# Relation between Free Energy barrier and relaxation time?

I'm studying a cylinder that is surrounded by water molecules. If I know how long in average the water molecules stay on its surface (the relaxation time, say 20ps), is there any way of estimating the energy they need to leave the surface (free energy, as we have to break bonds to make them escape but they win entropy when they escape)?

I imagine that longer relaxation times need more energy to leave, as it is harder for them to escape, but I have no idea of how to relate these two concepts.

Transition rates are proportional to $\exp(-\Delta F/k_BT)$ where $\Delta F$ is the free energy barrier. This is known as the Arrhenius equation.