Exfoliation mechanisms of 2D materials and their applications

Since the first report of mechanical exfoliation of monolayer graphene in 2005,¹ hundreds of two-dimensional (2D) materials, which are crystalline solids of one or few atomic thicknesses, have been synthesized using various exfoliation and deposition techniques. These 2D materials have attracted significant attention due to their unprecedented mechanical strength,^2–4 electrical and thermal conductivities,⁵ extremely high surface area-to-volume ratio,⁶ and quantum mechanical effects.⁷ Despite numerous unique properties, wafer-scale applications of 2D materials have been limited due to the lack of scalable synthesis or fabrication processes. Bottom-up processes such as chemical vapor deposition (CVD)^8–11 and physical vapor deposition (PVD)^12–14 can deposit few-layer and low-defect density 2D materials on the desired substrate but are costly and time-consuming so face significant challenges in commercial-scale applications. Fortunately, most applications do not require monolayer precision for 2D material thicknesses, including reinforcements for composites,^15–17 solid lubrication,^18,19 conductive inks,^20–22 purification and filtering,^23–25 drug delivery,^26,27 biomarkers,²⁸ coatings,^29,30 or supercapacitors.^31–33 Exfoliation processes such as micromechanical cleavage, ball milling, and electrochemical intercalation (Fig. 1) can produce few-layer or even monolayer 2D materials that are hundreds of micrometers wide and, for certain techniques, in bulk quantities. Meanwhile, shear flow and ultrasonication exfoliation techniques tend to produce laterally smaller 2D materials sheets but in greater quantities and as a continuous process. These different exfoliation techniques present a wide variance in processing time, yield, and material quality, which makes it essential to choose the proper process for a given application, material, or resulting quality. There exists a series of excellent reviews on specific exfoliation processes;^34–36 however, the present work aims to present a comprehensive comparison between the various exfoliation techniques including discussions on the underlying mechanisms, material quality (e.g., density of defects), yield, and respective end-use applications to aid the reader in selecting the most appropriate synthesis method.

Within most layered materials such as graphene, molybdenum disulfide (MoS₂), or hexagonal boron nitride (hBN), weak van der Waals bonds act to hold the layers together in the (001) direction, while covalent bonds act within the layers in the (100) and (010) directions. The van der Waals bonds have a weaker bond strength (0.4–4 kJ/mol) accompanied by a longer bond length (0.3–0.6 nm), whereas covalent bonds possess a stronger bond strength (e.g., 345 kJ/mol for C–C bonds) accompanied by a much shorter bond length (∼0.154 nm for C–C). Therefore, it is easy to separate these layers in the (001) plane by mechanical, chemical, or electrochemical techniques by overcoming the weak van der Waals forces. By exfoliating the bulk material into individual sheets of nanometer thickness, a wide variety of unique material properties are enabled that are not present in their bulk form. For example, the surface area-to-volume ratio is dramatically increased by exfoliation, thereby enhancing the reactivity and catalytic capability of these materials.³⁷ Additionally, in a bulk crystal, the nature of the electronic wave function is three-dimensional, while electrons are limited to planar dimensions when the material is confined to 2D. The confinement results in a 2D electron wave function that modifies the band structure of the material.^38,39 Furthermore, the vibration of surface atoms is not restricted in the out-of-plane direction, leading to the appearance of forbidden phonon modes and surface properties.⁴⁰ 2D materials thereby exhibit uniquely enhanced physical, electrical, and chemical properties compared to their bulk counterparts.

The first-ever atomically thin material exfoliated from its bulk counterpart was graphene.⁴¹ Its excellent electron mobility was first predicted back in 1940 and was realized when Geim and Novosolov isolated monolayer graphene by exfoliation in 2005.⁴² They reported carrier mobility at >200 000 cm² V⁻¹ s⁻¹ with an electron density of 2 × 10¹¹ cm⁻², making it one of the highest values ever reported.⁴³ Additionally, graphene exhibits a unique ambipolar electric field effect where room temperature electron or hole concentrations can be tuned by changing the applied gate voltage.⁴¹ The unique electrical properties of graphene enabled the development of ultrafast integrated circuits, with single device speeds up to 100 GHz having been demonstrated.⁴⁴ Graphene also has a very high surface area-to-volume ratio, making it an ideal material for applications such as high-efficiency batteries and supercapacitors in which high electrical conductivity and a large contact area are required. In addition to its excellent electrical properties, graphene also exhibits distinctive mechanical properties; the Young modulus of graphene was reported to be >1 TPa with an intrinsic strength of 100 GPa, making this the highest known Young's modulus in any material.^4,45–47

In addition to graphene, there is an enormous range of 2D materials, as over 1500 different materials have been identified or isolated to date.⁴⁸ Some common examples include hexagonal boron nitride (hBN), molybdenum disulfide (MoS₂), tungsten disulfide (WS₂), and phosphorene (Fig. 2). Due to the similarity in the hexagonal crystal structure and its white powder bulk form, boron nitride is often referred to as “white graphene” [Fig. 2(a)]. Its stacking structure is highly stable and allows hBN to maintain its structure up to 1000 °C in air or 2850 °C in an inert environment.^49,50 hBN shows high in-plane thermal conductivity up to 390 W/m K, which makes it an excellent material for thermally conductive polymers,⁵¹ ceramic composites,⁵² UV emitters,⁵³ and thermal radiators.⁵⁴ However, despite having a similar structure to graphene, hBN has a wide bandgap (E_g) of 5.9 eV,⁵⁵ making it an electrically insulating material, whereas graphene is electrically conducting. Additionally, monolayer hBN has been reported to exhibit an ultrahigh Young's modulus of 0.75–0.865 TPa (Ref. 56), which is comparable to the Young's modulus of monolayer graphene (⁠$∼$1 TPa).

Transition metal dichalcogenides (TMDs) are another common type of 2D material, which are predominantly semiconductors of the form MX_2, where M is a transition metal atom, and X is a chalcogen atom. TMD single layers consist of a metal atom sandwiched between two chalcogen atoms with covalent bonding. Figure 2(b) shows the structure of Mo atoms (blue) sandwiched between two S atoms (yellow) in single-layer MoS₂. TMDs exhibit tunable electronic band structures, which creates opportunities in fabricating miniaturized field-effect transistors (FETs), which form the basic building block of modern electronics.⁵⁷ MoS₂ has a layer-dependent bandgap with a crossover from indirect (1.2 eV) for monolayer thickness to direct (1.9 eV) in the bulk material.^58–60 It also shows relatively high mobility for transistor applications (∼200 cm² V⁻¹ s⁻¹) plus a high on/off ratio (∼10⁸) at room temperature, making MoS₂ an excellent semiconductor material.^61–64 MoS₂ also exhibits favorable mechanical properties, such as a high Young's modulus of 170–370 GPa, which is comparable to steel and an in-plane breaking strength of $∼$23 GPa, making it a good candidate for mechanical applications.³ 

Another well-known TMD is tungsten disulfide (WS₂), which consists of a prismatic structure similar to MoS₂ [Fig. 2(c)].⁶⁸ Simulations of WS₂ have estimated the bandgap of bilayer WS₂ to be 1.42 eV (indirect), monolayer WS₂ to be 1.91 eV (direct),⁶⁹ and the Young's modulus to be ∼15 GPa.^69,70 Finally, phosphorene is a direct bandgap semiconductor 2D material of its own structural classification [Fig. 2(d)]. The bandgap of phosphorene varies from 0.3 eV in bulk black phosphorous to ∼2 eV in single-layer phosphorene.⁷¹ Interestingly, phosphorene is significantly anisotropic in-plane, unlike most 2D materials, with a conductivity 50% lower in the zigzag direction than in the armchair direction due to its unique structure.⁷² To date, over 1500 2D materials have been identified which enables an enormous library of 2D material properties and combinations for a wide selection of given applications. For further reading on the properties of 2D materials, the readers are directed toward several excellent reviews on the subject.^55,73,74 However, while the intrinsic material properties are crucial for a given application, selecting the proper exfoliation process to produce the desired material quality, dimensions, and yield is equally critical.

The process of overcoming interlayer bonds to cleave thin layers of 2D materials is a complex balance of forces that depends on a number of parameters. Prior to discussing the various exfoliation techniques, we consider the governing mechanisms, which regulate the exfoliation process. The feasibility of exfoliation depends primarily on the interlayer strength of the material. The van der Waals interaction energy between two surfaces per unit area is given by⁷⁵ 

where $D$ is the distance between the two surfaces, and $A$ is the Hamaker constant, defined as $A=π2CvdWρ1ρ2$⁠, where $CvdW$ measures the van der Waals force between the two materials, and $ρi$ is their atomic density. Hence, the effective van der Waals force between the two surfaces per unit area, $Fad$⁠, is given by⁷⁵ 

However, although the cohesion energy between two layers is uniquely defined by their interactions at equilibrium interlayer distance, the cohesion force depends on the exfoliation pathway (the exact way the two layers are pulled apart). For instance, Eq. (3.3) models the force acting on the layers as they are separated while remaining parallel to each other and perpendicular to the separation distance $D$⁠. In the case of the upper layer being peeled away from the lower one along a distance $d$⁠, the peeling force (per unit area), $Fpeel$⁠, is⁷⁵ 

Since the typical interlayer distance $D$ is much smaller than any in-plane length $d$⁠, the peeling force $Fpeel$ is considerably lower than the adhesion force $Fad.$⁷⁵ This is what makes exfoliation possible.

Since exfoliation energy cannot be directly determined via experiments, density functional theory (DFT) has been a powerful tool to investigate exfoliation, as it can be used to calculate cohesion and adhesion energies.^76–78 Consequently, this approach has been used to calculate the exfoliation energy for several 2D materials such as graphene and graphene oxide (GO),⁷⁹ TMDs,⁸⁰ borophene,⁸¹ phosphorene,⁸² hBN,⁸³ MXenes,⁸⁴ among many others. A comparative study found exfoliation energies of 18.5 and 22.7 meV/Ų for graphene and MoS₂, respectively, pointing out the role of polarized bonds in increasing interlayer strength.⁸³ Since a threshold of 20.0 meV/Ų is typically adopted for easy exfoliation, these results also reflect the difficulty of exfoliating TMDs. Another work screened multiple materials, finding that exfoliation energy decreases with charge separation, which induces greater Coulombic repulsion between layers.⁸⁰ Surface coverage also plays a key role; for example, MXenes ending in OH groups can form H-bonds, exhibiting cleavage energy twice as high as F and O coverages.⁸⁴ The exfoliation energy computed with DFT is widely used as an indication for the feasibility of experimental isolation of new 2D materials.^85,86

Machine learning (ML) approaches have also recently been explored for the prediction of exfoliation properties, since ML is less computationally expensive than DFT while allowing for good transferability with experimental properties. Wan et al.⁸⁷ trained several ML tools with the 2DMatPedia database,⁸⁸ which contains DFT-calculated exfoliation energy for over 4000 2D materials. The authors found that exfoliation energy increases with the number of valence electrons per atom, which allows stronger bonding between layers. Similarly, Siriwardane et al.⁸⁹ used 7000 layered ternary compounds from the Materials Project database⁹⁰ to train multiple ML models. They found that formation energy (a measure of thermodynamic stability) and exfoliation energy tend to follow the same trend, pointing out that stable bulk phases are harder to exfoliate. However, the results indicate that cleavage of Ga- and In-based MAB phases should be possible (M = metal, A = group III-A elements). Finally, Saito et al.⁹¹ recently used a deep learning method to identify the thickness of atomic layer flakes from optical microscopy images. Their artificial neural network was able to differentiate mono- from bi-layer graphene and MoS₂ with up to 80% success, which highlights the possibility of replacing part of manual work with AI systems for 2D material productions.

