BACKGROUND

[0001] Membranes are used in a variety of separation-based applications, including in desalination and water softening, in bioreactors for wastewater treatment, in biomedical and pharmaceutical materials separation, and in other chemical engineering applications. Most membranes are fabricated with polymers (e.g., cellulose, polyamides, polymethyl, methacrylate, etc.), though polymeric membrane utility is limited by poor chemical and thermal stability of the membranes. Further limiting membrane utility is the static selectivity of membranes produced with current materials and methods. That is, membranes that allow permeability of a compound based on one set of characteristics (e.g., based on size, charge, hydrophobicity, etc.) cannot easily be altered to select for compounds with a different set of characteristics. Thus, selecting for multiple compounds with differential respective characteristics typically requires the use of multiple membranes, which increases separation costs and decreases utilization efficiency.

SUMMARY

[0002] Some embodiments comprise membranes comprising (a) a first layer comprising a porous graphene-based material, (b) a second layer comprising a porous graphene-based material, (c) channel positioned between the first layer and the second layer, wherein the channel has a tunable channel diameter, and (d) at least one spacer substance positioned in the channel, wherein the spacer substance is responsive to an environmental stimulus.

[0003] In some embodiments, the spacer substance expands and/or contracts in response to the environmental stimulus. In some embodiments, the spacer substance reversibly expands and/or reversibly contracts in response to the environmental stimulus. In some embodiments, the spacer substances has an effective diameter that increases or decreases by from about 0.3 to about 50 nm in response to the environmental stimulus. In some embodiments, the spacer substance density such that the spacer substances cover up to about 50% of the surface area of the center of the channel. In some embodiments, the spacer substance is covalently bonded to at least one graphene-based material layer. [0004] In some embodiments, the spacer substance is selected from the group consisting of a polymer, a fiber, a hydrogel, a molecule, a nanostructure, a nanoparticle, a self-assembled monolayer, a magnetic particle, an allotrope, and combinations thereof. In some embodiments, the spacer substance is selected from the group consisting of a hygroscopic polymer, a thin polymer, an amorphous polymer, electrospun fibers, oxide nanoparticles,

octadecyltrichlorosilane nanoparticles, carbon nanotubes, fullerene, collagen, keratin, aromatic amino acids, polyethylene glycol, lithium niobate particles, nanocrystals of 4-dimethylamino-N- m ethyl -4-sti lbazol i urn tosylate, crystalline poly tetrafl uoroethy 1 ene, and combinations thereof.

[0005] In some embodiments, the channel diameter increases and/or decreases in response to the environmental stimulus. In some embodiments, the channel diameter is tuned via expansion and/or contraction of the spacer substance. In some embodiments, the channel has a maximum diameter that increases and/or decreases in response to the environmental stimulus. In some embodiments, the channel has a diameter of from about 20 nm to about 50 nm. In some embodiments, the channel diameter increases and/or decreases by from about 0.5 nm to about 50 nm in response to the environmental stimulus. In some embodiments, the channel is in a closed position before and/or after exposure to the environmental stimulus.

[0006] In some embodiments, the environmental stimulus is selected from the group consisting of variations in temperature, pressure, pH, ionic concentration, solute concentration, tonicity, light, voltage, electric fields, magnetic fields, pi-bonding availability, and combinations thereof.

[0007] In some embodiments, membrane permeability is responsive to the environmental stimulus. In some embodiments, the membrane (e.g., graphene based layers + spacers substances) is from about 5 nm to about 20 nm thick.

[0008] In some embodiments, the first layer and second layer contain pores with a diameter of from about 0.1 nm to about 200 nm. In some embodiments, the average pore diameter in the first layer is different from the average pore diameter in the second layer. In some embodiments, the spacer substance has an effective diameter that is larger than the average pore diameter in the first and second layers. [0009] In some embodiments, at least one functional group is attached to at least a portion of the pores in the first layer and/or the second layer. In some embodiments, the functional group is selected from the group consisting of a negatively-charged group, a positively-charged group, an adsorptive substance, a catalytic substance, a specific binding site, and combinations thereof.

[0010] In some embodiments, the porous graphene-based material in the first layer is structurally different from the porous graphene-based material in the second layer. In some embodiments, the porous graphene-based material in the first layer comprises a different number of graphene sheets than the porous graphene-based material in the second layer.

[0011] In some embodiments, the membrane comprises more than two layers comprising a porous graphene-based material. In some embodiments, the membrane comprises more than one channel.

[0012] In some embodiments, the graphene-based material is graphene.

[0013] Some embodiments comprise methods of altering membrane permeability by exposing a membrane to an environmental stimulus to thereby alter membrane permeability. In some embodiments, the membrane comprises a first layer with a porous graphene-based material, a second layer with a porous graphene-based material, and a channel between the first layer and the second layer, and the channel has a diameter that is altered upon exposing the membrane to the environmental stimulus. In some embodiments, the environmental stimulus is selected from the group consisting of variations in temperature, pressure, pH, ionic concentration, solute concentration, tonicity, light, voltage, electric fields, magnetic fields, pi-bonding availability, and combinations thereof. In some embodiments, the membrane permeability is altered by a change in the maximum diameter of a channel between the first layer and the second layer. In some embodiments, the membrane comprises at least one spacer substance positioned between the first layer and the second layer, wherein the spacer is responsive to the environmental stimulus. In some embodiments, the spacer substance expands and/or contracts in response to the

environmental stimulus.

[0014] Some embodiments comprise methods of water filtration, water desalination, water purification, immune-isolation, timed drug release, hemodialysis, or hemofiltration. In some embodiments, the methods comprise exposing a membrane to an environmental stimulus, wherein the membrane comprises a first layer with a porous graphene-based material, a second layer with a porous graphene-based material, and a channel between the first layer and the second layer, and wherein the channel has a diameter that is altered upon exposing the membrane to the environmental stimulus. In some embodiments, the environmental stimulus is selected from the group consisting of variations in temperature, pressure, pH, ionic concentration, solute concentration, tonicity, light, voltage, electric fields, magnetic fields, pi-bonding availability, and combinations thereof. In some embodiments, the membrane comprises at least one spacer substance positioned between the first layer and the second layer, wherein the spacer is responsive to the environmental stimulus.

[0015] Some embodiments comprise methods of making a membrane that comprises a first layer with a porous graphene-based material, a second layer with a porous graphene-based material, and a spacer substance that is responsive to an environmental stimulus. In some embodiments, the methods comprise combining a spacer substance with a graphene-based material layer in solution, and then inducing bonding between the spacer substance and the graphene-based material layer. In some embodiments, the bonding is induced by ion-beam, electron beam, heating, chemical reactions, or combinations thereof. Some embodiments further comprise adding a second graphene-based material layer to the solution.

[0016] Some embodiments comprise membranes comprising a first layer comprising a porous graphene-based material; (b) a second layer comprising a porous graphene-based material; (c) a channel positioned between the first layer and the second layer, wherein the channel has a tunable channel diameter; and (d) a means for increasing and/or decreasing the diameter of the channel in response to an environmental stimulus. In some embodiments, the means for increasing and/or decreasing the diameter of the channel comprises a spacer substance positioned between the first layer and the second layer, wherein the spacer substance is responsive to the environmental stimulus. In some embodiments, the environmental stimulus is selected from the group consisting of variations in temperature, pressure, pH, ionic concentration, solute concentration, tonicity, magnetic fields, light, voltage, electric fields, pi-bonding availability, and combinations thereof. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] FIG. 1 illustrates some embodiments having a membrane with two porous graphene- based material layers, where the membrane allows passage of both water and salt ions.

[0018] FIG. 2 illustrates some embodiments having a membrane with two porous graphene- based material layers, where applied pressure on the membrane excludes passage of salt ions.

[0019] FIG. 3 illustrates some embodiments having a membrane with three porous graphene- based material layers, where applied pressure on the membrane excludes passage of salt ions.

[0020] FIG. 4 illustrates some embodiments having a membrane with two porous graphene- based material layers, where applied voltage across the membrane excludes passage of salt ions.

