208 



THE PHYSICS OF VIRUSES 



order to observe the reflections corresponding to the large 

 separations between whole virus particles. They found sharp 

 reflections and were able to make accurate measurements of the 

 interparticle distances. The X-ray diffraction pattern corre- 

 sponded to a hexagonal, close packed array. 



The interparticle distance varied with the virus concentration 

 in the manner shown in Fig. 8.7. The interparticle distance R, 

 in A, was found to be 7? = 1,650 /N'^, where N is the number of 



500 



/(Gram Concentration) 



Fig. 8.7. Variation of the intervirus distance for TMV at various concen- 

 trations, as observed by Bernal and Fankuchen (1941). The fact that a linear 

 relation with the reciprocal of the square root of concentration is observed 

 means that a close packed array exists. 



grams of dry virus per 100 cm^. The plot in the figure is R versus 

 the reciprocal of the square root of the concentration. This 

 separation into a hexagonal array can be explained by a repul- 

 sion between the particles, causing them to fit the space in the 

 container with as much distance between particles as possible. 

 The results have been analyzed by Oster and Onsager and can 

 be fully explained by repulsive forces only. 



The repulsive potential due to the double-layer interaction 

 for two spheres, radius a, can be calculated for a variety of 

 cases. For a thin double-layer, corresponding to a moderate 

 ionic concentration (about one-tenth molar for example) , 



