Relationship between Carbon Nitride Structure and Exciton Binding

Article pubs.acs.org/JPCC

Relationship between Carbon Nitride Structure and Exciton Binding Energies: A DFT Perspective Sigismund Melissen,* Tangui Le Bahers, Stephan N. Steinmann, and Philippe Sautet Université de Lyon, Université Claude Bernard Lyon 1, Ecole Normale Supérieure de Lyon, Centre Nationale de Recherche Scientifique, 46 allée d’Italie, Lyon F-69007 Cedex, France S Supporting Information *

ABSTRACT: Graphitic (g)-CxNyHz has become a popular element in photocatalytic water splitting cells. Recently, the crystal structures of completely polymerized g-C3N4 and incompletely polymerized g-C6N9H3 crystals based on the triazine and heptazine monomers have been characterized. In this manuscript we evaluate the atomic and electronic nature of these structures using DFT. The study revealed strongly corrugated structures for the fully polymerized g-C3N4 and planar structures for the incompletely polymerized g-C6N9H3. The exciton binding energies of the heptazine-based structures are lower than that of their triazine-based analogues and lower for the completely polymerized structures than their incompletely polymerized analogues. The rather low dielectric constant and charge mobilities result in high exciton binding energies and hence low dissociation probabilities for these excitons. This confirms the necessity of a morphology inspired by bulk heterojunction architectures to ensure efficient charge carrier generation. The studied compounds can be considered intermediates between typical inorganic and organic semiconductors in terms of their photoabsorption properties.

1. INTRODUCTION The sun is a virtually inexhaustible natural source of energy, the total solar power over the earth’s surface amounting to 65 Petawatts at any instant, with roughly half of this energy falling within the visible light range.1 One major drawback of solar energy is its diurnal variation, making its direct storage into chemical bonds an attractive alternative to photovoltaics. In the search for such energy solutions, inspiration can be drawn from photosynthesis. In this biological process, the chloroplasts inside a plant’s leaves use photons to generate excited electrons and holes that are able, after several transfers, to initiate chemical reactions. Artificial photosynthesis reproduces all these steps in a manmade device, allowing the use of sunlight to induce chemical reactions. Among the possible chemical reactions, the splitting of water is the most interesting one since it leads to the production of hydrogen.2,3 The two redox half reactions are provided 2H+(aq) + 2e− → H 2(g)

(1a)

2H 2O(l) → O2 (g) + 4H+(aq) + 4e−

(1b)

synthesis history of these macromolecules contains elements of controversy, due to several insufficiently substantiated claims that a graphitic C 3N4 structure was found, and with confusionas terms such as polymer, graphitic, and graphene-like structures are used interchangedly. The main reasons for this confusion are that the obtained macromolecules are often both amorphous and insoluble in most organic solvents, making them difficult to characterize.8 Two forms of g-CxNyHz are described in the literature: triazine-based (leading to gt-CxNyHz) and heptazine-based (forming gh-CxNyHz). Their tectons are displayed in Figure 1. Although a gt-C3N4 structure was recently characterized,8,9 no definitive experimental evidence for crystalline gh-C3N4 has been put forward.10 Moreover, it is commonly believed that

Figure 1. g-CxNyHz tectons. (i) Melamine (R = NH2), based on triazine (R = H). (ii) Melem (R = NH2) based on heptazine (R = H).

Graphitic carbon nitride, with general formula g-CxNyHz, has been extensively studied as a light-absorbing element in photocatalytic water splitting cells.4 The existence of graphitic Si3N4-analogous C(IV) nitrides (g-C3N4) was postulated5,6 by Liu et al. 25 years ago; however, the notion of macromolecular C3N4-based structures dates back to the 19th century.7 The © 2015 American Chemical Society

Received: July 21, 2015 Revised: October 16, 2015 Published: October 16, 2015 25188

DOI: 10.1021/acs.jpcc.5b07059 J. Phys. Chem. C 2015, 119, 25188−25196

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The Journal of Physical Chemistry C

Figure 2. 2D chemical structures of completely (left) and incompletely (right) polymerized gt- and gh-CxNy studied in this manuscript. Individual tectons are highlighted in blue.

