Molecules, birefringence symmetry

This result demonstrates the tendency of an optically active material to rotate the electric vector as it propagates through the sample. Materials possessing this property are normally composed of molecules having chiral symmetry. This effect leads to circular birefringence and circular dichroism, two optical properties that are frequently used in the characterization of biomaterials. 

One of the mechanisms responsible for the emergence of linear birefringences is the temperature (7) dependent orientational effect the fields have on the molecules of the sample, through the interaction with their permanent multipoles. On the other hand this fact alone would not explain the occurrence of birefringences also for atoms or molecules with spherical symmetry. Electronic rearrangements, involving high order responses to... 

The liquid phase of molecular matter is usually isotropic at equilibrium but becomes birefringent in response to an externally applied torque. The computer can be used to simulate (1) the development of this birefringence —the rise transient (2) the properties of the liquid at equilibrium under the influence of an arbitrarily strong torque and (3) the return to equilibrium when the torques are removed instantaneously—the fall transient. Evans initially considered the general case of the asymmetric top (C2 symmetry) diffusing in three-dimensional space and made no assumptions about the nature of the rotational and translational motion other than those inherent in the simulation technique itself. A sample of 108 such molecules was taken, each molecule s orientation described by three unit vectors, e, Cg, and parallel to its principal moment-of-inertia axes. 

On the assumption of total symmetry of the tensor of third-order nonlinear polarizability c(— co coi, cog, cog), its non-zero and independent elements are the same as those of Table 12. Direct theoretical calculations of c = c(0 0,0,0) have been performed for the atoms of inert gases and some simple molecules. Values of the tensor elements = c(— cu cu, 0,0) have been determined for numerous molecules from static Kerr effect studies and values of c = c(— cd ot>,coi — col) from measurements of optical birefringence induced by laser li t. Measurements of second-harmonic generation by gases in the presence of a static electric field yield the tensor elements c " = c( — 2co co, to, 0), which can also be obtained from second-harmonic scattering in centro-symmetric liquids. The elements of the tensor c = c(— 3co co, co, co)... 

As a first example consider birefringence in an electric field by a gas of molecules with D3h symmetry and a twofold degenerate ground electronic term belonging to representation E. Using the explicit form of the matrices of the components of the operators of the dipole moment [Eq. (20)] and polarizability and by means of Eqs. (84) and (85a)-(85c), we obtain for the molecular constant in the Kerr effect in the E term case under consideration the expression... 

The classical ideas about the isotropy of electrical properties of spherical-top molecules are usually extrapolated to the magnetic properties. This leads to the conclusion about the isotropy of the magnetic susceptibility in high-symmetry molecules and hence about the disappearance of the orientational contribution to the birefringence in magnetic fields (the Cotton-Mouton effect). In the case of degenerate electronic terms or in the pseudodegeneracy situation, these conclusions are incorrect and have to be reconsidered. 

The simplest phase, which contains only molecular-orientational ordering, is the nematic. The term "nematic" means thread in Greek. All known nematics have one symmetry axis, called the director, n, and are optically uniaxial with a strong birefringence. The continuous rotational symmetry of the isotropic liquid phase is broken when the molecules choose a particular direction to orient along in the nematic phase. Since the nematics scatter light intensively, the nematic phase appears turbid. 

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. 

It has been assumed so far that the behaviour of the molecules could be described with sufficient accuracy by the distance between the two ends. The fact that these ends are connected by a series of chain-elements was expressed by the introduction of the fictive force K [equation (11)]. The further development of the theory required some additional assumptions. We may mention, for instance, that the friction experienced in the motion of the two ends towards each other was assumed to be proportional to the total number N of statistical chain-elements, since on the average all these chain-elements will be involved. Further, a quantitative treatment of the birefringence of flow was only made possible by assuming that the molecules on the average retain their symmetry of rotation in the streaming liquid. 

From our daily life it is well known that chiral objects like spiral staircases or flowers look different from different directions. Therefore, it seems evident that chiral molecules and chiral suprastructural phases are anisotropic, too. Until now, chiroptical methods have been only very sparsely applied to chiral anisotropic systems because of serious experimental problems. At first one has to draw attention to artifacts induced by the always existent linear dichroism and birefringence of anisotropic systems (elliptical dichroism and birefringence). Secondly, objects without symmetry do not allow to measure directly chiral and achiral anisotropies without additional requirements. That is, new techniques and unequivocal definitions are needed to decompose the results of measurements with chiral anisotropic phases into chiral and achiral components. A minimum of symmetry is needed to adapt suitable situations where the CD and ORD as chirality measurements of anisotropic systems can be observed directly. 

Determination of molecular symmetry. Molecular symmetry of P. can be determined from measurements of viscosity, streaming birefringence, rates of sedimentation and diffusion, or directly by electron microscopy, For a known M, the frictional coefficient can be calcnlated from ultracentrifugal measurements, e.g. from the sedimentation /= [Mfl - vp)]/S, where v is the partial specific volume, p is the density and S is the sedimentation constant. The axial ratio a/b of a P. can be derived from the frictional ratiowhereis the/of a spherical molecule. The value of a/b for most globular P. is between 2 and 20, and greater than 20 for fibrous R, e, g. the axial ratio of fibrinogen is 30. 

The identification of the appropriate order parameter for nematic liquid crystals is aided by a consideration of the observed structure and symmetry of the phase. As in any liquid, the molecules in the nematic phase have no translational order i.e., the centers of mass of the molecules are distributed at random throughout the volume of the liquid. Experiments of many varieties, however, do demonstrate that the nematic phase differs from ordinary liquids in that it is anisotropic. The symmetry, in fact, is cylindrical that is, there exists a unique axis along which the properties of the phase display one set of values, while another set of values is exhibited in all directions perpendicular to this axis. The symmetry axis is traditionally referred to as the director . The optical properties of nematics provide an example of how the cylindrical symmetry is manifest. For light passing parallel to the director, optical isotropy is observed, while for all directions perpendicular to the director, optical birefringence is observed. Rays polarized parallel to the director have a different index of refraction from those polarized perpendicular to the director. 

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