Extinction, angles measurement

Fig. 1.4. Evidence for the validity of the stress-optical law [Philippoff (8, 9)]. 15 per cent solution of poiyisobutylene B-100 in decalin. (A) extinction angle % and flow birefringence An vs. shear stress pa at 30° C. (o) and An at 50° C. ( ) calculated % according to eq. 1.3 from cone-and-plate measurements at 30° C. ( , An sin2 at 30 and 50° C, respectively...

To check whether eq. (1.5) is valid also for fluids of more general properties than those of the just described solution, flow birefringence, extinction angle and shear stress should be measured in a sufficient range of shear rates. When a plot is made according to eq. (1.5), a straight line should result. The fact that the shear rate is eliminated, indicates the quasistatic character of the stress-optical consideration. 

Instead of checking the second stress-optical relation, viz. eq. (1.6), Philippoff preferred to use eq. (1.3), assuming % = %. That this assumption is justified, can be seen in the same Fig. 1.4, In this figure also the extinction angle is plotted against the shear stress. Orientation angles calculated with the aid of eq. (1.3), fit rather well on the extinction angle curve. The normal stress difference (pn — p22) has been measured in the way explained in the previous section. Similar results were published later by the same author for solution of carboxy methyl celluose in water (33) and for S 111 in Aroclor (34) a chlorinated biphenyl. 

This relation has first been proposed by Philippoff (9). It becomes particularly suitable on condition that the stress-optical law, eq. (1.4), is valid. In this case dynamic measurements can be compared with the extinction angle of flow birefringence. 

Fig. 2.4. Doubled extinction angle 2% vs. shear rate (open circles) and loss angle <5 vs. angular frequency (closed circles) for the melt of anionic polystyrene Sill at a measurement temperature of 196° C [Wales, Den Otter (56)]...

Anionic polystyrene Sill seems to be a suitable polymer for this type of investigation. Some solution properties of this polymer have already been discussed in the previous chapter. Fig. 2.4 gives some properties of the melt of this polymer at a measurement temperature of 196° C (56). In this figure the doubled extinction angle 2% as a function of shear rate q (open circles) is compared with the loss angle d as a function of angular frequency (closed circles). In accordance with eq. (2.22) the initial slopes of these curves coincide. This coincidence, however, appears to persist even into the non-linear part of the functions. Such a persistence... 

Fig. 2.7. Drop off of doubled extinction angle 2"/ during stress-relaxation after cessation of steady shear flow according to Wales (59). Measurements on the melt of a high-density polyethylene (Marlex 6002) at a measurement temperature of 147° C. Shear rate of the steady shear flow q = 0.06 sec-1...

This equation will be particularly useful for the comparison of extinction angle and shear stress measurements. For the purpose, the second eq. (1.4) is used in the form ... 

When a low viscous solvent must be used in combination with a rather low molecular weight of the polymer, measurements are restricted to low /3-values, due to the discussed onset of turbulent flow. As in such a case the extinction angle % does not deviate very much from 45 degrees within the regime of laminar flow, it must be measured with a high absolute accuracy to furnish a reliable value for cos 2% or cot 2% [cf. eq. (3.42) or (3.44a)]. Measurements on a polydisperse sample become more reliable under such conditions due to the fact that cot 2 is increased by the polydispersity factor [eqs. (3.75a) and (3.83a)]. Examples for such a behaviour will be discussed in Section 3.8.3. 

Fig. 3.8. Extinction angles % vs. reduced shear rate for solutions of a high density polyethylene fraction (Dow Chem. Corp.) in transdecalin at 160° C (75). The concentrations are indicated near the curves in g/100 cm. Open and closed symbols indicate repeat measurements. The dotted line gives the extinction angle vs. at zero concentration, as obtained by linear extrapolation at several...

As a final remark it may be mentioned that the discussed polypropylene melts do not at all behave like second-order fluids in the range of shear rates and angular frequencies accessible to measurement. This is shown in Fig. 4.6. In this figure the doubled extinction angle 2 is plotted... 

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)...

From the foregoing it becomes evident that only a measure of the magnitude of the form birefringence, but not of its influence on the extinction angle, can be given. For this purpose the reader may be reminded that the stress-optical coefficient of an infinitely dilute solution can be expressed by one half of the ratio of Maxwell constant to intrinsic viscosity [eq. (2.33)]. In the absence of the form birefringence the limiting... 

If it would be possible to increase the accuracy of the determination of extinction angles so that measurements could be carried out at very low flow rates q, it probably would be possible to show that, at low values, the measuring points for the high molecular weight fractions of... 

Fig. 5.11. Initial slopes tanaof extinction angle curves vs. parameter = M[rf]ridRT for infinitely dilute solutions of various fractions of polymethyl methacrylate in tetrabromo-ethane according to Tsvetkov and Budtov (192). For each fraction x is varied by changing the temperature of measurement, i.e. the factor r]0IT. The molecular weights of the fractions are I/I.. . 15.2 x 10, A. .. 12.4 x 10, II. .. 11.0 x 10 , III... 5.8 x 10 , IV. .. 3.7 x 10 and V. .. 1.6 x 10 ...

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... 

Let us consider the anisotropy of polymer system undergoing simple steady-state shear. This situation can be realised experimentally in a simple way (Tsvetkov et al. 1964). The quantity measured in experiment are the birefringence An and the extinction angle x which are defined by formulae (10.19) and (10.20), correspondingly, through components of the relative permittivity tensor. 

Another method to calculate viscoelastic quantities uses measurements of flow birefringence (see Chap. 10). In these measurements, two quantities are determined as functions of the shear rate y the birefringence An and the extinction angle y. The following relationships exist with the stress tensor components ... 

With the development of the non-Newtonian viscosity theories it is now possible to compare the rotary diffusion coefficient and thereby the calculated length (or diameter) of the rigid particles as obtained from this technique with that from the commonly used flow birefringence method. Since both measurements depend upon the same molecular distribution function (Section III) they should give an identical measure of the rotary diffusion coefficient. Differences, however, will arise if the system under study is heterogeneous. The mean intrinsic viscosity is calculated from Eq. (7) whereas the mean extinction angle, x, for flow birefringence is defined by the Sadron equation (1938) ... 

The flow birefringence and the extinction angle of DNA solution are measured with a Rao birefringence apparatus Model-B-22. The extinction angle, x, is related to a parameter, a, in the equation of Boeder (2) and that of Peterlin and Stuart (17) ... 

Normal stress measurements on concentrated solutions of helical polypeptides were conducted by lizuka [1,42]. However he used these to calculate extinction angles, from which the rotary diffusion constant was deduced, and thence an apparent particle size from tables given by Scheraga [43]. In a personal communication to Kiss and Porter, lizuka commented that he had observed negative normal stresses in solutions of PBLG + Ch Br with concentrations of greater than 10% (i.e. probably liquid crystalline) however he ascribed this to the adhesive force of the solution (E. lizuka, personal communication, April 1977). 

Figure 9.14 The cross of isocline. The cross forms an angle with the polarizer axis (P-P). The same angle is formed py the cross and the analyzer axis (A-A). This is the extinction angle x- The intersection of the long axis of the particle with the stream line also gives rise to the same angle. However, the former relationship is utilized to measure x-...

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