1.Introduction

Over the last 30 years,the main interest in initiation of high energy materials has been focused on studies of shock and impact sensitivities[1,2].In comparison with these,no similar attention has been paid to the Friction sensitivity(FS)of such materials.We have dealt with FS intensely over the last five years[3-8].Our experience shows that the results of the FS determination can be heavily in fluenced by “human variability”.Nevertheless,careful measurements[3]by a single researcher provide results showing relationships which correlate with the output of other sensitivity parameters[4-8],with15N NMR chemical shifts of the key nitrogen atoms in the reaction center of the molecule[7]or with the DFT calculation outputs[8].Therefore,it should not be without interest to use in the FS outputs analysis recent knowledge about free spaces in crystal lattice of energetic materials(EMs),ΔV,and about their in fluence on the EMs'impact sensitivity[9-13].Recently we have analyzed a relationship between theΔV values and impact sensitivity of eighteen nitramines[13].In the present paper,which can be taken as a continuation of those studies[4-8],we use the same approach in analyzing similar relationships for friction sensitivity of thirteen nitramines.

2.Data sources

2.1.Nitramines under study

Chemical names,code designations and impact sensitivity,expressed as friction energy of the nitramines studied are summarized inTable 1.For a better illustrative view,structural formulas of these nitramines are presented in Scheme 1.

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2.2.Friction sensitivity

The friction sensitivity of all the nitramines studied were determined[4,7]by means of the BAM friction test apparatus operated under standard test conditions[15]with evaluation of the output by Probit analysis[16](only the normal force at which 50%of initiations occur is reported in Table 1).

Table 1 A review of the nitramines studied and their friction sensitivity(FS)from papers[4,7].

aDetermined in the present paper;RS-ε-HNIW is a product with reduced sensitivity prepared according to patent[14].

Data No. Chemical name of nitramine Code designation FS[4,7]/N 1 2-Nitro-2-azapropane DMNA 82.4 2 1,4-Dinitro-1,4-diazabutane EDNA 47.4 3 2,5-Dinitro-2,5-diazahexane DMEDNA 57.9 4 2,4-Dinitro-2,4-diazapentane OCPX 74.9 5 2,4,6-Trinitro-2,4,6-triazaheptane ORDX 147.7 6 1,3-Dinitroimidazolidine CPX 57.7 7 1,4-Dinitropiperazine DNDC 122.3 8 1,3,5-Trinitro-1,3,5-triazinane RDX 148.5 9 1,3,5-Trinitro-1,3,5-triazepane HOMO 119.9 10 β-1,3,5,7-Tetranitro-1,3,5,7-tetrazocane β-HMX 154.4 11 cis-1,3,4,6-Tetranitrooctahydroimidazo[4,5-d]-imidazole BCHMX 66.1 12 4,10-Dinitro-2,6,8,12-tetraoxa-4,10-diazaisowurtzitane TEX 161.3 13.1 ε-2,4,6,8,10,12-Hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane RS-ε-HNIW 84.4a 13.2 ε-HNIW 69.0

Scheme 1.Structural formulas of the nitramines studied.

2.3.Results of calculation for crystal lattice free volume of nitramine explosives

The object molecules were optimized at computational level of B3LYP/6-311+g(d,p)by using the Gaussian 09 package[17].All of the optimized structures were characterized to be true local energy minima on the potential energy surfaces without imaginary frequencies.The crystal volume[V(0.003)]was calculated by using the Multiwfn[17-19]software.The effective volume per molecule(Veff)is calculated as

This relationship is broken into the partial straight lines which are strongly limited by the molecular structure similarity.Only straight lines D and F correspond to the expected trend of increase in friction sensitivity with the increase in theΔV values;in all the nitramines,the data for which are associated with these lines,it is possible to find the molecular skeleton of DMEDNA(or part of it).

where M is molecular mass,and d is crystal density.The intrinsic gas phase molecular volume(Vint)is calculated by the 0.003 au surface according to Ref.[13],Vint=V(0.003).Therefore,the free space per molecule(ΔV)is

The position of ε-HNIW in Fig.1 is interesting.Its data correlate well with those of DMEDNA and EDNA using the straight line E.Comparison with the nitramines associated with the straight line D clearly shows that the difference between ε-HNIW and its RS-analogue(product with reduced sensitivity[14])rests in the difference in the intensity and uniformity ofintermolecular interactions in their crystals.From this comparison it seems as if in the ε-HNIW crystals only the nitro groups in positions 2,4,6,and 8 had a major part in the intermolecular force in its crystals-in so doing,the most reactive nitramino grouping is in position 2 of this particular nitramine[1,7,20-22].

