Osmotic Pressure of Solutions Containing Flexible Polymers Subject to an   Annealed Molecular Weight Distribution
  The osmotic pressure $P$ in equilibrium polymers (EP) in good solvent is investigated by means of a three dimensional off-lattice Monte Carlo simulation. Our results compare well with real space renormalisation group theory and the osmotic compressibility $K \propto \phi \upd \phi/\upd P$ from recent light scattering study of systems of long worm-like micelles. We confirm the scaling predictions for EP based on traditional physics of quenched monodisperse polymers in the dilute and semidilute limit. Specifically, we find $P\propto \phi^{2.3}$ and, hence, $K \propto \phi^{-0.3}$ in the semidilute regime --- in agreement with both theory and experiment. At higher concentrations where the semidilute blobs become too small and hard-core interactions and packing effects become dominant, a much stronger increase % $\log(P/\phi)\approx \log(\Nav^2/\phi) \propto \phi$ is evidenced and, consequently, the compressibility decreases much more rapidly with $\phi$ than predicted from semidilute polymer theory, but again in agreement with experiment. 
A. Milchev, J.P. Wittmer, P. van der Schoot, D. Landau