2D Electrolytes: Theory, Modeling, Synthesis, and Characterization

Abstract

A class of compounds sharing the properties of 2D materials and electrolytes, namely 2D electrolytes is described theoretically and demonstrated experimentally. 2D electrolytes dissociate in different solvents, such as water, and become electrically charged. The chemical and physical properties of these compounds can be controlled by external factors, such as pH, temperature, electric permittivity of the medium, and ionic concentration. 2D electrolytes, in analogy with polyelectrolytes, present reversible morphological transitions from 2D to 1D, as a function of pH, due to the interplay of the elastic and Coulomb energies. Since these materials show stimuli‐responsive behavior to the environmental conditions, 2D electrolytes can be considered as a novel class of smart materials that expand the functionalities of 2D materials and are promising for applications that require stimuli‐responsive demeanor, such as drug delivery, artificial muscles, and energy storage.

2D electrolytes are stimuli‐responsive materials that possess the chemical and physical properties of 2D materials and electrolytes. These materials can undergo reversible morphological transformations according to the environmental conditions, such as pH, temperature, electric permittivity of the medium, and ionic concentration, and exhibit flexible functionalities, being promising for highly dynamic systems, such as drug‐delivery applications, artificial muscles, and energy‐storage systems.

1. Introduction

The field of 2D materials has evolved dramatically in the last 15 years due to its enormous interest in many different areas.^{[ 1} , ² , ^{3 ]} Unlike their standard 3D counterparts, 2D materials have special properties due to their low dimensionality, sharing characteristics of “soft” and “hard” materials. In 2D materials, electronic (hard) properties can be controlled by conformation (a soft property) leading to an intricate interplay between structure and functionality.^{[ 4 ]} We show that the soft aspects of 2D materials can be exploited also chemically, and that 2D materials in dispersion can undergo reversible conformational changes by appropriately modifying the external conditions. We functionalized 2D materials, such as graphene, graphene oxide (GO), reduced graphene oxide (rGO), and molybdenum disulfide (MoS₂), with different chemical groups that experience either protonation or deprotonation in dispersion and become positively (2D cations) or negatively (2D anions) electrically charged, respectively. Hence, we call these materials “2D electrolytes”.

From the physical and chemical perspective, the electrical repulsion between the surface charges in a 2D material leads to a flat conformation. Meanwhile, by changing the charge content of the dispersion (for instance, by changing the pH) the surface charge density of a 2D material can be electrically screened and, due to its elasticity, undergoes a conformational change by forming different morphologies, the most stable one being 1D‐like structures or scrolls. This shift shape transition from 2D to 1D is reversible by altering the external conditions back to their original values. One can think of 2D electrolytes as the higher dimensional analogs of 1D electrolytes, commonly known as polyelectrolytes.^{[ 5} , ^{6 ]} Important examples of polyelectrolytes include many biologically relevant materials, such as DNA and RNA.^{[ 7} , ^{8 ]} These electrically charged polymers also undergo conformational transitions from molecular chains (1D) to globular objects (0D) and vice versa, by the addition of acids, bases, or salts. Such dimensional reduction is a universal phenomenon since Coulomb and elastic forces tend to increase dimensionality, whereas van der Waals forces tend to reduce it.

2. Results and Discussions

We have prepared different examples of 2D electrolytes using functionalized 2D materials. It should be stressed that there are an uncountable number of ways to functionalize graphene and other 2D materials to transform them into a 2D electrolyte. We observed reversible transitions from 2D to 1D (from flat‐like to scroll‐like) structures in dispersions with different pH values by means of optical microscopy of the dispersion (Figure  1a–d; see the “Experimental Section” for experimental details). We have characterized the scrolls microscopically using high‐resolution scanning transmission electron microscopy (HR‐STEM) (Figure 1e,f), and atomic force microscopy (AFM) under dry conditions (Figure 1g–i), including their respective height profiles (Figure 1j–l).

Figure 1.

Characterization of different 2D electrolytes. a–d) Optical images of a dispersion containing reduced functionalized graphene oxide (rGO‐SH‐FITC) at pH 3.0, where flat 2D structures are observed (a,b), and the same material in a dispersion at pH 9.0, where scrolls are seen (c,d). e,f) HR‐STEM images for functionalized graphene (G‐COOH) scroll (e), with its interlayer distance (f). AFM images and their respective height profiles of rGO‐SH‐FITC at pH 3.0 (flat) (g,j) and pH 9.0 (scrolls) (h,i,k,l).

The change in morphology is ubiquitous in all these characterization techniques. Figure 1e,f shows an HR‐STEM image of a functionalized graphene, named as 5‐azidopentanoic acid (C₅H₉N₃O₂, G‐COOH) (see the “Experimental Section”), in which the scroll structure can be observed with its layers (Figure S1a, Supporting Information). One can see the layered structure of G‐COOH, which is reminiscent of multiwall carbon nanotubes (MWCNTs) both in their pristine^{[ 9 ]} and unzipped forms.^{[ 10} , ^{11 ]} The morphological transition has also an impact on the electronic transitions in the material. In Figure S2 (Supporting Information), we show the optical absorption spectra for both flat and scrolled structures. While the flat structures respond electronically in a way similar to graphene (namely, featureless), the scrolled structures behave more like MWCNT showing a π plasmon transition around 310–155 nm (4.0–8.0 eV).^{[ 12} , ^{13 ]} Hence, the scrolls have an Archimedean spiral structure with an interlayer distance of d ≈ 0.43 nm, slightly larger than that of graphite (≈0.34 nm).