[0021] FIG. 5 shows photographs of some embodiments of contamination-based spacer substances formed into various shapes or patterns. Figure 5A shows contamination-based substances formed into a single line. Figure 5B shows contamination-based substances patterned into a star. Figures 5C and 5D show contamination-based spacer substances formed into a dot array (Figure 5D provides a photograph with increased magnification as compared to Figure 5C).

DETAILED DESCRIPTION

[0022] Some embodiments include membranes, and methods of making membranes, with tunable selectivity, e.g., where the membrane can adapt to environmental conditions. In some embodiments, the membrane can be tuned as a result of being adjusted to alter selectivity. Some other embodiments include methods of altering membrane permeability and methods of using membranes with tunable selectivity.

Tunable Membranes

[0023] Membranes of some embodiments are formed with multiple layers of porous graphene- based material, where the layers are positioned or stacked such that a space between the layers can function as a channel or conduit. In some embodiments, the membrane comprises at least two layers of porous graphene-based material, such as from about 2 to about 10 layers, or from about 2 to about 5 layers of porous graphene-based material. In some embodiments, the membrane comprises 2, 3, 4, 5, 6, 7, 8, 9, or 10 layers of porous graphene-based material. The number of channels in the membrane depends in part on the number of graphene-based material layers in the membrane. Thus, two graphene-based material layers can form one channel; three graphene-based material layers can form two channels. In some embodiments, the walls of the channel comprise the graphene-based material layers.

[0024] In some embodiments, a graphene-based material layer comprises a single sheet of graphene-based material. In some other embodiments, a graphene-based material layer comprises multiple sheets of graphene-based material, such as from about 2 to about 5 sheets of graphene-based material. When a layer comprises multiple sheets of graphene-based material, the sheets of can be combined in the layer via, e.g., covalent bonding and/or van der Waals forces. Graphene-based materials are discussed in greater detail later in this application.

[0025] The porous graphene-based material layers in the membrane can be structurally similar, structurally identical, or structurally different from other porous graphene-based material layers in the membrane. For instance, in some embodiments, all graphene-based material layers have the same number of graphene sheets. In some embodiments, the number of graphene sheets in a layer is different from the number of graphene sheets in a different layer. The porous graphene- based material layers in the membrane can be chemically similar, chemically identical, or chemically different from other porous graphene-based material layers in the membrane. In some embodiments, graphene-based material layers can be functionalized with similar, identical, or different functional groups from other graphene-based material layers.

[0026] The thickness of the membrane depends in part on the number of layers present in the membrane and/or on the number of graphene-based material sheets in the membrane. In some embodiments, the membrane is at least 5 nm thick, such as from about 5 nm to about 250 nm thick, from about 5 to about 20 nm thick, or from about 20 to about 50 nm thick.

[0027] Membranes of some of the embodiments provide a means for increasing and/or decreasing the diameter of the channel. For example, at least one spacer substance can be positioned in the channel between the graphene-based material layers. In some embodiments, the spacer substance is responsive to an environmental stimulus. Exemplary environmental stimuli include changes in temperature, pressure, pH, ionic concentration, solute concentration, tonicity, light, voltage, electric fields, magnetic fields, pi-bonding availability, and combinations thereof. In some embodiments, the spacer substance is responsive to a single environmental stimulus. In some embodiments, the spacer substance is responsive to two or more

environmental stimuli.

[0028] The properties of the responsive spacer substances can be altered upon exposure to an environmental stimulus. For instance, in some embodiments the spacer substance can expand and/or contract in response to an environmental stimulus. By way of example, the effective diameter of the spacer substance can be reduced in response to an increase in applied pressure. This is demonstrated in Figures 1-3, which shows a membrane channel with altered selectivity following application of pressure (initially, both water and ions, electrolytes, and/or salts in solution can traverse the membrane— Figure 1; increased pressure compresses the spacer substance and prevents the salt from traversing the membrane— Figure 2; Figure 3 demonstrates that pressure can be used to compress a spacer substance in a membrane with three graphene layers). The term "effective diameter" as it relates to spacer substances refers to the distance between two points on the spacer substance, where the points interact with different graphene- based material layers that form a channel of the membrane (i.e., the height of the spacer substance in the membrane). In this way, the effective diameter of the spacer substance influences the diameter of the channel. An initial effective diameter of the spacer substances can be determined prior to incorporating the spacer substance into the membrane, for instance via transmission electron microscopy (TEM) tomography. For some spacer substances, such as nanoparticles and other particle-based spacer substances, the effective diameter can be determined via scanning electron microscopy (SEM). [0029] In some embodiments, the effective diameter of the spacer substance can be increased upon removal of or reduction in applied pressure. In some embodiments, the effective diameter of the spacer substance increases upon hydration and/or decreases upon dehydration. In some embodiments, the spacer substance is capable of undergoing a physical and/or chemical transformation in the membrane based on an interaction with an activating substance, such as an affinity-based interaction or a chemical reduction. In some embodiments, the environmental stimulus induces a conformational change in the spacer substance that alters the effective diameter of the spacer substance. For instance, conformational changes between trans and cis forms of a spacer substance can alter the effective diameter of the spacer substance (by way of example, a spacer substance could be a polymer with an embedded diazo dye, where exposure to the appropriately colored light alters the volume of the dye based on cis-/trans- conformational changes). In some embodiments, the spacer substance undergoes a physical and/or chemical transformation that is pH-modulated or optically modulated. In some embodiments, the environmental stimulus degrades the spacer substance to alter the effective diameter of the spacer substance.

[0030] In some embodiments, the effective diameter of the spacer substance can be altered by applying a voltage to the membrane or via electrowetting. See, for instance, Figure 4, showing that the spacing between layers can be altered via voltage-sensitive spacer substances. In some embodiments, a voltage or field source is applied across the membrane. In some embodiments, the voltage assists in moving the permeant across the membrane. In some embodiments, the voltage is applied across the membrane using a power source, such as a battery, a wall outlet, or an applied RF field (or other beam). In some embodiments, a voltage of about 1 mV to about 900 mV is applied across the membrane. In some embodiments, the voltage is applied to a graphene-based material layer in-plane. In some embodiments, the graphene can be biased, for instance with the use of an insulating material. In some embodiments, the voltage applied across the membrane is low enough that the graphene does not delaminate and/or low enough that the voltage does not induce electrolysis.

[0031] The responsive change in spacer substance properties can be reversible or irreversible. In some embodiments, the spacer substances reversibly expands and/or reversibly contracts in response to the environmental stimulus. Therefore, in some embodiments, the size of the spacer substance can be repeatedly increased and then decreased in succession. In some embodiments, the size of spacer substance can be increased or decreased, but not both. In some embodiments, the size of the spacer substance can be increased or decreased irreversibly.

[0032] Spacer substances can include polymers, fibers, hydrogels, molecules, nanostructures, nanoparticles, self-assembled monolayers, and allotropes that are responsive to an environmental stimulus. In some embodiments, the spacer substance is a smart polymer, such as a hygroscopic polymer; a thin polymer that expands when hydrated; or an amorphous polymer, such as a porous amorphous polymer. In some embodiments, the spacer substance comprises electropun fibers that can be swelled upon exposure to a solvent. In some embodiments the spacer substance comprises materials with a high thermal expansion coefficient, which expand or contract in response to a temperature stimulus. In some embodiments, the spacer substance is deliquescent. In some embodiments, the spacers are substantially inert. In some embodiments, the spacers are not inert (i.e., they can be reactive).

[0033] Exemplary spacer substance includes particle substances such as metal nanoparticles (e.g., silver nanoparticles), oxide nanoparticles, octadecyltrichlorosilane nanoparticles, carbon nanotubes, and fullerenes. In some embodiments, the spacer substance includes nanorods, nano- dots (including decorated nano-dots), nanowires, nanostrands, and lacey carbon materials.

[0034] Exemplary spacer substances also include structural proteins, collagen, keratin, aromatic amino acids, and polyethylene glycol. Such spacer substances can be responsive to changes in tonicity of the environment surrounding the spacer substance, pi-bonding availability, and/or other environmental stimuli.

