6208
J. Phys. Chem. B 2007, 111, 6208-6213
Computational Investigation on the Desensitizing Mechanism of Graphite in Explosives versus Mechanical Stimuli: Compression and Glide Chaoyang Zhang Laboratory of Material Chemistry, Institute of Chemical Materials, China Academy of Engineering Physics (CAEP), P. O. Box 919-327, Mianyang, Sichuan 621900, People’s Republic of China ReceiVed: February 2, 2007; In Final Form: April 3, 2007
A desensitizing mechanism of graphite in explosives versus mechanical stimuli was investigated using computational methods including density function theory and molecular dynamics. Dependences of energy change versus compression ratio and internal stress versus compression at absolute zero degree showed that the most possible compression was along the c-axis of graphite crystal. The result of molecular dynamics at room temperature indicated that the slide can readily occur between neighbor layers, but the distance between them can hardly change. The calculated potential energy of the slide of graphite within 0-0.19 kJ/cm3 is much larger than the potential energy of compression of common explosives to the extent of no detonation, for example, HMX, 0-0.046 kJ/cm3. It implied that the kinetic energy induced by mechanical stimuli can easily and partly convert into the potential energy of the slide and prevent explosives from forming hot spots. This should be the root reason for graphite used as a desensitizer in explosives.
1. Introduction Graphite has extensive applications in many fields because of its special structure and excellent characteristics. Among these applications in explosives, the most important, it has been found that graphite is used as desensitizer, which can efficiently decrease the sensitivities of explosives and enhance their stabilities. For example, comparing pure cyclotetramethylene tetranitramine (HMX) with many HMX-based plastic explosives (PBX) containing graphite, we find that the percentages of explosions distinctly decrease from 100% to 16, 8, and 4, and even zero under a certain experimental condition of the impact test.1 That is to say, graphite has good ability to stabilize explosives versus external mechanical stimuli. It is therefore very practical, interesting, and meaningful to investigate the desensitizing mechanism of graphite in explosives. At least, it may be useful to find new desensitizers or to understand the sensitivity mechanism of explosives versus external mechanical stimuli such as impact or shock. However, it is well-known that the sensitivity mechanism involves many factors, including molecular structures, crystal structures, chemical and physical properties, and surface and interface properties of explosive components, and many related details still remain unclear. Hot spot is a basic and widely accepted concept in mechanical sensitivity theory and is a small region in an explosive crystal where thermal energy resulting from external stimuli such as an impact or shock is localized. According to the theory of hot spot, after hot spot formation, sufficient molecular vibration can lead to bond-breaking, the beginning of decomposition. Certainly, exothermic chemical reaction of explosive decomposition should produce enough thermal energy to sustain and expand decomposition. That is to say, the hot spot must be large and hot enough and be sufficiently long-lived to ensure a well-underway reaction or else it will be quenched by dissipation of heat through thermal diffusion.2-4 The process of external mechanical forces, such as impact and shock wave, can be logically described as the storage and
Figure 1. Model for external forces (impact or shock) acting on graphite crystal. Any external force F can be analyzed into three forces Fa and Fb, parallel to the (001) face of graphite and possibly resulting in the slide of the layer, and Fc, perpendicular to the (001) face of graphite and possibly resulting in compression. The spheres denote carbon atoms.
conversion of mechanical energy, the formation and propagation of a hot spot, rapid chemical reaction, and the last detonation. In past decades, people tried to clarify the mechanism of hot spot using molecular simulation on three levels. The first is to explore the relationship between molecular stability and explosive sensitivity on the smallest molecular level using quantum chemistry methods. And the geometrical and electronic structures of explosive molecules are usually the most interested in these cases.5-8 The second is to simulate the processes of external mechanical forces acting on explosive crystals. These simulations on the bigger crystal level using molecular dynamics are closer to practice. For example, Bowden and Yoffe concluded the dimensions, temperatures, and durations of hot spots, 0.1-10 um, above 700 K, and 10-5 to 10-3 s, respectively.9 Many simulations, especially molecular dynamics, also including ab initio molecular dynamics, have focused upon explosive crystals and crystal defects resulting in strain in the crystals including lattice
10.1021/jp070918d CCC: $37.00 © 2007 American Chemical Society Published on Web 05/12/2007
Desensitizing Mechanism of Graphite in Explosives
J. Phys. Chem. B, Vol. 111, No. 22, 2007 6209
Figure 2. Model of graphite. A is the unit cell. B is the plane perpendicular to its (001) face. Blue and red atoms are located on the top and bottom layers, respectively. And R is the reference atom whose fractional ordinates are (0.667, 0.333, 0.750). C is the section of the (001) face. Only 35 girding points, i.e., the possible location of the R atom after sliding, in the red region, should be considered for calculating the slide energy because of graphite’s space group, P63/mmc.