Theoretically, the stability of a scroll depends on its binding energy, U(D,H), which is determined by the balance between elastic bending energy, D/R ², where D is the bending stiffness^{[ 14 ]} and R is the curvature radius, and the van der Waals adhesion, −H/d² , where d is the interlayer distance and H is the Hamaker's constant.^{[ 15 ]} In a dispersion, the material acquires a surface charge that creates a repulsion between the overlapping areas with the strength depending on the Debye screening. To unroll a scroll, the interlayer osmotic pressure has to overcome the binding energy U. The work done by the osmotic pressure, W (D,H,ε,λ,L,σ), is a function of the relative permittivity of the dispersion (ε ≈ 80 for aqueous solutions), the Debye length of the dispersion, $\lambda (\lambda =\sqrt{{\epsilon }_0\epsilon k_{\mathrm{B}}T\mathrm{/}2e^2{\rho }_{\infty }}$, where ε₀ is the dielectric permittivity of the vacuum, k _B is the Boltzmann constant, and e is the electric charge), the sample size, L, and the surface charge density of the 2D material, σ (which is also connected to the zeta potential, ζ, of the material in dispersion). Notice that these parameters are all temperature, T, and ion density, ρ_∞, dependent and, hence, they depend on the pH of the medium. The stability of the system depends on the variation of enthalpy, δH = U − W; namely, if δH > 0, the scrolls are stable, otherwise, if δH < 0, the flat phase is stable—see the “Experimental Section” for details. The transition from one state to another requires that energy is given to the system so that it can overcome the energy barrier that separates these two states. In our experimental setup, the energy is transferred via sonication (Figure S3a,b, Supporting Information). We have calculated the phase diagram of a generic 2D electrolyte in terms of the pH, the zeta potential, and the characteristic size of the 2D flake as shown in Figure  2 .

Figure 2.

a,b) Phase diagrams for 2D electrolytes: a) G‐COOH and b) rGO‐SH in an aqueous dispersion. The experimental points for ζ potential versus pH are shown by the blue squares (2D flat) and the red circles (1D scrolls) depending on the morphological state. The theoretical regions of instability are shown by the green shaded area for a given average flake size (L = 0.48 µm and L = 2.33 µm for G‐COOH and rGO‐SH, respectively). The bending stiffness is 0.025 eV for soft GO‐like materials.^{[ 14 ]} The Hamaker constant is 0.624 eV for graphene‐like materials,^{[ 15 ]} but it is very large for rGO‐SH at pH > 7 to simulate strong covalent S–S bonding formed in alkaline conditions (see the main text).

The phase diagrams in Figure 2 show that the scrolls, once formed, remain stable at ζ → 0, as there is no surface charge, hence, no interlayer repulsion. At ζ ≠ 0, the stability is determined by the pH. If the pH is nearly neutral, then the ion concentration is low, making the interlayer osmotic pressure similarly low, and the scroll morphology stable. Away from pH neutrality, the interlayer ionic concentration and osmotic pressure increase making the scrolls unstable. Despite that, in our model, the scroll binding energy is only determined by the material parameters, H and D, and the flake size, L, also plays an important role in the dispersion the layers with larger area experience stronger overall repulsion at the same interlayer pressure. In our phase diagram, shown in Figure 2, we have used the average flake size, L, which is determined from the statistical distribution of flake sizes. If the average sizes are larger than 10 µm, then the scroll stability region shrinks to a very narrow slit near ζ = 0 and pH 7. The reversibility of the scrolling morphological transition relies on the 2D materials’ aversion to create strong sigma bonds between the layers. Although unsaturated, graphene is chemically robust because its out‐of‐plane p _z orbitals are engaged in π‐bonds that extend through the whole material.^{[ 16 ]} Thus, the adhesion between the adjacent layers created during the scrolling is weak enough to be peeled off again. We have performed first principles calculations of the scroll stability and found that even epoxy groups, the most common form of oxygen defect, do not create permanent bonds between the graphene sheets upon scrolling, so that scrolls can subsequently be unrolled (see Figure S1b,c in the Supporting Information).

We synthesized 2D electrolytes using organic molecules as reactive species to adduct different functionalities to GO, rGO, graphene, and MoS₂ by means of covalent modifications. The functionalization routes that we describe in this work (see the “Experimental Section”) are only a few possible examples among many others. The first example of a 2D electrolyte is GO, a functionalization of graphene with oxygen‐based groups such as epoxy, carbonyl, hydroxyl, and carboxyl.^{[ 17 ]} Earlier reports indicate that a “permanent,” nonreversible, morphological transition of GO from 2D flat to 1D scroll‐like structures can be obtained by different methods.^{[ 18} , ¹⁹ , ²⁰ , ²¹ , ^{22 ]} GO is an amorphous, nonstoichiometric material, which is hydrophilic and has properties of an acid when dispersed in water. As GO has many oxygenated functional groups over a heterogeneous chemical surface, we observed 1D scroll morphologies, after pH adjustments followed by sonication, in a wide range of pH values (see Figure  3a), even for extreme cases, as for highly acidic at pH 2.5–3.0, or alkaline dispersions at pH 11. For intermediate values, as at pH 6, we also observed several 1D scroll structures. Originally, GO is a weak acid (pH ≈ 4.5) when dispersed in water, with a 2D flat structure. However, after sonication, we noted scroll formation at this specific pH by scanning electron microscopy (SEM; see Figure S3a in the Supporting Information). The morphological transition of GO under different pH values can be observed in Figure 3a by SEM and by AFM (Figure S4a–g, Supporting Information).

Figure 3.

Morphological configurations as a function of pH for different 2D electrolytes. a–d) SEM images of GO (a), rGO‐SH (b), rGO‐SH‐FITC (c), and G‐COOH (d). The pH for all samples was adjusted using HCl and KOH under sonication.

