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