Overall, several approaches can be used to model exfoliation, from fundamental physical–chemical theory to simulation techniques and machine learning tools. Sections III B–III F dive deeper into each of the main exfoliation techniques, which are studied with models that are specific to each case. Additionally, Table I presents an index summary of the five exfoliation techniques including material yields, advantages, and disadvantages to help direct the reader toward the appropriate techniques. Table S1 (supplementary material) further presents a summary of applications employing exfoliated 2D materials used in energy and storage, mechanics and design, polymer composite, and cement composite applications.

The first exfoliation of 2D atomic layers from bulk crystals was performed using the “Scotch tape” method.⁴¹ In this process, a graphite flake is placed on a piece of tape, stuck against itself, and then peeled repeatedly. The graphite flakes become thinner on each subsequent peel, and then, the tape is pressed on a substrate to leave behind an assortment of 2D material thicknesses [Figs. 3(a)–3(c)]. The first-ever isolation of a single layer of 2D material was similarly reported by Novoselov et al.¹ by mechanical exfoliation, also referred to as micromechanical cleavage. In their study, a fresh surface of a graphite was rubbed against another surface, which left a variety of flakes on it and was later determined by transmission electron microscopy (TEM) and atomic force microscopy (AFM) to contain monolayers.

One challenge with the scotch tape method is that due to the repeated mechanical stresses by folding the tape multiple times, the 2D material flakes can break apart which results in low yield and low lateral dimension 2D sheets.⁹² To increase the yield of this process, the interaction between the monolayer 2D material and the underlying substrate is enhanced by exposing the substrate to oxygen plasma to remove any organic absorbates on the surface.⁹³ After that, the scotch tape with the thinned graphite flakes is placed on the substrate and heated at 100 °C for 2–5 min. This annealing process vents the trapped gas between the interface of the 2D material and the substrate, thus ensuring a more uniform interaction between the substrate and the 2D layers. This produces larger sheets of monolayer 2D materials without mechanical deformations such as buckles or wrinkles.

The first isolation and experimental study on thin sheets of hBN was reported by Pacilé et al. by micromechanical cleavage, where layers of hBN were peeled off using adhesive tape attached to a SiO₂ substrate. The thinnest regions of exfoliated hBN were 3.5 nm or ∼10 layers thick.⁹⁷ Although the synthesis of monolayer graphene is relatively straightforward and consistent using micromechanical cleavage, it is not the case for the isolation of most other 2D materials. For example, even though hBN includes weak van der Waals bonds, there is a robust lip–lip interaction between the basal planes of BN. As AA′ is the preferred stacking order in exfoliated hBN, favorable electrostatic or polar–polar interactions lead to B atoms eclipsing N atoms on the adjacent layers. These unique lip–lip interactions between different layers of BN nanosheets are stronger than the interlayer bonding of the layers in graphene.⁹⁸ Additionally, the lack of availability of large, ordered microcrystals of hBN also contributes to this problem. Despite these challenges, single-layer hBN was recently reported to be exfoliated using the scotch tape method, with the thickness of a single layer of boron nitride reported as 0.48 nm.⁵⁶ It should be noted that the yield remains very low, which is not scalable for most applications.

Micromechanical cleavage faces challenges for the isolation of many layered 2D materials, such as TMDs, due to the low adhesion energy between the substrate and the 2D material. This poses a significant challenge in exfoliating these layered materials for practical applications. To address this, Huang et al. reported a metal-assisted exfoliation method [Fig. 3(e)].⁹⁶ For TMDs, the group 16 (VIA) chalcogen atoms (S, Se, and Te) show a high affinity with gold, so the substrate is coated with a thin layer of gold to exfoliate large areas of 2D TMD sheets with high yield.⁹⁹ This process produces the layered material firmly adhered to an engineering-relevant substrate without any alteration in its chemical or mechanical properties while facilitating the separation of monolayer and few-layer thicknesses. Late et al.⁶⁴ first reported the mechanical exfoliation of single layer MoS₂ achieving a thickness of 0.7 nm, while other TMDs, such as MoSe₂, WSe₂, WS₂, or NbSe₂, have also been reported to be mechanically exfoliated to a few layers.^100,101 Recently, a fully automated micromechanical exfoliation system for MoS₂ and molybdenum ditelluride (MoTe₂) was designed by DiCamillo et al.¹⁰² where adhesive tapes were applied using a non-movable base and movable tool of a rheometer. A program was set to apply force and rotate the rheometer tool, thus creating a shear cleavage force between bulk MoS₂ or MoTe₂ and the substrate which facilitates the exfoliation process.

The fundamental mechanisms, which enable micromechanical cleavage, are extremely complex to model and calculate as it is a multifaceted dynamic system. For example, micromechanical exfoliation does not remove a single layer from the bulk, but a multilayer slab, which makes it very challenging for DFT simulations. However, Sinclair et al.¹⁰³ developed a Monte Carlo mathematical model to predict repeated graphite exfoliation. Exfoliating n times, the model predicts how many steps are necessary before a single layer is produced. The matrix $B$ is built to group the transition probabilities among transient states, and a vector $b$ is modeled to group the probabilities from any state to the adsorbing one. The resulting probability density function g(c) is¹⁰³ 

Starting with 30 000 layers (∼10 μm thickness) and using $α=0.01$⁠, the expected number of steps for reaching monolayer graphene is 11 when each cleavage happens at a random location. However, the authors used molecular dynamics simulations (MD) to show that polymer-based mechanical exfoliation favors cleavage near the surface. When the probabilities are changed to follow this finding, the number of steps needed to reach monolayer graphene is only 4, pointing out the importance of engineering the exfoliation method for optimal performance.

In addition to multilayer peeling, micromechanical cleavage may involve fracture. To understand this scenario, a few different approaches have been used. Yang and Vijayanand introduced a continuum model for the peeling process of graphene,¹⁰⁴ which combined von Karman's plate theory, elastic fracture mechanics, and a cohesive spring model for interlayer delamination. As exfoliation happens, intermediate layers are partly attached to the upper stack and partly to the lower substrate, which sets the stage for delamination fracture. The main crack opening profile is governed by¹⁰⁴ 

where w is the total deflection resulting from the applied force, with a long- and a short-range contribution; $Γ$ is the cleavage toughness for each type of fracture (the long-range term coinciding with the interlayer cohesive energy); $S11′$ and $e$ are derived from the elastic constant matrix of the material as defined elsewhere;¹⁰⁵ and $Dm$ is the film flexural rigidity, which depends on the in-plane Young's modulus $Em$ and Poisson's ratio of the 2D material $vm$ as¹⁰⁴ 

Graphene delamination was described by an interlayer potential that yields tangential traction (⁠$pα$⁠) as a function of energy density (⁠$γt$⁠), C–C bond length $(d$⁠, or $d0$ for optimal distance), and tangential displacement between layers (⁠$rα$⁠, measured from the ground-state stacking), where $α$⁠, m, and l are integers that count the dimensions of the system, following the definitions introduced by Yang:¹⁰⁶ 

Finally, a cohesive model was used for tearing initiated crack growth. The total energy release (⁠$Γ$⁠) depends on the length of the layer (l), and the x- and z-components of the cohesive force at the tearing crack line (ku and kw, respectively, where k is a spring constant, and u and w are the displacement components)¹⁰⁴ 

A finite difference method was used to simulate the system. The graphene layer undergoes in-plane stretching and shearing, as well as out-of-plane bending, which can only be captured with von Karman's nonlinear plate theory. As a result, the layer is torn mainly by stretching, not by tearing within the fracture zone. In addition, the distance between the tearing crack tip and the main cleavage crack front is predicted to be approximately 45 nm.

While DFT can only model simplified systems, as discussed in Sec. III B and illustrated in Fig. 4(a), classical MD can simulate more complex processes. For example, Jayasena and Sinclair independently simulated graphene exfoliation by polymer “sticky tapes” (PMMA and PDMS) [Fig. 4(b)].^103,107 Even when pulling the polymer orthogonally, a mixed mechanism was observed for graphene exfoliation, with normal and shear components, which characterizes peeling. Other mechanical exfoliation mechanisms have also been studied with MD, such as the wedge-based method [Fig. 4(c)]¹⁰⁸ or contact with an atomic force microscope tip [Fig. 4(d)].¹⁰⁹ The atomic force microscope tip was modeled using van der Waals forces with a Lennard–Jones potential; by bringing the surfaces together and then separating them, the authors observed micromechanical cleavage in which the top graphene layer was separated from the lower ones. Thanks to the usage of a reactive force field, breakage of C–C bonds was observed at high separation rates and increased van der Waals forces, leading to the formation of a graphene nanoflake.

Although micromechanical cleavage is a well-known technique capable of producing 2D materials with high crystallinity and was used to exfoliate graphene for the first time, this method remains mostly relevant for laboratory-scale studies due to low throughput and consistency. In this regard, micromechanical cleavage has been most successfully used to investigate the benchmark properties of high-quality 2D materials for many fundamental studies. For example, in 2008 the Young's modulus and intrinsic strength of defect-free exfoliated monolayer graphene was measured by Lee et al.⁴ to be 1.0 TPa and 130 GPa, respectively, making it one of the strongest materials available. This mechanical cleavage method has also been used to exfoliate pristine 2D sheets of MoS₂,^3,110 hBN,⁵⁶ and graphene oxide¹¹¹ proving their exceptional mechanical strength and fracture behavior. The ultrahigh strength and stiffness values of these 2D materials are attributed to the pristine nature of 2D materials when produced by exfoliation, including a structure free of point defects and without out-of-plane bonding (i.e., only covalent sp² bonding in graphene sheets).^4,112

Interestingly, despite exhibiting nearly identical structures, the Young's modulus and fracture strength of micromechanically exfoliated graphene has been demonstrated to decrease with increasing layer thickness, but that of hBN was found to be independent of the layer number up to 9 layers [Figs. 5(a) and 5(b)].⁵⁶ This can be attributed to the increased lip–lip interaction in hBN, which makes the interlayer coupling more pronounced. Exfoliated 2D materials have also shown exceptional properties in several unique dynamic loading applications. The lifetime of micromechanical exfoliated graphene under cyclic fatigue loading exhibited the longest fatigue life of any known material, reaching over one billion cycles at loads greater than 50% of its fracture strength.¹¹³ Additionally, exfoliated graphene displayed remarkable ballistic shielding properties due to its high in-plane strength and kinetic energy absorption at supersonic speeds [Fig. 5(c)]. At comparable densities, the specific penetration energy of multilayer exfoliated graphene was 2–3× higher than that of other materials, such as Kevlar and steel.

Due to the pristine nature of mechanically exfoliated 2D materials, they have also been widely used to fabricate ultrathin field effect transistors (FETs). FETs use an electric field to control current flow from the source to the drain with a control electrode forming the gate and make up the basic component of logic devices [Figs. 5(d)–5(f)]. The potential exhibited by exfoliated graphene for FETs is driven by the excellent electron mobility due to its near defect-free nature, which is reported to be as high as 2 × 10⁵ cm² V⁻¹ s⁻¹ at room temperature.⁵ In contrast, there is a significant difference in the electron mobility of exfoliated graphene compared to graphene synthesized using other methods, such as CVD,¹¹⁷ which shows electron mobility of only 12 000 cm² V⁻¹ s⁻¹.¹¹⁸ Bandgap materials such as 2D MoS₂ have also been successfully used to develop FETs as semiconducting phases.^115,116

Micromechanical exfoliation was the first technique to isolate 2D materials from their bulk forms owing to the ease of mechanically overcoming the van der Waals forces in the material to split apart the layers. This technique can repeatably produce 2D materials with minimal defects and large lateral sizes, making it ideal for identifying and evaluating the fundamental properties of the materials and creating proof-of-concept designs such as 2D material FETs. However, as mechanically separating layers of 2D materials are a tedious process with low throughput, this technique has been largely limited to bench-scale applications.