3.Results and discussion

It is interestingthat the composition and sequence of nitramines associated with straight line I in Fig.2 are the same as in the corresponding partial relationship between FS and the15N NMR chemical shifts of nitrogen atoms in the most reactive nitro groups of these nitramines(see straight line A in Fig.3)[7].The oxygen atoms of nitro groups,by their dipole-dipole interactions,contact the oxygen and nitrogen atoms of nitro groups in neighboring nitramine molecules in the crystal[24-26],which is the decisive factor governing the crystal structure of nitramines.The type of interaction mentioned will act against the shear slide during friction.Aza atoms(i.e.bearers of these nitro groups)in fluence the mutual orientations of nitro groups in neighboring molecules by means of conformation of molecular skeletons.This conformation has a determining in fluence on the crystal lattice free volume.As aza atoms are “inner”atoms of the nitramines'molecular skeleton,their effect on the intermolecular potential will be lower than that of the nitro groups attached to them[7].Therefore,the crystal lattice free volumes should have a similar in fluence on this potential.This has already been shown in the case of the relationship between impact sensitivityand crystal lattice free volumes inpaper[13].

Table 2 A survey of the molecular mass,M,crystal densities,d,effective volume per molecule,Veff,intrinsic gas phase volume,Vint,and free space per molecule,ΔV.

Note:TheΔV values listed in brackets are taken from Ref.[11].

Comp. Mol.mass M×10-24/g D/(g·cm-3) Veff/(Å3) Vint/(Å3) ΔV/(Å3)DMNA 90.1 149.67 1.36 110.05 81.72 28.33 EDNA 150.1 249.34 1.71 145.9 119.69 26.21 DMEDNA 178.1 295.85 1.45 204.03 153.19 50.84 OCPX 164.1 272.59 1.50 181.73 135.88 45.85 ORDX 238.2 395.68 1.66 238.36 189.56 48.80 CPX 162.1 269.27 1.65 163.19 126.03 37.16 DNDC 176.1 292.52 1.63 179.46 142.23 37.23 RDX 222.1 368.94 1.81 203.83 161.97 41.86(46)HOMO 236.1 392.19 1.77 221.58 178.06 43.52 HMX 296.2 492.03 1.91 257.61 214.79 42.82(49)BCHMX 294.2 488.70 1.92 254.53 206.06 48.47 TEX 262.2 435.55 1.99 218.87 179.33 39.54 ε-HNIW 438.2 727.91 2.04 356.82 290.84 65.98

高中数学高效解题，即在短时间内完成大量的数学题，并保持较高的准确率。要想在数学考试中取得较好的成绩，做题速度和准确度缺一不可。而在速度和准确率都有基本保证的情况下，如何让自己在简单题上花费更少的时间，并在难题上取得更多的分值，便成为了我们学生必须面对的问题。

The above-mentioned disintegration of the nitramine groups in Fig.1,namely differences between compositions of groups with positive and negative slopes of the corresponding straight lines,on the first look is connected with kind and character of intermolecular interactions in crystals of these compounds.Interpretation of these facts needs another study by means the quantum chemical approaches in combination with X-ray spectroscopy.

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Results of these calculations are summarized inTable 2,together with crystal densities of the nitramines studied.

Data for compounds which can theoretically be generated from the DMNA molecule are associated with the straight lines B and C.The OCPX molecule,whose data lie at the straight line A,is as if an“opened”molecule of 1,3-dinitroimidazolidine(CPX)in whose skeleton the ethylenedinitramine grouping can be found.