[0035] In some embodiments, the spacer substance is a piezoelectric, electrostrictive, or ferroelectric magnetic particle. In some embodiments, the magnetic particle comprises a molecular crystal with a dipole associated with the unit cell. In some embodiments, the magnetic particles can be oriented based on an external magnetic field. Exemplary magnetic particles include lithium niobate, nanocrystals of 4-dimethylamino-N-methyl-4-stilbazolium tosylate (DAST)), crystalline poly tetrafl uoroethy 1 ene (PTFE), electrospun PTFE, and combinations thereof. [0036] In some embodiments, the spacer substance heats up faster or slower than its surroundings. Without being bound by theory, it is believed that such embodiments will allow the rate of passage of permeants, or a subset of permeants, across the membrane to be increased and/or decreased.

[0037] In some embodiments, spacer substances respond to electrochemical stimuli. For instance, a spacer substance can be an electrochemical material (e.g., lithium ferrophosphate), where a change in oxidation state of the spacer substance (e.g., from 2 ^" to 3 ^" ) alters permeability of the membrane. In some embodiments, changing the oxidation state of the spacer substances alters the interaction between the spacer substance and potential permeants. In some

embodiments, the change in oxidation state results from a redox-type reaction. In some embodiments, the change in oxidation state results from a voltage applied to the membrane.

[0038] In some embodiments, the spacer substance comprises contamination structures formed by utilizing a focused ion beam, e.g., to modify heavy levels of contamination on graphene-based material into more rigid structures. For instance, in some embodiments, mobilization and migration of contamination on the surface of the graphene-based material occurs— coupled in some embodiments with some slight beam induced deposition— followed by modification and induced bonding where the beam is applied. In some embodiments, combining contamination structures allows the geometry, thickness, rigidity, and composition of the spacer substance to be tuned to respond to an environmental stimulus (e.g., pressure). Exemplary contamination-based spacer substances are shown in Figures 5A-D.

[0039] In some embodiments, spacer substances have an affinity for graphene. In some embodiments, spacer substances have a higher affinity for graphene than for substances or solutions that can permeate the membrane.

[0040] In some embodiments, the spacer substance is chemically modified to have a functional group or a desired physiochemical property. For example, in some embodiments the spacer substance is modified to be hydrophobic. In some embodiments, the spacer substance is modified to be hydrophilic. In some embodiments, the spacer substance is modified by addition of hydroxyl groups. In some embodiments, the spacer substance is attached to antibody receptors. In some embodiments, the spacer substance is attached to proteins, enzymes, and/or catalysts. For example, in some embodiments a metallic, organometallic, and/or zeolite-based functional group can act as a catalyst for precursors that enter the membrane. In some embodiments, spacer substances are functionalized to preferentially orient a permeant (e.g., water or a solvent). In some embodiments, a permeant that is in the preferential orientation can traverses the membrane in that preferential orientation, whereas a permeant that is not the preferential orientation does not.

[0041] In some embodiments, membranes include a plurality of a single type of spacer substance (e.g., a plurality of nanoparticles). In some embodiments, membranes include a multiple types of spacer substances (e.g., nanoparticles and polymers). In some embodiments, the spacer substance is a porous layer, such as a porous amorphous polymer layer. In some embodiments, the spacer substance is a self-assembled co-polymer that leaves channels between graphene-based material layers (e.g., the channels can be a sub-nm in diameter to about 40 nm in diameter). In some embodiments, the spacer substance or substances between two graphene- based material layers can be the same as or different from the spacer substance or substances between two other graphene-based material layers. That is, the spacer substance or substances in one membrane channel can be the same as or different from the spacer substance or substances in a different membrane channel.

[0042] The diameter of the channel can be tailored based on the density and/or size of the spacer substance incorporated into the membrane. For instance, without being bound by theory, an increase in spacer substance density is believed to be associated with an increase in channel diameter as compared to a channel comprising the same spacer substance, but at a lower density. Indeed, an increased distance between spacer substances (i.e., a low density) allows flexible graphene-based material layers to attain stable configurations in which portions of different layers are in close proximity, thereby lowering the diameter of the channel.

[0043] In some embodiments, the spacer substances are incorporated at a sufficiently low density to allow inter-layer interactions (e.g., interactions between graphene in different layers). In some embodiments, the spacer substances are incorporated at a sufficiently high density to allow chemical interactions (e.g., covalent or van der Waals interactions) between the layers and the spacer substances, but to prevent inter-layer chemical interactions. In some embodiments, both layer-spacer substance and inter-layer chemical interactions are present in the membrane.

[0044] In some embodiments, the spacer substances are positioned in the channel with an average distance between spacer substances of from 10 nm to about 150 nm. In some embodiments, the spacer density is such that spacer substances cover up to about 50% of the surface area of center of the channel— i.e. , in a 2D-plane along the center of the channel, spacer substances cover up to about 50% of the area of that plane. In some embodiments, the spacer density is such that the spacer substances cover up to about 40%, up to about 30%, up to about 20%), or up to about 10% of the surface area of the center of the channel. Spacer density can be calculated, for instance, based on the amount of spacer substance used, the dimensions of the membrane, and the dimensions of the spacer.

[0045] As mentioned above, the size of the spacer substances can also impact properties of the membrane. For instance, spacer substances with a relatively large effective diameter can be used to prepare channels with a relatively high maximum diameter. The term "maximum diameter" as it relates to channel width is defined by the diameter of the channel at a point of interaction between a layer and the spacer substance in the channel with the largest effective diameter. Notably, because of the flexibility/conformity of graphene-based materials, the diameter of a channel at any given location can be higher or lower than the maximum diameter. In some embodiments, spacer substances with relatively small effective diameter can be used to prepare channels with a relatively low maximum diameter. In some embodiments, the spacer substances have an effective diameter of from about 0.3 nm to about 100 nm, such from about 0.3 nm to about 0.5 nm, from about 0.5 nm to about 2 nm, or from about 20 nm to about 50 nm.

[0046] In some embodiments, the spacer substance is restricted from traversing the graphene- based material layers. For example, in some embodiments, the spacer substance is larger than the size of the pores in the graphene-based material layers, or larger than a portion of the pores in the graphene-based material layers. In some embodiments the spacer substance is larger in one dimension than the size of the pores, or a portion thereof, in the graphene-based material layers. In some embodiments, the spacer substance interacts with the graphene-based material layer {e.g. , via covalent bonding or van der Waals interactions). In some embodiments, the interactions between the spacer substance and the graphene-based material layer is stronger than an interaction between the spacer substance and permeants that pass through the membrane.

[0047] The effective diameter of the spacer substance can be tunable, i.e., it can be altered upon exposure to an environmental stimulus. In this regard, the effective diameter of spacer substances can be altered, upon exposure to an environmental stimulus, by about 0.3 nm to about 50 nm, such as from about 0.3 nm to about 0.5 nm, from about 0.5 nm to about 2 nm, from about 10 nm to about 20 nm, or from about 20 nm to about 50 nm. In some embodiments, the effective diameter of the spacer substance can be reduced by about 0.3 nm to about 50 nm, such as from about 0.3 nm to about 0.5 nm, from about 0.5 nm to about 2 nm, from about 10 nm to about 20 nm, or from about 20 nm to about 50 nm. In some embodiments, the effective diameter of the spacer substance can be increased by about 0.3 nm to about 50 nm, such as from about 0.3 nm to about 0.5 nm, from about 0.5 nm to about 2 nm, from about 10 nm to about 20 nm, or from about 20 nm to about 50 nm.

[0048] In some embodiments, the membrane comprises one or more channels that are impermeable {i.e., the channel diameter is about 0, and the channel is referred to as being in a closed position) before and/or after exposure to an environmental stimulus. In some

embodiments, the diameter of the channel is from about 0.3 nm to about 100 nm, such from about 0.3 nm to about 0.5 nm, from about 0.5 nm to about 2 nm, or from about 20 nm to about 50 nm. In some embodiments the channel diameter is about 0.5 nm, about 1 nm, about 2 nm, about 5 nm, about 10 nm, about 15, nm, about 20 nm, about 25 nm, about 30 nm, about 35 nm, about 40 nm, about 45 nm, or about 50 nm. In some embodiments, the channel diameter is smaller than the diameter of pores, or a portion of pores, in the graphene-based material layers. The phrases "channel diameter" and "diameter of the channel" are defined by the diameter of substances that can traverse the membrane. For example, substances with a diameter of more than 10 nm are inhibited from traversing a membrane with a channel diameter of 10 nm or less; substances with a diameter of 50 nm or more are inhibited from traversing a membrane with a channel diameter of 50 nm or less. Channel diameter can be assessed, for example, using a flow test to determine the size cutoff for substances that can traverse the membrane. In some embodiments, particles smaller than the diameter of the channel are also inhibited from traversing the channel, for instance due to interactions with the graphene-based material layer or due to a solvation shell around the particle.