While adhesive tape-based micromechanical exfoliation was the first to demonstrate successful isolation of 2D materials, ball milling employs a similar mechanical exfoliation technique but is more suitable for batch scalability. Conventionally, ball milling is used for fragmentation and mixing metallic powder to fabricate alloys, but recently, researchers have employed this method to exfoliate layered 2D materials in bulk quantities. As the balls roll and bounce in the mill along with the 2D material, they exhibit shear, rolling, and impact forces on the 2D material, which can overcome the van der Waals bonding and separate 2D layers. For example, Lee et al.¹¹⁹ demonstrated a technique to ball mill hBN in the presence of sodium hydroxide (NaOH), as seen in Fig. 6(a). Synergistic shear and hydroxylation enables cutting into the hBN plane, which induces minimal structural damage [Fig. 7(a)] while yielding a high percentage of flakes up to 1.5 μm in width with a yield of 18%. However, ball milling alone is very aggressive and has been shown to induce basal plane and edge defects in layered materials [Figs. 6(b) and 6(c)].¹²⁰ This is because two significant mechanisms are in play during the ball mill exfoliation process; shear forces by rolling of the balls allow for large area exfoliation of 2D materials, while the impact forces of bouncing balls break the agglomerated particles into smaller ones. The impact forces can additionally fragment the 2D sheets, which can lower yield, reduce lateral size, and induce defects in the exfoliated sheets.⁹² Despite this disadvantage, ball milling produces a significantly higher yield of layered materials compared to other 2D material synthesis techniques and is easily scalable to industrial volumes.

Ball milling is a widely employed technique used to exfoliate a variety of 2D materials including MoS_2,^121,122 graphene,¹²³ SnS₂/graphene hybrid nanosheets,¹²⁴ MoS₂/rGO sandwiches,¹²⁵ and hBN.¹²⁶ These high-yield processes have successfully produced exfoliated 2D materials for use in lubrication oil,¹²⁷ electrochemical energy storage,¹²⁵ conductive polymers,¹²⁸ and Li-ion batteries.¹²⁴ Part of this success can be attributed to milling-generated defects, which are actually beneficial in engineering the properties of 2D materials for applications such as energy storage where the defects provide more active adsorption sites, allow faster diffusion, and enhance storage capacity.¹²⁹ One major consideration for ball milling is that different milling parameters are vital in determining product quality and yield. Deepika et al.¹²⁷ systemically studied milling parameters such as milling speed, ball-to-powder ratio, and ball size to optimize the system for the highest efficiency and product yield. Smaller balls (0.1–0.2 mm), intermediate speeds of approximately 800 rpm, and a ball-to-powder ratio of 10:1 exfoliated layered BNNSs most efficiently. Under this optimum condition, they reported a yield as high as 13.8%, and the BNNSs were 0.5–1.5 μm in diameter and a few nanometers thick.

Plasma- and hydrothermal-assisted ball milling are two enhanced forms of ball milling that have received considerable attention for commercial applications. Lin et al.¹³⁰ reported the exfoliation of few-layer graphene using plasma-assisted ball milling to avoid the formation of amorphous carbon during the exfoliation from bulk graphite. The generated plasma keeps the bulk powder in a high-stress state, ensuring crystallinity throughout exfoliation. Additionally, Xia et al. used a hydrothermal-assisted ball milling process to produce SnS₂/graphene composite nanosheets that showed excellent rate capability and cycling stability of LL-SnS₂ electrodes for lithium-ion batteries (LIB).¹²⁴ One gram of SnS₂, 0.2 g of graphite, and 20 ml anhydrous ethanol were mixed in a planetary ball mill to produce the composite exfoliated graphene structure that was used as an anode material.

Since ball milling was historically used for size reduction in many types of processes, several attempts were made to model its underlying mechanisms.¹³¹ A key aspect of ball milling is the energy provided to the material by the balls. For instance, Burgio's model¹³² calculates the transferred energy by a single ball in a single impact (⁠$ΔEb$⁠), which depends on the density of the milling material (⁠$ρb$⁠), the ball diameter (⁠$db$⁠), the speed of the ball mill main disk (⁠$Wd$⁠), the vial diameter (⁠$Dv$⁠), the main disk diameter (⁠$Dd$⁠), and the transmission ratio between the main disk and the vial (⁠$RT$⁠)¹³² 

Equation (3.9) features different geometrical parameters of the mill. As a result, the energy $ΔEb$ depends on the free space within the vial. A factor $ϕb$ was proposed to describe the degree of filling, allowing for the accumulated energy (⁠$ΔEac$⁠) to be more accurately modeled as a function of time (t), using a constant that captures the elasticity of the collisions (K), as shown in Eq. (3.10). For a given experimental setup, all the variables in brackets have constant values, which allows simplification to an expression whose terms can be controlled experimentally. By using this model, Ghayour found that increasing the number of balls has minimum impact on transferred energy due to a decrease in their kinetic energy and mobility.¹³³ Martinez-Garcia used this approach to model the mechanosynthesis of hexagonal Re₂C, finding that there exists a minimum transferred energy necessary to trigger the process equivalent to overcoming the interlayer binding energy¹³⁴ 

MD can also be used to simulate the micromechanics of the ball milling process,^135,136 although, to our knowledge, this approach has not been used to model the mechanics of exfoliation in particular. Hara, for instance, used MD to study the milling-induced allotropic transformation of cobalt, by compressing a nanoparticle at different angles between two walls.¹³⁶ This methodology could be extended to investigate exfoliation, since both compressive and shear forces are generated. Indirect approaches, on the other hand, have been applied to investigate the processes during exfoliation. For instance, Arao investigated salt-assisted ball milling for graphene production and used MD to show that salt adsorption takes place on active carbon at graphitic sheets.¹³⁷ 

Ball milling also offers a unique ability among synthesis methods in the one-step manufacturing of composite or functionalized structures. For example, TMD/graphene nanocomposites have recently attracted researchers' attention for their potential application as electrode materials. Using MoS₂ and graphene oxide as bulk precursors, large-scale MoS₂/reduced GO electrode composites were prepared from a one-step solvent-free ball milling process without postprocessing requirements.¹²⁵ Interestingly, a planetary ball milling process with ammonia borane has been used to exfoliate fluorinated graphene sheets from bulk graphite fluoride.¹³⁸ Fluorographene is challenging to exfoliate but the strong dipole interactions between NH₃BH₃ and FG along with the shear forces by ball milling produced high-quality nanosheets that were 1–6 nm thick with a lateral size of 0.3–1 μm. Additionally, hBN is often sought as a filler for polymer composites due to its excellent thermal conductivity; however, due to the inert nature and strong ionic bonds of hBN, exfoliation and functionalization are very challenging.¹³⁹ Yu et al.¹²⁸ addressed this through co-ball milling of polymer and hBN in solution as an effective one-step synthesis process for producing polymer-functionalized few-layer boron nitride for cellulose composites with high thermal conductivity.

Polymer-2D material composites represent one of the most common methods to exploit the enhanced properties of exfoliated 2D materials for macroscale applications. While polymers are typically very inexpensive to produce, they lack electrical or thermal conductivity as well as high strength and stiffness, which are some of the predominant benefits of 2D materials. By dispersing exfoliated 2D materials throughout the polymer matrix, often during the polymer mixing and molding process, the composite can exhibit enhanced properties from the nanoscale material at a level of macroscale applicability. Scalability is one of the most important parameters as polymer composites require significant volumes of 2D materials. Additionally, in many cases, tens of layers are preferable to few-layer 2D materials, which makes ball milling an ideal synthesis method for preparing polymer composites as shown for hBN,¹²⁸ MoS_2,¹²² graphene,¹³⁰ reduced GO,¹⁴⁰ and other 2D materials. This process is demonstrated in Fig. 7(a) wherein the graphene is exfoliated and dispersed into the epoxy solution throughout a 30-h ball milling process before being cured into the final composite shape.¹⁴¹ 

As 2D materials present strengths and stiffnesses that are typically many orders of magnitude greater than polymers, the mechanical properties of polymers can be greatly enhanced by composite synthesis. For example, dispersion of exfoliated graphene in polyurethane has demonstrated increases in the strength and stiffness by over two orders of magnitude at a mass fraction of 55%.¹⁴² Similarly, the Young's modulus has been found to increase by 60% at 20 wt. % exfoliated graphene,¹⁴³ and the tensile strength of various polymers has been found to increase by 12%–90% with the addition of exfoliated MoS₂.¹⁴⁴ The potential of polymer reinforcement can also be clearly noted for several cases involving low concentrations of reinforcement. At low loading volumes, the Young's modulus of graphene/epoxy composites are nearly doubled at 0.1 wt. % graphene [Fig. 7(b)].¹⁴¹ Shen et al.¹⁴⁵ produced PEO composites with eight different 2D materials at 0.5 wt. % and found the strength and stiffness to be reliant on the exfoliation capacity of the respective 2D material and the morphology of the composite [Fig. 7(c)]. hBN-reinforced PVA showed a linear increase in the strength and stiffness with the volume fraction up to a 40% increase at 0.3 vol. % hBN.¹⁴⁶ Graphene reinforcement of PVA has also shown strength increases of greater than 90% for volume fractions below 0.4 vol. %.¹⁴⁷ This demonstrates the potential for exfoliated 2D material additives to significantly enhance polymers' properties without greatly increasing the cost or altering the composition. Additionally, exfoliation techniques such as ball milling of 2D materials is especially beneficial for mechanical reinforcement as larger particles, which are facile to produce at scalable quantities by ball milling and other exfoliation processes, produce greater strengthening effects due to greater volumes of interconnected material.¹⁴⁸ 

The other significant drawback with polymer materials is that pure polymers are electrically and thermally insulating in almost all cases. However, similar to the effective mechanical reinforcement achieved in 2D material–polymer composites, composites of exfoliated 2D materials in polymers have yielded electrically conductive composites that have found applications in electromagnetic shielding^151,152 anti-static components,¹⁵³ and strain sensors.^154,155 Predominantly, exfoliated graphene has been used as the filler in these composite matrices due to its high conductivity; however, TMDs, including exfoliated MoS₂¹⁵⁶ and WS₂¹⁵⁷ are also common for applications that require semiconducting properties. Similarly, the thermal conductivity of polymers can be significantly enhanced with the addition of 2D materials. Most prominently, this presents new applications in thermal dissipation for small-scale electronic systems with demonstrated applicability by exfoliated graphene,^158,159 MoS₂,¹⁶⁰ and hBN¹⁴⁹ [Figs. 7(d) and 7(e)].

One drawback of 2D material–polymer composites is the significant heterogeneity in the out-of-plane direction due to fillers' alignment and planar orientation during molding. Kim et al.¹⁵⁰ found that the thermal conductivity of exfoliated graphene nanoplatelet composites differed by close to an order of magnitude between the in-plane and through-plane directions [Figs. 7(f) and 7(g)]. Similarly, Sullivan et al.¹⁶¹ noted that the electrical conductivity of exfoliated graphene nanoplatelet composites differs by two orders of magnitude in the through-plane direction compared to the in-plane direction. This can serve as an engineered parameter to produce orientation-dependent conductivity for shielding applications of polymer composites.

