112 FUNDAMENTALS OF SUBMICROSCOPIC MORPHOLOGY I 



(Hermans, 1938), whereas a dried mass of micellar strands should 

 represent a more airy structure with a much lower density. Examples 

 of xerogels are gelatin and celloidin. 



We are therefore compelled to assume the existence of short-range 

 order. Given this short-range order of the micellar strands, one can 

 imagine continuous strings intersecting the whole gel (Fig. 54, p. 70). 

 The orientation never changes abruptly; deviations from parallel 

 alignment are only gradual. Following such a continuous string or 

 micellar strand in an isotropic gel, one finds a curve; neighbouring 

 strands are approximately parallel (Fig. 85, p. 127). Shrinkage causes 

 the strings to approach each other; if the distance between them re- 

 mains the same at all points, the result must be a decrease in the radius 

 of curvature (Hermans, 1941). It follows that, on the assumption of 

 short-range order, the gel is capable of shrinking uniformly in all 

 directions until the structural elements are close-packed, without 

 kinks in the micellar strands (Fig. 76, p. 108). 



Discrepancy in the density of dry gels. The transparent brittle state of 

 dry xerogels (dried glue, gelatin foil, horny celloidin, etc.) has led 

 Hermans and Vermaas (1946) to compare these substances with glass. 

 In the manufacture of glass the rapid cooling of melts gives the un- 

 wieldy molecules of quartz, silicates, borates, etc. no time to crystallize. 

 The glassy amorphous state is, therefore, characterized by a similar 

 molecular framework to that of the gels with amicroscopic framework, 

 i.e., with chain molecules as structural units. Glasses possess a some- 

 what lower density than crystals of the same compound, since the 

 closest packing of the molecules is attained in the crystal lattice only. 

 For instance, the difference between the densities of butyl alcohol 

 CH3CH2CH2CH2OH in the crystalline and in the supercooled glassy 

 state amounts to 6%. Gels with micellar structure contain ordered 

 crystalline regions of micellar strands next to less ordered, more or 

 less amorphous regions. For the latter Hermans (1946) assumes an 

 amorphous glassy state. Hence the gel consists of crystalline and glassy 

 amorphous parts. If the densities of the crystalline and the amorphous 

 compounds are known, the amount of crystalline material in the gel 

 can be calculated. Using the reciprocal densities, i.e., the specific 

 volumes, the following holds good : X 9?-^^., + (i — x) y^^^^j = 9?, where 

 ff = experimentally determined specific volume of the gel, ^^j^r) = 

 specific volume of the crystalline part, rp^^^^^ = average spec.vol. 