Another example of a 2D electrolyte comes from the functionalization of GO with (3‐mercaptopropyl)trimethoxysilane, GO‐SH (see the “Experimental Section” for details). After the preparation of GO‐SH, a mild hydrothermal reduction is performed to eliminate some oxygenated groups, forming thiolate GO (rGO‐SH). The characterizations of GO, GO‐SH, and rGO‐SH are presented in Figure S5a–d and Table S1 (Supporting Information). In Figure 3b, we demonstrate by SEM that scroll‐like structures are predominantly formed as pH increases. The thiol groups deprotonate (SH → S⁻) at higher pH and, stimulated by sonication, can bind internally forming disulfide bonds, which leads to the scroll‐like morphology. The formation of disulfide bond is evidenced by using dl‐dithiothreitol (DTT), a strong reducing agent that reduces the disulfide bonds and prevents inter‐ and intramolecular disulfide formation (Figure S6, Supporting Information).^{[ 23 ]} In contrast, 2D flat structures are predominant at low pH. The reversible formation of disulfide bonds is a mechanism used by proteins, a type of polyelectrolyte, to maintain their tertiary structure.^{[ 24 ]}

The third example of a 2D electrolyte is produced by means of further functionalizing rGO‐SH using fluorescein isothiocyanate isomer I (FITC), producing rGO‐SH‐FITC (see the “Experimental Section” and also Figure S5e,f in the Supporting Information). The insertion of a fluorescent molecule on the graphene surface can expand its applications, e.g., in the biomedical field, demonstrating the multifunctional ability of these materials. In analogy to the case of rGO‐SH, 2D flat structures of rGO‐SH‐FITC are observed at low pH, and 1D scrolls are observed at higher pH values (see Figure 3c), showing that the addition of the fluorescein molecule does not compromise the 2D electrolyte's pH‐responsive ability to change its morphology.

Finally, we have synthesized 2D electrolytes derived directly from graphene. For this, graphene is initially functionalized using G‐COOH via decomposition of the azide, ${\mathrm{N}}_3^{-}$, group^{[ 25} , ^{26 ]} (see the “Experimental Section” and also Figure S7 in the Supporting Information). The morphology of G‐COOH under different pH is investigated by STEM (Figure 3d), where 1D scrolls are observed as the pH decreases. 2D flat structures are mainly observed at pH 7, whereas folded or partially scrolled structures are predominant at lower pH < 5. The darker contrast and reduced lateral size at acidic pH indicate the formation of 1D scroll structures. These results corroborate the phase diagram of Figure 2a. We observed that two main factors are important in the scrolling formation: i) the dispersion concentration, where at lower concentrations (0.04 mg mL⁻¹) the 1D scroll structures are favored against the stacking and aggregation;^{[ 21 ]} and ii) the effect of sonication, for which the 1D scroll yield is considerably improved (see Figure S3a in the Supporting Information). Beyond carbon‐based materials,^{[ 27} , ²⁸ , ^{29 ]} we have also functionalized a transition metal dichalcogenide (TMD), namely lithium‐intercalated molybdenum disulphide (Li _x MoS₂), with 3‐mercaptopropionic acid (MPA) that we call MPA–LiMoS₂ (see details in the “Experimental Section” and also in Figure S8 in the Supporting Information). The HR‐STEM images (Figure S8l,m, Supporting Information) show the distance between turns in the scroll of ≈0.65 nm, which is consistent with the interlayer distance in crystalline MoS₂ (≈0.62 nm).

Since the morphological transitions are of statistical nature due to the distribution of sizes and thicknesses of the 2D material flakes used in our studies, the information collected by SEM and STEM is also used to interpret the results by statistical means. We have estimated the percentage of 1D scrolls formed in suspension as a function of pH by using a statistical analysis. The dispersions with different pH values are drop‐cast on appropriate substrates (silicon for GO and its functionalized forms, and transmission electron microscopy (TEM) grids for G‐COOH), and at least 100 structures are imaged to obtain their lateral dimensions (length, L—defined as the largest dimension—and width, W—defined as an average of two measurements of the smallest dimension). Beyond the percentage of 1D scrolls, we also identified other morphological configurations. The structures observed are further classified into planar, folded, scrolled and isolated, or scrolled and twisted, depending on their morphology (Figure S9, Supporting Information). As such, the number of counts based on multiple structures as a function of the aspect ratio (r = L/W ≥ 1) is provided in a size distribution chart in Figure S10 (Supporting Information).

From the statistical analysis, we show that GO forms scrolls in a broad pH range (from the lowest to the highest pH observed), which is mostly attributed to the chemical surface heterogeneity of this material (see Figure S10 in the Supporting Information). Interestingly, GO presents a significant amount of scrolled species through all the pH range (Figure S11a,b, Supporting Information), but the amount of scrolls detected decreases dramatically under two circumstances for GO with original pH 4.5: i) without sonication (Figure S11a, Supporting Information) and ii) after readjustment of pH from 3.0 to 4.5 (pH 3.0–4.5R) (Figure S10a, Supporting Information). R indicates the reversible process. .

