Role of Defects on Regioselectivity of Nano Pristine Graphene

Article pubs.acs.org/JPCA

Role of Defects on Regioselectivity of Nano Pristine Graphene Gururaj Kudur Jayaprakash,† Norberto Casillas,‡ Pablo D. Astudillo-Sánchez,§ and Roberto Flores-Moreno*,‡ †

Departamento de Ingeniería de Proyectos, Centro Universitario de Ciencias Exactas e Ingenierías, Universidad de Guadalajara, Boulevard Marcelino García Barragán 1421, Guadalajara, Jalisco, C.P. 44430, Mexico ‡ Departamento de Química, Centro Universitario de Ciencias Exactas e Ingenierías, Universidad Guadalajara, Boulevard Marcelino García Barragán 1421, Guadalajara, Jalisco, C.P. 44430, Mexico § Departamento de Ingenierías, Centro Universitario de Tonalá, Universidad Guadalajara, Av. Nuevo Periférico No. 555, Ejido San José Tatepozco, Tonalá, Jalisco, C.P. 48525, Mexico

ABSTRACT: Here analytical Fukui functions based on density functional theory are applied to investigate the redox reactivity of pristine and defected graphene lattices. A carbon H-terminated graphene structure (with 96 carbon atoms) and a graphene defected surface with Stone−Wales rearrangement and double vacancy defects are used as models. Pristine sp2-hybridized, hexagonal arranged carbon atoms exhibit a symmetric reactivity. In contrast, common carbon atoms at reconstructed polygons in Stone−Wales and double vacancy graphene display large reactivity variations. The improved reactivity and the regioselectivity at defected graphene is correlated to structural changes that caused carbon−carbon bond length variations at defected zones.

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INTRODUCTION

In particular, we believe that quantum chemistry could provide valuable tools for a better understanding of electronic properties of graphene. Quantum chemical studies will enhance the knowledge of the impact that defects have on graphene chemistry. Many quantum chemists are interested in getting new information on intrinsic defects like Stone−Wales (SW) rearrangement and vacancy defects.14,16 In SW rearrangement, four hexagonal rings of graphene are reconstructed into two pentagons and two heptagons by in plane 90° rotation of C−C (C4−C10) bond of graphene in Figure 1a to produce the configuration shown in Figure 1b. Large part of theoretical studies are concentrated more to analyze the effect of defects on chemisorption of foreign atoms. For instance, L. Chen et al.17 studied the chemisorption of H, N, and P atoms at the SW rearrangement sites of graphene. Cabrera-Sanfelix18 used density functional theory to know about the absorption of CO2 at defected regions of graphene, O. Leenaerts et al.19 studied the penetration of helium atoms through a graphene monolayer with defects.

Graphene can be taken as the basic building block of important carbon allotropes such as carbon nanotubes and fullerenes. It is made by a two-dimensional sp2-hybridized honeycomb network of carbon atoms.1−5 Novelty and remarkable electronic properties of graphene have attracted considerable attention to both experimental and theoretical fields. Graphene based materials have great applications in current generation devices for nanoelectronics,6 nanosensors,7 supercapacitors,8,9 ecofriendly batteries,10 and nanostructured electrodes.11 Understanding surface chemical properties of graphene will be helpful for its futuristic applications.12 Atomic scale defects are naturally occurring in graphene structure. In this framework, the defects may be intrinsic (an intrinsic defect occurs when a particle is not where it should be) or extrinsic (occurs when impurities/foreign atoms are added to crystals). It is worthy to mention that any type of defect involves a change in the physical and chemical properties of graphene.13−15 Characterization and systematic studies on defects will be important research motivation for graphene materials applications; it raises huge curiosity for both experimentalists and theoreticians. © XXXX American Chemical Society

Received: August 31, 2016 Revised: October 27, 2016 Published: October 31, 2016 A

DOI: 10.1021/acs.jpca.6b08810 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

Figure 2. Different ideal graphene models.

symmetric systems. We will show how to overcome these problem in graphene models taking care of orbital degeneracy in analytical Fukui functions.35

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Figure 1. Ideal and defected graphene.

