Nanoscale Structural and Electronic Properties of Cellulose/Graphene Interfaces

The development of electronic devices based on the functionalization of (nano)cellulose platforms relies upon an atomistic understanding of the structural, and electronic properties of the combined system, cellulose/functional element. In this work, we present a theoretical study of the nanocellulose/graphene interface (nCL/G) based on first-principles calculations. We find that the binding energies of both hydrophobic/G (nCL$^{\rm phob}$/G) and hydrophilic/G (nCL$^{\rm phil}$/G) interfaces are primarily dictated by the van der Waals interactions, and are comparable with that of their 2D interface counterparts. We verify that the energetic preference of nCL$^{\rm phob}$/G has been reinforced by the inclusion of an aqueous media via the implicit solvation model. Further structural characterization was carried out using a set of simulations of Carbon K-edge X-ray absorption spectra to identify and distinguish the key absorption features of the nCL$^{\rm phob}$/G and nCL$^{\rm phil}$/G interfaces. The electronic structure calculations reveal that the linear energy bands of graphene lie in the band gap of the nCL, sheet, while depletion/accumulation charge density regions are observed. We show that external agents, i.e. electric field and mechanical strain, allow for tunability of the Dirac cone and the charge density at the interface. The control/maintenance of the Dirac cone states in nCL/G is an important feature for the development of electronic devices based on cellulosic platforms.


I. INTRODUCTION
Designing new biodegradable electronic devices based on renewable and environmentally sustainable platforms has been intensively investigated with the motivation to combat resource constraints and waste disposal challenges [1]. Most electronics are still assembled from nonrenewable and nonbiodegradable materials and occasionally use production techniques that rely on hazardous compounds.
The possibility of building flexible devices using paper has led to the development of novel green electronic alternatives [2][3][4]. Cellulosic substrates have been explored for many applications, including transistors [5], supercapacitors [6], and organic solar cells [7]. More recently, nanoparticles extracted from cellulose pulps (cellulose nanocrystals-CNC and cellulose nanofibers-CNF) have also been considered lightweight and robust materials for electronic devices [8,9]. Substrates produced from CNCs and CNFs display advantages over regular paper, including smoothness, high optical transparency, and superior mechanical properties [10,11]. Besides, due to relatively inexpensive isolation methods, nanocellulose has excellent potential as a sustainable nanomaterial for designing many functional structures.
To impart electrical conductivity to cellulose, metallic particles [12], conductive polymers [13], carbon-based particles [14], and 2D materials [15] are usually integrated into nanocellulose through different techniques (coating, dipping, printing, blending, etc.). The combination of nanocellulose and 2D nanomaterials such as graphene, MoS 2 , and MXene has recently triggered great inter-est in the scientific community as a new class of multifunctional hybrid compounds. By assembling graphene and nanocellulose within a stretchable elastomer matrix, Weng et al. [16] fabricated a robust strain sensor for efficient human-motion detection. Moisture-responsive foldable actuators were also produced from exfoliated graphene and amphiphilic nanocellulose by a simple vacuum filtration method [17]. Tian et al. [18] combined the excellent mechanical properties of CNF with the metallike electrical conductivity of MXenes to design supercapacitor electrodes with high electronic conductivity of 2.95 × 10 4 S m −1 .
For electronic applications, 2D/nanocellulose hybrid materials should be able to tolerate mechanical stress and deformations while maintaining the satisfactorily electrical conductivity of 2D materials. Therefore, fundamental understanding of how the insertion of cellulose, a dielectric compound, influences the electrical properties of 2D materials is essential to guide the development of (nano) devices. Considerable experimental works on 2D/nanocellulose hybrids have shown promising outcomes. However, they only focus on the global electrical response and ignore the effect of nanocellulose/2D interaction at the nano and atomic levels on the electronic properties. Our group recently used first-principles calculations with a machine learning approach to evaluate relevant chemical and structural parameters that govern the binding energy of graphene oxide/nanocellulose interfaces [19], which have been considered promising polymeric composites for gas barriers [20] and water decontamination [21]. In the same direction, Zhu et al. [22] employed first-principles methods to study the interface bonding behavior of graphene oxide and cellulose derivatives composite systems. Despite such previous studies, a detailed picture of the interaction between the different cellulose surfaces and graphene is hitherto unexplored.
