High Energy Chemistry, Vol. 38, No. 5, 2004, pp. 306–314. Translated from Khimiya Vysokikh Energii, Vol. 38, No. 5, 2004, pp. 346–354. Original Russian Text Copyright © 2004 by Makarevich, Pak, Ryabykh.

RADIATION CHEMISTRY

Paramagnetic Centers in Irradiated Potassium Picrate G. G. Makarevich, V. Kh. Pak, and S. M. Ryabykh Kemerovo State University, ul. Krasnaya 6, Kemerovo, 650043 Russia Received August 13, 2002

Abstract—The formation of paramagnetic centers in potassium picrate in a radiation field was found using EPR spectroscopy. Stable paramagnetic centers were identified as 2,6-dinitro-para-quinone, iminoxyl, and é− radicals. The kinetics of buildup of stable paramagnetic centers was studied over a wide dose range (0.14– 5 MGy), and the temperature stability was studied at 77–550 K. It was found that the decay of paramagnetic centers in the temperature range 373–523 K obeyed the laws of polychronous kinetics. A reaction scheme for the radiation-thermal decomposition of sodium picrate with the participation of radical radiolysis products was proposed.

Potassium picrate (trinitrophenolate) is the nitroaromatic compound C6H2(NO2)3OK, which is an energyrich explosive. Along with explosion, it can undergo all types of slow solid-phase decomposition under continuous exposure to an external energy factor (heat, light, radiation, or electromagnetic fields); therefore, it is of interest as a model system in the physics and chemistry of solids. In this work, we report the results of studies on the formation, accumulation, stability, and properties of paramagnetic centers generated in potassium picrate by irradiation. EXPERIMENTAL Polycrystalline potassium picrate used in the study was prepared by neutralizing a hot picric acid solution with a KOH solution. At pH 7, fine yellow crystals precipitated. The precipitate was washed with cold water and ethanol. Chemically pure reagents were used. Potassium picrate single crystals were grown by slowly evaporating hot (60°ë) aqueous solutions. After a few days, the single crystals precipitated as needles of size 15 × 3 × 4 mm and 20–30 mg in weight. The chemical analysis for the picrate ion demonstrated 95.5 ± 0.5% purity of the preparation. X-ray diffraction analysis showed that the crystal structure of the synthesized single crystal is fully consistent with published data [1]. Irradiation was performed with 60Co γ-rays and ~150-keV fast electrons on RKhM-γ-20 and MIRA-2D facilities, respectively. Dosimetry was performed with the use of solid KNO3 as a dosimetric system by moni–

toring the formation of NO 2 , whose yield (1.6 ± 0.2 ion/100 eV) is constant over the range of dose rates up to 1010 Gy/s [2]. In our case, the use of this dosimetric system was particularly appropriate because the absorption coefficients of KNO3 and potassium picrate, which are chemically close to each other, differ only slightly (0.0266 and 0.0271 g/cm2, respectively, for

γ-radiation). The absorbed dose rate was 1.4– 2.8 Gy/s for γ-radiation or 7 × 103 Gy/s for fast electrons. Irradiation on the RKhM-γ-20 unit was performed at a central-channel temperature (317 K) or liquid nitrogen temperature; at room temperature, electron-beam irradiation was performed on a pulse accelerator (MIRA-2D). The thermal annealing of irradiated potassium picrate crystals was performed in a WS-50 thermostat in the range 338–570 K; the accuracy of thermostatting was ±2 K. The EPR spectra were measured on a Rubin radiospectrometer with a modulation frequency of 100 kHz at room temperature and 77 K. Errors in the determination of g values, T-tensor values, radiation-chemical yields, and relative EPR line intensities were ±0.0005, ±0.05 mT, 20%, and 10%, respectively. 60Co

RESULTS AND DISCUSSION EPR spectra and Paramagnetic Centers The irradiation of potassium picrate single crystals with γ-rays and a pulse electron beam at 77 K generated an EPR signal, which is shown in Fig. 1a. This is a broad (1.45 mT) isotropic asymmetric singlet with unresolved hyperfine structure (HFS). As the orientation of a single crystal in the magnetic field was changed, a change in the line shape of this singlet was observed, but no resolution of this singlet into individual components was achieved. There were no detectable changes in the g-factor because of the asymmetry and a large width of the singlet. As the microwave power was increased, an increase in the intensity of the entire spectrum was observed with a weak change in the line shape. The change in the line shape suggests the formation of several types of defects in a radiation field; these defects, which are stable at 77 K, exhibited different sensitivities to microwave power saturation. Thus, it is problematic to identify this paramagnetic center (PC-0 or an ensemble of paramagnetic

