Background

[0001] Two-dimensional nanomaterials have emerged as promising materials in field-effect transistors, structurally reinforced composites, chemical/biological sensors, and transparent conductors. Among them, monolayer graphene, a two- dimensional single-atomic layer of carbon, has generated considerable attention as a result of its outstanding electronic, mechanical, and chemical properties. Since its discovery in 2004, monolayer graphene has demonstrated an array of impressive properties, such as charge carrier mobilities in excess of 10,000 cm ² V ^"1 s ^"1 (see Zhang et al., Nature, 438: 201 (2005)), the quantum Hall effect at room temperature (see Novoselov et al., Science, 315: 1379 (2007)), and a variable band gap depending on adsorbate coverage (see Ohta et al., Science, 313: 951 (2006)). Other two- dimensional nanomaterials also have been studied, including those derived from boron nitride (BN), transition metal dichalcogenides, graphite oxide, and the high temperature superconductor Bi ₂ Sr ₂ CaCu ₂ O _x . Further, the semiconducting properties of single flakes of molybdenum disulfide (MoS ₂ ) and graphene oxide have been exploited in field-effect transistors.

[0002] Despite the technological potential of two-dimensional nanomaterials, methods of synthesizing and purifying them are in their infancy. The most common of these methods, known as micromechanical cleavage, involves drawing a layered crystallite such as graphite over a substrate of interest leaving thin crystallites on the surface (see Novoselov et al., Proc. Nat. Acad. Sci. U.S.A., 102: 10451 (2005)).

Although micromechanical cleavage can produce samples of high crystal quality, it has several disadvantages. First, it is difficult to control the position at which crystallites will be placed; consequently, considerable effort is required to locate them. Second, cleavage does not provide control over the thickness of flakes produced, resulting in a limited number of atomically thin crystallites with the majority being tens of nanometers thick. Third, the prospects for large scale production of graphene and other crystallites through micromechanical cleavage are unfavorable.

[0003] Other groups have studied epitaxial growth of two-dimensional

nanomaterials on various substrates. For example, graphene can be grown directly on metal surfaces or through thermal decomposition of SiC (see Berger et al, Science, 312: 1191 (2006)). However, while these epitaxial graphene samples have the benefit of spanning large areas, full control over the thickness of the resulting crystallites remains a challenge. Moreover, because epitaxial synthesis can occur only on suitable growth substrates, methods of transferring crystallites to other substrates are required for practical applications.

[0004] Solution-based methods represent a third route to two-dimensional nanomaterials and can offer several significant advantages over the two approaches described above. First, the desired two-dimensional nanomaterials often can be generated from inexpensive and readily available starting materials. Second, solution- phase techniques do not require transfer from the growth substrate, and can employ existing technologies for scaling up to large volume processing. Several of these methods involve intercalation of graphite and transition metal dichalcogenide crystallites followed by sonication or rapid heating to generate thin flakes (see Viculis et al., J. Mater. Chem., 15: 927 (2005); Yu et al., J. Phys. Chem. C, 111 : 7565 (2007); and Joensen et al., Mater. Res. Bull, 21 : 457 (1986)). Yet, because of the often violent reactions between the intercalation compounds and water or other solvents, the resulting crystallites usually are at least partially oxidized or otherwise have defect sites which impair their properties (see Li et al., Science, 319, 1229 (2008)).

[0005] With respect to the production of monolayer graphene, several groups have explored exfoliating functionalized graphite, such as graphite oxide and graphite fluoride. Unlike pristine graphite, graphite oxide is hydrophilic, and individual graphene oxide layers can be dispersed readily into water. However, graphene oxide is insulating. To regain their electrical conductivity, the exfoliated functionalized graphite materials must be chemically reduced. Despite these treatments, the electronic properties of reduced graphene oxide remain different from those of pristine graphene (see e _^ g., Tung et al., Nature Nanoteck, 4: 25 (2009)).

Furthermore, while it is possible to generate monolayer graphene oxide by ensuring that graphite is sufficiently oxidized, it is unlikely that bilayer graphene oxide (or n- layer graphene oxide) could be formed preferentially through controlled oxidation. Graphene nanomaterials have diverse properties depending on the number of layers. For example, monolayer graphene is a 0 eV bandgap semiconductor. Bilayer graphene, on the other hand, has been shown to have a tunable bandgap in the infrared. Meanwhile, trilayer graphene is a semimetal whose band overlap can be controlled by an applied electric field.

[0006] Accordingly, there is a need in the art for methods of preparing and purifying two-dimensional nanomaterials with controlled number of layers. In particular, there is a need in the art for methods of preparing and purifying graphene nanomaterials with controlled number of layers, including methods of preparing monolayer graphene and isolating it from other graphene nanomaterials having two or more layers. In addition, there is a need in the art for methods that enable effective dispersion of graphite or graphene in a fluid medium, particularly in water, such that the dispersion can remain stable for an extended period of time.

Summary

[0007] In light of the foregoing, the present teachings provide one or more methods and/or compositions related to generating nanomaterials having controlled thickness or number of atomic layers, which methods and compositions can overcome various deficiencies and shortcomings of the prior art, including those outlined above.

[0008] In one aspect, the present teachings can be directed to sorting two- dimensional (planar) nanomaterials by atomic layer thickness. Specifically, a poly disperse population of planar nanomaterials which is poly disperse at least with respect to thickness can be first contacted with one or more surface active components to provide a nanomaterial composition. In various embodiments, the nanomaterial composition is a stable dispersion of the nanomaterials in water, in which the nanomaterials are dispersed effectively by the one or more surface active components. The one or more surface active components can be selected for their ability to associate differentially with the nanomaterials of different thickness such that individual nanomaterial crystallite or flake of different thickness, upon association with the surface active components, can exhibit different buoyant densities in a fluid medium. Separation by buoyant density subsequently can be accomplished by, but is not limited to, density gradient ultracentrifugation, after which physically separated nanomaterials, grouped according to atomic layer thickness, can be recovered.

[0009] Generally, density gradient ultracentrifugation (DGU) involves introducing the dispersion into a density gradient medium, that is, a fluid medium that includes a density gradient. The density gradient can include a linear gradient including three or more layers of different densities. Once introduced, the fluid medium can be agitated, for example, by ultracentrifugation, to allow separation of the nanomaterials by thickness along the density gradient. After sufficient agitation, nanomaterials of different thickness are allowed to settle into a plurality of separation fractions, where at least one of the separation fractions is enriched with nanomaterials of a specific thickness. For example, a first separation fraction can be enriched with monolayer nanomaterials, a second separation fraction can be enriched with bilayer

nanomaterials, a third separation fraction can be enriched with trilayer nanomaterials, and so on. The separation fractions can be visibly distinguishable among each other by human eye, or can be distinguishable outside the visible spectrum by various light scattering or spectroscopic methods. For example, two or more separation fractions can be distinguishable by different colors and/or different shades of a particular color in the visible spectrum. Further, the two or more separation fractions can be separated from each other by a layer of fluid medium in which only a negligible amount of nanomaterials is present. For separation fractions that are enriched with monolayer, bilayer, and/or trilayer nanomaterials, the mean thickness of the nanomaterials in such enriched separation fractions can be expected to be less than the mean thickness of the nanomaterials in the starting nanomaterial composition, which includes a non- negligible amount of nanomaterials having four layers or more. For example, the mean thickness of the nanomaterials in the starting nanomaterial composition can be about 5 nm or greater, and the mean thickness of the nanomaterials in an enriched separation fraction can be between about 1 nm and 3 nm.

[0010] As used herein, the "mean thickness" is the average thickness of

nanomaterials in a sample otherwise known as the arithmetic mean. Typically, an enriched separation fraction also can have a mode thickness that is less than the mode thickness of the nanomaterials in the starting nanomaterial composition. As used herein, the "mode thickness" is the thickness with the highest frequency in a sample. For example, the mode thickness of the nanomaterials in an enriched separation fraction can be less than 2 nm, whereas the mode thickness of the nanomaterials in the polydispersion population can be 4 nm or greater.

[0011] A single separation cycle according to the present methods often leads to enrichment that is satisfactory for most applications. Accordingly, following one separation cycle, one or more separation fractions can be collected from the density gradient and used for various applications. However, performing one or more additional sorting or separation cycles can improve the quality of the separation and provide increasingly enriched separation fractions.