vacancies, interstitial occupancy, molecular rotations, edge and screw dislocations, twinning, possible imperfections, and so forth. Respectable simulations have indicated the relief of this strain produced by external stimuli can lead to the disproportionate localization of energy in the neighborhood of the defect, creating a hot spot and leading to vibrational excitation and further chemical reaction.10-15 The third is on the meso-scale with many difficulties. All above-mentioned investigations have taken positive roles in understanding and explaining the initiation mechanism of detonation, including the sensitivity mechanism. Surely, hot spot is a core factor influencing this mechanism. Different from the above-mentioned research, graphite, used as an additive, i.e., a desensitizer, rather than major energetic components, was considered in this paper. That is, theoretical methods were employed to study the compression and slide of graphite, which should be helpful in understanding its desensitizing mechanism. Figure 3. Dependence of internal stress (p) versus the compression ratio (η) of graphite.
2. Models and Computational Details 2.1. Compression of Graphite. Any external mechanical force acting on an object can lead to a shape change, which produces strain and stores mechanical energy. Any impact or shock acting on graphite crystal can be regarded as an external force F in Figure 1, which can result in crystal compression and/or slide. To investigate the stress-strain relationship of graphite crystal, we calculated the stress relative to different compression ratios along with lattice orientations a, b, and c, corresponding to three presses Fa, Fb, and Fc in Figure 1. The investigation object in this paper can be seen as a closed system for there is no substantial exchange and no other energy but volume work exchange. So there is a thermodynamic equation
dU ) TdS - pdV
(1)
Under the condition of absolute zero or very low temperature, eq 1 can be converted into
p)-
dU dV
(2)
Compression ratio is defined as
η)
∆V VT
(3)
where ∆V and VT are the volume change and the initial volume of the graphite crystal. At the same time, the internal energy change ∆U can be seen as the total energy change ∆E. Therefore, the internal stress p can be obtained from eq 4, where ∆Ecomp is the total energy difference of the graphite crystal after and before compression, Ecomp and E0.
p)
1 ∆E VT η
∆Ecomp ) Ecomp - E0 p)
1 Ecomp - E0 VT η
(4) (5) (6)
So, using eq 6, we calculated the internal stress induced by compressing the crystal along three lattice orientations at the absolute zero degree. The initial crystal structure of graphite was cited from the structural base in Material Studio (lattice parameters are a ) b ) 2.46 Å, c ) 6.8 Å, R ) β ) 90°, and γ ) 120°; the layer distance is 3.40 Å; the space group is P63/ mmc; and the crystal density is 2.25 g/cm3).16 The graphite crystal was compressed in an equal proportion along the orientations of crystal axes. Namely, by compressing any crystal
6210 J. Phys. Chem. B, Vol. 111, No. 22, 2007
Zhang
Figure 4. (A) The 2 × 2 × 2 supercell of graphite. M, N atoms on the OC axis are regarded as reference atoms for investigating the movement of correlative layers. The distance between M, N atoms and their Z coordinate difference denoted as rM-N and zM-zN, can respectively reflect the relative distance of the glide and between neighboring layers. (B) Derivation of potential energy versus frame, equal to the dynamic time. (C) Derivations of rM-N and zM-zN versus the frame.
