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Exfoliation of 2D Materials: The Role of Entropy Wei Cao, Jin Wang, and Ming Ma J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.9b00204 • Publication Date (Web): 18 Feb 2019 Downloaded from http://pubs.acs.org on February 19, 2019

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The Journal of Physical Chemistry Letters

Exfoliation of 2D Materials: The Role of Entropy Wei Cao1,2, Jin Wang3,4, Ming Ma*1,2,3

1

State Key Laboratory of Tribology, Tsinghua University, Beijing, 100084, China

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Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China

3

Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China

4

Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China

Corresponding Author * E-mail: [email protected]

ACS Paragon Plus Environment

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ABSTRACT: Liquid phase exfoliation (LPE) is the best-known method for the synthesis of two-dimensional (2D) nanosheets. Compared to enthalpy, entropy is hardly considered to be a factor in choosing energy efficient solvents and has not even been verified to be negligible. In this letter, we explored the entropy contribution in LPE, by performing molecular dynamics (MD) simulation of the structural flexibility effect, including graphene, hexagonal boron nitride (hBN) and molybdenum disulfide (MoS2). Our results show that surface vibration favors the exfoliation of graphene and hBN, and destabilizes the reaggregation of nanosheets in water at 300 K. While the opposite is found for MoS2. The entropy change is found to be 41%, 48%, and 4% of the enthalpy gain for graphene, hBN, and MoS2 in LPE, respectively, and 64%, 32%, and 56% in reaggregation, thereby amounts to a step advancement for solvent screening in LPE of 2D materials.

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KEYWORDS: graphene, hBN, MoS2, free energy, temperature.


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During the past decade, 2D nanomaterials, such as graphene, hBN and MoS2, have received broad interest because of their unique dimension-related properties and promising applications in energy storage, separation, catalysis, and nanoelectronics.1-3 To synthesize 2D materials with single- or few-atoms thickness from bulk phase, the strongly adhesive van der Waals (vdW) interactions between layers should be replaced by other interactions. A versatile and widely applicable method, namely LPE, is such a method that the vdW energy is reduced by liquid-solid interface energy, through liquid intercalation between layers. The method is mainly realized by shear force or sonication of bulk crystals in suitable liquids.4-6 These liquids include N-methyl-pyrrolidone (NMP)7, ortho-dichlorobenzene (ODCB)8, ionic liquids9, polymers and surfactants10. The choice of energetic efficient solvents is well reviewed.11 An early model suggests that this depends on the difference in surface tension between the layered materials and solvents: the lower the difference, the better the solvents in LPE.12-13 Further research holds the idea that the matching of the ratio of two components of surface tension, i.e. polar and dispersive, determines the screening of efficient solvents.14 Nevertheless, these theories come with an assumption that the entropy is too small to have sufficient impact on the free energy


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of the exfoliation.15-16 Texter proposed that the interfacial surface tension should be a key to the dispersion of nanosheets in solvents.17 Therefore, both the solid-liquid interaction energy and interfacial surface entropy should be considered. However, the entropy change has been hardly addressed in literatures related to LPE of 2D materials. MD simulations are recognized to be a useful tool for studying the LPE of nanomaterials.18 The molecularity of solvents at the interface is found to be important in determining the LPE processes.19 Work has been done by Blankschtein and co-workers in terms of low dimensional materials, such as carbon nanotubes (CNT), graphene, graphene oxide (GO), phosphorene, and MoS2.20-24 They obtained the free energy in the LPE process through the potential of mean force (PMF) at a certain reaction coordinate. Along with the molecular structure and solid-liquid interaction energies, MD simulations have been successfully applied to screen solvents in terms of their abilities to exfoliate 2D materials.25 Throughout these simulations, solid structures were often considered to be rigid bodies. The lattice vibrations of solids and the corresponding entropy changes are not included in the simulations. The entropy component constituting the free energy of exfoliation has also not been verified to be negligible.


