STUDIES IN GELS 



91 



cylinder remains at rest. As shown by Fig. 64b, this gives rise to a 

 velocity gradient in the gap and thus to a force couple on the rodlets 

 dissolved. This force couple, however, is counteracted by the Brown- 

 ian movement of the particles, which tends to annihilate the orienta- 

 tion brought about by the shear. As a result of this competition 



'Z, 



u \ 



^ 



\: 



y 



b) 



Fig. 64. a) Scattering of rodlets when oriented; a angle of scattering, b) Orientation of 



rodlets by a gradient of flow. Zj revolving inner cylinder, Zg immobile outer cylinder, 



d gap between the two cylinders, u maximum velocity of flow, u' velocity' of a rodlet 



which is oriented by the velocity gradient. 



between orienting forces and Brownian movement, the rodlets are 

 scattered with respect to the axis of orientation. The distribution 

 function of the rodlets is very complicated, but can be derived from 

 theory (see, for instance, Peterlin and Stuart, 1943)- It is found 

 that the direction of the axis of orientation depends on the length 

 of the rods. With short rods (axis ratio a:b ^ i) the orientations are 

 spread about an axis enclosing an angle of 45° to the direction of flow. 

 With increasing length of the rods (a:b> i), the axis tends to be 

 oriented in the direction of flow, finally (when a : b -> 00) becoming 

 parallel to the tangent plane of the cylinder. The direction of the axis 

 of orientation can be ascertained in the polarization microscope by 

 the direction of extinction. The extinction angle therefore provides in- 

 formation as to the length of the micelle rodlets or macromolecules 



