29. DEOXYRIBONUCLEIC ACIDS AS MACROMOLECULES 9 



In this case 



L 2 = Nb 2 (17) 



where N is the number of elementary oscillators, and L the mean square 

 value of the distance between the two ends of the chain. 



5. Zigzag chain molecule. It is very interesting to examine the case of a 

 thin chain molecule which can be figured as a succession of rods of length 

 b and have all the possible relative orientations with a random distribution. 



If each rod has a length which is well under X/20 it behaves — as we have 

 said — like a single oscillator and the P(9) function is then the same as for 

 the necklace assembly of beads. But if the elementary length is larger than 

 X/20 one has to consider first the interferences produced by the oscillators 

 pertaining to each single rod and then, for each value of 9, to compose the 

 intensities of the light scattered by all the rods. 



In this case, the resulting P(0) function is the sum of two terms: one 

 depending upon the P «(9) function for a rod [Eq. (14)]; and the second 

 taking into account the correlation of the rods in the whole chain. 



Such cases have been recently treated by J. J. and J. Hermans. 5 How- 

 ever, here we shall give the results of the calculation in the form previously 

 established by Benoit and Luzzati who give the expression for P(Q) 



P(e) = ^P R (e) + [^&w] Pm(Q) (18) 



with 



f ,(e) '"i 1 - «>-', + a" (i9) 



N 2 (1 — a) 



where 



sin hb 



w 



a = 



These chains will be called zigzag chains. It is clear that they will behave 

 according to Eq. (16) if b is smaller than X/20. 



In Fig. 2 is shown the shape of P(9) as a function of sin (9/2) in some 

 simple cases. 



b. Limiting Expressions of P(Q) 



(1) Small Values of hL. For very small values of hL the expression of 

 P(9) can be replaced by its expansion in increasing powers of hL, which, 

 limited to the first two terms, is: 



5 J. J. Hermans and J. Hermans, Jr., J. Phys. Chem. 62, 1543 (1958). 



6 H. Benoit and V. Luzzati, unpublished (1959). 



