Birefringence time dependent

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). 

Dynamic behaviour. Time dependent curves of the birefringence An(t) induced by applying successively a positive and a negative electric... 

Figure 1. Time dependence of the birefringence signal under the action of a reversing electric pulse of a PVC solution at C = 10 gcm and T = 25°C. The quenching concentration was 0.5 10 g cm". The single exponential curve (dotted line) deduced from the best fit of "Equation 8" to birefringence decay curve is indistinguishable from the experimental curve. Residues (i.e. difference between theoretical and experimental curve) are plotted below the birefringence curve.

Figure 2. Time dependence of the "birefringence decay signal, at the removal of the electric field, of a PVC solution at C = 10" g cm and for a quenching concentration of 1.6 10 g cm . Temperatures are T = 25°C (Fig,2a) and T = 60°C (Fig.2b). Dotted lines represent the single exponential curves deduced from the "best fit of Equation 8 to the experimental curves. Residues (i.e. difference between these two curves) are plotted below.

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. 

K. Osaki, N. Bessho, T. Kojimoto, and M. Kurata, Flow birefringence of polymer solutions in time-dependent field, J. Rheol., 23,457 (1979). 

A.W. Chow and G.G. Fuller, Response of moderately concentrated xanthan gum solutions to time-dependent flows using two-color birefringence, J. Rheol., 28, 23 (1984). 

F. H. Gortemaker, M. G. Hanssen, B. de Cindio, H. M. Laun, and H. Janeschitz-Kriegl, Flow birefringence of polymer melts application to the investigation of time-dependent rheological properdes, Rheol. Acta, 15, 256 (1976). 

Depending on the scheme chosen, the birefringence experiments provide [143,144] direct measurements of either Av or (Av)2. To present the theoretical results in a form suitable for comparison with the experimental data, let us consider the orientational oscillations induced in the dipolar suspension by a harmonic held H = Hq cos (at and analyze the frequency dependencies of the spectra of the order parameters (P2) and (Pi)2- As formula (4.371) shows, the latter quantities are directly proportional to Av and (Av)2, respectively. Since the oscillations are steady, let us expand the time-dependent orientational parameters into the Fourier series... 

The simplified schematic in Figure 2a shows the essential features of the effect. Optically anisotropic molecules in the solution are preferentially oriented by the applied field E(t), resulting in a difference of refractive indices for components of polarized light parallel and perpendicular to the bias field which is measured as a birefringence. The basic theoretical problem is to evaluate this effect in terms of anisotropies of polarizability Aa. referred to molecular axes which produce a time dependent effect when the molecules are preferentially oriented by the field. For no anisotropy in absence of the field, the effect must be an evgn function of field strength, and at low fields proportional to E. A remarkable feature of the effect is that for molecules with permanent dipole moments the response af-... 

The electric birefringence of liquid crystalline solutions of PBLG is time dependent, and the birefringence of the polymer, An/cy, at complete orientation, 2Tt g — g2)ln, as calculated by the following equation (22) ... 

The birefringence of liquid crystalline solutions of polypeptides is time dependent (Fig. 12) it takes more time for the solutions to attain the equilibrium orientation of the same degree in tl magnetic field than in the electric field. A time lag is observed in some cases and the birefringence increases patently in two steps. 

The response of most materials to mechanical, electrical, optical and other force fields is time-dependent. The study of the responses to these force fields allows one to determine, respectively, the rheological, dielectrical and birefringence properties of materials. According to the second law of thermodynamics, part of the input energy involved in the perturbation must invariably be dissipated, and part of it is stored. It should be pointed out... 

Photoinduced birefringence illustrates what is happening in bulk, but use of time-dependent polarization modulation infrared spectroscopy can offer a detailed insight at the molecular level. Different infrared bands can be monitored in time, and the change in their orientation function allows one almost to watch the different groups move in real time. In order to do this, the process must be slowed down considerably, which is achieved by using a fraction of the pump intensity. 

The coupled phonon-polariton oscillations can be detected by measurement of oscillatory birefringence with a variably delayed probe pulse. (The transit time and the spectral content of the probe pulse also should show oscillatory time dependences.) As in forward ISRS, this pulse surfs along a crest or null of the polariton wave. Since the polariton radiates outward from the excitation beam, the probe pulse need not be overlapped spatially with the excitation pulse. By varying the spatial separation between the two parallel-propagating beams, the polariton group velocity and dispersion can be determined. Phonon-polariton dynamics in LiTaOj crystals were determined in this manner [36, 59]. An example of data is shown in Figure 9. 

Figure 9. Oscillations of phonon-polariton mode in lithium tantalate crystal excited through inverse electro-optic effect and impulsive stimulated polariton scattering. Time-dependent birefringence measured with probe pulse, which propagated parallel to but not collinear with excitation pulse. (Reprinted with permission from ref. 36.)...

Dynamic birefringence techniques have been developed by Stein et al. (66), Read (54), Yamada and Hayashi (85) and Hopkins (25). By this technique the stress, strain and birefringence are measured simultaneously while the applied strain varies. By making such measurements as a function of frequency and temperature one can in principle separate the time dependencies of orientation of molecular response in a multiphase system as well as correlate the optical behavior with the mechanical spectrum. This technique can be correlated for example with the dynamic X-ray technique allowing separation of the amorphous and crystalline behavior. 

Benoit (1) performed a calculation similar to that of O Konski at a somewhat earlier date and included equations for the rise and decay of the birefringence under the action of a rectangular voltage pulse. Since the rise time depends on both permanent and induced dipole moments, it is a complex function involving more than one time constant and rather difficult to deal with experimentally. The decay time of birefringence, however, depends only on the molecular dimensions and for a rigid rod Benoit obtained the simple formula... 

We interpret the flare effect as a cooperative extension of molecules over the volume seen as birefringent. This cooperative extension would arise if the chains were behaving as if connected, that is, like a transient network. The fact that this connectedness arises only beyond a given concentration signifies that a cooperative effect is involved, implicit in the network model just described. The fact that it appears only at a critical strain rate, e , however, introduces a new important factor the time dependence of the connectedness. Namely, the connectedness can exist only over a very short time (t J defined by... 

Labarthet, E L., Buffeteau, T., and Sourisseau, C. Azopolymer holographic diffraction gratings Time dependent analyses of the diffraction efficiency, birefringence, and surface modulation induced by two linearly polarized interfering beams. J. Phys. Chem. B 1999, 103, pp. 6690-6699. 

Dynamic mechanical and dynamic stress-optical measurements have been performed on side-chain LCEs with different crosslinking densities [8]. It was found that the relaxation strengths depend strongly on the crosslinking density demonstrating that the vicinity of the crosslinking points perturbs the liquid crystalline order. In this experiment the samples were exposed to a time-dependent stress <7(t), and the time-dependent responses, that is the time-dependent strain e(t) and the time-dependent birefringence An (t), were measured. The real part... 

This behavior is apparent in the top panel of Figure 6.17, showing that the birefringence perpendicular to the strain direction has the same time-dependence as the stress. 

For a monodisperse size distribution of noninteracting ellipsoids, the relations between 9 and the rise and decay of the electrical birefringence have been established [15-17]. At low field strength, for the time-dependent rise of the birefringence one finds... 

The total time-dependent birefringence of the system can be considered to be the sum of contributions from each phase, A, Ag, and Aq. Then, we obtain... 

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