Polypropylene orientation functions

Fig. 19. Plot of birefringence as measured by the compensator technique against the orientation function as measured by the sonic method. Values in parenthesis represent theoretical values for Nylon 66, cellulose, and polypropylene from top to bottom respectively...

In a stretched rubber, the molecules elongate, and the r vectors move towards the tensile axis. Fience the variation of Pi with extension ratio will differ from the pseudo-affine model. For moderate strains the increase of Pi with extension ratio is linear, but at high extensions the approximation used in Eq. (3.12), that both q and q are large, breaks down. Treloar (1975) described models which consider the limited number of links in the network chains. Figure 3.33 shows that the orientation function abruptly approaches 1 as the extension ratio of the rubber exceeds v. Although the model is successful for rubbers, it fails for the amorphous phase in polypropylene (Fig. 3.32), presumably because the crystals deform and reduce the strain in the amorphous phase. 

For semi-crystalline polymers, the average orientation function 2 for the crystal c axes can be calculated from X-ray diffraction measurements (Chapter 3). Figure 8.15 shows how 2 increases linearly with the draw ratio, for polypropylene fibres and films, while the spherulitic microstructure survives. At 2 = 0.9, where the spherulites are destroyed and replaced by a microfibrillar structure, there is an increase in the slope of the 2 versus true strain relationship. It is impossible to achieve perfect c axis orientation... 

It should be noted that the orientation functions do not specify the distribution of crystallite orientation. More than one distribution may produce the same orientation functions. In the case of monoclinic polypropylene, the u-axis makes an angle of 99.3° with the c-axis, and Equation 3.11 does not hold. For convenience, it is customary to define an axis, which is not a true crystallographic axis but is one perpendicular to both the b- and c-axes. Then the orientation of the a-axis may be determined from Equation 3.11,/, and f. 

The features of the Nadella study are similar to those observed for polypropylene by other authors. The variations in the crystalline orientation functions are also similar to those reported for high-density polyethylene. Dees and Spruiell [196] interpreted these variations for polyethylene to indicate spherulitic structure at low spinning stresses but which undergo a... 

In some crystalline systems where there are no reflecting planes normal to the desired crystallographic direction, one can still obtain the orientation for this direction providing the crystalline structure is defined. This method has been developed by Wilchinsky, where he showed that by measuring the orientation functions associated with various known hkl) planes, one can calculate the value of the desired orientation function. This method should not be confused with the application of the direction cosines relationship as discussed earlier. A specific example is given for the case of polypropylene in eqn. (22) where the value of ooi, can be found (and therefore the orientation of the chain axis) by measuring the diffraction from the (110) and (OkO) planes." " ... 

Fig. 50. Orientation function triangle diagram for the b and c-axes for isotactic polypropylene (O) hot drawn samples (Il(fC) ( ) melt spm fibres (—) cold...

Similar measurements have been made by Samuels - on as-spun and drawn polypropylene fibres and they are correlated with crystalline orientation functions, light and low angle X-ray scattering studies. 

Fig. 12-15 Tensile strength vs orientation function for polypropylene fiber [11].

Fig. 16. Relationship between orientation function of polypropylene and IR dichroism at 1220 cm" band (6). Samuels, R. J., J. Polymer Sci. A, 3 (1965), Wiley, NY. Reprinted by permission of John Wiley Sons, In ...

Orientation functions derived from dichroic ratio of the isotactic polypropylene films stretched at different draw ratios are shown in Table 2. 

Orientation Functions of Polypropylene Tapes as Determined by IR Dichroic Ratio... 

Fortunately, the Herman orientation function, F, can be determined by a number of independent techniques, including X-ray diffraction, birefringence, sonic modulus, and refractive index measurements. These methods, coupled with IR dichroic measurements of absorption, can be used to calculate quantitative values for the transition-moment angles by using Eq. (2.15). A plot of F measured by X-ray diffraction versus (i — )/(/ -f 2) will be linear with a zero intercept. A least-squares evaluation of the data from this line will yield the slope, (/ o + 2)/(Ro — ) When is 0° (parallel to the molecular chain axis) the slope equals 1.0 and when equals 90°, the slope equals —2.0. A quantitative value of the transition-moment angle can then be calculated. Transition-moment angle measurements have been published for isotactic polypropylene and some of the results are as follows [22] ... 

Once the transition-moment angles have been identified for a particular chemical group of the polymer, it is possible to measure the orientation of the polymer molecules in a sample by measuring the IR dichroism at the appropriate absorption frequencies. By using the data for polypropylene just presented, the Herman orientation function for samples of pol5rpropylene that are oriented can be calculated from the dichroic measurements. The results are shown in Table 2.3 [23]. 

Dichroic ratios, orientation function, and average angles of orientation for drawn polypropylene films... 

Table 3. Breaking stresses for polypropylene with 30% of glass fibers in function of the angle between the fiber orientation and direction of load application [157]...

Fig. 4.6. Doubled extinction angle 2y (closed triangles) and doubled orientation angle 2% (open circles and triangles) as function of shear rate q, and loss angle 6 as a function of angular frequency (closed circles, connected by dashed lines) for the melts of two polypropylene samples. Data of samples are given in Table 3.3. Measurement temperature 210° C (36)...

The method of incomplete mold filling is effective for investigating injection molding of fiber glass-loaded polypropylene and polystyrene melts.283 After solidification, samples were prepared for microscopic investigation. The authors determined the distribution and orientation of the fibers in different sections of the article and thus were able to clarify the pattern of flow in different parts of the mold as a function of the process parameters. They concluded that the width of the (cavity)... 

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