Thermodynamically Controlled High-Pressure High-Temperature

Oct 29, 2015 - (1) One potential pathway to synthesize such networks is the ... Color code: carbon/phosphorus, dark gray; fluorine, green; bonds, red...
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Thermodynamically Controlled High-Pressure High-Temperature Synthesis of Crystalline Fluorinated sp3‑Carbon Networks Kamil Klier and Kai Landskron* Department of Chemistry, Lehigh University, Bethlehem, Pennsylvania 18015, United States S Supporting Information *

ABSTRACT: We report the feasibility of the thermodynamically controlled synthesis of crystalline sp3-carbon networks. We show that there is a critical pressure below which decomposition of the carbon network is favored and above which the carbon network is stable. Based on advanced, highly accurate quantum mechanical calculations using the allelectron full-potential linearized augmented plane-wave method (FP-LAPW) and the Birch−Murnaghan equation of state, this critical pressure is 26.5 GPa (viz. table of contents graphic). Such pressures are experimentally readily accessible and afford thermodynamic control for suppression of decomposition reactions. The present results further suggest that a general pattern of pressure-directed control exists for many isolobal conversions of sp2 to sp3 allotropes, relating not only to fluorocarbon chemistry but also extending to inorganic and solid-state materials science.

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ew crystalline sp3-carbon networks are of tremendous importance for both basic and applied research with applications as ceramics, in electronics, and in biomedicine.1 One potential pathway to synthesize such networks is the highpressure polymerization of unsaturated organic molecules. A major problem associated with the synthesis is that the crystallization is associated with significant kinetic barriers due to the strong covalent carbon−carbon bonds. High temperature could overcome such kinetic barriers; however, the uncontrolled decomposition to form known carbon allotropes (graphite, diamond) and small molecules under such conditions is a challenge. Consequently, all sp3-carbon networks synthesized at high pressure to date are amorphous materials, except diamond.2−15 A one-dimensional (1D) crystalline carbon nanothread material has been recently reported.16 Herein, we show that this problem can be overcome in the case of fluorinated carbon networks at sufficiently high pressures. Fluorine forms the strongest covalent single bond with carbon. With an average bond strength of 485 kJ/mol it is significantly stronger than the average C−C single bond (385 kJ/mol). Consequently, in any binary chemical system containing the elements carbon and fluorine, the number of carbon−fluorine bonds should be maximized when the system is in its absolute thermodynamic minimum. This circumstance suggested to us that unsaturated perfluorocarbon molecules may be able to form extended, crystalline sp3-carbon networks under thermodynamically controlled high-pressure high-temperature conditions without the elimination of fluorine from the network. The role of the pressure would be to induce the change from the sp2 to sp3 hybridization in the carbon atoms. The high temperature would ensure that kinetic activation barriers have no influence on the product identity and the reaction occurs under thermodynamically controlled condi© 2015 American Chemical Society

tions. The carbon network would be made of covalent C−C bonds and additional terminal C−F bonds whereby the exact structure would be determined by the C:F ratio as well as the pressure and temperature conditions. For example, for a composition CF one would expect a structure made of CC3F tetrahedra (carbon is surrounded by one fluorine and three other carbon atoms). For a ratio C:F < 1:1 additional CC2F2 units would be expected. If the ratio C:F is larger than 1:1, CC4 tetrahedra would be anticipated in addition to the CC3F units. The structures may be fundamentally different from that of diamond because of the different framework connectivity stemming from the terminal C−F fragments. Because of the structural differences, the materials properties should also be significantly different from that of diamond. The materials could be potentially interesting as ceramic materials with superhydrophobic properties, as well as optoelectronic, biomedical, and electroactive materials.1 To evaluate the feasibility of the synthetic concept, our first aim was to determine what pressure would be needed to polymerize a perfluorinated molecule to form a crystalline carbon network. The second goal was to see if the carbon network would be thermodynamically stable with respect to decomposition into graphite/diamond and small fluorocarbon molecules. Decomposition pathways are an important consideration because high temperatures are necessary to ensure a thermodynamically controlled synthesis and to allow for the formation of crystalline products. We have chosen carbon networks with the empirical formula CF as a starting point for our investigations. A carbon network Received: September 17, 2015 Revised: October 27, 2015 Published: October 29, 2015 26086

