Layer-by-layer sorting of rhenium disulfide via high-density isopycnic density gradient ultracentrifugation

Abstract

Separation of rhenium disulfide nanomaterials and related fluid density gradient media.

Claims

1. A method for separating planar nanomaterials by thickness, the method comprising: centrifuging a rhenium disulfide nanomaterial composition in contact with an aqueous fluid medium comprising a density gradient and an adjuvant component providing said medium a buoyant density greater than the buoyant density of said rhenium disulfide nanomaterial composition, wherein the rhenium disulfide nanomaterial composition comprises one or more surface active components and a polydisperse population of planar rhenium disulfide nanomaterials which is polydisperse at least with respect to thickness and has a mean thickness on the order of nanometers; and separating the rhenium disulfide nanomaterial composition into two or more separation fractions each comprising a subpopulation of planar rhenium disulfide nanomaterials from the polydisperse population, wherein the subpopulation of planar rhenium disulfide nanomaterials in at least one of the two or more separation fractions has a mean thickness that is less than the mean thickness of the polydisperse population.

2. The method of claim 1, wherein the planar nanomaterials comprise mono- and bilayer rhenium disulfide nanomaterials.

3. The method of claim 1, wherein the one or more surface active components comprise a planar organic group.

4. The method of claim 3, wherein the one or more surface active components is sodium cholate.

5. The method of claim 1, wherein said aqueous fluid medium comprises iodixanol and an adjuvant component to increase the buoyant density of said medium.

6. The method of claim 5, wherein said adjuvant component is CsCl.

7. A method for separating rhenium disulfide nanomaterials by thickness, the method comprising: sonicating a rhenium disulfide material in a first fluid medium to provide a rhenium disulfide nanomaterial composition; centrifuging the rhenium disulfide nanomaterial composition in contact with an aqueous second fluid medium comprising a density gradient and an adjuvant component providing said medium a buoyant density greater than the buoyant density of said rhenium disulfide nanomaterial composition, wherein the rhenium disulfide nanomaterial composition comprises one or more surface active components and a polydisperse population of planar rhenium disulfide nanomaterials comprising monolayer, bilayer, trilayer and n-layer rhenium disulfide nanomaterials, where n is an integer in the range of 4 to 10; and separating the rhenium disulfide nanomaterial composition into two or more separation fractions each comprising a subpopulation of planar rhenium disulfide nanomaterials from the polydisperse population, wherein the subpopulation in at least one of the two or more separation fractions comprises greater than about 50% of the monolayer rhenium disulfide nanomaterials, bilayer rhenium disulfide nanomaterials, trilayer rhenium disulfide nanomaterials, or combinations thereof.

8. The method of claim 7, wherein the subpopulation in at least one of the two or more separation fractions comprises greater than about 50% of the monolayer or bilayer rhenium disulfide nanomaterials, or a combination thereof.

9. The method of claim 7, wherein the one or more surface active components comprise a compound having a planar organic group.

10. The method of claim 8, wherein the one or more surface active components is sodium cholate.

11. The method of claim 7, wherein the subpopulation in one of the separation fractions comprises greater than about 50% of the monolayer rhenium disulfide.

12. The method of claim 7, wherein said second aqueous fluid medium comprises iodixanol and CsCl.

13. The method of claim 12, wherein the subpopulation in one of the separation fractions comprises greater than about 50% of the monolayer rhenium disulfide and is deposited on the substrate.

14. The method of claim 13, wherein the substrate and rhenium disulfide deposited thereon are incorporated into an electronic device.

15. The method of claim 7, wherein a subpopulation of at least one of the two or more separation fractions is deposited on a substrate.

16. A method for separating monolayer rhenium disulfide nanomaterials, the method comprising: centrifuging a rhenium disulfide nanomaterial composition in contact with an aqueous fluid medium comprising iodixanol and CsCl, said medium having a density gradient, wherein the rhenium disulfide nanomaterial composition comprises sodium cholate and a polydisperse population of planar rhenium disulfide nanomaterials comprising monolayer, bilayer and trilayer rhenium disulfide nanomaterials; and separating the rhenium disulfide nanomaterial composition into two or more separation fractions each comprising a subpopulation of planar rhenium disulfide nanomaterials from the polydisperse population, wherein the subpopulation in one of the two or more separation fractions comprises greater than about 50% of the monolayer rhenium disulfide nanomaterials.

17. The method of claim 16, wherein a subpopulation of at least one of the two or more separation fractions is deposited on a substrate.

18. The method of claim 17, wherein the subpopulation in one of the separation fractions comprises greater than about 50% of the monolayer rhenium disulfide and is deposited on the substrate.

19. The method of claim 18, wherein the substrate and rhenium disulfide deposited thereon are incorporated into an electronic device.

20. The method of claim 16, wherein said fluid medium and said sodium cholate are removed from a said separation fraction.