[0012] In another aspect, the present teachings relate to producing aqueous dispersions of two-dimensional (planar) hydrophobic nanomaterials. In contrast to the prior art, the present teachings provide stable aqueous dispersions of two- dimensional hydrophobic nanomaterials without chemical modification such as oxidation. Instead, stable aqueous dispersions are obtained by providing the hydrophobic nanomaterials in composition with one or more surface active components described herein, in particular, surface active components having one or more planar organic groups. Without wishing to be bound by any particular theory, it is believed that one or more surface active components described herein can encapsulate individual flakes of nanomaterials and allow a large amount of the nanomaterials to be effectively dispersed in water. For example, aqueous dispersions having a minimum concentration of 40 μg/mL of nanomaterials according to the present teachings can remain stable for weeks without visible aggregation.

[0013] Other objects, features, and advantages of the present teachings will be more fully understood from the following figures, description, examples, and claims.

Brief Description of Drawings

[0014] It should be understood that certain drawings are not necessarily to scale, with emphasis generally being placed upon illustrating the principles of the present teachings. The drawings are not intended to limit the scope of the present teachings in any way.

[0015] FIG. IA is a schematic illustration of the solution-phase exfoliation process according to the present teachings.

[0016] FIG. IB is a schematic illustration of a monolayer two-dimensional nanomaterial encapsulated by an ordered monolayer of surface active components on each side.

[0017] FIG. 1C is a photograph showing a centrifuge tube containing graphene nanomaterials after one iteration of density gradient ultracentrifugation (DGU) according to the present methods. The concentrated graphene was diluted by a factor of 40 to ensure that all graphene bands could be clearly resolved in the photograph. Lines mark the positions at which sorted graphene fractions f4, flO, fl6, f22, and f28 were extracted within the centrifuge tube.

[0018] FIG. 2 A is a histogram comparing the mean flake thickness (calculated using AFM images) for sedimented, concentrated, and DGU fraction f4 graphene dispersions.

[0019] FIG. 2B is a histogram plotted by relative frequency (mode thickness scaled to unity) comparing the mean flake thickness (calculated using AFM images) for DGU fractions f4, fl6, and f28.

[0020] FIG. 3 A is a schematic illustration of a buoyant density model for surfactant-encapsulated few-layer graphene nanomaterials in which a flake of thickness N is coated by a surfactant with a packing density σ and an effective thickness I _A and a hydration layer of thickness fa.

[0021] FIG. 3B shows the fit between the buoyant density model and the experimental data. The uncertainty in graphene flake thickness was taken as the full- width at half maximum (FWHM) of the flake thickness distribution.

[0022] FIG. 4A shows representative Raman spectra of sorted graphene flakes from fractions f4, fl6, and f28 on SiO ₂ in the D and G band region with the intensity of the G band normalized to unity.

[0023] FIG. 4B shows the 2D band of the spectra in FIG. 4A, as well as fractions flO and f22, with the same G band normalization.

[0024] FIG. 4C plots the ratio of 2D and G band intensity I(2D)/I(G) and

FWHM(2D) as a function of the mean graphene thickness. Triangles and squares represent I(2D)/I(G) and FWHM(2D), respectively. Open symbols mark values obtained from the concentrated graphene dispersion. Solid symbols mark values obtained from DGU-processed fractions.

[0025] FIG. 5A shows the effect of annealing on the transmittance and sheet resistance of graphene transparent conductors produced from the concentrated and f4 graphene dispersions. Triangles and circles represent the films before and after annealing for two hours at 25O ⁰ C in air, respectively. Lines are drawn between points to aid the eye. [0026] FIG. 5B shows the sheet resistance and transmittance of pristine (not annealed) graphene transparent conductors made from various sedimented dispersions. Lines are drawn between points to aid the eye.

[0027] FIG. 6A plots the transmittance of graphene transparent conductors produced from sedimented, concentrated, f4, fl6, and f28 dispersions as a function of their sheet resistance at wavelengths of 550 nm. Lines are drawn between points to aid the eye.

[0028] FIG. 6B plots the transmittance of graphene transparent conductors produced from sedimented, concentrated, f4, fl6, and f28 dispersions as a function of their sheet resistance at wavelengths of 1000 nm. Lines are drawn between points to aid the eye.

Detailed Specification

[0029] Throughout the description, where compositions are described as having, including, or comprising specific components, or where processes are described as having, including, or comprising specific process steps, it is contemplated that compositions of the present teachings also consist essentially of, or consist of, the recited components, and that the processes of the present teachings also consist essentially of, or consist of, the recited processing steps.

[0030] In the application, where an element or component is said to be included in and/or selected from a list of recited elements or components, it should be understood that the element or component can be any one of the recited elements or components or can be selected from a group consisting of two or more of the recited elements or components. Further, it should be understood that elements and/or features of a composition, an apparatus, or a method described herein can be combined in a variety of ways without departing from the spirit and scope of the present teachings, whether explicit or implicit herein.

[0031] The use of the terms "include," "includes," "including," "have," "has," "having," "contain," "contains," or "containing" should be generally understood as open-ended and non-limiting unless specifically stated otherwise.

[0032] The use of the singular herein includes the plural (and vice versa) unless specifically stated otherwise. In addition, where the use of the term "about" is before a quantitative value, the present teachings also include the specific quantitative value itself, unless specifically stated otherwise. As used herein, the term "about" refers to a ±10% variation from the nominal value unless otherwise indicated or inferred.

[0033] It should be understood that the order of steps or order for performing certain actions is immaterial so long as the present teachings remain operable. Moreover, two or more steps or actions may be conducted simultaneously.

[0034] As used herein, a "planar nanomaterial" or a "two-dimensional

nanomaterial" refers to a planar structure having a thickness on the order of nanometers, generally 100 nm or less, for example, less than about 50 nm, usually less than about 10 nm, and in some embodiments, less than about 5 nm thick. The thickness of the present planar nanomaterials can be measured in terms of the number of atomic or molecular layers, and can have one to about 50 atomic or molecular layers. For example, the planar nanomaterials of the present teachings can include monolayer nanomaterials, that is, nanomaterials consisting of a single atomic or molecular layer; bilayer nanomaterials, that is nanomaterials consisting of two atomic or molecular layers; trilayer nanomaterials, that is nanomaterials consisting of three atomic or molecular layers; and few-layer nanomaterials, which refer to planar nanomaterials consisting of four to about ten atomic or molecular layers. Typically, planar nanomaterials of the present teachings have large length-to-thickness and/or width-to-thickness ratio(s). For example, a planar nanomaterial of the present teachings can have a length in the range of about 1 μm to 20 μm, in which case, the length-to-thickness ratio is on the order of 10 ³ or larger. In embodiments where the present planar nanomaterials have a large aspect ratio (large length-to-width ratio), for example, when the nanomaterials have a nanoscale width in addition to the nanoscale thickness, the nanomaterials can be referred herein as "nanoribbons." In other embodiments, the present planar nanomaterials can be referred herein as "nanosheets" or "nanoflakes" (or simply "flakes") with the former generally having larger length and width dimensions than the latter.

[0035] The present teachings can be practiced on various elemental or molecular nanomaterials including those composed of carbon, BN, transition metal

dichalcogenides such as WS ₂ and MoS ₂ , and the high temperature superconductor Bi ₂ Sr ₂ CaCu ₂ O _x . In various embodiments, the present planar nanomaterials can include graphene nanomaterials. As used herein, "graphene nanomaterials" include n- layer graphene nanomaterials, wherein n is an integer in the range of 1 to 10, and specifically include monolayer graphene (n = 1), bilayer graphene (n = 2), trilayer graphene (n = 3), and few-layer graphene (n = 4-10) nanomaterials. As understood by those skilled in the art, monolayer graphene is a one atomic layer (or monolayer) thick planar sheet of sp ² -bonded carbon atoms that are densely packed in a honeycomb crystal lattice, whereas n-layer graphene nanomaterials (n = 2-10) have stacked planar structures consisting of two to ten graphene sheets. In various embodiments, graphite (e.g., naturally occurring crystalline flake graphite) can be used as the starting material for preparing graphene nanomaterials including monolayer graphene.

However, other forms of graphite including synthetic forms of graphite (e.g., highly ordered pyrolytic graphite (HOPG)) also can be used. As understood by those skilled in the art, graphite is a three-dimensional layered material consisting of many (usually hundreds or more of) stacked graphene sheets and has a typical thickness that is greater than 100 nm. As such, graphene and graphite, as used herein, do not encompass other non-planar allotropes of carbon such as carbon nanotubes which are very different from graphene and graphite not only in terms of shape but also physical, chemical, optical, and electronic properties. While the description and examples herein may refer specifically to graphene and graphite, the present teachings are intended to encompass two-dimensional planar nanomaterials in general regardless of their composition.

