Computer Graphics & Geometry

 

COMPUTER MODELING OF THE POLYMER NITROGEN – NEW TYPE OF “GREEN” FUEL.

 

N.Degtyarenko, V. Elesin, N. Matveev, K. Pazhitnyh

NNDegtyarenko@MEPHI.RU

Moscow Engineering Physics Institute (State University), Russia

 

Contents

1. INTRODUCTION
2. NITROGEN CLUSTERS OF AND THEIR ENSEMBLES
3. MODELLING OF PHASE CHANGE OF THE MOLECULAR PHASE IN A METASTABLE PHASE
4. OPTIMIZATION OF PROCESS OF FORMATION OF CLUSTER N4
5. REFERENCES

 

Abstract

The main result of our theoretical investigations [1] started in 1997 is the prediction of a possibility of the existence of ensembles composed of N8 clusters (so-called “boats”), i.e., a condensed phase formed from the N8 clusters as from “bricks”.

We have shown that this new nanomatter can accumulate the energy 3-4 times greater than the best “chemical” energy materials; it can be stable under normal pressure and heating up to 800 K. We have also found that the energy release from nitrogen clusters upon their fission into N2 molecules occurs completely and in a very short time. We have shown that the process of the energy release from non-molecular nitrogen is fundamentally different from the process of the energy release from “chemical” energy carriers where it takes place upon synthesis of fuel and oxidant.

The quantum calculations of the nitrogen clusters and their ensembles for various configurations are presenteded. The most stable ensemble configurations of the clusters N8 (boat) are found. The pieces of Gosh phase, tree-dimensional ensembles of the clusters N8 (“boats”), and also their periodical three-dimensional structures are found too. Every possible isomers of cluster N4 with various multiplicities and the space symmetries for the purpose of optimisation of process of their synthesis are explored. Equilibrium geometries and energies for all explored isomers within the limits of the MCSCF method have been found. For the most perspective configurations the disintegration mechanisms have also been explored.

1. INTRODUCTION

1. There are several reasons that we choose to study the nitrogen structures as a promising element for the synthesis of high energy density materials (HEDM). First, it is well known that nitrogen does not form the condensed matter in normal conditions but exists in the form of diatomic molecules N2. In a N2 molecule, the nitrogen atoms are bound to each other by a very strong triple covalent bond N≡N. This bond is one of the strongest in Nature, its energy equals to 4.95 eV/atom (Figure 1). In cluster and polymeric nitrogen structures, the interatomic bonds are either double or single, and hence their energies are lower than that of the triple bond. The energy of the double bond N=N equals to 2.17 eV/atom, while the single bond N-N is even more weaker, its energy equals to 0.87 eV/atom. So, for nitrogen, the sum of the energies of three single bonds is much less than the energy of a triple bond. This fact gives an opportunity to accumulate energy in a matter that contains nitrogen atoms coupled to each other by double or single bonds.

Figure 1. N₂ bonds order, energy and length

Such a relation between the bond energies is not a characteristic one for other elements. So, for carbon, the energy of three single bonds is somewhat greater than the energy of one triple bond (we recall that three single bonds per atom are characteristic for graphite layers). Second, such probable nitrogen structures should release the energy upon their fission into stable nitrogen molecules. The transition from metastable phases in the ground state is accompanied by decreasing of the system energy and realizing the accumulated one preferentially in the form of the thermal energy of finished products which are the nitrogen molecules. Disintegration at such transition is characteristic for the elements which are not forming a condensed phase in the ground state under normal conditions [1].

2. Theoretical investigations aimed at the study and synthesis of polymeric non-molecular nitrogen are carried out in USA , France , Germany , and other countries. In 1985, McMahan et al. [3] had predicted the transition of the molecular _-phase of nitrogen into the monoatomic simple cubic structure at a pressure of the order of 100 GPa.

3. For more than twenty years, experimental efforts aimed at the synthesis of non-molecular nitrogen were unsuccessful. In recent 3 years, the first successful experimental results were obtained at extremely high pressure of 100-200 GPa. The parent material to be compressed was pure molecular nitrogen. The basic idea of those experiments was that the molecules N2 get closer to each other upon strong compression, resulting in formation of non-molecular structures.

