4 STUDIES IN GELS IO7 



If the distribution were one which covers a sector with uniform 

 density (Fig. 64a, p. 91), as was assumed on p. 90, the sickle inter- 

 ferences would be circular arcs with sharp boundaries, extending over 

 a sector angle dependent on the angle of scattering. As shown by 

 Fig. 75, however, the density in the sickle decreases very gradually 

 towards the poles, and the distribution function is a very complicated 

 one : the micellar strands which enclose a small angle with the direc- 

 tion of the stretch are more frequent than 'those which form a large 

 angle with this direction, and this distribution is a function of the 

 degree of deformation (Hermans, Kratky and Treer, 1941). In 

 order to explain the distribution curves found experimentally (in- 

 tensity depending on angular distance from the equator), and their 

 change with the degree of stretch, Kratky (1940) has made two 

 different assumptions with regard to gel structure and has calculated 

 how the distribution alters in the stretching process. Comparing these 

 theoretical curv^es with those obtained experimentally, it is possible to 

 decide which of the two hypotheses is the more likely. 



The first limiting case considered by Kratky (1935, 1940) conforms 

 to the older ideas about gel structure, assuming rod-shaped "freely 

 suspended micelles", which are independent of each other (Fig. 59b, 

 p. 77). Their orientation in the stretching process is achieved, as it 

 were, by the flow of liquid (swelling medium) which turns the rodlets 

 distributed at random into positions which are parallel to the direction 

 of the stretch. On this assumption the distribution of the micellar 

 orientations can be calculated for any degree of stretch (= final length 

 divided by original length of the gel). Advanced parallel arrangement 

 of the rodlets is only reached at high degrees of stretch. A number of 

 very swollen gels of cellulose esters (cellulose amyl oxalate, trinitro- 

 cellulose) show a behaviour which is in conformity with this theoret- 

 ical distribution. 



On the other hand, it seemed surprising at first that, in the case of 

 relatively low degrees of swelling (between 1.5 and 2), neighbouring 

 micelles do not disturb each other's movements and behave according 

 to formulae which have been derived for particles freely suspended 

 in a large amount of liquid. To explain this, Kratky (1954) suggested 

 that the arrangement of micellar rods is not completely random, but 

 that there must exist short-range order (i.e., order in small regions). This 

 means that if small, submicroscopic regions are considered, a certain 