COMPUTATIONAL METHODS AND MODEL All carbon atoms of graphene were arranged in hexagonal lattice, and borders were terminated with hydrogen atoms to neutralize carbon atoms at the edges as shown in Figure 2. Model structures of graphene were constructed using MOLDEN software.36 Geometry optimizations were performed using deMon2k37 code. For geometry optimizations, we have fixed the hydrogen Cartesian coordinates, after building using planar angles of 120° and 1.0 Å for carbon− hydrogen bond length. With fixed hydrogen positions structures were reoptimized. Fukui functions and Hirshfeld charges on graphene carbon atoms were computed using VWN38 correlation functional with DZVP39 basis set. Energies of the ideal and defected graphene were computed with a more reliable but computationally more expensive setting using PBE40,41 functional with TZVP39 basis set. Fukui functions were graphically plotted using Sinapsis package.42

Vacancy is another class of topological defect, which has significant impact on the chemical nature of graphene. Vacancies in graphene can be created by removing adjacent carbon atoms (C4 and C10) from their lattice positions as shown in Figure 1c. In this case two pentagons and one octagon are formed in the place of four hexagons shown in Figure 1a. Sometimes, double vacancy (DV) defects are created by the fusion of two adjacent single vacancy defects. K. M. Fair et al.20 used first-principles calculations to investigate hydrogen adsorption at adatoms present in DV defected graphene. S. Malola et al.21 investigated bonding and diffusion of Au at DV defected graphene. X. Fan et al.22 studied Li interaction at DV defects and reported that DV defects enhance adsorption energies of Li because of extra potential trap. However, there is still need to research more about defects on general chemical properties of graphene. Defects in graphene are observed and studied by experimental methods such as high resolution transmission electron microscopy,23 Raman spectroscopy,24 and scanning tunneling microscopy.25 Defects also enhance the local paramagnetic ring currents in graphene.26 Defects are usually generated by the surface oxidation of graphene/graphite electrodes to improve its performance like sensing and storing properties and provide a speed track for electrolyte transport. Recently some electrochemical evidence suggests differences in kinetic properties, when electron transfer processes occur at the edges and defective sites in comparison with the basal planes.27 There are few reports mentioning that generating defects in graphene is an interesting approach to improve electrodes by creating more edge sites.28 In recent theoretical investigations the role of defects in organic reactions was investigated by P. A. Denis et al.29,30 They studied cycloadditions and Diels−Alder reactions at defected graphene. They also found that SW rearrangement and vacancies facilitate addition of azomethine ylides. In this work, a systematic first-principles study of pristine graphene and the effect of defects on graphene reactivity is presented. We have calculated the defect formation energies and analytical Fukui functions31−34 for graphene surfaces. The utility of Fukui functions in theoretical calculations for a better understanding of the reactive sites on graphene is discussed. To the best of our knowledge, there are no previous reports about using analytical Fukui functions for understanding reactivity of surfaces. We were able to calculate analytical Fukui functions for graphene surfaces with 96 carbon atoms and 24 hydrogen atoms for molecular models shown in Figure 2 to know about regioselectivity at graphene surface. Symmetry breaking might become a problem for Fukui function analysis for large

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DETERMINATION OF APPROPRIATE MODEL SIZE In order to simulate defects in the graphene structure, we first tested different model sizes in ideal graphene. The model size in which central carbon atoms are very little or unaffected from artificial H termination will be good for further study. Three different graphene models with different number of carbon atoms were constructed; they are shown in Figure 2. Description of carbon atoms numbered in Figure 2 and the associated geometrical parameters will be contrasted for different model sizes. Geometry Optimizations. Structures corresponding to each model were optimized by keeping constant Cartesian coordinates of hydrogen atoms. Bond angles between carbon atoms are ∼120° in all graphene models. Bond lengths between the selected carbon atoms are shown in the Figure 3 for all graphene models. Bond lengths are almost constant at C96H24 but present substantial variations at C54H18 and C26H12. Therefore, this was the first support for us to assume that in C96H24 the selected 24 carbon atoms can be considered as similar to carbon atoms which are located in infinite graphene. Charge Analysis. Charges of the carbon atoms may also be affected by artificial terminal H atoms. We used Hirshfeld charge analysis to support our selection of appropriate model size for graphene. Hirshfeld charges at different ideal graphene models are shown in Figure 4. As we can see from the Figure 4, the selected carbon atoms in C56H18 and C96H24 models are almost unaffected from the artificial terminations. In the infinite limit carbon charge should be zero; these results are very close. Selected Model Size. The selected seven hexagons of the graphene model shown in Figure 2c have constant bond angle B


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Figure 5. SW defect and DV defect at C96H24.