In the pioneering paper published in 2001 [7], the experimental results on transformation of molecular nitrogen into some non-molecular phase were presented. That phase was shown to be semiconducting and had a huge transformation hysteresis on pressure. No marked features in Raman and IR spectra were detected. The new phase was suggested to be amorphous and consist of both nitrogen molecules and clusters.

In 2004, the results on the synthesis of a polymeric phase of nitrogen with single bonds were presented [8-9]. That phase has a cubic gauche structure predicted earlier by McMahan and identified experimentally by means of X-ray diffraction and Raman spectroscopy [see also 10]. It is important that the synthesized non-molecular phases were broken down upon partial decompression. This was accompanied by the energy release.

4. In recent years, a great number of theoretical works were concerned with the search for the structures of separate clusters, ranging from N4 to N60 (Figure 2). However, we are not aware of works aimed at the study of ensembles of such clusters. Extraordinary capability of those clusters to release the energy much higher than the energy released from the most powerful (at present and in the forecast future) high-energy materials stimulated the fancy of engineers and technologists specialized in the field of propellants. Studies on a possibility of existence of other perspective poly-nitrogen compounds are carried out in numerous scientific centers [11].

                     

Figure 2. Different nitrogen clusters

2. NITROGEN CLUSTERS OF AND THEIR ENSEMBLES.

We don’t know other experimental or theoretical researches of other authers concerning of ensemble formation of nitrogen clusters.

In present work within the limits of the first principles and by various methods (semi empirical PM3, method HF taking into account MP2, densities functional DF taking into account corrections B3LYP and using of ECP approach) the configurations and properties more than hundred aspects of the nitrogen clusters and their ensembles are explored. All systems were calculated by the above mentioned methods for the detailed analysis. The importance of the account of correlation corrections at calculation of energy performances of the nitrogen clusters has been shown, and also the necessity of using MCSCF for calculation of magnitudes of the energy barriers.

Different ensembles from clusters N₈ are shown on Figures 3-5.

Figure 3. W-ensemble configuration from clusters N8 (“boat”)

Figure 4. L-ensemble configuration from clusters N8 (“boat”)

Click here for animation

Figure 5. ensemble from clusters N8 (“boat”) N₁₉₆

The calculations of structures, energy parameters and spectrums of quasi one-dimensional, layer and tree-dimensional ensembles of clusters N8 "boat" are presented. The results of our modeling by means of computer (computer modeling) are the following:

1. Clusters N8 (“boat”) are able to form metastable ensembles without loss of their individuality;

2. Formation of covalent bonds between clusters in ensemble does not result in decrease of the energy reserved in an isolated cluster which is 1.0 - 1.7 eV/atom, that considerably exceeds the energy evolved at combustion of "chemical" fuel;

3. The energy reserved in tree-dimensional ensembles of boats N8, makes Eacc ≈ 1.5 eV/atom, that is ≈ 0.5 eV/atom more than the energy reserved in isolated boat N8. In three-dimensional structure of boats a little more energy, than in gosh-structure is reserved.

4. The feature of these configurations is that the surface of ensembles of "boats" does not contain radical atoms of nitrogen, i.e. their surface is stable.

5. At fission of ensembles of boats into molecules N2 the energy reserved in them release practically completely. On Figures 6-8 are shown processes of fusion of different ensembles.

The properties of a polymeric nonmolecular phase of the nitrogen having periodic gosh-structure [3] and its pieces are calculated also:

6. The effects for the pieces of gosh-structure with free surface are received for the first time. It is shown, that there are radical atoms of nitrogen with unpaired electrons appear inevitably on this surface, which result under certain requirements, in development of instability of gosh-structure and its disintegration.

7. Requirements of possible stabilization of the pieces of polymeric nitrogen of gosh-structure are obtained. The structure of this surface layer reorganization is found. Peices of a gosh-phase with the rearranged surface are stable to under normal conditions (zero pressure), i.e. have a vibration spectrum free of imaginary frequencies.

