Universal curves of the thermodynamic properties of multichain lattice systems via extrapolation of computer experiment data to the scaling limit

Abstract

According to the recent polymer theories, the thermodynamic properties of polymer solutions in a good solvent, at the scaling limit, are governed by a scaling variable composed of the polymerization degree n, the concentration φ, and the polymer dimension exponent ν. Our computer experiments on multichain lattice systems with the nearest-neighbor interaction afford us the configurational free energy or the osmotic pressure. The nearest-neighbor interaction or the solvent condition where the free energy best obeys the scaling is reinterpreted as the fixed point solvent condition in a lattice space RG context. We approach the scaling limit by extrapolating the data obtained at that solvent condition to the limit n → ∞. The osmotic pressure obtained by the procedure shows an excellent agreement with Ohta and Oono’s theory. The nonextrapolated chain dimensions at that solvent condition are also in a good agreement with the theory. It is found that a weak nearest-neighbor attractive interaction works between the chain elements at that solvent condition. We, therefore, should take care for saying about the scaling from experiments on athermal solutions. Many of our data appear to be successfully interpreted in terms of the RG context by the help of some optimistic expectation for the convergence.