DZVP39 basis set (VWN/DZVP) and 5.73 eV (PBE40,41/ TZVP39). The obtained SW formation energy is in good agreement with previously published results.43−45 Double Vacancy Defect. To induce DV defect into the C96H24 model, 2 adjacent carbon atoms (5th and 6th) are removed. As result of further optimization, here 4 hexagons are transformed into 1 octagon and 2 pentagons (3rd and 7th), as shown in Figure 5a. DV defect formation energy (EDF DV) was calculated by eq 2

Figure 3. Carbon−carbon bond lengths at different ideal graphene models.

DF E DV = E DV + EC−C − E P

where EDV and EC−C are energies of defected graphene and carbon dimer which were removed to induce a defect. DV defect formation energies are 16.25 eV (VWN/DZVP) and 13.81 eV (PBE/TZVP). Comparison of Defects. In accordance with our results, SW rearrangement is thermodynamically more favorable when compared to DV defect. SW rearrangement is simple isomerization, but DV defect formation is removal of 2 carbon atoms. Therefore, SW rearrangement requires less energy. In addition it is important to take into account that DV defect causes breaking of planarity of graphene structure. Ideal, SW, and DV graphene bond lengths are compared and presented in Figure 6. After the formation of a defect, bond lengths and bond angles were deviated from the ideal graphene. In SW rearranged graphene, distances between the rotated carbon atoms (C5−C6) were decreased up to 1.30 Å, similar to a triple carbon−carbon bond. In DV defected graphene newly formed bonds (C1−C7 and C4−C22) become larger in length,

Figure 4. Hirshfeld charges at different ideal graphene models.

and bond lengths, and these hexagons are unaffected by artificial termination at C96H24 model. We can consider 1−7 hexagons of the current model as similar to graphene hexagons which were present in infinite graphene; hereafter we are using only the C96H24 model.

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DEFECT FORMATION ENERGIES Stone−Wales (SW) rearrangement and double vacancy (DV) defect were introduced into the C96H24 model as shown in Figure 5. In this section we focus on the calculation of defect formation energies. Stone−Wales Rearrangement. To induce SW rearrangement into the model, the 5th and 6th carbon atoms on C96H24 are rotated by 90° around an axis perpendicular to the graphene plane and passing through the midpoint of the line segment joining them. As a result of further optimization, 4 hexagons (1, 2, 3, and 7) are changed to 2 heptagons (3 and 7) and 2 pentagons (1 and 2) as shown in the Figure 5a. The surface remained flat even after the SW rearrangement and relaxation. Defect formation energies (EDF SW) for the SW rearrangement can be calculated by eq 1, DF ESW = ESW − E P

(2)

(1)

where ESW and EP are energies of SW rearranged and pristine graphene, respectively. Rearrangement energies are found to be 5.63 eV for VWN38 exchange−correlation functional and

Figure 6. Carbon−carbon bond lengths at different graphene models. C


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The Journal of Physical Chemistry A reaching 1.54 Å which resembles saturated carbon−carbon bond length (single bond).

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REDOX REACTION SITES BEFORE AND AFTER DEFECT IN C96H24 MODEL If we consider C1−C24 carbon atoms, 1−7 hexagons as shown in Figure 2c, of the C96H24 graphene model as a first step towards understanding of nanographene electrodes, it is possible to analyze the local reactive sites of graphene electrodes by using chemical reactivity theory descriptors like Fukui functions. Fukui functions are not completely new in electrochemistry. There are few reports about using condensed Fukui functions for understanding corrosion inhibition processes.46−49 In electrochemical terms Fukui functions are able to predict the liability of an electrode portion/zone for acceptance or release of an electron. However, in our experience condensed Fukui functions can lead to erroneous conclusions. We recommend using direct analysis of isosurface instead. Parr and Yang31 proposed the modern definition of Fukui functions based on the earlier works of Kenichi Fukui.32−34 It has been used previously to explain regioselectivity in chemical reactions with density functional theory.50,51 This function is defined as the derivative of the electron density ρ(r) with respect to the total number of electrons of the system N, under a constant external potential, ν(r).52−55 ⎛ ∂ρ(r) ⎞± ⎟ f ± (r) = ⎜ ⎝ ∂N ⎠ν(r)

