Draw axis

Here we averaged the structure function S3D(q) around the draw axis to give S2d(<2 q ), where q and q are the components of the wave vector along the draw axis and perpendicular to it, respectively. 

Fig. 39 Snapshots (upper) and the structure functions averaged around the draw axis, S2d(<2 ><2 )> (lower) at 350 K...

This model is incorrect because the linear thermal expansivity for both components in the isotropic and oriented state is assumed to be the same. The concequences of this assumption are quite different for Px and For px, it does not play any essential role, because in the isotropic and oriented state perpendicular to the draw axis the thermal expansivity is determined solely by intermolecular interactions. For P, this suggestion may lead to a principal inconsistency. This conclusion is evident from comparison of the calculated and experimental -dependences of P and P for PE and PP according to Eqs. (107) and (108). For Px, the agreement between the model calculation and the experiment is quite satisfactory for all draw ratios. On the other hand, Eq. (108) does not describe the X-dependence of P( at all. This equation does not yield negative values of P even in case of a limited orientation of crystallites (fc = 1) because it is based on the suggestion that Pam is always positive and pam > Pcr. ... 

Values of piezoelectric constants are, however, very scattered among polymers. In the case of oriented poly(y-methyl L-glutamate) film, the piezoelectric strain constant (d-constant) amounts to as much as 10 x 10 8 cgsesu when elongated in a direction at 45° to the draw-axis (Fukada, 1970), which is comparable with d = 6.5 x 10 8 cgsesu for X-cut... 

The anisotropy of piezoelectricity in oriented polymer films is quite different among polymers. The piezoelectric effect in oriented polypeptide films is greatest when elongated along a direction at 45° to the draw-axis. On the contrary, the effect is most remarkable for elongation along the draw-axis for roll-drawn poly(vinylidene fluoride) film. 

In an uniaxially oriented film in which the c-axes of crystallites are oriented equally along the z- and — z-axes of the film (draw-axis) but the other two axes of the crystallites (a, b) are randomly oriented around the z-axis, the tensor related to the film coordinates is reduced to a simple form (Fukada and Yasuda, 1964),... 

Fig. 9. Piezoelectric strain constant of uniaxially drawn poly(y-methyl L-glutamate) film (a-helical form) plotted against the angle 6 between draw-axis and stress direction. Draw-ratio = 2. Drawn after Fukada, Date, and Hirai [Nature 211, 1079 (1966)] by permission of Macmillan (Journals) Ltd.

In the drawn film in which the c-axis of the crystal is oriented along the draw-axis (z-axis) and a, b-axes are randomly oriented around the z-axis, the polarization P, along the x-axis of the film is not expected with elongation in the plane yz. The observed piezoelectricity of roll-drawn PVDF film, therefore, may be ascribed to the embedded charge as will be evidenced in the following. 

Fig. 24. Piezoelectric stress constant of roll-drawn polyfvinylidene fluoride) films plotted against angle 0 between draw-axis and elongational strain (O) draw-ratio =2.1, ( ) draw-ratio = 1.6. Drawn after Nakamura and Wada [J. Polymer Sci. A-2,9,161 (1971)] by permission of John Wiley Sons, Inc.

The electrostriction constant of roll-drawn PVDF was measured by Nakamura and Wada (1971) and the result is given in Fig. 25. The value of k is greatest when stretched along the draw-axis. The ratio of e values at 6 = 0° and 0 = 90°, (e13/e12), is about 8 for the film of draw ratio a = 1.6,... 

Group (A) includes materials with intrinsic piezoelectricity and dtA is twice the d-eonstant for elongation along the direction at 45° to the draw-axis. The value depends on the degree of orientation and degree of crystallinity. 

An elliptic flaw which is not perpendicular to the major draw direction (i.e., / = =7t/2) is depicted in Figure 7B. This ellipse will rotate toward the draw axis and change ellipticity as increases. Such an ellipse does not exhibit an R = 1 condition. This is shown in more detail below. 

Figure 5, crazes I and II can clearly be distinguished, the large and isolated crazes I and the dense pattern of very fine crazes II. The axes of both coincide with the draw axis. Other examples of the coexistence of two distinct types of crazes, whose axes however do not coincide, may be found in the literature 09,ii5,n6) Unfortunately, the phenomena reported in these publications are not very well understood. 

Figure 4. A practical distinction between optically uniaxial and optically biaxial drawn (or extruded) material. For optically uniaxial material, the area fraction exhibiting extinction between crossed circular polars is greatest when the normal to the plane of the thin section is parallel to the draw axis. For optically biaxial material, the greatest area fraction is observed in a section cut so that the angle between its normal and the draw axis is equal to half the optic axial angle of a monodomain.

This step introduces the statistical distribution of units into the analysis. In the most general case, there is a distribution of orientations, P(a, /3, y), describing the sample anisotropy. When the orientation is uniaxial, the distribution is cylindrically symmetrical about the draw axis, and P(a, )S, y) reduces to a function of one variable, P(i8) [3, 5]... 

Fig. 18.5. Fluorine-19 MREV8 spectra of static PTFE samples (left) under tension (draw ratio 1.40) and (right) under compression (draw ratio 0.82), with (top) the draw axis parallel to the magnetic field, and (bottom) the draw axis perpendicular to the magnetic field. [Spectra taken with permission from Ref. 28.]...

TABLE 9.1. Absorption Maxima of Drawn Poly(ethylene)-Gold Nanocomposites (Draw Ratio 15) at Different Reaction Conditions and Different Angles (p Between the Polarization Plane of the Incident Linearly Polarized Light and the Drawing Axis of the Specimen"... 

Figure 9.13. A twisted-nematic iiquid crystal display (LCD) equipped with a poly(ethylene)-silver nanocomposite that had been annealed at 180°C for 15 hr and subsequently drawn as described in the text. The drawing axis of the nanocomposite is oriented paraiiei to the poiarizer in the left image and perpendicular in the right image. See coior insert.

In accordance with the conclusion derived from the absorption spectra, the emission spectra also reveal the partially ordered structure of the film. As in the case of absorption, I and Ij., the fluorescence intensities parallel and perpendicular to the dipping direction, respectively, differ appreciably, in this case by a factor of three to four. Much higher dichroic ratios have been found with other oriented systems, e.g. with highly aligned films consisting of blends of polyethylene with 1 wt.% MEH-PPV (see Chart 1.8) [31, 32]. The films, fabricated by tensile drawing over a hot pin at 110-120 °C, proved to be highly anisotropic (dichroic ratio >60), with the preferred direction parallel to the draw axis. 

Objects for investigation are highly oriented flexible- and rigid-chain polymers in the form of films and fibers. In such samples, macromolecules are packed quite perfectly along the draw axis, and the most extended conformations are realized. 

With all the independent stiffness constants known, it is possible to calculate the Young s modulus at an angle 9 relative to the draw axis. This is a valuable parameter which is very difficult to measure on a conventional tensile machine. As shown in the Young s modulus vs. 6 plots at 2 = 15 (Figure 14.20), the Young s modulus increases with increasing PLC content at all angles, but the reinforcement effect becomes weaker as 0 increases. 

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