THE PHYSICAL PROPERTIES OF INFECTIVE PARTICLES 275 



If the solute molecules are polydisperse the molecular weight term in 

 Equation 32 must be taken to represent some sort of average. It is readily 

 seen that this is the weight average molecular weight, previously defined as 



M = — - — - 



where c^ and M,- are respectively the weight concentration and molecular 

 weight of the i*'^ component of a polydisperse mixture. We can write for the 

 i^^ component: 



K _ 1 



Since R^q ^bs = '^^miy a-^d %^^ = 2c,, we have: 



Hence, 



1-90 obs -^''90 obs 



c. Large-Particle Scattering. It is to be recalled that Equation 33 is valid 

 only for solutions containing solute particles whose largest dimensions are 

 small (< 1/10) compared with the wavelength of the scattered light. If the 

 particles are comparable in at least one dimension with the wavelength, a 

 correction to this equation must be introduced, owing to interference effects 

 that are intraparticle in origin (Debye, 1947), If we consider the relative 

 intensities of light scattered in the generally forward and backward direc- 

 tions, it is evident that in the latter case there will be some destructive inter- 

 ference owing to phase differences between scattered wavelets that have 

 originated at different places along the particle. In the forward direction, 

 the phase differences are on the average much nearer zero. The consequence 

 of the interference effects is to warp the shape of the envelope of scattered 

 intensity so as to decrease the magnitude of the backward portion. 



The correction factor for dissymmetry in the scattering envelope is 

 generally called the "particle-scattering factor," P{d). Its reciprocal, P~^{6), 

 is used to multij^ly the observed Rg in order to correct for the interference 

 effects. P{6) is a function of 6 and of the size of the scattering particles 

 compared to the wavelength of the hght employed. For example, in the case 

 of spheres of diameter equal to A/2, the value of P-^{d) is 2.7, for d = 90°. 

 For spheres of this size, then, the observed J?9o must be multiplied by 2.7 

 before it can be used in Equation 33 for the calculation of M. 



In practice, of course, the value of P~^(^) must be calculated from measure- 

 ments that do not include knowledge of particle dimensions or shapes. What 