[0036] As used herein, a "population" of nanomaterials can include greater than about 10 ⁸ , greater than about 10 ⁹ , greater than about 10 ¹⁰ , greater than about 10 ¹¹ , greater than about 10 ¹² , greater than about 10 ¹³ , greater than about 10 ¹⁴ , greater than about 10 ¹⁵ , greater than about 10 ¹⁶ , or greater than about 10 ¹⁷ nanoribbons, nanosheets, or nano flakes. Further, by weight, a population of nanomaterials can have a mass of about 0.001 μg, greater than about 0.01 μg, greater than about 0.1 μg, greater than about 1 μg, greater than about 10 μg, greater than about 100 μg, greater than about 1 mg, greater than about 10 mg, greater than about 100 mg, or greater than about 1 g. In certain embodiments of the present teachings, a separation cycle can be used to sort bulk quantities of nanomaterials, for example, populations of

nanomaterials that include more than about 10 ¹² , more than about 10 ¹³ , more than about 10 ¹⁴ , more than about 10 ¹⁵ , more than about 10 ¹⁶ or more than about 10 ¹⁷ nanoribbons, nanosheets, or nano flakes; or more than about 10 μg, more than about 100 μg, more than about 1 mg, more than about 10 mg, more than about 100 mg, or more than about 1 gram of nanomaterials by mass.

[0037] As used herein, "enrichment" or "enriched" refers to an increase in the statistical proportion of nanomaterials comprising one or more specific characteristics in a fraction (or subpopulation) obtained from a sample population as compared to the sample population as a whole. As described herein, a nanomaterial subpopulation that is "enriched" according to the present teachings by one or more properties, such as thickness, shape, aspect ratio, or combinations thereof, means that the subpopulation (i.e., the enriched population) has a higher percentage of nanomaterials having the one or more properties when compared to the starting population (i.e., the mixed population) from which the subpopulation is derived. For example, a starting population of planar nanomaterials can exhibit polydispersity in thickness and can include monolayer, bilayer, trilayer, and few-layer (n > 4) planar nanomaterials.

Using methods of the present teachings, a subpopulation derived from the

polydisperse population can be enriched with monolayer, bilayer, and/or trilayer planar nanomaterials and as a result of which, have a reduced mean thickness compared to the starting population.

[0038] Various methods have been used to different degrees of success for separating carbon nanotubes by one or more characteristics such as chirality, diameter, and electronic type. However, the extension of separation methods for carbon nanotubes to graphene nanomaterials by one or more selected properties has not been described in the literature. Because of their geometrical differences (planar versus tubular) and different properties such as surface energy, optical properties, and electronic properties, graphene can be expected to respond very differently to a particular separation method when compared to carbon nanotubes. For example, to the inventors' knowledge, there has been no reported method for separating graphene nanomaterials by thickness that allows isolation of monolayer graphene from bilayer, trilayer, and/or few-layer graphene nanomaterials. In addition, when graphene nanomaterials are generated in situ from graphite, in particular by exfoliation in aqueous systems, further challenges exist with regard to dispersing the highly hydrophobic graphite at sufficiently high concentrations.

[0039] Accordingly, in one aspect, the present teachings provide a solution-phase method for generating two-dimensional planar nanomaterials from three-dimensional crystalline materials. For example, using methods of the present teachings, two- dimensional planar nanomaterials can be generated from three-dimensional crystalline materials including, but not limited to, graphite, MoS ₂ , and BN crystallites. The resulting two-dimensional planar nanomaterials subsequently can be separated by thickness using density gradient ultracentrifugation (DGU) as described in further detail below.

[0040] According to the present teachings, the starting three-dimensional materials are first exfoliated into two-dimensional planar nanomaterials having ten or less atomic or molecular layers. More specifically, in the first stage of the exfoliation process, the three-dimensional starting materials are added to a fluid medium containing one or more surface active components to provide a dispersion. The dispersion containing the starting materials and the surface active components is then subjected to a non-thermal, non-oxidative agitation process to exfoliate the three- dimensional materials into two-dimensional nanomaterials. More specifically, ultrasonic agitation (or ultrasonication) can be used to induce effective exfoliation.

[0041] In various embodiments, the three-dimensional starting materials can be from a natural source. For example, graphite and MoS ₂ (in the form of molybdenite) can be mined from ores. In certain embodiments, the three-dimensional layered materials can be pristine (i.e., as naturally-occurring or as-synthesized) and have not been subjected to post-extraction or post-synthesis treatment (e.g., thermal treatment at a temperature above 100 ⁰ C and/or chemical modification such as treatment under oxidative (acidic) and/or reducing conditions). For example, the starting materials can be pristine graphite flakes, which are to be differentiated from graphite oxide, graphite fluoride, or other functionalized forms of graphite. In addition, to increase the yield of exfoliated nanomaterials, the starting materials can be provided in powder form, although in certain embodiments, bulk crystals also can be used.

[0042] It has been found that a variety of surface active components are effective at dispersing both the three-dimensional starting materials and the exfoliated two- dimensional planar nanomaterials. For example, anionic surfactants such as bile salts and alkali salts of alkyl sulfate and alkyl benzene sulfonate; and cationic surfactants such as quaternary ammonium salts have been found effective and useful in accordance with the present teachings. In addition, polymers including cyclic groups in the backbone and/or the side chains such as polyvinylpyrrolidone and carboxymethylcellulose; non-ionic block copolymers of oxyethylene and

oxypropylene; and polymers including one or more polyoxyethylene chains such as polyoxyethylene alkylphenyl ethers and polyoxyethylene sorbitan alkyl ethers have been found useful.

[0043] In certain embodiments, surface active components that include one or more planar organic groups can be particularly useful both for effectively dispersing the starting materials and subsequently enabling separation of the nanomaterials by thickness. Without wishing to be bound by any particular theory, it is believed that surface active components which have one or more planar organic groups can intercalate between the layers of the three-dimensional layered materials more effectively, thereby promoting exfoliation and increasing the yield of two-dimensional planar nanomaterials, in particular, monolayer nanomaterials. Accordingly, in certain embodiments, the one or more surface active components can include an amphiphilic non-polymeric compound having a planar hydrophobic core and one or more hydrophilic groups. For example, the one or more surface active components can include a compound having a cyclic (e.g., carbocyclic) core and one or more charged groups, particularly, a benzene group or a sterane group and one or more anionic groups selected from hydroxyls, carboxylates, sulfates, sulfonates, and combinations thereof. In particular embodiments, the one or more surface active components can include one or more bile salts and/or an alkali salt of linear alkyl benzenesulfonate such as sodium dodecylbenzenesulfonate. Bile salts can be more broadly described as a group of molecularly rigid and planar amphiphiles with one or more charged groups opposing a hydrophobic face. Examples of bile salts include salts (e.g., sodium or potassium salts) of conjugated or unconjugated cholates and cholate derivatives including deoxycholates, chenodeoxycholates, taurodeoxycholates,

glycochenodeoxycholates, ursodeoxycholates, and glycoursodeoxy cholates. In certain embodiments, the one or more surface active components can include a polymer having one or more cyclic groups in its backbone and/or side chains. For example, polyvinylpyrrolidones over a large molecular weight range (e.g., between about 5 kDa and about 1500 kDa) have been found useful. It also has been

discovered that sodium carboxymethylcelluose is particularly effective as a surface active component for dispersing hydrophobic two-dimensional nanomaterials, despite the fact that the glucose rings in the polysaccharide can assume both planar and non- planar configurations.

[0044] Other useful surface active components include alkyl sulfates such as sodium hexyl sulfate, sodium octyl sulfate, sodium decyl sulfate, sodium undecyl sulfate, sodium dodecyl sulfate, and lithium dodecyl sulfate; quaternary ammonium salts such as dodecyltrimethylammonium bromide, myristyltrimethylammonium bromide, hexadecyltrimethylammonium bromide, hexadecyltrimethylammonium chloride, and hexadecyltrimethylammonium hydrogen sulfate; polyoxyethylene alkylphenyl ethers such as Triton® X-IOO; polyoxyethylene sorbitan alkyl ethers such as Tween® 20 and Tween® 85; poloxamers (or non-ionic triblock copolymers of oxyethylene and oxypropylene known under the trade name Pluronic®) which can be represented by the general formula HO(C ₂ H ₄ O) _a (C ₃ H ₆ O) _b (C ₂ H ₄ O) _a H, wherein a and b are integers in the range of 10 to 300; and non-ionic tetrafunctional block copolymers of oxyethylene and oxypropylene known under the trade name Tetronic®.

