Osmotic pressure and polymer size in semidilute polymer solutions under good-solvent conditions

We consider the lattice Domb–Joyce model at a value of the coupling for which scaling corrections approximately vanish and determine the universal scaling functions associated with the osmotic pressure and the polymer size for semidilute polymer solutions (⁠$c/c∗≤10$⁠, where $c$ is the concentration of the solution and $c∗$ is the overlap concentration) in good-solvent conditions. Our result for the osmotic pressure agrees with previous renormalization-group calculations (the relative difference is less than 1%) but differs significantly from previous numerical determinations in which polymers were modeled as lattice self-avoiding walks. We show that for $c/c∗≳6$ simulations of lattice self-avoiding walks give results that are affected by strong scaling corrections even for chain lengths as large as 1000: The self-avoiding walk model is therefore unsuitable for the determination of universal properties of polymer solutions deep in the semidilute regime.