The mechanical exfoliation of 2D materials by ball milling is a batch-scalable process that has demonstrated extremely high yields of many types of 2D materials. However, the aggressive nature of the technique leads to high defect densities and smaller lateral sizes, which is restrictive for some of the end applications of these materials. As a result, one of the best applications for ball-milled 2D materials is the production of polymer composites, including mechanical reinforcement and thermal and electrical conductivity enhancement for multifunctional applications.¹⁶² 

While micromechanical cleavage and ball milling induce exfoliation by physically separating layers, many materials can be solution-processed and exfoliated through the relatively gentler process of ultrasonication. During ultrasonication, a solution containing dispersed bulk materials is exposed to a transducer that emits ultrasonic waves throughout the material. These ultrasonic waves generate vast swarms of unstable cavitation bubbles that, upon their inward collapse, emit high temperature, pressure, and velocity jets of liquid in the local environment. This creates a hydrodynamic shear force that leads to deagglomeration of the bulk materials and is strong enough to overcome the weak van der Waals forces between layers to exfoliate relatively small 2D layers from the bulk material.^163,164 2D materials exfoliated via ultrasonication tend to have lateral sizes of a few micrometers, and with thicknesses no more than a few layers.¹⁶⁵ Yields of ∼1 wt. % are routinely achievable, which can be improved to 7–12 wt. % with further processing.¹⁶⁴ This process is shown as a schematic in Figs. 8(a),¹⁶⁶ while 8(b) shows a high-speed image sequence of ultrasonic exfoliation of a graphene flake.¹⁶⁷ 

Liquid-phase exfoliation is a chemical process assisted by mechanical mechanisms, and vice versa. Therefore, the choice of medium for ultrasonication is a governing parameter and different solvents can help achieve different production objectives.^165,168,169 A study of over 40 different solvents identified surface tension as one of the most important solvent parameters and characterized solubility parameters for highly efficient exfoliation.¹⁷⁰ A common mechanism in which a solvent assists the exfoliation process is through interfacial tension by reduction of the potential energy within layers to overcome van der Waals forces of the layered material. The greater the difference between the surface tension of the solvent and the 2D material, the greater heterogeneity of the exfoliated sheets. Solvents with surface tensions close to that of the 2D material, such as ortho-dichlorobenzene in the case of graphene, have shown to produce relatively large and highly homogenous dispersions without a noticeable Raman D band indicating low defect concentration.¹⁷¹ Arifutzzaman et al.¹⁷² exfoliated graphene using sonication in N-methyl-2-pyrrolidone (NMP) and N,N-dimethylformaldehyde (DMF), which showed that the defect population of graphene exfoliated in NMP was significantly lower than that in DMF due to the lower energy cost for creating new surface areas in NMP, which is a result of similar surface energies.

Additionally, several additive compounds can assist the ultrasonication mechanism. Stabilizers such as surfactants, polymers, pyrene derivatives, and supercritical fluid solvents have been employed to improve the efficiency and reduce the toxicity of liquid-phase exfoliation.^175–177 Surfactants, ionic or nonionic, can charge individual flakes to cause electrostatic repulsion between them to aid the exfoliation process.^177,178 Also, surfactants lower the liquid–vapor interfacial energy, promoting greater cavitation events by sonication. This improves the yield without needing to increase the sonication power, as the cavitation bubbles only need to be powerful enough to overcome the weak van der Waals forces and prevents material degradation as the strong in-plane covalent bonding is largely preserved without the introduction of defects.^167,173 Furthermore, the surfactant absorbs onto the exfoliated sheets, creating an additional repulsive force that prevents the reaggregation of the sheets post-sonication.¹⁷⁴ Similarly, adding alkali metal ions such as Na⁺ during the sonication process can lead to ion intercalation between the 2D sheets. This intercalation further weakens the van der Waals forces, thus improving the 2D material yield of the supernatant, as represented in Fig. 8(c).^179,180 Various polymers such as polyvinyl chloride (PVC), poly (methylmethacrylate) (PMMA), and polyvinylpyrrolidone (PVP) have been employed and introduced into the sonication medium.^181,182 It has been revealed that through steric stabilization, polymers are effective in preventing aggregation of exfoliated sheets in solvents.¹⁸³ Additionally, polymers can mediate the surface energy mismatch between solvents and layered materials. Ethyl cellulose was mixed with ethanol to exfoliate graphene to address the surface energy mismatch between ethanol and graphene, demonstrating that polymeric stabilizers can also allow for exfoliation in nontraditional solvents.¹⁸³ Pyrene stabilizers have been demonstrated to be highly effective stabilizers for high-yield exfoliation of monolayer graphene with exfoliated sheets showing high levels of purity.^184–186 The interaction between π orbitals of pyrenes and graphene reduces the surface energy of the dispersion increasing purity.^165,185 Supercritical fluids have also been employed in liquid-phase exfoliation^187,188 as they have densities like liquids and diffusion and solubility characteristics like gases. Therefore, they can easily diffuse between layered materials and assist in exfoliation.

The evolution of particle size distribution during ultrasonication can be calculated with an equation for the mass fraction (⁠$mi$⁠, i being the size class) as a function of time (t), as originally used to model ball milling.^189,190 The process depends on the selection function (⁠$Si$⁠), which is the rate constant for particles to be broken to smaller sizes; and the breakage distribution function (⁠$bi,j$⁠), which is the mass fraction of particles broken (from j to i):^189,190

This function can be written in a cumulative form. In this case, the cumulative size distribution function $[Rit=∑j=1imj(t)$ for particles of size greater than i] depends on the cumulative breakage function (⁠$Bi,j=∑k=i+1nbk,j$ for the probability for fragments from particles j to have a size less than i)^189,190

These formulations are useful since the parameters $Si$ and $Bi,j$ can be estimated experimentally from particle size distribution, by solving the equations above. For instance, Kapur¹⁹¹ proposed an approximate solution where $f(t)$ is the residual ratio that represents the fraction of particles that have not been broken yet:¹⁹¹ 

In Eq. (3.13), the approximation can be used for short exfoliation times. This expression can then be used to estimate the operation parameters. Li et al.¹⁹² applied this methodology to the liquid-phase exfoliation of GO, finding that its breakage happens mainly due to sheet fracture (rather than abrasion) which governs its lateral size.

A similar approach to model the kinetics of exfoliation is to use an approach akin to polymer decomposition.¹⁹³ In this case, the concentration of the i-layered material $Pi$ is a function of a kinetic constant k, as shown in Eq. (3.14). This model shows that, at long periods of time, monolayers dominate over thicker slabs, which can help target a specific thickness distribution by engineering process parameters such as operation time¹⁹⁴ 

Since ultrasonication exfoliates by cavitation, modeling pressure distribution in the liquid system can provide great mechanistic insight. This can be done by solving the linear steady-state wave equation by FEM, which considers the coupling between the acoustic field of the solution and the vibration of the surrounding vessel. The model includes acoustic pressure (P), density (⁠$ρ$⁠), and the speed of sound (c), as shown in the following equation:¹⁹⁴ 

If the sonication system uses a transducer that works at constant frequency f, then pressure is simply a time harmonic $Pr,t=p(r)eiωt$⁠, where $ω=2πf$ and $p(r)$ is the pressure amplitude. The space-dependent wave equation then becomes¹⁹⁴ 

The numerical solution of this equation can be obtained with FEM. Yi et al.¹⁹⁴ found that changing cavitation in the synthesis vessel can critically affect exfoliation, with injected power being nearly proportional to cavitation volume and therefore sample volume, and pressure amplitude and cavitation intensity having effects on graphene yield as well.

Using a different strategy to investigate vibration, Pupysheva et al.¹⁹⁵ performed MD simulations to study the exfoliation mechanism of graphene under ultrasonication with and without a surfactant. A classical force field was used to estimate the soft and hard modes of vibration of graphene, corresponding to parallel and perpendicular displacements between successive layers, respectively. The obtained data were fit to harmonic curves for the estimation of the effective force constant (k), which in turn was used to calculate the resonance frequency (f) from the reduced mass (⁠$μ$⁠), as shown in Eq. (3.17). They found that parallel exfoliation along the zigzag edge is the most likely and that adsorbed surfactants have no major impact on resonance frequencies, which suggests that they facilitate exfoliation only by preventing exposed layers to regroup¹⁹⁵ 

Unlike other cleavage techniques, liquid-phase exfoliation has been widely explored by MD. Since these simulations can capture dispersive, polar, and hydrogen-bonding interactions at the solvent–nanomaterial interface, they can be used to evaluate how efficient a liquid is at exfoliating and specially at dispersing the material.¹⁹⁶ For instance, Shih et al.¹⁹³ studied graphene in different polar solvents, calculating the potential of mean force (PMF) between parallel sheets to estimate their stability in a dispersion. The authors investigated the atomic mechanism of confinement and desorption of solvent molecules from interlayer space, as well as the kinetics of graphene aggregation. To achieve this, they developed a kinetic theory of colloid aggregation that can be used to predict the lifetime and time-dependent layer distribution of graphene in different solvents. Starting from only monolayers in the dispersion, the concentration of i-layer graphene sheets (⁠$Ni$⁠) depends on a kinetic constant (k),¹⁹³ 

and k can be calculated from the diffusivity of monolayer graphene (D), the closest interlayer distance (⁠$r0≈$ 3.5 Å), the PMF per unit area between parallel sheets (⁠$Φ$⁠), the average collision area (⁠$AC$⁠), the temperature (T), and Boltzmann's constant (k_B), as shown in Eq. (3.19). In this model, $Φ$ can be extracted from MD simulations, and $AC$ is the only adjustable parameter¹⁹³ 

Furthermore, MD has been used to unveil the mechanism of liquid-phase exfoliation of several other 2D materials. For instance, it showed that intercalated polar solvents are strongly adsorbed on hBN surfaces, forming quasi-stable states that reduce interlayer binding,¹⁹⁷ that polar solvents also favor exposed edges in MoS₂, promoting exfoliation, and hindering aggregation,¹⁹⁸ and that the efficiency of phosphorene exfoliation is enhanced when solvent molecules can reach planarity and therefore “sharpen” the molecular wedge that separates layers.¹⁹⁶ DFT too can shine light on the energy variations due to molecule or ion intercalation. For example, it showed that the intercalation of many solvent molecules within graphene is energetically favorable.¹⁹⁹ 

Smith et al.¹⁷⁴ demonstrated the exfoliation of monolayers and a few layers of a wide variety of TMDs and hBN using low-power bath sonication stabilized in water with sodium cholate [Fig. 8(d)]. Following ultrasonication, the solutions containing nanosheets are typically centrifuged to separate the exfoliated nanosheets from the unexfoliated bulk material and dried to a powder as shown in Fig. 8(d). Since many TMDs are degraded in the presence of air, ultrasonic exfoliation in a liquid medium (i.e., alkali-stabilized water, isopropanol, cyclohexanone, dimethylsulfoxide, N-methyl-pyrrolidone, dimethylacetamide) promises larger scalability for layered TMDs. The process is widely applicable as most layered materials have binding energies appropriate for bath sonication with appropriate liquid mediums. Graphene dispersions, for example, were prepared using NMP as a solvent by Hernandez et al.¹⁶⁴ to minimize the energy mismatch between the exfoliated material and solvent for efficient low defect exfoliation.