[0049] The channel diameter can be the larger than, about the same as, or smaller than the diameter of pores on the graphene-based material layer. In some embodiments, the channel diameter is smaller than the average diameter of pores in the graphene-based material layer, such as about 5% smaller, about 10% smaller, about 20% smaller, or about 50% smaller. In some embodiments, the channel diameter is about the same as the average diameter of pores in the graphene-based material layer. In some embodiments, the channel diameter is larger than the average diameter of pores in the graphene-based material layer, and the channel is

functionalized; in such embodiments, the channel diameter can be estimated based on the diameter of the spacer substances.

[0050] In some embodiments, the channel diameter is tunable, i.e., it can be altered upon exposure to an environmental stimulus, by from about 0.3 nm to about 50 nm, such as from about 0.3 nm to about 0.5 nm, from about 0.5 nm to about 2 nm, or from about 20 nm to about 50 nm. In some embodiments, the channel diameter can be reduced by about 0.3 nm to about 50 nm, such as from about 0.3 nm to about 0.5 nm, from about 0.5 nm to about 2 nm, or from about 20 nm to about 50 nm. In some embodiments, the channel diameter can be increased by about 0.3 nm to about 50 nm, such as from about 0.3 nm to about 0.5 nm, from about 0.5 nm to about 2 nm, or from about 20 nm to about 50 nm. By altering the properties of the spacer substances with an environmental stimulus, permeability and/or selectivity of the membrane {e.g., as measured by a flow test) can also be altered. Thus, membranes of some of the embodiments are responsive to one or more environmental stimuli. For instance, channels located between membrane layers can be increased or decreased in diameter as a result of changes in the size of the spacer substances. In exemplary embodiments, a membrane that allows passage of water but excludes salt ions (e.g. Na ⁺ and CI ^" ) can be tuned to allow passage of both water and salt ions. In other exemplary embodiments, the membrane can be tuned to allow passage of biological compounds such as insulin, proteins and/or other biological material {e.g., RNA, DNA, and/or nucleic acids), but to exclude passage of other larger biological compounds such as antibodies. In some embodiments, the membrane can be tuned to be permeable to oxygen and nutrients, but to exclude passage of cells (such as immune cells), viruses, bacteria, antibodies, and/or complements of the immune system. In some embodiments, the membrane can be tuned from one that allows passage of antibodies to one that inhibits passage of antibodies.

[0051] Tunable membranes have broad application, including in water filtration, immune- isolation (i.e., protecting substances from an immune reaction), timed drug release (e.g., sustained or delayed release), hemodialysis, and hemofiltration. Some embodiments described herein comprise a method of water filtration, water desalination, water purification, immune- isolation, timed drug release, hemodialysis, or hemofiltration, where the method comprises exposing a membrane to an environmental stimulus, and wherein the membrane comprises a first layer with a porous graphene-based material and a second layer with a porous graphene-based material.

[0052] Some embodiments include methods of filtering water comprising passing water through a membrane. Some embodiments include desalinating or purifying water comprising passing water through a membrane. The water can be passed through the membrane by any known means, such as by diffusion or gravity filtration, or with applied pressure (e.g. applied with a pump or via osmotic pressure).

[0053] Some embodiments include methods of selectively separating or isolating substances in a biological environment, wherein the membrane separates or isolates biological substances based on characteristics of the substance, such as size. Such methods can be useful in the context of disease treatment, such as in the treatment of diabetes. In some embodiments, biological substances below a certain size threshold can migrate across the membrane. In some embodiments, even biological substances below the size threshold are excluded from migrating across the membrane due to functionalization of membrane pores and/or channels.

[0054] In some embodiments, the pores, or at least a portion thereof, are functionalized. In some embodiments, the channels, or at least a portion thereof, are functionalized, for instance by attaching or embedding a functional group. In some embodiments, the functionalization moieties are trapped between two graphene-based material layers, but are not restricted to a single position in the channel (i.e., they are mobile within the channel, but are inhibited from traversing the two-dimensional material layers, e.g., based the size of the pores in the graphene-based material layers). In some embodiments, functionalization comprises surface charges (e.g., sulfonates) attached to the pores and/or channels. Without being bound by theory, it is believed that surface charges can impact which molecules and/or ions can traverse the membrane. In some embodiments, functionalization comprises specific binding sites attached to the pores and/or channels. In some embodiments, functionalization comprises proteins or peptides attached to the pores and/or the channel. In some embodiments, functionalization comprises antibodies and/or antigens (e.g., IgG-binding antigens) attached to the pores and/or channels. In some embodiments, functionalization comprises adsorptive substances attached to the pores and/or channels. In some embodiments, functionalization involves catalytic and/or regenerative substances or groups. In some embodiments, functionalization comprises a negatively or partially negatively charged group (e.g., oxygen) attached to the pores and/or channels. In some embodiments, functionalization comprises a positively or partially positively charged group attached to the pores and/or channels.

[0055] In some embodiments, functionalizing the pores and/or channels functions to: restrict contaminants from traversing the membrane; act as a disposable filter, capture, or diagnostic tool; increase biocompatibility (e.g., when polyethylene glycol is used for functionalization); increase filtration efficiency; position the spacer substances in the channels (e.g., spacers can be positioned near the pores via affinity -based functionalization in the pores; additional spacers can be positioned in interlaminar areas); increase selectivity at or near the pores or in asymmetric membranes; and/or protect spacer substances (e.g., from the external environment or from a particular vulnerability such as degradation).

Substrate Layer

[0056] In some embodiments, a substrate layer is disposed on one or both surfaces of the membrane. Without being bound by theory, it is believed that the substrate layer can improve biocompatibility of membranes, for instance by reducing biofouling, preventing protein adsorption-related problems, and/or enhancing vascularization. In some embodiments, the substrate layer can increase vascularization and/or tissue ingrowth near the membrane, thus prompting the formation of blood vessels and/or tissue ingrowth in close proximity to the membrane.

[0057] In some embodiments, the substrate layer has a thickness of about 1 mm or less, about 1 μπι or less, or about 100 nm or less. In some embodiments, a thickness of the substrate layer can range from about 100 nm to about 100 μπι, or about 1 μιη to about 50 μπι, or about 10 μιη to about 20 μπι, or about 15 μιη to about 25 μιη. In some embodiments, the substrate layer has a thickness about 10 μιη or greater, or about 15 μιη or greater. In some embodiments, the substrate layer has a thickness of less than 1 μιη. In some embodiments, the substrate layer has a thickness of about 10 nm to about 100 nm, or about 20 nm to about 50 nm.

[0058] In some embodiments, the enclosure can be supported by one or more support structures. In some embodiments, the support structure can itself have a porous structure wherein the pores are larger than those of the two-dimensional material. In some embodiments, the support structure is formed as a frame at a perimeter of a two-dimensional material. In some embodiments, the support structure is positioned, at least in part, interior to a perimeter of a two- dimensional material. In some embodiments, the substrate layer can convey a desired degree of structural support (e.g., to prevent tearing and/or buckling) to the two-dimensional material layer.

[0059] In some embodiments, two or more substrate layers are positioned on the same side of the membrane (e.g., two or more substrate layers can be positioned on the outside of an enclosure comprising the membrane). In some embodiments, the substrate is disposed directly on (or affixed directly to) a graphene-based material layer. In some embodiments, the substrate is disposed on or affixed to the graphene-based material layer with high conformance (e.g., by disposing a slightly wet substrate on the graphene-based material layer). In some embodiments, the substrate is disclosed with low conformance. In some embodiments, the substrate is disposed indirectly on (or affixed indirectly to) the graphene-based material; for instance, an intermediate layer can be positioned between the substrate layer and the graphene-based material layer. In some embodiments, the substrate layer is disposed or directly or indirectly on (or affixed directly or indirectly to) another substrate layer. In some embodiments, the graphene-based material layer is suspended on a substrate layer. In some embodiments, the substrate layer is affixed to the graphene-based material layer.

