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
PβΟ2.3 and, hence, KβΟβ0.3 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 Ο than
predicted from semidilute polymer theory, but again in agreement with
experiment.Comment: 7 pages, 4 figures, LATE