In the current study, based on first-principles calculations, we investigate the (i) energetic stability, (ii) structural, and (iii) electronic properties of the nanocellulose/graphene interface (nCL/G). The hydrophobic (nCL phob /G) and hydrophilic (nCL phil /G) interfaces were addressed in this study. In (i), we have examined the role played by the vdW interaction on the nanocellulose -graphene binding strength and the aqueous media effect on the nCL/G binding energy. The structural characterization [(ii)] was performed by a set of X-ray near edge absorption structure (XANES) simulations of the nCL phob /G and nCL phil /G interfaces to identify the corresponding X-ray fingerprints. In (iii), we show that the Dirac bands of graphene lie in the nCL's bandgap, with the Dirac point at about 2 eV above the valence band maximum of the nanocellulose (∆E DP ), followed by a small net charge transfer (∆ρ ∝ 10 12 e/cm 2 ) from graphene to the nCL/G interface region. In the sequence, we investigate the role of external agents such as electric field and mechanical strain in the electronic properties of nCL/G.

II. COMPUTATIONAL DETAILS
All calculations were performed within the density functional theory (DFT), where the exchange-correlation term was described by the generalized gradient approximation (GGA-PBE) [23] proposed by Perdew, Burke and Ernzerhof. The periodic image interaction was avoided by using at least 25Å vacuum perpendicular to graphene sheet. The Kohn-Sham orbitals were expanded in a plane wave basis set with an energy cutoff of 400 eV and the electron-ion interaction have been evaluated using the PAW (projected augmented wave) method [24]. The Brillouin Zone (BZ) sampling was performed according to the Monkhorst-Pack scheme [25], using a 6×6×1 mesh. The search for binding energies, equilibrium geometry and electronic properties were performed using Vienna Ab-initio Simulation Package (VASP) [26,27], and the influence of an aqueous environment was simulated based on the implicit solvation model implemented in DFT code VASP (VASPsol [28][29][30]). The equilibrium configuration was calculated taken in account a fully relaxed of atomic positions, considering a convergence criteria of 25 meV/Å for the atomic forces. In order to provide a more complete picture of the energetic features of the nCL/G interfaces, we have examined role played by the vdW dispersion interaction on the nCL/G binding energies. We have considered two different non-local vdW approaches, viz.: vdW-DF [31][32][33], and vdW-optB86b [34,35].
The Carbon K-edge X-ray absorption near edge structure (XANES) spectra were simulated using XSpectra package [36][37][38], implemented in Quantum ESPRESSO FIG. 1. Structural models of graphene interacting with the hydrophobic (a1)-(a2), and hydrophilic (b1)-(b2) nanocellulose sheet described by a single layer (a1)-(b1), and bilayer (a2)-(b2) of cellulose nanofibrils. [39,40]. To describe the K-edge spectra, we used a reconstructed ultrasoft pseudopotential with a core-hole in C-1s orbital and the electron wave functions were recovered using GIPAW [41] reconstruction. Here, the BZ sampling was the same previously described and the energy cutoffs for the plane wave basis set and self-consistent total charge density were respectively 48 and 192 Ry.

III. RESULTS
The structural models of nCL/G interface are depicted in Fig. 1. The graphene layer interacts with the hydrophobic and hydrophilic nanocellulose sheets described by a single layer of cellulose fibrils, labelled as nCL phob /G and nCL phil /G in Fig. 1(a1) and (b1), and bilayer of cellulose fibrils, nCL phob 2 /G and nCL phil 2 /G in Fig. 1(a2) and (b2).

A. nCL/G Binding Energy and Geometry
We start our investigation by examining the energetic stability and equilibrium geometry of the nCL/G interface, and the role played by the long-range vdW forces on the nanocellulose -graphene binding strength. The hydrophobic interface is characterized by the predominance of CH-π bonds, whereas in nCL phil /G the interface interaction is mainly dictated by the OH-π bonds. The nCL/G interface binding energy (E b ) was calculated by comparing the total energy of the final system (E[nCL/G]) and the sum to the total energies of the isolated components; for example, in Figs. 1(a1) and (b1) a single sheet of celulose nanofibrils (E[nCL]) and single layer graphene (E[G]), (1) For each interface, i.e. nCL phob /G and nCL phil /G, we have considered three different stacking geometries. We found that E b and the (averaged) equilibrium vertical distance between the nCL and graphene sheet (h) change by less than 0.06 meV/Å 2 and 0.01Å. Our results of E b and h, summarized in Table I, reveal an energetic preference for the nCL phob /G interface. By using the vdW-DF approach to describe the long-range vdW interactions we found binding energies of 12.92 and 11.63 meV/Å 2 for nCL phob /G and nCL phil /G, respectively. Comparing with other layered 2D counterpart systems, we find that the nCL phob /G binding energy is (i) comparable with that of boron-nitride/G bilayer (∼12 meV/Å 2 [42]); (ii) about 13% smaller compared with the intersheet binding energy of nCL; [43] and (iii) between 16% and 40% higher when compared to graphene oxide (GO) and nCL phob interface, depending on the oxygen concentration [19]. In order to verify the reliability of our results, we have also calculated the binding energies (i) by using another vdW functional (optB86b in Table I), and (ii) adding a second layer of cellulose nanofibrils, nCL phob 2 /G and nCL phil 2 /G, as depicted in Figs. 1(a2) and (b2), respectively. Our E b results, Table I, confirm the energetic preference for the nCL phob /G interface.