Numerous reports on the exfoliation of graphene by sonication are available,^{136,161,162,200,201} and many TMDs have also been widely exfoliated by sonication for their potential applications in semiconducting devices.^202–204 Umar et al. demonstrated the exfoliation of hBN in polyvinyl alcohol (PVA), producing exfoliated nanosheets of ∼3 layers on average.¹⁴⁶ In addition to these standard materials, other unique 2D materials, such as phosphorene,²⁰⁵ molybdenum trioxide (MoO₃),¹⁷³ and ultrathin WO₃·2H₂O,²⁰⁶ have been reported. WO₃·2H₂O was exfoliated by bath sonication for application in memory devices by Liang et al.,²⁰⁶ producing nanosheets of 2–3 nm thickness. It should also be noted that the amplitude of the sonicator and the sonication time significantly affects the quality of the 2D flakes. Baig et al.²⁰⁷ found that the defect density in exfoliated graphene increased with both amplitude and sonication time. With the increase in sonication time from 10 to 120 min, the Raman I_D/I_G ratio increased from 0.07 to 0.182, which corresponded to a 61% increase in the defect content at 120 compared to 10 min. Similarly, an increase in sonicator amplitude from 60% to 100% corresponded with a significant introduction of defects in exfoliated graphene. Interestingly, Tyurnina et al.²⁰⁸ employed a dual-frequency ultrasonication technique with concurrent 1174 and 20 kHz waves to exfoliate graphene in water, which created a wider population and size distribution of cavitation bubbles. As a result, they demonstrated a high yield of mono- to tri-layer graphene flakes with widths exceeding 1 μm. The mechanism of cavitation toward exfoliation of graphene was examined in detail by Morton et al.²⁰⁹ who determined the shockwaves to emit a pressure magnitude up to 5 MPa and liquid jets on the order of 80 m/s. They further noted that stable cavitation resulting in bubble oscillations produced a higher yield with reduced defects as the repeated gentle forces slowly separate graphene layers.

As ultrasonication is a solution-based exfoliation technique, it has become the most common exfoliation technique for preparing 2D material lubricant fluids. This is due to the dual process of 2D material dispersion and exfoliation during sonication, which can be directly performed in the base lubricant in a one-step process.^210–212 Exfoliated 2D materials can significantly reduce the friction and wear rates of the contact when trapped between the sliding faces due to their van der Waals forces between the layers, which creates a low coefficient of friction due to shear energy dissipation.²¹³ The majority of exfoliated 2D materials have been used as lubricants, including graphene, GO, MoS₂, hBN, WS₂, and many others.²¹³ As ultrasonication produces a dispersion of few-layer exfoliated 2D materials in an aqueous solution, this allows for a facile one-step approach for the production of 2D material-dispersed lubricants such as MoS₂ and WS₂ in mineral oils,^214,215 graphene in SAE 15W-40,²¹⁶ or hBN, graphene, and MoS₂ in water-based lubricants.^210,211,217

The affinity of graphene to water makes it an ideal additive to water-based lubricants; the exfoliation of graphene and GO in DI water has demonstrated a reduction in the coefficient of friction by a factor of 6 and 2, respectively, in a steel-steel contact.²¹⁰ hBN has also been used extensively as an additive to water-based lubricants with concentrations as low as 0.01 wt. % exfoliated hBN in water reducing the friction and wear behavior by up to 20%.²¹⁷ Conversely, TMDs degrade in water and are commonly used in oil-based lubricants; 0.5 wt. % chemically exfoliated MoS₂ in oil-based lubricants can reduce the total wear by 40%–50% and the friction by up to 15%–20%.²¹⁴ Meanwhile, 1.0 wt. % exfoliated WS₂ dispersed in oil has shown a reduction in wear by 43% and friction by up to 39%.²¹⁵ 

As additives in bulk lubricants, nanomaterials must be effectively dispersed in the solution to be trapped within the tribological running surfaces for effective lubrication. However, dispersion can be a challenge for 2D materials due to the aggregation and viscosity of lubricant oil. In such cases, functionalization can improve the dispersion and lubricating properties of exfoliated 2D materials. For example, surface functionalization using thiol molecules has been employed in situ during the ultrasonic exfoliation process to prevent aggregation of MoS₂ sheets in the final lubricant composition. 0.1 wt. % of this functionalized MoS₂ in a water-based lubricant was enough to reduce the friction by 50% and the wear volume by 70%.²¹¹ MD simulations suggest that the enhancement of 2D materials dispersion due to functionalization is related to increased attraction between the material and the solvent, which agglomerates near the layers and improves repulsion between the sheets.²¹⁸ Functionalization can also enhance lubrication directly. For instance, DFT calculations show that graphene functionalization reduces friction by decreasing the energy corrugation at the interface due to the repulsion between similarly charged atoms.²¹⁹ However, charge displacement does not always enhance lubrication, as oxidation of MoS₂ increases friction due to a less uniform charge distribution and interlayer bonding.²²⁰ Additionally, the size of 2D material particles after exfoliation influences the friction and wear behavior. Exfoliated hBN particles showed optimal wear reduction properties at an average size of 70 nm in SAE 40W-15 oil,²²¹ while reduction of the MoS₂ particle size from 2 μm to 180 nm by extended ultrasonication reduced the friction coefficient and wear rates by a factor of more than 2.²²² 

As macroscopic lubricants require significant volumes of material to be dispersed throughout liquid media, and as 2D materials require multilayer thicknesses to provide van der Waals shear effectively, ultrasonication is an ideal exfoliation method for preparing 2D material lubricants. Ultrasonication has been demonstrated to be effective for exfoliating a wide variety of 2D materials, thereby offering promise for many commercial tribological applications that may require different tribochemical conditions. Through the exfoliation of these materials directly in the lubricant medium, ultrasonication provides a simple one-step scalable method for producing 2D material lubricants.

An alternative method for solution exfoliation of 2D materials, which is also highly scalable, is high shear mixing. This technique involves exfoliating nanoparticle agglomerates in a solution by the viscous forces that flow through a narrow channel with very high velocity. The viscous forces in the channel cause the solvent to exert high shear forces across the 2D particles, which, when combined with the weakening of van der Waals forces by the solvent solution, break the van der Waals bonds producing thinner sheets.²²³ Additionally, the shear forces in the solvent mechanically enhance the degree of intercalation for molecules between 2D layers, which further decreases van der Waals forces in a synergistic effect.^224,225 This results in 2D sheets with a low defect content as the forces required are much weaker than other exfoliation methods.²²⁵ Nonetheless, this process requires a balance of forces to ensure efficient exfoliation without breaking the exfoliated 2D sheets.

Paton et al.²⁰⁰ first demonstrated a rotary mixing process where a critical shear rate of ∼10⁴ s⁻¹ was necessary for the shear exfoliation of graphene in NMP. The rotor–stator gap was maintained on the order of 100 μm to create high shear rates in the narrow channel. However, due to the breaking of the nanosheets, high-defect contents were recorded in 2D graphene exfoliated at high rotor speed. To address this issue, Liu et al. used a high shear mixer to exfoliate relatively low-defect density graphene nanosheets.²²⁶ The shear mixer consisted of a high-speed rotor and a stator [Fig. 9(a)] where the rotor's blades spin at high speed, expelling the solvents into the surrounding space and resulting in high-speed fluid flows in the tight space between the stator and rotor. The fluid's velocity gradient generates an enormous shear force across the 2D material, which separates the weakly bonded 2D nanosheets from the bulk material. Moreover, jet cavitation due to the high-pressure difference and collision between the particles also facilitates the exfoliation of layered materials [Fig. 9(a)].

The mechanics behind this process are of utmost importance, as the critical shear rate of the solvent plays a significant role in determining the quality of the exfoliated nanosheets. The critical shear rate $(γ)̇$ depends on several factors, including the fluid density (ρ) and viscosity (μ), the bulk particle's mechanical properties (length L, width W, Young's modulus E, bending rigidity D, the total number of layers N, flaw size a), interfacial adhesion energy between the sheets (Γ), and area of contact. The relation between the critical shear rate and the adhesion energy between the 2D sheets in bulk particles is shown in the following equation:²²⁷ 

It can be noted that an increase in flaw size will make the material weaker, and thus, shear rate (⁠$γ̇$⁠) must decrease with increasing flaw size (a) to preserve the material integrity. Conversely, any increase in adhesion energy must be matched with an increased shear rate to avoid agglomeration. For large aspect ratio particles suspended in a solution, it can be assumed that the particles are aligned with the fluid flow. The instantaneous equilibrium between the external work, the change in adhesion energy, and the change in bending energy for an inextensible sheet can be used to compute the critical value for exfoliation. The critical shear rate can thus be explained as a function of a, D, and μ, which takes the form:²²⁷ 

and this equation can be rewritten in terms of the nondimensional shear rate and nondimensional adhesion energy²²⁷ 

Botto et al.²²⁷ reported that the bending rigidity of the of the 2D sheets has little contribution on the exfoliation efficiency for strongly stressed nanosheets, so Eq. (3.21) can be simplified as²²⁷ 

For mildly stressed sheets, the contribution of bending rigidity is significant, so the critical shear rate for peeling of one layer of 2D material from bulk crystal is expressed as follows:²²⁷ 

In a more recent paper, Botto's team used numerical solutions of the Stokes equations to predict a realistic hydrodynamic load distribution.²²⁸ By combining the results with an analytical model, they proposed that the critical shear rate also depends on $q0$⁠, which characterizes the loading, and $χ$⁠, which represents the ratio between crack length (a) and cohesion length (⁠$λ4=4D/ke$⁠), as given by $χ=kea4/4D$⁠. The expression for the critical shear rate is thus²²⁸ 

Extending this mechanism of shear-induced exfoliation, Paton et al.²²⁹ demonstrated the production of few-layer graphene using microfluidizers. A pneumatic or hydraulic powered piston pumps fluid down a microchannel in a microfluidizer, producing considerable pressure at a very high fluid speed. This results in a high shear rate, which is applied uniformly to the sample. Natural graphite was dispersed in de-ionized (DI) water containing surfactants (sodium cholate), and a pressure of 209 MPa was maintained in the microfluidizer. The final concentration reported was 0.31 g/l, which corresponds to a 3% yield, with the overall production rate reported to be 72 mg/h. Most flakes were relatively thin (∼10–12 layers), and a small percentage of flakes contained an average of 2 layers. Tran et al.²³⁰ demonstrated shear exfoliation of graphene using Taylor–Couette flow, which consists of a viscous fluid confined in the gap of two rotating cylinders. In this case, the authors used an outer cylinder with a diameter of 57 mm and an inner cylinder with a diameter of 52 mm. The liquid in the 2.5-mm gap between the cylinders created enough shear force to exfoliate graphene with a reported yield of approximately 5%, and most of the flakes showed a thickness less than or equal to 3 nm. This technique was noted to induce few defects with the Raman Δ(I_D/I_G) of the exfoliated graphene reported as 0.14. However, one issue with rotary shear exfoliation is the lack of scalability and economic feasibility. As such, scalable techniques such as non-rotary shear and high-speed liquid flow through a narrow channel have become preferable and noted to generate a sufficient shear rate to exfoliate of graphene.²⁰⁰ 

A recent technique in exfoliating layered materials using shear force has been demonstrated by Rizvi et al. using a compressible flow exfoliation (CFE) process [Fig. 9(b)].²³¹ This technique uses a high-pressure compressible gas rather than a liquid to produce a yield as high as 10%. A unique advantage also arises from decoupling the exfoliation step from the dispersion step by making the process solvent independent. Unlike ultrasonication, CFE introduces minimal defects in the exfoliated layered materials due to the rapid movement of the bulk material through ultrasonic shock waves (∼0.2 s) in the gaseous medium compared to liquid-based shear exfoliation.