[0045] State-of-the-art exfoliation methods for preparing nanomaterials often are performed in expensive organic solvents due to the highly hydrophobic nature of most planar nanomaterials and their starting materials. By using the surface active components described herein, it was surprisingly found that highly hydrophobic materials such as graphite and graphene can be uniformly dispersed in water at high concentrations. For example, for the initial exfoliation step, graphite can be effectively dispersed at concentrations higher than about 50 mg/mL in an aqueous solution containing the surface active components. The fact that the present methods can be practiced with a high concentration of the starting materials help ensure a high throughput of the process. In addition, aqueous dispersions of graphene in

composition with one or more surface active components described herein can have a graphene concentration higher than about 0.10 mg/mL, higher than about 0.20 mg/mL, higher than about 0.30 mg/mL, higher than about 0.40 mg/mL, higher than about 0.50 mg/mL, higher than about 0.60 mg/mL, higher than about 0.70 mg/mL, higher than about 0.80 mg/mL, higher than about 0.90 mg/mL, or higher than about 0.95 mg/mL and remain stable (e.g., without visible aggregation) for at least two weeks, for at least three weeks, for at least one month, or for at least two months. Stable aqueous dispersions OfMoS ₂ and BN also can be obtained similarly with one or more surface active components described herein. [0046] In embodiments where the present methods are used to generate graphene nanomaterials, planar surface active components such as sodium cholate, sodium carboxymethylcellulose, and other surface active components including one or more planar organic groups can be used. Both the starting layered materials (i.e., graphite) and the exfoliated nanomaterials (i.e., graphene nanomaterials) can form a complex with the surface active components. According to the present methods, sodium cholate and other surface active components are not intended to chemically modify or functionalize the starting materials or the exfoliated nanomaterials. Instead, the one or more surface active components typically are selected to ensure non-covalent association with the materials, whether it is by ionic interaction, π-π orbital interaction, hydrogen bonding, Van Der Waals interaction, or combinations thereof. In some embodiments, the materials can be considered as being "encapsulated" by the surface active components. As used herein, "encapsulate," "encapsulated," or "encapsulating" refers to non-covalent association with a target. For example, the one or more surface active components can arrange themselves as a sheet and cover at least 50% of one or more surfaces of the target. In certain embodiments, the one or more surface active components can form an ordered layer on each side of the target, yet not be present at one or more edges of the target.

[0047] FIG. IA is a schematic illustration of the solution-phase exfoliation process according to the present teachings. In particular, the exfoliation process can be performed in an aqueous solution containing one or more surface active components. For example, a three-dimensional layered material such as graphite flakes can be combined with a surface active component such as sodium cholate in an aqueous solution. Horn ultrasonication then can be used to exfoliate the three-dimensional graphite flakes into graphene nanomaterials that are encapsulated by the surface active components. FIG. IB provides a schematic illustration of a monolayer nanoflake (e.g., monolayer graphene) encapsulated by an ordered monolayer of surface active components (e.g., sodium cholate) on each side.

[0048] Following ultrasonication, the sonicated dispersion can include two- dimensional nanomaterials as well as three-dimensional materials. Among the two- dimensional nanomaterials, there can be a poly disperse population of monolayer nanomaterials, bilayer nanomaterials, trilayer nanomaterials, and higher-order few- layer nanomaterials. Before separating the two-dimensional nanomaterials by thickness, the three-dimensional materials can be removed and/or the sonicated dispersion can be concentrated to improve the quality of the separation process.

[0049] For example, the sonicated dispersion can be subjected to sedimentation centrifugation. In various embodiments, the sonicated dispersion can be centrifuged at about 21,000 relative centrifugal force for several minutes to remove fast sedimenting large crystallites from the dispersion. The supernatant then can be recovered to form a base dispersion. The crystallites in the base dispersion can comprise a concentration of at least about 0.05 mg/mL and be stable. For example, the crystallites in the recovered base dispersion may not show signs of reaggregation for at least two weeks following their initial dispersion.

[0050] Following the procedures described above, a well-dispersed aqueous solution of two-dimensional nanomaterials can be obtained. Because the

nanomaterials provided by the present teachings are produced without any covalent chemical modification, the nanomaterials of the present teachings can offer greater crystallinity and environmental stability than those obtained using prior art methods such as intercalation. Aqueous dispersions of the present two-dimensional nanomaterials can be used for controlled deposition using methods previously developed to deposit other nanomaterials such as carbon nanotubes and inorganic nano wires. Such deposition methods include dielectrophoresis (see R. Krupke et al, Science 301, 344 (2003)), self-assembled monolayer mediated adhesion (see M. Burghard et al., Adv. Mater. 10, 584 (1998)), and Langmuir-Blodgett assembly (see X. Li et al., J. Am. Chem. Soc. 129, 4890 (2007)). Atomic force microscopy (AFM) images of thin films deposited onto Siθ2-capped Si wafers from base dispersions according to the present methods confirm the presence of crystallites with thicknesses ranging from about 1 nm to about 10 nm.

[0051] For further refinement, the base dispersions described above can be concentrated by ultracentrifugation in a step gradient. More specifically, a base dispersion can be layered on top of a dense underlayer, e.g., a dense underlayer of 60% w/v iodixanol, and ultracentrifuged in the resulting step gradient.

Ultracentrifugation causes the nanomaterials in the base dispersion to sediment into the step gradient formed at the interface between the two layers, producing a concentrated band of two-dimensional nanomaterials that can be removed by fractionation. In addition to producing a concentrated dispersion of crystallites, ultracentrifugation in a step gradient also removes thick crystallites (including nanomaterials consisting of more than ten layers) whose buoyant density exceeds the density of the step gradient.

[0052] To provide two-dimensional nanomaterials having a controlled thickness (or number of atomic layer), the base dispersion or the concentrated dispersion can be subjected to density gradient ultracentrifugation (DGU). During DGU, the differences in the buoyant density of the two-dimensional nanomaterials and that of the surrounding medium drive the two-dimensional nanomaterials to their respective isopycnic points, where the buoyant density of a particular nanomaterial crystallite matches that of the surrounding medium. In particular, because monolayer nanomaterials, bilayer nanomaterials, trilayer nanomaterials, and higher-order few- layer nanomaterials have different buoyant densities upon association with the present surface active components, ultracentrifugation in a density gradient will cause the encapsulated nanomaterials to separate by thickness into distinct often visible bands (or separation fractions) of nanomaterials. For example, it was empirically found that the buoyant density of graphene nanomaterials increases with thickness when centrifuged in composition with sodium cholate; accordingly, the topmost separation fraction is expected to be enriched with monolayer graphene. To illustrate, after the sedimentation and/or the concentration step(s), the nanomaterial dispersion can include less than about 30% monolayer nanomaterials among all the graphene nanomaterials in the dispersion. After one iteration of the DGU process, the topmost separation fraction can include at least about 50%, at least about 60%, at least about 70%, at least about 80%, or at least about 90% monolayer nanomaterials among all the graphene nanomaterials in that topmost separation fraction.

[0053] Generally, density gradient ultracentrifugation uses a fluid medium with a predefined variation in its density as a function of position within a centrifuge tube or compartment (i.e., a density gradient). Fluid media useful with the present teachings are limited only by nanomaterial aggregation therein to an extent precluding at least partial separation. Accordingly, aqueous and non-aqueous fluids can be used in conjunction with any substance soluble or dispersible therein, over a range of concentrations, so as to provide the medium a density gradient for use in the separation techniques described herein. Such substances can be ionic or non-ionic, non- limiting examples of which include inorganic salts and alcohols, respectively. Such a medium can include a range of aqueous iodixanol concentrations and the corresponding gradient of concentration densities. As understood by those skilled in the art, aqueous iodixanol is a common, widely used non-ionic density gradient medium. However, other media can be used in methods of the present teachings, as would be understood by those skilled in the art.

[0054] More generally, any material or compound stable, soluble or dispersible in a fluid or solvent of choice can be used as a density gradient medium. A range of densities can be formed by dissolving such a material or compound in the fluid at different concentrations, and a density gradient can be formed, for instance, in a centrifuge tube or compartment. More practically, with regard to choice of medium, the two-dimensional nanomaterials in composition with the surface active

components should be soluble, stable or dispersible within the fluids/solvent or resulting density gradient. Likewise, from a practical perspective, the maximum density of the gradient medium, as determined by the solubility limit of such a material or compound in the solvent or fluid of choice, should be at least as large as the buoyant density of the nanomaterial-surface active component complexes for a particular medium. Accordingly, any aqueous or non-aqueous density gradient medium can be used provided that the nanomaterials are stable; that is, do not aggregate to an extent precluding useful separation. Alternatives to iodixanol include inorganic salts (such as CsCl, Cs ₂ SO ₄ , KBr, etc.), polyhydric alcohols (such as sucrose, glycerol, sorbitol, etc.), polysaccharides (such as polysucrose, dextrans, etc.), other iodinated compounds in addition to iodixanol (such as diatrizoate, nycodenz, etc.), and colloidal materials (such as Percoll ^® ). Other parameters which can be considered upon choice of a suitable density gradient medium include the diffusion coefficient and the sedimentation coefficient, both of which can determine how quickly a gradient redistributes during centrifugation. Generally, for more shallow gradients, a larger diffusion coefficient and a smaller sedimentation coefficient are desired.

