Osmotic pressure of solutions containing flexible polymers subject to an annealed molecular weight distribution

The osmotic pressure P of equilibrium polymers (EP) in a good solvent is investigated by means of an off-lattice Monte Carlo simulation. Our results compare well with conformation space renormalisation group theory and the osmotic compressibility K as obtained by recent light scattering measurements of long worm-like micelles. The present study allows for the first time the mapping of the relevant energy scale of a standard coarse-grained model on data from real experiments. We also confirm the scaling predictions for EP in the dilute and semidilute limit. In particular, we find P 2.3 for the scaling of the pressure with the volume fraction and, hence, K -0.3 in the semidilute regime -in agreement with both theory and laboratory experiment. At higher concentrations where the semidilute blobs become too small and hard-core interactions and packing effects become dominant, a much stronger increase is evidenced and, consequently, a compressibility that decreases much more rapidly with than predicted from semidilute polymer theory, but again in agreement with experiment. Our results apply both to EP systems with and without rings