influences the exciton binding energy Eb, and the charge carrier effective masses m* (invariably expressed in terms of the free electron mass me) involved in their mobilities μ. In Table 1, desired ranges of values for the electronic properties above are reported.24

imperfections in the g-C xN yHz macrostructure do not necessarily hinder the photoactive process and possibly even constitute the catalytic sites and the ability of the fully polymerized photoactive material to perform the actual chemical conversions being generally contested.11 The overall photocatalytic performance of g-C3N4 is enhanced by adding cocatalysts through techniques such as nanoparticle decoration or by doping through elemental substitution.12 The general objective of nanoparticle decoration is the creation of catalytic sites for H2 and O2 evolution. For the first reaction, noble metals and their alloys are used,13,14 exploiting their possibilities to bond covalently to the NHx termini.15−17 For O2 evolution, transition metal oxides such as RuO2 are frequently used.18 Although the graphitic nature of the compound suggests a planar structure and some calculations are still performed on planar sheet geometries,10,19 several papers have stressed the importance of corrugation.20−23 In this study, four crystalline models of bulk g-CxNyHz will be studied using a theoretical approach. First, the fully polymerized and characterized g-C3N4 will be studied, starting from the results obtained earlier through molecular dynamics (MD) for the triazine-9 and heptazine-based20 variants. Then, the influence of the partial polymerization is investigated through g-C6N9H3 structures taken from the work by Schnick and co-workers. The proposed gh-C6N9H3 structure known as melon21 with P21/a symmetry and the fully characterized gtC6N9H3 structure22 from which LiCl was removed were considered as starting points. In Figure 2, the 2D chemical structures of the four systems are provided. Recently, the possibilities to calculate some of the fundamental properties governing a semiconductor’s ability to generate free charge carriers, marking the starting point for photocatalytic activity, using density functional theory (DFT) were pointed out24 and applied25,26 to several semiconductor families by some of us. These properties include the bandgap Eg (governing light absorption), the dielectric constant ϵr that

Table 1. Desired Ranges of Electronic Properties of Photoactive Semiconductors solar spectrum absorption

exciton dissociation

charge carrier diffusion

1.8 eV < Eg < 2.2 eV

Eb < 25 meV, ϵr > 10

m* < 0.5me

We have applied this approach9 to the g-CxNyHz structures and will detail our findings here as follows: the Computational Details section will outline the first-principles method employed here and briefly detail the semiconductor properties used to compare the studied structures. The comparison of experimentally obtained structures and our geometry optimizationsall of which are provided in the Supporting Informationis followed by a discussion of the influence of monomer nature and degree of polymerization on the material’s photoactivity. To the authors’ best knowledge, no systematic study into the ability of different g-CxNyHz structures to generate free charge carriers has been done, and the authors hope to draw some conclusions aiming to contribute to the discussion on structure−property relationships in g-CxNyHz-based photocatalytic cells.

2. COMPUTATIONAL DETAILS 2.1. DFT Calculations. All DFT calculations were performed employing the CRYSTAL14 suite, due to its natural treatment of systems with different types of periodicity and the efficiency of calculations performed with hybrid functionals using Gaussian type orbitals (GTOs).27,28 25189


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Figure 3. Optimized 3D-g-CxNyHz systems. (i) gt-C3N4, (ii) gh-C3N4*, (iii) gt-C6N9H3, and (iv) gh-C6N9H3. The unit cells are delineated in light gray. N atoms are in blue, C in gray, and H in white. dAr−Ar refers to the (average) interlayer distance. *In the Supporting Information, the geometry of gh-C3N4 is supplied in the axis system in which calculations were performed.

Gatti’s40 all-electron 6-31G(d,p) basis set41 was employed for H, C, and N. Convergence (10) but higher than a classical organic one (with values usually found between 2 and 4).71 Upon inspection of the band structures, the orbitals of the incompletely polymerized structures are more localized, as expected. Furthermore, strong band curvature is only obtained in the polymerization directions, with some interlayer mobility in the case of gt-C3N4. In the polymerization directions, the charge carrier effective masses are not strongly affected by the nature of the monomer, but a more complete polymerization allows for a better mobility of both the electrons and the holes. In the case of gt-C3N4, it must be remarked that due to orbital degeneracy a heavy and a light electron can be defined upon light absorption. Only the light electron is discussed here. For all systems, Eb is much greater than kBT, and Re is smaller than the tecton size, meaning that these excitons are localized and do not easily dissociate. The anisotropy of the different structures is expressed both in their dielectric constants, with ϵr,(100) > 3ϵr,(001), and effective masses, with m*(001) > 10m*(100), for both the hole and the electron. Thus, the exciton mobility is essentially limited to the two-dimensional molecular plane, accounting for the required factor 4 in eqs 4 and 5 (for the binding energies in 3D cf. Supporting Information).

