Equipartition of Energy Defines the Size–Thickness Relationship in Liquid-Exfoliated Nanosheets

Abstract

Liquid phase exfoliation (LPE) is a commonly-used method to produce 2D nanosheets from a range of layered crystals. However, such nanosheets display broad size and thickness distributions and correlations between area and thickness, issues which limit nanosheet application-potential. To understand the factors controlling the exfoliation process, we have liquid-exfoliated 11 different layered materials, size-selecting each into fractions before using AFM to measure the nanosheet length, width and thickness distributions for each fraction. The resultant data shows a clear power-law scaling of nanosheet area with thickness for each material. We have developed a simple non-equilibrium thermodynamics-based model predicting that the power-law pre-factor is proportional to both the ratios of in-planetearing/out-of-plane-peeling energies and in-plane/out-of-plane moduli. By comparing the experimental data with the modulus ratio calculated from first principles, we find close agreement between experiment and theory. This supports our hypothesis that energy equipartition holds between nanosheet tearing and peeling during sonication-assisted exfoliation.

Enriching and Quantifying Porous Single Layer 2D Polymers by Exfoliation of Chemically Modified van der Waals Crystals

“…Since sonication-assisted LPE has been shown to result in colloidally stable dispersions for ar ange of materials (see above) in reasonable yields without material specific optimization, we subjected 2D-P-1 to this process with the aim to improve the exfoliation quality and quantity.W ec hose sodium cholate (SC) in aqueous solutions as surfactant stabilizer rather than organic solvents due to the ease of handling.I np articular,i th as been demonstrated in the case of graphite/graphene that larger populations of monolayers can be obtained in aqueous surfactant compared to solvents. [25] Thea s-sonicated dispersion was then subjected to size selection by liquid cascade centrifugation (see Supporting Information). [5] In this iterative centrifugation process,asample is centrifuged with subsequently increasing relative centrifugal force (RCF,e xpressed in units of the Earths gravitational field, g).…”

“…Theexfoliation of the single crystalline 2D polymers 2D-P-1 and 2D-P-2 was investigated concerning nanosheet integrity and efficiency. Although sheet integrity did not turn out to be of amajor concern in both cases,only 2D-P-2 led to satisfactory results regarding exfoliation efficiency,monolayer content and sheet size.O nly the uncharged 2D-P-2 could be exfoliated in aqueous surfactant solution, where higher degrees of exfoliation [25] are expected. In case of the positively charged 2D-P-1, aloss of crystallinity is observed when using this efficient exfoliation medium.…”

“…Samples are labelled by indicating the lower and upper centrifugation rates.W hile nanosheet thickness control by LCC is poorer than by density gradient ultracentrifugation (DGU), [16] it has the advantage of higher yield and the possibility to produce ar ange of size/thickness distributions which is essential to quantify the efficiency of the exfoliation process. [25] Thes ize-selected fractions of 2D-P-1 exfoliated in aqueous SC were first deposited on Si/SiO 2 wafers and subjected to atomic force microscopy (AFM) to assess the result of exfoliation and size selection qualitatively.A ss hown by AFM imaging (Figure S1, Supporting Information), nanosheets with mostly sharp edges are obtained. As expected, nanosheets isolated at lower centrifugal acceleration are larger and thicker than nanosheets isolated at higher centrifugal accelerations,t hat is,t he stacks contain ad ifferent number of individual layers.I nf ractions isolated at high centrifugal accelerations (> 30k g), deposits with not welldefined shape are observed along with characteristic nanosheets.W hile these might be due to residual surfactant, it cannot be excluded that some disintegration of the sheets occurred.…”

“…[6] To test this,w e performed LPE in aqueous surfactant solution and size selection by cascade centrifugation, as in the case of the pyrylium-based 2D-P-1.W ec hose sodium cholate as surfactant stabilizer,asweexpect no specific,chemical interactions to occur which allows for ad irect comparison of the ease of exfoliation with other layered materials such as graphite as delineated below.Inaddition, we aim to establish astandard protocol that can potentially be applied to other organic sheet stacks regardless of their chemical structure.E xfoliation in solvents was also evaluated ( Figure S14) and seems to be dominated by solution thermodynamics similar to graphene and other layered compounds.T his is encouraging as it suggests that in contrast to 2D-P-1,2 D-P-2 can be treated analogous to inorganic crystals that have been extensively studied in LPE. While solvent exfoliation seems feasible,w e decided to focus on the water surfactant system in the following due to the potentially larger accessible monolayer contents, [25] as mentioned above.…”

Rapid and Low‐Temperature Salt‐Templated Production of 2D Metal Oxide/Oxychloride/Hydroxide

“…Recently, 2D materials such as graphene, metal oxide, metal carbide, metal dichalcogenides, and pure metal, have played an important role in electronics, sensors, optics, electrocatalysis, and energy storage, owing to the unique atomic thin feature, high specific surface area, and large aspect ratios. Many methods for the preparation of 2D materials have been explored, including liquid phase exfoliation (LPE), mechanical repeated folding and calendaring (RFC), chemical vapor deposition (CVD) or van der Waals epitaxy approach, and salt‐templated or molten salt‐templated method (MSM) . The liquid phase exfoliation method is confined to the layered materials (graphite, MoS 2 , and antimony), in which the layers are connected by van der Waals force.…”