Insight into the local composition of the Wilson equation at high temperatures and pressures through molecular simulations of methanol-water mixtures

Methanol-water mixtures are known to be microscopically inhomogeneous and show nonideal properties at ambient conditions and also at higher temperatures and pressures. To understand the nonideality of methanol-water mixtures, the behaviors of local compositions were studied through evaluating the local mole fractions by the well-known activity coefficient equation, Wilson equation, and by molecular dynamics (MD) simulation at three conditions: 25 °C-0.1 MPa, 300°C-25 MPa, and 350°C-25 MPa. The Wilson parameters were redetermined to generate the reference values for the comparison in this study. The deviation of local mole fraction from bulk mole fraction was selected as an indicator for local composition. The deviations by the Wilson equation were positive in all compositions, and its magnitude for water was much larger than that for methanol, which is principally independent of temperature and pressure and was completely supported by the results by MD simulation. The MD simulation provided the dependence of the local mole fraction deviation on the intermolecular distance and indicated that the immediate neighbor in the Wilson local mole fraction approximately corresponds to the distance range from first valley to second peak in the radial distribution function. In addition, the general trends of local mole fraction by MD simulation are similar at ambient and high temperature and pressure conditions, suggesting the applicability of the Wilson equation for methanol-water mixture to high temperature and pressure conditions in terms of representing the local mole fraction.