determining the degree of polymerization. Overall, a good qualitative and quantitative agreement is obtained by comparing the geometries of the calculated structures to the experimentally characterized ones. Comment on the Phonon Band Spectrum of gt-C6N9H3. A measure for the interlayer interaction can be provided by phonon dispersion spectra. In particular, the splitting of the longitudinal and transverse acoustic (LA & TA) phonons starting at the Γ-point and determined at the A-point in the Brillouin Zone yields the required information. The validity of using an HSE06/D2 approach to compute such spectra can be seen by comparing experimentally and computationally obtained57,58 splitting values for hexagonal (h-) BN in the order of 100 cm−1. Graphite is known to exhibit a Γ-point splitting of 50 cm−1.59 Our calculation (cf. Table S1 and Figure S2 in the Supporting Information) of a splitting of ∼70 cm−1 confirms what can be hypothesized from both the geometry optimizations (with dAr−Ar equal to 3.14, 3.26, and 3.32 for hBN, gt-C6N9H3, and graphite, respectively) and the fact that in terms of electronegativity C lies between B and N. The relatively localized charges on h-BN allow for a stronger interlayer interaction than the delocalized electron cloud in the graphene layers in graphite, with gt-C6N9H3 lying between these two extremes. These spectra can be used further for a comprehension of properties such as the material’s thermal conductivity.60 3.2. Photoactivity Descriptors. The main numerical results of the photoactivity study are provided in Table 3, Table 3. Main Numerical Results of the Free Charge Carrier Generation Study gt-C3N4

gh-C3N4

gt-C6N9H3

gh-C6N9H3

gap nature

Γ→Γ

Γ→Γ

K→K

Γ→Γ

Eelg (eV) me*, mh* (me) ϵr {ϵ∞, ϵvib} Eb (meV) Eopt g (eV) Re (Å)

3.4 0.4, 1.4 6.8 {5.0, 1.8} 367 3.0 2.88

2.8 0.4, 1.4 7.2 {5.0, 2.3} 328 2.5 3.05

4.3 0.7, 1.9 4.6 {3.4, 1.2} 1350 3.0 1.16

3.4 0.9, 1.6 6.1 {4.1, 2.0} 840 2.6 1.38

while the band structures of the different studied systems are provided in Figure 5. To give the reader an idea of the influence of the choice of the PBE0 functional for the CPHF calculation,61 the band structures using the PBE0 functional were calculated and added to the Supporting Information, showing a similar band structure and a systematic increase (∼0.7 eV) in Eelg , as expected.24 A comparison between bandgap values obtained here and those found in the literature is provided in Figure 6. Note that in the reference study by Lotsch et al.21 for gh-C6N9H3 no photoabsorption study is carried out, and results by Niu et al.62 were used for comparison. All comparisons and particularly this last comparison demonstrate that the Wannier−Mott analysis presented in this paper acts as a first correction to determine Eopt g accurately. An advantage of this type of material is that for all structures the first electronic transition is direct. The first remarkable difference in their electronic properties is that the bandgap decreases markedly (∼0.6 eV) upon going from an incompletely to a completely polymerized system and upon going from a triazine- to a heptazine-based system. Upon

4. DISCUSSION The values for Eb obtained by Wei et al.19 using G0W0-BSE are between 1 and 2 eV. These values are slightly higher than the ones obtained by us using the Wannier−Mott model. The major reason for this discrepancy comes from the inclusion of 25192


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Figure 5. Band structures of different g-CxNyHz systems. The path corresponding to the [001] direction is highlighted in gray.

Figure 6. Comparison between the bandgap values obtained here and in the literature. Notes: §ref 9, ¶ref 10, ∥ref 62, †ref 63, ‡ref 64, *ref 65, and #ref 19.