[0055] It has been discovered that the point at which the encapsulated nanomaterials are introduced into the density gradient in the fluid medium can be important to the quality of the separation. In some embodiments, the encapsulated nanomaterials are introduced into the density gradient at a density that is expected to be greater than the buoyant density of any of the encapsulated nanomaterials. In some embodiments, the encapsulated nanomaterials are introduced into the density gradient at a density that is expected to be lower than the buoyant density of any of the encapsulated

nanomaterials.

[0056] In certain embodiments, the nanomaterials (e.g., the concentrated dispersion) can be injected at the bottom of the linear density gradient and centrifuged. Under such condition, the nanomaterials are expected to move upwards to their isopycnic points and settle into multiple bands or separation fractions of nanomaterials. The nanomaterials in these separation fractions can be sufficiently monodisperse or selective for most applications, and therefore, can be collected and used 'as is' (optionally after removal of the surface active components) for processing into various composites and devices.

[0057] In certain embodiments, it can be desirable to purify further the separation fractions to improve their selectivity by performing additional iterations of the present methods. Specifically, a separation fraction can be provided in a composition with the same surface active component system or a different surface active component system, and the composition can be contacted with the same fluid medium or a different fluid medium, where the fluid medium can have a density gradient that is the same or different from the fluid medium from which the separation fraction was obtained. In certain embodiments, fluid medium conditions or parameters can be maintained from one separation to another. In other embodiments, at least one iterative separation can include a change of one or more parameters including the identity of the surface active component(s), medium identity, medium density gradient, and/or medium pH, as well as the duration and the rotational speed of the centrifugation process, with respect to one or more of the preceding separations. In certain embodiments, the surface active component(s) encapsulating the

nanomaterials can be modified or changed between iterations, allowing for even further refinement of separation. Separation fractions isolated after each separation can be washed before further complexation and centrifugation steps are performed.

[0058] For example, after a first separation cycle where the nanomaterials (e.g., the concentrated dispersion) are injected at the bottom of the linear density gradient and centrifuged, one or more resulting separation fractions can be collected and be subjected to a second iteration of the DGU process. For this second iteration, the separation fractions can be loaded at the top of a second density gradient forcing the graphene nanomaterials to move downward in the centrifuge tube to their respective isopycnic points. This second DGU iteration can help remove slow-moving, low buoyant density materials that did not reach their isopycnic points in the first iteration. Again, after ultracentrifugation, the nanomaterials are expected to settle into multiple bands or separation fractions, where the separation fractions resulting from the second DGU process can have higher monodispersity in thickness compared to the separation fraction(s) resulting from the first DGU process.

[0059] The selectivity of the fraction(s) collected can be confirmed by various analytical methods including optical absorbance, Raman spectroscopy, transmission emission spectroscopy (TEM), fluorescence spectroscopy, atomic force microscopy, and other methods known in the art.

[0060] Nanomaterials provided by the present methods can be highly monodisperse in thickness. For example, the present methods allow production of graphene nanomaterials having a high percentage of monolayer graphene, bilayer graphene, and/or trilayer graphene, and substantially free of few-layer (n > 4) graphene nanomaterials. In addition, because the present methods generally do not include any thermal or chemical (e.g., oxidative and/or reductive) treatment, nanomaterials provided by the present methods can be considered pristine, that is, they have not been oxidized, reduced, and/or otherwise chemically modified in any way. For example, monolayer graphene provided by the present methods generally is substantially defect-free. Compared to graphene nanomaterials which are prepared from reduction of exfoliated graphite oxide, the present graphene nanomaterials generally have better electronic properties, specifically, in terms of higher electrical conductivity (or lower sheet resistance).

[0061] The nanomaterials according to the present teachings can be processed into various composites and devices. For example, the present nanomaterials can be prepared as an aqueous dispersion in composition with sodium cholate and/or other surface active components and processed via various solution-phase techniques known in the art such as spray coating, drop casting, spin coating, dip coating, and printing. In addition, thin films of nanomaterials can be prepared by filtering a nanomaterial dispersion under vacuum (i.e., by vacuum filtration) through a porous membrane as known by those skilled in the art. Films prepared from sorted nanomaterials according to the present teachings can have various desirable properties over those prepared from unsorted nanomaterials. For example, films obtained from graphene nanomaterials having a high percentage of monolayer graphene can exhibit high optical transmittance (e.g., > 50%) in a wide transmittance window (from -300 nm to 3300 nm) and a low sheet resistance (e.g., 5 kΩ/D or less). The electrical conductivity of the films can be further improved by annealing the films at relatively low temperature (< 300 ⁰ C), reducing the sheet resistance to about 2 kΩ/D or less, for example, about 1.5 kΩ/D with a transmittance of about 65% in the visible range. By comparison, films produced from polydisperse graphene/graphite nanomaterials using conventional sedimentation-based centrifugation techniques typically exhibit a sheet resistance of greater than or about 10 kΩ/D with a transmittance of about 60% in the visible range.

[0062] The present teachings also encompass articles of manufacture such as various electronic devices, optical devices, and optoelectronic devices that incorporate one or more transparent and electrically conductive components. Instead of using existing transparent and electrically conductive materials such as indium tin oxide, graphene films according to the present teachings can be used as transparent conductors. For example, sensors for detecting chemical or biological species can be fabricated where the graphene film forms one of the conducting channels. Solar cells, light emitting diodes, and plasma and liquid crystal displays also can be fabricated based on graphene films according to the present teachings. The present graphene films can confer new advantages to the devices described above such as mechanical flexibility and/or longer lifetime.

[0063] The following examples are provided to illustrate further and to facilitate the understanding of the present teachings and are not in any way intended to limit the invention.

[0064] Example 1: Solution Phase Preparation of Graphene

[0065] Graphene nanomaterial dispersions were prepared by horn ultrasonication of naturally occurring graphite flakes in an aqueous solution containing a surface active component. More specifically, six grams of natural graphite flakes (3061 grade material from Asbury Graphite Mills, Asbury, New Jersey, USA) were added to 70 mL of a 2% w/v sodium cholate (SC) aqueous solution inside a -120 mL stainless steal beaker. This mixture was chilled in an ice water bath and ultrasonicated using a Fisher Scientific Model 500 Sonic Dismembrator with a 13-mm-diameter tip for one hour at a power level of 51-52 W. Large initial loadings of graphite were chosen to maximize the concentrations of graphene exfoliated into the SC solution given the low cost of graphite flakes (~$0.02 per gram). The sonicated graphene nanomaterial dispersions appeared as a gray-black slurry, suggesting the presence of both thin graphene nanosheets and thicker graphite flakes.

[0066] Example 2: Sedimentation Centrifugation

[0067] Sedimentation centrifugation was performed to remove the fast sedimenting thick graphite materials from the sonicated graphene nanomaterial dispersions from Example 1. Specifically, the graphene nanomaterial dispersions were centrifuged in filled 2 mL eppendorf tubes using a tabletop centrifuge (Eppendorf Model 5424 Microcentrifuge) using four different conditions summarized in Table 1. The black supernatant resulting from the sedimentation centrifugation processing was believed to consist of predominantly few-layer graphene nanoflakes. The sedimented graphene nanomaterial dispersions were observed to be stable for several weeks at loadings in excess of 90 μg/mL. After centrifugation, the top 1 mL layer of the dispersion was decanted carefully from each eppendorf tube. Optical absorbance measurements were taken with a Cary 500 spectrophotometer (Varian) to estimate the concentration of graphene nanomaterials in the dispersions using an average absorption coefficient for graphene of 2,460 mL mg ^"1 m ^"1 at a wavelength of 660 nm. Contributions from the optical cuvette and sodium cholate solution were subtracted from the spectra of the graphene dispersions. Table 1 lists the concentration of graphene nanomaterials in the sedimented dispersions as determined from the absorbance measurements.