axis 10% with a change step of 1% and keeping the crystal angles and other two axes invariable, we could obtain the dependence of the compression ratio versus its induced stress. The density functional theory (DFT) implementing the generalized gradient approximation method (GGA), the Beck-LYP hybrid functional, and the double-numeric quality basis with polarization functions (DNP) in Acceryls’ code Dmol3, comparable in size but more accurate than the commonly used 6-31G** Gaussian orbital basis set, were employed to complete all calculations.17,18 At the same time, the mathematical dependences of p vs η and ∆Ecomp vs η were obtained using the least-squares fit. 2.2. Slide between Neighbor Layers of Graphite. We used the molecular dynamics (MD) method to investigate the gliding behavior of graphite at room temperature. The first ab initio-based force fields, which have been parametrized using extensive data for molecules in the condensed phase, COMPASS,19 canonical ensemble NVT, Nose thermostat, and atom-based summation method, were adopted to simulate.16 The simulation system is the 2 × 2 × 2 supercell expanded from the unit cell of graphite. The time step and dynamic time were set to 1 fs and 100 ps, respectively. And the frame output yielded every 2500 step. That is, there was a total of 40 frames, and every frame included 2.5 ps. (See the details in section 3.2.) Also, in view of the layer-shaped crystal structure of graphite, the most-readily occurring glide parallel to the (001) face can result in the conversion of kinetic energy into the potential energy of the glide when an external force acts on the graphite crystal. The potential energy of the slide, denoted as eq 7, is the energy change after sliding. We only discuss the slide between neighbor layers in the unit crystal, that is, as denoted in Figure 2, the bottom atoms shown in red are fixed, whereas the top atoms shown in blue are transferred parallel to the (001) face. The R atom is taken as the reference atom for investigating the relationship between the potential energy of the slide and the relative location of neighboring layers, which is described by the X and Y fractional coordinates of the R atom.
∆ESE ) ESE - E0
(7)
3. Results and Discussion 3.1. Compression of Graphite.
p(Pa) ) 1.494 × 1011η
(8)
p(Pa) ) 1.365 × 1012η
(9)
∆Ecomp m (J/mol) ) 3.21 × 108η2
(10)
∆Ecomp m (J/mol) ) 2.93 × 109η2
(11)
We can find from Figure 3 that there are approximately linear relationships, described as eqs 8 and 9, between internal stress and compression ratios along c, a, and b axes. Because the mole volume of the unit crystal of graphite is Vm ) 2.145 × 10-5 m3/mol, we can also obtain the relationship between the potential energy of compression and the compression ratio, such as eqs 10 and 11 along c, a, and b axes, respectively. From eqs 8 to 11, it can be found that the coefficient of the a- or b-axis is approximately 8 times larger than that of the c-axis. This reflects the layer-shaped structure of the graphite crystal: there are smaller interactions, van de waals forces, leading to a bigger volume decrease between neighboring layers, whereas much stronger interactions, covalent bonds, leading to less volume decrease within the layers when it is against the same external force. Namely, these smaller interactions between neighboring layers result in much easier compression perpendicular to the (001) face than that parallel to the (001) face. 3.2. Slide between Neighbor Layers. Dynamic results show that graphite is a soft matter, which accords with the known experiment. Figure 4B indicates that the interested system can easily arrive at an equilibrium state for it almost needs no relaxation. The sharp change of rM-N and the smooth change of zM-zN in Figure 4C demonstrate the sliding behavior of neighboring layers of graphite: no matter where the layer can slide, there is the same perpendicular distance between neighboring layers. It means the slide occurs without volume change and compression. Therefore, the soft characteristics of graphite should be attributed to its ability to readily slide and ease in storing energy (potential energy increase but no volume change).
Desensitizing Mechanism of Graphite in Explosives
J. Phys. Chem. B, Vol. 111, No. 22, 2007 6211
Figure 5. Potential energy of the slide of graphite (units in kilojoules per mole). A and B are the slide energy and its distribution, respectively. a, b fractional coordinates in A are of the reference atom R in B. Only data in the range demarcated by blue dashes are primitively calculated, and other data are added according to the symmetry of the graphite crystal. Diagonals denote the symmetry of the graphite crystal. The number of total energy points in B is not 121 but 100 because of the periodic boundary condition, i.e., 4 × 1/4 + 36 × 1/2 + 81 × 1 ) 100. Different colors show energy points belonging to different energy ranges.
Figure 6. Slide of the top layer demonstrated by sliding reference carbon atom R from initial position A to four face angles B-E, respectively. The slide top atoms in blue are just overlapped with the bottom atoms in red perpendicular to the (001) face.
