84 



METHODS FOR DETERMINING MOLECULAR SIZE AND SHAPE 



Axis of rotation 



Fig. 38. Tubes spinning about an axis of rotation with an angular velocity a) 

 and with the particle of interest at a distance r from the axis. The particle is at 

 P and is suspended in a liquid L. 



Inner edge 



> 



Boundary 



I 





Aijfw*:** 



Axis of rotation 



Particles in solution 

 moving to the right 



Particles which have 



reached the outer end 



of the tube and have 



formed a pellet 



Fig. 39. A representation of the situation some time after a tube containing 

 particles denser than the suspending liquid has been started spinning in a cen- 

 trifuge. The particles which were at the inner edge at time zero move together 

 to the right and thus form a boundary whose movement can be photographed 

 for determination of the velocity of the movement. 



(b) The rate at which a particle will move when being spun at a 

 given frequency w at a given radius r will depend on its density, the 

 density and viscosity of the liquid, and on the size of the particle, as wall 

 be demonstrated below. 



The individual particle cannot be studied, but the particles at the inner 

 edge of the tube form a boundary which moves radially outward as a 

 result of the centrif ligation, as indicated in Fig. 39. This boundary can 

 be made visible by optical methods, so that the rate of displacement of 

 the particles can be deduced by photographing the transparent tube at 

 various times after starting the centrifuge. Since the density and vis- 

 cosity of the liquid can be measured, it is possible to compute the ratio of 

 the mass of the particle (its molecular weight) to its size. If the particle 

 is spherical, the molecular weight can be deduced directly. If it is not 

 spherical, a somewhat more complicated procedure is required which 

 gives us the size of the particle by measuring the diffusion of particles 

 through a liquid. Then, by a combination of these measurements, the 

 molecular weight can be deduced. The mathematics of this method will 