21. A method of using an increased buoyant density limit for separating planar nanomaterials by thickness, the method comprising: providing a composition comprising a nanomaterial and one or more surface active components, said composition comprising a polydisperse population of planar nanomaterials comprising monolayer, bilayer, trilayer and n-layer nanomaterials, where n is an integer selected from 4-about 10, said composition having a buoyant density; providing an aqueous fluid medium comprising a density gradient, said medium having a maximum buoyant density; introducing a component to said medium, said component having a maximum density limit greater than said composition buoyant density, to provide said medium a buoyant density greater than said composition buoyant density; centrifuging said nanomaterial composition in contact with said aqueous fluid medium; and separating said nanomaterial composition into two or more separation fractions each comprising a subpopulation of planar nanomaterials from the polydisperse population, wherein the subpopulation of planar nanomaterials in at least one of the two or more separation fractions comprises a greater population of the monolayer nanomaterials, bilayer nanomaterials, or a combination thereof as compared to adjacent separation fractions; wherein said nanomaterial is rhenium disulfide.

22. The method of claim 21 wherein the planar nanomaterials comprise mono- and bi-layer rhenium disulfide nanomaterials.

23. The method of claim 21 wherein the one or more surface active components comprise a planar organic group.

24. The method of claim 23 wherein the one or more surface active components is sodium cholate.

25. The method of claim 21 wherein said aqueous fluid medium comprises iodixanol.

26. The method of claim 25 wherein said component introduced to said fluid medium is CsCl.

27. The method of claim 21 wherein a subpopulation of at least one of the two or more separation fractions is deposited on a substrate.

28. The method of claim 27 wherein a substrate and rhenium disulfide deposited thereon are incorporated into an electronic device.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the office upon request and payment of the necessary fee.

(2) FIGS. 1A-I. (A) Experimental procedure to enrich few-layer ReS.sub.2 nanosheets (digital images). ReS.sub.2 powder is exfoliated in water with 2% w/v sodium cholate (SC) using tip ultrasonication (step 1) and then centrifuged at 7,500 rpm for 10 min to remove unexfoliated ReS.sub.2 powder (step 2). The supernatant is subsequently collected and ultracentrifuged at 20,000 rpm for 30 min to sediment large nanosheets (step 3). The sediment is finally redispersed in water with 2% w/v SC. (B) Optical absorbance spectrum of the resulting ReS.sub.2 aqueous dispersion with a peak at 811 nm. Inset: photograph of the as-prepared ReS.sub.2 dispersion with the schematic illustrating ReS.sub.2 nanosheets surrounded by SC. (C) Atomic force microscopy (AFM) image of solution-processed ReS.sub.2 following deposition on a Si wafer. (D) A schematic of the atomic structure of ReS.sub.2 (blue: Re atom; yellow: S atom; red dotted line: Re chain direction). (E) A transmission electron microscopy (TEM) image of a ReS.sub.2 nanosheet and a high-resolution TEM (HRTEM) image. The red arrow indicates the direction of a Re chain. (F) Selected area electron diffraction (SAED) pattern of a ReS.sub.2 nanosheet. X-ray photoelectron spectroscopy (XPS) data for the (G) Re 4f and (H) S 2p core levels. (I) Raman spectrum of ReS.sub.2 nanosheets.

(3) FIGS. 2A-B. (A) Reference X-ray photoelectron spectroscopy (XPS) data for the Re 4f core level (FIG. 1G). (B) Depth profiling confirms that the 42.7 eV Re 4f.sub.7/2 peak is related to ReS.sub.2, since ion depth profiling preferentially removes S, giving rise to metallic ReS.sub.2-x.

(4) FIGS. 3A-D. (A) Solid-state PL spectrum of assembled ReS.sub.2 thin films. Two Voigt fitted curves at 1.47 eV (red) and 1.60 eV (green) indicate contributions from thick and thin nanosheets. (B) Liquid-phase photoluminescence excitation (PLE) plot of a ReS.sub.2 dispersion showing an emission peak at 757 nm. The water OH Raman mode is the linear feature in the upper left corner of the PLE plot. (C) Wavelength-dependent I-V characteristics of a ReS.sub.2 thin film device in the dark and under illumination (L=5 m, W=4380 m). The spot size of the Gaussian beam is 0.36 mm.sup.2. Inset: optical image of the interdigitated electrode array preceding ReS.sub.2 thin film transfer. (D) Normalized photocurrent (I.sub.pc) versus wavelength (blue: V.sub.d=50 V, red: V.sub.d=50 V).

(5) FIGS. 4A-B. I-V curve of a ReS.sub.2 thin film before (A) and after (B) annealing at 100 C. for 10 min in ambient conditions.

(6) FIG. 5. Output power spectrum for the xenon lamp obtained through the monochromator and fiber cable.

