138 BIG MOLECULES 



at various concentrations and extrapolation to zero concentrations so that 

 intermolecular interactions cannot interfere, gives the value of M, as before. 

 Here p is the ratio of densities of solvent to solute, and a> the angular ve- 

 locity of the centrifuge (radians/sec). 



A more rapid method, used within the past few years, takes advantage of 

 the fact that small volumes bounded by the top and the bottom of the tube 

 reach equilibrium very rapidly; measurements of concentrations in these 

 volumes can be made within a few hours, and an "average" molecular 

 weight then evaluated. 



Direct Measurement of Size and Shape via the Electron Microscope. For those 

 polymers whose shape and weight are the same, dry or wet, the direct meas- 

 urement by the electron microscope is possible. A comparison of the results 

 of different methods on the globular molecule icthyocol is shown in Figure 

 6-6. The nonequilibrium methods will now be outlined. 



Dynamic Methods 



These are based on four transport processes which are discussed as a 

 group in more detail in Chapter 8. The following outline sumcies here: 



Diffusion under a concentration gradient and sedimentation under a centrif- 

 ugal force can both be stated as the speed of the process under specific condi- 

 tions, and these speeds expressed as D and s, respectively. An argument 

 involving factional force offered by the water against movement of the 

 macromolecules shows that the ratio of the two speeds, D/s, is related to the 

 molecular weight, M, by 



(1 ~ P) D _ J_ 

 RT s M ' 



an expression originally derived by Svedberg. Measurements of D and s, 

 and of the densities of solid and solute permit evaluation of molecular 

 weight. 



Intrinsic Viscosity. This property, /c as c — » (where rj is the 



Vo / 

 viscosity of the solvent and r\ that of the solution), can be related to the vol- 

 ume of the molecule and molecular weight by two expressions which in 

 simplest form are: 



(1) \r\\ = 2.5 V for spheres (7000 V for a big, randomly coiled molecule 

 such as DNA) — here Fis cc/g; and 



(2) [77] « M a where a is an empirical constant, usually 0.5 to 1 .0. 

 Although measurement of viscosity is easy enough, the proportionality 



constants have an empirical character, and hence one always suspects the 

 absolute values of size and shape so obtained. However, they are quite reli- 