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In this letter, we would explore the water-assisted LPE of 2D nanomaterials. Compared to those aforementioned liquids, water has a much larger surface tension. The water molecule is smaller and the orientation changes when penetrating into layered structures seem to hardly influence the interfacial energy of 2D materials. Despite all this, water has found its place in LPE with good outcomes.26-28 For example, 2D materials were exfoliated in pure water via temperature control, and the concentrations of some platelets solutions comparable to those dissolved in organic solvents or surfactants.26 Further researches are still needed to draw attention to the role of water and the mechanisms in LPE for layered structures. More importantly, water has been proved to be able to reveal the coupling between lattice flexibility of these materials and dynamics of solvents on flat surfaces or in various confining geometries.29-30 To reveal the lattice vibration and the corresponding entropy fluctuation, we studied the LPE of three typical 2D nanomaterials (graphene, hBN, and MoS2) in pure water by using extensive MD simulations. We calculated the PMF along a given reaction coordinate (the detailed models and methods are found in Supporting Information). The exfoliation and reaggregation processes were both calculated, as shown in Figure 1. In exfoliation,


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pulling the upper layer along the direction perpendicular (peeling) to and parallel (shearing) to the lower layer have been addressed separately,

Figure 1. Schematic of simulation models for exfoliation (peeling and shearing) and reaggregation of graphene, hBN, and MoS2. Atoms of carbon, boron, nitrogen, molybdenum, and sulfur are shown in gray, pink, blue, green, and yellow, respectively.

according to the exfoliation experiments.4, 31 The free energy was calculated according to the Jarzynski’s equality32, 〈𝑒 ―𝑊/𝑘B𝑇〉 = 𝑒 ―Δ𝐺/𝑘B𝑇, where the free energy equals to the reversible work in isothermal simulations. The steered MD method was applied, with the


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spring constant and velocity been discussed in Figure S3. After exfoliation, the separated nanosheets would then reaggregate in water. For the reaggregation process, the reaction coordinates were chosen to be the distance between two parallel nanosheets. The PMF of this process was calculated by numerically integrating the forces of the two monolayers ∞

at various intersheet separations, D, calculated as PMF(𝐷) = ― ∫𝐷 〈𝐹(𝑟)〉𝑑𝑟. This method can be applied to study the flexibility effect of nanosheets with a finite size (Figure S5). The detailed verification of the choice of the reaction coordinates can be found in Figure S7. From the experiments33 and simulations34, the nanosheets could form a metastable nanosheet-water-nanosheet sandwich structure. We note that the nanosheets would aggregate parallelly and reach a metastable state at a certain initial separated state, e.g. the tilted angle between two nanosheets is less than ~33° (Figure S8). We also note that this work does not include the edge to edge aggregation, which is estimated to be quite rare in comparison with the parallel aggregation in dilute solutions.23 We first focus on the entropy change in the peeling exfoliation. From thermodynamics, the free energy in the LPE of two nanosheets is given by Δ𝐺 = 2𝛾slΔ𝐴, where 𝛾sl is the


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solid-liquid surface tension, and A is the contact area. The free energy difference can then be decomposed to contributions of entropy and enthalpy Δ𝐺 = Δ𝐻 ― 𝑇Δ𝑆, and Δ 𝑆 = ―𝑑(Δ𝐺)/𝑑𝑇 (see section 4 in supporting information for more details about the calculation of Δ𝑆 and Δ𝐻). To this end, we performed PMF calculations at a temperature range from 273 K to 373 K. The free energies in the peeling exfoliation for flexible models in vacuum, rigid and flexible models in water are calculated in Figure 2. The results of the shearing process are not shown here due to the poor linearity of Δ𝐺 dependent on T. The PMF of the shearing process is also questionable due to the difference from the retraction process (Figure S4), and the fluctuations resulted from the heterogeneous sliding friction between layered structures35. The rigid and flexible models of 2D materials are anticipated to simulate the exfoliation of nanosheets with infinite and minimum rigidity, respectively. Hence the reported results would cover the range of the available energy consumption. In Figure 2, we find three different roles of water in LPE for the studied materials at the range of temperatures studied in this work: inhibition, facilitation, and negligible, for graphene, hBN, and MoS2, respectively. For example, the water-hBN energy is so large


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(Figure S1) that water molecules have a great tendency to cover the solid surface, leading to the exfoliation, which is found in experiments36. We also see the flexibility effect on the free energy of LPE, showing that the surface vibration favors the exfoliation of graphene and hBN, and disfavors peeling MoS2, compared to those of rigid nanosheets. However, the flexibility effect would change with temperature due to the entropy variation.