Of course, this dynamic result of an easy slide is the basis of the following static calculation of the slide energy. The slide energy of graphite demonstrated in Figure 5 was calculated using eq 7. Some interesting results can be found from the figure. At first, the slide energy of graphite is within 0-4.1kJ/mol, much less than the activation energy of the decomposition of common explosives, about 160-250 kJ/mol.20 That is to say, it is very easy to overcome the potential obstacle for graphite sliding without explosive decomposition. This should be the main reason why graphite feels slippery and is used as a lubricant. At the same time, according to the distribution of the slide energy shown in Figure 5B, 81% of the points are less than 3.0 kJ/mol and 39% of the points are less than 2.0 kJ/mol. It means the most slides are in the easier cases. Second, the four biggest sliding energy points are just on the four angles in Figure 5A. On these slide positions, the top and bottom carbon atoms are just overlapped perpendicular to the (001) face, i.e., along the c-axis (Figure 6). Namely, the repulsion between two neighboring layers is the most if the distance between the two carbon atoms respectively on the neighboring layers is the shortest. At last, by converting Figure 5 into Figure 7, we can make clear the orientation of graphite slide. Obviously, as mentioned above, the most possible slide path should be the path to avoid two layer atoms overlapping perpendicular to the (001) face. That is, the orientations of the easiest slides indicated in blue
in Figure 7 are along the lines through the halves of the OA and/or the OB axis. Overall, above-mentioned results show that graphite can be readily slid. 3.3. Desensitizing Mechanism of Graphite Crystal. A good review on computational treatments of detonation initiation and sensitivity in energetic compounds has been presented by Politzer and Alper.21 A model has been developed that describes the initial steps of shock-induced chemistry in terms of multiphonon up-pumping. A shock wave produces a bath of highly excited phonons, which flow into the lowest vibrational modes (doorway modes) of the molecules that make up a crystal. Continued flow of energy from the hot phonon bath into the doorway modes leads to higher and higher levels of vibrational excitation. The internal vibrational molecular modes equilibrate very rapidly, and internal temperature of the molecule rises. If the initial phonon temperature is sufficiently high, multiphonon vibrational up-pumping will heat the molecules to temperatures at which chemical bonds break, and the explosive may be ignited.3,21-23 So, the following so-called desensitizing mechanism of graphite should be discussed as its properties of preventing the formation of a hot spot when mechanical forces act on explosives containing it. First, graphite itself is a kind of matter possessing high chemical and physical stability and cannot afford any energy to form hot spots when there are some external stimuli. Second, graphite has less heat conduction coefficient, 0.093 J‚m-1‚S-1‚K-1, than common explosives TATB, HMX, RDX, and TNT, 0.544, 0.345, 0.106, and 0.213 J‚m-1‚S-1‚K-1.1 It means the heat can easily conduct from explosive to graphite by their contact once heat concentrates on the explosive. This heat loss from the explosive can decrease the temperature of the interaction point between external stimuli (such as impact or shock wave) and explosive and prevent the formation and propagation of a hot spot. Namely, graphite plays a role in desensitizing the explosive. Third, graphite can more readily convert kinetic energy into potential energy than common explosives when external mechanical stimuli are acting on them. For graphite, the most potential energy is stored by easily sliding, whereas, for most
6212 J. Phys. Chem. B, Vol. 111, No. 22, 2007
Zhang
Figure 7. Potential energy (SE, kJ/mol) graphs of the graphite slide. A-C are the 3D color map surface of one cell, the color filled contour of the 2 × 2 supercell, and the legend map, respectively.
Figure 8. Graph of external force F acting on graphite, which can result in easy slide parallel to the (001) face (analyzed forces fa and fb) and difficult compression along the orientation of c-axis (analyzed force fc).
explosives, the most potential energy is stored by compression due to their difficultly sliding. According to the data in Figure 5, and the crystal density of graphite, 2.24 g/cm3, we can deduce that the potential energy of the graphite slide is within 0-0.19 kJ/cm3. For an explosive such as HMX, the compression potential energy can be up to 0.046 kJ/cm3, equal to 41.2 GPa stress,24 more than its detonation pressure, 39 GPa (barrel test, F ) 1.894 g/cm3) when it compressed 1% along its c crystal axis. It shows that HMX is too hard to store potential energy, or else the potential energy can readily lead to chemical bond rupture. But, for graphite, it can store potential while keeping its volume invariable. That is, the kinetic energy acting on explosive can partly and easily convert into graphite’s sliding potential energy, which is disadvantageous in forming hot spots. Therefore, as mentioned in the Introduction, only 1% graphite dispersed in a HMX-based PBX has the obvious function of a good desensitizer.
