Monte Carlo analysis of the osmotic pressure of athermal polymer solutions in dilute and semi-dilute regimes

The enrichment Monte Carlo algorithm is applied here, for the first time, to calculate the osmotic pressure of an athermal solution of linear chains on a lattice, in dilute and semi-dilute regimes. Complementarily to the Widom's test particle insertion method, the algorithm enables one to estimate directly the free energy and the osmotic pressure of the solution. The result shows that there is a large deviation in the free energy from the Flory–Huggins theory which may be attributed to the chain internal entropy. Moreover, the osmotic pressure shows des Cloizeaux's c^9/4 behavior clearly when the concentration, c, is greater than the estimated overlap concentration. We estimate also the second and third virial coefficients that are compared with experimental values.