Fig. 3: Ion free energy from thermodynamic integration (TI).
From: Molecular dynamics simulations of the evaporation of hydrated ions from aqueous solution
a Water mass density profile ρm(z) of the water–vapor interface. b Chloride free energy profile U(z) obtained by TI (protocol (III), black spheres) where the ion is held at different fixed positions. The error bars are of the same size as the data points. The black solid line shows the analytic image–charge potential for a charged sphere at a sharp flat dielectric interface29, the black dashed line is shifted by the vapor hydration free energy Uhyd = −26 kBT. The red solid line is a cubic polynomial fit to the TI data in the range −2.0nm < z < 0.4 nm. Colored dots show the free energy obtained from the logarithm of the ion distribution of protocol (IV) simulations at constant force Fpull.
