Draw ratio birefringence

Equation (32a) has been very successful in modelling the development of birefringence with extension ratio (or equivalently draw ratio) in a rubber, and this is of a different shape from the predictions of the pseudo-affine deformation scheme (Eq. (30a)). There are also very significant differences between the predictions of the two schemes for P400- In particular, the development of P400 with extension ratio is much slower for the network model than for the pseudo-affine scheme. 

Figure 16.8. Relationship between the crystal orientation factor and birefringence and the draw ratio-of BPDA-PFMB fibers. 

The relationships between the stress-strain curves of undrawn and drawn yam, borne out by the "master curve", again stress the key role of the draw ratio and elongation with respect to the physical properties of yams, as already shown by the relations to birefringence (Eq. (10.24)) and dynamic modulus of elasticity (Eqs. (13.98) and (13.101)). 

Fibers with E modulus ranging from 30 to 50 GPa could very easily be produced. Break tenacities very generally around 400 MPa, but could be increased to approx. 600 MPa by heat treatment. The draw ratio had no significant effect on the fiber-birefringency but remained constant at 0.32, within experimental error. 

Differences in draw ratio in PET fibres can be analysed by microscopic determination of their specific birefringence, whereby higher tension results in a higher birefringence whereas the influence of temperature varies. In Section... 

In contrast to observations in polystyrene, we do not observe permanent bands our specimens exhibit no residual birefringence upon release from stress. Neither do we observe crazing before failure. However, the specimens do whiten just before failure when viewed edge-on, and this whitening disappears within a few seconds after fracture occurs. We think the oscillations in intensity we observe are likely to be due to incipient shear deformation which disappears after specimen failure. Unpublished results of other workers are reported (see References 11 and 14 in the present Reference 12) to be consistent with the idea that such bands should be difficult to observe in PMMA and in polycarbonate because of their lower draw ratios compared to polystyrene. Studies of an unfilled epoxy polymer (14) in cyclic tensile deformation indicate that shear bands do not remain after removal of stress until a threshold amplitude of deformation is exceeded. 

Figure 9.1 Dependence of birefringence lAnI on the macroscopic draw ratio XatT = 135 °C for PMMA. 1 experimental data [6] 2 calculation by Equation (9.3) ...

Fig. 10.8 Birefringences for three sets of uniaxially drawn PVC samples plotted against the draw ratio ...

The birefringence An for a uniaxially oriented sample with draw ratio X = 3.5 was found to be 8.1 x 10 . Assuming that the orientation of the polymer molecules is adequately described by equation (11.6) using only the first term on the RHS, deduce An for a similarly drawn sample with X = 2.0. 

Fig. 11.6 Birefringence plotted against draw ratio for a series of drawn samples of low-density polyethylene. The broken curve shows values calculated according to the pseudo-affine deformation scheme. (Adapted by permission of I. M. Ward.)...

The variation of birefringence with draw ratio for a set of uniaxially drawn samples of a certain polymer is found to be consistent with the simplest version of the affine rubber model when the draw ratio is less than 3.5. If the birefringence is 7.65 x 10 for draw ratio 3.0, calculate its value for a sample of draw ratio 1.5. If the birefringence for a very highly oriented sample is 0.045, what is the effective number of random links per chain ... 

The birefringence A of a certain uniaxially drawn polymer is found to vary with the draw ratio X as follows. 

Deduce whether the affine rubber or the pseudo-affine aggregate model better describes these data. Given that the birefringence observed for a very highly uniaxially oriented sample of the polymer is 0.078, deduce what numerical information you can about a sample with draw ratio 3.0. 

Figure 9.1 Wavelength dependence of orientation birefringence (closed symbols] and normalized orientation birefringence (open symbols] for stretched PMMA films at draw ratios of 1.5 (circles], 2.0 (diamonds], and 2.5 (triangles].

Figure 9.5 Contribution of (closed diamonds] hydroxyl and (open diamonds) acetyl groups to the orientation birefringence of (closed circles) CDA at a draw ratio of 2.0. The birefringence values of both groups are derived from the experimental results of CTA and CDA. Reproduced with permission from M. Yamaguchi, K. Okada, M. E. A. Manaf, Y. Shiroyama, T. Iwasaki, and K. Okamoto, Macromolecules, 2009, 42, 9034. 2009, ACS Publications [44].

Figure 9.23 Wavelength dispersion of (a) in-plane birefringence and (b) out-of-plane birefringence for a cast film ( ) and stretched films with draw ratios of 1.1 ( ), 1.3 (A), and 1.5 ( ). The cast films with a thickness of 100 pm were prepared by CH2CI2/ CH3OH at the standard condition. Reproduced with permission from K. Songsurang, A. Miyagawa, M. E. A Manaf, R Phulkerd, S. Nobukawa, and M. Yamaguchi, Cellulose, 2013,20,83. 2013, Springer Link [11].

Figure 9.24 Wavelength dependence of orientation birefringence for CAP and CAP/PLA blends stretched at a draw ratio of 2.0 PLA (circles), 1 wt% of PLA (diamonds), 3 wt% of PLA (triangles), andS wt% of PLA (squares). Reproduced with permission from M. Yamaguchi, S. Lee, M. E. A. Manaf, M. Tsuji, and T. Yokohara, Eur. Polyrn. ., 2010,46,12, 2269. 2010, Elsevier [8],...

FIGURE 3.41 Birefringence as a function of draw ratio for polypropylene fibers. (From Nadella, H.P. Spruiell, J.E. White, J.L. J. Appl. Polym. Sci., 1978, 22, 3121. With permission.)... 

FIGURE 10.36 Birefringence of the Lyocell filament in the air gap with different draw ratios (DR) as a function of distance (From Mortimer, S.A., Peguy, A.A., and Ball, R.C., Cellul. Chem. TechnoL, 30, 251, 1996.)... 

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