Figure 2. (a) Snapshot of water-assisted peeling exfoliation. (b) Entropy energy change (𝑇 Δ𝑆) (bars in the figure) and ratio of entropy and enthalpy change (𝑇Δ𝑆/Δ𝐻) (scatters in the figure). For exfoliation of rigid models in vacuum, Δ𝑆 ≈ 0. (c) The PMF as a function


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of pulling distance, D, for peeling 2D materials at 300 K, from top to bottom are graphene, hBN, and MoS2, respectively.

The Δ𝑆 mainly derives from the interfacial properties of water on solid surfaces, i.e. conformation, rotation, and translation. The Δ𝑆 for water surface is ~0.9 meV K-1 nm-2, according to the reported entropy of liquid-vapor water interface relative to bulk water37. The estimated water-induced entropy energy, 𝑇Δ𝑆, is larger than those in Figure 2c, indicating the comparable small water-solid interfacial entropy. Specifically, the surface vibration-induced entropy change is found to be 50.2% and 62.5% of the water-induced part for the exfoliation of graphene and hBN respectively. Oppositely, the entropy change of peeling MoS2 is reduced by both adding water or surface flexibility. Moreover, the 𝑇Δ𝑆/ Δ𝐻 ratio is reported, with the variation similar to that of Δ𝑆 (Figure 2b), where MoS2 is opposite to graphene and hBN. For example, the 𝑇Δ𝑆/Δ𝐻 ratio is 41%, 48%, and 4% for flexible graphene, hBN, and MoS2, respectively. For comparison, the ratios in the wetting process of water on layered materials are provided, i.e. 33% for graphene, and 46% for MoS2 at room temperature38-39.


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The free energy of the reaggregation of the three double-layered materials in water was quantified using the PMF as a function of vertical distance, D, as shown in Figure 3. The average force on the nanosheets is found to be positive, at the smallest D at which one or two water layers can just fill the slits (see Figure S6). In these windows, the confined water molecules seem to squeeze the sheets outwards, indicative of the decrease of PMF and the corresponding energy minima. The water density (Figure S9) and orientation (Figure S10) inside the interlayer space would also suddenly change near the two windows. The free energy barrier of reaggregation is computed based on the difference between the energy minima and maxima of PMF curves, which corresponds to the desorption of water molecules. The energy consumption for the desorption of doublelayer water is larger than that of monolayer water, and is recognized as the controlling step in the reaggregation process. We see a more favorable free energy for the aggregation of flexible graphene and hBN nanosheets than rigid models at room temperature (see Figure S11), facilitating the water desorption. The free energy reduction is up to 28% (39 meV/nm2) and 37% (73 meV/nm2) for graphene and hBN, respectively. Indeed, the flexible nanoplates have been expected to have a greater tendency to


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aggregate than rigid ones.22, 40 Conversely, the vibration MoS2 surface would stabilize the metastable state, with a 18% (21 meV/nm2) improvement of the free energy barrier.

Figure 3. (a) Snapshots of the reaggregation of flexible 2D materials in water near the energy maxima window. (b) The PMF as a function of D at 300 K, from top to bottom are graphene, hBN, and MoS2, respectively. The insets show the enlarged view of the dashed box. (c) Entropy change (𝑇Δ𝑆) (bars in the figure) and ratio of entropy and enthalpy


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change (𝑇Δ𝑆/Δ𝐻) (scatters in the figure). (d) The mean out-of-plane displacements, ℎ, in the reaggregation process as a function of D (from top to bottom: graphene, hBN, MoS2). The unit of ℎ is nm. Red lines denote the inward direction (point to confined water) of ℎ, blue lines denote the outward direction (point to bulk water) of ℎ.

The kinetics of colloidal suspensions of nanosheets aggregation in solvents is important in evaluating the LPE process41. Here we analyzed the lifetime change as a function of lattice flexibility at 300 K. The lifetime can be predicted according to the model proposed by Shih et al.23 from the transition-state-theory-based framework, which is written as 𝑡1/2 ∞

∝ 1/𝐷∫𝑟 𝑒𝑥𝑝 (𝑃𝑀𝐹/𝑘𝐵𝑇)/𝑟2𝑑𝑟, where r is the interlayer distance, and D is diffusivity of 0

the nanosheets. Thereafter, the lifetime change resulted from surface vibration is calculated by 𝜖 = (𝑡𝑓1/2 ― 𝑡𝑟1/2)/𝑡𝑟1/2 by supposing the negligible difference between the diffusion of rigid and flexible models. As a result, by taking the lattice flexibility into account, the lifetime for graphene and hBN is reduced to only less than 2% of their rigid counterparts. On the other hand, the lifetime for MoS2 is increased by ~3.5 times. Such dramatic change in lifetime clearly shows the importance of lattice flexibility.