0018-1439/04/3805-0306 © 2004 MAIK “Nauka /Interperiodica”

PARAMAGNETIC CENTERS IN IRRADIATED POTASSIUM PICRATE

307

DPPH

0.5 mT (‡) DPPH

.....

.....

2

....

.....

.... ..

....

1

3 4

2

.....

0.5 mT

(b)

0.5 mT DPPH

(c) Fig. 1. EPR spectra of irradiated potassium picrate at the orientation H || axis b of the single crystal at (a) 77 and (b) 298 K and (c) the spectrum of PC-4 measured immediately after the irradiation of potassium picrate with fast electron pulses at 298 K.

centers) by spectroscopic parameters; therefore, its nature will be considered later on based on other properties. The irradiation of potassium picrate single crystals with γ-rays at 317 K and with fast electrons at room temperature generated a complex EPR signal [3] with hyperfine structure (HFS), which is shown in Fig. 1b. An analysis of spectroscopic parameters was performed in accordance with standard procedures [4, 5]. The angular dependences for the A tensor, the anisotropic hyperfine coupling tensor, and the g tensor were HIGH ENERGY CHEMISTRY

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obtained. This analysis suggests that the observed EPR spectrum is due to the presence of four types of paramagnetic centers. PC-1 is responsible for an anisotropic triplet with a splitting of 0.15–0.53 mT and an intensity ratio of 1 : 2 : 1. PC-2 gives two nonequivalent triplets, and PC-3 gives an isotropic singlet of width 0.25 mT. PC-4 gives a singlet of 0.55 mT in width. The table summarizes the spectroscopic parameters of paramagnetic centers. Types 1–3 centers were stable at room temperature, whereas the concentration of PC-4 slowly decreased during storage for a day.

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Spectroscopic parameters of paramagnetic centers in irradiated potassium picrate Paramagnetic center

Txx

0 1 2 3 4

– 0.199 1.214 – –

Tyy

Tzz

gxx

gyy

gzz

2.0033 2.0086 2.0098 2.0028 2.0032

2.0033 2.0046 2.0045 2.0028 2.0032

2.0033 2.0019 2.0018 2.0028 2.0032

mT – –0.291 –0.205 – –

– 0.090 –0.705 – –

Let us consider the possible nature of these paramagnetic centers. From published data [4, 6–8], it follows that the formation of a number of paramagnetic centers in nitroaromatic compounds under irradiation is expected: the radical anions and radical cations of nitrophenol; phenoxyl, nitrosoiminoxyl, and cyclohexadienyl radicals; NO; NO2; oxygen centers; and a colloid metal. Paramagnetic center 1. Hyperfine splitting in PC1 is due to coupling of the unpaired electron delocalized on the benzene ring to two equivalent protons in the meta-position; hyperfine coupling to the 14N nuclei of nitro groups is insignificant, and it changed the line shape at different orientations of a single crystal. Hence, it follows that PC-1 is likely to be the 2,6-dinitro-para-quinone radical, which is formed by the elimination of NO from the picrate anion [9]. Therefore, we consider in more detail main directions of its g and T tensors in the crystallographic coordinate system [1]. For the T tensor of the 2,6-dinitro-para-quinone radical, the axis X is parallel to the C–H bond, and the axis Z is normal to the plane of the benzene ring. For the g tensor, the X axis coincides with the direction of the crystallographic axis b, and the Y axis lies in the benzene-ring plane; that is, it is deflected from the axis a through 25°. The Z axis is perpendicular to the ring plane and is deflected from the crystallographic axis c through 25°. The lowest g-factor value was observed when the magnetic force vector was directed parallel to the axis bb, that is, perpendicular to the oxygen 2pz orbital on which an unpaired electron is delocalized. Correspondingly, the lowest value is observed at H || axis c ± 25°, that is, when H || oxygen 2pz orbital and perpendicular to the ring plane. This g-factor value should insignificantly differ from the g-factor of free electron (2.0023), as indeed was observed in actual practice. In radicals with heteroatoms, low-energy n π* transitions play the most important role. These transitions increase the gxx and gyy components by 2λ/∆Enπ* (λ is the spin– orbital interaction constant); in these radicals, always gxx > gzz and gyy > gzz. The spin–orbital coupling constants for heteroatoms are much greater than that for the carbon atom [4]. Therefore, g-factors are usually