[0060] In some embodiments, the substrate layer can increase vascularization near the membrane, thus prompting the formation of blood vessels and/or tissue ingrowth in close proximity to the membrane. In some embodiments, the increased vascularization contributes to decreasing the effective distance between the blood stream and substances being eluted through the membrane. In some embodiments, the increased vascularization contributes to viability of substances, such as cells, enclosed within an enclosure comprising the membrane.

[0061] The substrate layer can be porous and/or nonporous. In some embodiments, the substrate layer contains porous and nonporous sections. In some embodiments the substrate layer comprises a porous or permeable fibrous layer. Porous substrates include, for example, one or more of ceramics and thin film polymers. Exemplary ceramics include nanoporous silica (silicon dioxide), silicon, SiN, and combinations thereof. In some embodiments, the substrate layer comprises track-etched polymers, expanded polymers, patterned polymers, woven polymers, and/or non-woven polymers. In some embodiments, the substrate layer comprises a plurality of polymer filaments. In some embodiments, the polymer filaments can comprise a thermopolymer, thermoplastic polymer, or melt polymer, e.g., that can be molded or set in an optional annealing step. In some embodiments, the polymer filaments are hydrophobic. In some embodiments, the polymer filaments are hydrophilic. In some embodiments, the substrate layer comprises a polymer selected from the group consisting of polysulfones, polyurethane, polymethylmethacrylate (PMMA), polyglycolid acid (PGA), polylactic acid (PLA), polyethylene glycol (PEG), polylactic-co-glycolic acid (PLGA), polyamides (such as nylon-6,6, supramid and nylamid), polyimides, polypropylene, polyethersulfones (PES), polyvinylidine fluoride (PVDF), cellulose acetate, polyethylene, polypropylene, polycarbonate, polytetrafluoroethylene (PTFE) (such as Teflon), polyvinylchloride (PVC), polyether ether ketone (PEEK), mixtures and block co-polymers of any of these, and combinations and/or mixtures thereof. In some embodiments, the polymers are biocompatible, bioinert and/or medical grade materials.

[0062] In some embodiments, the substrate layer comprises a biodegradable polymer. In some embodiments, a substrate layer forms a shell around an enclosure comprising the membrane (e.g., it completely engulfs the enclosure). In some embodiments, the substrate layer shell can be dissolved or degraded, e.g., in vitro. In some embodiments, the shell can be loaded with additives, including additives that protect substances inside the enclosure from air or prevent the need for a stabilizing agent.

[0063] Suitable techniques for depositing or forming a porous or permeable polymer on the graphene-based material layer include casting or depositing a polymer solution onto the graphene-based material layer or intermediate layer using a method such as spin-coating, spray coating, curtain coating, doctor-blading, immersion coating, electrospinning, or other similar techniques. Electrospinning techniques are described, e.g., in US 2009/0020921 and/or U.S. Application No. 14/609,325, both of which are hereby incorporated by reference in their entirety.

[0064] In some embodiments, the process for forming a substrate layer includes an

electrospinning process in which a plurality of polymer filaments are laid down to form a porous mat, e.g., on the graphene-based material layer. In some embodiments, the mat has pores or voids located between deposited filaments of the fibrous layer. Figure 5 shows an illustrative SEM micrograph of a graphene or graphene-based film deposited upon a plurality of electrospun PVDF fibers. In some embodiments, the electrospinning process comprises a melt

electrospinning process or a solution electrospinning process, such as a wet electrospinning process or a dry electrospinning process. (See, e.g., Sinha-Ray et al. J. Membrane Sci. 485, 1 July 2015, 132-150.) In some embodiments, the polymer can be present in a spin dope at a concentration of 2 wt.% to 15 wt.%, or 5 wt.% to 10 wt.%, or about 7 wt.%. Suitable solvents for the spin dope include any solvent that dissolves the polymer to be deposited and which rapidly evaporates, such as m-cresol, formic acid, dimethyl sulfoxide (DMSO), ethanol, acetone, dimethylacetamide (DMAC), dimethylformamide (DMF), water, and combinations thereof. In some embodiments, the spin dope solvent is biocompatible and/or bioinert. In some

embodiments, the amount of solvent used can influence the morphology of the substrate layer. In dry electrospinning processes, the spun fibers of the fibrous layer can remain as essentially discrete entities once deposited. In some embodiments, wet electrospinning processes deposit the spun fibers such that they are at least partially fused together when deposited. In some embodiments, the size and morphology of the deposited fiber mat (e.g., degree of porosity, effective pore size, thickness of fibrous layer, gradient porosity) can be tailored based on the electrospinning process used.

[0065] The porosity of the fibrous layer can include effective void space values (e.g. measured via imagery) up to about 95% (i.e., the layer is 95% open), about 90%, about 80%, or about 60%, with a broad range of void space sizes. In some embodiments, a single spinneret can be moved to lay down a mat of the fibrous layer. In some embodiments, multiple spinnerets can be used for this purpose. In some embodiments, the spun fibers in an electrospun fibrous layer can have a fiber diameter ranging from about 1 nm to about 100 μπι, or about 10 nm to about 1 μπι, or about 10 nm to about 500 nm, or about 100 nm to about 200 nm, or about 50 nm to about 120 nm, or about 1 μπι to about 5 μπι, or about 1 μπι to about 6 μπι, or about 5 μπι to about 10 μπι. In some embodiments, the fiber diameter is directly correlated with a depth (Z-axis) of a pore abutting the graphene-based material layer (disposed in the X-Y plane), and large diameter fibers can lead to large unsupported spans of material.

[0066] In some embodiments, the substrate layer can have pores (e.g., void spaces) with an effective pore size of from about 1 nm to about 100 μπι, or about 10 nm to about 1 μπι, or about 10 nm to about 500 nm, or about 100 nm to about 200 nm, or about 50 nm to about 120 nm, or about 1 μπι to about 5 μπι, or about 1 μπι to about 6 μπι, or about 5 μπι to about 10 μπι. Pore diameters in the substrate layer can be measured, for example, via porometry methods (e.g., capillary flow porometry) or extrapolated via imagery.

[0067] In some embodiments, the substrate layer can have an average pore size gradient throughout its thickness. "Pore size gradient" describes a layer with a plurality of pores, where the average diameter of the pores increases or decreases based on the proximity of the pore to the graphene-based material layer. For example, a fibrous layer can have an average pore size gradient that decreases nearer the surface of a graphene-based material. In some embodiments, an average pore size of the fibrous layer is smaller nearer the surface of the graphene-based material than at an opposite surface of the fibrous layer. For example, the fibrous layer can have effective pore diameters of less than about 200 nm close to the intermediate layer or the graphene-based material layer which can increase to greater than 100 μπι at the maximum distance away from the intermediate layer or graphene-based material layer.

[0068] In some embodiments, the fibrous layer can have a "porosity gradient" throughout its thickness, which can be measured for instance using imagery. "Porosity gradient" describes a change, along a dimension of the fibrous layer, in the porosity or total pore volume as a function of distance from the graphene-based material layer. For example, throughout the thickness of the porous fibrous layer, the porosity can change in a regular or irregular manner. A porosity gradient can decrease from one face of the fibrous layer to the other. For example, the lowest porosity in the fibrous layer can be located spatially closest to the graphene-based material layer, and the highest porosity can be located farther away (e.g., spatially closer to an external environment). A porosity gradient of this type can be achieved by electrospinning fibers onto a graphene-based material layer such that a fiber mat is denser near the surface of the graphene- based material layer and less dense further from the surface of the graphene-based material layer. In some embodiments, a substrate layer can have a relatively low porosity close to the graphene- based material layer, a higher porosity at a mid-point of the fibrous layer thickness (which can, for example, contain a supporting mesh for reinforcement or other particles), and return to a relatively low porosity at an external surface distal to the graphene-based material layer.