Other unconventional approaches have also been pursued in shear exfoliation; Varrla et al.²³³ exfoliated graphene from graphite using only household detergent and a kitchen blender. Most of the exfoliated flakes were ten layers or less and had Δ(I_D/I_G) values from 0.2–0.5 with a process yield of 1%. The same approach was also applied to several exfoliated TMDs, including MoS₂ with a thickness of ∼2–12 layers²⁰⁴ and a concentration as high as ∼0.5 mg/ml, corresponding to a yield of 1% from the bulk material and an optimized production rate of ∼60 mg/h. Gravity-based exfoliation was described by Yin et al.²³⁴ for MoS₂ nanosheets, which employed a combination of shear and collision forces generated in the gap between the stator and rotor of a shear homogenizer to produce the exfoliation. Almost 84% of the nanosheets were reported to be less than five layers thick, with 22% of the flakes as bilayers and ∼40% of the flakes as trilayers. Another interesting approach was demonstrated by Chen et al. using a vortex fluidic device (VFD) to exfoliate graphene and BNNSs.²³⁵ Exfoliation occurs in the thin film of the VFD, which contains a rapidly rotating 45° inclined glass tube. Due to the interplay between centrifugal force and gravitational force, efficient exfoliation occurs. They reported a yield of ∼1% for graphene monolayer and ∼5% for a monolayer of BNNSs. Large-scale production of luminescent quantum dots of exfoliated TMDs has also been reported using a high shear mixer²³⁶ wherein the MoS₂ or WS₂ crystals were mixed with DMF, and homogenization of the mixture took place in a high shear mixer. After running the mixture for 1 h at 5000 rpm, the dots formed from the bulk crystals with a lateral length of ∼5 nm and a thickness of 3–5 layers.

Wet jet milling is another solution-based shear exfoliation technique [Figs. 9(c) and 9(d)] that has been reported in recent years as a scalable and continuous method to exfoliate few-layer 2D materials. Bellani et al.¹²³ reported a three-pass wet jet milling technique to produce 20 g/h single- or few-layer graphene for supercapacitor materials. This process uses a high pressurized (180–250 MPa) jet stream that is produced by a hydraulic piston to force the solvent and layered crystal mixture through perforated disks with 0.1–0.3 mm nozzle diameters.²³² This creates a high shear flow that homogenizes and exfoliates the layered materials by taking advantage of the fluid shear forces in the processor. Castillo et al. also reported a similar wet jet milling method to produce very thin (∼1.5 nm) graphene dispersions. Almost half of the flakes produced were between 1.5 and 5 nm in thickness, and the production rate was reported to be 2.35 l/h.²³² Examples of low-defect 2D materials produced by wet-jet milling and CFE are shown in Figs. 9(e)–9(g).^200,232

One of the most common applications of shear exfoliation, as a rigorous solution-based technique that also effectively disperses the material within the matrix, is in the formation of cement composites with graphitic materials. Cement, the binder and predominant source of strength in concrete, forms an effective composite material by exfoliating graphene and its derivative materials into the matrix to improve the overall macroscopic properties. While concrete performs excellently in compression, it fails easily in tension or shear, where the high mechanical strength and specific surface area of graphene materials make them exceptional additives.^41,237,238 Typically, bulk quantities (kilograms) of graphite materials are required for cement-based composites,^140,238,239 and shear exfoliation-based methods can produce large amounts of exfoliated 2D materials with high yields compared to other bottom-up methods. Additionally, shear exfoliation methods allow for combined exfoliation and mixing of cement composites and are less complicated and time-consuming than other synthesis methods.

The mixing of graphene-cement composites is principally conducted in two stages: (i) dispersion and exfoliation of graphene materials in water and (ii) mixing of graphene supernatant with dry cement and aggregates.^238–242 The effective dispersion and exfoliation of graphene derivatives are concurrent when preparing the supernatant and have been demonstrated to be highly effective through continuous high-speed shear mixing.^{239,243–245} One challenge, however, is that pristine graphene is hydrophobic and challenging to disperse in water. This has resulted in the adoption of functionalized graphene such as GO, which is hydrophilic and highly dispersible in water for graphene–cement composites.^239,242,246 However, even with appropriate dispersion in water, the dispersion of graphene and its derivatives is challenging in a highly alkaline cement paste matrix saturated with ions such as Ca²⁺, K⁺, Na⁺, and OH⁻.^245,247,248 As such, shear mixing is often combined with chemical exfoliation by surfactants, particularly perchloroethylene (PCE), to prepare cement-based composites. PCE improves the dispersion and exfoliation of GO in an aqueous solution due to two major effects: (i) stronger hydrogen bonding and (ii) steric repulsion between GO and PCE.²⁴⁹ The steric stabilization effect and self-agglomeration of GO-PCE suspensions are schematically presented in Fig. 10(a). The mixing sequence of graphene derivatives, surfactants, water, cement, and aggregate also plays a vital role in the exfoliation and dispersion of graphene derivatives in aqueous solutions. Figure 10(b) presents a series of GO dispersion in four mixing sequences (samples 1–4) among PCE, cement, and GO in water from a study by Lu et al.²⁴⁹ 

Exfoliated 2D materials can significantly improve the mechanical properties of cement in different loading modes by acting as high strength and stiffness aggregate particles in the mixture. For graphene derivatives, this enhancement occurs due to two primary mechanisms in cement-based composites: enhancing the mechanical properties by biphasic reinforcement and modifying the microstructural properties. For example, the oxygen-containing functional groups of GO facilitate its efficient dispersion during shear exfoliation, enhance cement hydration, and reinforce the composite microstructure, which demonstrate increases in the compressive and flexural strength by 28% and 80%²³⁹ or 21% and 26%²⁵⁰ in two different studies compared to the standard cement mix. Exfoliated graphene materials also considerably modify the microstructural properties in the composite by influencing the exothermic reaction between cement and water during the cement hydration process, which alters the composite microstructure at the nano- and microscales.²³⁹ Three typical examples of GO-cement composite microstructures are presented in Fig. 10(c).²⁴⁶ The exfoliated 2D planes of GO and the different functional groups, such as carboxylic acid groups, encourage the precipitation of CaOH₂ and C–S–H gel and bond with those hydration products within the cement composite matrix.^251–255 These factors effectively reinforce the cement-based composite matrix and fill pores, densifying the microstructure. Indeed, MD simulations have shown that GO acts as a nucleation site for C–S–H gel hydration, thanks to H-bond formation between OH groups and water molecules, producing a hydrophilic interface.^256,257 They also pointed out that strengthening in these composites happens mainly by H-bonds and covalent-ionic bonds (O–Ca–O or O–Al–O) involving OH groups.²⁵⁷ 

Shear exfoliation is a truly continuous process where the constant flow of material through the rotor or nozzle can produce bulk quantities of material in a liquid solution, making it an ideal synthesis method for applications requiring significant amounts of material when specific defect concentrations and monolayer precision are not required. Several different techniques can be used to produce continuous shear forces within the supernatant solution, including compressible flow exfoliation and wet-jet milling. As shear exfoliation provides a scalable, facile, and concurrent method for synthesizing 2D material in a liquid medium, cement composites are quickly produced in a two-step process, enhancing the dispersion, mixing, and curing processes. As the most used material globally, cement reinforcement and enhancement are of utmost concern for structural applications, and cement-2D material composites have demonstrated vastly enhanced structural properties.

Electrochemical exfoliation is a scalable method capable of producing a large quantity of 2D nanosheets in a liquid solution (electrolyte) using an electrical current either by cathodic reduction or anodic oxidation. The electrical current introduces ions within the electrolyte that are attracted to the bulk 2D material and intercalate between layers. This intercalation thereby weakens van der Waals bonds and separates layers through a one-step rate-controlled exfoliation process. Electrochemical exfoliation methods are relatively simple to design, assemble, and operate under ambient conditions. In 2014, Liu et al. first demonstrated a mechanism for anodic exfoliation of MoS₂ in an aqueous Na₂SO₄ solution.²⁵⁸ The $OḢ$ and $Ȯ$ radicals are created by oxidation of water SO₄ (2−); The charge of the ion is not mentioned and intercalate into MoS₂ layers when a positive voltage is applied to the bulk MoS₂ electrodes [Fig. 11(a)]. As a result of the oxidation of the radicals and anions, O₂ and/or SO₂ gas is produced, which considerably extends the interlayer distance of MoS₂ and accumulates enough to separate MoS₂ flakes from the bulk MoS₂ crystals. However, because the electrooxidation reaction takes place on the surface of the bulk material electrode, the products are oxidized quickly, which affects the quality and degree of the exfoliated MoS₂.

Parvez et al.²⁵⁹ demonstrated efficient electrochemical exfoliation of graphite using ammonium sulfate [(NH₄)₂SO₄], sodium sulfate (Na₂SO₄), and potassium sulfate (K₂SO₄). They reported that ∼85% of the exfoliated nanosheets were three or fewer layers thick. The suggested mechanism of exfoliation for this system was as follows: Applying a bias voltage results in a reduction of water at the cathode, creating hydroxyl ions (OH⁻) that act as a strong nucleophile in the electrolyte. The nucleophilic attack of graphite by OH⁻ ions initially occurs at the edge sites and grain boundaries, which leads to depolarization and expansion of the graphite layers, thereby facilitating the intercalation of sulfate ions (SO₄²⁻) within the graphitic layers. During this stage, water molecules may also intercalate with the SO₄²⁻ anions. Reduction of SO₄²⁻ anions and self-oxidation of water produce gaseous species such as SO₂ and O₂, as evidenced by the vigorous gas evolution during the electrochemical process, which separates the 2D layers. There have also been numerous other reports on the electrochemical exfoliation of graphene using ions of H₂SO₄, Bu₄NBF, and other electrolytes with good yields.^{121,260–265}

Unlike other exfoliation strategies, no analytical models exist of the electrochemical process as a whole. However, the physical and chemical mechanisms at play during the process are known to some degree and the general process can be broken down into three main steps: (i) electrochemical generation of ions in the electrolyte, (ii) interlayer diffusion and intercalation of these ions in the bulk material, and (iii) electrochemical reaction turning the ions into gases within the material, thus separating the layers.

Steps (i) and (iii) are electrochemical reactions and therefore their thermodynamics follows the Nerst equation.²⁶⁷ Considering a simple reduction reaction $Ox+ze−→Red$⁠, the half-cell reduction potential (⁠$Ered$⁠), taking as a reference the standard potential (⁠$Ered0$⁠), can be computed from the universal gas constant (R), the temperature (T), the number of electrons transferred (z), the Faraday constant (F), and the chemical activity of the involved species (a), as shown in Eq. (3.26), where activity is generally replaced by concentration. The same can be written for an oxidation process, as well as the full cell. Although the effective potentials can be altered by surface effects such as electrocatalysis at the electrode, this modeling can provide estimates for the necessary potential to induce the reduction or oxidation of specific species, as well as to point out any parallel electrochemical reactions that might happen²⁶⁷ 

The kinetics of these electrochemical reactions can be modeled with the Butler–Volmer equation.²⁶⁸ The electrode current density (j) depends on the exchange current density (⁠$j0$⁠), the cathodic and anodic charge transfer coefficients (⁠$α$⁠), the activation overpotential (⁠$η=E−Eeq$⁠), and other previously mentioned variables, as shown in Eq. (3.27). It allows the prediction of the expected current for a given applied potential, or vice versa, depending on which variable is being controlled. As the current defines the speed of exfoliation, while the potential constrains the electrochemical reactions taking place, being able to predict both can help optimize the synthesis of 2D materials²⁶⁸ 

Step (ii), in its turn, is a process of interlayer diffusion, and its nature depends on the interlayer distance and the ion. For large enough distances, the process can be treated as free diffusion, while for short distances, it is a case of Knudsen diffusion, since it happens in a length that is comparable to the mean free path of the particles.²⁶⁹ The mechanism may vary from system to system, considering that ionic intercalation may be facilitated by modification of layer edges, leading to some degree of separation before formation of gas.²⁶⁷ 

In the case of Knudsen diffusion of a species A, the self-diffusion coefficient (⁠$DAA$⁠) depends on the path length (⁠$λ$⁠) and the molar mass of the species (⁠$MA$⁠), as shown in Eq. (3.28).²⁶⁹ This model can estimate diffusibility of ions between layers, although the effective rate of mass transport can be modified by surface effects such as adsorption²⁶⁹ 

Comparing the rate of electrochemical reactions with the rate of interlayer diffusion may help optimize the exfoliation process, as the goal is to produce gas between the layers of the bulk material, not at its surface, as well as to avoid excessive voltages and currents that damage the 2D material. However, to our knowledge, no unified mathematical approach has been made in that sense.

