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9029 dx.doi.org/10.1021/ja201786y | J. Am. Chem. Soc. 2011, 133, 9023–9035 Journal of the American Chemical Society ARTICLE On packing these layers in three dimensions, one can obtain a number of polytypes. Figure 9 shows four of these; others may be found in our detailed study. 41 We
(except for graphane I) by using an evolutionary algorithm structure search (USPEX) at one pressure. The structures so obtained were then taken over a wide pressure range. Figure 10 shows the static lattice enthalpies of various CH systems, including benzene phase III, benzene phase V, the two polymeric structures mentioned earlier, and the graphane-type phases obtained by us using the evolutionary algorithm search. The corresponding most stable carbon (graphite below 10 GPa and cubic diamond above 10 GPa) and H 2 phases 50 are taken as references. The graphite-to-diamond phase transition around 10 GPa causes the apparent kink in the graphane relative enthalpy curves at that pressure; there is no discontinuity in their intrinsic enthalpy curves. For the CH system, the most stable phase we found in the range 0
À10 GPa is the all-chair graphane -AA- stacking or -AB- stacking, both dynamically stable (see SI). These phases are close in energy over a wide pressure range. Graphane III becomes the most stable phase in the range of 10 À200 GPa. The calculated phonon dispersion for both graphanes III and IV shows no imaginary frequencies at 200 and 300 GPa, indicating that both are dynamically stable. The reasons for the increasing stabiliza- tion of graphanes III and IV with pressure (relative to I and II) are discussed elsewhere; the di fferential can be traced to the balance of inter- and intrasheet H 3 3 3 H interactions. 41 Graphanes I and II should interconvert easily, for what is involved is merely the sliding of layers. But the interconversion between this pair and graphane III or IV should be di fficult— many CC bonds would have to break in the process. These are geometrical isomers, not conformers. So why do the benzene phases (III and V) not convert spontaneously to these four-connected polymers? Because there are likely signi ficant barriers to polymerization. Organic chem- istry as a whole is an exercise in kinetic persistence. The isomers of benzene itself (Figure 11) are but one example of this. So prismane, benzvalene, and Dewar benzene are respectively no less than 114, 81, and 80 kcal/mol less stable than benzene. However, they were made in the 1960s and 1970s; 51 À53
despite slow decomposition to benzene, they have a half-life long enough Figure 8. Four isomeric single-sheet graphanes. Side views are at left, top views at right. Figure 9. Graphane I (at 10 GPa), II (at 10 GPa), III (at 200 GPa), and IV (at 300 GPa) structures. Figure 10. Enthalpy of various CH systems as a function of pressure. The reference is the most stable phase of carbon and H 2 : graphite below 10 GPa and cubic diamond above 10 GPa; for H 2 , P6 3 /m (<100 GPa), C2/c (100 À250 GPa), and Cmca-12 (>300 GPa). Note that zero-point energies are not included in these calculations.
9030 dx.doi.org/10.1021/ja201786y | J. Am. Chem. Soc. 2011, 133, 9023–9035 Journal of the American Chemical Society ARTICLE to allow isolation. The reversions of these to benzene are forbidden reactions. 54 To summarize: at every pressure studied, saturated, four-coordi- nate CH phases, and graphanes in particular, are more stable than any phase retaining discrete benzene molecules. Furthermore, the transformation from benzene to saturated hydrocarbon may well be local or nucleated. The outcome would be an amorphous, approximately four-coordinated polymer. We will return to the first stages of nucleated polymerization later in this paper. It seems to us likely that such polymers, di fficult if not impossible to calculate, are in fact the experimentally observed polymeric products of the pressurization of benzene. DFT computations apply to the T = 0 K and static situation. To analyze the e ffect of temperature on benzene phase III, we performed an annealing simulation using the ab initio molecular dynamics (MD) method. 55 For the annealing process, the initial temperature of the system is increased to 300 K, and a final
temperature of 0 K is requested. The annealing analysis indicates that the chemical transformation (to a saturated polymer) occurs in phase III when the pressure is above 150 GPa at elevated temperature. If the temperature is higher still, the transformation may occur at a still lower pressure. Ciabini et al. 7 used MD simulations to study several amorphi- zation events in benzene from con figurations equilibrated (phase III) at 23 GPa and 540 K. All the reactive events are irreversibly initiated when the nearest-neighbor (nonbonded) C 3 3 3 C dis- tance approaches 2.5 À2.6 Å. In our case, the nearest-neighbor C 3 3 3 C distance in phase III at 190 GPa and 0 K is 2.4 Å, which is similar to the distance at 23 GPa and 540 K obtained by Ciabini et al. In fact, Ciabini et al. did not observe any reaction in a pressure range up to 150 GPa —only an increase of the atomic kinetic energy (up to 1500 K at 23 GPa) was able to induce the amorphization in a few hundred femtoseconds. This indicates, as suspected, that temperature is also an important factor in the phase transitions of benzene. Note that there is a di fference in the structures obtained by Ciabini et al. and us: our polymer II is an ordered crystal structure and not amorphous. The length of the simulation and the tempera- ture may be responsible for the di fference.
