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I want to model the capture of ions by a negatively charged grid made of some proton conductor material like graphene oxide.

Are ions captured as soon as they cross the surface, or do they have some capture mean path that depends on the incoming momentum?

I'm interested in protons incoming with energies in the range keV-MeV

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That depends on your definition of "capture". Energetic particles will have to slow down (and lose energy) before they "find their place" in the capturing grid. This will typically take some distance. For keV protons interacting with carbon atoms, a single collision is clearly not sufficient to thermalize - so I would say that their mean path definitely depends on their incoming energy.

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    $\begingroup$ Ranges of energetic ions in solids can be estimated using SRIM (available at srim.org). A 1 MeV proton will have a mean range of over 10 microns in graphite. Also be aware that you will have Rutherford scattering occurring, so not all incident ions will stop in the material even if it is thick enough... $\endgroup$ – Jon Custer Dec 23 '14 at 21:08

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