Finally, graphite has multiorientations of slide (Figure 7), which can lessen the restriction of its slide and prevent the formation of hot spots. By the way, its not only “soft” (slide) but also “hard” (high and invariable density) performance makes it very different from explosives and other desensitizing agents. 4. Conclusion Graphite’s behavior of compression and slide induced by external mechanical stimuli can be summarized as Figure 8: the most possible slide is parallel to the (001) face and the most possible compression is along the c-axis. This slide leads to a “soft” characteristic of graphite. That is, this slide can easily convert kinetic energy induced by mechanical stimuli into sliding potential energy and prevent the formation of hot spots, and it is the root reason for its use as a desensitizer in explosives. Certainly, this understanding of the desensitizing mechanism
Desensitizing Mechanism of Graphite in Explosives of graphite may be useful in making clear the related mechanism of other desensitizers, such as fluoric graphite, TATB, which still have layer-shaped and graphite-like crystal structure. Acknowledgment. I greatly appreciate the financial support from CAEP’s funds (Grant Nos. 42604020403 and 626010910). References and Notes (1) Dong, H. S.; Zhou, F. F. High Energetic ExplosiVes and RelatiVes; Science Press: Beijing, 1994. (b) Dong, H. S. Chin. J. Energy Mater. (in Chinese) 2004, 12 (S), 1. (2) Dremin, A. N. Philos. Trans. R. Soc. London, Ser. A 1992, 339, 335. (3) Tokmakoff, A.; Fayer, M. D.; Dlott, D. D. J. Phys. Chem. 1993, 97, 1901. (4) Hong, X.; Chen, S.; Dlott, D. D. J. Phys. Chem. 1995, 99, 9102. (5) Zhang, C.; Shu, Y.; Huang, Y.; Zhao, X.; Dong, H. J. Phys. Chem. B 2005, 109, 8978. (6) Rice, B. M.; Samir, S.; Owens, F. J. J. Mol. Struct. (THEOCHEM) 2002, 583, 69. (7) Politzer, P., Murray, J. S., Eds. Energetic Materials, Part 2; Elsevier B. V.: Amsterdam, 2003; pp 25-52. (8) Heming, X. Molecular Orbital Theory of Nitro-compound (in Chinese); Publishing House of the Defense Industry: Peking, 1994.
J. Phys. Chem. B, Vol. 111, No. 22, 2007 6213 (9) Bowden, F. P.; Yoffe, A. D. Fast Reactions in Solids; Butterworth: London, 1958. (10) Tsai, D. H.; Armstong, R. W. J. Phys. Chem. 1994, 98, 10997. (11) Mintmir, J. W.; Robertson, D. H.; White, C. T. Phys. ReV. B 1994, 49, 14859. (12) Hauser, H. M.; Field, J. E.; Mohan, B. K. Chem. Phys. Lett. 1983, 99, 66. (13) Armstrong, R. W.; Ammon, H. L.; Elban, W. L.; Tsai, D. H. Thermochim. Acta 2002, 384, 303. (14) Holmes, W.; Francis, R. S.; Fayer, M. D. J. Chem. Phys. 1999, 110, 3576. (15) Manaa, M. R.; Reed, E. J. J. Chem. Phys. 2004, 120, 10146. (16) Material Studio3.0; Accelrys Inc.: San Diego, CA, 2003. (17) Delley, B. J. Chem. Phys. 1990, 92, 508. (18) Delley, B. J. Chem. Phys. 2000, 113, 7756. (19) Sun, H. J. Phys. Chem. B 1998, 102, 7338. (20) Feng, C. G. Theory of Thermal Explosion (in Chinese); Science Press: Beijing, 1988; p 7. (21) Politzer, P.; Alper, H. E. In Computational Chemistry, ReViews of Current Trends; Leszczynski, J., Ed.; World Scientific: Singapore, 1999; Vol. 4, Chapter 6, pp 271-286. (22) Hong, X.; Chen, S.; Dlott, D. D. J. Phys. Chem. 1995, 99, 9102. (23) Chen, S.; Hong, X.; Hill, J. R.; Dlott, D. D. J. Phys. Chem. 1995, 99, 4525. (24) Unpublished data.