Figure 7. g-CxNyHz valence and conduction band edge positions with respect to the water splitting half reactions for the optimized five-layer (5L) slabs. *NHE = Normal Hydrogen Electrode. Left-hand axis: electrochemical potential. Right-hand axis: absolute energy scale.

the vibrational term of the dielectric constant that reduces Eb by a factor ∼2. However, the qualitative conclusion remains similar: whatever model is used to calculate its energy, the excitons are not spontaneously dissociated at room temperature. This result confirms the similarities of these materials to classical semiconductor polymers that have exciton binding energies much higher than kBT. In the case of semiconductor polymers used in photovoltaics, the community developed the so-called “bulk heterojunction” architecture to allow the exciton

dissociation at the interface between the polymer and an electron-accepting material.72−74 For g-CxNyHz materials, the interface with the cocatalyst (Pt for instance) plays a similar role. The exciton is dissociated at the interface, and the electron is transferred to the co-catalyst in 25193


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Figure 8. Conceptualization of the free charge carrier generation in g-CxNyHz structures as proposed in this work.

the case of a hydrogen evolution reaction. As for the bulk heterojunction, the larger the interface, the better the exciton dissociation efficiency. This confirms why these materials have to be coated with highly dispersed nanoparticle cocatalysts,13,14,18 maximizing the uptake probability of the charge carriers before recombination. These ideas are visualized in Figure 8. The overall increases in charge carrier mobility and dielectric constant upon going from triazine- to heptazine-based systems and upon going from partially to completely polymerized systems are ultimately translated in the lowest Eb for gh-C3N4. Arguably, the use of incompletely polymerized g-C6N9H3 is still of intrinsic interest because of the ability of the NHx termini to bond to noble metal nanoparticles that perform the proton reduction reaction,15−17 but the experimental search for higher degrees of g-CxNyHz condensation in terms of tecton size and polymerization degree can be justified by the results above.

charge carrier uptake probability before recombination are vital for this type of material’s photocatalytic efficiency.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b07059. (1a) calibration of the optimization protocol; (1b) band structures calculated with PBE0; (2) crystal information: primary reference, number of atoms and Gibbs free energy per unit cell followed by structures in CIF-format; (3) exciton binding energies and radii within the framework of the 3D Wannier−Mott model; (4) further details on the phonon dispersion calculations (PDF)

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AUTHOR INFORMATION

Corresponding Author

5. CONCLUSIONS A set of selected properties governing the capacity of a material to create free charge carriers upon illumination were computed for four graphitic (g)-CxNyHz structures by DFT using the range-separated hybrid functional HSE06. The effects of the nature of the monomer and degree of polymerization are studied. The incompletely polymerized g-C6N9H3 structures are planar and have relatively wide bandgaps. Excitons created in these structures have large binding energies; the advantage of this type of structure is the presence of primary and secondary amines that allow a cocatalyst such as Pd, Pt, or Au to bond to the material. The completely polymerized g-C3N4 structures show a marked corrugation of the molecular plane, and excitons generated in these materials have a lower binding energy, although still significantly higher than the thermal energy. The nonionicity and low polarizability of these materials is translated in a dielectric constant that is high compared to a typical polymeric semiconductor but low in comparison to the typical value for an inorganic semiconductor. This is subsequently translated in relatively localized excitons with a high binding energy, leading to a low dissociation probability at room temperature. It was found that heptazine-based materials and materials with higher degrees of polymerization should outperform triazine-based materials and those with a lower degree of polymerization. Bulk heterojunction-inspired interactions with dispersed nanoparticle cocatalysts maximizing

* E-ma il: [email protected]. Ph o n e : +33.4.7272.8640. Fax: +33.4.7272.8860. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Funding for this work was provided by the King Abdullah University of Science and Techonology (KAUST), within the framework of Special Academic Partnership Program “Water Splitting” (projects ENS 14.065 and KAUST 1974-02). The authors gratefully acknowledge Dr. A. Winfer and Dr. I. Shore (KAUST Supercomputing Laboratory), the computational resources provided by l’Institut du développement et des ressources en informatique scientifique (IDRIS, under project x2015080609) of the Centre Nationale de la Recherche Scientifique (CNRS), Prof. R. Orlando (University of Torino) for advice on the use of the CRYSTAL14 suite, and Prof. B. Lotsch (Max Planck Institute for Solid State Research), Dr. R. Kerber (Cambridge University), and Prof. K. Takanabe (KAUST) for valuable discussions on this topic.

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ABBREVIATIONS CB, Conduction Band; CPHF, Coupled-Perturbed Hartree− Fock; DFT, Density Functional Theory; GTOs, Gaussian Type Orbitals; SCF, Self-Consistent Field; VB, Valence Band 25194


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Relationship between Carbon Nitride Structure and Exciton Binding

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