4 C. L. SADRON 



Knowing the experimental values of A, B, S, and [?j], it is then possible 

 to derive the morphological characters of the macromolecule. 



For instance, one obtains directly from Eqs. (1) and (3) the relation 



M = 8mJcT/A(l - poF sp ) (5) 



Then, having measured V ap [generally by pycnometry, a method which is 

 not above all criticism; see ref. (1)], we see that the value of M can be 

 calculated from the experimental values of S and A. 



The derivation of the shape and dimensions from the values of /, C, or 

 F calculated from A, B, or [77] is not straightforward. In fact, we have to 

 find out from empiric experience or from theory, or from both, the relation- 

 ship between /, C, or F and the dimensions of the particle, and that for 

 every possible shape of the latter. This is conceivable only in the case of 

 very simple geometric shapes, for which dimensions can be fixed with very 

 few — one or two — linear parameters. 



A method which is widely used is to assume that the particle is a compact 

 ellipsoid of rotation of volume V and elongation p, moving in a continuous 

 medium (the solvent). Explicit equations giving respectively /, C, and F 

 as functions of V and p are then derived from the application of the general 

 theory of the hydrodynamics of continuous fluids. Knowing the values of 

 /, C, and F from experimental determination, it is possible to calculate 

 V and p from these hydrodynamical equations. 



It is evident that it remains to determine what could be the relationship 

 between the shape and dimensions of a real particle and the "equivalent 

 ellipsoid." Each case has to be specially discussed in the light of all possible 

 data obtained from the consideration of the chemical structure or of the 

 various physical properties of the given macromolecule. 



b. Poly dispersed Solutions 



In this case, each special category of macromolecules contained in the 

 mixture behaves as if it were alone in the solution (at least at infinite dilu- 

 tions) and the experimental effect is the sum of the effects which would 

 have been observed for each component. 



1. The most general case is that of a mixture of molecules of which 

 weight, shape, and dimensions are simultaneously different and with no 

 correlation between them: for example, a mixture of ellipsoids of revolution 

 of different V and p and of different densities ( polydispersity of the third 

 order). 



2. Fortunately, experience shows that things are generally simpler. For 

 instance, the particles in the mixture very often have the same density. 

 It means in the case of the ellipsoids of rotation that only two of the three 

 parameters V, p, and M can vary independently (polydispersity of the 



