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



employing viscometry, since theoretical investigations have shown that both 

 the volume and shape of the hydrodynamic imit are involved in the fric- 

 tional term for molecules that are almost symmetrical. Therefore, a miique 

 answer as to the shape of hydration cannot be expected from rotational 

 diffusion measurements alone. As with other hydrodynamic techniques, 

 paired measurements are required if assumptions as to the shape or hydration 

 are to be avoided. 



b. Experimental Methods. In recent years both theoretical and experimental 

 innovations have led to additional methods for the measurement of rota- 

 tional diffusion coefficients. As a result there are now available five different 

 techniques which will be outlined here. Some methods are more general than 

 others. Some have attained a greater degree of success experimentally, 

 whereas others rest on a firmer theoretical fomidation. Some are more 

 desirable for very elongated macromolecules while others are preferable for 

 the more symmetric particles. Specialized apparatus not commonly avail- 

 able is required for some; whereas improvising with common laboratory 

 equipment will suffice for others. Only uifrequent application of rotational 

 diffusion methods to viruses have thus far been reported; these have dealt 

 with the rodlike viruses only, although the techniques are not restricted, in 

 principle, to elongated particles. 



i. Electric Birefringence. Most direct of the different methods is that 

 involving a kinetic study of the rate of disorientation of molecules which 

 had first been oriented by the imposition of an electric field. The pulse of 

 current is exceedingly brief in duration and the dipolar macromolecules 

 orient themselves according to their own distribution of charges and the 

 polarity of the electric field. As soon as the electric potential is removed, the 

 oriented or partially oriented molecules tend toward a more random dis- 

 tribution relative to the direction of the field. Not all of the molecules are 

 aligned in the direction of the field during the brief interval (10"^ sec.) that 

 the field intensity has its maximum value. However, a steady state is 

 attained in which the tendency toward alignment by the impressed field is 

 counterbalanced by the tendency toward randomness due to Brownian motion. 

 Once the field is removed, the latter becomes dominant and the rate of decay 

 is conveniently measured. Alignment or even partial orientation of aniso- 

 metric particles like tobacco mosaic virus causes the solution to become 

 birefringent, a state which can be detected and measured quantitatively 

 through the use of crossed polarizers. With suitable apparatus that is 

 complex both optically and electronically, the decay of birefringence with 

 time is portrayed as a decay curve from which the rotary diffusion co- 

 efficient can be calculated accurately (Benoit, 1951; O'Konski and Haltner, 

 1956). Moreover, the shape of the decay curve is defined theoretically, so 

 that mixtures of rodlike particles of different sizes can be differentiated from 



