Ion transportation through bulk porous solids is important for real world applications. Ion transportation at the nanoscale occurs through nanopores or channels surrounded by graphene, but current methods for mass production of graphene allow for little control over horizontal dimensions, producing defects and alterations. Structural imperfections found in bulk carbon materials make it hard to research ion transportation on the nanoscale.
Advances in graphene chemistry have allowed for the assembly of bulk carbon materials in a more efficient and precise manner. The Layered Graphene Gel (LGG) membrane follows this method, allowing for ion transportation that can be controlled using capillary pressure. The result is a tuneable material system, which allows for comparable data and establishment of structure-property relationships.
To start off, LGG membranes were prepared via capillary compression. Interlayer distance was calculated, assuming that individual graphene sheets would not stack into graphite (see figure 1), performing a SANS analysis, in which neutrons are shot to travel at constant speed between the graphene sheets without reflecting off obstacles, confirming multi-layered graphene, rather than graphite, which would have rebounded neutrons. These neutron patterns, plotted on a Porod-behavior graph, produce a descending curve indicating the absence of a defined structural order. The slope (F) of the linear regression is around 2 nm in range from 0.001 to 0.01 A-1. This deviates from a Porod-behavior graph (F=4), demonstrating that the structure is shown to be rough across a wide range of length scales. The fluidic nature of the trapped liquids prevents graphene from collapsing, leaving the continuous porous network of cascading nanoslits intact. The evidence of the LGG remaining intact demonstrates the successful compression technique, resulting in a multi-layered gel with nanoslits used to diffuse ions through a permeable membrane.
In order to quantify ion permeability, a model is made by using a layered membrane of nanosheets containing an array of nanoslits, allowing sustained ion flow, which is accurate as the array is structurally similar to the membrane itself. Variables used to describe the model include: height between nanosheets (d), the size of nanosheets (L) and distance between each sheet (????). d in the model is determined by the membrane after exposed to varying levels of pressure. The values for L and ???? were found by correlating results of ion diffusivity found in the LGG. The model is then used to demonstrate material diffusivity through different calculated values of d in the LGG. It is shown that as d decreases, the particles diffused per minute are significantly less. However, additional scenarios show that all variables have an influence on membrane permeability, especially L, which quadruples permeability when increased from 10nm to 100nm. When d is small, an increase in both L and ???? can also increase diffusivity. This suggests that the parameters of the entire structural system are fundamental in ion diffusivity, not ion channel size alone. Therefore, in order to define the characteristics of LPG it is important to consider geometric components of the sheets in addition to distance between layers. This knowledge enables constant values of L and ???? to be set, possibly resulting in optimal diffusivity at many intersheet channel sizes for varying pressures.
To prove structural integrity, effects of spatial confinement and surface charge (the difference in charge between the inner and outer surfaces of a stream of ions) were measured. The LGG was able to withstand significantly increased liquid flow and spatial confinement was reduced in the model using theoretical calculations. Simulation and experimental results show that unless the distance between sheet ends was especially small (0.5 nm), changing ion solubility did not impede diffusion.
The length of one nanosheet, L, (see figure B) was measured using the correlation analysis of the diffusion obtained from the simulation and experiment, resulting in approximately 50 nm. Since the length of the nanosheet is vital in the modeling of the cascading fluidic channel, the obtained value must be very close to the actual one.
Corrugations of the graphene nanosheets can affect the ion fluidity if the pores are too small. For example, when L is 50 nm in a membrane with nanosheets separated at 11 nm (d=11), the diffusivity obtained from the experiment is close to the one predicted in the simulation. However, if the value of L is greater (1 µm), meaning that the pores are smaller, the diffusivity is 500 times greater than what was predicted in the simulation. The deviations are due to corrugation of the graphene sheets, size of the sheets, and the presence of pores.
Electrokinetic ion transport through the cascading nanoslits was simulated and the membrane conductivity, d, was predicted. Then, the conductance characteristics of the LGG membranes, using the ratio of κm,exp/κm,sim were measured. The results show that when dexp is larger than 5 nm, κm,exp/κm,sim tends to values close to 1. This proved that the as-derived structural element catches the main characteristics of the porous. However, when the size of the nanoslits becomes smaller than ~3 nm, the scaling behavior starts to deviate. In addition, when dexp is 0.85 nm and measured in 1 mM KCl, the value of κm,exp becomes greater than κm,sim. The value of κm,exp reaches a maximum as the channel size is reduced, and the concentration is increased from 1 to 100 mM. Then, the channel conductivity changing to larger dexp, from 0.85 to 2.2 nm.
