  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.