DOI: 10.1021/acs.jpcc.5b09084 J. Phys. Chem. C 2015, 119, 26086−26090

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other structures seem possible because the steric requirements as well as electronic properties of C−F and P fragments are only somewhat but not extremely similar. In the carbon− hydrogen (CH) system several two-dimensional (2D) and three-dimensional (3D) carbon network structures have been computationally predicted and these structures would also be plausible candidates in the CF system.19,20 Also, the formation of 1D nanothreads is a possibility.16 The structures are novel over that of diamond because in diamond each carbon atom is bound to four others while in CF each carbon is bonded only to three other carbon atoms. In the first step we have calculated the internal energies of the perfluorobenzene as well as graphite fluoride in the solid state using the Wien2k package for periodic systems21 and starting with available crystallographic data for these two compounds. Crystal structures HFBENZ.cif and HFBENZ02.cif were imported from the Cambridge Crystallograhic Data Centre, http://www.ccdc.cam.ac.uk/, and their internal energies calculated using the Wien2k platform. The structure for HFBENZ02 was found to be by 1.7 kcal/mol (CF) more stable than HFBENZ, and was therefore used as the starting point for subsequent calculations of the expanded and compressed structures. Perfluorobenzene “HFBENZ02” crystallizes in a herringbone structure (space group no. 14; monoclinic unit cell; lattice parameters: a = 16.82 Å, b = 9.17 Å, c = 5.76 Å, β = 95.80). For graphite fluoride only powder X-ray diffraction data are available. For our calculations we have used the lattice parameters reported by Mahajan et al. (a = b = 2.530 Å, c = 5.760 Å, γ = 118.8°)22 and computationally optimized atom positions using the PORT minimization routine available in the Wien2k package. Then the internal energies and enthalpies of the perfluorobenzene and the graphite fluoride were calculated as a function of pressure P. This process involved intermediate calculation of internal energy E as a function of volume V in the range +5% (expansion) to −50% (compression) from equilibrium volume V0, minimization of internal coordinates for each volume, fitting the calculated E(V) dependence by third-order Birch−Murnaghan equation of state to yield the bulk modulus B0 and its volume derivative B0′, using analytical relationship for pressure P as a function of (V0/V), B0, and B0′, and obtaining the E(P) dependence for each compound investigated.23,24 Calculations were performed for T = 0, with temperature effects due to entropy changes assessed separately (vide infra). All present calculations were performed with the Wu-Cohen functional,25 muffin-tin radius for the C and F atoms RMT = 1.1 au, matrix size RKMax ≡ RMT*Kmax = 9.0, where Kmax is the plane-wave cutoff, and the magnitude of the largest vector in charge density Fourier expansion GMAX = 21.0 Ry. Internal coordinates were optimized using the PORT routine for each volume change from the starting equilibrium volume at the energy minimum. The choice of the WC functional is deemed justified by its excellent account for the difference in internal energies of the carbon allotropes diamond and graphite, 0.03 eV, at T = 0 and P = 0, in agreement with experiment. The difference is larger for the PBE functional and in fact reversed for the LDA functional, a trend consistent with that reported by Tran et al.26 While the performance of WC for fluorine is less documented, it was nevertheless used herein for all C−F compounds for the sake of consistency. Third-order Birch−Murnaghan Equation of State (B-M EOS) was presently used as follows: First, internal energy E,

with this composition would be composed of interconnected sp3-C−F fragments. To estimate how these fragments may interconnect, we have applied the concept of isolobality which is suitable to guess stable structures from molecular fragments.17 According to the concept of isolobality, two molecular fragments are isolobal when the number, symmetry properties, approximate energy, and shape of the frontier orbitals and the number of electrons in them are similar. A molecular fragment that can be considered to be isolobal to C−F is a P atom. Hence, carbon network structures made of sp3-C−F fragments may be isostructural to phosphorus allotropes (Figure 1).

