Crystal lattice free volume and thermal decomposition of nitramines

Svtopluk Zemn ,Ning Liu ,Ahmed K.Hussein

a Institute of Energetic Materials,Faculty of Chemical Technology,University of Pardubice,CZ-532 10,Pardubice,Czech Republic(Czechia)

b Xi'an Modern Chemistry Research Institute,Xi'an,Shaanxi,710065,China

Keywords:Crystal lattice Thermal decomposition Initiation reactivity Nitramines

A B S T R A C T The linear,directly proportional,equations between the Arrhenius parameters(Ea and log A)of the thermal decomposition and the crystal lattice free space per molecule,ΔV,of 22 nitramines are described.It is shown that,because of a significant limitation by the molecular structural characteristics of such compounds,they are divided into a number of partial relationships.These partial relationships divide the nitramines into a group of substances relating to dimethyl nitramine and a sub-group related to ε-HNIW.These directly proportional equations mean that an increase in the ΔV values is related to an increase in the thermal stability of the corresponding nitramines.A comparison with similar published dependencies for the impact and friction sensitivities,on the one hand,and with the relationship between the Ea values and the sum of the negative and positive extremes of molecular surface electrostatic potentials,on the other,confirms the well-known fact that intermolecular interaction in the nitramines studied plays a decisive role in the thermal reactivity of such compounds.The crystal lattice free space manifests itself here perhaps only in the solid state thermal decomposition of RDX,HMX and DINGU.This study again confirms a level of disorder in the distribution of the forces in the crystal lattice of the“common”quality of ε-HNIW,compared with its “reduced sensitivity(RS)”or pure analogues.

1.Introduction

Sensitivity of energetic materials(EMs)is intimately connected with their chemical reactivity and/or that of their components(see for example Refs[1,2]and quotations therein).Such reactivity depends on the molecular structure,the intermolecular interactions and the material state of the particular EM and also on their possible admixtures.The selection of nitramines chosen for the work described in this paper as energetic materials are,in their molecular structures,relatively simple polynitro compounds,for which the mechanism of the primary homolysis of their molecules is well understood[3-7](see Scheme 1).

Aza atoms form part of the molecular skeletons of nitramines,and their electron configuration is thus connected with the conformation of such molecules.However,in spite of the fact that they are “inner”atoms of the skeleton,their effect on the intermolecular potential will be lower than that of the atoms in the nitro groups attached to them.The oxygen atoms of the nitro groups,by their dipole-dipole interactions,are in contact with the oxygen and nitrogen atoms of the nitro groups in neighbouring nitramine molecules in the crystal[8-11],which is the decisive factor governing the crystal structure of nitramines.

Taking account of these facts,and from a physical organic chemistry point of view,the initiation reactivity,including initiation of detonation,has been extensively studied for individual organic energetic materials(EMs).Techniques such as the NMR chemical shifts of the key atoms in the reaction centres[1,2,5,12-17]and the modified Evans-Polaniy-Semenov relationship are widely used not only for individual energetic materials[1,2,5,12,18,19]but also for emulsion[20]and plastic bonded explosives[21]and mixtures with peroxides[22,23].In addition,the crystalline aspects of impact and friction sensitivities have been studied using the heats of fusion for such compounds[1,12,24-26].However,intensive use of quantum chemical methods in the study of EMs in general is head and shoulders above the mentioned chemical approach,as well as in the study of their initiation reactivity[1,27-35]but with a tendency to make a general conclusion for several EMs with different molecular structures.However,Politzer and Murray have shown that the correlations found here[30]are restricted to specific classes(i.e.nitroaromatics,nitroheterocyclics and nitramines)which is perfectly in line with findings from approaches based on physical organic chemistry principles(see Refs.[1,5,12,14,15,17,25]).

Scheme 1.Structural formulas of the nitramines studied.

The already mentioned dipole-dipole interactions are connected with the non-binding inter-atomic distances between oxygen atoms inside and outside all of the nitro groups in these poly-nitro compounds.These are shorter than those corresponding to the intermolecular contact radii for oxygen in carbonyl or nitro groups[36-40];this distance is especially short inside the most reactive nitro groups[40-42].These facts led to the research of the free spaces in crystal lattices of EMs and of their in fluence on EMs'impact sensitivity[32-34]but originally without taking into account the very important molecular-structural similarity[2,32-35].This deficiency has already been remedied by recent studies of the in fluence of the free spaces in crystal lattices on the impact[41]and friction[42]sensitivities of nitramines.In both these cases it seems that it is not the free volume in the crystal lattice,but intermolecular interaction which plays a decisive role in initiation reactivity under mechanical impulses.