Table 1: Sedimentation Processing Parameters

[0068] Example 3: Concentration of Graphene Dispersions By Ultracentrifugation in a Step Gradient

[0069] To obtain concentrated dispersions of graphene nanoflakes, the sedimented dispersions from Example 2 were centrifuged in a step density gradient. Specifically, the step gradients were prepared from a dense 6 mL underlayer containing about 60% w/v iodixanol (density of about 1.32 g mL ^"1 ) and about 2% w/v SC, followed by a graphene overlayer of ~32 mL (density of about 1.0 g mL ^"1 ) added carefully on top, and ultracentrifuged in an SW 28 rotor (Beckman Coulter) for 24 hours at 28 krpm and a temperature of 22 ⁰ C. Ultracentrifugation of the step gradients caused the graphene nanosheets to sediment rapidly to the point where the density of the medium changed discontinuously. In this region, the few-layer graphene nanoflakes with low buoyant densities halted their sedimentation as they reached their isopycnic points while the denser thick graphite flakes continued their motion until they eventually form a pellet at the bottom of the centrifuge tube. This step gradient approach thereby eliminated a large portion of the thick components in the dispersion without removing valuable few-layer nanomaterials that also could be eliminated by simple

centrifugation without the use of a dense underlayer. Following ultracentrifugation, a 60% w/v iodixanol, 2% w/v SC displacement layer was slowly infused near the band of concentrated graphene nanomaterials to both separate it from the dense material below and to raise the position of the band in the centrifuge tube for more reliable fractionation. The concentrated nanomaterials was then collected near the step in the gradient using a piston gradient fractionator (Biocomp Instruments) to provide a highly concentrated graphene nanomaterial dispersion.

[0070] Example 4: Separation of Few-Layer Graphene Materials by

Thicknesses Using Density Gradient Ultracentrifugation

[0071] To separate the few-layer graphene nanomaterials by their thicknesses, the concentrated graphene nanomaterial dispersion collected from Example 3 was subjected to two iterations of density gradient ultracentrifugation (DGU). The relevant DGU conditions used for the first and second iteration separations are summarized in Table 2. The first iteration used the maximum volume of concentrated graphene nanomaterial dispersion that could be added to a 4 mL solution with a density of 46% w/v iodixanol. For the second DGU iteration, the graphene nanomaterial dispersions were diluted to 9-16% w/v iodixanol to decrease viscosity, increase the graphene sedimentation rate, and enable layering on the top of the density gradient.

[0072] More specifically, in the first iteration, the concentrated graphene dispersion was injected at the bottom of the linear density gradient and centrifuged for 24 hours at a maximum centripetal acceleration of 141,000 g. During this process, the graphene nanosheets moved upwards in the centrifuge tube to their isopycnic points. FIG. 1C is a photograph of the centrifuge tube following the separation. Multiple gray bands at different locations inside the gradient were observed. These bands were recovered in 1 mm steps using a piston gradient fractionator. Of the resulting 32 fractions, five were selected for a second iteration of DGU: fractions f4, flO, and f22, which corresponded to the thinnest bands observed; and fractions fl6 and f28, which were part of broader bands. To achieve further density gradient refinement, the graphene nanomaterial dispersion was loaded at the top of a second density gradient forcing the graphene flakes to move downward in the centrifuge tube to their respective isopycnic points. This second DGU iteration removed slow moving, low buoyant density materials that did not reach their isopycnic points in the first iteration.

Table 2: Conditions used for DGU Separations

[0073] Example 5: Assessment of Thicknesses of Graphene Nanomaterials by Atomic Force Microscopy and Raman Spectroscopy

[0074] Example 5.1. Sample Preparation

[0075] The DGU-processed graphene nanomaterials were characterized by both atomic force microscopy (AFM) and Raman spectroscopy. Samples were prepared by depositing graphene nano flakes onto Si wafers capped by a 100-nm thick oxide. Prior to deposition, the wafers were immersed in an 2.5 mM (3-aminopropyl)

triethoxysilane aqueous solution to functionalize them with a self-assembled monolayer, dried with a stream of N ₂ , rinsed with water, and then dried again. The graphene nanomaterial dispersion was typically diluted by a factor of five with a 2% w/v sodium dodecyl sulfate aqueous solution to improve the yield of the deposition. A drop of this diluted solution was then applied to the receiving wafer and left for 10 minutes. The drop was blown off the wafer with a stream of N ₂ , followed by rinsing the wafer in water for ~15 seconds, and drying by nitrogen. To remove residual surfactants and iodixanol, the graphene samples were annealed in air for one hour at about 25O ⁰ C. For better AFM imaging, graphene samples that had undergone density processing were sometimes dialyzed to remove iodixanol. For ~2 mL of graphene dispersion, dialysis was typically done with 20,000 molecular weight cut-off dialysis cassettes (Pierce Slide -A-Lyzer) using a 1.75 L, 2% w/v SC aqueous bath for -48 hours.

[0076] Example 5.2. Atomic Force Microscopy

[0077] AFM images were obtained using a Thermo Microscopes Autoprobe CP- Research AFM operating in tapping mode with conical probes (MikroMasch, NSC36/Cr-Au BS). All AFM images used for thickness measurements were generated using one of two AFM probes. To ensure the two probes produced the same thickness values, multiple graphene flakes from fraction f4 were imaged by both probes and compared. In addition, highly-oriented pyrolytic graphite (HOPG) was imaged as a calibration standard for accurate height measurements. All images in the analysis were 2 μm x 2 μm and collected under identical scan parameters. Graphene sheets that were part of bundles were excluded from the analysis. In addition, sub- 2500 nm ² area flakes were neglected due to the uncertainty in their thickness measurements as were residual SC or iodixanol whose thickness exceeded 5 nm.

[0078] Graphene flakes from fraction f4 exhibit an average thickness of about 1.1 nm. Single-layer graphene on SiO ₂ typically has an apparent thickness of ~1 nm as a result of adsorbed water (see Novoselov et al., Science, 306(5696): 666-669 (2004)). The slightly increased thickness of the materials from fraction f4 could be due to residual sodium cholate molecules on the graphene surface. In contrast, the graphene sheets from fl6 were found to have an average thickness of 1.5 nm. [0079] FIGS. 2A and 2B present the thickness histograms of several sorted graphene fractions (Example 4) as well as the concentrated (Example 3) and sedimented (Example 2) graphene dispersions. These histograms were calculated from at least 100 individual flakes using multiple 2 μm x 2 μm AFM images with the average thickness measured over the area of each flake. Comparison of the thickness distributions of the sedimented, concentrated, and f4 graphene solutions in FIG. 2 A shows progressive sharpening of the distributions with increasing buoyant density refinement.

[0080] With continued reference to FIG. 2A, it can be seen that for the sedimented graphene solution, 37% of the flakes was found to have thicknesses greater than 2 nm. By comparison, following concentration step gradient processing, only 2.6% of the dispersion was found to have thicknesses greater than 2 nm. Furthermore, it can be seen that following DGU, flakes having thicknesses greater than 2 nm essentially are absent in fraction f4. Instead, at least about 80% of the graphene flakes from fraction f4 were found to have thicknesses of 1.2 nm or less, suggesting that most of these graphene flakes likely correspond to single-layer graphene. In contrast, only 24% of the concentrated graphene consisted of single-layer material.

[0081] Referring to FIG. 2B, the thickness distributions of the graphene sorted using DGU show a monotonic increase in the average flake thickness with increasing buoyant density. Comparing the mean flake thickness of the graphene materials in fractions f4, fl6, and f28 to the sedimented or concentrated dispersion shown in FIG. 2A, it can be seen clearly that the present methods allow separation of two- dimensional nanomaterials by their thicknesses.

[0082] Example 5.3. Geometrical Model for Determining Buoyant Density of Few- Layer Graphene Flakes

[0083] Without wishing to be bound by any particular theory, it is believed that upon contact with the appropriate surface active component(s) according to the present teachings, the graphene materials can be dispersed as individual encapsulated flakes, thus providing a graphene dispersion that can remain stable for an extended period of time. To gain further insight into the ordering of surface active components such as sodium cholate on the graphene surface, the inventors developed a

geometrical model of the buoyant density of the graphene-SC complex. In this model, and as schematically illustrated in FIG. 3 A, the thickness of the graphene sheet is defined by N, which specifies the average number of graphene layers inside the sheet separated by the graphene interlayer distance t = 0.34 nm. On both sides of the graphene sheet is an anhydrous layer of thickness I _A containing the SC encapsulation layer. The SC molecules in this region coat the graphene surface with surface packing density σ. Surrounding this SC layer is an electrostatically bound hydration shell of thickness tπ- This hydration layer has the lowest density of any of the components in the complex and hence serves to decrease the buoyant density of the graphene-SC assembly. The resulting buoyant density P(N) is then:

Qy) ₌ ^{Ps N + 2nisc <T + 2} P ^H ₁ ^O1H

^P[ > ^~ (N + l)t _{gr +} 2t _Λ + 2t _H where p _s = 7.66xlO ^~8 g cm ^"2 is the sheet density of graphene, m _sc = 7.15xlO ^~22 g is the mass of one SC molecule, and p _{H 0} is the density of water.

