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.

Eyring的速率过程理论和自由体积概念用于处理质子（或其他粒子）通过2D（二维）晶体（如石墨烯和六方氮化硼）的传输。假定质子首先被激活以便参与传导，并且传导速率取决于系统中可用的自由体积。所获得的质子电导率方程表明，只有导电质子的数量，质子尺寸和堆积结构以及与2D晶体相关的能垒才是关键。通过简单的Arrhenius型温度依赖性意外地预测了量化电导。