228 H. K. SCHACHMAN AND R. C. WILLIAMS 



In some physical determinations of molecular weight (as will be shown 

 later) the quantitative effect of the presence of a molecule depends on the 

 weight of the molecule. We then refer to the weight average molecular weight, 

 defined as 



M. ^ -^ (2) 



It is apparent that some properties may depend on the square of the mole- 

 cular weight or the length, for example. For such a case the so-called Z- 

 average molecular weight is referred to: 



There are ways of obtaining M^ although these are less popular than the 

 methods which yield M^ and M „. It is important to note here that the 

 characteristic dimensions of large particles determined from light-scattering 

 measurements correspond to the Z-average dimension. 



If a solution is monodisperse, the three molecular weights just defined 

 will be identical. Conversely the degree of agreement of two or more of the 

 average molecular weights provides experimental evidence indicating that 

 the preparation is monodisperse. For instance, the number average mole- 

 cular weight is obtained by a quantitative application of electron microscopy 

 while the weight average molecular weight can be secured by sedimentation 

 equilibrium or light-scattering studies. The ratio of weight to number average 

 molecular weight can be used to calculate parameters describing the spread 

 in molecular weights for certain types of distributions. 



An important consequence of the possibility of obtaining two or more 

 kinds of molecular weight on the same material lies in the implications of 

 such results with regard to the biosynthetic mechanisms involved in the 

 syntheses of the macromolecule. It is evident that a polydisperse product 

 wiU result from polymerization processes involving random condensation 

 reactions. The distribution of molecular weights resulting from such a process 

 is termed the most probable distribution, and it can be shown that the ratio 

 of ilf ^ : Mn is 2 : 1 for this mixture. Other polymerization mechanisms have 

 been shown to yield distributions for which M^/Mn approaches unity. It 

 would be expected that biosynthetic mechanisms involving templates would 

 lead to a homogeneous collection of macromolecules. Thus the determination 

 of the different types of average molecular weight may provide some insight 

 about the mechanism of synthesis of the polymer. 



2. Viscometry 



a. General Considerations. Despite gross inadequacies in our knowledge of 

 the structure of liquids and of the factors responsible for the wide variations 



