For all cases, the chemical potential of ion exchange is fluctuating around a mean value over the pressure investigated. It is understandable because no new particle are inserted in the system, only water molecules are replaced by ions. However, for CsCl, the chemical potential becomes more positive for pressure higher than 200 MPa. Consequently, we assume that chemical potential of ion exchange does not depend on the pressure up to 200 MPa, allowing us to use the chemical potential calculated in our former study in this work.