02 FUNDAMENTALS OF SUBMICROSCOPI C MORPHOLOGY I 



dissolved, since short particles give extinction angles of about 45°, 

 whereas filaments give angles near 0°. 



Having determined the extinction angle, one can also measure the 

 retardation (technical notes in Wissler, 1940, and historical review in 

 PiLNiK, 1946). 



The birefringence of flow is not a constant as is the double refraction 

 of crystals, because the retardation does not only depend on the thick- 

 ness of the layer, but also on the velocity gradient and the viscosity, 

 and on the concentration of the solution. All these variable quantities 

 are combined in Maxwell's constant, by which the anisotropy of 

 flow of different sols can be characterized and compared. With sols 

 in which the particles of the solute are chain molecules (molecular 

 colloids), the method can be used to obtain data on the anisotropy 

 of single macro molecules. 



In the case of single chain molecules we can no longer speak of 

 refractive indices, since the surface of a molecule does not represent a 

 phase boundary where the velocity of propagation of light is changed 

 by a definite amount. The optical properties of the molecules are 

 therefore characterized by another quantity, designated as optical 

 polan':(ability, -which, is a measure for the influence of the electromagnet- 

 ic field of a fight wave on the orbits and oscillations of the electrons 

 in the molecule. This influence depends on the direction of vibration 

 of the fight, and in a rod-shaped molecule with rotational symmetry 

 we must therefore distinguish two different principal polarizabifities, 

 the one parallel and the other perpendicular to the mohcule axis, in 

 the same way as we must distinguish two principal refractive indices in 

 an optically uniaxial crystal. 



More than once the question has arisen (e.g., Schmidt, 1938) as to 

 whether chain molecules, like micellar strands, cause rodlet bire- 

 fringence when they are in parallel alignment. This problem has been 

 solved by Sadron (1957). It follows from the theory developed by 

 him that the formula for the double refraction of flow consists of two 

 parts. The first part depends only on the polarizabifity of the molecule 

 (compare intrinsic double refraction), whereas the second part contains 

 also the influence of the shape of the particles (compare form bire- 

 fringence). In contrast to the conditions prevailing in micellar systems, 

 however, both terms depend on the refractive index of the solvent 

 (Snellman and BjornstAhl, 1941). 