∆Hmax

Aiso mT – –0.342 3.125 – –

1.450 0.150 0.245 0.550 0.250

greater in radicals containing oxygen, nitrogen, sulfur, chlorine, and other heteroatoms [6]. In our case, ∆gxx and ∆gyy with reference to ge are equal to 0.0062 ± 0.0005 and 0.0023 ± 0.0003, respectively. Thus, there is a considerable contribution to the ∆gii value by virtue of electron localization on oxygen atoms. Let us analyze the hyperfine coupling tensor. The distribution of spin density in phenoxyl radicals, regardless of substituents, obeys the following relation: ρmeta
ρpara > ρortho with ρmeta ≈ –0.05–0.07, ρpara ≈ 0.3– 0.4, and ρortho ≈ 0.2 [7]. Thus, the spin density found (0.127) corresponds to an intermediate value between ρortho and ρmeta but is closer to ρortho. Consequently, a somewhat higher spin density was localized on oxygen that was added in the course of NO2-group isomerization in the para position. Wertz and Bolton [4] showed that aN is of the order of 0.05 mT if nitro groups lie out of the ring plane as in our case; at an individual line width of 0.015 mT and as follows from the results of mathematical simulation, this splitting can only broaden the side components of the triplet. It is evident that the splitting due to 14N should be anisotropic [5]. According to Buchachenko and Vasserman [6], the greatest splitting should be observed in the case of H || nitrogen 2pz orbital, i.e. at H || aa + 70° in the given crystallographic coordinate system [1], which was indeed observed in practice. Based on the above considerations, PC-1 was identified as the 2,6-dinitro-para-quinone radical, which was produced in the course of NO2-group isomerization into the nitrite group at the para-position of the benzene ring followed by the elimination of nitrogen monoxide. This reaction is well known in the organic chemistry of nitro compounds [10]. Paramagnetic center 2. Based on a comparison of the obtained spectroscopic characteristics with published data, PC-2 was tentatively identified as an iminoxyl radical formed by oxygen abstraction from the nitro group in the ortho position. In the case that the radical is formed by oxygen abstraction in the ortho position, the greatest value of HFS is observed at b || H ± 45°, i.e., when H is parallel to the unoccupied orbital of nitrogen hybridized in HIGH ENERGY CHEMISTRY

