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COMMUNICATION

Cite this: Nanoscale, 2016, 8, 15521

Received 4th July 2016,Accepted 30th July 2016

DOI: 10.1039/c6nr05309b

www.rsc.org/nanoscale

Boron doping of graphene–pushing the limit†

Vitaly V. Chaban*a and Oleg V. Prezhdob

Boron-doped derivatives of graphene have been intensely investi-

gated because of their electronic and catalytic properties. The

maximum experimentally observed concentration of boron atoms

in graphite was 2.35% at 2350 K. By employing quantum chemistry

coupled with molecular dynamics, we identified the theoretical

doping limit for single-layer graphene at different temperatures,

demonstrating that it is possible to achieve much higher boron

doping concentrations. According to the calculations, 33.3 mol%

of boron does not significantly undermine thermal stability,

whereas 50 mol% of boron results in critical backbone defor-

mations, which occur when three or more boron atoms enter the

same six-member ring. Even though boron is less electro-negative

than carbon, it tends to act as an electron acceptor in the vicinity

of C–B bonds. The dipole moment of B-doped graphene depends

strongly on the distribution of dopant atoms within the sheet.

Compared with N-doped graphene, the dopant–dopant bonds are

less destructive in the present system. The reported results motiv-

ate efforts to synthesize highly B-doped graphene for semi-

conductor and catalytic applications. The theoretical predictions

can be validated through direct chemical synthesis.

Introduction

Graphene is a well-known allotrope of carbon. A two-dimen-sional, single-atom-thick, honeycomb layer of graphite,graphene exhibits unusual properties and promises vibrantapplications.1–21 Doping, co-doping and supporting graphene-based nanostructures have been vigorously investigated both

experimentally and theoretically with the goal of tuning elec-tronic and catalytic properties, carrier mobility, thermal con-ductivity, etc.22–29 The researchers’ interest is fostered by anumber of important fundamental and technological appli-cations of doped graphenes.30–36 The existing chemical dopingtechniques offer relatively straightforward approaches to substi-tute carbon atoms with selected non-metal heteroatoms, whilepreserving the original hexagonal arrangement. Doping withnitrogen, sulfur and boron has been demonstrated. Certaincombinations of these atoms result in stable nanostructures.

The total number of valence electrons in the dopant atomis responsible for the type of doping. That is, addition ofboron results in p-type doping, whereas the addition of nitro-gen or sulfur results in n-type doping. Boron- and nitrogen-doped graphenes exhibit interesting electrocatalytic activityand higher electrical conductivity compared to pristinegraphene. Purpose-specific covalent doping gives rise to hydro-gen and energy storage applications for graphene37 andgraphene-based heterostructures.38

Substitutional doping introduces significant chemical dis-order, since the boron–carbon covalent bond is longer thanthe carbon–carbon bond in the pristine graphene lattice.Additional disorder is expected from thermal motion and thenewly introduced oscillation frequencies of the boron–carbonbonds. The maximum reported solubility of boron in graphiteis 2.35% at 2350 K.39 Boron-doped graphene is of fundamentalinterest because high boron concentrations give rise toquantum interference effects while at the same time preser-ving the remarkable transport properties of graphene.40

The existence of a fullerene-like molecule consistingentirely of boron atoms was recently recorded by the photo-electron spectroscopy experiments of Zhai and coworkers.41 Incontrast to the buckyball, the all-boron fullerene surface,which is bonded uniformly via delocalized σ and π bonds, isnot perfectly smooth and exhibits unusual heptagonal faces.The stability of such a system greatly enriches the chemistry ofboron and promotes efforts to obtain new boron-rich andboron-based nanomaterials. Therefore, it is both natural andimportant to consider various CxBy nanostructures.