The energetic preference of the nCL phob /G interface is in agreement with recent theoretical findings based on molecular dynamic simulations [44,45]. Both studies indicate that the presence of trapped water molecules at the nCL/G interface reduces the binding energy; moreover in Ref. 44 the authors verified the exclusion of the water molecules from the nCL phob /G interface. Indeed, by using the implicit solvation model [29,30] we find a reduction of the interface binding energy [Eq. 1], E b = 12.92 → 11.80 meV/Å 2 in nCL phob /G, and 11.63 → 9.51 meV/Å 2 in the nCL phil /G interface, while the equilibrium geometries of the nCL/G interfaces are nearly the same as those obtained previously with no solvent effects. It is worth noting that the larger binding energy reduction in the latter is due to the hydrophilic nature of the interface, which is in agreement with our results of solvation energies (E s ) [46], namely 2.87 and 10.77 meV/Å 2 in nCL phob /G and nCL phil /G, respectively, and 4.21 and 11.19 in the nanocellulose bilayer systems, nCL phob 2 /G and nCL phil 2 /G. Long range vdW dispersion interaction plays an important role in the interchain and intersheet binding energy between the cellulose fibrils and nCL sheets, respectively [43,47]. To quantify the role played by the vdW interaction on the nCL -G binding energy, we have calculated E b by turning off the vdW contribution. In this case, the binding energy of the nCL phob /G (nCL phil /G) interface reduces to 0.51 (0.81) meV/Å 2 , and the vertical distance h increases to 3.04 (2.90)Å. Thus, similarly to the intersheet binding energy in pristine nCL, [43] we can deduce that the non-covalent (vdW) interactions rules the formation of nCL/G interfaces.

B. Structural Characterization, XANES
Core-level spectroscopy is a powerful tool to provide the structural characterization of materials in an atomic scale based on the local electronic properties of the probed element. Currently, the combination of experimental X-ray absorption near edge structure (XANES) data and first-principles simulations has proven to be a highly successful strategy to understand the atomic structure of novel materials [37,[48][49][50]. In this subsection, we present XANES simulation results of the Carbon K-edge absorption spectra of nCL/G interfaces in order to find spectroscopic finger prints of the atomic structures of the nCL phob /G and nCL phil /G interfaces.
Let us start with the XANES of the pristine isolated systems, graphene and single layer nCL. In Fig. 2(a), we present the absorption spectra of graphene as a function of the orientation (θ) of the radiation polarization vector (ˆ ), where we can identify the C-1s → π * [→ σ * ] transition forˆ =ˆ ⊥ (θ = 90 • ) [ˆ =ˆ (θ = 0 • )]. The energy positions of these absorption peaks, around 285 and 292 eV, respectively, indicated as g 1 and g 2 in Fig. 2(a), and the dependence of their intensities with the orientation of the polarization vector are in good agreement with the previous experimental findings [51,52].
Experimental results of XANES spectra of cellulose [53,54] indicate the presence of two absorption peaks, at 289.3 and 290.7 eV, both attributed to the C-1s → π * transition, associated to the C-OH and C-H bonds, respectively. Those bonding structures are present in the single layer nCL, and, indeed, the respective absorption spectra are captured in our simulations. In Fig. 2(b), we show our results for a single-layer nCL sheet which are characterized by (i) two absorption peaks, denoted c 1 and c 2 , lying at about 287 and 290 eV, and (ii) reduced angular dependency with the direction of the polarization vector compared to the one of graphene [ Fig. 2(a)]. As shown in Fig. 2(b), the energy positions of c 1 and c 2 changes by 0.36 and 0.21 eV, respectively, for θ = 0 → 90 • . [55] The absorption spectra in the nCL bulk phase (not shown) have a similar characteristic, with c 1 and c 2 shifted by ∼ +2 eV, for example c1: 287 → 289 eV.
