29. DEOXYRIBONUCLEIC ACIDS AS MACROMOLECULES 



Fig. 1. Definition of the 9 angle in light-scattering experiments. 



ent from the index n of the solvent. We shall assume that there is no ab- 

 sorption of the incident light. 



If V„ is the difference of the intensity of the light scattered — in direction 

 6 (Fig. 1) — by the same volume r of the solution and of the pure solvent, 

 one knows that V v is given by the relationship : 



V v = a-c-MP(Q) (10) 



where a is a factor which can be calculated from the conditions of the ex- 

 periment. P(0) is a scalar function of 6 and of the dimensions and shape 

 of the scattering particles. Its maximum is equal to unity when G = 0; 

 and its value decreases continuously when increases. 

 Equation (10) is often written: 



- = - — (11) 



K MP(Q) 



where again K — a quantity proportional to V v — can be measured by a 

 proper device. In principle, Eq. (11) applies only when c = zero. It is an 

 approximation of the more complete expression 



f-W)- +a& (12) 



where B is the second virial coefficient of the solutions. 



The experiment consists in measuring K/c for different values of 0, each 

 set of experiments being made for solutions of decreasing concentrations. 

 Then, with proper extrapolations, one obtains K/c for all the values at 

 concentration, c = 0. 



Plotting (K/c)c=o as a function of 0, one obtains the curve MP(Q), the 

 intercept of which with the axis of ordinates = is equal to M. At the 

 same time the graph gives the function P( 0) . 



The light-scattering technique is then of great interest, since it gives 

 simultaneously the molecular weight of the particles, and a function P(Q) 

 which depends only on their shape and dimensions. 



When— as is the case for DNA solutions — the whole of the scattered light 

 is vertically polarized, it is possible to calculate the P(0) function for a 

 particle of a given shape. 



In fact, we consider a particle as formed by an assembly of punctual 