†Electronic supplementary information (ESI) available: Fig. S1–S5 represent theRDFs for all the simulated systems. Fig. S6 depicts the orbital populations forboron and carbon atoms. Fig. S7 depicts the RDF for the larger graphene sheet.Table S1 investigates the size effect on the structure properties. The link “https://dx.doi.org/10.6084/m9.figshare.2068284.v1” contains molecular dynamics trajec-tory movies. See DOI: 10.1039/c6nr05309b

aInstituto de Ciência e Tecnologia, Universidade Federal de São Paulo, 12231-280,

São José dos Campos, SP, Brazil. E-mail: vvchaban@gmail.combDepartment of Chemistry, University of Southern California, Los Angeles, CA 90089,

USA

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The current work determined the maximum boron concen-tration in the B-doped graphene that would preserve thermalstability. In particular, our calculations demonstrate that it ispossible to achieve far higher doping concentrations comparedto the current experimental record. Using molecular dynamicssimulations based on a reliable and efficient electronic-struc-ture method, we consider a range of C : B ratios, starting froma single dopant atom per hexagonal ring and finishing withtriple boron–boron–boron chains. Various arrangements ofboron atoms within the sheet were analyzed, and the resultsgive a detailed interpretation of the boron chemistry context.A broad span of temperatures was considered. The conclusionswere validated by several independent criteria, including for-mation energies, structure functions, and visual inspection ofthe trajectories. The properties of boron-doped graphene werefound to be quite different from those of nitrogen-dopedgraphene. The simulation results can be verified directly bychemical synthesis.

Methodology

PM7-MD simulations were used to record 100 ps long trajec-tories at 300, 500, and 1000 K. Additionally, the duration ofthe simulation on the “B–B” system was extended to 1 ns totest convergence. A constant temperature was maintained bythe Anderson temperature coupling procedure with a relax-ation constant of 50 fs.42 The equations-of-motion were propa-gated with the 0.5 fs time-step. At every step of the moleculardynamics, the self-consistent field (SCF) was achieved at thePM7 semi-empirical level of theory43 and a specifically tuned,computationally efficient Slater-type basis set. The resultingforces acting on every atom in the system, including hydro-gens, were used to obtain accelerations and forces for the vel-ocity Verlet algorithm. The energy convergence criterion forthe SCF procedure was set to 5 × 10−6 Hartree. Prior to simulat-ing finite-temperature dynamics, the geometry of each systemwas optimized to remove all forces exceeding 10 kJmol−1 nm−1.

PM7 is a last-generation, semi-empirical method43–45 thatoriginates from the Hartree–Fock (HF) formalism. A numberof integrals were substituted with empirical data, resulting in ahuge increase in the computational efficiency and a competi-

tive accuracy. Empirical data allows one to include electron-correlation effects implicitly. Therefore, PM7 is free of systema-tic faults produced by ab initio HF. PM7 benefits frompurpose-specific corrections for hydrogen bonding, weak vander Waals attraction, and peptide bonds to accurately representproteins, etc.46,47 Ab initio and experimental data for morethan 9000 compounds were used for the parametrization.47

PM7 employs effective-core potentials to represent non-valenceelectrons. Diminishing the number of explicit electrons greatlyincreases the speed of the wave function convergence.Employing PM7-MD in the present work made it possible toobserve up to 2 000 000 consequent single-point calculationsof relatively large graphene quantum dots, whose propersampling is currently not feasible with density functionaltheory methods.

We used the Gabedit (ver. 2) software48 to build and func-tionalize the B-doped graphene nanostructures, the VMD (ver.1.9) software49 to visualize trajectories and prepare artwork,and the MOPAC2012 code (openmopac.net)43 to obtainimmediate energy gradients. The PM7-MD simulations repro-duce the system’s dynamics in real-time following an energygradient and accounting for thermal motion at a given temp-erature. Observation of a chemical reaction (e.g. decompo-sition) is possible provided that the reaction’s rate constant iscommensurate with the trajectory length. The PM7-MDmethod was successfully applied before to problems in chem-istry such as competitive solvation of ions,50 global minimumsearch for precious metal nanostructures,51 aminatedgraphene stability,52 gas capture,53 etc.

