Osmotic pressures studied using a simple equation-of-state and its applications

We have developed new equations for general osmotic pressures based on a simple equation of state for solutions. The present method is a completely different approach (directly solving the osmotic equilibrium), compared with the conventional formulation. The model equations are analytical and valid for the entire range of solute concentrations, but require numerical iterations to solve the osmotic pressure, which can be easily made by a simple Newton–Raphson method. The model calculations reveal highly rich and complex behaviors including critical phenomena in the osmotic pressure. Then, we demonstrate that the present model can be applied successfully to actual osmotic data, such as aqueous polymer solutions and aqueous salt solutions of proteins using a single adjustable parameter, which has a physical meaning.