The channel dependence on ionic concentration and its conductivity nonlinear increase, while the channel size decreases from ~10 to ~2 nm, can be explained by the surface-charge-governed transport mechanism. Some ion selectivity measurements were used to examine the surface charge status of CCG. The conclusions were that the layered graphene-based membranes are slightly cation selective and has a reversal potential of 20 to 30 mV, which means that the CCG sheets are negatively charged in the LGG membranes. The simulation shows that the ionic concentration of cations in the nanochannel increases more than the anions, even when a small surface charges density is established on the slit walls.
While previous articles have been unable to experiment on nanofluidic systems below 2 nanometers due to technical limitations, Cheng’s research group’s approach of graphene based membranes has found unusual behaviors from less than a nanometer to 10 nanometers. The results are consistent with previous research in terms of conductivity enhancement in relation to channel height of 2 nanometers or above. They also show that when the nanoslits are smaller than 2 nanometers, the previously observed enhancement of nanoslit conductivity drops. This offers statistical insight into ion transport behaviors on a sub-nano level. Although previous research has attributed these differences to systematic error, the process used in this article proves that it is more likely that these findings are not random. Previous research has used the traditional 1-dimensional nanochannel model, thus the unusual behavior observed in the 3-dimensional model used in this research could possibly be a result of the interfering variables or surface imperfections. Combining experimental and simulational data,the relationship between microscopic structures and macroscopic properties has been described, possibly opening new doors to medical advancement.
Following data analysis, a method was created to test the effect of porous graphene layers on the passing of nanoparticles through the material. The LGG membranes (made up of molecularly porous carbon), are set up with an interlayer spacing of about 10nm and multiple layers in depth to filtrate CCG (chemically converted graphene) colloids. This is best shown in figure 2.B, with graphene converging to allow gaps where filtration occurs. The method used a constant concentration of colloids, while interlayer spacing was adjusted through capillary compression. After the miscible solution (water/sulfuric acid mix) was evaporated, the membrane shrunk from about 10 nm to about 0.5 nm interlayer spacing. Ion permeation experiments were done using a homemade device, while ion diffusion was monitored by looking at electrical conductance change in the reservoir. Membrane conductivity was mapped using Current-Voltage Characteristic Curves. Simulations were also performed using the COMSOL Multiphysics program to analyze the membrane’s structure and properties.
Angstroms: 1 ten-billionth of a meter, 10-10
Bulk Porous: Having many pores
Capacitance: Ability of a system to store electric charge
Capillary Pressure: The pressure difference across immiscible (non-combining or mixing) liquids due to capillary forces (surface tension and interfacial tension)
Capillary Compression: The adding of volatile and nonvolatile liquids and then evaporating them to adjust the interlayer space
Cascading: Arranged/arranging in a series or sequence
COMSOL Multiphysics: A finite element solver and analyzer used in physics and engineering.
Corrugated: Shaped into alternate ridges and grooves
Current-Voltage Characteristic Curves: A graph showing the relationship between a current and the voltage.
Diffusion coefficient: The measurement of the diffusion of particles in cm2 per second
Electrophoretic: relating to electrophoresis, the movement of dispersed particles relative to a fluid in an electric field with constant strength.
Electrostatic Forces: Forces of attraction or repulsion dependent on their charge.
Electric field: A kind of physical field existing around electrical charges, able to convey the interactional effects of electric charges
Exfoliation: The removal of the oldest dead skin cells on the epidermis.
Fluidic Systems: The core area where the particles are inserted into the object, usually by injection.
Graphene: An allotrope of carbon where each carbon atom is covalently bonded to three others, allowing it to conduct electricity; form of carbon in 2 dimensions that is the base of other carbon forms such as graphite, charcoal, and carbon nanotubes
Hydration shell: A cluster of water molecules surrounding or attached to a hydrophilic substance
Interparticle: Between particles
Ion Diffusivity: The ability of ions to move through a membrane
Ion Transport: Process that moves ions against the concentration gradient through active transport across a membrane
Ionic Species: Subjected to a chemical process or measurement
Lateral Size: Size measured at the side of the material
LGG: Layered Graphene Gel
mM KCl: Molar mass of potassium chloride
Micro Corrugation: Corrugation, but on a microscopic level.
Nanofluidic systems: Liquids confined in containers with nanoscale dimensions
Nanoslits: A slit in a material on the nanoscale
Permeation: To pass through the pores of of permeate.
Physicochemical: Relating to physiology and chemistry
Si-based: Silicon based
Slip Condition: The relative velocity of a fluid to the boundary along which it passes.
SANS Analysis: Diffracting neutrons to recreate an image of a microscopic object; neutrons can permeate a structure and only bounce off of individual atoms.
Stochastic: Randomly determined
Structural-Property Relationship: The relationship between the structure of the material and its properties.
Substrate: A substance or layer that underlies something, or on which some process occurs.
Supramolecular: Relating to or denoting structures composed of several or many molecules.
Tunable interlayer spacing: A technique to create nanoslits of various sizes through parallel stacking multiple graphene sheets.