Results and discussion

The systems for the PM7-MD simulations were constructed toaccount for both the concentration of the boron atoms andtheir distribution within the sheet. We compared systems withone, two and three dopant atoms per hexagonal ring, with–B–B–, –B–B–B– and –C–B– covalent bonds in the starting con-figuration (Table 1). These positions for the dopant atomswere found to be the most stable based on preliminary esti-mations of formation enthalpies. Only carbon atoms, whichare two bonds away from the sheet edge, were substituted byboron atoms. This condition was met to decrease undesirable

Table 1 List of simulated systems and their composition. The number of electrons refers to electrons treated explicitly and thus, determines thecomputational cost for each system

Nickname n(C) n(B) n(H) # Electrons Comments

“1B” 87 9 27 402 One B per ring“para” 84 12 26 398 Two B per ring, in para position“meta” 66 30 26 380 Two B per ring, in meta position“B–B” 84 12 26 398 One B–B bond per ring“3B” 74 22 26 388 3 B per ring with one B–B bond“B–B–B” 72 24 26 386 3 B per ring with two B–B bonds“big” 162 16 36 732 Larger system; 2 B in para-position“B–B + B10H14” 84 22 40 442 “B–B” interacting with B10H14“B–B + C20” 104 12 26 478 “B–B” interacting with C20

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finite-size effects and to extrapolate the obtained results to aninfinite graphene sheet. Two sizes of graphene sheets werecompared (Table 1). In both cases, the edge carbon atoms wereterminated by hydrogen atoms. All simulated systems were intheir singlet states, and the corresponding electronic-structurecalculations were based on the restricted HF method. Sincestability of B-doped graphene can depend on interactions withboron and carbon containing particles in the environment, weadditionally simulated a boron hydride cluster B10H14 and asmall fullerene C20 in direct contact with the B-dopedgraphene (Table 1). Both fullerene, C20, and decaborane,B10H14, are reactive compounds.

Fig. 1 depicts equilibrated configurations of the B-dopedgraphene systems at 1000 K. Visual inspection of these snap-shots allows for characterization of the systems thermal stabi-lities. Whereas the “1B”, “para”, and “B–B” systems remainperfectly stable with minor shape violations, the “meta”, “3B”,and “B–B–B” systems exhibit significant deformations.Interestingly, B–B bonds in the starting configuration, per se,do not undermine stability. However, the presence of three ormore boron atoms within a single six-member ring leads tosignificant deformations. The boron–boron bond length isequal to 1.56 Å, as derived from simulations at 300–1000 K. Itis 10% longer than the C–C bond, 1.41 Å. Thus, certain pertur-bations of the honeycomb lattice of graphene are inevitable. Itis, therefore, important in which positions the dopant atomsare located, since higher symmetry of the nanostructure is ableto compensate for perturbations. In turn, the C–B bond lengthin the “B–B” system is 1.52 Å. Since the difference in electro-negativity between carbon, 2.55, and boron, 2.04, is relatively

small, the discussed bonds are expected to be weakly polar. Byanalogy with principles of organoboron chemistry, these com-pounds must be stable, although susceptible to oxidation pro-cesses. The computed B–B bond length (the “B–B” system) inB-doped graphene is smaller than that in boranes, 1.924(3) Å,obtained experimentally.54 Note that the C–C bond length isnot modified upon doping. It ranges from 1.38 to 1.42 Ådepending on the system and temperature. One could antici-pate that the longer B–B bonds strain the C–C bonds. Hence,the hexagonal ring is expected to be significantly strained.A strained ring implies an elevated reactivity of the compound.

The heat of formation, H, denotes a change in enthalpyduring the formation of one mole of the compound from itsconstituent elements (simple substances). The PM7Hamiltonian was specifically parametrized to provide highlyaccurate H values for multiple molecules and crystals. Fig. 2and 3 compare H for different doping sites at 300–1000 K.Higher temperatures significantly increase H. This increase isa convenient energetic measure of lowering the thermo-dynamic stability. Surprisingly, the “1B” system exhibits ahigher H = 1.933 MJ mol−1 at 300 K than the “para” system,H = 1.665 MJ mol−1 at 300 K, despite featuring a smaller boronconcentration per ring. Boron atoms in the para positionsclearly stabilize one another. In turn, the “meta” systemappears much more unstable, H = 2.902 MJ mol−1 at 300 K.The instability increases up to H = 4.022 MJ mol−1 at 1000 K.The corresponding structure deformations, including theeffect of thermal motion, are shown in Fig. 1.

