Scattering by Many Polymer Chains

The first term is a contribution from two monomers on the same chain, and the second term is a contribution from two monomers on different chains. There are various chain configurations occurring simultaneously on different chains. The summations in Eq. 2.56 can therefore be replaced by statistical averages  

At low concentrations, polymer chains are sufficiently separated from each other. Interference by monomers on different chains are cancelled out on the average therefore, the second term is negligible compared with the first term. Thus, the scattering intensity 7(k) is given by 

In the absence of constractive interference between different monomers, only terms with i = j would survive and therefore 5 i(k) would be equal to 1. The interference makes 5i(k) and 7(k) depend on k. With iCk), Eq. 2.58 becomes to 7(k)/7o = NSiik). Note that uncorrelated pA(monomers in solution have 7(k)/7o = /k )(a/Thus we find that 5i(k) indicates how 

The static structure factor (also called scattering function) that applies also to finite concentrations is obtained from Eq. 2.57 as 

The second term is due to correlations between different chains. Note that chains 1 and 2 have to be nearby to scatter beams that interfere constructively. At low 

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