[0084] The graphene buoyant density model was applied to the experimental data by assuming the anhydrous shell thickness I _A was 0.355 nm (see Arnold et ah, ACS Nano., 2(11): 2291-2300 (2008)). Furthermore, the apparent thickness for single- layer graphene was taken to be the average thickness of 1.1 nm measured for graphene sheets from fraction f4. N for subsequent fractions was then calculated from their average mean thicknesses and the graphite interlayer spacing. With these conditions in place, the model yields a SC surface packing density σ of 1.35 nm ^"2 and a hydration layer thickness fø of 3.3 nm. Because SC occupies approximately a -0.7 nm ² area on the graphene surface (see Arnold et al, ACS Nano., 2(11): 2291-2300 (2008)), this surface density corresponds to -94% surface coverage of SC

(schematically illustrated in FIG. IB). The small area of graphene occupied by each SC molecule also implies that it is possible for the SC encapsulation layer to accommodate variations in graphene thickness on length scales of several nanometers. Consequently, without wishing to be bound by any particular theory, it is believed that a continuum of mean graphene flake thicknesses can be separated using DGU depending on how the flakes are exfoliated (FIG. 3B). [0085] Example 5.4. Raman Spectroscopy

[0086] Raman spectroscopy of graphene flakes on SiO ₂ was performed using a Renishaw in Via Raman Microscope at an excitation wavelength of 514 nm. To obtain a random sampling of the graphene at multiple locations, spectra were measured at multiple positions spaced at least 5 μm apart. Spectra were obtained using a beam size of 1-2 μm on samples with a high surface coverage of graphene enabling multiple flakes to be probed in a single measurement. For these map scans, 2D, G, and D bands were measured consecutively to ensure the relative intensities of the peaks were not affected by drift of the translation stage.

[0087] Typical Raman spectra from the sorted graphene samples display four main peaks: the G band at -1590 cm ^"1 , the 2D (or G') band at -2700 cm ^"1 , and the disorder- related D and D' peaks at -1350 cm ^"1 and -1620 cm ^"1 , respectively (FIGS. 4A and 4B). The Raman spectra show systematic changes in the G and 2D peaks as a function of the thickness distribution of the graphene flakes. For example, it can be observed that the 2D peak decreases in intensity and broadens with increasing mean flake thickness. To gather sufficient statistics for these variations, spectra were collected from at least 30 different locations and mean and standard deviation information was extracted from these data. FIG. 4C presents the I(2D)/I(G) ratio and full- width at half maximum (FWHM) of the 2D band as a function of the average thickness of the sorted and concentrated graphene dispersions.

[0088] It was observed that as the thickness of the graphene flakes increases, I(2D)/I(G) decreases monotonically from a high of 2.1 ± 0.2 for single-layer graphene to 0.8 ± 0.1 for quadruple-layer graphene. FWHM(2D), on the other hand, increases with graphene thickness nearly doubling between single- and quadruple-layer samples. Similar trends in both I(2D)/I(G) and FWHM(2D) as a function of graphene layer number have previously been observed for CVD grown graphene samples (see Reina et al, Nano. Lett., 9(1): 30-35 (2009)), and should prove useful for more rapid screening of DGU-sorted graphene. Similar to CVD-graphene samples and those grown on SiC (see Faugeras et al, Appl. Phys. Lett., 92(1): 011914-3 (2008)), the 2D band of multilayer graphene appears to be best described by a single Lorentzian lineshape, as opposed to the four component lineshape observed for samples produced by micromechanical cleavage (see Ferrari et al, Phys. Rev. Lett., 97: 187401 (2006)). Because these four components arise from the close interaction between ABAB stacked graphene layers, their absence implies weak interlayer coupling and hence non-ABAB stacking. This source of disorder could be caused during horn

ultrasonication or from rebundling of previously exfoliated graphene sheets. The disorder-related D peak is relatively intense compared to the G band in these samples, most likely as a result of defects within the graphene sheets or from the small size of the flakes, which should increase the number of disordered graphene edges probed in the measurement. The ratio of the intensities of the D and G peaks I(D)/I(G) remains fixed at -0.93 for both the sedimented and density-refined material, which indicates that ultracentrifugation did not contribute additional defects to the graphene. This I(D)/I(G) value is comparable to that observed in highly reduced graphene oxide (see Gao et al. Nature Chem., doi:10.1038/nchem.281 (2009)), and is less than that measured for lithographically patterned graphene nanoribbons (see Jiao et al., Nature, 458(7240): 877-880 (2009)).

[0089] Example 6: Graphene Transparent Conductors

[0090] Example 6.1. Preparation of transparent conductive films

[0091] To assess the electrical properties of graphene material sorted by the present methods, graphene films were prepared using the method described in Wu et al., Science, 305: 1273 (2004), by filtering approximately 2 mL of graphene dispersion in a 2% w/v SC aqueous solution under vacuum through mixed cellulose ester membranes (Millipore) having a 50 nm average pore size. After the dispersion had passed through the membrane, the film was left to set over 15 minutes. Residual surfactant and iodixanol were rinsed out of the film by filtering through -30 mL of water. To prevent the film from lifting off the membrane during this step, a protective layer of isopropyl alcohol was slowly added on top of the film followed by a slow but steady stream of the water rinse. The filtered films were then affixed to glass substrates by soaking them in ethanol and pressing the graphene side firmly into the glass. The still wet graphene film and membrane were promptly introduced to an acetone vapor bath that dissolved away the mixed cellulose ester membrane. The membranes were further dissolved in three subsequent acetone liquid baths and a final ethanol liquid bath. [0092] Example 6.2. Effect of Annealing of Graphene Transparent Conductors

[0093] It was found that the sheet resistance of graphene transparent conductive films (Example 6.1) could be decreased by an average factor of 2-4 by annealing them in air. Specifically, film samples were annealed for two hours at about 25O ⁰ C, which was observed to have the effects of increasing the film conductivity, while increasing the transmittance by about 1%. Without wishing to be bound by any particular theory, it is believed that annealing likely removed some of the iodixanol and sodium cholate remaining in the film and enabled the graphene sheets to reorder to improve flake-flake contacts. The sheet resistance and transmittance of films produced from concentrated graphene and the sorted fraction f4 before and after annealing are shown in FIG. 5A. It was observed that annealing provided greater improvements in sheet resistance for films of higher transmittance. Without wishing to be bound by any particular theory, it is believed that films of high transmittance are closer to the percolation threshold of graphene and are more sensitive to changes in flake network connectivity.

[0094] AFM images of the annealed films indicate the graphene flakes form a disordered network. Folded flakes can be discerned in the images along with rough areas that are most likely caused by residual surfactants, iodixanol, or the filter membrane. The films possess high optical transmittance from -300 nm to 3300 nm, revealing a wide transmittance window that is well suited for infrared applications.

[0095] Example 6.3. Transparent Conductors Produced from Sedimented

Dispersions

[0096] To compare between the properties of transparent conductive films prepared from DGU processing and those prepared from sedimented graphene solutions, transparent conductors from sedimented graphene dispersions were prepared under different centrifugation conditions. FIG. 5B presents the sheet resistance and transmittance of films prepared from the graphene dispersions described in Table 1. The variation in the performance of these films is relatively small compared to that observed following density differentiation. This result indicates that any size sorting effect is small for SC-encapsulated graphene produced by this type of sedimentation centrifugation. [0097] Four-point probe measurements of the film sheet resistance indicated that DGU processing yields significant improvements in the transparent conductive properties of the graphene films. Firstly, all films produced using buoyant density sorting demonstrated improved conductivity compared to films produced from sedimented graphene solutions (FIGS. 6A and 6B). For the films produced from the concentrated, fl6, and f28 dispersions, this improvement is -45%. Secondly, the films produced using predominantly single layer graphene flakes (f4) offer the best transparent conductor performance. These highly refined materials exhibit sheet resistances that are approximately half that of the other density processed material. Analysis of the graphene flakes indicates that the f4 material has the largest mean area (16,000 nm ² ) of all the materials used for transparent conductors. A large lateral area should result in fewer graphene-graphene contacts required for charge transport across the film and thus implies increased film conductivity. However, the differences in transparent conductor performance between the concentrated and sedimented solutions suggest that the graphene thickness distribution also can play an important role in the connectivity of the graphene network. The larger proportion of thick graphene sheets in the sedimented solution may disrupt the ideal close packed structure of the network, which would reduce the overlap between neighboring sheets. In contrast, the highly flexible single-layer graphene sheets deposited from solution are expected to coat underlying layers with greater conformity, resulting in improved graphene-graphene contacts.

