90 FUNDAMENTALS OF SUBMICROSCOPIC MORPHOLOGY I 



can be made by assuming that within a certain angle all possible 

 orientations about the reference axis occur with equal frequency. The 

 assembly of orientation then forms a sector (in a plane) or a cone (in 

 space), whose vertical angle a can be computed from the double re- 

 fraction of the gel when the intrinsic double refraction ng — n^, of the 

 micellar strands is known, provided that by judicious choice of the 

 imbibition liquid negligible form birefringence is assured. The angle 

 of scattering a is then given by the following simple relation (Frey- 

 Wyssling, 1945): 



r ■ ■ , A , . sin 2a 



for scattering in a plane Zln = (ng — nj 



for scattering in space An = (n^ — nj 



2a 

 COS a + cos'^a 



For example, the space angle in cellophane paper, referred to the 

 preference direction, imposed by the manufacturing stress, was found 

 to be 71°. 5. The anisotropy of cellophane is, therefore, rather strong, 

 for the angle of scattering corresponding to the isotropic state, i.e., 

 completely uniform distribution, would have been 90°. The micellar 

 strands with their numerous orientations in space may be replaced 

 by a gel in which only a single orientation occurs. This orientation 

 angle is called the average orientation angle am- With the assumptions 

 made by us am becomes ^a, as shown by Fig. 64a. 



The orientation of the strands in a micellar texture can be brought 

 about by a variety of means other than tension or pressure, e.g., by 

 drying or freezing a gel (Ambronn, 1891 ; Ullrich, 1941); the strings 

 or strands of the frame are then shifted into more or less parallel 

 positions. 



Birefringence of flow. The best-defined orientation, however, is that 

 in a field of flow, if one succeeds in liquefying the gel to a sol by re- 

 leasing the junctions. If such a solution is subject to flow, the colloid 

 rodlets are turned parallel at all points where a velocity gradient 

 exists. A well-defined velocity gradient can be obtained by introducing 

 the sol into a narrow gap (width below 14 m^i) between a fixed hollow 

 cylinder and a revolving inner cylinder (Signer, 1930, 1933; Boehm, 

 1939; Frey-Wyssling and Weber, 1941). When rotating the inner 

 cylinder, the liquid in contact with the surface of the rotor acquires 

 its velocity, while the liquid in contact with the wall of the fixed 



