Preparation of Liquid-exfoliated Transition Metal Dichalcogenide Nanosheets with Controlled Size and Thickness: A State of the Art Protocol

Sample preparation

The samples described here are produced by tip sonication. Alternative exfoliation procedures can be used, but will lead to different concentrations, lateral sizes and degrees of exfoliation. Higher amplitudes and longer on pulses during the sonication should be avoided to prevent damaging of the sonicator. Similar results were obtained using 500 W processors. However, sonication time and amplitude has an impact on the nanosheet exfoliation and variations from this protocol may result in different nanosheet sizes and concentrations than presented here. We emphasize that cooling is critical during the sonication, as heating can damage and degrade the nanosheets and deteriorate the resulting optical properties of the material obtained. While higher initial concentrations of the TMD powder can increase the nanosheet concentration beyond that obtained here, this does not occur linearly. For tip-sonication, the dispersed concentration typically saturates beyond initial TMD concentrations of 30-40 gL^-1.

The chosen size-selection cascade can be modified readily to suit a desired outcome. While this specific procedure yields nanosheet sizes and thicknesses over a broad size range in the different fractions, if only specific sizes are targeted the centrifugation steps can be skipped. For instance, if medium-sized nanosheets are desired, the sample can be centrifuged at only two different centrifugal accelerations and the sediment redispersed. Alternatively, more complex cascades can be applied to achieve monolayer enrichment (see ¹³ for further clarification). This flexibility in combination with the ability to redisperse the samples at high concentrations is a unique advantage of LCC over other size-selection protocols.

It is recommended to use filling heights in the centrifuge vials of < 10 cm for this protocol. If larger filling heights in the vials are used, the centrifugation times need to be increased to obtain comparable results. The sediment should always be pellet-like for efficient size selection and the supernatant decanted carefully and completely. If the sediment is not pellet-like, the centrifugation time needs to be increased. Higher temperatures (also during the centrifugation) should be avoided and samples are best stored in the refrigerator to minimize material degradation after preparation. If the centrifugation is carried out at lower temperatures, sedimentation is slower and centrifugation times may require adjustment. Different centrifuge and rotor geometries may result in length and thickness deviations from the representative data shown. However, despite these subtleties, in general, the size selection procedure is robust and can be applied to various materials in solvents as well as surfactants. The final supernatant after centrifugation at high accelerations is typically discarded, as it contains very small (< 30 nm) nanosheets with properties dominated by edges only. The size selection scheme can be carried out in any benchtop centrifuge (i.e., no ultracentrifuge is required opposed to density gradient centrifugation). Here, all centrifugations were performed at 15 °C for 2 h in each step using the 220R centrifuge (see Materials List). Two different rotors were used; for speeds ≤ 3,500 x g, a fixed angle rotor was employed where the centrifugation rate, f (in krpm) is related to the centrifugal force via RCF = 106.4 f². In this case, 28 mL glass vials containing ~10 mL aliquots = 10 cm filling height were used. For speeds > 3,500 x g, samples were centrifuged in 1.5 mL plastic centrifuged tubes in a fixed angle rotor, where f is related to the centrifugal force via RCF = 97.4 f ².

For the analysis of the nanosheet length, TEM is recommended as analysis tool due to the higher resolution compared to scanning electron microscopy and the higher throughput compared to AFM. Furthermore, AFM also has the disadvantage that lateral sizes are typically overestimated due to tip broadening and pixilation. Any conventional TEM even with acceleration voltages of 200 kV can be used. In this case, imaging was performed on holey carbon grids (400 mesh). For very small nanosheets, continuous film grids can be beneficial but are not required. In turn, AFM is recommended as analysis tool to determine nanosheet layer number. This is because TEM thickness determination by edge counting can be problematic, as nanosheets become thinner towards the edge, necessitating that multiple regions for each nanosheet would need to be inspected to determine the mean thickness. This is much less problematic when using AFM as the measured thickness is readily averaged over inhomogeneous nanosheets. For AFM analysis it is particularly critical to avoid re-aggregation of nanosheets on the wafer during solvent evaporation. To avoid this, it is recommended that the dispersion is drop-cast on pre-heated wafers. The water-carrier immediately evaporates and bubbles are formed, resulting in more uniform deposition compared to drop casting on wafers at lower temperature. Si/SiO₂ wafers with 200-300 nm oxide layer are recommended as nano-scaled objects can be seen with an optical microscope/optical zoom as blue spots.²² This is a useful guide to allocate regions of interest for imaging. The field of view should be adjusted according to nanosheet size. For the data presented here, AFM was carried out on 13 µm scanner in tapping mode. Typical image sizes ranged from 2 x 2 µm² to maximum 8 x 8 µm² for the larger nanosheets at scan rates of 0.4-0.7 Hz with 512 lines per image. Alternatively, depending on the specific AFM or scanner, scanning of larger areas at a higher resolution (e.g., up to 16 x 16 µm² with 1,024 lines) could be convenient. A typical image is shown in Figure 2A, B. Residual surfactant can make the thickness measurements very tedious especially for very small nanosheets that are more difficult to distinguish from surfactant. In this case, phase images can provide a guide, as they usually give a good contrast between different materials. If problems with residual surfactant persist, the wafers can be soaked in water overnight without significant loss of the nanosheets on the wafer.