[0098] Example 7: Sorting of Non-Graphene Two-Dimensional Nanomaterials by Thickness

[0099] Using methods of the present teachings, two-dimensional nanomaterials of controlled thickness can be generated from crystalline materials including, but not limited to, graphite, MoS ₂ , and hexagonal BN. MoS ₂ is a semiconducting transition metal dichalcogenide consisting of layers of molybdenum coordinated with six sulfide ligands. Hexagonal BN is a semiconductor material with a structure analogous to that of graphite.

[0100] Step 1 - Dispersion: Base dispersions of the starting crystalline materials typically were generated by loading 10 mL of a 2% w/v SC (Sigma-Aldrich) aqueous solution with one gram of bulk crystallite powder. The mixtures were then subjected to horn ultrasonication at 160 W for one hour using a Fisher Scientific Model 500 Sonic Dismembrator with a tapered microtip probe. Poorly dispersed materials were removed by centrifugation at 21,130 g relative centrifugal force for 5 minutes. The supernatant from each centrifuge tube was recovered to form the base dispersion. The base dispersion of MoS ₂ was observed to have a yellow/orange color, whereas the base dispersion of BN was iridescent and appeared slightly white. Atomic force microscopy (AFM) images of thin films deposited onto SiO ₂ -capped Si wafers from base dispersions of graphite, MoS ₂ , and hexagonal BN prepared according to the procedures described above confirm the presence of crystallites with thicknesses ranging from about 1 nm to about 10 nm.

[0101] Step 2 - Concentration in step gradient: The base dispersions were then inserted into a step gradient and concentrated. Step gradients were formed by first adding a -2.5 mL layer of solution of about 1.32 g/mL density consisting of -2% w/v sodium cholate and -60% w/v iodixanol to the bottom of the centrifuge tube. A -9.5 mL layer of the base dispersion was added on top of the underlay er completing the step gradient. The layered centrifuge tubes were ultracentrifuged at 41 krpm in a SW41 Ti (Beckman Coulter) rotor for 14 hours. The concentrated dispersions were recovered using a two-step fractionation process. First, a displacement layer consisting of 2% w/v sodium cholate and 60% w/v iodixanol (OptiPrep; Sigma- Aldrich; 1.32 g/mL density) was slowly infused just below the band of concentrated material. This solution, mixing relatively little with the surrounding liquid, migrated to the position in the step gradient that matched its density and displaced upwards all crystallites with buoyant densities less than 1.32 g/mL. Following upward displacement, the thin band of concentrated two-dimensional nanomaterials was recovered using a piston gradient fractionator (Biocomp Instruments).

[0102] Step 3 - Sorting in density gradient: The crystallite dispersions were added to density gradients loaded with 2% w/v sodium cholate throughout. To generate the density gradients, a 1.5 mL underlayer consisting of 60% w/v iodixanol was added first to the bottom of the centrifuge tube and a 5 mL linear gradient with density varying from about 20% to about 45% w/v iodixanol was formed above. The dispersion of crystallites with iodixanol content adjusted to about 40.8% w/v was then slowly infused into the lower portion of the gradient to a volume of 0.88 mL. Then, the remaining volume of the centrifuge tube was filled with 2% w/v sodium cholate aqueous solution to prevent tube collapse under high centrifugal forces. The centrifuge tubes were spun at 41 krpm for 14 hours in a SW41 Ti (Beckman Coulter). Following centrifugation, the separated two-dimensional nanomaterials were collected using a piston gradient fractionator.

[0103] Following ultracentrifugation of concentrated dispersions of graphite, MoS ₂ , and hexagonal BN, discrete bands of material were observed inside the centrifuge tube for all three materials. For graphite crystallites, gray bands of spatially separated material were observed under multiple density gradient conditions. For the MoS ₂ crystallites, a single isolated yellow band was detected following DGU with denser material forming a broader yellow region nearer the bottom of the centrifuge tube. For BN samples, crystallites were difficult to detect directly by eye since hexagonal BN is a large band gap semiconductor and hence is transparent in the visible portion of the electromagnetic spectrum. However, by recording the light scattered by the crystallites inside the centrifuge tube, it was possible to observe a discrete band of buoyant material isolated from a broad band of much higher density.

[0104] The formation of discrete bands of two-dimensional nanomaterials following DGU provides strong evidence for sorting by number of atomic layers. The buoyant density of the crystallite-surfactant complex is most strongly affected by the atomic structure of the two-dimensional nanomaterial. Hence, the existence of crystallites with distinct buoyant densities implies that these crystallites differ by characteristics that vary discretely. As a result, and without wishing to be bound by any theory, it is believed that the crystallites having different buoyant densities consist of different numbers of atomic layers.

[0105] Example 8: Preparation of Graphene Nanoribbons

[0106] Graphene nanoribbons (GNRs) were obtained from highly oriented pyrolytic graphite (HOPG) dispersed in sodium cholate solution. HOPG flakes were initially added to a 1% w/v sodium cholate aqueous solution at a 1 mg/mL loading and horn ultrasonicated for 3 hours at 200 W. The resulting dispersion was then concentrated in a step gradient as described in Examples 3 and 7 and fractionated using a piston gradient fractionation system without infusing a displacement layer. Subsequently, the concentrated dispersion was incorporated into a density gradient similar to that described in Example 7 except with 1) a linear gradient varying from 20% to 50% w/v iodixanol, 2) an initial graphene layer density of 45% w/v iodixanol, and 3) a loading of 1% w/v sodium cholate throughout the gradient. The layered centrifuge tube was then ultracentrifuged in a SW41 Ti rotor at 41 krpm for 20 hours. Following centrifugation, the separated GNRs were collected using a piston gradient

fractionator.

[0107] AFM analysis of the separated GNRs reveal that the GNRs have widths below about 10 nm and lengths up to about 1 μm. Typical thicknesses range from about 0.8 nm to about 1.8 nm.

[0108] Example 9: Dispersion of Graphene Using Various Surface Active Components

[0109] Graphene suspensions were prepared in a variety of surface active components to determine their efficiency at stably encapsulating graphene in aqueous solutions. All graphene dispersions listed below were prepared in an identical manner. Natural graphite flakes (3061 grade material from Asbury Graphite Mills) weighing 600 mg ± 5 mg were added to 8 mL of an aqueous solution containing a loading of the surface active component of 1% weight per volume. The mixture was horn ultrasonicated (Fisher Scientific Model 500 Sonic Dismembrator equipped with a 3-mm-diameter tip) at a power level of 16-18 W for 30 minutes in a cooling bath of water. Following ultrasonication, the graphite/graphene slurry was centrifuged (Eppendorf Model 5424 Microcentrifuge) in 1.5 mL plastic tubes for 5 minutes at 15 krpm (21,130 x g). The top 1 mL of solution containing few-layer graphene nanomaterials was carefully decanted. The concentration of graphene in each of the suspensions was determined using optical absorption measurements. An extinction coefficient of 2460 mL mg ^"1 cm ^"1 at a wavelength of 660 nm previously reported for graphene was used for all measurements (see Y. Hernandez et al, Nature Nanotech. 3, 563 (2009)).

Table 3: Graphene Dispersion Efficiency of Bile Salt Surfactants Table 4: Graphene Dispersion Efficiency of Anionic Surfactants

Table 5: Graphene Dispersion Efficiency of Cationic Surfactants

Table 6: Graphene Dispersion Efficiency of Polymeric Surfactants

Table 7: Graphene Dispersion Efficiency of Polyvinylpyrrolidone

Table 9: Graphene Dispersion Efficiency of Tetronic® Block Copolymers

[0110] The present teachings encompass embodiments in other specific forms without departing from the spirit or essential characteristics thereof. The foregoing embodiments are therefore to be considered in all respects illustrative rather than limiting on the present teachings described herein. Scope of the present invention is thus indicated by the appended claims rather than by the foregoing description, and all changes that come within the meaning and range of equivalency of the claims are intended to be embraced therein.