The systems with one or more B–B covalent bonds (Fig. 3)exhibit similar heats of formation, wherein higher concen-

Fig. 1 Equilibrated molecular configurations of the B-doped graphene: (top left) 1 B per ring; (top center) 2 B per ring, in the para position; (topright) 3 B per ring, in the meta position; (bottom left) 2 B per ring, in the ortho position; (bottom center) 3 B per ring, with one B–B bonds; (bottomright) 3 B per ring, with B–B–B bonds.

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trations of boron and more B–B bonds are less favorable:H(“B–B”) < H(“3B”) < H(“B–B–B”). Importantly, the –B–B–B–C–C–C– pattern is more thermodynamically stable than the –C–B–C–B–C–B– pattern, 2.567 vs. 2.902 MJ mol−1. This obser-vation is drastically different from the case of N-dopedgraphene, for which we recently showed N–N bonds to be acritical defect.55

Although all computed H values are above zero, this doesnot mean that the B-doped graphene structures cannot be syn-thesized. Although they cannot be obtained by self-assemblystarting from the corresponding simple compounds directly,more sophisticated experimental techniques can be employed.

The radial distribution functions (RDFs) for C–C, B–B, andC–B distances within the B-doped graphene sheet, system“1B”, are given in Fig. 4 at 300–1000 K. These atom-atompeaks constitute an aid for deciphering X-ray diffractionexperiments and analyzing the high-temperature behavior ofthese nanostructures. The RDFs for all the simulated systemsare given in Fig. S1–S5.† The peak heights decrease withincreasing temperature and distance. Narrower and tallerpeaks suggest higher stabilities at the designated temperature.Fig. 4, S1–S5† confirm the visual analysis of Fig. 1 by indicat-ing the poor, long-range order for all systems with three boronatoms per ring: “meta”, “3B”, and “B–B–B”. In turn, very sharp,long-range orders are observed in the “1B” and “para” systems.The “B–B” system exhibits intermediate features. To test the

Fig. 2 Heats of formation of systems (a) “1B”, (b) “para”, (c) “meta”versus simulated time at 300 (blue dash-dotted line), 500 (green dashedline), and 1000 K (red solid line).

Fig. 4 Radial distribution functions for carbon–carbon (red solid line),boron–boron (green dashed line), and carbon–boron (blue dash-dottedline) distances computed from the 100 ps long trajectory (system “1B”).

Fig. 3 Heats of formation of systems (a) “B–B”, (b) “3B”, (c) “B–B–B”versus simulated time at 300 (blue dash-dotted line), 500 (green dashedline), and 1000 K (red solid line).

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validity of our results with respect to the simulation time, weperformed a ten times longer, 1 ns simulation for the “B–B”system at 300, 500 and 1000 K. We observed no differencesbetween the data averaged over the 0.1 ns and 1 ns trajectories.Note that the results of the RDF analysis are in excellent agree-ment with the heats of formation, discussed above.

The C–C covalent bonds and the C–C non-covalent dis-tances (Table 2) characterize the graphene backbone. The“meta” system exhibits the most differences from the othersimulated systems. It has a fourth peak at a higher distance,4.40 Å, which means that the expected peak at ca. 3.80 Å isabsent. The peak height provides another straightforwardmeasure of structure stability. For instance, the least stablesystems generally have lower peaks. Note that the locations ofthe first two peaks, but not heights, are quite similar in all thesystems. The computed values are also in agreement with theexperimental lengths of the C–C bonds in the aromaticcompounds.

