Ion transport in complex layered graphene-based membranes with tuneable interlayer spacing

Abstract

Investigation of the transport properties of ions confined in nanoporous carbon is generally difficult because of the stochastic nature and distribution of multiscale complex and imperfect pore structures within the bulk material. We demonstrate a combined approach of experiment and simulation to describe the structure of complex layered graphene-based membranes, which allows their use as a unique porous platform to gain unprecedented insights into nanoconfined transport phenomena across the entire sub-10-nm scales. By correlation of experimental results with simulation of concentration-driven ion diffusion through the cascading layered graphene structure with sub-10-nm tuneable interlayer spacing, we are able to construct a robust, representative structural model that allows the establishment of a quantitative relationship among the nanoconfined ion transport properties in relation to the complex nanoporous structure of the layered membrane. This correlation reveals the remarkable effect of the structural imperfections of the membranes on ion transport and particularly the scaling behaviors of both diffusive and electrokinetic ion transport in graphene-based cascading nanochannels as a function of channel size from 10 nm down to subnanometer. Our analysis shows that the range of ion transport effects previously observed in simple one-dimensional nanofluidic systems will translate themselves into bulk, complex nanoslit porous systems in a very different manner, and the complex cascading porous circuities can enable new transport phenomena that are unattainable in simple fluidic systems.

Keywords: Porous materials; graphene; nanoconfined ion transport; nanofluidics; nanoionics.

Fig. 1. LGG membranes with tuneable interlayer spacing.

(A) Top: Scanning electron microscopy images of the cross-section of the LGG membranes with d_exp compressed to 3.2 nm (left) and 0.5 nm (right), respectively. Bottom: Isotropic SANS patterns of the compressed gel membranes with d_exp of 3.9 nm (left) and 0.5 nm (right), respectively. The inset at the upper left corner is a photograph of the LGG membrane. (B) A schematic showing the formation of an array of cascading nanoslits through parallel stacking multiple graphene nanosheets. L, d, and δ are the key geometrical variables of the proposed structural model for describing the porous structure of the LGG membrane. (C) Reduced 1D SANS data offset from the absolute intensity scale. The upper inset on the right shows the slope F from the linear regressions in the q range from 0.001 to 0.01 Å⁻¹ as a function of d_exp.

Fig. 2. Ion permeation through the cascading nanoslits embedded in the LGG membranes.

(A) A schematic of the experimental setup. (B) The concentration-driven ion permeation through the LGG membranes with d_exp varied from 11 to 0.85 nm. (C) Dependence of ion permeation rate on d_exp.

Fig. 3. 3D data space showing the dependence of log(D_bulk/D_m,sim) as a function of L, δ, and d.

The ranges of the variables L, δ, and d are set as to 8 to 1000, 0.5 to 12, and 1 to 20 nm, respectively. The competing role of L and δ, specifically the increase in L and the decrease in δ, enhance the barrier properties of the LGG membrane as reflected by an increase in log(D_bulk/D_m,sim). When the variables L and δ are close in value, D_m,sim experiences a sharp increase, and such an increase is more pronounced as d is reduced.

Fig. 4. Comparison between experiment and simulation of the scaling behavior of ion diffusion as a function of interlayer spacing through the layered membrane.

Similar comparison is made between experiment and simulation after a hindrance factor H is introduced in the simulation and is shown as red triangles. The inset shows the determination of the geometrical variables L through a reverse Monte Carlo method. The minimization was performed between D_m,exp (d) and D_m,sim (d, L, δ). The variable L rapidly converges after 10 iterations.

Fig. 5. Scaling behaviors of the electrokinetic ion transport as a function of channel size across the range of sub–10 nm and of varied ionic concentrations.

(A to C) Black symbols show the comparison between experimentally measured and simulated channel conductivity, denoted as κ_m,exp/κ_m,sim made in electrolyte concentrations of (A) 1 mM, (B) 10 mM, and (C) 100 mM KCl. κ_m,sim was calculated with zero surface charge, also denoted as κ_{m,sim (σ = 0)} for comparison with the conditions of various surface charge. The colored scatter plots are the theoretical predictions of the scaling behaviors when a surface charge of σ = −2.3 mC/m² (red triangles), σ = −11.2 mC/m² (blue triangles), or σ = −56.1 mC/m² (green diamonds) was imposed in the cascading nanoslits model.