Figure 1. Isolobality of C−F and P fragments.

One phosphorus allotrope is the black phosphorus which makes a corrugated sheet structure of edge-sharing sixmembered P6 rings. A similar structure is the graphite fluoride structure in which the P atoms are formally replaced by sp3-C− F fragments (Figure 2a, b). The difference between the two

Figure 2. Structures of graphite fluoride with optimized internal coordinates by Wien2k (a) and black phosphorus (b). Both structures are 2D structures made of edge-sharing six-membered rings with chair conformations (a single P6 ring is highlighted in blue). Color code: carbon/phosphorus, dark gray; fluorine, green; bonds, red. The topological difference is that the six-rings in graphite fluoride are transoriented (c), while they are cis-oriented in black phosphorus (d).

structures is that in graphite fluoride the six-rings are transoriented, while in black phosphorus they are cis-oriented (Figure 2c, d). The cis orientation leads to a stronger corrugation of the sheets. Graphite fluoride is accessible from graphite and elemental fluorine at temperatures between 300 and 400 °C in a kinetically controlled reaction in which F2 is added to the C−C double bonds in the graphene sheets.18 The fact that experimental crystallographic data exist for graphite fluoride makes it ideal as a model system for computations. It must be stressed though that structures other than the graphite fluoride structure could be obtained in actual laboratory experiments. This could be the structure of a phosphorus allotrope, but also 26087

DOI: 10.1021/acs.jpcc.5b09084 J. Phys. Chem. C 2015, 119, 26086−26090

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They are important because graphite fluoride may be only a local thermodynamic minimum relative to that of the decomposition products. The most plausible thermal decomposition pathway at high pressure is a decomposition into carbon (graphite or diamond, respectively) and small fluorocarbon molecules. There is experimental support for the relevance of this decomposition pathway. The hightemperature behavior of graphite fluoride has been studied in vacuum and at 8 GPa.27,28 It was found that from ca. 500 °C amorphous carbon and graphite were formed at 0 and 8 GPa, respectively, together with small fluorocarbon molecules. The formation of graphite at 8 GPa indicates that the system is still only in a local thermodynamic minimum because at 8 GPa diamond is the thermodynamically stable carbon phase. To get preliminary insight if pressure opposes the decomposition into elemental carbon and molecular fluorocarbons, we have estimated the volume change for the decomposition reaction:

calculated by the quantum mechanical method21 for each compressed and expanded volume V, was plotted and fitted by a nonlinear user-defined routine in Origin for E(V) to yield numerical values of equilibrium volume V0, energy E0, bulk modulus B0, and its pressure derivative B0′, E (V ) = E 0 +

9V0B0 2/3 [(η − 1)3 B0 ′ 16

+ (η2/3 − 1)2 (6 − 4η2/3)]

where η = V0/V. Excellent regression R2, typically 1.0−5 × 10−5, was obtained for all the E(V) curves. Next, pressure P was calculated for each V using the analytical expression for the isothermal EOS with the values of V0, B0, and B0′ determined from the above E(V) dependence, P(V ) =

⎤ ⎡ 3B0 5/3 2/3 3 η (η − 1)⎢1 + (B0 ′ − 4)(η2/3 − 1)⎥ ⎦ ⎣ 2 4

4(CF)graphite fluoride → 3Cdiamond + CF4

Note the relation P = −(∂E/∂V) . Finally, the pressure dependence of the internal energy E(P) was rendered for each compound investigated, and the energy difference ΔE is given for reactions of these compounds, that is, polymerization of hexafluorobenzene to graphite fluoride and disproportionation of graphite fluoride to diamond or graphite and CF4. Results are presented as graphs E(P) and ΔE(P). The calculations revealed that graphite fluoride is more stable than perfluorobenzene at all pressures, as shown in Figure 3.

