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



is the rotary Browiiian motion, and a different balance is achieved at each 

 shear gradient. A theoretical expression and tables of computed results can 

 be used to relate the rotational diffusion coefficient to the observed depen- 

 dence of intrinsic viscosity on shear gradient. Thus far this method has been 

 used in only a preliminary way with solutions of tobacco mosaic virus 

 (Wada, 1954). Ideally a Couette viscometer should be employed for the 

 measurements. 



iv. Dielectric Dispersion. One of the older methods for measuring rota- 

 tional diffusion coefficients is based on the analysis of the contribution of 

 the macromolecules to the dielectric constant of the solution (Oncley, 1942). 

 In an alternating electric field of relatively low frequency the periodic oscilla- 

 tion of the field is matched by the rotation of the macromolecules, which are 

 first oriented m one direction and then in the opposite sense in response to 

 the alternating field. As long as the particles can reverse their orientation in 

 keeping with the alternating field, a dielectric constant is obtained which 

 includes a contribution from the charged particles. However, an increase in 

 the frequency of the alternating current soon leads to a situation in which 

 the macromolecules can no longer rotate sufficiently rapidly. As a conse- 

 quence the observed dielectric constant decreases since fev»'er macromole- 

 cules make their maximum contribution. From the change in dielectric 

 constant with frequency, known as the dispersion of dielectric constant, a 

 value for the rotational diffusion coefficient can be derived. Complex ap- 

 paratus is required for this technique, and rigorous limitations are imposed 

 with regard to the types of solutions that can be examined. 



V. Polarization Fluorescence. In each of the four methods discussed thus 

 far some type of force, electric or hydrodynamic, is imposed in order to 

 cause some degree of orientation of the macromolecules. The field may then 

 be removed and the rate of decay of the orientation examined to produce a 

 value for the rotational diffusion coefficient. Alternatively, a steady state is 

 achieved in which there is a balance in the effect of the orienting and dis- 

 orienting forces; from an evaluation of the balance, the rotational diffusion 

 coefficient is calculated. There is still another method, not involving the 

 application of any external field to produce preferential orientation of the 

 macromolecules. Instead, attempts are made to measure the angular rotation 

 of the molecules in the brief time interval between the absorption of light 

 of a certain wavelength and the emission of that light as fluorescence. 

 The degree of depolarization of the fluorescent light is a fmiction of the 

 extent of rotation of the macromolecules during the lifetime of the excited 

 state (about 10~^ sec). With polarized incident light, the emitted light also 

 is plane-polarized if the molecules do not rotate during the time period 

 between absorption and emission. If the rotational diffusion coefficient is 

 very large, as with small molecules, the emitted light will be depolarized. 