Thermal decomposition of energetic materials has also been extensively studied X[1,4,6,7,43].In the area of EM testing it is sometimes not entirely clear in which physical state the given substance decomposes;facts reported in paper[44]suggest a need to study the pre-decomposition states of thermal decomposition and the beginning phase of the heat initiation of nitramine crystals.Nevertheless,it is not without interest to determine the relationship between the free volumes in crystal lattices and the Arrhenius parameters of the thermal decomposition of the nitramines.This is the subject of this paper.

2.Data sources

2.1.Arrhenius parameters of thermal decomposition

The thermoanalytical data used for the study of individual nitramines were taken from the published literature and are grouped in Table 1 for both the Arrhenius parameters of the monomolecular decomposition.The majority of the data was obtained by the Russian isothermal manometric(RMM)method,making use of Bourdon's glass compensation manometer[4,7,45].These data are known to correspond to the primary nonautocatalysed stage of thermal decomposition of the energetic materials[1,4,7,45,46,48,52,53].In the case of thermal decomposition in the condensed state,only the results of some thermoanalytical methods are directly comparable with the results of RMM,especially those from differential scanning calorimetry(DSC,e.g.Refs.[51,55,58,60,63])and some output from thermo-gravimetry(TG)of EMs which have been evaluated by means of the modified Kissinger-Akahira-Sunose (KAS) isoconversional method[61,65,66].The formulas of the nitramines studied are shown in the chart below:

2.2.Results of calculations for crystal lattice free volume of nitramine explosives

All compounds were optimised at computational level of B3LYP/6-311+g(d,p)by using the Gaussian 09 software.The crystal volume[V(0.003)]was calculated by using the Multiwfn 3.3.9 software.The effective volume per molecule(Veff)was calculated as:V eff=M/d,where M is molecular mass,d is crystal density.The intrinsic gas phase molecular volume(Vint)was calculated by the 0.003 au surface according to Ref.34,Vint=V(0.003).Therefore,the free space per molecule(ΔV)is:

Results of these calculations are summarised in Table 2,together with crystal densities of the nitramines studied.

2.Results and discussion

Simple relationships of the activation energies,Ea,and thecrystal lattice free volume values,ΔV,of the nitramines studied are reproduced in Fig.1.Due to molecular-structural similarity and the various states of thermal decomposition(solid or liquid state,premelting or dissolution in products,etc.),the relationship obtained is not unambiguous(this is also the case for impact and friction sensitivities[41,42]).Nitramines in Fig.1 appear as if divided into two groups,one derived from dimethyl nitramine(DMNA)and one related to 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane(HNIW).Fig.1 is very strongly reminiscent of a similar relationship between the Eavalues and the sum of the negative and positive extremes of molecular surface electrostatic potentials,VS,Σ,of the nitramines studied[2,44],but with this difference-that the straight lines A and B create in the referenced case only one line which corresponds there to nitramines,decomposed in the solid state[2,44].On the basis of comparing also with results of paper[21]the straight lines C and D in Fig.1 associate nitramines in which it is not entirely clear in what physical state they were found(micro-regions in their crystals)during the initial phase of their thermal decomposition(similar to the case in Ref.[21])and line E corresponds to crowded molecules decomposed in the liquid state.

Table 1 A list of the nitramines studied,showing the Arrhenius parameters(Ea in kJ·mol-1 and log A in s-1)of their low-temperature monomolecular thermal decomposition.

Table 2 A survey of the molecular mass,M,crystal densities,d,effective volume,V eff,crystal volume,V(0.003)and free space per molecule,ΔV.

Fig.1.Molecular-structural analysis of the relationship between activation energies of thermal decomposition,and the crystal lattice free volumes,ΔV.

How it is possible that theΔV values also correlate with data for thermal decomposition in the liquid state?This decomposition can proceed in the bulk of the crystal,on its surface and/or on defects in the crystalline lattice.The reaction occurring on defects has the same activation energy as in the liquid phase(or close to it)[69].However,decomposition of solid compounds proceeds very often through the liquid phase,formed as a result of the melting of impurities,the decomposition products,or theireutectic mixture with the original substance[7].Reaction in the bulk of the crystal requires the formation of a cavity with a volume exceeding the activation volume,so that the leaving group does not feel the forces of interatomic attraction[69].In the second case,the crystal lattice free volume might play a certain role in decomposition.Already,interrelations between theΔV values and sensitivities to impact[41]and friction[42]have been reported,where the intermolecular interactions should play a decisive role in such initiation activities.In the case of Fig.1,the crystal lattice free volume might have some in fluence on the thermal decomposition of DINGU,RDX and HMX in the solid state(straight line A);for the other nitramines intermolecular interaction should be the dominating factor,similar to the already mentioned comparison with analogous relationships between the Eavalues and a sum of the negative and positive extremes of molecular surface electrostatic potentials,VS,Σ[2,44].The warping and subsequent collapse of the crystalline lattice during melting leads to the removal of the resistance against the formation of the activated complex in the molecular crystals and thus to a reduction in the activation energy,but the principal intermolecular interaction should be preserved.