Click here for animation

Figure 6. L-ensemble configuration fusion

Click here for animation

Figure 7. W-ensemble configuration fusion

Click here for animation

Figure 8. ensemble N₁₉₆ fusion

3. MODELLING OF PHASE CHANGE OF THE MOLECULAR PHASE IN A METASTABLE PHASE

As a result of modelling (within the limits of the density functional method) the squeezing process it is shown:

• The molecular solid phase of nitrogen (molecules N2 on the sitse of initial ε-phases) transfers in a polymeric nonmolecular phase at the pressure of order 140-150GPa (phase transition). The resulting structure has preferentially bonds of the first order. Some number of pairs of atoms have bonds of the second order.
• If the initial phase consists of clusters boat N8, than the phase transition in a polymeric nonmolecular phase (with the structure close to a gosh-phase) occurs at smaller pressure of order 70GPa. Probably the finished product corresponds to a principle of the total energy minimization which lies in the base of calculations. The received structure has bonds of the first order only.

4. OPTIMIZATION OF PROCESS OF FORMATION OF CLUSTER N4

Theoretical investigations of the nitrogen clusters are conducted for a long time, the most part of the publications are devoted to separate configurations of a studied cluster. The isomer is explored in the area of its local minimum, and only in some publications its disintegration [12-13] is explored. Detailed theoretical investigation of cluster N4 which has been detected recently by experimentally by mass spectrometer methods [14] is carried out.

Necessity of exceeding the bounds of the Hartri-Foka method that provides sufficient reliability of effects of calculations is shown. The multiconfiguration method (MCSCF) which in some cases was improved by use of perturbation theory of the second order (MCQDPT2) has been used. These methods possess rather high accuracy, but need strong requirements to computing expenses (especially MCQDPT2). The received results allow to formulate the basic requirements to synthesis of nitrogen clusters:

The potential barrier for the cluster formation in case of excited molecules be found approximately 30 times less, than at squeezing of nonexcited nitrogen molecules, i.e. synthesis is preferable for making with the assistance of excited molecules of nitrogen N*2.

The most perspective is using of an intermixture of molecules N2 (3 Σ-u) and N2 (3Πg) in the ratio 50:50.

The whole set of the results of modeling allows to suppose that synthesis of HEDM on the basis of nitrogen can be optimized.

It should be mentioned that described above theoretical results were obtained with help of computer modeling of studied objects, included means of computer visualization. Such visualization of computer modeling results was represented on Figures 2-8.

5. REFERENCES

1.      V.F.Elesin, N.N.Degtyarenko, L.A.Openov,”Ensembles of metastable clusters consisting of elements that do not form the condensed matter in normal conditions”. Engineering Physics №3 (2002) 2, in Russian. (review).

2.      N.N.Degtyarenko, V.F.Elesin, L.A.Openov, A.I.Podlivaev, «Metastable quasi-one-dimensional ensembles of nitrogen clusters N8». Phys. Low-Dim. Struct., Vol. 1/2 (2002) 135.

3.      C.Mailhiot, L.H.Yang, A.K.McMahan, Phys. Rev. B 46 (1992) 14419.

4.      W.J.Lauderdale, J.F.Stanton, R.J.Bartlett, J. Phys. Chem. 96 (1992) 1173

5.      M.L.Leininger, C.D.Sherrill, H.F.Schaefer, J. Phys. Chem. 99 (1995) 2324.

6.      C.Chen, K.-C.Sun. Int. J. Quant. Chem.: Quant. Chem. Symp. No 30 (1996) 497.

7.      M.I.Eremets, R.J.Hemley, H.K.Mao, E.Gregoryanz, Nature 411 (2001) 170.

8.      M.I.Eremets et al., Nature Materials 3 (2004) 558.

9.      M.I.Eremets et al., J. Chem. Phys. 120 (2004) 10618.

10.  M. Popov, Phys. Letters A 334 (2005) 317.

11.  M.B.Talavar, R.Sivabalan, S.N.Astana, X. Singh, «New super-power energy materials», Physics of burning and explosion, т.41, (2005), № 3, 29-45.

12.  B.M. Gimarc, M.Zhao Strain Energies in Homoatomic Nitrogen Clusters N4, N6, and N8 // Inorg. Chem., т. 35, с. 3289 (1996)

13.  M. Bittererova et. al. Ab initio study of the ground state and the first excised state of the rectangular (D2H) N4 molecule . // Elsevier Chem. Phys. Let., т. 347, с. 220 (2001).

14.  F. Cacace, G. de Petris, and A. Troiani Experimental Detection of Tetranitrogen. // Science, т. 295, с. 480 (2002).

15. http://classic.chem.msu.su/gran/gamess/index.html