Birefringence relaxation

The addition of salts modifies the composition of the layer of charges at the micellar interface of ionic surfactants, reducing the static dielectric constant of the system [129,130]. Moreover, addition of an electrolyte (NaCl or CaCli) to water-containing AOT-reversed micelles leads to a marked decrease in the maximal solubihty of water, in the viscosity, and in the electrical birefringence relaxation time [131],... 

Gao J, Weiner JH (1994) Monomer-level description of stress and birefringence relaxation in polymer melts. Macromolecules 27(5) 1201-1209 Gardiner CW (1983) Handbook of stochastic methods for physics, chemistry, and the natural sciences. Springer, Berlin... 

The mechanical and rheo-optical properties of Kraton 101 have been studied by Stein136) using films cast from methylethyl ketone and from toluene solutions. The stress-strain curves, birefringence-strain curve, stress relaxation, birefringence relaxation, and dynamic mechanical spectra are dependent upon the morphology of the copolymer which in turn is dependent upon the conditions of preparations of the samples. 

Besides being enormously expanded and spheroidal, the mucins also appear very flexible evidence for this derives from the ease with which these molecules are deformed with shear, as shown in streaming-birefringence experiments, from the concentration dependence of viscosity, and the temperature-dependence of sedimentation coeflScients. Mikkelsen and co-workers confirmed these observations by using the dependence on field strength of electric birefringence relaxation-phenomena. Evidence for local flexibility in the carbohydrate side-chains has come from, for example, n.m.r.-spectral studies. ... 

Ookubo N, Hirai Y, Ito K, Hayakawa R. Anisotropic counterion polarization and their dynamics in aqueous polyelectrolytes as studied by frequency-do-main electric birefringence relaxation spectroscopy. Macromolecules 1989 22 1359-1366. 

Figures 4 and 5 show that during jump tests the birefringence relaxes toward its equilibrium value in much the same way as the extent of reaction evolves during a chemical reaction. This suggests an improvement of the theories discussed in Section 3 based upon the idea that birefringence enter the theory as an independent variable whose evolution is governed by a rate law. It Is the purpose of this section to deduce some of the elementary consequences of a theory of this kind.

Figure 7.3 Birefringence relaxation signals for the transitions Li ->L (42% CigEOg in 4 M NaCl at 26°C curve 1), direct hexagonal Hi Li (42% CisEOg in 1 M NaCl at 26°C curve 2), and bicontinuous micellar Vi L (60% CigEOg in 1 M CsCl at 26 °C curve 3). Reproduced from Reference 12 with permission of the American Chemical Society.

The rise and decay of the electric birefringence of a fluorinated surfactant are shown in Fig. 9.18 [283]. The birefringence relaxation time, Tb, is related to the rotational diffusion constant, D/ ... 

An interesting feature of polarized IR spectroscopy is that rapid measurements can be performed while preserving molecular information (in contrast with birefringence) and without the need for a synchrotron source (X-ray diffraction). Time-resolved IRLD studies are almost exclusively realized in transmission because of its compatibility with various types of tensile testing devices. In the simplest implementation, p- and s-polarized spectra are sequentially acquired while the sample is deformed and/or relaxing. The time resolution is generally limited to several seconds per spectrum by the acquisition time of two spectra and by the speed at which the polarizer can be rotated. Siesler et al. have used such a rheo-optical technique to study the dynamics of multiple polymers and copolymers [40]. 

In observing the time dependent changes in birefringence and stress-optical coefficient, for elongated samples at 25 C, it was found that the rate of crystallization of high trans SBR s was very much faster, some 10 times more rapid, than that for NR (8). This is consistent with the reported rates of isothermal crystallization for NR (2.5 hours at -26°C) and for 807. trans-1,4 polybutadiene (0.3 hours at -3°C) in the relaxed state (12). 

However, further analysis of the behavior of the system in LC cells cast doubt on this interpretation. First, while intuitively attractive, the idea that relaxation of the polarization by formation of a helielectric structure of the type shown in Figure 8.20 would lower the free energy of the system is not correct. Also, in a thermodynamic helical LC phase the pitch is extremely uniform. The stripes in a cholesteric fingerprint texture are, for example, uniform in spacing, while the stripes in the B2 texture seem quite nonuniform in comparison. Finally, the helical SmAPF hypothesis predicts that the helical stripe texture should have a smaller birefringence than the uniform texture. Examination of the optics of the system show that in fact the stripe texture has the higher birefringence. 

Figure 4.1. Time scales for rotational motions of long DNAs that contribute to the relaxation of the optical anisotropy r(t). Experimental methods used to study these motions in different time ranges are also indicated along with the authors and dates of some early work in each case. FPA, Fluorescence polarization anisotropy (Refs. 15, 18-20, and 87) TPD, transient photodichroism (Refs. 28 and 62) TEB, transient electric birefringence (Refs. 26 and 27) DDLS, depolarized dynamic light scattering (Ref. 116) TED, transient electric dichroism (Refs. 25, 115, and 130) Microscopy, time-resolved fluorescent microscopy (Ref. 176).

A single exponential curve (cf. "Equation U") has been fitted to the birefringence decay curve after removal of the electric field the agreement is good for Cq = 0.5 at 25°C (Fig.l) and moderately good for Cq = 1.6 at 60°C (Fig.2b).The fits lead to the relaxation times Tj = 1/6 Dj reported in Table I. As to the other cases, the agreement is very poor (Fig.2a) a two exponential curve is then necessary to describe the decay curves behaviour.The two-time constants are reported in Table I. 

The values of R are reported in Table I. When the decay curve of birefringence is characterized by two relaxation processes, a radius is attributed to each time constant. 

Fig. 5.14. Reduced compliance vs molecular weight for undiluted polystyrenes of narrow molecular weight distributions. Symbols are O from creep recovery (163), Cr from G (w) (192), O- from flow birefringence (180), (X from (189), 9 from G (a>) (M>105 only) (124), jO extrapolated from steady state creep (191), -O from stress relaxation (165), and...

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. 

It, of course, remains questionable whether it ever will be possible to determine this limiting value, since the birefringence which is used in determining y, decreases during the relaxation process. 

With the aid of these relaxation times other rheological properties like normal stresses, flow birefringence and dynamic shear moduli can be calculated. A more detailed discussion of this procedure wiE be given in Chapter 4. 

The rotational diffusion constant in water at 25° and neutral pH as measured by electric birefringence (258) is 230 X 105 sec-1 or 0.73 X HT8 sec as a relaxation time. For a hydrodynamic ellipsoid of dimensions 66 X 22 A and a molecular weight of 14,000, the calculated relaxation tilde is 0.72 X 10-8 sec. However, the apparent asymmetry of the molecule from the X-ray structure corresponds to an axial ratio of no more than 2 1 rather than 3 1. 

As in the case of low-molecular liquid crystals the majority of information about the structure of LC polymers is obtained from their optical textures and X-ray diffraction data. Because of high viscosity of polymer melts, which results in retardation of all structural and relaxation processes it is quite difficult to obtain characteristic textures for LC polymers. As is noted by the majority of investigators smectic LC polymers form strongly birefringent films as well from solutions, as from melts11 27-... 

In an investigation of the birefringence and stress relaxation of Kraton 101 cast from solution in toluene and in methyl ethyl ketone, Wilkes and Stein (33) considered the relaxation modulus to be a weighted average of the moduli of the pure polybutadiene and polystyrene phases. Ferry and co-workers, in their investigations of time-temperature superposition in polymethacrylates with relatively long side chains, found the com-... 

---