The average Coulson charges computed at 1000 K amountto −0.29 ± 0.02 (“1B”), +0.07 ± 0.00 (“para”), −0.16 ± 0.01(“meta”), −0.04 ± 0.00 (“B–B”), +0.04 ± 0.00 (“3B”), and+0.01 ± 0.00 (“B–B–B”). The averaging and standard error cal-culations were performed over all the boron atoms in the sheetand over the simulated time. In most systems, the charge issufficiently close to zero. The largest deviations are observed in“1B” and “meta”. By intercalating into the graphene sheet, theboron atom affects three covalent bonds, including B–B bondsin some configurations. Fig. S6† shows that the doped boronatoms contain 2.5 p-electrons and only 0.63 s-electrons. Thesevalues were averaged over the “1B” and “meta” structures at0 K. The averages computed separately for “1B” and “meta”were identical. The carbon atoms of graphene are sp2 hybri-dized, and donate one p-electron into the π-electron system.

Each of the s, px, py and pz orbitals contain one electron.Boron has one less electron than carbon. Half of the missingelectrons de-occupy the s-orbital, and the other half comefrom a p-orbital. Despite its lower electronegativity, accordingto the Pauling scale, boron pulls a certain amount of electrondensity from carbon. This is because boron requires anadditional electron to achieve the half-filled shell configur-ation, which is more energetically favorable. For instance,most boron atoms in the “1B” system acquire slightly negativecharges (Fig. 5a). Thermal fluctuations of the charge on theselected boron atom at 1000 K are modest (Fig. 5b, note the0.1|e| scale on the y-axis). Fig. S6† shows that the doped boronatoms contain 2.5 p-electrons and only 0.63 s-electrons. Thecarbon atoms, located near the edge of the sheet and termi-nated by hydrogens, obtain some s-electron density from thehydrogens, which are less electronegative.

The results for the systems containing 2 boron atoms perring are in agreement with the basic principles of electrophilicsubstitution. An electron withdrawing group decreases theelectron density in the ortho- and para-positions, but not inthe meta. Indeed, the charge on boron is negligible in both the“para” and “B–B” systems, whereas the charge is mostly nega-tive in the “meta” system.

The dipole moment of the entire sheet greatly depends onthe distribution of the B atoms (Fig. 6). The smallest dipolemoments are observed in the “para” (2.27 D) and “3B” (2.33 D)systems. Both molecules contain boron atoms in the para-posi-tions: 1, 4 and 1, 2, 4, respectively. The boron atoms in thepara-positions compensate each other to a certain extent. Incomparison, the dipole moment is up to four times larger insystems without such compensation, including the “1B”,

Table 2 Most probable carbon–carbon distances and RDF peaks in theB-doped graphene. R1–R4 are the positions of the first four peaks,whereas h1–h4 are the dimensionless heights of the first four peaks

System R1, Å h1 R2, Å h2 R3, Å h3 R4, Å h4

T = 1000 K“1B” 1.40 23.2 2.48 8.5 2.90 2.5 3.80 2.9“para” 1.40 22.3 2.48 7.4 2.92 2.3 3.82 2.6“meta” 1.40 16.8 2.52 6.8 3.80 1.5 4.40 1.3“B–B” 1.40 23.7 2.48 8.3 2.86 2.1 3.80 2.6“3B” 1.40 24.1 2.46 7.6 2.82 2.5 3.78 1.9“B–B–B” 1.40 23.6 2.46 6.8 2.84 1.4 3.76 2.0T = 500 K“1B” 1.42 28.1 2.48 10.5 2.88 3.1 3.80 3.6“para” 1.38 26.7 2.48 9.3 2.92 2.8 3.82 2.8“meta” 1.42 19.7 2.48 8.3 3.80 1.7 4.46 1.3“B–B” 1.40 28.8 2.48 10.2 2.86 2.3 3.80 3.1“3B” 1.40 28.4 2.46 9.4 2.82 2.7 3.78 2.3“B–B–B” 1.38 26.0 2.46 8.3 2.88 1.4 3.76 2.4T = 300 K“1B” 1.42 31.2 2.48 12.0 2.88 3.6 3.80 3.9“para” 1.38 28.7 2.48 10.2 2.92 3.1 3.82 2.8“meta” 1.42 21.9 2.48 9.2 3.78 1.8 4.34 1.5“B–B” 1.40 32.2 2.48 11.4 2.86 2.3 3.80 3.4“3B” 1.40 29.8 2.46 11.2 2.82 2.8 3.78 2.5“B–B–B” 1.38 26.4 2.46 9.4 2.90 1.5 3.76 2.6

Fig. 5 (a) Coulson charges averaged along the 100 ps trajectory andtheir standard deviations on different boron atoms of the B-dopedgraphene (system “1B”); (b) typical fluctuations of the charge on aB atom due to thermal motion at 1000 K.