Similarly to other fluid-phase strategies, electrochemical exfoliation can be studied with DFT and MD simulations by estimating the energetic changes of the material due to intercalation with other species (in this case, ions). For instance, DFT calculations showed that sulfate anions are the most efficient for graphene production, demonstrating a mechanism in which their intercalation causes a higher repulsive binding energy between layers [Fig. 12(a)].²⁷⁰ Lee et al.²⁷¹ performed MD simulations of graphite in different electrolytes that are relevant for battery applications, where exfoliation is not wanted. They unveiled a sliding displacement mechanism for exfoliation and estimated which solvent provides higher and lower energy barriers [Fig. 12(b)]. FEM has also been used to investigate electrochemical exfoliation. Muhsan et al.²⁷² studied the continuum diffusion of sulfate anions within graphite, estimating that the resulting stresses on the graphene layers are high enough to break van der Waals bonds [Fig. 12(c)], and Si et al.²⁷³ used a cohesive zone model to study the bending and delamination of MoS₂ [Fig. 12(d)].

The oxidation of 2D materials during the electrochemical process results in altered materials that can be unsuitable for certain applications, so efforts have been directed toward nonoxidative exfoliation. For example, Cooper et al.²⁷⁴ reported a nonoxidative exfoliation approach of graphite via the intercalation of tetraalkylammonium cations into pristine graphite. Na⁺/dimethyl sulfoxide complexes were used as intercalation agents in a graphite cathode²⁷⁵ producing exfoliated graphene flakes of 3.1 nm thickness on average (∼7 layers). The resulting film fabricated from exfoliated graphene showed a high electrical conductivity of 380 Sm⁻¹. Many other 2D materials have also been electrochemically exfoliated, including a wide range of TMDs from MoS₂ to WS₂, TiS₂, TaS₂, ZrS₂, MoTe₂, NbSe₂, and Bi₂Te₃.^276,277 Li et al.²⁶⁶ demonstrated ultrafast cathodic exfoliation of phosphorene with a reported yield of ∼80% [Figs. 11(b)–11(f)]. Phosphorene nanoparticles have also recently been reported to be exfoliated using bipolar electrodes.²⁷⁸ A series of back-gated FETs were fabricated from few-layer black phosphorous synthesized by cathodic exfoliation, which demonstrated high mean hole mobility up to ∼100 cm² V⁻¹ s⁻¹ with a high on/off ratio (∼10⁴ on average). Similarly, Liu et al.²⁷⁹ exfoliated 5–50 μm lateral sized MoS₂ in a Na₂SO₄ electrolyte to produce a back-gated FET of exfoliated MoS₂ nanosheets exhibiting carrier mobility of 1.2 cm² V⁻¹ s⁻¹ and a very high on/off ratio (∼10⁶).

Unlike mechanical exfoliation processes, one can control the number of exfoliated layers using the electrochemical approach. Huang et al.²⁸⁰ demonstrated the exfoliation of few-layer phosphorene using the cationic intercalation method and manipulated the layer number by changing the applied potential to the electrode. A negative potential of −2.1 V was required to initiate the intercalation of cations into the bulk BP. When a negative potential of −5 V was applied, the exfoliated flakes were ∼0.8 nm (∼2–3 layers) thick, while changing the applied potential to −10 and −15 V led to increasing thicknesses of 2.5- to 3.7- and 2.9- to 3.3-nm-thick flakes, respectively. Similarly, controlled exfoliation of graphene by regulating the intercalating potential was reported by Murat et al.²⁸¹ where increasing the intercalating potential led to larger and thinner graphene sheets. Although exfoliation using DC power is the most popular input for electrochemical exfoliation of layered materials, there have also been reports using AC currents. Yang et al.²⁸² reported exfoliating high-quality graphene nanosheets (∼1–3 layer) with a high yield (∼75%) by AC applied potential. A moderate potential of ±10 V was applied, and the current frequencies varied from 0.05 to 0.25 Hz. The best quality graphene (I_D/I_G = 0.15) was obtained when the potential was ±12 V at frequency = 0.1 Hz, and the lateral size of the flakes varied from 1 to 5 μm.

The inherent size, exceptional electrical properties, and mechanical robustness exhibited by exfoliated 2D materials make them premium candidates for integration with energy storage applications. Specifically, the ability to synthesize 2D materials with relatively high yield, extremely high surface area-to-volume ratio, and control over the number of layers make electrochemically exfoliated 2D materials highly favorable for use in energy storage and discharge. In particular, supercapacitors and high-efficiency batteries have demonstrated considerable performance improvements compared to conventional storage devices when prepared using exfoliated 2D materials.

Supercapacitors, also called ultracapacitors, are a type of electronic energy storage device typically characterized by values several orders of magnitude higher than conventional electrolytic capacitors. Conventional capacitors comprise two layers of conductive materials separated by a dielectric medium. In supercapacitors, high capacitance is achieved through increased surface area conductive electrodes coated with a porous material, typically activated carbon, immersed in electrolyte solution,²⁸³ and are capable of storing >100 times the energy per unit volume as electrolytic capacitors at high current for short durations.²⁸⁴ 2D materials are ideal for integration into supercapacitors as the electrode material on either side of a conducting spacer [Fig. 13(a)]. Supercapacitors based on exfoliated 2D materials have demonstrated extremely high power densities and long capacitance retention lifecycles, which can be attributed to the high surface area-to-volume ratio and electrical conductivity they exhibit.³³ The fabrication of 2D material-based supercapacitors requires scalability, high crystallinity for low sheet resistance,²⁸⁵ and ease of processability for transferring and forming 2D materials as electrode materials [Fig. 13(b)].²⁸⁶ Electrochemical exfoliation offers advantages, as it is a scalable production method capable of producing highly crystalline and solution-processable 2D materials at a competitive production cost.^35,287,288 Additionally, two other notable benefits of 2D materials are their inherent size and flexibility, which makes them suitable for developing micro-supercapacitors, and flexible supercapacitors.

Some of the most notable examples of supercapacitors produced by the exfoliation of 2D materials take advantage of tuning material properties, such as phase and thickness, during the exfoliation process to produce high specific capacitances from various materials. For example, monolayer 1T MoS₂ produced by chemical exfoliation exhibits a two-order magnitude increase in specific capacitance compared to bulk MoS₂ (366.9 F g⁻¹ compared to 3.15 F g⁻¹ for bulk 2H MoS₂²⁸⁹). Additionally, Acerce et al.²⁹⁰ prepared supercapacitor electrodes of exfoliated 1T MoS₂ by performing ion intercalation (H⁺, Li⁺, Na⁺, and K⁺) during the electrochemical exfoliation process to control the phase and reported specific capacitance values in the range of $∼$400 to $∼$700 F g⁻¹ with retention greater than 93% over 5000 cycles. Similarly, Khanra et al.²⁹¹ modified graphene during electrochemical exfoliation using 9-anthracene carboxylate ions (ACA) as the electrolyte solution. ACA-functionalized graphene sheets were used to prepare an electrode that demonstrated a specific capacitance of 577 F g⁻¹ with 83% retention after 1000 cycles.

In addition to this functionalization, exfoliation of 2D materials in a solution can also offer opportunities for scalable production; Liu et al.²⁹² developed an inkjet-printable solution by electrochemical exfoliation of graphene with an electrochemically active polymer and used a commercial printer to produce flexible micro-supercapacitors with an areal capacitance of 5.4 mF cm⁻² and capacitance retention of 98.5% after 1000 bending cycles at a radius of 5 mm. These micro-supercapacitors can be connected in arrays of several hundred units to reliably charge and deliver 12 V across repeated charging [Figs. 13(c)–13(e)]. However, the capacitances reported for 2D material-based supercapacitors remain relatively low compared to their theoretical maxima. For example, graphene has a theoretical capacitance of 550 F g⁻¹, but typical graphene supercapacitors exhibit values less than half of the theoretical, typically around 200 F g⁻¹.²⁹³ This is due to inherent imperfections during synthesis, characterization, and device development,²⁹⁴ so improving the electrochemical performance of 2D materials to deliver supercapacitors with even higher energy and power density and cycle life remains an ongoing area of critical focus.

Another application of interest for 2D materials within energy storage is high-efficiency batteries, which are characterized by high energy density and significant energy retention rates after repeated cycling. Lithium-ion batteries (LIBs) are the most common energy storage device available and induce current between the anode, typically a porous carbon, and cathode, typically a metal oxide, through an electrolyte. Due to their excellent electrochemical performance, high surface area, and stable chemical structure, exfoliated 2D materials have been successfully used as electrode materials, both for the cathode and anode, to develop high-efficiency batteries.²⁹⁹ The highly crystalline and thin structure of exfoliated 2D materials allows for efficient and reversible conversion reactions with electrolyte ions such as Li⁺ as both sides of the 2D material sheet are accessible to ions, leading to enhanced storage capabilities [Fig. 13(f)].²⁹⁷ As such, many of the experimental values for 2D material systems are orders of magnitude greater than standard battery materials. Electrochemical exfoliation offers advantages in the synthesis of 2D materials for high-efficiency batteries including that they are solution-processable,^35,300 which is common practice in scalable LIB manufacturing,³⁰¹ and inexpensive compared to bottom-up methods such as CVD.³⁵ Additionally, sonication-assisted liquid exfoliation is highly suitable for producing 2D material-based LIB electrodes because it can provide high yield and processability.³⁰² An example of the workflow by ultrasonication for the exfoliation of C₃N₄ and reduced-GO LIBs is shown in Fig. 13(g).²⁹⁸ 

The production of high-efficiency LIBs has been demonstrated for a wide variety of 2D materials to produce remarkably high specific capacities. For example, Lian et al.³⁰³ produced electrothermally exfoliated few-layer graphene anodes with specific capacities as high as 936 mA h g⁻¹ and 91% capacity retention after 40 cycles. This high performance was attributed to the high specific surface area resulting from the porous, defective, and few-layer structures that are produced by electrothermal exfoliation. Beyond graphene, many other electrochemically exfoliated 2D materials show significant promise as electrode materials, with recent examples including MoS₂,³⁰⁴ covalent organic frameworks,³⁰⁵ MoS₂/WS₂,³⁰⁶ and V₂O₅,³⁰⁷ GeS,³⁰⁸ and TiO³⁰⁹ exfoliated nanosheets. In combination with electrochemical exfoliation, ultrasonication can enhance yield and production of 2D materials for electrode development. For example, MoS₂/polyethylene oxide (PEO) composite anodes were prepared by Xiao et al.³¹⁰ through hydrolysis and ultrasonication, which achieved discharge capabilities above 1000 mA h g⁻¹, significantly higher than conventional LIB capacities, which are limited to a theoretical maximum of ∼370 mA h g⁻¹.³¹¹ The high capacity achieved with the addition of 5% PEO was attributed to the increasing MoS₂ interlayer spacing by PEO intercalation during exfoliation, thereby increasing lithium-ion transfer compared to conventional exfoliated or CVD-grown MoS₂. The interlayer spacing of MoS₂ has also been enhanced through a process in which MoS₂ was exfoliated through a combination of a chemical and thermal process, and then annealed to form a multilayer hybridized structure containing mesoporous carbon. This structure benefits from the synergy of the two phases to produce a specific capacity of 1113 mA h g⁻¹ with 92% retention over 500 cycles.³¹² DFT calculations attributed this enhancement to the efficient Li⁺ intercalation at the interface. However, it should be noted that issues remain with the adoption of 2D materials as electrodes, including the structural reliability of these ultrathin materials.³¹³ Despite these challenges, their demonstrated potential makes them ideal candidates for future energy storage devices.