The XANES spectra of nCL phob /G and nCL phil /G interfaces are shown in Figs. 3(a) and (b). In both spectra we identify the C-1s → π * and → σ * absorption features from graphene for θ = 90 • and 0 • , respectively. Between these two transitions energies, we can identify the following differences on the absorption features in nCL phob /G and nCL phil /G attributed to the nCL absorption spectra. (i) The presence of absorption peaks 1a and 2a [ Fig. 3(a)] for θ = 0 • , while in the nCL phil /G we find one absorption feature, 1b in Fig. 3(b); (ii) the absorption peak 2b at 287.5 eV is clearly visible in the nCL phil /G interface for θ = 90 • , but it is attenuated in nCL phob /G; and (iii) due to the tilted geometry of cellulose fibrils with respect to the graphene layer, the absorption spectra in nCL phil /G are no longer symmetric for positive and negative values of radiation polarization angles. For instance, the absorption features for θ = +15 • and −15 • (dot-dashed lines) present different intensities, as seen in Fig. 3(b).
Because the formation of nCL/G heterostruture is ruled by the vdW interactions, with no covalent bonds between the nCL sheet and the graphene layer, the nCL/G interfaces' absorption spectra are primarily determined by the superposition of the ones of isolated components. Indeed, the absorption spectra can be better understood by XANES computations of hypothetical structures, namely, an isolated single-layer graphene, and nCL sheet (both) constrained to the respective nCL/G interface equilibrium geometry. The XANES simulations of these constrained structures reveal that the features 1a and 2a in nCL phob /G emerge from the superposition of the edge transitions in graphene with the absorption peaks c1a and c2a of the nCL, Figs. 3(a1) and (a2). Similarly, the absorption peak 1b in nCL phil /G results from the superposition of graphene edge absorption structure with the c1b peak of the tilted layer of cellulose fibrils, Figs. 3(b1) and (b2), and for θ = 90 • the absorption feature 2b is composed by the superposition of graphene near-edge structure with the absorption peak c2b of the  The absorption spectra of the nCL/G systems, Figs. 3(a) and (b), were calculated by considering graphene on a single layer of cellulose sheet. However, when the number of nCL sheets grows, it is worthwhile to examine the changes on the XANES spectra. Our results reveal that as the number of nCL layers increases, the absorption characteristics from the C -H and Electronic band structure of nCL phob /G (a) and nCL phil /G (b). The zero energy was set at the vacuum level, the Fermi level is indicated by the dashed black lines, and red circles indicates cellulose contribution in band.
C -OH bonds grow more pronounced between 285 and 292 eV. In Fig. 3(c) and (d) we present the absorption spectra for three layer of cellulose fibrils, nCL phob 3 /G and nCL phil 3 /G. In the former interface the absorption peaks 1a and 2a become more apparent [labelled as 1c and 2c in Fig. 3(c)], similarly the features 1b and 2b of nCL phil /G become more intense in nCL phil 3 /G, indicated as 1d and 2d in Fig. 3(d), and thus reinforcing the differences in the XANES signatures of the hydrophobic and hydrophilic nCL/G interfaces.

C. Electronic properties
The electronic properties of nCL/G are characterized by an insulator/semi-metal interface with the linear energy bands of graphene lying within the bandgap of nCL. In Figs. 4(a) and (b), we present the orbital projected electronic band structures of nCL phob /G and nCL phil /G, where we find (i) the graphene's Dirac-point (DP) at about 2 eV above the valence band maximum (VBM) of the nCL layer; and (ii) the emergence of an energy gap of ∼0.04 eV at the DP. There is a small amount of charge accumulation at the nCL/G interface. Based on the Bader analysis [56], we found a net charge transfer (∆ρ) of 0.23 (0.28) × 10 13 e/cm 2 from graphene to the nCL phob /G, (nCL phil /G) interface, followed by a reduction of the graphene work-function (Φ) [57] by 0.2 eV compared with that of free-stading graphene sheet, 4.33 → 4.13 eV. Similar results were obtained in the nCL phob 2 /G and nCL phil 2 /G interfaces. In Figs. 5(a) an (b) we present a map of the charge accumulations in the nCL phob /G and nCL phil /G interfaces, where the following characteristics are noteworthy: (i) the inhomogeneous (net) charge distribution on the graphene sheets [Figs. 5(a1) and (b1)], which can be attributed to the differences in the orbital hopping between the nCL surface and the graphene's π orbitals; and (ii), as depicted in Figs. 5(a2) and (b2), those charge transfers occurs primarily at the nCL/G interface, since ∆ρ ≈ 0 in the subsurface nCL layers, Figs. 5(a3) and (b3). Such a net charge localization suggest the emergence of localized electronic transmission channels at the nCL/G interface. On the other hand, it is worth mentioning that such an inhomogeneous net charge distribution [(i)], giving rise to electron-and hole-rich regions in graphene, will play a deleterious role on the electronic transport properties throughout the nCL/G layers.