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nearly the sp2 mode or, in other words, along the bisector of the CNO angle. According to Buchachenko and Vasserman [6], this angle is 140 ± 3°. In this position, the g-tensor should have a minimum value in accordance with published data; in more exact terms, the lowest value will be observed at b || H ± 45° if the H field direction coincides with the ring plane, i.e., at an angle of 25° with respect to the plane ab [1], which is what is observed in practice. In iminoxyl radicals, spin density is distributed approximately equally between nitrogen and oxygen. In this case, its considerable part occurs on the oxygen 2s orbital; i.e., hyperfine coupling due to nitrogen has a considerable isotropic contribution. The distribution of spin density weakly depends on the carbon skeleton of the radical and on the donor–acceptor properties of substituents; it is primarily determined by the structure of the C=N–O moiety. Only hyperfine coupling to the proton located in the ortho-position to this group was observed experimentally; in this case, the splitting was no higher than 0.22 mT, as in the case under consideration (the width of an individual line between maximum-slope points ∆Hmax is 0.25 mT). This can result only in line broadening and is undetectable by the EPR technique. Based on an analysis of the angular dependence, the iminoxyl radical is formed via oxygen abstraction from NO2 ortho to the hydroxyl group. Indeed, if the abstraction were from the para-position, only one center would be observed on changing the angle between the plane ab and the direction of a magnetic field, whereas we detected two spatially nonequivalent type 2 paramagnetic centers in actuality (Fig. 1). It is likely that the difference of the hyperfine coupling tensor from the axially symmetric one [6] is explained by the effect of the cationic sublattice. Note that another triplet with an intensity ratio of 1 : 1 : 1 was present in the EPR spectrum. This triplet is seems to be due to an iminoxyl radical in the para-position. It was not studied in detail because of a low concentration and the fact that at an orientation other than bb || H (at an angle greater than 35°) individual lines split into fuzzy components, most likely, because of the anisotropic hyperfine interaction with ring protons. This interaction is possible because the nitro group in question lies in the plane of the benzene ring [1]. Paramagnetic center 3. The EPR signal of this paramagnetic center is superimposed on the spectrum of PC-4, and it is separated only in the case of the subsequent thermal treatment. The EPR spectrum of PC-3 is an isotropic singlet (g = 2.0028) with ∆Hmax = 0.25 mT. As the recording temperature was changed to 77 K, an insignificant broadening of the EPR signal was observed. This EPR signal cannot be ascribed to colloidal potassium particles by analogy with data obtained in alkali metal azides [11] because we detected a paramagnetic center with an analogous behavior and similar spectroscopic characteristics in irradiated picric acid crystals, where the formation of a colloidal metal is HIGH ENERGY CHEMISTRY

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Concentration of paramagnetic centers, 1018 g–1 PC-1 9 6 PC-3 + PC-4

3

PC-2 0

1

2

3 D, MGy

4

5

Fig. 2. Kinetic curves of buildup of PC-1–PC-4 in the course of γ-radiolysis.

impossible in principle. Moreover, we also detected a similar signal both in the case of lead trinitroresorcinolate, where an iminoxyl radical was also formed, and in sodium picrate. In all of the matrices, the concentration of paramagnetic centers with such spectroscopic parameters increased upon thermal heating. The decay of any paramagnetic radiolysis products that give EPR signals was not observed in the temperature range in which the concentration of PC-3 increased. Unlike the case of picric acid, no EPR signals were detected on the thermal heating of unirradiated potassium picrate. In the formation of an iminoxyl radical, the second radiolysis product is the é– radical, which is one of the most frequently occurring radiation defects in both ionic and ion–molecule crystals [12, 13]; this radical was studied in detail in a number of matrices. By analogy with the results obtained in alkali nitrates [14], we identified PC-3 as é–. Note that the validity of this identification should be additionally checked. Paramagnetic center 4. This paramagnetic center gives a 0.55-mT wide singlet. It is unstable at 298 K, and its concentration slowly decreased to an undetectable value for a time of about 20 h at room temperature. Figure 1c demonstrates the spectrum of PC-4 measured immediately after the pulse electron-beam irradiation of potassium picrate. Hypothetically, we identified PC-4 as a radical containing the nitrite group at the para position of the benzene ring. Buildup Kinetics and Thermal Stability of Paramagnetic Centers The buildup rate curves have similar patterns for all the paramagnetic centers detected: the concentration of paramagnetic centers increased proportionally to absorbed dose in the initial dose range up to about 1 MGy (Fig. 2). At a dose higher than 1 MGy, the rate of formation of paramagnetic centers began to decrease up to a dose of 5.1 MGy; however, saturation was not further reached at a PC-1 concentration of ~1019 radi-

MAKAREVICH et al. Concentration of paramagnetic centers, 1017 g–1

310 9

(‡) 1

6 2 3

0

50 0

100 D, kGy t, h 5 10 50

150

20

20

(b)

c × 10–17, g–1

9

III

II

I

6

3

30

60

90 120

150 180 210 240 D, kGy

Fig. 3. (a) Kinetics of changes in the concentration of the 2,6-dinitro-para-quinone radical in potassium picrate (1) under intermittent irradiation at 298 K (arrows indicate the instants of the termination/onset of irradiation), a pause of 5 h; (2) the concentration of the 2,6-dinitro-para-quinone radical under continuous irradiation at 298 K. (b) The kinetic curve of changes in the concentration of the 2,6-dinitro-para-quinone radical (I) in the course of irradiation, (II) during a dark pause, and (III) in the course of repeated irradiation.

