G C. L. SADRON 



Since, for each species we have 



= M(l - F sp po) A 

 ffikT 



it means that even if the particles have different shapes and dimensions, 

 M is the same for all the molecules, and it is then possible to calculate its 

 value. 



2. When we measure some property of the solution in a permanent state 

 (say its viscosity), we no longer obtain a distribution curve, but rather a 

 mean value of the parameters. For instance, it will be easily seen that the 

 specific viscosity of a solution containing a mixture of particles of known 

 distribution function g(M), and for which the morphological coefficient F 

 [see Eq. (4)] is supposed to be a function of M only, is 



rviF(M) ,_-. ,,, 



Vsp = J M 9 



And we have 



^p- g(M) dM / ' f" g(M) dM 



M = f 



Jo 



Then [77] is equal to the mean value of 3lF(M)/M. 



Let us recall, on this occasion, that if X is a parameter and /(X) or g{\) 

 its distribution functions, it is possible to calculate the following different 

 averages Jor_X : 



number average X„ = / X/(X) d\ / I /(X) d\ 



weight average X ( , = J \ 2 f(\)d\/J \f(\)d\ (9) 



z average X 2 = f \ 3 f(X)d\/f X 2 /(X) d\ 



If X is a function of M , we have g(\) = Mf(\) and we obtain, by replac- 

 ing in the above equations /(X) by g(\)/M, the expressions of the different 

 averages of X as functions of ^(X). 



2. Optical Methods 4 



a. Monodispersed Solutions 



Let us consider a parallel beam of vertically polarized light passing 

 through a solution of macromolecules whose index of refraction n is differ- 



4 K. A. Stacey, "Light Scattering in Physical Chemistry," Butterworths, London, 

 1956. 