(7) FIGS. 6A-C. (A) Buoyant density model for SC-encapsulated ReS.sub.2 in aqueous solution, where N is the number of ReS.sub.2 layers, t.sub.ReS2 is the thickness of a ReS.sub.2 layer, t.sub.A is the anhydrous layer thickness, t.sub.H is the hydration shell thickness, and is the packing density. (B) Buoyant density as a function of ReS.sub.2 layer number. The black line represents the expected buoyant density when ReS.sub.2 is encapsulated with SC in water. The red and green lines indicate the density limit of iodixanol and CsCl, respectively. (C) Density profiles of different density gradient media after ultracentrifugation.

(8) FIGS. 7A-B. Density profiles of (A) iodixanol (diffusion coefficient, D=0.035 cm.sup.2/s) and (B) CsCl (D=0.38 cm.sup.2/s) before (black) and after 3 hr (red), 6 hr (green), and 12 hr (blue) of density gradient ultracentrifugation (DGU), respectively.

(9) FIGS. 8A-E. (A) ReS.sub.2 layer sorting iDGU process flow (digital images). After process steps 1 to 3 (FIG. 1A), the collected ReS.sub.2 dispersion is placed onto a step gradient (step 4). After the concentration process (step 5), the ReS.sub.2 supernatant is placed in a linear density gradient (step 6). After iDGU, the ReS.sub.2 dispersion is separated by thickness and layer number (step 7). (B-E) Centrifuge tube digital images and corresponding density profiles for steps 4 to 7.

(10) FIGS. 9A-D. (A) A digital image of the product of step 4 (before step gradient DGU). Dark ReS.sub.2 dispersion is placed onto the density gradient medium. Digital images of different density gradient medium-surfactant combinations after step 5. (B) Iodixanol (Iod) with Pluronic F68. Pluronic F68 is utilized to reduce the buoyant density by increasing the hydration layer thickness. (C) Iod and CsCl mixture with Pluronic F68. A density of 1.54 g/cm.sup.3 is obtained by mixing 50 mL of iodixanol with 15 g CsCl. White unstable precipitates are observed due to the low water solubility of Pluronic F68 (10% at room temperature). (D) Iod and CsCl mixture with sodium cholate (SC). The water solubility of SC is 40% at room temperature, providing a stable dark brown ReS.sub.2 dispersion after step 5.

(11) FIGS. 10A-B. (A) Optical absorbance spectra of each fraction (F1-F13) after layer sorting, and (B) the actual concentrations extracted from Beer's law using the extinction coefficient =1216 Lg.sup.1 m.sup.1.

(12) FIGS. 11A-G. (A) ReS.sub.2 band separation in a centrifuge tube after iDGU with the buoyant density (blue) and concentration (red) of each fraction. (B) AFM images of ReS.sub.2 nanosheets from F4 and F10 on a Si substrate. (C) Fit of the buoyant density model to the experimental data. (D-E) Thickness and area histograms extracted from AFM measurements for F4 (red), F10 (green), and sedimented ReS.sub.2 (blue) with Gaussian fitting curves. (F) Raman spectra measured on F4, F10, sedimented ReS.sub.2, and concentrated ReS.sub.2. (G) PL spectra obtained from F4 (red), F10 (green), and sedimented ReS.sub.2 (blue) with overlaid Voigt fitting curves. The peak positions are at 1.58 eV (red), 1.53 eV (green), and 1.51 eV (blue).

(13) FIG. 12. The extinction coefficient of ReS.sub.2 dispersion is obtained to be 1216 Lg.sup.1 m.sup.1 by plotting the absorbance per length (A/l) at 700 nm versus the concentration of ReS.sub.2.

DETAILED DESCRIPTION OF CERTAIN EMBODIMENTS

(14) As can relate to certain non-limiting embodiments, the present invention can be directed to the exfoliation and layer-by-layer iDGU sorting of high-density ReS.sub.2 in aqueous surfactant solutions, using density gradient media based on mixtures of iodixanol and CsCl that combine the high viscosity of iodixanol with the high buoyant density of CsCl. Successful layer-dependent separation of ReS.sub.2 by iDGU is confirmed with a variety of characterization methods including atomic force microscopy (AFM), Raman spectroscopy, and PL spectroscopy. Solution-processed ReS.sub.2 thin films are also shown to provide a photocurrent response that is consistent with optical absorbance and PL spectra. Overall, this invention provides a scalable means for producing optoelectronically functional ReS.sub.2 nanosheets with well-defined thicknesses in a manner that can be generalized to other high-density nanomaterials.

