Long Range Bond-Bond Correlations in Dense Polymer Solutions

The scaling of the bond-bond correlation function P₁(s) along linear polymer chains is investigated with respect to the curvilinear distance s along the flexible chain and the monomer density ρ via Monte Carlo and molecular dynamics simulations. Surprisingly, the correlations in dense three-dimensional solutions are found to decay with a power law P₁(s)∼s^-ω with ω=3/2 and the exponential behavior commonly assumed is clearly ruled out for long chains. In semidilute solutions, the density dependent scaling of P₁(s)≈g^-ω₀(s/g)^-ω with ω₀=2-2ν=0.824 (ν=0.588 being Flory's exponent) is set by the number of monomers g(ρ) in an excluded volume blob. Our computational findings compare well with simple scaling arguments and perturbation calculation. The power-law behavior is due to self-interactions of chains caused by the chain connectivity and the incompressibility of the melt.