Alternatively, for the anionic 2D electrolyte rGO‐SH, which has a much more controlled chemical surface, 2D flat sheets are mostly formed at pH 2.9, whereas 1D scrolls are predominantly found at higher pH. The reversibility of this process, presenting a size distribution analysis within a pH sweep from 3 to 10 and back, can be seen in Figure S10b (Supporting Information). The average aspect ratio of 2D flat sheets is about 2.5, as can be seen in Figure  4a. However, as the pH is raised toward the alkaline range, one can see a significant increase in the average aspect ratio up to about 7.0, owing to the increased presence of 1D scroll structures. For rGO‐SH (Figure 4b) a clear trend emerges demonstrating an increase in scroll content with increasing pH (from 9.5% at pH 2.9 to 79.4% at pH 10.2 of 1D scroll structures), while reducing the amount of 2D flat structures (from 65% at pH 2.9 to 1.3% for pH 10.2 of 2D flat structures) with similar reduction for folded structures. In Figure 4c, we show that the majority of the 1D scroll structures at pH 10.2 are unrolled at pH 3.1, in response to the external conditions. After pH readjustment, the average aspect ratio is reduced back to about 2.9 (see the red dot in Figure 4a), nearly the same as observed for the planar sheets at lower pH values (Figure S10b, Supporting Information).

Figure 4.

Statistical analysis of 2D electrolytes: rGO‐SH and G‐COOH. a) Average aspect ratio as a function of pH for rGO‐SH showing the tendency for scroll formation with increasing pH. The red dot indicates the value achieved after pH readjustment, from pH 10.2 to 3.1. b) Statistical distribution of morphologies for rGO‐SH (scrolled—including both twisted and isolated structures, folded, and planar) identified in samples at different pH. c) SEM images demonstrating the reversibility effect of rGO‐SH from 1D scroll structures at pH 10.2 to 2D flat sheets at pH 3.1, respectively. d) Average aspect ratio, showing the increase of 2D flat structures with increasing pH, and e) statistical distribution of structures for G‐COOH. f) STEM images showing the reversibility process for G‐COOH.

For G‐COOH, we observe the opposite behavior for rGO‐SH, namely, a reduced percentage of scrolls in response to the increase of pH (Figure 4d,e). As mentioned previously, these morphological changes can be explained by modifications of the G‐COOH surface charge density. At low pH, carboxylic groups are fully protonated and, consequently, the hydrophobicity increases, resulting in folding, stacking, and precipitation.^{[ 20 ]} At higher pH, the dissociation of carboxylic acid (COOH) to carboxylate (COO⁻) groups increases the negative surface energy (ζ‐potential ≥ −30 mV), favoring 2D flat morphologies. The reversible behavior is also demonstrated in this case (Figure 4f), as well as the statistical distribution of morphologies as a function of the pH in Figure S10c (Supporting Information). The interplay between extreme pH values demonstrates the ability of the 2D electrolytes to undergo reversible morphological transitions.

3. Conclusion

We have proposed theoretically modeled, computationally synthesized, and characterized experimentally, a class of smart materials that we call 2D electrolytes. These 2D electrolytes are ionized in dispersion and undergo reversible morphological transformations from 2D to 1D due to external stimuli. We have demonstrated that these materials consistently obey a morphological phase diagram as a result of: i) the competition between the Coulomb and van der Walls interactions, ii) the bending stiffness, and iii) the Debye screening in the dispersion. Moreover, we have shown that GO is a member of this class, albeit with an inconsistent behavior due to its heterogeneous nature. Additionally, we have synthesized and fully characterized other examples of 2D electrolytes with pH‐responsive behavior, capable of producing reversible scrolling on demand. Thus, these results allowed us to demonstrate that 2D electrolytes are higher dimensional versions of the well‐known polyelectrolytes (1D electrolytes), to which important biological molecules belong to, therefore, expanding the range and applicability of electrolytes to new dimensions.

4. Experimental Section

Synthesis of 2D Electrolytes

Initially, GO (Sigma Aldrich) was dispersed in ethanol (1 mg mL⁻¹) by centrifugation. Next, of (3‐mercaptopropyl) trimethoxysilane (5 µL) was added to the GO dispersion (5 mL). The dispersion was kept under stirring for 24 h at room temperature, followed by two cycles of centrifugation in ethanol and one in deionized (DI) water to remove residues of silane molecules. After functionalization (GO‐SH), a mild hydrothermal reduction was performed to eliminate part of the oxygenated groups. The reaction was conducted by adding ascorbic acid (7.5 mg) to the GO suspension (15 mL) under stirring and nitrogen atmosphere. After 15 min, the temperature was increased to about 60 °C for 50 min. Finally, the system was washed with DI water. After reduction, the percentage of oxygenated groups, such as C=O (dark green color) and O—C=O (violet color), was decreased by ≈50%, when compared to GO‐SH, as COOH groups were eliminated (see Table S1 in the Supporting Information). The resulting material, namely rGO‐SH, which is a 2D anion, was slightly darker than GO‐SH, also agreeing with the reduction.

The evidence for the formation of disulfide bond during the scrolling process was carried out using the strong reducing agent DTT. DTT can reduce the disulfide bonds and prevent inter‐ and intramolecular disulfide formation. It is commonly used to prevent the formation of disulfide bonds between proteins.^{[ 30 ]} For this, a scrolled rGO‐SH sample (pH ≈ 7.1) was incubated with DTT (10 mmol L⁻¹) for 2 h at room temperature. The final pH after the incubation was about 6.7. Optical and electron microscopy showed that most of the scroll structures disappeared and open sheets were prevalent, indicating, therefore, the formation of disulfide bond during the rGO‐SH scrolling (Figure S6, Supporting Information).

FITC was used without further purification. For the functionalization, FITC was first dissolved in anhydrous dimethyl sulfoxide ((CH₃)₂SO, DMSO) (1 mg mL⁻¹). Then, 1 mL of this solution was added to 30 mL of rGO‐SH (0.2 mg mL⁻¹, pH = 6–7). The system was left under stirring for 6 h at room temperature and, finally, dialysis was performed with ultrapure water to remove the excess of FITC. As a control, FITC solutions at pH 3.0 and 9.0 were drop‐cast on Si/SiO₂ (300 nm thickness) substrates, for which the absence of large structure was clear. For rGO‐SH‐FITC, 2D planar sheets can be seen at pH 3.0, whereas 1D scroll structures can be seen at pH 9.0 (see Figure S12 in the Supporting Information).