A volume increase would indicate that the chemical equilibrium will shift to the left with increasing pressure because high pressure favors systems with smaller volumes. We have chosen diamond as the decomposition product because diamond is the thermodynamically stable polymorph of carbon at high pressure. CF4 was chosen as the simplest and most stable molecular fluorocarbon. We have assumed a density of 2.9 g/cm3 for graphite fluoride based on its crystal structure,22 2.1 g/cm3 for CF4 and 3.54 g/cm3 for diamond. The density of CF4 is the crystallographic density of CF4 in the solid state, which is reasonable to assume at high-pressure conditions.29 With use of these densities, the stoichiometry of the reaction, as well as the molar masses of the respective compounds, the volume change in the decomposition reaction is calculated to be +24% (see Supporting Information for details). The result suggests that high pressure should shift the chemical equilibrium to the left side and eventually suppress the decomposition of graphite fluoride at sufficiently high pressure. To determine at which pressure the disproportionation reaction may be suppressed, we have calculated the dependence of its internal energy and enthalpy change in the entire pressure range of 0−100 GPa, employing the quantum mechanics method21 for the E(V) dependence combined with the Birch− Murnaghan conversion of E(V) to E(P) dependence. Figure 4 summarizes the results normalized to the conversion per carbon atom, 1/4(C4F4 → 3C (diamond) + CF4), where C4F4 represents the stoichiometry of graphite fluoride in the reaction.

Figure 3. Internal energy of hexafluorobenzene and graphite fluoride as a function of pressure showing a greater stability of the sp3 graphite fluoride than sp2 perfluorobenzene.

This finding implies that a polymerization of perfluorobenzene is enthalpically favorable already at ambient pressure. This situation is analogous to that of benzene (C6H6), which is energetically higher than that of graphane at all pressures.19 The driving force for polymerization is further increased with increasing pressure because of negative contributions PΔV to enthalpy changes due to volume contraction associated with perfluorobenzene conversion to graphite fluoride, calculated as ΔV from −21 Å3 for ambient pressure to −30 Å3 at P = 100 GPa. This behavior can be explained by the fact that the sp3-C becomes energetically more favorable compared to sp2-C with increasing pressure. The relative enthalpies of perfluorobenzene and graphite fluoride alone seem insufficient to evaluate the experimental feasibility of a thermodynamically controlled polymerization because thermal decomposition reactions are not considered.

Figure 4. Internal energy, PΔV, and enthalpy changes for the decomposition of graphite fluoride into diamond and CF4. 26088

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of the fluorocarbon and were +27%, + 28%, and +30% for perfluoroethane, -butane, and -cyclohexane, respectively. The results indicate that the decomposition into CF4 is the enthalpically most favorable among fluorocarbon molecules at all pressures. This means that a thermodynamically controlled high-pressure high-temperature synthesis of sp3-carbon fluorides from sp2-fluorocarbon molecules may indeed be feasible at experimentally achievable pressures unless entropic effects become very strong at high temperature. Of these entropic effects, increase of translational and rotational entropy with temperature, dominated by the motions of CF4, is to a large degree offset by its decrease with pressure due to confinement of the system in the compressed volume. Further, the vibrational entropy component for the entire disproportionation reaction is expected to be small due to compensation of similar vibrational modes in the reactant (CF)n and product diamond, with even smaller contributions from the relatively high-frequency modes of CF4. These considerations suggest that entropy effects may not shift the chemical equilibrium so that the break-even pressure would lie in a region of experimentally unachievable pressures. Diamond anvil cells can routinely achieve pressures of 200 GPa, and experiments up to 640 GPa have been reported.30 Because of the thermodynamic control of the reaction, the synthesis would not depend on a specific starting material. For example, instead of perfluorobenzene, also a reaction of diamond and fluorine or a reaction between diamond and CF4 would lead to the target structures according to the equation