(15) FIG. 1A schematically illustrates preparation of ReS.sub.2 aqueous dispersions. Initially, ReS.sub.2 powder is exfoliated via ultrasonication in deionized water with the amphiphilic small molecule surfactant sodium cholate (SC). The resulting dispersion is then centrifuged at 7,500 rpm to remove unexfoliated ReS.sub.2 powder, and then further ultracentrifuged at 20,000 rpm to collect nanosheets with relatively large lateral sizes. The resulting optical absorbance spectrum is provided in FIG. 1B, which shows a peak at 811 nm that is consistent with the PL emission position from previous literature reports. As-prepared ReS.sub.2 dispersions are dark brown in color (FIG. 1B, inset). In FIG. 1C, an atomic force microscopy (AFM) image of the solution-processed ReS.sub.2 nanosheets on Si confirms the ReS.sub.2 nanosheet morphology and the mechanical integrity of the dispersed flakes. For reference, a schematic of the ReS.sub.2 atomic structure is provided in FIG. 1D, with the Re atoms (blue), S atoms (yellow), and Re chain direction (red arrow) indicated.

(16) The ReS.sub.2 structure of FIG. 1D is verified with atomic-scale characterization by transmission electron microscopy (TEM). Specifically, a droplet of ReS.sub.2 solution is deposited onto holey carbon TEM grids for bright-field and high-resolution TEM (HRTEM) analysis. FIG. 1E shows a low-resolution TEM image of a ReS.sub.2 nanosheet accompanied by a magnified HRTEM image. These images show a cleavage direction along the Re chains, which is consistent with literature precedent. (See, e.g., Lin, Y. C.; Komsa, H. P.; Yeh, C. H.; Bjorkman, T.; Liang, Z. Y.; Ho, C. H.; Huang, Y. S.; Chiu, P. W.; Krasheninnikov, A. V.; Suenaga, K. ACS Nano 2015, 9, 11249-11257.) Furthermore, in FIG. 1F, the expected ReS.sub.2 crystal structure is confirmed with selected area electron diffraction (SAED), thus showing that the solution-processed ReS.sub.2 nanosheets maintain their original crystalline nature without phase transformations.

(17) The chemical state of the ReS.sub.2 nanoflakes are probed with X-ray photoelectron spectroscopy (XPS). Core level XPS spectra for Re 4F (FIG. 1G) and S 2p (FIG. 1H) show Re 4f.sub.7/2 and S 2p.sub.3/2 subbands at 42.7 eV and 163.1 eV, respectively, which are close to the expected values for bulk ReS.sub.2. (Depth-profiled XPS measurements, presented in FIG. 2, corroborate the existence of unoxidized ReS.sub.2.) A Raman spectrum taken on solution-processed ReS.sub.2 is presented in FIG. 1I, where six Raman modes (labeled I to VI) are observed at 137 cm.sup.1, 145 cm.sup.1, 153 cm.sup.1, 163 cm.sup.1, 215 cm.sup.1, and 238 cm.sup.1, respectively. These modes further confirm the integrity of the solution-processed ReS.sub.2 nanoflakes and correspond to E.sub.g-like (I to IV) and A.sub.g-like (V and VI) vibrations.

(18) The semiconducting direct bandgap nature of ReS.sub.2 is investigated in FIG. 3. In particular, FIG. 3A shows a PL spectrum (532 nm excitation) from a ReS.sub.2 thin film assembled from solution. The PL spectrum possesses an emission doublet at 1.47 eV (red Voigt fitted line) and 1.60 eV (green Voigt fitted line), presumably related to PL emission from thick and thin nanosheets. These results are consistent with previous reports that have shown that the PL emission from ReS.sub.2 blue-shifts in the ultrathin limit due to quantum confinement effects. Solution-based photoluminescence excitation (PLE) mapping is shown in FIG. 3B for excitation wavelengths ranging from 400 nm to 540 nm and emission wavelengths ranging from 600 nm to 1000 nm. The emission peak at 758 nm (1.64 eV) for the ReS.sub.2 solution likely differs from the peak position for the thin film sample (FIG. 3A) due to differences in the surrounding dielectric environment.

(19) Charge transport measurements are performed on the ReS.sub.2 thin films to verify that electronic and photoconductive properties are preserved following solution processing. Bottom-contacted ReS.sub.2 devices are fabricated with interdigitated electrodes on thermally oxidized Si wafers (inset of FIG. 3C) and then annealed in ambient conditions at 100 C. for 10 min to improve flake-flake contacts. Symmetric, linear current-voltage (I-V) output characteristics at low biases suggest Ohmic contact between the Au electrodes and the ReS.sub.2 thin film (FIG. 4). Non-linearity in I-V curves at high bias can be attributed to space-charge limited transport. Transfer characteristics reveal negligible gating (on/off ratio 1.1) due to high screening and thus weak field penetration in this film (thickness: 20623 nm). Nevertheless, the measured sheet conductivity of 1.6510.sup.2 S/m is among the highest reported for solution-processed nanomaterial thin films and exceeds that of solution-processed MoS.sub.2 thin films by 8 orders of magnitude. FIG. 3C compares the wavelength-dependent dark and illuminated output characteristics for a ReS.sub.2 thin film device from 550 nm to 1050 nm. FIG. 3D shows the photocurrent (I.sub.pc=I.sub.lightI.sub.dark) as function of wavelength at V.sub.d=50 V and 50 V. The I.sub.pc curves are normalized to an incident power of 1 W for all wavelengths (starting power fluence is 510.sup.5 W/m.sup.2) by accounting for the measured power spectrum of the Xe arc discharge lamp irradiation source (FIG. 5). The resulting photocurrent shows a peak at 800 nm in agreement with the optical absorbance (FIG. 1B) and PL measurements (FIG. 3A-B).