Already mentioned usage of the 15N NMR chemical shifts in specification of the key nitrogen atoms in the reaction center of nitramine molecules[7]led to Fig.3 like to the one from corresponding outputs.Here a skeleton of DMEDNA(better of ethylene-1,2-diimine)seems to be a dominating-directional structure in these relationships.

Fig.1.Molecular structure analysis of the relationship between friction sensitivity and free space per molecule,ΔV.

Fig.2.Molecular structure analysis of the relationship between friction sensitivity and intrinsic gas phase molecular volume,Vint,in the nitramines studied.

For all the nitramines studied a direct proportionality exists between their intrinsic gas phase volume,Vint(V(0.003)),and corresponding friction sensitivity,as shown in Fig.2.This is understandable because the friction force during shearing is proportional to the contact area.Also here it is possible to observe a limitation by molecular structure similarity.In this case,the difference in both kinds of HNIW is good visible by comparison of the straight lines I and J,with the same possible explanation as in the case of Fig.1.In each case this comparison shows that ε-HNIW(technical or“common”quality)gives the impression of disorder in the distribution of the forces in its crystal lattice in comparisonwith its RS or chemically pure analogue[13].

In papers[4,7]we found a semi-logarithmic relationship between impact and friction sensitivity of the nitramines which isdivided into a number of partial relationships in close correlation with the molecular structure characteristics of these compounds[7].If we also take into account our findings from paper(impact sensitivity versus theΔV values)[13],it should be clear that friction sensitivity is in a semi-logarithmic relationship with the crystal lattice free volume per molecule,ΔV,of the nitramines studied,as shown in Fig.1.

Fig.3.A relationship between friction sensitivity and 15N NMR chemical shifts of nitrogen atoms of primary reacting nitro groups in initiation of the studied nitramines(the positions in molecule are given in parenthesis);taken from Ref.[7]and modified by insertion of data for 1,4-dinitroimidazole(1,4-DNI,theδN value of-20 ppm specified according to procedure[7]and friction sensitivity of 32N accepted from Ref.[23]).

4.Conclusion

The relationship between friction sensitivity(FS,shear slide with fixed volume)and the crystal lattice free space per molecule,ΔV,of the nitramines studied is described by a linear equation which is divided into a number of partial relationships with a strong limitation created by the molecular structure of such compounds.It is not possible to say clearly that increasingΔV values leads to increasing FS and vice versa.It is possible to see some similarity with the in fluence of aza atoms on FS[7].These atoms,as part of the molecular skeleton of nitramines,in fluence the mutual orientations of nitro groups in neighboring molecules by means of conformation of the nitramine molecules and thus determine simultaneously the crystal lattice free space per molecule.Also,in friction sensitivity,the dominating in fluence is thus the dipoledipole interaction on the base of mutual contacts of the oxygen and nitrogen atoms of nitro groups in neighboring nitramine molecules.In concordance with this interaction,a directly proportional relationship was found between FS and the intrinsic gas phase molecular volume,Vint,of the nitramines mentioned,which is divided into several straight lines according to relatively tight molecular structure similarity.Both types of friction sensitivity relationships found again con firm unbalance in distribution of the forcesin the crystallattice ofthe “common” quality of ε-2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane, in comparison with its RS or chemically pure analogue.

自从20世纪70年代末以来，尤其是90年代末至今的10年间，与汉语副词相关的语法研究，进入一个人才辈出，理论纷呈，局面繁荣，成果迭出的快速发展时期。纵观这些年来的副词研究，真可谓研究队伍不断扩大，研究理论趋向多元，研究方法不断更新，研究成果蔚为大观。接下来我也把自己对关于现代汉语副词的小小的研究跟自己所感受到的综述一下。

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Acknowledgement

The work described in this paper partially received financial support from the Students Grant Projects No.SGSFCHT_2016002 of the Faculty of Chemical Technology at the University of Pardubice,partially it was created in the framework of the six month traineeship of Dr.LIU Ning in Institute of Energetic Materials at University of Pardubice in 2016 under financial support of the Chinese State Administration of Foreign Experts Affairs.

Appendix A.Supplementary data

Supplementary data related to this article can be found at https://doi.org/10.1016/j.dt.2018.01.001.

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