Graphene (2D Materials Pte. Ltd.) was functionalized with G‐COOH via decomposition of the azide (${\mathrm{N}}_3^{-}$) group. Upon thermal activation, the release of N₂ and addition of nitrene (R–N) onto graphene in DMSO lead the molecules to be incorporated, resulting in graphene functionalized with carboxylic acids (COOH).^{[ 25} , ²⁶ , ^{31 ]} The reaction was performed as follows: 40 mL of 0.2 mg mL⁻¹ of graphene in DMSO was prepared in a round‐bottom flask under N₂ environment and sonicated for 15 min at 18 °C. Then, the system was connected to a condenser and, under magnetic stirring, 5‐azidopentanoic acid (250 mg) was added. The reaction was kept at 45 °C under N₂ atmosphere and stirred for 72 h. Sonication was performed once a day (15 mins at 18 °C). After that, the system was centrifuged and suspended in isopropanol. This process was repeated, followed by washing in DI water and sonication for 5 min at 10 °C. After functionalization, graphene presents good stability in water.

Li _x MoS₂ from Sigma–Aldrich was functionalized with MPA. For this, Li _x MoS₂ (50 mg) was added to an aqueous solution of MPA (75 × 10⁻³ m). The system was sonicated for 30 min at 18 °C and then stirred for 2 h at room temperature. The 2D electrolyte, namely MPA–LiMoS₂, was obtained after cleaning the system by dialysis against DI water for 48 h.

Characterization of 2D Electrolytes

The 2D electrolytes were characterized via optical microscopy to demonstrate the morphological transition in liquid dispersion as a function of pH. First, rGO‐SH at 0.01 mg mL⁻¹ (25 µL) was deposited onto precleaned glass slides. The dispersion was enclosed by a thin well of parafilm with an 8 mm × 8 mm opening. Subsequently, a precleaned coverslip was used to cover both the droplet and the parafilm. The coverslip prevents the formation of the meniscus and reduces the rate of evaporation of the solution. Finally, the edges were sealed with epoxy glue. Further characterization was carried out using an immersion 100× lens in an upright fluorescence microscope under bright‐field mode.

The 2D‐electrolyte dispersions were drop‐cast on Si, Si/SiO₂, and Au‐coated substrates for characterization by SEM and AFM. For STEM and HR‐STEM, the dispersions were drop‐cast on lacey carbon gold TEM grids (TedPella) and quantifoil Cu TEM grids (SPI).

GO samples were characterized via AFM to image and assign the height profile of GO flat sheets at pH 4.5 (Figure S4a,b, Supporting Information), scrolled structures at pH 6.0 (Figure S4c–e, Supporting Information), and GO flat sheets at pH 4.5 (Figure S4f,g, Supporting Information), after pH readjustment (from pH 3.0 to pH 4.5) to demonstrate the reversibility of the scrolling mechanism. The chemical states of elements and the presence of functional groups of GO were investigated by X‐ray photoelectron spectroscopy (XPS) (Figure S5a, Supporting Information). After deconvolution of the high‐resolution C1s region, five different chemical states can be identified: 284.34 eV (C=C), 285.03 eV (C—C), 286.96 eV (C—O), 287.41 eV (C=O), and 288.38 eV (O—C=O).

The high‐resolution C1s XPS spectra in Figure S5a (Supporting Information) show that, after functionalization of GO (GO‐SH), the relative intensities increase in the regions related to C—Si (orange color) and C—S (pink color) binding energies, indicating that the silane and thiol groups are successfully introduced onto the GO surface.^{[ 32 ]} Also, the high‐resolution S2p spectrum of rGO‐SH shows the formation of C—S bonds (Figure S5a,b, Supporting Information). In Figure S5c (Supporting Information), the zeta potentials of GO‐SH and rGO‐SH were measured at different pH values (from 2 to 12) to verify the stability of the dispersions and their surface charge densities. As expected, the zeta potential values were slightly less negative for pH higher than the pK _a of the carboxylic groups (pH 4–5) after reduction. However, it was still highly negative, which made it difficult to separate the S–H groups’ contribution. The pK _a for SH groups was at basic pH; therefore, as the pH increases, the thiol groups can deprotonate (SH → S⁻), as they are extremely reactive to form reversible disulfide bonds.^{[ 24 ]} As such, no significant changes were observed between GO‐SH and rGO‐SH. Raman spectra (Figure S5d, Supporting Information) revealed that, after functionalization and reduction, the relative intensity of the D band was slightly increased. This was expected since the number of chemical groups and defects was increased, and phonon vibrations changed after the reactions.

Fourier transform infrared (FTIR) spectroscopy was acquired using Si substrates. Figure S5f (Supporting Information) compares the spectra of FTIC, GO‐SH, rGO‐SH, and rGO‐SH‐FITC. It was expected that the isothiocyanate groups (S=C=N) bind to the thiol (S—H) groups of rGO‐SH. After bond formation, the peak attributed to isothiocyanate group S=C=N in FITC molecules at 2051 cm⁻¹, which can be observed for the FITC spectrum, disappeared, indicating that the covalent coupling of the FITC molecules with rGO‐SH led to the formation of another 2D electrolyte, namely rGO‐SH‐FITC. The mild reduction of GO‐SH generates a decrease in the intensity of peaks attributed to oxygenated groups of rGO‐SH. Zeta potential as a function of pH revealed no significant changes due to the coupling of the FITC, indicating that free thiol groups were still attached to GO surface and survive to the morphological transition (Figure S5e, Supporting Information).