(20) While the aforementioned results show that ReS.sub.2 can be effectively exfoliated using aqueous surfactant solutions, the resulting ReS.sub.2 nanoflakes are polydisperse with respect to thickness and layer number. Consequently, it is an objective of this invention to adapt iDGU to the high-density limit in order to achieve layer-by-layer sorting of ReS.sub.2. Towards this end, FIG. 6A shows a geometrical buoyant density model that allows the constraints on the density gradient medium for ReS.sub.2 iDGU to be determined. Specifically, the density profile for SC-encapsulated ReS.sub.2 is given by:

(21) $\begin{array}{cc}\left(N\right)=\frac{{}_{S}N+2m_{\mathrm{sc}}+2{}_{H_{2}O}{t}_H}{\left(N+1\right)t_{{\mathrm{ReS}}_2}+2t_A+2t_H}& \left(1\right)\\ =\frac{{}_{S}N+2m_{\mathrm{sc}}+2{}_{H_{2}O}{t}_H}{\left(N+1\right)t_{{\mathrm{ReS}}_2}+2V_{\mathrm{sc}}+2t_H}& \left(2\right)\end{array}$
where .sub.ReS2=3.4110.sup.7 g/cm.sup.2 is the sheet density of ReS.sub.2, m.sub.sc=7.1510.sup.22 g is the mass of one SC molecule, a is the surface packing density of SC on a ReS.sub.2 nanosheet, p.sub.H2O=1 g/mL is the density of water, t.sub.H is the equivalent hydration shell thickness, and t.sub.A=V.sub.SC is the equivalent anhydrous shell thickness of SC. The calculated buoyant density as a function of ReS.sub.2 layer number is shown in FIG. 6B. Evidently, SC-encapsulated ReS.sub.2, even for monolayers, is predicted to possess a buoyant density than exceeds the iodixanol density limit (.sub.max=1.32 g/cm.sup.3), but is less than the CsCl density limit (.sub.max=1.9 g/cm.sup.3).
While CsCl has sufficiently high density for ReS.sub.2 iDGU, the diffusion coefficient of CsCl (0.38 cm.sup.2/s) in aqueous solution is 10 higher than that of iodixanol (0.035 cm.sup.2/s) at room temperature; which implies that a linear gradient is formed throughout the entire solution after fewer than 3 hours of ultracentrifugation (FIG. 7). This observation is consistent with the Lamm equation, which describes the time evolution of the density profile (d/dt):

(22) $\begin{array}{cc}\frac{d_{}}{\mathrm{dt}}=\frac{1}{r}\frac{d}{\mathrm{dr}}\left[\mathrm{rD}\frac{d_{}}{\mathrm{dr}}-s{}^2{r}^2\right]& \left(3\right)\end{array}$
where r is the distance from the center of rotation, t is time, s is the sedimentation coefficient, D is the diffusion coefficient, and cow is the rotor angular velocity. (Brown, P. H.; Schuck, P. Comput. Phys. Commun. 2008, 178, 105-120.) To further illustrate the differences between CsCl and iodixanol, FIG. 6C compares the experimental density profiles of CsCl (linear) and iodixanol (nonlinear). Since nonlinear density gradient profiles provide the best sorting efficacy, an adjuvant component such as CsCl cannot be used directly as a replacement for iodixanol. In contrast, by forming a mixture between iodixanol and CsCl, FIG. 6C shows that the desirable gradient nonlinearity of iodixanol and the higher maximum buoyant density of CsCl are achieved concurrently.

