Conductivity Equations of Protons Transporting Through 2D Crystals Obtained with the Rate Process Theory and Free Volume Concept

The Eyring’s rate process theory and free volume concept are employed to treat protons (or other particles) transporting through a 2D (two dimensional) crystal like graphene and hexagonal boron nitride. The protons are assumed to be activated first in order to participate conduction and the conduction rate is dependent on how much free volume available in the system. The obtained proton conductivity equations show that only the number of conduction protons, proton size and packing structure, and the energy barrier associated with 2D crystals are critical; the quantization conductance is unexpectedly predicted with a simple Arrhenius type temperature dependence. The predictions agree well with experimental observations and clear out many puzzles like much smaller energy barrier determined from experiments than from the density function calculations and isotope separation rate independent of the energy barrier of 2D crystals, etc.. Our work may deepen our understandings on how protons transport through a membrane and has direct implications on hydrogen related technology and proton involved bioprocesses.