Intramolecular long-range correlations in polymer melts: the segmental size distribution and its moments.

We present theoretical arguments and numerical results to demonstrate long-range intrachain correlations in concentrated solutions and melts of long flexible polymers, which cause a systematic swelling of short chain segments. They can be traced back to the incompressibility of the melt leading to an effective repulsion $u(s)\ensuremath{\approx}s∕\ensuremath{\rho}{R}^{3}(s)\ensuremath{\approx}{c}_{e}∕\sqrt{s}$ when connecting two segments together where $s$ denotes the curvilinear length of a segment, $R(s)$ its typical size, ${c}_{e}\ensuremath{\approx}1∕\ensuremath{\rho}{b}_{e}^{3}$ the ``swelling coefficient,'' ${b}_{e}$ the effective bond length, and $\ensuremath{\rho}$ the monomer density. The relative deviation of the segmental size distribution from the ideal Gaussian chain behavior is found to be proportional to $u(s)$. The analysis of different moments of this distribution allows for a precise determination of the effective bond length ${b}_{e}$ and the swelling coefficient ${c}_{e}$ of asymptotically long chains. At striking variance to the short-range decay suggested by Flory's ideality hypothesis the bond-bond correlation function of two bonds separated by $s$ monomers along the chain is found to decay algebraically as $1∕{s}^{3∕2}$. Effects of finite chain length are briefly considered.