In general, counting less than 150-200 nanosheets may be sufficient for samples with smaller mean size, as these tend to be less polydisperse. If a non-size-selected stock dispersion is analyzed, it is recommended that at least 200 nanosheets should be recorded. If solvents are used throughout the procedure instead of surfactant/water solutions, the dispersions have to be diluted with the respective solvent prior to deposition. Care must be taken during imaging not to bias the counting towards larger nanosheets, which are easier to discern. The concentration of the deposited dispersions is important as nanosheets tend to re-aggregate for excessive nanosheet concentrations, leading to inaccurate size/thickness determination. Outliers towards extreme nanosheet sizes on either the larger or smaller end can bias the statistics dramatically. In extreme cases, these should not be included in the determination of the mean values. Histograms are typically log-normal in shape²³ (Figure 2D, E). If this is not the case, the counting and/or imaging may be biased. From these histograms and the statistical analysis, the arithmetic number mean is obtained. This is typically also related to the volume fraction weighted mean value and therefore a valid measure of lateral size/thickness.

Size selection and metrics

Both mean nanosheet length, <L> and nanosheet thickness, <N> are reduced as the centrifugation rates are increased, i.e., as the dispersion progresses through the cascade. We can quantify these effects by plotting <L> (from TEM) as a function of the centrifugal acceleration (RCF) associated with the midpoint of centrifugation rates denoted as central RCF (Figure 2F). The mean nanosheet length falls off as (central RCF)^-0.5 for both MoS₂ and WS₂. At the same central centrifugal accelerations, the lateral sizes of MoS₂ are slightly larger than for WS₂ which is attributed to the lower density of the material. Similarly, <N> (from AFM statistics) is plotted versus central RCF in Figure 2G. It falls with central rotational speed via (central RCF)^-0.4. Interestingly, the data from MoS₂ and WS₂ roughly collapses on the same curve. Reasons for this behavior are currently not understood and require further exploration. In conclusion, smaller and thinner nanosheets are separated from larger and thicker ones as illustrated in Figure 2H.

Even though this may be expected from centrifugation, we note that this is not necessarily related to the centrifugation process alone. This is also because we consistently find for a number of materials exfoliated by sonication (MoS₂¹², WS₂¹³, MoO₃²⁴, black phosphorus¹⁶, GaS¹⁵) that thinner nanosheets tend to be smaller, while thicker nanosheets tend to be larger. An analysis of the lateral dimensions for nanosheets of a given thickness in each fraction previously showed that the mean length of the nanosheet is roughly constant within one sample for different thicknesses.¹³ This is interesting, as it implies that this centrifugation is a length separation process in first approximation. This suggests that equilibrium in the centrifugation is not reached after the relatively short centrifugation times of 2 h in each step so that, back diffusion and friction can play a prominent role. This also means that different nanosheet length-thickness relations can be produced by modifying the cascade.¹³

The spectral profile of optical extinction spectra strongly depends on nanosheets dimensions due to edge and confinement effects. Here we use the fractions produced by LCC to investigate the effect of nanosheet size and thickness on the extinction spectra of MoS₂ and WS₂. Extinction spectra measured in standard transmission contain contributions from both absorbance and scattering.^12,25 Absorbance spectra can be obtained by a measurement in the center of an integrating sphere where all scattered light is collected. In the resonant regime, i.e., where the nanomaterial absorbs light, the scattering spectrum follows the absorbance roughly in shape. Therefore, information encoded in an absorbance spectrum can be obtained from an analysis of extinction spectra.^12,13,15-17 In the non-resonant regime (above ~ 700 nm for MoS₂ and WS₂), the scattering exponent can be determined which is also related to the nanosheet (lateral) size. See references ^12,13,15-17.

