Field-induced birefringence function

The usefulness of electrical response measurements of solutions is not limited to effects linear in applied field. Transient birefringence induced by polarizing electric fields (the transient or dynamic Kerr effect) has given valuable information about biopolymers in solution the effect must by symmetry be an even function of E(t), beginning with terms in E (t). In both cases, a response theory treatment of transient behavior meets with difficulties not encountered in linear problems, but recent progress in deriving correlation function expressions for such effects is described in III. 

Empirical models of the induced anisotropy have also been obtained from measurements of the pressure- and field-induced optical birefringence (Kerr effect) [20]. While these are not spectroscopic procedures, we include such references here because of their significance for CILS [20, 24-26, 52, 53]. Other modeling attempts are based on measurements of depolarization ratios as a function of pressure [163, 178, 179]. In recent work satisfactory consistency of the anisotropies derived from second virial Kerr coefficients, pressure-induced depolarization ratios, and depolarized CILS has been reported [11, 80]. We note that the confusion that has existed in the early years of CILS studies is now understood to have been due to the previous lack... 

A version of Coupled Cluster theory for use in the calculation of linear response functions (LRCCSD) has been developed by Piecuch et a/.135 and applied to the case of ammonia where the dipole and parallel polarizablity has been calculated as a function of the symmetric stretch and inversion internal coordinates. Coriani et a/.136 have also used CCSD response theory to calculate the electric-field-gradient induced birefringence in H2, N2, C2H2 and CH4. 

The induced birefringence is a function of the polarizabilities and the extent of alignment of the resultant dipole moments // of the particles in the solution by the external field E. Under the assumption that interparticle interaction is negligible (dilute solutions) and the energy of interaction U between E and fi is less than the thermal energy kT, the following expressions can be derived [3] for the low-field limit ... 

After the sample has been excited, the probe beam propagates in the sample probing the modified index of refraction. We assume the probe beam linearly polarized at 45° with respect to the excitation beam in the xy plane. The expression of the laser beam before the sample has been reported in the appendix. After the beam has propagated through the sample, the anisotropic index of refraction produces a modification of phase, which is different for the probe components along x and y. Neglecting the effect of the induced birefringence (see appendix) on the probe envelope functions, , the expression for the probe electric field after the sample is... 

Formula (4.371) proves explicitly that the suspension birefringence is an even function of the applied field amplitude. For this reason, in response to the excitation of the frequency go the optical anisotropy Av oscillates with the basic frequency 2co. The higher-rank harmonics induced by the saturation behavior of Av((0) are the multiples of the basic one. It is also clear that besides the oscillatory contribution, the frequency spectrum of Av contains a constant component. 

One notes that the optical birefringence induced by the static electric field is no longer a quadratic function of the field strength but, by (164a) and (171), is given as follows ... 

In regime III, the flow field is very strong and shear-induced molecular orientation becomes important. According to birefringence measurements for anisotropic HPC/H2O solutions and HPC/ m-cresol solutions, the molecular orientation is a monotoni-cally increasing function of the steady state shear rate. 

Although any functional form of the electric field E(t) can be applied to induce the birefringence, the interpretation of the response function An(t) is the simplest if a square-pulse perturbation is used, with rise and fall times significantly shorter than the relaxation times t, of the birefringence response. The corresponding equations in the preceding section are valid only for such conditions. 

As for purely electro-optic polymers the electro-optic functionality can be achieved in a variety of different ways including guest/host systems, side-chain and main-chain polymers, crosslinked polymers and self-assembly approaches (36-38). In amorphous polymers, the NLO chromophores which have a permanent dipole moment are oriented with an electric field to induce electro-optic effects (39). Orientation of these dipoles leads not only to macroscopic electro-optic properties but also to birefringence (40). In the oriented gas model and for a poling field applied along the Z axis these two effects can be described by (39) ... 

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