The internal energy change ΔErxn is nearly constant up to a pressure of ca. 50 GPa, but then goes up increasingly steeply above this pressure. This behavior results from a superposition of smooth trends for each individual component, sharpest for diamond, and smallest for CF4 and graphite fluoride, in the order of calculated bulk moduli B0 (448.9 GPa for diamond, 105.1 GPa for CF4, and 104.7 GPa for graphite fluoride). The PΔV term increases nearly linearly up to a pressure of 40 GPa but its slope tapers off at higher pressure. The primary cause of this trend is a diminishing compressibility of CF4 at high pressures. At pressures above 100 GPa, the CF4 molecules collide and calculations would require reduction of the muffintin radii (RMT), leading to inconsistency with all other calculations done with constant RMT = 1.1. Because of this constraint by the product CF4, the modeling of the E(P) dependence for the disproportionation of graphite fluoride was terminated at pressures exceeding 100 GPa. This limitation does not affect our main finding of a lower critical pressure for this reaction. The reaction enthalpy change ΔH = ΔE + PΔV increases nearly linearly over the entire pressure range, confirming that pressure tends to shift the chemical equilibrium to the left. The result is in accordance with the previous qualitative estimates based on volume changes. A pressure of 26.5 GPa separates a region in which ΔH is negative at lower pressures and where ΔH is positive at higher pressures. This result suggests that above a pressure of 26.5 GPa the equilibrium lies on the left side and the decomposition is suppressed. Hence, a thermodynamically controlled crystallization of a fluorinated carbon network may actually be possible above this pressure. A pressure of 26.5 GPa is easily achievable in a diamond anvil cell and even in a conventional 8/ 3 multianvil cell with tungsten carbide anvils (albeit at high blowout risk) which has an approximate pressure limit of 27 GPa. One must consider, however, that the theoretical predictions could only translate to a real-world synthesis if entropic terms do not shift the equilibrium unfavorably and there are no other thermodynamically significantly more favorable decomposition reactions into other molecular fluorocarbons but CF4. In CF4 the number of carbon−fluorine bonds per carbon atom are maximized relative to all other molecular fluorocarbons which means that the internal energy should be lowest for the decomposition into CF4 relative to other fluorocarbon molecules. Hence, other decomposition reactions are unlikely to be more favorable with respect to internal energy considerations. In addition to internal energy also the PΔV term needs to be taken into account. If the volume increase becomes smaller, the slope of the PΔV term and also that of the ΔH term is expected to become less steep. If the slope is decreased to an extent which would lead to crossover of the ΔH curves below 26.5 GPa, then the threshold pressure for decomposition would be shifted to higher pressures. To estimate the slope of the ΔH term for other fluorocarbon molecules relative to CF4, we have calculated the percent volume increases for decomposition reactions into perfluoroethane, -butane, and -cyclohexane, respectively. The calculations were performed analogously to those previously described for CF4 using the molar masses and the stoichiometry of the respective decomposition reactions. In the absence of crystallographic data for perfluoroethane, -butane, and -cyclohexane, the same solid-state density as that for CF4 was assumed (see Supporting Information for exact calculations). In all cases the volume increases were somewhat larger compared to that of the CF4 system. They increased with the chain length

3Cdiamond + CF4 → 4sp3 −CF

Perfluorobenzene has only been chosen because it would be a convenient starting material in an experimental synthesis. The structural scope of the carbon networks could be even more expanded by variation of the C:F ratio, leading to more interconnected networks for a ratio C:F > 1 and less interconnected structures for a ratio C:F < 1:1.

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ASSOCIATED CONTENT

S Supporting Information *

Volume calculations for disproportionation reactions. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b09084. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The design of the research was supported by EFree, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award No. DE-SC0001057. The authors gratefully acknowledge allocation of computational resources at the Brookhaven National Laboratory - Center for Functional Nanomaterials under the U.S. Department of Energy Contract No. DE-SC0012704, ID 32849.

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