Birefringence apparatus

Figure 8.4 Two-color flow birefringence apparatus. CSgrcen color splitter passing the...

Schematic diagram showing the integration of a polarization modulated birefringence apparatus within a laser Doppler velocimeter. This shows the side view. L light source (a diode laser was used) PSG rotating half-wave plate design LS lens FC flow cell (flow is into the plane of the figure) CP circular polarizer D detector 2D-T two dimensional translation stage 3D-T three dimensional translation stage LDVP laser Doppler velocimeter probe.

Hopkins, R. C. Dynamic strain birefringence apparatus for polymer films. J. Polymer Sci. A-2, 7,1907 (1969). 

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) ... 

Figure 1 Block diagram of a typical electrical birefringence apparatus using either square-pulse (for transient electrical birefringence) or oscillating field (for dynamic electrical birefringence) perturbations. P, polarizer A, analyzer A/4, quarter-wave retardation plate P.S., power supply P.M.T., photomultiplier tube HP-214A, wave-form generator. (Reprinted with permission from Ref. 41. Copyright 1994 American Chemical Society.)...

The block diagram of a typical transient electrical birefringence apparatus is shown in Fig. 1. The sample solution is located between the two electrodes (3 mm apart) of the Kerr cell, which is equipped with windows and has an optical path length 1 — 5 cm. The high voltage (up to a few kilovolts) square pulse is produced by a pulse generator (Cober 605P), with the rise and fall times of the pulse < 50 ns. 

Figure 7 Schematic diagram of the laser-induced electrical birefringence apparatus. Path of Nd YAG laser pulse EP, extracavity polarizers PC, Pockels cell L, lens (focal length 63.5 cm, focal point about 20 cm past the sample cell) D, dichroic mirror SC, sample cell C, calorimeter BS, beam splitter FI, UV-Vis cutoff filter F2, narrow-bandpass filter (1.060 /im) PD, photodiode LT, light trap. Path of He-Ne monitoring beam P, polarizer 2/4, quarter-wave plate A, analyzer F3, narrow-bandpass filter (632.8 nm) G, glass plate diffuser PM, photomultiplier. OSC, oscilloscope X timing and trigger. (Reprinted with permission from Ref 27. Copyright 1995 American Chemical Society.)...

Cor of this polymer as a function of temperature was determined using a flow birefringence apparatus developed by Janeschitz-Kriegl and co-workers (see ref. 11). In this method an independent determination of the melt viscosity at the same temperature is needed. 

The failure of the SOR can be due to several effects, such as saturation of the orientation at very high shear rates or extra dissipative mechanisms in the local dynamics (chain stiffness, internal viscosity, etc.) (Janeschitz-Kriegl, 1969,1983 Larson, 1988 Fuller, 1990). Nevertheless, it is patently difficult in practice to achieve these conditions with conventional rheometers and birefringence apparatuses. 

Flow birefringence of polymer solutions is, in general, measured with the aid of an apparatus of the Couette type, containing two coaxial cylinders. One of these cylinders is rotated at constant speed, the other is kept in a fixed position. The light beam for the birefringence measurement is directed through the annular gap between these cylinders, in a direction parallel with the axis of the apparatus. In this way, the difference of principal refractive indices An is measured just in the above defined plane of flow (1—2 plane). 

For polymer melts another type of apparatus has been designed in order to measure flow birefringence in the same plane (17). This apparatus is of the cone-and-plate type. In this apparatus the light beam is directed in a radial direction. The principles of other arrangements, which were designed for the measurement of flow birefringence in a plane perpendicular to the plane of flow, will receive special attention in Section 1.5. 

After these theoretical considerations, it seems of interest to glance over some experimental results. Philippoff (37) investigated a 9 per cent solution of polyisobutylene (Vistanex B-100) in decalin and a 30 per cent solution of polystyrene (PX 134, Dow Chem. Corp.) in toluene. He used a conventional concentric cylinder apparatus for the flow birefringence measurements in the 1—2 plane and the parallel plate apparatus just sketched for the measurements in the 1—3 plane. For comparison, the results in the 1—2 plane are given in the form ... 

At this point it should be noted that the conclusion drawn from flow birefringence measurements, viz. that p22 — p33 of polymer systems is very small compared with pn — pn is not always supported by other types of measurement. With the aid of pressure measurements in the walls of various rheometers (e.g. cone-and-plate apparatus) results have been obtained by a number of authors (refs. 26, 43, 44), showing that p23 — p33 should be positive and can have values up to 20 per cent of Pn Pta- 1-7 suggests for the investigated polyisobutylene solution... 