The understanding of the electronic properties of the nCL/G interface in the presence of external agents is an important issue for the development of electronic devices/sensors based on a combination of cellulosic materials and graphene. Thus, in the sequence, we will focus on the effects of external electric field (EEF) and mechanical compressive strain in the nCL/G interface.
Let us start with the effect of EEF. [58] As shown in Fig. 6, the energy position of the Dirac point with respect to the VBM of the nCL (∆E DP ) increases from 1.6 (1.1) to 2.3 (2.6) eV in nCL phob /G (nCL phil /G), for EEF of −0.25 and +0.25 V/Å, respectively. Concomitantly, the G → nCL/G net charge transfer, ∆ρ, varies from 0.08 (0.14) to 0.36 (0.47) ×10 13 e/cm 2 . Such tuning of ∆E DP and ∆ρ is nearly linear with respect to the EEF. In particular, for ∆E DP as a function of the EEF we find the following rates, −1.43 eV/(V/Å) and −3.14 eV/(V/Å) in nCL phob /G and nCL phil /G, respectively. Assuming that such a linear relationship is preserved for larger values of EEF, we can infer that in nCL phil /G the DP becomes resonant with the nCL valence band for EEF > 0.6 V/Å, and thus suppressing the G → nCL/G charge transfer.
Further control of the electronic properties of 2D systems can be achieved through mechanical strain, "straintronics" [59,60]. Indeed, such an approach has been used to control the electronic doping level in bilayer graphene and boron-nitride/graphene vdW heterostructures [61][62][63]. In nCL/G, the compressive strain will promote the strengthening the CH-π (OH-π) orbital overlap at the nCL phob /G (nCL phil /G) interface. Here, we investigate the net charge transfer, ∆ρ, and the work function (Φ) in nCL/G, as a function of compressive strain. The strain in the nCL phob /G and nCL phil /G interfaces was applied by considering bilayers of nCL and graphene, nCL phob 2 /GBL [ Fig. 7(a)] and nCL phil 2 /GBL [ Fig. 7(b)]. In Figs. 7(a1) and (a2) we present the spatial distribution of ∆ρ of pristine nCL phob 2 /GBL and compressed by 9 %, respectively; similarly in Figs. 7(b1) and (b2), we present ∆ρ for the hydrofilic interface, nCL phil 2 /GBL. Interestingly, these ∆ρ maps reveal that the charge transfers are localized at the nCL 2 /GBL interface region, and as shown in Figs Fig. 8]. Finally, we found that we can reach a p-type doping of about 1.1 (1.3) ×10 13 e/cm 2 of graphene upon an EEF of −0.25 V/Å in the 9% compressed nCL phob /G (nCL phil /G) interfaces. Thus, suggesting that suitable combinations of these external agents can be exploited to further modify the electrical characteristics of the nCL/G interface.

IV. SUMMARY AND CONCLUSIONS
We have performed a theoretical investigation of the energetic, structural, and electronic properties of nanocellulose/graphene (nCL/G) interface, where we have addressed the hydrophobic (nCL phob /G) and hydrophilic (nCL phil /G) interfaces. We find that the binding energy of nCL/G is primarily ruled by the vdW interactions, being comparable with that of boron-nitride/graphene. The structural fingerprints of nCL phob /G and nCL phil /G interfaces were identified through a detailed study of the Carbon K-edge absorption (XANES) spectra. The electronic structure of nCL/G is characterized by linear energy bands of graphene lying within the bandgap of nCL, with the Dirac point at about 2 eV above the valence band maximum of the nCL sheet, ∆E DP ≈ 2 eV, and a net charge accumulation, ∆ρ of ∼ 0.2 × 10 13 e/cm 2 , localized at the nCL/G interface. External electric fields (EEFs) and mechanical strain were used to investigate the tunability of these quantities, where we found that ∆E DP varies from 1.6 (1.1) to 2.3 (2.6) eV in nCL phob /G (nCL phil /G), for EEF of −0.25 and +0.25 V/Å, respectively; whereas there is an increase of G→ nCL/G ∆ρ up to 1×10 13 e/cm 2 upon an external pressure of 3.73 GPa. We believe that our findings provide not only the energetic and atomic scale structural understanding of the nCL/G interface, but also a set of important information of the electronic properties to the development of electronic devices based on the combination of nanocellulose and graphene.