol (2G) to form bis(2-hydroxyethyl) terephthalate [959-26-2] (BHET) which is coadeasatioa polymerized to PET with the elimination of 2G. Moltea polymer is extmded through a die (spinneret) forming filaments that are solidified by air cooling. Combinations of stress, strain, and thermal treatments are appHed to the filaments to orient and crystallize the molecular chains. These steps develop the fiber properties required for specific uses. The two general physical forms of PET fibers are continuous filament and cut staple. 

Eurther heat treatment in excess of 2000°C is referred to as graphitization. Eiber stmcture further densifies as molecular packing and orientation increase. At temperatures of 3000°C or above, the fiber stmcture begins to approach a truly graphitic stmcture with three-dimensional order. Typically, fiber strain to failure decreases as the carbonization temperature exceeds 1500°C because of reaction of impurities with the carbon fiber and the development of an increasingly flaw-sensitive graphitic stmcture (31,34)... 

The elastie limit funetion is assumed to be eontinuous and smooth, i.e., differentiable in e and k. At a fixed value of k, this equation defines a smooth elosed surfaee in strain spaee oriented in sueh a way that the outward normal... 

Identification of crystalline phases determination of strain, and crystallite orientation and size accurate determination of atomic arrangements... 

Thin-film XRD is important in many technological applications, because of its abilities to accurately determine strains and to uniquely identify the presence and composition of phases. In semiconduaor and optical materials applications, XRD is used to measure the strain state, orientation, and defects in epitaxial thin films, which affect the film s electronic and optical properties. For magnetic thin films, it is used to identify phases and to determine preferred orientations, since these can determine magnetic properties. In metallurgical applications, it is used to determine strains in surfiice layers and thin films, which influence their mechanical properties. For packaging materials, XRD can be used to investigate diffusion and phase formation at interfaces... 

As previously stated, molecular orientation occurs during melt processing of polymers. On removal of the deforming stresses the molecules start to coil up again but the process may not go to equilibrium before the polymer cools to below its Tg. This leads to residual orientation (frozen-in strain) and corresponding frozen-in stresses. 

First, consider uniaxial tension loading in the 1-direction on a flat piece of unidirectionally reinforced lamina where only the gage section is shown in Figure 2-20. The specimen thickness is not just one lamina, but several laminae all of which are at the same orientation (a single lamina would be too fragile to handle). The strains and E2 are measured so, by definition,... 

The maximum torque to be measured is 20,000 ft-lb. Using the same type of gages, properly placed on the sub, show that with two gages conveniently oriented the differential pressure strain and weight-on-bit strain do not register on the bridge. 

Other forces can arise as a result of elastic strain on the growing film, which can be due to a surface-induced ordering in the first few layers that reverts to the bulk liquid structure at larger distances. This elastic energy is stored in intermolecular distances and orientations that are stretched or compressed from the bulk values by the influence of the substrate at short distances [7]. Similar phenomena are well known to occur in the growth of epitaxial layers in metals and semiconductors. 

The diffraction lines due to the crystalline phases in the samples are modeled using the unit cell symmetry and size, in order to determine the Bragg peak positions 0q. Peak intensities (peak areas) are calculated according to the structure factors Fo (which depend on the unit cell composition, the atomic positions and the thermal factors). Peak shapes are described by some profile functions 0(2fi—2fio) (usually pseudo-Voigt and Pearson VII). Effects due to instrumental aberrations, uniform strain and preferred orientations and anisotropic broadening can be taken into account. 

Ferroelasticity is the mechanical analogon to ferroelectricity. A crystal is ferroelastic if it exhibits two (or more) differently oriented states in the absence of mechanical strain, and if one of these states can be shifted to the other one by mechanical strain. CaCl2 offers an example (Fig. 4.1, p. 33). During the phase transition from the rutile type to the CaCl2 type, the octahedra can be rotated in one or the other direction. If either rotation takes place in different regions of the crystal, the crystal will consist of domains having the one or the other orientation. By exerting pressure all domains can be forced to adopt only one orientation. 

IR dichroism has also been particularly helpful in this regard. Of predominant interest is the orientation factor S=( 1/2)(3—1) (see Chapter 8), which can be obtained experimentally from the ratio of absorbances of a chosen peak parallel and perpendicular to the direction in which an elastomer is stretched [5,249]. One representation of such results is the effect of network chain length on the reduced orientation factor [S]=S/(72—2 1), where X is the elongation. A comparison is made among typical theoretical results in which the affine model assumes the chain dimensions to change linearly with the imposed macroscopic strain, and the phantom model allows for junction fluctuations that make the relationship nonlinear. The experimental results were found to be close to the phantom relationship. Combined techniques, such as Fourier-transform infrared (FTIR) spectroscopy combined with rheometry (see Chapter 8), are also of increasing interest [250]. 

Figure 11.11 shows the stress-strain curves of PET, PTT and PBT fibers [4], Both PTT and PBT have a knee or a plateau region at about 5 and 7 % strains respectively, whereas PET stress increases smoothly with strain and does not have the plateau region. Table 11.6 compares the moduli of the three polyesters before and after annealing. The modulus of PET is nearly four times higher than those of PTT and PBT. After annealing, the PET modulus decreased by nearly half due to relaxation and loss of orientation. However, the PTT modulus increased by... 

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