Normal stress using birefringence

For systems where the stress-optical rule applies, birefringence measurements offer several advantages compared with mechanical methods. For example, transient measurements of the first normal stress difference can be readily obtained optically, whereas this can be problematic using direct mechanical techniques. Osaki and coworkers [26], using a procedure described in section 8.2.1 performed transient measurements of birefringence and the extinction angle on concentrated polystyrene solutions, from which the shear stress and first normal stress difference were calculated. Interestingly, N j was observed to... 

Transient birefringence measurements were used by Larson et al. [112] to test the validity of the Lodge-Meissner relationship for entangled polymer solutions. This relationship states that the ratio of the first normal stress difference to the shear stress following a step strain is simply Nx/%xy - y, where y is the strain. Those authors found the relationship was valid, except for ultrahigh molecular weight materials. 

Optical measurements often have a greater sensitivity compared with mechanical measurements. Semidilute polymers, for example, may not be sufficiently viscous to permit reliable transient stress measurements or steady state normal stress measurements. Chow and coworkers [113] used two-color flow birefringence to study semidilute solutions of the semirigid biopolymer, collagen, and used the results to test the Doi and Edwards model discussed in section 7.1.6.4. That work concluded that the model could successfully account for the observed birefringence and orientation angles if modifications to the model proposed by Marrucci and Grizzuti [114] that account for polydispersity, were used. 

Failure to use Eq. (7.9) has resulted in several errors in the literature Zimm s (79) calculation of flow birefringence, as pointed out by Williams (76) Kirkwood and Plock s (40) calculation of large amplitude oscillatory response, as pointed out by Paul (62) Williams and Bird s (78) calculation of oscillatory normal stresses, as pointed out by themselves in a later publication (77). 

Although nearly all shear normal stress data reported in the literature are measured by total thrust methods, some work has been done with the distribution of pressure across the plate with small flush transducers (Christiansen and Leppard, 1974 Magda et al., 1991 see Figure 5.4.2). Meissner and co-workers (1989) have used the total thrust on a central disk of smaller radius than the sample. Both techniques permit measurement of N2 as well as A i. Birefringence methods, discussed in the next chapter, can also give normal stress distributions. 

In Section 10.8.1 it was noted that molecular orientation results in flow birefringence in a polarizable polymer, and if the melt is transparent, optical techniques can be used to determine the three components of the stress tensor in uniform, shear flows [91-93]. To determine the transient normal stress differences, the phase-modulated polarization technique was developed by Frattini and Fuller [ 126]. Kalogrianitis and van Egmond [ 127] used this technique to determine the shear stress and both the normal stress differences as functions of time in start-up of steady simple shear. Optical techniques are particularly attractive for measurements of normal stress differences, since such methods do not require the use of a mechanical transducer, whose compliance plagues measurements of normal stress differences by mechanical rheometry. 

Another method of determining segmental anisotropy (which is seldom used) is through the measurement of stress birefringence in swollen polymers (74). The stress optical coefficient e = An/Ap (where Ap is the normal stress in the sample) determined experimentally is equal to An/2At (2), where An/At is also related to (at 0 2) according to Eq. (Al). Data obtained by this method are marked in the table with the symbol SW. p. (swollen polymer). 

In the present work, viscoelastic numerical simulation of birefringence and gas/polymer interface distribution for GAIM is presented and compared with experimental data obtained on polystyrene moldings. A nonlinear constitutive equation proposed by Leonov [7] was employed to describe the development of shear and normal stresses. Afterward, the birefringence was calculated from stresses using the stress-optical rule [8]. 

The viscous heating was taken into account using the energy dissipation function [12], The polymer density change due to temperature and pressure variations was calculated using the Tait equation [13]. The flow-induced birefringence was calculated from the normal and shear stresses using the stress-optical rule [8]. 

Figure 3 Orientation of the phenyl rings in stretched PET films, with respect to the machine (X,), transverse (X2), and normal (X3) directions, as a function of applied stress, a0, at 90°C. Birefringence results were obtained using refractrometry. Reproduced with permission from Lapersonne et al. [11]. Copyright Elsevier 1994.

In the same way that close-packed directions in a crystal have larger refractive indices, so too can the application of a tensile stress to an isotropic glass increase the index of refraction normal to the direction of the applied stress. Uniaxial compression has the reverse effect. The resulting variation in refractive index with direction is called birefringence, which can be used as a method of measuring stress. 

Fig. 2.3. "Recoverable shear" 5 vs. shear stress p21 for a 4.15 per cent solution of polyisobutylene L-100 in white oil at 25° C according to Philoppoff and Stratton (55). (A) shear recovery, ( ) calculated from flow birefringence, using eq. (2.12), (O) calculated from normal thrust measurements, using eq. (2.12)...

Transparency, gloss, color, refractive index, and reflectance are the properties normally associated with aesthetics of plastic materials. In some areas, changes in optical properties, increases in haze after abrasion testing (285), color differences after weathering, and birefringence analysis of residual stress within a transparent part (286) are all used to measure the effects of applied stresses. Measurements of color, gloss, refractive index, and haze apply to many products beyond plastics and use similar techniques. Reference should be made to this general topic for detailed information (see Color). 

A common measurement useful in predicting threadline behavior is fiber tension, frequently misnamed spinline stress. It is normally measured after the crystallization point in the threadline when the steady state is reached and the threadline is no longer deformed. Fiber tension increases as take-up velocity increases (38) and molecular weight increases. Tension decreases as temperature increases (41). Crystallinity increases slightly as fiber tension is increased (38). At low tension, the birefringence increases as tension is increased, leveling off at a spinline tension of 10 MPa (1450 psi) (38). 

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