Birefringence theory

Figure 7 shows the data on PBD in the swollen and in the unswollen state. From this it is evident that the product of stress optical coeffient and temperature is almost constant with temperature in the swollen state, while in the unswollen state it exhibits considerable deviation from birefringence theory (eqn. 6) due to crystallization. Therefore, it is best to compare experiments and theory in the swollen state. Gumbrell et al. (60) use the following empirical relationship for the stress in the swollen state. 

When the chain length (i.e. x) increases, factor bo rapidly becomes unity. Therefore, if the chain thickness d both at moderate and high x is taken into account this does not introduce any changes into the birefringence theory. 

Isihara, A. and Guth, E. Theory of Dilute Macromolecular Solutions. Vol. 5, pp. 233-260. Janeschitz-Kriegl, H. Flow Birefringence of Elastico-Viscous Polymer Systems. Vol. 6, pp. 170-318. 

Cao J, Berne BJ (1993) Theory of polarizable liquid crystals optical birefringence. J Chem Phys 99(3) 2213-2220... 

Birefringence. The birefringence of a crosslinked Gaussian rubber subjected to an affine deformation is described by the theories of Kuhn and Grun (1 ) and Treloar (2). These predict a stress-optical coefficient given by... 

The natural way to increase the efficiency of such a frequency conversion process is to use a focused fundamental beam (or, alternatively, a waveguide structure). An established theory of SHG using focused cw beams " predicts, for negligible birefringence waUc-off, an optimal focusing condition which is expressed by the ratio L/b 2.83, where b is the confocal parameter (b = k wQ, where Wqi and ky are the focal spot radius and the wave vector of the fundamental wave respectively). However, this theory applies only to the long-pulse or cw case, where GVM is negligible... 

Theory. In the general case where rigid revolution ellipsoidal particles in solution possess both a permanent and an induced dipolar moment colinear with the particle optical axis, the theory derived by Tinoco predicts the following behaviour of the solution birefringence An(t) in the limit of weak electric field (6). 

Lodge AS. A network theory of flow birefringence and stress in concentrated pol3mier solutions. Trans Faraday Soc 1956 52 120-130. 

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 above three groups of workers evaluated Dr by analyzing the birefringence and light scattering data using the theories for rods. Since PBLG is not... 

A general theory of dichroism induced by strain in polymeric networks Is developed by adaptation of methods developed earlier for treating strain birefringence. It is generally applicable to dichrolc bands associated with any specified conformation involving sequences of one or more consecutive bonds. The transition dipole moment is introduced in the local framework of the skeletal bonds associated therewith. Possible differences in transition moments for various conformations and repeat units are taken into account. Numerical calculations for PE chains show gauche bonds, rather than trans, to be more favorably oriented with respect to the chain vector r. 

The theory of strain birefringence is elaborated in terms of the RIS model as applied to vinyl polymer chains. Additivity of the polarizability tensors for constituent groups is assumed. Stress-birefringence coefficients are calculated for PP and for PS. Statistical weight parameters which affect the Incidences of various rotational states are varied over ranges consistent with other evidence. The effects of these variations are explored in detail for isotactic and syndlotact/c chains. 

Atactic PVAc prepared in a free-radical polymerization is crosslinked by means of benzoyl peroxide. The resulting elastomertic networks are studied in elongation, both unswollen and swollen with triethylbenzene, over the range 273 - 363 K. The most important experimental results obtained are values of the network birefringence, which is negative. Calculations carried out to interpret the birefringence are based on Monte-Carlo simulations of the atactic structure, and on the RIS theory. 

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