cal/g. Since the EPR spectra of PC-3 and PC-4 overlap by 90%, their total concentration is shown. On heating from 77 K to room temperature, PC-1 irreversibly and completely decayed at a critical temperature of 230–235 K. The signal intensity changed only slightly below Tcrit, whereas the signal disappeared almost instantaneously as Tcrit was attained. In this case, a new EPR signal did not appear. However, during the storage of an irradiated (at 77 K) crystal at 298 K, an EPR signal was detected in this crystal after ~1 h; this signal was fully identical to that of PC-1 and PC-3 in the case of irradiation at 317 K. In the course of storage, the concentration of PC-1 increased, tending to saturation for 24 h. Within the limits of experimental error, the maximum concentration of PC-1 was equal to that in potassium picrate irradiated at 317 K to the same dose. For example, as can be seen in Fig. 3a, the kinetic curve of PC-1 buildup under intermittent irradiation has an interesting shape in the region of low doses. After cessation of irradiation, the concentration of PC-1 con-

tinued to increase and reached a steady-state value within about 10 h. The relative increase in the concentration for the holding time was inversely proportional to the absorbed dose, and the value of this effect fell within the limits of experimental error. This effect can be observed repeatedly [15]. The above result allowed us to conclude that the decay of PC-1 also occurred in the course of irradiation (Fig. 3b); however, we observed only the final stage of this process because the irradiation time was equal to several hours. The subsequent irradiation resulted in a decrease in the concentration of PC-1 to a value that would be observed on continuous irradiation. The concentration further increased as in the case of continuous irradiation. In our opinion, the above data suggest that the 2,6-dinitropara-quinone radical is the product of PC-4 decomposition. This was demonstrated by the results of analogous experiments performed with a pulse radiation source, which provides an opportunity to reach a high radiation dose within a short time (a few minutes). We found that the EPR lines of the 2,6-dinitro-paraHIGH ENERGY CHEMISTRY

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PARAMAGNETIC CENTERS IN IRRADIATED POTASSIUM PICRATE Relative concentration 15

311

PC-1

10 PC-3 + PC-4 5

PC-2

0

500

1000 1500 Irradiation time, s

2000

2500

Fig. 4. Kinetic curves for the buildup of PC-1–PC-4 under irradiation with fast electron pulses. Arrows indicate the instants of the termination/onset of irradiation.

PC-4 concentration ×10–18, g–1 423 456 4 3 476 506

2 1

393

0

100

200

300

Time, min Fig. 5. Stepwise kinetics of decay of the 2,6-dinitro-para-quinone radical in potassium picrate γ-irradiated at room temperature (dose of 1.20 MGy). Arrows indicate the onset of heating at a specified temperature (in kelvins).

quinone radical appeared against the background of the spectrum of PC-4 during a dark pause; the intensity of these lines increased, whereas the intensity of the singlet of PC-4 decreased below the limit of detection (Fig. 4). The treatment of the kinetic curve of PC-1 formation in the course of storage at 298 K yielded straight lines in the c/c∞–lnt coordinates. This means that the formation of PC-1 is due to a first-order or a pseudofirst-order reaction. The thermal stability of PC-1 was studied over the range 293–506 K. The storage of γ-irradiated (at 317 K) potassium picrate at room temperature resulted in an increase in the concentration of PC-1, which tended to saturation as in the previous case. After attaining the saturation concentration c∞, the concentration of PC-1 remained constant at least for six months. On heating at a constant rate, PC-1 was stable to 360 K. As the temHIGH ENERGY CHEMISTRY

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perature was further increased, its concentration decreased, and the center completely disappeared at T > 500 K. Therefore, the kinetics of PC-1 decay was studied at fixed temperatures in the range 423–506 K. Figure 5 demonstrates corresponding kinetic curves. It was found that the thermal decay of PC-1 followed polychronous kinetic laws. At a fixed temperature, the concentration of PC-1 decreased to reach a limiting value characteristic of a given temperature. After increasing the temperature, PC-1 began to decompose again; its concentration reached a new steady-state value; etc. The treatment of these kinetic curves yielded straight lines in the c/c∞–lnt coordinates. This indicates that the thermal decay of PC-1 is similar to the recombination of geminate radical pairs. The ranges of activation energies and preexponential factors obtained for this process under continuous irradiation at 298 K are Eact = 30–44 kJ/mol and lnk0 = 7.8–12, respectively.