L-100 (Mw — 1.4 0.1 x 10 , Mw/Mn — 2.2)4 in medicinal white oil as a rather high viscous solvent (1.50 poise at 25° C). In this figure the directly measured shear recovery (s ) (open triangles) is plotted against shear stress pzl of the preceding shear flow. From flow birefringence measurements (in a coaxial cylinder apparatus) and normal thrust measurements (in a cone-and-plate apparatus) values of normal stress difference (pn — p22) were calculated. These values were transformed with the aid of eq. (2.12) into recoverable shears s. The full circles (from... 

As already mentioned in Chapter 1, there are mainly three geometries suitable for the measurement of flow birefringence, viz. those of the concentric cylinder apparatus, the adapted cone-and-plate apparatus and the slit-capillary with a rectangular cross-section. The general principles of the pertinent techniques have been described in the same chapter. The purpose of the present chapter is to give details of the design and construction in order to enable the reader to form a judgement as to the efficiency of the proposed methods, i.e. the relation between information and experimental effort. 

If the present author would be asked why he did not first try to investigate the flow birefringence of polymer melts with the aid of a concentric cylinder apparatus, he could only answer because of the inconveniences experienced with such a type of an apparatus, when the viscosity of polymer melts is measured. As a matter of fact, the apparatus for polymer solutions, as described in the previous sections, would not.be suitable because of the impossibility to fill it with a polymer melt. As a consequence, a new type of apparatus had to be designed in any case. 

The decision was taken in favour of a cone-and-plate apparatus, as such a type of apparatus has proven to be very suitable for the viscometry of polymer melts. Afterwards, as a consequence of the experiences gathered with this apparatus, it is felt that also a concentric cylinder apparatus would be useful, viz. for the investigation of the flow birefringence in... 

The cone-and-plate apparatus for the measurement of the flow birefringence of polymer melts has been described in detail very recently (77). Nothing particular has been changed on this apparatus meanwhile. For the present purpose, only the essential parts of this apparatus will be described. These parts are shown in Fig. 6.6. This figure shows a cross-... 

As has already been pointed out in Sections 1.3 and 1.5, the slit-geometry is interesting for two reasons. First, it enables the measurement of flow birefringence in the 1—3 plane. Second, it furnishes the possibility to investigate polymer melts at high shear rates, where the cone-and-plate geometry fails. In the present section it remains to give a short description of the apparatus. 

Fig. 6.7. Slit-apparatus for the measurement of flow birefringence in the 1—3 plane. (A) outer body, (V) conical member enclosing the slit with a rectangular cross-section (this part is split into pieces), (E) entrance, (Wt, IV2) windows, (Hlt Ht, Ha)...

The optical apparatus used in this study was designed according to the strategy described in section 8.4.3, which permits the simultaneous measurement of birefringence and dichroism. The source was a infrared diode laser that generates light at a wavelength in the... 

The optical apparatus used in this work was described in section 8.6 and has the capability of providing both Raman scattering and birefringence measurements simultaneously. The Fourier expansion of the overall Raman scattering signal is given by equation (8.51), and the coefficients are given by equations (8.52) to (8.54). In these expression, a simple, uniaxial form for the Raman tensor was assumed. From these coefficients, the anisotropies in the second and fourth moments of the orientation distribution can be solved as... 

Birefringences are mostly observed in condensed phases, especially pure liquids or solutions, since the strong enhancement of the effects allows for reduced dimensions (much shorter optical paths) of the experimental apparatus. Nowadays measurements of linear birefringences can be carried out on liquid samples with desktop-size instruments. Such measurements may yield information on the molecular properties, molecular multipoles and their polarizabilities. In some instances, for example KE, CME and BE, measurements (in particular of their temperature dependence) have been carried out simultaneously on some systems. From the combination of data, information on electric dipole polarizabilities, dipole and quadrupole moments, magnetizabilities and higher order properties were then obtained. 

The birefringence is measured using apparatus of the type shown in Fig. 8.10(a). He-Ne laser light (/. = 0.633 /mi) is passed through the polarizer P, and then through the electroded specimen. The specimen is in the form of a polished plate, of thickness t typically 250 /mi, carrying gold electrodes with a gap of approximately 1mm. 

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