G‐COOH was characterized by Raman, STEM, and XPS (Figure S7, Supporting Information). The increase of the I _D/I _G ratio in the Raman spectra (Figure S7a, Supporting Information) showed evidence of the covalent functionalization. The typical lateral size of the G‐COOH sheets was in the range from 0.5 to 2 µm (Figure S7b, Supporting Information). The deconvolution of the high‐resolution C1s XPS spectra for G‐COOH showed, beyond the asymmetric C=C peak at 284.4 eV, that other small peaks attributed to the presence of minority oxygen‐containing functional groups (Figure S7c, Supporting Information). They were ascribed as hydroxyl (C—O) at 285.9 eV, epoxy/ether (C—O—C) at 286.7 eV, carbonyl (C=O) at 287.5 eV, and carboxylate (O—C=O) at 288.4 eV. Peaks from 291 to 294 eV are attributed to π–π* transitions.^{[ 33} , ^{34 ]} By comparing both C1s spectra, a relative increase of the sp³ bonds and oxygen/nitrogen groups could be observed, after the functionalization with 5‐azidopentanoic acid, corroborating the evidence for surface modification. The high‐resolution N1s spectra (Figure S7d, Supporting Information), after the first step of functionalization, could be resolved into two peaks at 400.3 and 401.3 eV. These energies differed from that expected for azido groups (N⁻=N⁺=N⁻),^{[ 35 ]} and are characteristics of tertiary amine and amide, agreeing with their attachment onto the graphene surface by elimination of N₂.^{[ 36 ]}

The original Li _x MoS₂ and MPA–LiMoS₂ were characterized by Raman spectroscopy, XPS, FTIR, zeta potential titration (pH range from 2 to 12), AFM, SEM, STEM, and HR‐STEM (Figure S8a–m, Supporting Information). Due to the pH adjustment of MPA–LiMoS₂, a conformational change was observed between flat and scrolled configurations. For this, a dispersion (0.3 mg mL⁻¹) of MPA–LiMoS₂ was sonicated for 5 min at 10 °C, followed by the addition of 0.1 m KOH solution to the system at pH 9.5. Next, the dispersion was sonicated for 20 min at 10 °C. For XPS, the measured data were decovolunted into the characteristics peaks of Li _x MoS₂, showing that, after functionalization with MPA, the peak located at 233.38 eV (Mo3d 2H) was significantly increased, which was an indicative that the Li _x MoS₂ surface was successfully modified (see Figure S8a,d in the Supporting Information). Accordingly, the Raman spectra (Figure S8b,e, Supporting Information) showed the presence of the in‐plane E_2g peak (383 cm⁻¹) and out‐of‐plane A_1g peak (406 cm⁻¹), which are the characteristics for this type of material. The FTIR corroborated the successful surface modification by indicating the binding of COOH groups at 1130 cm⁻¹ from MPA (Figure S8c, Supporting Information). Additionally, the zeta potential titration as a function of pH showed a vertical shift upward to lesser negative values of zeta potential for MPA–LiMoS₂ compared with Li _x MoS₂ (Figure S8f, Supporting Information). The MPA–LiMoS₂ was further characterized by means of AFM immediately after functionalization (Figure S8h, Supporting Information), where open sheets were observed. After pH adjustment (pH 2.5 and 9.5), the presence of scrolled structures could be observed by STEM in Figure S8g,I (Supporting Information). Scrolls formed at alkaline pH (9.5) could be seen with higher magnification by STEM (Figure S8j, Supporting Information) and SEM (Figure S8k, Supporting Information). HR‐STEM images (Figure S8l,m, Supporting Information) showed the distance between turns in the scroll formed at pH 9.5 of ≈0.65 nm, which was consistent with the interlayer distance in crystalline MoS₂ (≈0.62 nm).

Factors Affecting the Scrolling Mechanism

Both pH and sonication were used for the conformational changes of all synthesized 2D electrolytes as shown in Figure S3a,b (Supporting Information). It was demonstrated that for GO and G‐COOH the formation of scrolls was dependent on the exposure of 2D‐electrolyte dispersions to sonication (Figure S3a, Supporting Information). The sonication was performed at 10 °C to guarantee an intense cavitation regime, favoring the scrolling mechanism. For pH adjustment, the presence of scrolls could be seen for rGO‐SH in alkaline pH, whereas flat structures were observed for acidic range (Figure S3b, Supporting Information). Also, the presence of scrolls for GO dispersions was observed at both pH 4.5 and 11.0 that were spin‐coated on Si/SiO₂ substrates (see Figure S3c in the Supporting Information). For this, 5 µL of GO dispersions was spread over the substrates.

In Figure S3d (Supporting Information), it is shown that thermal effects can also trigger the scrolling mechanism in 2D‐electrolyte dispersions at alkaline conditions. By exposing the dispersions to high (80 °C) and low temperatures (via lyophilization), scrolls were observed. For the former, FITC‐rGO‐SH was kept under stirring for 5 min, then KOH (25 µL, 0.1 m) was added (pH = 11.0), and the system was stirred for 5 min more. Next, the temperature was increased to 80 °C for 2 min, leading to the formation of scrolls. For the latter, rGO‐SH dispersion at pH 10.62 was drop‐cast on Si/SiO₂ and Au‐coated substrates, and subsequently freeze‐dried by pouring liquid nitrogen into a Petri dish. Next, the substrates were gently approximated to the setup using a pair of tweezers for 2 min. The droplet was frozen to guarantee the stability in the dry state, and the substrates were lyophilized for 24 h assuring the complete removal of water without excessive heating of the material.

