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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.

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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.

The proportionality constant (known as the kinetic prefactor) can be estimated using transition state theory. However, for your particular system (water) it will not be particularly accurate because the transitions will be highly diffusive. So you may want to look through the literature for kinetic prefactors for water transitions.

Another option is to compute/measure the relaxation times at different temperatures, then you can find the barrier without knowing the prefactor. Or you could compute the free energy barriers directly using, say, umbrella sampling.

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