Field-induced birefringence moment

Electric field-induced birefringence, also known as Buckingham birefringence, is used for the experimental determination of molecular quadrupole moment. In the case of infinite dilute solutions, the Buckingham birefringence molar constant, which is related to the anisotropy of the refractive index induced by a field gradient, reads ... 

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). 

Coriani, S., Halkier, A., Rizzo, A. The electric-field-gradient-induced birefringence and the determination of molecular quadrupole moments. In Pandalai, G. (ed.) Recent Research Developments in Chemical Physics, Vol. 2, pg. 1, Transworld Scientific, Kerala, India (2001)... 

Ritchie, G.L.D. Field-gradient induced birefringence a direct route to molecular quadrupole moments. In Clary, D.C., Orr, B., (eds) Optical, Electric and Magnetic Properties of Molecules, pg. 67, Elsevier, Amsterdam, The Netherlands (1997)... 

Several factors contribute to the field-induced structural anisotropy that leads to optical anisotropy and hence to birefringence. All involve the particles polarization by the field and the partial alignment of their resultant dipole moments parallel to E. The resultant dipole moment / of a particle is the vector sum of its permanent and induced dipole moments. At the molecular level, electronic and atomic polarization occurs, the extent of which depends on the nature and symmetry of the molecule and on its polarizabilities (a and ax) along the parallel and perpendicular directions relative to the electric field or, for cylindrical symmetry, along the molecular axes a and b (a and a ). Naturally, the concept of the polarizability tensor is applicable to an assembly of molecules as a whole, e.g., a colloidal particle, as well. For such systems, and also for macromolecules and polyelectrolytes in an insulating medium, interfacial polarization may also have a major or even dominant contribution to the resultant dipole moment. 

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 ... 

The utility of laser-induced birefringence is based on the high frequency of the perturbation field used, which allows only electronic polarization to occur. If the duration of the laser pulse is sufficiently long, the induced dipoles are partially reoriented parallel to the E of the laser pulse. Comparison of the rate and amplitude of the resulting birefringence with that observed in square-pulse (dc) experiments permits elucidation of the contributions of different polarization mechanisms to the induced dipole moment of the particles [27]. 

We have seen that molecules may be oriented in an electric field. If these molecules are anisotropic, such orientation produces birefringence. This is the Kerr effect. The orientation may occur because molecules have a permanent dipole moment, or else they may arise because of an anisotropic induced dipole moment with molecules having anisotropic polarizabilities. 

The static Kerr-constant is 1C = An/[XE ] where An is the optical birefringence, measured at a wavelength X, which is produced by a directing electric field E. 1C is made up of contributions from induced dipole moments ( C d) permanent... 

The goal of the following discussion is to study the low-frequency dynamic birefringence induced by an alternating field in a suspension of acicular particles with dipole moments, that is, the system of type 1 according to the classification given above. The results presented are obtained avoiding any... 

The clasdcal fundamentals of the theory of the Kerr effect are due to Voigt in terms of dectron theory of the atom as an anharmonic oscillator and to Langevin in terms of statistical optical reorioitation of anisotropic molecules in a static dectric fidd. Buckingham proposed a theory and method of measurement of the optical birefringence induced by the gradient of a static electric field permitting the determination of electric quadrupole moments. 

Molecular quadrupole moments may be obtained directly by observing the optical birefringence induced in a gas by an electric field-gradient Exx = —Eyy <35—37 The birefringence nx -ny, like the dielectric polarization in Debye s treatment, is comprised of a temperature-independent contribution due to distortion of the molecule and an orientation term proportional to T l 35 ... 

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) ... 

---