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“meta” and “B–B” systems (Fig. 6). A single boron atom perring, system “1B”, already produced a large dipole moment of8.55 D. The value of the dipole moment characterizes thenanostructure’s response to an external electric field. Forinstance, sensor applications should be sensitive to theB-doping pattern.

The simulation of the “B–B” system in direct contact withfullerene C20 and decaborane B10H14 allowed us to study theeffect of the interaction of B-doped graphene with boron andcarbon containing particles available in the environment. Wedid not observe any chemical changes during a 1000 ps longPM7-MD trajectory at 500 K. The boron–carbon covalent inter-actions in the B-doped graphene are stronger than the inter-molecular interactions between these elements in theconsidered compounds. Both fullerene C20 and decaboraneB10H14 are reactive compounds. The simulation demonstratesthat the B-doped graphene is stable to chemical transform-ations with reactive boron and carbon structures.

The chemical integrity of the graphene derivatives wasmaintained over the 0.1–1 ns times used in our investigation.Sampling of macroscopic times is beyond the reach of ourmethodology, as well as other computational methods thataccount for the quantum-chemical nature of the simulatedentities. Stability of the simulated systems over the simulatedtimes suggests stability over larger time scales, since the simu-lations sample a significant number of bond oscillations,angle deformations, etc. It should be noted that rare events,which can possibly initiate decomposition of the entire struc-ture, could not be accounted for.

The presented results are based on a relatively smallgraphene sheet, and one may wonder whether the structureand stability depend on the system size. Fig. S7 and Table S1†compare the “para” system to the “big” system that also rep-resents the para arrangement of two borons per ring (Table 1).While all peak positions were found to be very similar, onaverage, the peaks are higher for the “para” system. This islikely explained by the higher flexibility in larger structures.Note that this effect is pronounced for the B–B and C–B peaks,but it is not clear for the C–C peaks, since the C–C peaks are

closer together and are harder to resolve. The fourth C–C peakis positioned only at 3.82 Å, while the fourth B–B peak is posi-tioned at 5.78 Å.

Conclusions

We have demonstrated theoretically that it is possible toachieve a high boron doping concentration in graphene, farexceeding the concentrations currently obtained in experi-ments. Using molecular dynamics simulations based on areliable and computationally efficient electronic-structuremethod, we have investigated the stability of B-doped grapheneover a range of temperatures as a function of boron concen-tration and dopant atoms distribution. One and two boronatoms per hexagonal ring were found to provide stable hetero-atomic nanostructures. Therefore, 100/6 and 100/3 mol% ofboron in graphene are theoretically stable, even at high temp-eratures. Higher boron concentrations, involving three dopantatoms per hexagonal ring, result in significant structure per-turbations upon thermal motion. Out of those systems, theone containing only a single B–B bond per ring is the mostsustainable. The results were validated using several criteria,including heats of formation, RDFs, and geometry inspection.Although the systems under investigation did not decomposeinto monomolecular constituents during the simulation, weexpect many of them to be highly reactive in a real chemicalenvironment, containing oxidants, hydrogen sources andother reactants. Unlike the case of the N-doped graphene,55

the dopant–dopant bonds do not undermine the system stabi-lity. This conclusion agrees well with the previous knowledgeabout boron compounds with multiple boron–boron covalentbonds, e.g. boranes and boron fullerene B80, in which the B–Bbonds are stable. The theoretical predictions can be verified bydirect chemical synthesis.

Acknowledgements

OVP acknowledges support of the Computational MaterialsSciences Program funded by the U.S. Department of Energy,Office of Science, Basic Energy Sciences, Award NumberDE-SC00014607.

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Fig. 6 Dipole moments of the B-doped graphene systems.

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