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MAKAREVICH et al.

Scheme of the Formation and Decay of Paramagnetic Centers The experimental data allowed us to propose a reasonably substantiated reaction scheme involving paramagnetic centers. We believe that PC-1–PC-4 result from the decomposition of a molecular exciton into heavy and light fragments. As the light fragments, NO2, O–, and NO can be eliminated from the molecular exciton, whereas iminoxyl, quinone, and intermediate (PC4) radicals are the heavy fragments. However, these processes are not elementary, as evidenced by the EPR spectra of potassium picrate irradiated at 77 K. At this temperature, a spectrum without HFS was generated. Based on general considerations, we believe that PC-0 is most likely an autolocalized molecular exciton, in which electron density is redistributed to the cation. Next, an interesting process takes place. In the course of freezing-out, the signal of PC-0 disappears at the

critical temperature Tcrit = 230 K; however, this is the transformation of PC-0 into a certain reactive intermediate X, which gives no EPR signals, rather than recombination or relaxation. The transformation in question is a threshold reaction; the critical energy that corresponds to Tcrit is about 0.02 eV. Because the unpaired electron does not disappear in this case and only its orbital is transformed to a position at which an EPR signal is not detected, it is most likely that the product X is the reorientation of PC-0 from a stable position in an ideal crystal lattice to another metastable position. Since PC-0 is smaller than the picrate anion and the lattice of potassium picrate is loose, this turn of PC-0 seems reasonable in principle. The presence of free volume makes the structural rearrangement of the picrate radical to a more reactive structure possible via the transformation of one of the NO2 groups into the nitrite group:

O

O O

O N

O

O

O N

N O

PC-1 + NO

N

O

P-2 + P-3

O

–

N O

O

PC-0

P-4 + NO 2

O N O Product X

The X center is thermally unstable and undergoes parallel decomposition into three genetic radical pairs. The stability of these pairs depends on the following two processes: recombination and diffusion of a light fragment into the bulk. Evidently, NO and O–, which are small, can diffuse, whereas more bulky NO2 cannot diffuse. Earlier [16], we reported the formation of a KNO2 phase, which is possible only in the presence of mobile NO and O– capable of diffusing to reaction regions enriched in cationic interstitials in the crystal. The possibility of pair recombination is consistent with the fact that the thermal decay of pairs is described by the laws of polychronous kinetics. Paramagnetic center 1, which is thermally stable to the onset recombination temperature (373 K), undergoes radiation decay. This is likely due to secondary ionization, as a result of which PC-1 loses the unpaired electron. Probably, this process is reversible in a radiation field. The general scheme of radical processes in potassium picrate is as follows.

Product X PC-1 + NO PC-1+

–

–

PC-2 + PC-3 ( O )

PC-4 + NO 2

KNO2

The kinetics of formation and decay of PC-1 was mathematically simulated, and the fullest set of reliable data was obtained for this species up to the onset temperature of recombination [17]. A simplified scheme of this process is as follows: Ä

GaI k1

Ç

k2

ë

GcI

products,

where A, B, and C are the picrate anion, the unstable radical containing a nitrite group, and the 2,6-dinitropara-quinone radical, respectively. The set of rate equations has the following form: HIGH ENERGY CHEMISTRY

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d[A] ------------ = – G a I [ A ] + k 1 [ B ], dt d[B] ------------ = G a I [ A ] – ( k 1 + k 2 ) [ B ], dt d[C] ------------ = k 2 [ B ] – G c I [ C ]. dt Here, Ga and Gc are the radiation-chemical yields of degradation for species A and C, respectively; I is the dose rate absorbed by the system as a whole; and k1 and k2 are reaction constants according to the scheme. Denoting gc = GcI, g‡ = G‡I, and k = k1 + k2 and solving the above set of differential equations in the general form, we obtain rate equations for every particular member of the scheme: ga – k  λ λ - sinh  --- t [ A ] ( t ) =  [ A ] 0 cosh  --- t – -----------2   λ 2 

