Uniaxial and Biaxial Orientation

In an undeformed, isotropic polymer all directions are equivalent crystallites are oriented in different directions with equal probabilities. When a polymer is uniaxially 

The statistical distribution of the orientation of w in the sample can be represented, in a general way, by a function r( , I ) defined for 0 n and 0 lit. In other words, the probability, weighted according to the mass of the crystallites, of finding the vector w in the direction specified by the range ( , + d ) and ( , 4 + d ) is equal to r( , d ) d d . We call /( , I ) the plane-normal (or pole) orientation distribution function, or the pole distribution for short. For a sample having uniaxial orientation, directions having the same but different O are all equivalent, and therefore the pole distribution can be written as a function of only, t ( ), defined for 0 it. The pole distributions t ( , O) or t ( ) are normalized so as to have 

The diffraction phenomenon is unable to distinguish the diffraction by (hkl) planes from the diffraction by (hkl) planes. As a result, the pole distribution f( , l ) as determined experimentally is centrosymmetric, that is, r(0, I ) = r(—0, — 4 ). The pole distribution therefore needs to be determined in practice only for the range 0 0 7r/2 and 0 O 2tc. 

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The most common examples of uniaxially oriented materials include fibers, films, and sheets hot-stretched in one direction and composites containing fibers all aligned in one direction. Some injection-molded objects are also primarily uniaxially oriented, but most injection-molded objects have a complex anisotropy that varies from point to point and is a combination of uniaxial and biaxial orientation. 

Fig. 13. Comparison of the calculated (curve) and the measured shift factors of the uniaxially and biaxially oriented PET films [35]...

The effects of orientation on the mechanical properties of polymers at both small and large deformations depend on the mode of orientation, which determines the preferred average chain alignment. For example, the mechanical properties obtained after uniaxial orientation (which biases the chain end-to-end vectors in one favored direction) differ from those obtained by biaxial orientation (which biases these vectors in two favored direction). Furthermore, the mechanical properties obtained after simultaneous equibiaxial orientation (where orientation in the two favored directions is imposed simultaneously, at equal rates, and to equal extents) often differ from those obtained after sequential orientation in the two favored directions, as well as after orientation by different amounts and/or at different rates in those two directions. See Seitz [35] for a review of the effects of uniaxial and biaxial orientation on the fracture of polystyrene, which fails by brittle fracture or crazing, under uniaxial tension and impact. 

The effects of uniaxial and biaxial orientation can be quite different. Although many commercial processing techniques impose a biaxial strain on the polymer melt, we will deal here primarily with uniaxially deformed materials. 

In Figure 6, one can see, as with amorphous materials, that the more unbalanced the biaxial orientation is the greater are the reductions in permeability. Interpretations of the transport data for biaxially and uniaxially drawn PET samples can be explained by observing conformational changes in the polymer backbone itself. Apparently, the chain packing efficiency of the amorphous phase improves as the number of trans isomers in the ethylene glycol unit increases. Polarized infrared analysis of uniaxially and biaxially oriented systems indicates that the fraction of... 

The film thickness and the degree of uniaxial and biaxial orientation of the material are controlled by the blow-up ratio and the haul-off rate. The haul-off rate controls the film orientation in the machine direction, while the blow-up ratio controls the orientation in the transverse direction. Common values for the blow-up ratio are in the range of 1.5-4, depending on the material and desired film thickness. Take-off speeds are usually around 10 to 50 m/min. 

Whilst this type of incidental orientation may constitute a minor disadvantage, there are whole industries which are based upon the deliberate exploitation of this effect. The production of synthetic fibres, and therefore of all synthetic textiles and ropes, depends upon orientation. Also the packaging industry makes extensive use of uniaxial and biaxial orientation. Recently the drawing and subsequent fibrillation of polyol uis has produced a cheap replacement for jute and sisal with profound repercussions on the economies of India and Pakistan. The extent to which synthetic fibres have supplemented natural fibres is shown in Fig. 2. 

In solids there are two general methods used for the determination of An. One is the transmission method while the other is a compensator technique. Each has advantages and disadvantages and thus the method chosen depends highly on the experimental circumstances as well as on the material itself. It is worth pointing out that the above discussion applies to both uniaxially and biaxially oriented systems. Two other methods not to be discussed here are interference microscopy and refractometry. ... 

The above general analysis is readily extended to the case of biaxially oriented samples, as shown by Nomura et al If the orientation distribution is symmetrical with respect to the X1X2, XjJ and X2 3 planes, then biaxial orientation fimctions of the form sin cos2 may be obtained from measurements of A2—Aj)l A3+A2+Ai). Assuming that the distributions over 6 and are independent, then functions such as cos2 = 2cos —1 can subsequently be obtained, as shown by Stein. Owing to experimental difficulties, however, no applications of these analyses seem to have yet been made. For both uniaxial and biaxial orientation. 

One approach to characterising the molecular orientation in both uniaxially and biaxially oriented samples of PET makes use of the ratio of the absorption bands near 1250 and 1725 cm, the first of which shows parallel dichroism and the second perpendicular dichroism. An equation is developed that relates this ratio to the molecular orientation with respect to the direction of measurement. Thus, it is possible to determine individually the orientation functions with respect to the machine and transverse directions (131). 

Two special types of orientation are of particular importance, uniaxial and biaxial orientation. In the former case, there is preferred orientation in one direction, in the latter case in two directions. The diagram in Fig. 54 may convey an idea of the two cases The structural units are represented by oblong lamellae. The length. 

The quantitative mathematical treatment of biaxial orientation is somewhat more complicated than that of uniaxial orientation and, entering into mathematical considerations later, we shall confine ourselves to the case of uniaxial orientation. It will be evident that systems with uniaxial and biaxial orientation will optically behave as uniaxial and biaxial crystals respectively. 

Oriented Composite Materials. Materials whose reinforcements are aligned in a specific way. Oriented materials are anisotropic. Orientation can generally be divided into two classes uniaxial and biaxial. Ideal uniaxial and biaxial orientations are illustrated below. 

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