Is there a universal equation of state for flexible polymers beyond the semi-dilute regime?*

We reconsider the isothermal equation of state (EoS) for linear homopolymers in good solvents,
p = p(c,T), which relates the osmotic pressure, p, of polymers with the bulk concentration, c,
and the temperature, T. The classical scaling theory predicts the EoS in dilute and semi-dilute
regimes. We suggest a generalized EoS which extends the universal behavior of polymer solutions
up to the highly concentrated state and confirmed it by molecular dynamics simulations and using
available experimental data. Our conjecture implies that properties of polymer chains dominate
the EoS in the presence of many-body interactions. Our theoretical approach is based on a viral
expansion in terms of concentration blobs leading to a superposition of two power laws in the regime
of concentrated solutions.