(23) By utilizing mixtures of iodixanol and CsCl, layer-sorting of ReS.sub.2 can be achieved by iDGU as shown in FIG. 8. In particular, ReS.sub.2-SC dispersions prepared according to FIG. 1A (steps 1 to 3) are placed in a step density gradient (=1.54 g/cm.sup.3, step 4) and then ultracentrifuged to yield a concentrated ReS.sub.2-SC dispersion (step 5) with buoyant density less than 1.54 g/cm.sup.3. Following step 5, the concentrated dispersion is fractionated and then CsCl powder is added to adjust the buoyant density to 1.58 g/cm.sup.3 after which the resulting solution is placed at the bottom of a linear density gradient (1.38 to 1.54 g/cm.sup.3, step 6). Subsequent ultracentrifugation drives ReS.sub.2 layer sorting. (It should be noted that ReS.sub.2 dispersions prepared with Pluronic F68 in place of SC precipitate after step 5 due to the low water solubility of the dispersant. Reference is made to FIG. 9). Following iDGU, the ReS.sub.2-SC nanosheets form bands at their respective isopycnic points throughout the ultracentrifuge tube (step 7). A piston gradient fractionator is then used to recover the sorted ReS.sub.2 in 2 mm steps (a number, n, of separation fractions F; in this instance, F1 to F13). FIGS. 8B-E present photographs of the centrifuge tubes and their respective density profiles for steps 4 to 7.

(24) Following iDGU, optical absorbance spectra for fractions F1 to F13 are measured (FIG. 10), and used to extract the ReS.sub.2 concentration using Beer's law. In FIG. 11A, these concentration results (red line) along with the buoyant density (blue line) are plotted against fraction number. Fractions F4 and F10 have a higher concentration than adjacent fractions, consistent with the band positions in the photograph of FIG. 11A. FIG. 11B shows AFM images of F4 and F10 with average thickness values of 1.030.11 nm and 2.090.09 nm, respectively. The measured thicknesses are slightly larger than previously reported values for monolayer and bilayer ReS.sub.2, likely due to residual hydration layers and surfactants. On the basis of the measured thickness and buoyant density values, the ReS.sub.2 experimental data are plotted with the geometrical buoyant density model in FIG. 11C. By fitting the density model to the experimental data, the values of and t.sub.H are determined to be =1.410.sup.15 cm.sup.2 and t.sub.H=5.5 nm, respectively. The thickness and area histograms for F4 (red), F10 (green), and sedimented ReS.sub.2 (blue) with Gaussian fits are shown in FIGS. 11D-E, indicating that ReS.sub.2 separation is driven by thickness instead of lateral size as expected for iDGU.

(25) F4, F10, sedimented ReS.sub.2, and concentrated ReS.sub.2 are further examined by Raman and PL spectroscopy in FIGS. 11F-G. The Raman spectra indicate that the weak interlayer interaction for ReS.sub.2 results in a decoupling of lattice vibration modes. In particular, no noticeable peak shift with layer number is observed, in contrast to thickness-dependent MoS.sub.2 Raman modes. However, the peak intensity of the IV mode (in-plane, E.sub.2g-like) is decreased and the V mode (out-of-plane, A.sub.1g-like) is stiffened by 2 cm.sup.1 with decreasing layer number, consistent with previous results. The PL spectra for F4, F10, and sedimented ReS.sub.2 occur at 1.58 eV (red), 1.53 eV (green), and 1.51 eV (blue), respectively, which is expected based on previous reports that found ReS.sub.2 layer-dependent quantum confinement effects. Compared to other TMDCs such as MoS.sub.2 and WS.sub.2, the PL emission energy for ReS.sub.2 possesses a weaker thickness dependence, which further supports the weak interlayer interactions that have been postulated for ReS.sub.2.

EXAMPLES OF THE INVENTION

(26) The following non-limiting examples and data illustrate various aspects and features relating to the methods and/or density gradient media of the present invention, including the sorting of high density 2D nanomaterials. In comparison with the prior art, the present methods and media provide results and data which are surprising, unexpected and contrary thereto. While the utility of this invention is illustrated through the use of several 2D nanomaterials, density gradient media, media adjuvant components and surface active components which can be used therewith, it will be understood by those skilled in the art that comparable results are obtainable with various other nanomaterials, media, media adjuvant components and surface active components, as are commensurate with the scope of this invention.

Example 1

(27) ReS.sub.2 Dispersion Preparation.

(28) 0.5 g of ReS.sub.2 powder (American Elements) and 90 mL of 2% w/v sodium cholate (SC, Sigma Aldrich) surfactant aqueous solution were placed in a 120 mL stainless steel beaker. The mixture was ultrasonicated (Fisher Scientific Model 500 Sonic Dismembrator) with a 0.5-inch diameter flat tip for 2 hours at a power level of 70 W in an iced bath (step 1). The as-prepared ReS.sub.2 dispersion was centrifuged at 7,500 rpm (Avanti J-26 XP, Beckman Coulter) for 10 min to remove unexfoliated ReS.sub.2 powder (step 2). Following the centrifugation, the supernatant was carefully decanted and ultracentrifuged at 20,000 rpm for 30 min using a SW32Ti rotor (Optima L-80 XP, Beckman Coulter) to collect large nanosheets (step 3). The sediment was redispersed in 10 mL of 2% w/v SC solution by bath sonication for 30 min.