As shown in Figure 3A and C, optical extinction spectra display the characteristic excitonic transitions,²⁶ but vary systematically with nanosheet size and thickness. In addition to variations in relative intensities across the entire spectral regions, shifts of the excitonic transitions are observed. This is best visualized from the second derivative spectra in the region of the A-exciton (Figure 3B and D).

Edge effects result in a dependence of the spectral profile on nanosheet length.¹² The changes in spectral shape with nanosheet lateral size can be rationalized by edges being electronically different from center regions. Therefore, the extinction coefficient associated with the nanosheet edge is different from extinction coefficients at the basal planes. This can be quantified via the ratio of extinction intensities at two different wavelengths. In principle, any peak intensity ratio can be related to the nanosheet size. However, the size metrics will be more reliable the larger the difference in the spectral shape at the given positions. Suitable examples are intensity ratios at the A-exciton to that at the local minima, Ext_A/Ext_min (Figure 3E) or at the high-energy maxima to that at the local minima, Ext_Max-HE/Ext_min, (Figure 3F).

The data in Figures 3E, F can be fitted to the following equation¹²

(Eq. 7)

Where ε_c is the extinction coefficient associated with the nanosheet basal plane, Δε ₌ ε_E – ε_c where ε_E is the edge region extinction coefficient, and L, x and k are the nanosheet length, edge thickness and length-width aspect ratio, respectively. We find this equation fits the data very well allowing us to generate functions relating the mean nanosheet length, L to the extinction peak intensity ratios (see equations 1 and 2). The intensity ratio Ext_A/Ext_min is extremely useful, as it can also be applied to solvent systems, where the solvent itself absorbs light in the UV region. However, it is less accurate and breaks down for smaller nanosheets. It is therefore recommended to use equation 2 involving Ext_Max-HE/Ext_min when the UV region is accessible.

As a result of these edge effects, extinction coefficients change as a function of nanosheet size (Figure 3G) making accurate concentration measurements of the nanosheets in the dispersion challenging. However, for both MoS₂ and WS₂, we were able to identify spectral positions, where the extinction coefficient is widely invariant with nanosheet size. For MoS₂, the extinction coefficient at 345 nm (ε_345nm(MoS₂) = 68 Lg^-1cm^-1) can be used as universal coefficient to determine dispersed concentration over a wide size range and for WS₂, the extinction coefficient at 235 nm (ε_235nm(WS₂) = 48 Lg^-1cm^-1) is widely size invariant.

In addition to length effects, the extinction spectra also contain information on mean nanosheet thickness. These result in shifts of the A-exciton position (Figure 3H) towards lower wavelengths as the nanosheet thickness is reduced. We determine the center of mass peak position of the A-exciton from the second derivatives to link changes in the spectral profile quantitatively to mean nanosheet thickness according to equations 5 and 6. Both MoS₂ and WS₂ follow a logarithmical relation with the same slope. We attribute these shifts to changes in the band structure with layer number and changes in the average dielectric constant around the TMD units with layer number.

The protocol describes the state-of-the-art liquid exfoliation of layered materials and their size selection by liquid cascade centrifugation. MoS₂ and WS₂ in aqueous surfactant solution are chosen as model systems. However, it can be applied to other layered materials or solvent systems. This versatility is a great strength, as it makes a broad range of materials with reasonably well-defined size available in liquids. In addition, a detailed description on the accurate lateral size and thickness determination using statistical microscopy is provided. Even though microscopy is widely used as an analysis tool, extreme care must be taken to obtain accurate and reliable statistics, as inadequate sample preparation (such as depositing high concentration samples) and inaccurate analysis and imaging can dramatically bias the statistical mean values.

Even though extremely important, this statistical microscopy is at the same time a bottle-neck in making high quality samples of liquid exfoliated nanomaterials accessible. This is simply because the procedure is tedious and time-consuming. In this manuscript, we also discuss an alternative to circumvent this problem. The principle is based on relating nanosheet sizes and thicknesses quantitatively to their optical spectra such as extinction spectra. These vary significantly and systematically as a function of size. This can be used to extract quantitative information on both nanosheet lateral size and thickness from the optical spectra. Such metrics are extremely powerful, as, once calibrated, they provide the nanosheet size and thickness information within minutes. The advantage of this is at least two-fold. On the one hand, they can be used to improve and understand both exfoliation and size selection by other techniques than the ones applied here. On the other hand, they offer the unique opportunity to produce samples with known size and thickness easily to enable the study of size effects both for fundamental studies and applications. In addition, it should be noted that the similarities between the MoS₂ and WS₂ metrics are highly encouraging and suggest that — with this protocol at hand — similar metrics can be established for other layered materials.