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The entropy change of the exfoliated 2D materials in water at 300 K is shown in Figure 3c. The linear fitting of Δ𝐺 ― 𝑇 can be found in Figure S11. The results show that both Δ𝐻 and 𝑇Δ𝑆 decrease as a result of lattice vibration for all the three 2D materials, though Δ𝐺 shows a distinct relation. The difference of Δ𝐺 stems from the decline magnitude of Δ𝑆, which follows the order MoS2 < graphene < hBN. The entropy would further result in various fluctuation of free energy with temperature, e.g. Δ𝐺 of hBN turns to be larger than that of MoS2 at a high temperature, i.e. 373 K (Figure S11). In addition, the ratio of entropy relative to enthalpy also decreases due to the lattice vibrations at 300 K. For flexible layers, the entropic component is found to be 64%, 32%, and 56% of the enthalpic component, compared to the 73%, 65%, and 71% for rigid graphene, hBN, and MoS2, respectively. The contribution of Δ𝐻 to Δ𝐺 is understood by the depletion of hydrogen bond of confined water between nanosheets when the interlayer distance decreases (Figure S12). The contribution of Δ𝑆 mainly stems from the rotation and translational of water molecules. In the water desorption process, the diffusion coefficient first increases and then decreases (Figure S13), which consumes entropic energy. To gain more insight into the


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entropy effect of the reaggregation, we explore the mean out-of-plane displacements, ℎ, of flexible sheets as a function of D at 300 K (Figure 3d). It is obvious to find that two solid curves, i.e. inward and outward, intersect near the energy minima shown in Figure 3b. The non-monotonous oscillation conforms the density discontinuous at these windows. We image this oscillation would induce a smaller Δ𝑆 compared to that for rigid models. The varied ℎ of nanosheets in water would also in turn result in a different coupling effect between the surface vibration and water diffusion (Figure S13). It is obvious to find the diffusion enhancement of water in graphene interlayer and inhibition of water in MoS2 interlayer. The different role of surface vibration in diffusion would further lead to a distinct free energy barrier in the reaggregation process. For hBN, the influence of flexibility on water diffusion is less than the other two materials, and the free energy barrier is primarily controlled by enthalpy. In conclusion, we have analyzed the free energy of LPE in water of three typical 2D materials, i.e. graphene, hBN, and MoS2, including the exfoliation and reaggregation processes. The entropy effect is emphasized, which is not well understood both in experiments and molecular simulations. Based on the comparison of the free energy of


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rigid and flexible solid models at different temperature, the entropy change has been addressed. Molecular dynamics simulation and enhanced sampling methods are applied to reveal the non-negligible of entropy. In the exfoliation process, the 𝑇Δ𝑆/Δ𝐻 ratio is 41%, 48%, and 4% for flexible graphene, hBN, and MoS2, respectively. In the reaggregation process, the corresponding ratio reaches 64%, 32%, and 56%. The results also show the more favorable free energy for the exfoliation of flexible graphene and hBN nanosheets than rigid models and smaller free energy barrier for the reaggregation of nanosheets at room temperature. The opposite is found for the exfoliation and reaggregation of MoS2. The reported surface entropy can be applied to predict the initial concentration and rate of precipitation of exfoliated dispersion solution as a function of temperature in experiments26. We also suggest that the surface entropy and free energy in LPE could be tuned by thermal treatment, edge functionalization42-44, and mechanical actuation45. We believe our results offer a step advancement for the screening of solvents in LPE of 2D materials by taking entropy into consideration.

ASSOCIATED CONTENT


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Supporting Information. Simulation models and methods, water density, orientation, hydrogen bond and diffusion analysis, the temperature effect on free energy barrier. This material is available free of charge via the Internet at http://pubs.acs.org/ Notes. The authors declare no competing financial interests.

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