Molecular Dynamics Simulations of Semi-Dilute and Concentrated Solutions: Unexpected Finite Size Effects in Osmotic Pressure

Abstract: We explore semi-dilute and concentrated oligomers and polymers in a broad range of polymerization indices N ranging from 1 to a 100 and in a range of monomer number densities $\phi$ from 0.1 to 0.8 via molecular dynamics simulations and under good solvent conditions. This parameter range covers both no-overlap and strong chain overlap regimes, as quantified by the polymer packing fraction $0.1\le\Phi\le{14}$. Contrary to some common beliefs, the non-ideal part of the osmotic pressure demonstrates strong finite size effects. In the overlap regime, it deviates substantially from the scaling form of de Cloizeaux. The finite size correction term is proportional to 1/N, irrespective of $\Phi$. We propose a simple phenomenological description of the osmotic pressure in the infinite chain limit and of the monomer density dependence of the 1/N correction term. We extend the treatment of finite size effects to cover binary mixtures with 2 different chain lengths, and demonstrate that the proposed equation of state is applicable with an effective mass-averaged inverse chain length $1/N_{eff}$. We also discuss finite size effects in the density dependence of the gyration radius.