Birefringence measurements

Although significant insight into the process of bond rupture has been gathered from the studies on the scission kinetics, it remains desirable at this stage to carry out further experimentation at a molecular level to get information on the chain conformation at the moment of fracture. As a first step in this direction, birefringence measurements have been attempted recently in the single jet cell... 

Fig. 69. Schematic of the optical train for birefringence measure ments. For microphotographs, an instant camera replaced the photodetector...

Tinland, B., Pernodet, N., and Weill, G., Field and pore size dependence of the electrophoretic mobility of DNA A combination of fluorescence recovery after photobleaching and electric birefringence measurements, Electrophoresis, 17, 1046, 1996. 

Only two birefringence indices are independent and necessary to describe the anisotropy of a biaxial system, while a single birefringence measurement is required for uniaxial samples because nx — ny. 

The compensation birefringence measurement is very easily coupled to optical microscopy in the transmission and reflection modes, thus allowing characterizing orientation with a spatial resolution of a few hundreds of nanometers [14]. Polarizing microscopes are widely available and are often used for birefringence studies even if spatial resolution is not required. Objectives specifically designed for cross-polarized microscopy are necessary to avoid artifacts. 

Birefringence measurements have been shown to be very sensitive to bimodality, and have therefore also been used to characterize non-Gaussian effects resulting from it in PDMS bimodal elastomers [5,123]. The freezing points of solvents absorbed into bimodal networks are also of interest since solvent molecules constrained to small volumes form only relatively small crystallites upon crystallization, and therefore exhibit lower crystallization temperatures [124—126]. Some differential scanning calorimetry (DSC) measurements on... 

Figure 18 shows the percent crystallinity obtained by birefringence measurements for NR at various elongations as a function of temperature. The relative shapes of the curves in this Figure show the pronounced temperature and strain dependence on the strain induced crystallization of NR. Of particular importance is the relatively high amounts of crystallinity that develop at room temperature. 

Figure 13 shows the optical birefringence measured on the (OOl)c and (llO)c faces [19]. According to the indicatrix deformation approach [25], the optical birefringence, An, for the (llO)c face can detect the antiferrodistortive transition, the square of long-range order (P>, and its fluctuation term (SP) in STO by ... 

Phase transitions are not only characterized by atomic or molecular structural changes - they can also be characterized by significant modifications in the microstmcture and domains and at a much larger size scale. One notable example has been recently reported by Glazer et al. [110] using linear birefringence measurements in LiTaOs and LiTa cNbi c03 crystals at high temperature. 

Analysis of polyelectrolytes in the semi-dilute regime is even more complicated as a result of inter-molecular interactions. It has been established, via dynamic light-scattering and time-dependent electric birefringence measurements, that the behavior of polyelectrolytes is qualitatively different in dilute and semi-dilute regimes. The qualitative behavior of osmotic pressure has been described by a power-law relationship, but no theory approaching quantitative description is available. 

The polarizing microscope can be used to observe morphological features of all crystalline polymers that can be prepared as thin films. Birefringence measurement is applicable to all polymers in which orientation or anisotropy can be induced. 

In this respect, another insufficiency of Lodge s treatment is more serious, viz. the lack of specification of the relaxation times, which occur in his equations. In this connection, it is hoped that the present paper can contribute to a proper valuation of the ideas of Bueche (13), Ferry (14), and Peticolas (13). These authors adapted the dilute solution theory of Rouse (16) by introducing effective parameters, viz. an effective friction factor or an effective friction coefficient. The advantage of such a treatment is evident The set of relaxation times, explicitly given for the normal modes of motion of separate molecules in dilute solution, is also used for concentrated systems after the application of some modification. Experimental evidence for the validity of this procedure can, in principle, be obtained by comparing dynamic measurements, as obtained on dilute and concentrated systems. In the present report, flow birefringence measurements are used for the same purpose. 

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). 

To give an impression of the nature of useful experimental results, some flow birefringence measurements which were obtained on a solution of polystyrene in methyl 4-bromo-phenyl carbinol, are reproduced in Figs. 1.2 and 1.3. The concentration of the solution was 2 wt. percents, measuring temperatures are indicated in the figures. The special polystyrene used was a well-known sample of anionically polymerized polystyrene, viz. S 111, provided by the courtesy of Dow Chem. Corp. Its molecular weight is 224,000. The indicated solvent is, at 18 °C, a 0-solvent and possesses practically the same refractive index as polystyrene itself (32). The measurement results are kindly provided by Daum from his still unpublished work. 

Very recently, flow birefringence measurements have been carried out also on polymer melts. Fig. 1.5 shows a check of eq. (1.5), as carried out in this Institute with the aid of a high density polyethylene of rather... 

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... 

After this manuscript had been prepared the present author became aware of the fact that also Murai, Mori and Mikami (45) have carried out flow birefringence measurements in a slit. 

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... 

When the stress components are evaluated with the aid of flow birefringence measurements, the following expressions derived from the stress-optical law as formulated in eqs. (1.5) and (1.6), are used ... 

Unfortunately, Fixman has not yet given a value for the reduced steady-state shear compliance. However, from a comparison of eqs. (3.60a), (3.64) and (3.66) the impression is obtained that the theory of Ptitsyn and Eizner overestimates the influence of the excluded volume on 0 and JeR. As will be shown in the experimental section of this chapter, this impression is supported by flow birefringence measurements on solutions in 0- solvents and in good solvents. 

Perhaps the most intriguing feature of the described theory is the validity of the stress-optical relation also for flowing systems. In fact, the validity of this relation forms the central point of the present concept, viz. the usefulness of flow birefringence measurements for the investigation of elastico-viscous properties. 

One arives at the conclusion that the internal viscosity of chain molecules in solution must not necessarily be so important that it can be detected with the aid of flow birefringence measurements at low shear rates. 

Very little is also known of the flow patterns near the ends of the cylinders. In this respect only one fact seems unquestionable, viz. that the end-effect is more pronounced in ordinary viscometry than with flow birefringence measurements. The reason is that the rectilinear light beam traverses only a very small portion of the liquid which flows near the edges between the end-surfaces of the internal cylinder and bottom and cover of the unit. 

From these measurements of linear dichroism, it can be concluded, that the linkage of l-l.c. s to a polymer backbone generally reduces the nematic order. This effect has been found so far for poly(acrylates), poly(methacrylates) and poly-(siloxanes) and is established by NMR 59,60), ESR61) and birefringence measurements. 

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