[0069] In some embodiments, the substrate layer can have a "permeability gradient" throughout its thickness. "Permeability gradient," as used herein, describes a change, along a dimension of the fibrous layer, in the "permeability" or rate of flow of a liquid or gas through a porous material. For example, throughout the thickness of the fibrous layer, the permeability can change in a regular or irregular manner. A permeability gradient can decrease from one face of the fibrous layer to the other. For example, the lowest permeability in the fibrous layer can be located spatially closest to the graphene-based material layer, and the highest permeability can be located farther away. Those of skill in the art will understand that permeability of a layer can increase or decrease without pore diameter or porosity changing, e.g., in response to chemical functionalization, applied pressure, voltage, or other factors. [0070] In some embodiments, both the graphene-based material layer and the substrate layer include a plurality of pores therein. In some embodiments, both the graphene-based material layer and the substrate layer contain pores, and the pores in the graphene-based material layer are smaller, on average, than the pores in the substrate layer. In some embodiments, the median pore size in the graphene-based material layer is smaller than the median pore size in the substrate layer. For example, in some embodiments, the substrate layer can contain pores with an average and/or median diameter of about 1 μιη or larger and the graphene-based material layer can contain pores with an average and/or median diameter of about 10 nm or smaller. Accordingly, in some embodiments, the average and/or median diameter of pores in the graphene-based material layer is at least about 10-fold smaller than the average and/or median diameter of pores in the substrate layer. In some embodiments, the average and/or median diameter of pores in the graphene-based material layer is at least about 100-fold smaller than are the average and/or media diameter of pores in the substrate layer.

[0071] In some embodiments, the substrate layer can provide a scaffold for tissue growth, cell growth and/or vascularization. In some embodiments, the substrate layer or wall comprises additives, such as pharmaceuticals, cells, growth factors (e.g., VEGF), signaling molecules, cytokines, clotting factors, blood thinners, immunosuppressants, antimicrobial agents, hormones, antibodies, minerals, nutrients or combinations thereof. In some embodiments, additives such as pharmaceuticals, cells, growth factors, clotting factors, blood thinners, immunosuppressants, antimicrobial agents, hormones, antibodies, antigens (e.g., IgG-binding antigens) or an antibody- binding fragment thereof, minerals, nutrients or combinations thereof are positioned on the inside of the disclosure. In some embodiments, the substrate layer or membrane comprises materials toxic to bacteria or cells (without being bound by theory, it is believed that incorporating toxic materials into the wall will prevent passage of potentially dangerous or detrimental cells across the membrane).

[0072] In some embodiments, additives beneficially promote cell or tissue viability or growth, reduce or prevent infection, improve vascularization to or near the membrane, improve biocompatibility, reduce biofouling, and/or reduce the risk of adverse reactions. In some embodiments, additives can modulate properties, such as hydrophobicity or hydrophilicity, of the substrate layer. In some embodiments, additives can be used to modulate elution of a substance from a compartment in the enclosure. For instance, additives can confer shell-like properties to a substrate layer, such that degradation or removal of the additives allows substances to traverse the membrane.

[0073] In some embodiments, an intermediate layer promotes adhesion between the graphene- based material layer and the substrate layer. Thus, in some embodiments, the enclosure comprises an intermediate layer disposed between the graphene-based material layer and the substrate layer. In some embodiments, the enclosure comprises an intermediate layer positioned between two substrate layers on the same side of the graphene-based material layer.

[0074] In some embodiments, the intermediate layer comprises carbon nanotubes, lacey carbon, nanoparticles, lithographically patterned low-dimensional materials, silicon and silicon nitride micromachined material, a fine mesh, such as a transmission electron microscopy grid, or combinations of these. In some embodiments, the intermediate layer can be a thin, smooth, porous polymer layer, such as a track etched polymer. In some embodiments, the intermediate layer has a thickness of from 3 nm to 10 μπι, 10 nm to 10 μπι, 50 nm to 10 μπι, 100 nm to 10 μπι, 500 nm to 10 μπι, 1 μπι to 10 μπι, or 2 μπι to 6 μπι.

Graphene-Based Materials

[0075] As discussed above, membranes of some of the embodiments comprise graphene-based materials.

[0076] Graphene represents a form of carbon in which the carbon atoms reside within a single atomically thin sheet or a few layered sheets (e.g., about 20 or less) of fused six-membered rings forming an extended sp ² -hybridized carbon planar lattice. Graphene-based materials include, but are not limited to, single layer graphene, multilayer graphene or interconnected single or multilayer graphene domains and combinations thereof. In some embodiments, graphene-based materials also include materials which have been formed by stacking single or multilayer graphene sheets. In some embodiments, multilayer graphene includes 2 to 20 layers, 2 to 10 layers or 2 to 5 layers. In some embodiments, layers of multilayered graphene are stacked, but are less ordered in the z direction (perpendicular to the basal plane) than a thin graphite crystal. [0077] In some embodiments, a sheet of graphene-based material may be a sheet of single or multilayer graphene or a sheet comprising a plurality of interconnected single or multilayer graphene domains, which may be observed in any known manner such as using for example small angle electron diffraction, transmission electron microscopy, etc.. In some embodiments, the multilayer graphene domains have 2 to 5 layers or 2 to 10 layers. As used herein, a domain refers to a region of a material where atoms are substantially uniformly ordered into a crystal lattice. A domain is uniform within its boundaries, but may be different from a neighboring region. For example, a single crystalline material has a single domain of ordered atoms. In some embodiments, at least some of the graphene domains are nanocrystals, having domain size from 1 to 100 nm or 10-100 nm. In some embodiments, at least some of the graphene domains have a domain size greater than from 100 nm to 1 cm, or from 100 nm to 1 micron, or from 200 nm to 800 nm, or from 300 nm to 500 nm. In some embodiments, a domain of multilayer graphene may overlap a neighboring domain. Grain boundaries formed by crystallographic defects at edges of each domain may differentiate between neighboring crystal lattices. In some embodiments, a first crystal lattice may be rotated relative to a second crystal lattice, by rotation about an axis perpendicular to the plane of a sheet, such that the two lattices differ in crystal lattice orientation.

[0078] In some embodiments, the sheet of graphene-based material is a sheet of single or multilayer graphene or a combination thereof. In some other embodiments, the sheet of graphene-based material is a sheet comprising a plurality of interconnected single or multilayer graphene domains. In some embodiments, the interconnected domains are covalently bonded together to form the sheet. When the domains in a sheet differ in crystal lattice orientation, the sheet is polycrystalline.

[0079] In some embodiments, the thickness of the sheet of graphene-based material is from 0.3 to 10 nm, 0.34 to 10 nm, from 0.34 to 5 nm, or from 0.34 to 3 nm. In some embodiments, the thickness includes both single layer graphene and the non-graphenic carbon.

[0080] In some embodiments, a sheet of graphene-based material comprises intrinsic or native defects. Intrinsic or native defects may result from preparation of the graphene-based material in contrast to perforations which are selectively introduced into a sheet of graphene-based material or a sheet of graphene. Such intrinsic or native defects may include, but are not limited to, lattice anomalies, pores, tears, cracks or wrinkles. Lattice anomalies can include, but are not limited to, carbon rings with other than 6 members (e.g. 5, 7 or 9 membered rings), vacancies, interstitial defects (including incorporation of non-carbon atoms in the lattice), and grain boundaries.

Perforations are distinct from openings in the graphene lattice due to intrinsic or native defects or grain boundaries, but testing and characterization of the final membrane such as mean pore size and the like encompasses all openings regardless of origin since they are all present.

[0081] In some embodiments, graphene is the dominant material in a graphene-based material. For example, a graphene-based material may comprise at least 20% graphene, 30% graphene, or at least 40% graphene, or at least 50% graphene, or at least 60% graphene, or at least 70% graphene, or at least 80% graphene, or at least 90% graphene, or at least 95% graphene. In some embodiments, a graphene-based material comprises a range of graphene selected from 30% to 95%, or from 40% to 80% from 50% to 70%, from 60% to 95% or from 75% to 100%. The amount of graphene in the graphene-based material is quantified as an atomic percentage utilizing known methods including scanning transmission electron microscope examination, or alternatively if STEM or TEM is ineffective another similar measurement technique.