Does this mean that we should desist and not study the e ffect
of pressure on benzene? Not at all. As our calculations also show, the various benzene phases are local minima, dynamically stable over a wide pressure range. They will face substantial barriers to transforming into graphanes. Phase III in particular is a benzene structure that in our calculations is persistent to ∼200 GPa at 0 K. Thus, it makes sense to inquire into the properties of the most persistent benzene phases, such as phase III, focusing on their eventual metallization. Approaches to Metalization while Maintaining a Benzene Structure. As we saw earlier in our calculations, benzene remains in phase III until ∼200 GPa at T = 0 K, despite saturated phases being more stable. At ∼200 GPa it transforms spontaneously to a polymeric saturated CH phase. As phase III is compressed, the band gap becomes smaller, and at ∼180 GPa it vanishes, within the tolerances of the GGA computational approach we use. This region, 180 À200 GPa, in which one has a metallic benzene phase that has a barrier to rearrangement to a saturated polymer, is of substantial interest to us. We next describe in some detail the approach to metallization. Figure 12 shows the computed relative compressions of benzene phase III as a function of pressure. The Wigner ÀSeitz
radius r s is de fined by 4πr s 3 /3 = 1/ F, where F is the average valence-electron density. Since F = N/V, where N is the number of valence electrons in the unit cell and V is the volume of the unit cell,
F scales as V À1/3
. The volume reduction for all the benzene phases, not only phase III, is rapid between 0 and 10 GPa and is attributable to the squeezing out of the van der Waals space between benzene units. Such behavior has been observed in many molecular crystals under pressure. 56,57
The remarkably useful Goldhammer ÀHerzfeld criterion for metallization 58 holds that an insulator or semiconductor is likely to become a metal when the conditions on the density are such that the bulk polarizability diverges; that is, electrons can be stripped o ff the atoms or molecules with a diverging local field associated with an in finitesimal perturbation. To be specific, the Goldhammer ÀHerzfeld criterion says that a material becomes metallic when the quantity (1 À fRV
m ) À1 diverges, where R is
the molecular polarizability, V m the volume per molecule in the solid, and f a dimensionless factor determined only by the packing of the molecules in the crystal. The divergence occurs when f R/V
m = 1. For cubic systems f = 4 π/3, and this gives V m = 4 πR/3. Using the definition of r s , 4
πr s 3 /3 = V m /N ve (where N
ve is the number of electrons), we then have the following condition for cubic systems, namely r s = ( R/N ve ) 1/3 . The average polariz- ability of benzene, R, is 67.55 bohr; 3 N
= 30 in one benzene molecule. One then gets r s = 1.31 for the metallization of benzene. The real benzene structure (phase III is under discussion) is, of course, not cubic. Still the arguments made above carry over well —as Figure 13 shows, the band gap goes to zero at P ≈ 180 GPa, where r s
Figure 11. Three known isomers of benzene. Figure 12. Computed relative compression as a function of pressure in benzene phase III. The relative compression is de fined by [r s (0)/r
s (p)]
3 , where r s (0) and r s (p) are the Wigner ÀSeitz radius at ambient pressure and calculated high pressure, respectively. Yüklə 4,89 Mb. Dostları ilə paylaş:
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