Concerning the pre-exponent of the Arrhenius equation,a semilogarithmic relationship exists with theΔV values(Fig.2)in the sense that the nitramines under study are divided again into two basic groups as in the case of Fig.1:data around the straight lines F,G and H have a relationship with the HNIW data and those around the straight lines I,J and K with the DMNA data.The preexponential factor is also known as a frequency factor,and in the transition state theory is connected with the internal structure,the rotational and vibrational behaviour of reactants and the activation complex(if the activated complex has freer rotation than the reactant,the first-order pre-exponential factor is high[70]).It has thus a relationship with the degrees of freedom of the given molecule(mobility of the molecule in the crystal lattice).When molecular complexity increases,activation entropy is increasingly more negative and the log A value declines[71].This means that an increase in molecular complexity corresponds here to a decrease in the crystal lattice free volume.

In both Figs.1 and 2 two different positions are visible for the HNIW data;points on the intersections of the straight lines B and C in Fig.1 and lines F,G,and H in Fig.2 correspond to measurements by Russian authors in isothermal conditions(see data 20.3 and 20.4 in Table 1[65,66]).Data forγ-HNIW have been derived using the same method[67].The HNIW points on the straight lines E and K were obtained using the non-isothermal TGA and DSC techniques.Reasons for these differences have already been discussed in our recent papers[2,21,41,42,44]:the correlation of theγ-HNIW data with the straight lines C and K clearly shows that this polymorphic modification substitutes for a liquid phase of HNIW[21].In the case of ε-HNIW it might be related to complications in its ε-γ polymorph transitions[21,44,67,72](mainly cracking of the HNIW crystals[21,44]),its level of purity,sublimation during measurement and flaws in the crystal lattice(the difference between“normal” and “reduced sensitivity” quality of ε-HNIW[2,21,41-44,73]).In defective crystals(“normal”quality of ε-HNIW)or crystals with impurities(NATO STANAG-4566 tolerates these up to 3%by wt.)conditions exist for a decomposition reaction in bulk to which Arrhenius parameters generally correspond as for thermal decomposition in the liquid phase[69,74].

3.Conclusion

Fig.2.Semi-logarithmic relationship of the pre-exponent of the Arrhenius equation for thermal decomposition of nitramines,and the crystal lattice free volume,ΔV.

The relationship between the Arrhenius parameters(Eaand log A)of the thermal decomposition,and the crystal lattice free space per molecule,ΔV,of 22 nitramines is described by linear,directly proportional equations.These are divided into a number of partial relationships caused by a significant limitation of the molecular structural characteristics of such compounds.These partial relationships divide the nitramines into a group of substances relating to dimethyl nitramine and a sub-group related to ε-2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane.The relationship mentioned in the case of the Ea values is very reminiscent of a similar relationship between them and the sum of the negative and positive extremes of molecular surface electrostatic potentials,VS,Σ,of the nitramines studied[2,44].Taking into account the findings from a study of the relationships of theΔV values to the impact[41]and friction[42]sensitivities,this would tend to confirm the well-known fact that intermolecular interaction in the nitramines under study plays a decisive role in the thermal reactivity of these compounds.The crystal lattice free space manifests itself here perhaps only in the solid state thermal decomposition of 1,3,5-trinitro-1,3,5-triazinane,1,3,5,7-tetranitro-1,3,5,7-tetrazocane and 1,4-dinitrotetrahydroimidazo[4,5-d]imidazole-2,5-(1H,3H)-dione.A directly proportional relationship between the Arrhenius parameters and theΔV values means that an increase in the latter is related to a rise of thermal stability of the corresponding nitramines.Similarly,as in our recent studies about initiation reactivity of nitramines[2,21,41-44,73],the ε-modification of 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane of the “normal”quality(impact sensitivity 2-4 J)is an exception which gives the impression of disorderliness in the distribution of the actions of force in its crystal lattice(and/or content of impurities in it)in comparison with its “reduced sensitivity”(RS-ε-HNIW)or pure analogue variants.

Acknowledgements

The work described in this paper received partial financial support from the Students Grant Projects No.SGSFCHT_2016002 of the Faculty of Chemical Technology at the University of Pardubice.Other financial support came from the Chinese State Administration of Foreign Experts Affairs,which funded the six month traineeship of Dr.LIU Ning in the Institute of Energetic Materials at the University of Pardubice in 2016.