[0082] In some embodiments, a sheet of graphene-based material further comprises non- graphenic carbon-based material located on at least one surface of the sheet of graphene-based material. In some embodiments, the sheet is exemplified by two base surfaces (e.g. top and bottom faces of the sheet, opposing faces) and side faces (e.g. the side faces of the sheet). In some further embodiments, the "bottom" face of the sheet is that face which contacted the substrate during growth of the sheet and the "free" face of the sheet opposite the "bottom" face. In some embodiments, non-graphenic carbon-based material may be located on one or both base surfaces of the sheet (e.g. the substrate side of the sheet and/or the free surface of the sheet). In some further embodiments, the sheet of graphene-based material includes a small amount of one or more other materials on the surface, such as, but not limited to, one or more dust particles or similar contaminants.

[0083] In some embodiments, the amount of non-graphenic carbon-based material is less than the amount of graphene. In some further embodiments, the amount of non-graphenic carbon material is three to five times the amount of graphene; this is measured in terms of mass. In some additional embodiments, the non-graphenic carbon material is characterized by a percentage by mass of said graphene-based material selected from the range of 0% to 80%. In some embodiments, the surface coverage of the sheet of non-graphenic carbon-based material is greater than zero and less than 80%, from 5% to 80%, from 10% to 80%, from 5% to 50% or from 10%) to 50%. This surface coverage may be measured with transmission electron microscopy, which gives a projection. In some embodiments, the amount of graphene in the graphene-based material is from 60% to 95% or from 75% to 100%. The amount of graphene in the graphene-based material is quantified as an atomic percentage utilizing known methods preferentially using transmission electron microscope examination, or alternatively if STEM is ineffective using an atomic force microscope.

[0084] In some embodiments, the non-graphenic carbon-based material does not possess long range order and is classified as amorphous. In some embodiments, the non-graphenic carbon- based material further comprises elements other than carbon and/or hydrocarbons. In some embodiments, non-carbon elements which may be incorporated in the non-graphenic carbon include hydrogen, oxygen, silicon, copper, and iron. In some further embodiments, the non- graphenic carbon-based material comprises hydrocarbons. In some embodiments, carbon is the dominant material in non-graphenic carbon-based material. For example, a non-graphenic carbon-based material in some embodiments comprises at least 30% carbon, or at least 40% carbon, or at least 50% carbon, or at least 60% carbon, or at least 70% carbon, or at least 80% carbon, or at least 90% carbon, or at least 95% carbon. In some embodiments, a non-graphenic carbon-based material comprises a range of carbon selected from 30% to 95%, or from 40% to 80%), or from 50% to 70%. The amount of carbon in the non-graphenic carbon-based material is quanitified as an atomic percentage utilizing known methods preferentially using transmission electron microscope examination, or alternatively if STEM is ineffective using atomic force microscope.

[0085] Perforation techniques suitable for use in perforating the graphene-based materials may include described herein ion-based perforation methods and UV-oxygen based methods. [0086] Ion-based perforation methods include methods in which the graphene-based material is irradiated with a directional source of ions. In some further embodiments, the ion source is collimated. In some embodiments, the ion source is a broad beam or flood source. A broad field or flood ion source can provide an ion flux which is significantly reduced compared to a focused ion beam. The ion source inducing perforation of the graphene or other two- dimensional material is considered to provide a broad ion field, also commonly referred to as an ion flood source. In some embodiments, the ion flood source does not include focusing lenses. In some embodiments, the ion source is operated at less than atmospheric pressure, such as at 10 ^{" 3} to 10 ^"5 torr or 10 ^"4 to 10 ^"6 torr. In some embodiments, the environment also contains background amounts (e.g. on the order of 10 ^"5 torr) of oxygen (0 ₂ ), nitrogen (N ₂ ) or carbon dioxide (C0 ₂ ). In some embodiments, the ion beam may be perpendicular to the surface of the layer(s) of the material (incidence angle of 0 degrees) or the incidence angle may be from 0 to 45 degrees, 0 to 20 degrees, 0 to 15 degrees or 0 to 10 degrees. In some further embodiments, exposure to ions does not include exposure to plasma.

[0087] In some embodiments, UV-oxygen based perforation methods include methods in which the graphene-based material is simultaneously exposed to ultraviolet (UV) light and an oxygen containing gas Ozone may be generated by exposure of an oxygen containing gas such as oxygen or air to the UV light. Ozone may also be supplied by an ozone generator device. In some embodiments, the UV-oxygen based perforation method further includes exposure of the graphene-based material to atomic oxygen. Suitable wavelengths of UV light include, but are not limited to wavelengths below 300 nm or from 150 nm to 300 nm. In some embodiments, the intensity from 10 to 100 mW/cm ² at 6mm distance or 100 to 1000 mW/cm ² at 6mm distance. For example, suitable light is emitted by mercury discharge lamps (e.g. about 185 nm and 254 nm). In some embodiments, UV/oxygen cleaning is performed at room temperature or at a temperature greater than room temperature. In some further embodiments, UV/oxygen cleaning is performed at atmospheric pressure (e.g. 1 atm) or under vacuum.

[0088] Perforations are sized as described herein to provide desired selective permeability of a species (atom, molecule, protein, virus, cell, etc.) for a given application. Selective permeability relates to the propensity of a porous material or a perforated two-dimensional material to allow passage (or transport) of one or more species more readily or faster than other species. Selective permeability allows separation of species which exhibit different passage or transport rates. In two-dimensional materials selective permeability correlates to the dimension or size (e.g., diameter) of apertures and the relative effective size of the species. Selective permeability of the perforations in two-dimensional materials such as graphene-based materials can also depend on functionalization of perforations (if any) and the specific species. Separation or passage of two or more species in a mixture includes a change in the ratio(s) (weight or molar ratio) of the two or more species in the mixture during and after passage of the mixture through a perforated two- dimensional material.

[0089] In some embodiments, the characteristic size of the perforation is from 0.3 to 10 nm, from 1 to 10 nm, from 5 to 10 nm, from 5 to 20 nm, from 10 nm to 50 nm, from 50 nm to 100 nm, from 50 nm to 150 nm, from 100 nm to 200 nm, or from 100 nm to 500 nm. In some embodiments, the average pore size is within the specified range. In some embodiments, 70% to 99%, 80% to 99%, 85% to 99% or 90 to 99% of the perforations in a sheet or layer fall within a specified range, but other pores fall outside the specified range.

[0090] Nanomaterials in which pores are intentionally created may be referred to as perforated graphene, perforated graphene-based materials or perforated two-dimensional materials, and the like. Perforated graphene-based materials include materials in which non-carbon atoms have been incorporated at the edges of the pores. Pore features and other material features may be characterized in a variety of manners including in relation to size, area, domains, periodicity, coefficient of variation, etc. For instance, the size of a pore may be assessed through quantitative image analysis utilizing images preferentially obtained through transmission electron

microscopy, and if TEM is ineffective, through atomic force microscopy, and if AFM is ineffective, through scanning electron microscopy, as for example presented in Figs. 1 and 2. The boundary of the presence and absence of material identifies the contour of a pore. The size of a pore may be determined by shape fitting of an expected species against the imaged pore contour where the size measurement is characterized by smallest dimension unless otherwise specified. For example, in some instances, the shape may be round or oval. The round shape exhibits a constant and smallest dimension equal to its diameter. The width of an oval is its smallest dimension. The diameter and width measurements of the shape fitting in these instances provide the size measurement, unless specified otherwise. [0091] Each pore size of a test sample may be measured to determine a distribution of pore sizes within the test sample. Other parameters may also be measured such as area, domain, periodicity, coefficient of variation, etc. Multiple test samples may be taken of a larger membrane to determine that the consistency of the results properly characterizes the whole membrane. In such instance, the results may be confirmed by testing the performance of the membrane with test species. For example, if measurements indicate that certain sizes of species should be restrained from transport across the membrane, a performance test provides verification with test species. Alternatively, the performance test may be utilized as an indicator that the pore measurements will determine a concordant pore size, area, domains, periodicity, coefficient of variation, etc.

[0092] The size distribution of holes may be narrow, e.g., limited to 0.1-0.5 coefficient of variation. In some embodiments, the characteristic dimension of the holes is selected for the application.