Electrochemical exfoliation is the most controllable exfoliation technique, which allows for precise tuning of the desired 2D material properties based on the applied voltage during electrochemical exfoliation. This synthesis technique uniquely suits applications requiring low throughput but high thickness control, such as energy storage applications. Additionally, the intercalation of ions during electrochemical exfoliation increases the interlayer thickness, making 2D materials produced by this method well suited for energy storage devices.

The five exfoliation techniques covered in Secs. III B–III F, represent the most prominent methods for exfoliating 2D materials. Examples of 2D materials exfoliated by these methods, and the prominent advantages and disadvantages of each technique are summarized in Table I below.

The library of two-dimensional materials is typically limited to the class of van der Waals crystals such as MoS₂ [Fig. 14(a)], despite the vast majority of technically viable materials in industrial-scale applications belonging to the class of non-van der Waals materials such as iron disulfide (FeS₂) [Fig. 14(b)]. The effect of confinement in one dimension on non-van der Waals 2D materials is only recently being explored, which is a result of the difficulty in fabricating these materials at atomic thicknesses with large lateral size or area. The main difference between van der Waals and non-van der Waals materials is how their layers are bonded together. In the case of the former, layers are held together by weak van der Waals interactions in the (001) direction, while for the latter, constituent atomic layers are held by much stronger bonds (metallic, covalent, or ionic). Recent advancement of cleaving non-van der Waals bulk materials to their ultra-thin counter parts through the state-of-the-art liquid phase exfoliation approach has led to renewed research interest among scientific community.³⁴⁵ The existence of cleaving/parting planes in certain directions of non-van der Waals materials, where the bonding strength is relatively weak compared to other crystallographic directions of the bulk crystal, facilitate smooth and preferential exfoliation along that plane when subjected to a high enough magnitude of shear force [Fig. 14(c)].

The preparation of non-van der Waals 2D materials is by no means a trivial approach. Unlike their van der Waals counterparts, non-van der Waals materials have a significant tendency to satisfy the surface dangling bonds that are created in the exfoliation process.³⁴⁶ Given the thermodynamic stability of typical layered van der Waals 2D materials, there exist multiple routes to overcome the weak van der Waals forces and synthesize 2D forms via effective exfoliation techniques as discussed in Secs. III B–III F. However, in order to synthesize non-van der Waals 2D materials, one must develop strategies that depart from the thermodynamic equilibrium. Due to strong three-dimensional covalent/ionic bonding, it is highly unlikely to obtain non-van der Waals 2D materials through top-down approaches such as conventional mechanical exfoliation. However, taking advantage of the cleavage planes along which intrinsic isotropic covalent/ionic crystals tend to be unstable due to very high broken bond density, Balan et al.,³⁴⁵ demonstrated that even covalent/ionic crystals can be exfoliated to atomic thickness by conventional liquid phase exfoliation in suitable organic solvents.

It is demonstrated that non-van der Waals exfoliation leads to thin layers with different sizes and crystallographic orientations, the characteristics of which are dependent on the crystalline structure of the bulk material and also on the exfoliation energy required to delaminate the layers along a given plane. The exfoliation energy value is an important parameter to guide experimentalists in predicting whether a non-van der Waals material can be easily exfoliated or not while the crystallographic structure of the bulk material can provide insight into the structural characteristics of the thin layers that could be obtained from the exfoliation process. Based on this information, the appropriate exfoliation process to be used can also be determined. The estimated exfoliation energy for layered and non-layered materials has been obtained mainly from ab initio simulations using DFT.⁷⁸ During the exfoliation process, the bulk material will experience shear stresses, which will induce dislocations and/or create sub-grain boundaries, thereby weakening the bonds among the layers and easing the peeling off process. These dislocations and defects will occur more frequently along the slipping planes of the crystalline structure, which are those with the highest atomic density. Due to this, it is expected that the exfoliation energy will be smaller for layers with the orientation of the slipping planes, which could suggest the preferential orientation found for the exfoliated thin layers. Moreover, besides the exfoliation energy, the crystal structure of the bulk material can provide helpful information of what could be obtained after the exfoliation process.

The exfoliation energies required to exfoliate non-van der Waals materials are significantly higher than those for van der Waals materials. The breaking of formal bonds demands over an order of magnitude more energy than required to overcome the van der Waals interactions in layered materials. However, a fine balance must be struck to ensure that the in-plane structure remains intact and without significant defects introduced during the process. In addition, the dangling bonds, which are created at the surface, can lead to reagglomeration, oxidation, and structural reorganization during exfoliation, which creates a process with significant complexity compared to conventional exfoliation processes. Nonetheless, due to the presence of parting/cleavage planes and the rich verity of oxides, sulfides, and nitrides, naturally existing earth ores and minerals such as Cr₂S₃, Al₂O₃, FeCr₂O₄, TiO₂, and many other non-vdW materials have been successfully exfoliated to atomic thicknesses. These exfoliated non-vdW 2D materials are being explored for 2D magnetism, low friction, electro and photocatalysis, piezoelectricity, and various optoelectronic properties.^{345,347–349}

Apart from the five well-studied exfoliation processes previously mentioned, there are reports of other interesting and unique methods to exfoliate layered materials. Some emerging methods that present potential but have not been widely explored and adopted have been included here for discussion. Tang et al.³⁵⁰ used the interaction between polymer chains and different surfaces of MoS₂ (edge and basal plane surfaces) by a functionalized atomic force microscope cantilever to initiate polymer-based exfoliation of thin layers of MoS₂ by creating shear forces with the AFM tip [Fig. 15(a)]. Another interesting technique uses plasma-assisted exfoliation of GO by Wang et al.³⁵¹ using a magnetically enhanced dielectric barrier discharge system to produce the plasma. This was employed to exfoliate N-doped graphene from polyaniline-modified GO to fabricate high-performance solid-state flexible supercapacitors. MXenes are an interesting unique class of 2D material, which are synthesized by selective etching (chemical exfoliation) of MAX phases, in which the A atoms are attacked by an acid, leaving a 2D MX structure behind.³⁵² This has been widely employed for various MXene materials, such as Ti₃C₂T_x and Nb₂CT_x, and has unlocked a new 2D material class since the first synthesis of a stable MXene in 2011.³⁵³ Finally, a novel and fast method (∼10 min) to exfoliate ultrathin 2D materials, including C₃N₄, graphene, hBN, and BP, using liquid nitrogen and microwave treatment, was demonstrated by Zhu et al.³⁵⁴ The bulk material is first soaked in liquid N₂ and then exposed to pulsed microwaves (∼700 W) to produce 2D materials of <5 nm thickness [Fig. 15(b)]. Liquid N₂ pretreatment weakens the van der Waals force between the layers of 2D materials before the microwaves add energy to overcome the bonds. While these techniques are indeed nonstandard, they employ the same mechanical, ultrasonic, or electrochemical approaches of the more common methods to accomplish similar outcomes through a unique methodology.

Given the disruptive potential offered by the remarkable properties of 2D materials, the study of 2D materials is currently a highly active field of research. Developing cost-effective, scalable, and high-throughput methods to produce quality 2D crystals remains a significant focus to scale the fundamental nanoscale properties of these materials to macroscopic applications. Given the enormous amount of research dedicated to the field, and as the applications mentioned in this review begin to penetrate commercial markets, the required improvements to enable mass production will also come to fruition. Table S1 (supplementary material) presents a summary of some of the major applications of exfoliated 2D materials used in energy and storage, mechanics and design, polymer composite, and cement composite applications.

While the remarkable properties of two-dimensional materials quickly became evident, these materials' scalable production and use in commercial products have remained a predominant focus throughout the past two decades. While top-down approaches can produce consistent material thicknesses, their scalability for bulk quantities of 2D materials remains limited. Exfoliation processes offer promise for batch-scale processes with a variety of defect densities and throughput scalabilities depending on the technique employed, which are appropriate for several different applications, as discussed in the present article.

The five predominant exfoliation processes—micromechanical exfoliation, ball milling, ultrasonication, shear exfoliation, and electrochemical exfoliation—all produce wide varieties of 2D materials, sizes, thicknesses, defect densities, and scalabilities. Therefore, selecting the appropriate exfoliation process becomes critical for the end application. In this article, we have identified the significant challenges and opportunities associated with the predominant exfoliation processes and we have provided a comprehensive review of the governing mechanisms and computational methods that have been used to simulate exfoliation. Furthermore, some of the major applications of exfoliated 2D materials have been highlighted including energy storage, FETs, lubricants, and composite materials for mechanical, electrical, and thermal enhancements.

In addition to developing and improving mass-scale production methods, it is also vital to enhance low-scale production methods used in laboratories for research purposes. Given that many 2D materials are still in the research and development stage and that new 2D materials are being synthesized, it is important to improve laboratory-scale production methods so that they are more efficient, reliable, and quick. Whether it is the development of devices to automate certain stages of the exfoliation process or the formal establishment of standard best practices, improvements in exfoliation-based production methods will enable the next generation of devices and composite materials to revolutionize many industries. Furthermore, there are still major gaps in the theoretical investigation of exfoliation methods, specifically, in the analytical modeling of electrochemical exfoliation.

Throughout this review, we have covered many areas of promise for exfoliated 2D materials but have also captured only a select portion of the extensive literature on the topic of exfoliated 2D materials. For further reading, the authors suggest the reviews of specific exfoliation processes by Huo et al.³⁶ for liquid exfoliation, Yi and Shen⁹² for mechanical exfoliation and ball milling of graphene, or Ciesielski and Samori³²⁶ for ultrasonication exfoliation.

See the supplementary material for applications of exfoliated 2D materials, Table S1.

The authors wish to acknowledge the support of the University of Toronto Centre for 2D Materials. The authors also wish to acknowledge the funding support of the Natural Science and Engineering Research Council of Canada, the Canada Foundation of Innovation, and the University of Toronto and the Vanier Canada Graduate Scholarship The Connaught Fund.

The authors have no conflicts to disclose.

M.A.I., P.S., and B.K. contributed equally. All authors contributed to the writing and editing of the manuscript.

Md Akibul Islam: Conceptualization (lead); Writing – original draft (lead); Writing – review & editing (lead). Pulickel M. Ajayan: Funding acquisition (equal); Project administration (equal); Supervision (equal). Daman Panesar: Funding acquisition (equal); Project administration (equal); Supervision (equal). Chandra Veer Singh: Funding acquisition (equal); Project administration (equal); Supervision (equal). Tobin Filleter: Funding acquisition (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal). Peter Serles: Conceptualization (lead); Writing – original draft (lead); Writing – review & editing (lead). Boran Kumral: Writing – original draft (lead); Writing – review & editing (lead). Pedro Guerra Demingos: Writing – original draft (equal); Writing – review & editing (equal). Tanvir Qureshi: Writing – original draft (equal); Writing – review & editing (equal). AshokKumar Meiyazhagan: Writing – original draft (equal); Writing – review & editing (equal). Anand B. Puthirath: Writing – original draft (equal); Writing – review & editing (equal). Mohammad Sayem Bin Abdullah: Writing – original draft (equal); Writing – review & editing (equal). Syed Rafat Faysal: Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.