Intramolecular form factor in dense polymer systems : Systematic deviations from the Debye formula

We discuss theoretically and numerically the intramolecular form factor F(q) in dense polymer systems. Following Flory's ideality hypothesis, chains in the melt adopt Gaussian configurations, and their form factor is supposed to be given by Debye's formula. At striking variance to this, we obtain noticeable (up to 20%) non-monotonic deviations which can be traced back to the incompressibility of dense polymer solutions beyond a local scale. The Kratky plot (q2F(q) vs wave vector q) does not exhibit the plateau expected for Gaussian chains in the intermediate q range. One rather finds a significant decrease according to the correction δ(F-1(q)) = q3/32ρ that only depends on the concentration ρ of the solution, but neither on the persistence length or the interaction strength. The non-analyticity of the above q3 correction is linked to the existence of long-range correlations for collective density fluctuations that survive screening. Finite-chain size effects are found to decay with chain length N as .