[0093] In some embodiments involving circular shape fitting the equivalent diameter of each pore is calculated from the equation A= π d ² /4. Otherwise, the area is a function of the shape fitting. When the pore area is plotted as a function of equivalent pore diameter, a pore size distribution may be obtained. The coefficient of variation of the pore size may be calculated herein as the ratio of the standard deviation of the pore size to the mean of the pore size as measured across the test samples. The average area of perforations is an averaged measured area of pores as measured across the test samples.

[0094] In some embodiments, the ratio of the area of the perforations to the ratio of the area of the sheet may be used to characterize the sheet as a density of perforations. The area of a test sample may be taken as the planar area spanned by the test sample. Additional sheet surface area may be excluded due to wrinkles other non-planar features. Characterization may be based on the ratio of the area of the perforations to the test sample area as density of perforations excluding features such as surface debris. Characterization may be based on the ratio of the area of the perforations to the suspended area of the sheet. As with other testing, multiple test samples may be taken to confirm consistency across tests and verification may be obtained by performance testing. The density of perforations may be, for example, 2 per nm ² (21 nm ² ) to 1 per μιη ² (1/ μιη ² ).

[0095] In some embodiments, the perforated area comprises 0.1% or greater, 1% or greater or 5% or greater of the sheet area, less than 10% of the sheet area, less than 15% of the sheet area, from 0.1% to 15% of the sheet area, from 1% to 15% of the sheet area, from 5% to 15% of the sheet area or from 1% to 10% of the sheet area. In some further embodiments, the perforations are located over greater than 10% or greater than 15% of said area of said sheet of graphene- based material. A macroscale sheet is macroscopic and observable by the naked eye. In some embodiments, at least one lateral dimension of the sheet is greater than 3 cm, greater than 1 cm, greater than 1 mm or greater than 5 mm. In some further embodiments, the sheet is larger than a graphene flake which would be obtained by exfoliation of graphite in known processes used to make graphene flakes. For example, the sheet has a lateral dimension greater than about 1 micrometer. In an additional embodiment, the lateral dimension of the sheet is less than 10 cm. In some further embodiments, the sheet has a lateral dimension (e.g., perpendicular to the thickness of the sheet) from 10 nm to 10 cm or greater than 1 mm and less than 10 cm.

[0096] Chemical vapor deposition growth of graphene-based material typically involves use of a carbon containing precursor material, such as methane and a growth substrate. In some embodiments, the growth substrate is a metal growth substrate. In some embodiments, the metal growth substrate is a substantially continuous layer of metal rather than a grid or mesh. Metal growth substrates compatible with growth of graphene and graphene-based materials include transition metals and their alloys. In some embodiments, the metal growth substrate is copper based or nickel based. In some embodiments, the metal growth substrate is copper or nickel. In some embodiments, the graphene-based material is removed from the growth substrate by dissolution of the growth substrate.

[0097] In some embodiments, the sheet of graphene-based material is formed by chemical vapor deposition (CVD) followed by at least one additional conditioning or treatment step. In some embodiments, the conditioning step is selected from thermal treatment, UV-oxygen treatment, ion beam treatment, and combinations thereof. In some embodiments, thermal treatment may include heating to a temperature from 200 °C to 800 °C at a pressure of 10 ^"7 torr to atmospheric pressure for a time of 2 hours to 8 hours. In some embodiments, UV-oxygen treatment may involve exposure to light from 150 nm to 300 nm and an intensity from 10 to 100 mW/cm ² at 6mm distance for a time from 60 to 1200 seconds. In some embodiments, UV- oxygen treatment may be performed at room temperature or at a temperature greater than room temperature. In some further embodiments, UV-oxygen treatment may be performed at atmospheric pressure (e.g. 1 atm) or under vacuum. In some embodiments, ion beam treatment may involve exposure of the graphene-based material to ions having an ion energy from 50 eV to 1000 eV (for pretreatment) and the fluence is from 3 x 10 ¹⁰ ions/cm ² to 8 x 10 ¹¹ ions/cm ² or 3 x

10 10 ions/cm 2 to 8 x 1013 ions/cm 2 (for pretreatment). In some further embodiments, the source of ions may be collimated, such as a broad beam or flood source. In some embodiments, the ions may be noble gas ions such as Xe ⁺ . In some embodiments, one or more conditioning steps are performed while the graphene-based material is attached to a substrate, such as a growth substrate.

[0098] In some embodiments, the conditioning treatment affects the mobility and/or volatility of the non-graphitic carbon-based material. In some embodiments, the surface mobility of the non-graphenic carbon-based material is such that when irradiated with perforation parameters such as described herein, the non-graphenic carbon-based material, may have a surface mobility such that the perforation process results ultimately in perforation. Without wishing to be bound by any particular belief, hole formation is believed to be related to beam induced carbon removal from the graphene sheet and thermal replenishment of carbon in the hole region by non grapheme carbon. The replenishment process may be dependent upon energy entering the system during perforation and the resulting surface mobility of the non-graphenic carbon based material. To form holes, the rate of graphene removal may be higher than the non-graphenic carbon hole filling rate. These competing rates depend on the non-graphenic carbon flux (e.g., mobility [viscosity and temperature] and quantity) and the graphene removal rate (e.g., particle mass, energy, flux).

[0099] In some embodiments, the volatility of the non-graphenic carbon-based material may be less than that which is obtained by heating the sheet of graphene-based material to 500°C for 4 hours in vacuum or at atmospheric pressure with an inert gas. [00100] In various embodiments, CVD graphene or graphene-based material can be liberated from its growth substrate (e.g., Cu) and transferred to a supporting grid, mesh or other supporting structure. In some embodiments, the supporting structure may be configured so that at least some portions of the sheet of graphene-based material are suspended from the supporting structure. For example, at least some portions of the sheet of graphene-based material may not be in contact with the supporting structure.

[00101] In some embodiments, the sheet of graphene-based material following chemical vapor deposition comprises a single layer of graphene having at least two surfaces and non- graphenic carbon based material may be provided on said surfaces of the single layer graphene. In some embodiments, the non-graphenic carbon based material may be located on one of the two surfaces or on both. In some further embodiments, additional graphenic carbon may also present on the surface(s) of the single layer graphene.

Methods of Making Tunable Membranes

[00102] Tunable membranes can be made by a variety of methods. For instance, a perforated graphene layer can be combined with spacer substances in solution, such that the spacer substances self-assemble to the perforated graphene layer. Then, the solution can be reduced to induce bonding between the spacer substance and the graphene layer. After that, an additional graphene layer can be added to the solution, which can bond to the graphene layer- spacer substance complex. Attachment of the additional graphene layer can be via van der Waals forces or induced covalent bonding (e.g., as a result of an applied energy such as ion radiation).

[00103] In some embodiments, spacer substances are covalently bonded to at least one graphene-based material layer. Without being bound by theory, it is believed that covalent bonding between a spacer substance and a graphene-based material layer can be induced via ion- beam induced bonding, electron-beam induced bonding, heating, chemical reactions (e.g., via reactants on— i.e., attached to— the spacer substance and the graphene-based material layer), and combinations thereof. [00104] In some embodiments, functional moieties are attached to the spacer molecules to facilitate self-assembly on or bonding to the graphene layers. In some embodiments, the functional moieties are removed in the process of making the membrane.

[00105] In some embodiments, the spacer substances are trapped between two graphene- based material layers. In some embodiments the spacer substances are trapped between two graphene-based material layers, but are not restricted to a single position in the channel (i.e., they are mobile within the channel).

[00106] Unless defined otherwise, all technical and scientific terms used in this description have the same meaning as commonly understood by those skilled in the relevant art.

[00107] For convenience, the meaning of certain terms employed in the specification and appended claims are provided below. Other terms and phrases are defined throughout the specification.

[00108] The singular forms "a," "an," and "the" include plural reference unless the context clearly dictates otherwise.

[00109] As used herein, the term "about" will be understood by persons of ordinary skill in the art and will vary to some extent depending upon the context in which it is used. If there are uses of the term which are not clear to persons of ordinary skill in the art given the context in which it is used, "about" will mean up to plus or minus 10% of the particular term.

[00110] Given the disclosure of the present invention, one versed in the art would appreciate that there may be other embodiments and modifications within the scope and spirit of the invention. Accordingly, all modifications attainable by one versed in the art from the present invention within the scope and spirit of the present invention are to be included as further embodiments of the present invention.