Example 2

(29) Optical absorbance spectroscopy. Optical absorbance spectra of the ReS.sub.2 dispersion were measured using a Cary 5000 spectrophotometer (Agilent Technologies). A cuvette with 1 cm path length was used for the measurement, and the baseline from the surfactant solution was subtracted from the spectra. To extract the ReS.sub.2 extinction coefficient, different volumes of ReS.sub.2 dispersion after step 3 were collected by vacuum filtration on an anodized alumina (AAO) membrane with 20 nm pore size and rinsed with 50 mL of deionized water to remove the surfactant. The actual concentration of ReS.sub.2 nanosheets was calculated from the weight difference on the AAO membrane before and after filtration. Using Beer's law, the ReS.sub.2 extinction coefficient was extracted from the slope of a plot of A/l with respect to the ReS.sub.2 concentration (FIG. 12).

Example 3

(30) Raman/Photoluminescence (PL) Spectroscopy.

(31) Raman/PL spectra of ReS.sub.2 nanosheets filtered on an AAO membrane were collected using a Horiba Xplora Raman/PL system with an excitation wavelength of 532 nm. The signal was collected for 30 sec using a 100 objective with a 2400 gr/mm grating for Raman spectra and a 600 gr/mm grating for PL spectra.

Example 4

(32) Photoluminescence Excitation (PLE) Spectroscopy.

(33) The ReS.sub.2 sediment after step 3 was redispersed in deionized water without surfactant to minimize the surfactant concentration. PLE mapping for the resulting ReS.sub.2 dispersion was obtained using a Horiba Fluorolog-3 spectrofluorometer. Each line spectrum was collected using solutions in a quartz cuvette with an acquisition time of 6 sec and a 10 nm slit width.

Example 5

(34) Atomic force microscopy (AFM).

(35) Si substrates were rinsed with acetone and isopropyl alcohol (IPA) and immersed in diluted (3-aminopropyl)-triethoxysilane (APTES) solution to promote nanosheet adhesion. ReS.sub.2 dispersion was dropcasted and dried on the pre-annealed substrate at 80 C. for 10 min. After the dispersion was fully dried, the substrate was mildly rinsed with deionized water to remove surfactant. The substrate was loaded on an Asylum Cypher AFM with Si cantilevers (290 kHz resonant frequency), and AFM images were obtained in tapping mode at a scanning rate of 0.4 Hz using a minimum of 512 pixels per line.

Example 6

(36) Transmission Electron Microscopy (TEM).

(37) A droplet of ReS.sub.2 dispersion was deposited on a holey carbon TEM grid (Ted-Pella) and dried with N.sub.2. TEM images were acquired using a JEOL JEM-2100 with an accelerating voltage of 200 keV under a TEM column pressure of 10.sup.7 Torr.

Example 7

(38) X-Ray Photoelectron Spectroscopy (XPS).

(39) XPS measurements were performed using a high vacuum Thermo Scientific ESCALAB 250 Xi XPS system at a base pressure of 110.sup.9 Torr. The XPS data had a binding energy resolution of 0.1 eV using a monochromated Al K.sub. X-ray source at 1486.7 eV (400 m spot size). All core-level spectra were the average of five scans taken at a 100 ms dwell time using a pass energy of 15 eV. When using charge compensation, all core levels were charge-corrected to adventitious carbon at 284.8 eV. Up to 25 nm deep depth profiles were made in the ReS.sub.2 thin films using a 3000 keV ion gun (ca. 0.40 nm/s etch rate). Using the software suite Avantage (Thermo Scientific), all subpeaks were determined in a manner detailed in the literature.

Example 8

(40) ReS.sub.2 Thin Film Transfer for Photocurrent Measurements

(41) ReS.sub.2 films were prepared using vacuum filtration. 4 mL of ReS.sub.2 dispersion prepared by steps 1 to 3 in FIG. 1A was diluted in 50 mL of deionized water and filtered through an anodized alumina (AAO) membrane with 20 nm pore size (Anodisc, Whatman). The residual surfactant was then rinsed with 100 mL of deionized water.

(42) Separately, electrodes were patterned on thermally oxidized silicon wafers (300 nm thick SiO.sub.2) by photolithography. Interdigitated electrodes (3 nm Ti/70 nm Au) were fabricated with varying channel length and width. ReS.sub.2 films prepared by vacuum filtration were transferred onto the electrode patterns. In particular, the films were first floated onto 3 M NaOH for 3 hours to etch the AAO membrane, neutralized with deionized water, and then transferred on the device substrate with interdigitated Au electrodes. The resulting film was subjected to an anneal at 80 C. for 30 min to dry the residual water.

Example 9

(43) Electrical and Photocurrent Measurement.

