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If this charge transfer is not connected to the pumped proton as we propose here, alternative transport mechanisms could be envisioned in which the proton is transported after PPi.
A phenomenological constitutive model is envisioned, in which the bulk material and the boundary layer obey (rate independent associative) coupled plasticity evolution laws, with kinematic hardening laws of differential nature for the bulk material, but of nondifferential nature for the layer.
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