Figure 7. Average ROS for FMOs of ideal graphene.

discussions, we are providing explanation for periodic reactivity of ideal graphene. Fukui results for ideal graphene are shown in Figure 8. In these Fukui plots, reactivity is increasing from blue to red (blue

(3)

where the + and − signs correspond to addition and remotion of electrons, respectively. If we remove an electron, f−(r) can predict the place where the maximum changes will occur. That place will be a nucleophilic site or oxidizing site. Similarly if we add an electron, f+(r) can predict the place where the maximum changes will occur. That place will be an electrophilic site or reducing site. The average Fukui value (f 0(r)) can be used to predict regioselectivity in addition of free radicals.50,56,57 In this work Fukui functions were calculated analytically.54,58 f 0 (r) =

f − (r) + f + (r) 2

Figure 8. Fukui results for ideal graphene.

< green < yellow < red). In Fukui plots (Figure 8) D6h symmetry is preserved for both negative and positive Fukui functions. This system presents not only degenerate frontier orbitals but also degenerate electronic states. Previously Cardenas et al.59−61 proposed a theoretical treatment for evaluating Fukui functions at degenerate states. Here we are capturing one of three equivalent states which differ only by translations along the graphene surface. Adding them all together would produce a perfect periodic pattern for Fukui functions and, therefore, for redox reactivity of graphene as can be expected for ideal perfectly planar graphene. FMO studies give information on the redox reactive locations without considering electronic relaxation, and Fukui results give information on the locations which will undergo maximum changes in the redox reactions, taking into account relaxation effects. Therefore, FMO studies and Fukui studies should be in good agreement with each other to predict redox reactivity sites more precisely. In our results, ROS for FMOs studies and Fukui studies have good agreement with each other for ideal graphene. Hence, our results are more faithful. Stone−Wales. ROS for FMOs of SW rearranged graphene is shown in Figure 9. From Figure 9a and Figure 9b one could locate redox active sites. If no relaxation of density would occur, C7, C9, C20, and C22 of SW rearranged graphene would have more probability to undergo oxidation and carbon atoms in pentagons (especially C5 and C6) would have more probability to undergo reduction. In order to take into account density relaxation after charge transfer, we are evaluating analytic Fukui functions. Fukui results for SW rearranged graphene are illustrated in Figure 10 using a colored isodensity. From this

(4)

For all graphene models C1−C24, 1−7 hexagons as shown in of Figure 2c are only considered in the analysis of our study because they are not affected by artificial terminations. Ideal. We are computing frontier molecular orbital (FMO) reactive orbital space (frozen orbital approximation to Fukui functions) to complement our results for analytical Fukui functions. HOMO of the ground state graphene reacts with the electrophile, and LUMO of the ground state graphene reacts with nucleophile.33 Here graphene preserves its symmetry, and as a result of this, FMOs are degenerated. Therefore, we have considered average reactive orbital space for ideal graphene, and the result is shown in Figure 7. Figure 7a represents the average reactive orbital space (ROS) for HOMOs of ideal graphene; at these sites electrophile reacts. Similarly Figure 7b represents the average ROS for LUMOs of ideal graphene; at these sites nucleophile reacts. Because of symmetry, results are perfectly periodic as indicated in Figure 7; i.e., all hexagons of the ideal graphene have equal probability for electron acceptation and remotion. These interpretations are further confirmed from Fukui results. In the next Fukui result D


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Figure 9. ROS for FMOs of SW rearranged graphene. Figure 12. ROS for FMOs of DV defected graphene.

occur, C4 and C19 atoms would have more probability to undergo oxidation. Figure 12b represents the ROS for LUMO of the DV defected graphene. Carbon atoms in the octagon and C20 would have more probability to undergo reduction if no relaxation would occur. Fukui results for DV defected graphene are shown in the Figure 13, as a colored isosurface. For the analysis of these

Figure 10. Fukui results for SW rearranged graphene, presented as colored isodensities.