(44) All ReS.sub.2 devices were measured at room temperature under vacuum (pressure <510.sup.5 Torr) using a probe station (LakeShore CRX 4K) equipped with Keithley source-meters and home-built LabView programs. Spectrally resolved light illumination was achieved by a 250 W Xenon arc discharge lamp coupled with a monochromator (Newport 74125). Light was focused into the input slit of the monochromator by a lens (Thor Labs) to increase the net power output. The monochromator was connected to the probe station via a fiber optic cable. The highest power (at wavelength of 600 nm) at the end of the fiber cable terminating inside the vacuum chamber was measured to be 2.5 W by a power meter fitted with a silicon photodiode (Thor Labs). FIG. 5 shows the power spectrum of the output light from the fiber cable. The linewidth of the spectrally resolved light was measured to be 20 nm, independent of wavelength. Photocurrent measurements were conducted by measuring DC current-voltage characteristics in dark and under illumination (I.sub.photocurrent=I.sub.lightI.sub.dark). The photocurrent was normalized with respect to the lamp power spectrum to ensure that the effective incident light power was 1 W at all wavelengths. For photoconductivity measurements, ReS.sub.2 were annealed at 100 C. for 10 min in ambient to improve overall conductivity. FIG. 4 shows the change in the I-V characteristics upon annealing.

Example 10

(45) Thickness Sorting of ReS.sub.2 Nanosheets.

(46) After step 2 of the ReS.sub.2 dispersion preparation process in FIG. 1A, the sediment from unexfoliated ReS.sub.2 powder was re-sonicated for further exfoliation. After five iterations of this recycling process, 28 mL of as-prepared ReS.sub.2 dispersion was placed onto 10 mL of density gradient medium (density of 1.54 g/cm.sup.3) with 2% w/v SC (step 4). The density gradient medium was prepared by mixing 50 mL of iodixanol with 15 g of CsCl powder. The resulting step gradient was ultracentrifuged for 6 hours at 32,000 rpm and 22 C. (step 5).

(47) Following step 5, the concentrated ReS.sub.2 dispersion was recovered in 1 mm steps using a piston gradient fractionator (BioComp Instruments). After the density of concentrated ReS.sub.2 dispersion was modified to 1.58 g/cm.sup.3 by adding CsCl powder, this dispersion was placed between a linear density gradient (density of 1.38 to 1.54 g/cm.sup.3) and a step gradient (density of 1.65 g/cm.sup.3) (step 6), and then thickness sorting of ReS.sub.2 was carried out via isopycnic density gradient ultracentrifugation (iDGU) for 12 hr at 32,000 rpm and 22 C. (step 7).

(48) For the microscopic and spectroscopic analysis, the layer-sorted ReS.sub.2 dispersion was recovered in 2 mm steps using a piston gradient fractionator. These fractions were labeled as Fn, where n increases with the order of recovery from the top. The recovered fractions were placed in a dialysis cassette (20,000 molecular weight cutoff, Thermo Scientific) and dialyzed in 750 mL of deionized water bath for 48 hours to remove the density gradient medium and excess SC. Following dialysis, each solution was ultracentrifuged for 1 hour at 41,000 rpm using a SW41Ti rotor (Optima L-80 XP, Beckman Coulter) and then redispersed with 5 mL of deionized water.

Example 11

(49) A variety of surface active components can be 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 can be 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 can be useful in conjunction with this invention.

(50) 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 and bilayer 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 glycoursodeoxycholates. 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. Other surface active components include but are not limited to 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.

Example 12

(51) 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, one or more suitable adjuvant components or additives introduced thereto 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 and components/additives can be used in methods of the present teachings, as would be understood by those skilled in the art.

(52) 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 and CsCl include other inorganic salts (such as Cs.sub.2SO.sub.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.

(53) As shown, the present invention demonstrates preparation of stable ReS.sub.2-SC aqueous dispersions with concentrations in excess of 0.2 mg/mL. The solution-processed ReS.sub.2 nanosheets are characterized with a comprehensive set of microscopic and spectroscopic methods, which confirm that the structure and properties of solution-exfoliated ReS.sub.2 are comparable to micromechanically exfoliated ReS.sub.2. Furthermore, solution-processed ReS.sub.2 thin films show significantly higher electrical conductivity than previously reported solution-processed TMDCs. Additionally, photocurrent measurements on ReS.sub.2 thin films show spectroscopic features that are consistent with optical absorbance and PL measurements. Despite the high buoyant density of ReS.sub.2, iDGU is used to achieve thickness sorting of ReS.sub.2 nanosheets by employing a mixture of iodixanol and CsCl as the density gradient medium. Characterization of the resulting layer-by-layer sorted ReS.sub.2 dispersions show weak thickness dependence in the Raman and PL spectra, which confirms weak interlayer coupling in ReS.sub.2 compared to other TMDCs. Overall, this work demonstrates effective solution-based exfoliation and thicknesses sorting for ReS.sub.2.