Finally, the effect of changing the ionic concentration could be seen in Figure S3e (Supporting Information). For this, HCl (25 µL, 0.1 m) was added to GO at pH 11.0—adjusted using KOH (20 µL,1 m) under sonication. A dialysis was performed to eliminate salt ions until pH 4.7. The dispersion was subsequently drop‐cast on Au‐coated substrates and lyophilized, leading to the observation of much thinner scrolls, due to salt removal.

Theoretical Analysis

The roll‐down work done by the osmotic pressure p can be written as^{[ 37} , ^{38 ]}

$$\begin{array}{c}W=S\underset{d}{\overset{\infty }{{\displaystyle \int }}}p\left(\xi \right)\mathrm{d}\xi \end{array}$$ (1)

where d is the interlayer distance and S is the layer overlap area. The presence of charges in the scroll surface creates a potential, ϕ _r , as a function of the radial distance r, that is described by the Poisson–Boltzmann equation

$$\begin{array}{c}\frac{{\partial }^2{\varphi }_r}{\partial r^2}+\frac{1}{r}\frac{\partial {\varphi }_r}{\partial r}=\frac{-e{\rho }_{\infty }}{{\epsilon }_0\epsilon }\left({\mathrm{e}}^{\frac{-e{\varphi }_r}{k_{\mathrm{B}}T}}-{\mathrm{e}}^{\frac{e{\varphi }_r}{k_{\mathrm{B}}T}}\right)\end{array}$$ (2)

where e is the elementary electric charge, ε₀ is the vacuum dielectric constant, ε ≈ 80 is the relative permittivity of water, ρ_∞ is the bulk ionic density, T is the temperature, and k _B is the Boltzmann constant. The same quantities determine the reciprocal Debye screening length given by

$$\begin{array}{c}\kappa =\frac{1}{\lambda }=\sqrt{\frac{2e^2{\rho }_{\infty }}{{\epsilon }_0\epsilon k_{\mathrm{B}}T}}\end{array}$$ (3)

Linearizing the Poisson–Boltzmann equation (Equation (2)) and representing the neighboring layers as two concentric cylinders of radii R ₁ and R ₂ (R ₂ > r > R ₁), its general solution was found as

$$\begin{array}{c}\hfill {\varphi }_r=\frac{{\varphi }_2-{\varphi }_1\frac{K_0\left(\kappa R_2\right)}{K_0\left(\kappa R_1\right)}}{\frac{I_0\left(\kappa R_2\right)}{I_0\left(\kappa R_1\right)}-\frac{K_0\left(\kappa R_2\right)}{K_0\left(\kappa R_1\right)}}\frac{I_0\left(\kappa r\right)}{I_0\left(\kappa R_1\right)}+\frac{{\varphi }_1\frac{I_0\left(\kappa R_2\right)}{I_0\left(\kappa R_1\right)}-{\varphi }_2}{\frac{I_0\left(\kappa R_2\right)}{I_0\left(\kappa R_1\right)}-\frac{K_0\left(\kappa R_2\right)}{K_0\left(\kappa R_1\right)}}\frac{K_0\left(\kappa r\right)}{K_0\left(\kappa R_1\right)}\end{array}$$ (4)

where I ₀ and K ₀ are the modified Bessel functions of the first and second kinds, respectively, and ${\varphi }_{1,2}={\varphi }_{r=R_{1,2}}$. The pressure (i.e., the force per unit area) can be found as the integration constant of (Equation (2)) given by

$$\begin{array}{c}p\left(\xi \right)=\frac{-{\epsilon }_0\epsilon }{2}{\kappa }^2\left[{\left(\frac{1}{\kappa }\frac{\partial \varphi }{\partial r}\right)}^2-{\varphi }_r^2+2{\displaystyle \int \frac{\mathrm{d}r}{r}{\left(\frac{1}{\kappa }\frac{\partial \varphi }{\partial r}\right)}^2}\right]\end{array}$$ (5)

where ξ = R ₂ − R ₁ and p(ξ) does not depend on r. Assuming that the inner and outer surfaces of a layer are charged equally so that the boundary conditions are given by the same zeta potential, ϕ_1,2 = ζ, and the curvature radii are much larger than Debye length, κR _1,2 ≫ 1, p(ξ) was simplified, integrated in Equation (1), and W was calculated.

The internal energy, U, of the scroll comprises elastic and van der Waals (London) energies. The former can be expressed through the surface integral^{[ 39} , ^{40 ]}

$$\begin{array}{c}{E}_{\text{el}}=\frac{D}{2}\int d^{2}r{R}^{-2}\left(r\right)\end{array}$$ (6)

where R(r) is the local curvature of the surface and D is the bending stiffness of carbon‐based layers.^{[ 14} , ^{41 ]} The Archimedean geometry (extended data in Figure 1a) was used and Equation (6) was integrated in cylindrical coordinates straightforwardly obtaining the following size‐independent relation

$$\begin{array}{c}{E}_{\text{el}}=D\frac{{\left(\phi -{\phi }_0\right)}^2}{2},\phi ,{\phi }_0\gg 1\end{array}$$ (7)

The intermolecular van der Waals–London contribution is given by^{[ 37} , ^{42 ]}

$$\begin{array}{c}{E}_{\text{mol}}=\frac{-HS}{12\pi d^2}\end{array}$$ (8)

where H is the Hamaker constant, which was assumed to be of the order of 0.624 eV for graphite‐like materials in water^{[ 15 ]} and S is the same layer overlap area as in Equation (2). It could also be written in terms of φ, φ₀ as

$$\begin{array}{c}{E}_{\text{mol}}=\frac{-H}{48{\pi }^2}{\phi }^2{\left(\phi -{\phi }_0\right)}^2,\phi ,{\phi }_0\gg 1\end{array}$$ (9)

