Double refraction orientation

A substance is anisotropic, if it has different properties in different directions. If the refraction index n differs for perpendicular and parallel-polarised light (n and Hy) the result is birefringence or double refraction (when transparent). Accordingly, birefringence is evidenced by the ability of a material to rotate the plane of polarised light. It is defined as the difference in refractive indices in the directions parallel and perpendicular to the direction of orientation ... 

The double refraction in the flowing solution is the product of an orientation factor f a, p) and an opticcd factor ... 

Birefringence, also known as double refraction, can be a useful technique for measuring orientation. Certain requirements must be met, as in all systems, before the data can be obtained or interpreted even if obtainable. 

Gurnee, E. F. Theory of orientation and double refraction in polymers. J. Appl. Phys. 25,1232 (1954). 

The ability of anisotropic and anisometric particles to assume some co-orientation in external force fields is not only responsible for significant changes in scattering properties but also causes birefringence (double refraction), i.e., the average refractive indexes of two beams polarized in perpendicular planes happen to be different. The specific orientation of particles and birefringecne may be caused by the action of electric field (Kerr effect), magnetic field (Cotton-Mouton effect), or in the case of anisotropic particles by flow of medium (Maxwell effect) [25]. 

Birefridgence may be observed with optically anisotropic particles of dispersed phase as well as with optically isotropic but anisometric particles, whose refractive index, n, is different from the refractive index of the medium, n0. One can reveal these two components of birefringence by varying the refractive index of dispersion medium. The own double refraction of particles, characterized by the difference in the refractive indexes of extraordinary, nE, and ordinary, nm, beams, is independent of the refractive index of medium and is maintained when particles are placed into the medium with the same refractive index. For optically isotropic but anisometric particles undergoing co-orientation in the flow, the double refraction, nE - nm, is proportional to (n2 - n20)2. The proportionality constant is positive for rod-like particles and negative for plate-like ones. In the case of particles that are both optically anisotropic and anisometric these effects are additive. 

The normal positive sign of the intrinsic double refraction indicates that intra-micellar (intrafibrillar) molecular chains run parallel to the fibril axis. The variations produced by the substances described in the last paragraph have been ascribed to intramicellar penetration by the added agents (130), either with oriented absorption (188) or accompanied by chemical reaction (79). 

Figure 3.8 Double refraction (a) two crystals with similar orientations (b) two crystals with different orientations of crystal axes.

The orientation of the molecules brought about by the velocity gradient is revealed by a double refraction. A detailed discussion of this double refraction on the basis of rigid ellipsoidal particles can be found in the work of Peterlin and Stuart In recent work the subject was treated from the point of view of randomly coiled flexible structures. The principal features of this treatment may be outlined as follows. 

However, when applying results of the type (57), it must be borne in mind that such equations apply to the amorphous constituent only, and must fail at advanced degrees of stretch where crystalliisation sets in since the influence of crystallisation on the double refraction of rubber-like polymers is considerable In addition to the intrinsic double refraction of the gel frame, the swollen gel may show structural double refraction and adsorption double refraction. The structural, or textural , birefringence is caused by the difference between the refractive indices of polymer substance and solvent. It was estimated by Wiener for rod-shaped particles and for platelets. Wiener s theory is not applicable to rods of molecular thickness, and the structual double refraction caused by oriented long-chain molecules has not yet been accessible to a reliable theoretical treatment. 

The adsorption double refraction results from orientated adsorption of solvent molecules on the polymer frame. There are indications that this effect plays a part in the double refraction of certain systems However, a theoretical approach to this type of birefringence does not exist. Notwithstanding these difficulties, Treloar ... 

In agreement with the foregoing, it could be shown experimentally that the double refraction of regenerated fibres changed if their crystalline portion (consistii of the crystalline modification cellulose II) was transformed into another modification (cellulose IV) without chai ir the orientation of the fibre These effects, which impose certain restrictions as to the possibility of quantitative evaluation of orientation from optical measurements, arise from the influence of the internal field (cf. p. 586). 

Structural birefringence is detected by varying the refractive power of the imbibition liquid and measuring the double refraction in dependence of its refractive index If a typical maximum or minimum curve is obtained, one may conclude that orientated anisodiametric particles occur . A reversal of this rule is, however, not permitted, since the outcome of the experiment may largely depend upon the accessibility of the relevant structure to the various liquids used for the imbibition. 

The question arises as to what is the contribution of the anisotropy of the amorphous fringe-like portion of the gel framework to the total birefringence. Since, in orientated gels, the amorphous parts will be also orientated, they certainly do add to the total double refraction, but, quantitatively, the question can not be answered at the present moment. The anisotropy of a molecular chain embedded in a solvent may be different according to the nature of the solvent. 

The intrinsic double refraction of cellulose nitrate being negative, the curves exhibit a maximum. It is seen that both the birefringence in the maximum and the Wiener component increase with orientation. Kratky and Platzek, as well as the other authors just cited, have endeavoured to interpret the results of their measurements using the equation... 

Dichroism is to be expected, when dealing with orientated molecules of a coloured substance. It was e. g, observed by Ambronn in cellulose fibres coloured with certain dyestuffs. The quantitative treatment of dichroism is analogous to that of double refraction, substituting absorption coefficients k for refractive indices or polarizabilities. 

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