figure one can conclude that pentagons and heptagons are most reactive at the SW rearranged graphene surface. Therefore, SW defects improve ET reactivity of graphene and they become the redox sites. In Figure 11, Fukui functions of SW rearranged graphene are presented by isosurfaces. Results of Fukui function can be rationalized if we recall that structural changes are due to decrease in bond length of C5−C6. As can be seen in Figure 11a, for nucleophilic reactions (loss of electrons), most reactive carbon atoms are those in positions C4 and C20 and their symmetry analogs. Those are linked to C5−C6 bond and the heptagon carbon most distant from this bond. These are the atoms more affected by C5−C6 bond length variations. We believe they have a certain amount of radical (unpaired electron) behavior. Figure 11b and Figure 11c indicate that for both electron addition and attack by radicals the most reactive part is the C5−C6 bond. This is in agreement with the results obtained by P. A. Denis et al.14,29,30,62 and H. Xu and collaborators.63 Double Vacancy. ROS for FMOs of DV defected graphene is shown in Figure 12. Figure 12a represents the ROS for HOMO of the DV defected graphene. If no relaxation would

Figure 13. Fukui results for DV defected graphene, presented as colored isodensities.

results remember that DV defect breaks planarity of our graphene model and causes occurrence of single carbon− carbon bonds in bond shared by pentagon and octagon. Once again, defected regions are the most reactive sites of the molecule. Since DV defects make graphene nonplanar and nonplanar regions act as edge sites, those sites will be more reactive than the ideal graphene.28 In Figure 14, Fukui functions of DV defected graphene are presented by isosurfaces. Figure 14a shows that atoms at position C10 and its analogs are more preferable for electron remotion (oxidation). Therefore, pentagons of DV defected graphene are more reactive for oxidation. Figure 14b shows that carbon atoms in

Figure 11. Fukui isosurfaces for SW rearranged graphene. E


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therefore these regions of graphene may have higher ionic adsorption properties. Probably it is a reason for an enhanced ion/electrolyte transport at vacancy defects, which confirms earlier reports.65,66 Earlier few experimental results suggest that structural defects are profitable for electrochemistry, becoming major sites for rapid heterogeneous electron transfer.27,67,68 Our Fukui analysis is in good agreement with previous experimental results.

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CONCLUSIONS Understanding the role of defects on the redox reactivity of graphene is of great importance for electroanalysis. In this work, we have modeled graphene (as shown in Figure 2). We are reporting for the first time the use of analytical Fukui functions for prediction of redox reactive sites at nanographene systems. As a calibration of our approach, we verified that ideal graphene displays symmetric redox reactivity. Then, it was applied to Stone−Wales (SW) and double vacancy (DV) defected models. It was found that both types of defects improve redox reactivity. Our results of geometry optimizations and defect formation energies provide a frame to rationalize our Fukui function results. We were able to discriminate the rings (pentagons, hexagons, heptagons, or octagons) that are more active in redox processes. Our results agree with P. A Denis et al.14,29,30,62 results for specific reactions with radicals. As a byproduct, our results suggest that SW rearrangement could be an intermediary stage of DV defect formation. Altogether, we found that application of Fukui function analysis can be a powerful tool in the analysis of charge transfer processes for electrochemistry.

Figure 14. Fukui isosurfaces for DV defected graphene.

octagon and C20 are more preferable for electron addition (reduction). Similarly Figure 14c shows that carbon atoms in octagon and C20 are more susceptible for radical attacks. These findings also agree very well with those of P. A. Denis et al.,14 for addition of specific radicals. Fukui isosurfaces for f−(r), f+(r) are shown in Figure 15 and Figure 16. From the figures, we can observe surface densities

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AUTHOR INFORMATION

Corresponding Author

*E-mail: roberto.fl[email protected]. Phone: +523314957095.

Figure 15. Fukui negative isosurface results for double vacancy defect graphene.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS CPU time is gratefully acknowledged to cluster Agave, University of Guadalajara (CUCEI). G.K.J. thanks CONACYT for a Ph.D. scholarship (Grant 300851). Funding from Secretariá de Educacón Pública (Grant DSA/103.5/15/3252) is also acknowledged. The authors give special thanks to the reviewers for very valuable suggestions.

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Figure 16. Fukui positive isosurface results for double vacancy defect graphene.

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