To find U, the sum of E _el and E _mol was analyzed. The elastic force is trying to unroll the scroll and is eventually balanced by the intermolecular adhesion that results in a local equilibrium with the energy E _min at a certain pair φ, φ₀. Starting from its minimum, the internal energy increases with the interlayer gap until the critical point with the energy E _crit is reached where interlayer attraction is no longer able to counteract the elastic forces and the scroll starts rolling down by itself. The difference

$$\begin{array}{c}U=E_{\text{crit}}-E_{\min }\end{array}$$ (10)

is the energy one has to spend to flatten the scrolls, i.e., this is the internal energy difference separating two conformations: 2D flat and 1D scroll. U can also be seen as the binding energy of a scroll. It is determined by the material parameters and does not depend on the flake size. U was calculated by assuming φ − φ₀ ≪ φ, φ₀ and it was compared with W to find out whether the scroll was stable or not. This assumption is equivalent to a small number of turns being of the order of 1 and is consistent with the understanding of the scrolling mechanism. The higher the number of turns, the higher the curvature, making the elastic force trying to flatten the scroll stronger. Since the interlayer distance does not depend on the curvature in the Archimedean spirals, the interlayer adhesion is not able to balance the elastic force at higher numbers of turns. Finally, the phase diagrams were plotted in the (pH, ζ) coordinates as in Figure 2. The ionic density was estimated as ρ_∞ ∼ N _A10^3−pH (m⁻³) for pH < 7 and ρ_∞ ∼ N _A10^pH−11 (m⁻³) for pH > 7.

First Principles Calculations

Density functional theory (DFT) calculations were used to study graphene scrolls. The scrolls were based on an Archimedean spiral structure, where the interlayer distance is constant. Scrolls with chiral indices (10,5)‐chiral, (20,0)‐zigzag, and (4,4)–armchair, based on the nanotubes with the same chiral numbers, were generated.^{[ 43} , ^{44 ]} Scrolls with 1.5 turns, 2 turns, and 2.5 turns were produced. The scrolls were modeled based on DFT, as implemented in the SIESTA code.^{[ 45 ]} The Lee–Murray–Kong–Lundqvist–Langreth nonlocal van der Waals density functional was used.^{[ 46 ]} The core electrons were modeled using pseudopotentials of the Troullier–Martins type.^{[ 47 ]} The basis sets for the Kohn–Sham states are linear combinations of numerical atomic orbitals. Due to the large number of atoms in the system, a single zeta polarized basis was used for all species. The charge density was projected on a real space grid with an equivalent cut‐off energy of 250 Ry to calculate the exchange‐correlation and Hartree potentials. Structural relaxations were performed using a combination of conjugate gradient optimization and the fast inertial relaxation engine algorithm.^{[ 48 ]} The latter was found to be more efficient at optimizing the relative configuration and orientation of the weakly bonded graphene sheets.

Different types of defects and bonding between the layers were investigated: 1) edges were found to be stable if fully saturated by hydrogen (Figure S1b, Supporting Information); unsaturated edges were found to be able to reconstruct by way of forming bonds to the inner layers, but this is an unlikely scenario in dispersions where hydrogen and oxygen are always present. 2) Interstitial oxygen between the layers, bonding covalently to both layers, was found to be unstable and relaxed to the epoxy configuration in Figure S1c (Supporting Information). This is the most common surface oxygen group in graphene oxide. One reason why epoxy oxygen seems to be more stable is that it requires no out‐of‐plane distortion of the sp² σ‐bonds, and leaves the π‐states nearly undisturbed.^{[ 49 ]} 3) Carbon vacancies do not reconstruct by means of interlayer bonds; rather, they have the same reconstruction pattern as in monolayer graphene. 4) Hydrogen bonded onto graphene changes the bonding from pure sp² toward sp³ and the σ‐bonds are no longer perpendicular to the plane normal.^{[ 50 ]} In certain configurations, this can promote the formation of interlayer C—C bonds.^{[ 51 ]} However, it was found that these bonds are always much weaker than in plane C—C bonds. The modeling of multiple pristine and defective scroll systems shows that, in the presence of hydrogen, the reversible weak bonding between layers is little affected by defects.

Conflict of Interest

The authors declare no conflict of interest.

Author Contributions

M.C.F.C., V.S.M., K.S.N., and A.H.C.N. designed the experiments. M.C.F.C., V.S.M., H.T.L.N., and P.R.N. performed the synthesis, functionalization, and characterization of all systems. S.X.L., R.K.D., and C.H.S. carried out the liquid optical imaging of the 2D‐electrolyte suspensions. X.Z. and S.J.P. performed HR‐STEM analysis. M.T. and A.H.C.N. performed the theoretical analysis, and A.C. performed the first principles calculations. M.C.F.C., V.S.M., M.T., A.C., and A.H.C.N. led the writing of the manuscript with the assistance of all co‐authors.

Supporting information

Supporting Information

Costa M. C. F., Marangoni V. S., Trushin M., Carvalho A., Lim S. X., Nguyen H. T. L., Ng P. R., Zhao X., Donato R. K., Pennycook S. J., Sow C. H., Novoselov K. S., Castro A. H. Neto, 2D Electrolytes: Theory, Modeling, Synthesis, and Characterization. Adv. Mater. 2021, 33, 2100442. 10.1002/adma.202100442

Data Availability Statement

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