4 STUDIES IN GELS 85 



of the isotropic rods and n^ that of the imbibition hquid; d^ and 62 are 

 the volume fractions of the two components (^1 + ^2 = i)- Clearly, 

 n?, — nl is a measure of the double refraction n^^ — n^. The formula 

 shows how this double refraction depends on the refractive index n.^ of 

 the imbibition medium. It is zero when n^ = n^, and positive for all 

 other values of n.,, because the numerator contains the square of 

 nf — n|. In other words, the rodlet birefringence is always positive : 

 n,, > nl- Since in birefringent objects the larger index is denoted by 

 ny and the smaller one by na, it follows that n^^ = ny and n^ = Ua. 

 Conversely, in composite bodies with layer texture and negative bi- 

 refringence we have nj_ = riy and n^^ = na. 



It is significant that besides the volume fractions 6^ and 62 no 

 quantities depending on the dimensions of the rods occur in the equa- 

 tion. The double refraction is independent of the thickness of the rods. 

 This is of particular importance to the study of submicroscopic 

 textures, as long as the size of the structural units is not known. 



The double refraction of the composite bodies has been termed 

 form birefringence (Frey, 1924), because its nature depends on the 

 form of the textural elements of the solid phase. The curves of form 

 birefringence are therefore used to examine whether intermicellar 

 spaces occur in a material and to decide whether the micellar phase 

 has the form of rods or platelets. Usually one does not measure the 

 birefringence n^^ — n^ itself, since this depends on the variable 

 thickness d of the swollen gel according to the formula 



njj — nj_ = yA/d, 



but simply the retardation yX, where y is the so-called phase difference 

 and A the wavelength of the light. The introduction of this method 

 of research into colloid optics is due to Ambronn. 



Measurement of tjje birefringence. The basic formula for birefringence 

 can be simplified by introducing the notations Zln for n^^ — nj^ and 

 r for the retardation or path difference yX. This gives 



/In = r/d, 



which shows clearly the linear dependence of the retardation on the 

 thickness d of the object, because zln for a given object in a given 

 medium is constant. 



The retardation F is measured by a compensator. This is a crystalline 

 lamella (quartz, gypsum, calcite) with known double refraction An which 



