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 $K \propto ϕ\upd ϕ/\upd P$ 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 $P\propto ϕ^{2.3}$ and, hence, $K \propto ϕ^{-0.3}$ 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 % $\log(P/ϕ)\approx \log(\Nav^2/ϕ) \propto ϕ$ is evidenced and, consequently, the compressibility decreases much more rapidly with $ϕ$ than predicted from semidilute polymer theory, but again in agreement with experiment.