313

repeated irradiation, when [Ç]0 = 0 and [ë]0 = cmax, the concentration [C] initially decreases because of radiation decay and begins to increase again only after attaining a sufficient concentration of radical B. The mathematical simulation of processes occurring on the irradiation of potassium picrate with the use of these rate equations demonstrated that the above scheme explains the effects of additional postradiation formation and initial decay of the 2,6-dinitro-para-quinone radical during second irradiation after a dark pause at a semi-quantitative level (disregarding the pathways of radiation decay of an iminoxyl radical and potassium picrate consumption in other reactions). The kinetic curve obtained by mathematical simulation for changes in the concentration of the 2,6-dinitro-para-quinone radical at G‡/GÒ = 0.05 adequately describes the experimental results in terms of the scheme proposed. CONCLUSIONS The results of this study were surprising to us for two reasons. First, the fact itself that radicals stable up to 400 K can be produced in an energetic material, which undergoes thermal degradation and is capable of explosion, was hardly expected. Second, the temperature transformation of an EPR spectrum—the unresolved diffuse singlet at 77 K and the appearance of hyperfine splitting at T > 300 K—is unusual.

ga + k

-t 2k λ  – ------------2 , + [ B ] 0 --------1 sinh  --- t e 2  λ 

g  λ [ B ] ( t ) =  [ A ] 0 ----a sinh  --- t 2  λ  ga + k

-t ga – k λ λ  – ------------2 - sinh  --- t e + [ B ] 0 cosh  --- t + -----------, 2  2  λ 

REFERENCES

[ C ] ( t ) = [ C ] 0 exp ( – g c t ) ga + k – -------------- t 2

k 2 ga e  λ -  [ A ] 0 exp ( – g c t ) + cosh  --- t + ------------------------------------------------- 2 ga k 2 – gc ( ga + k – gc )  ( g a + k – 2g c ) λ - sinh  --- t – -------------------------------2  λ g a – g c  –gc t λ - e – cosh  --- t  + [ B ] 0 ------------- 2  ga  ga ( ga + k 1 – k 2 ) – gc ( ga – k )  λ - sinh  --- t , – ----------------------------------------------------------------  2 λg a  2

where λ = ( g a + k 1 – k 2 ) + 4k 1 k 2 and [Ä]0, [Ç]0, and [ë]0 are the concentrations at the beginning of irradiation. The shape of a kinetic curve depends on initial conditions, i.e., on [Ä]0, [Ç]0, and [ë]0. Thus, on continuous irradiation, a practically linear increase in concentration [C] is observed after an induction period. During a dark pause when Gc, Ga = 0, the concentration [C] increases to a certain value ëmax; simultaneously, a symmetric decrease in [B] is observed. In the course of HIGH ENERGY CHEMISTRY

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1. Harrowfield, J.M., Skelton, B.W., and White, A.H., Aust. J. Chem., 1995, vol. 48, no. 7, p. 1311. 2. Ketskalo, V.M., Serikov, L.V., Sharapova, L.A, and Yurmazova, T.A., Abstracts of Papers, 7 Vsesoyuznaya konferentsiya po radiatsionnoi khimii (7 All-Union Conf. on Radiation Chemistry), Moscow, 1983, p. 41. 3. Makarevich, G.G., Borzdun, V.N., Pak, V.Ch., and Ryabykh, S.M., Abstracts of Papers, First International Congress on Radiation Physics and Chemistry of Condensed Matter, Tomsk, 2000, p. 64. 4. Wertz, J.E. and Bolton, J.R., Electron Spin Resonance: Elementary Theory and Practical Applications, New York: McGraw-Hill, 1972. Translated under the title Teoriya i prakticheskoe prilozhenie metoda EPR, Moscow: Mir, 1975. 5. Bazhin, N.M. and Tsvetkov, Yu.D., STS spektrov EPR svobodnykh radikalov (Hyperfine Structure of EPR Spectra of Free Radicals), Novosibirsk: Novosib. Gos. Univ., 1971. 6. Buchachenko, A.L. and Vasserman, A.M., Stabil’nye radikaly (Stable Radicals), Moscow: Khimiya, 1973. 7. Pokhodenko, V.D., Fenoksil’nye radikaly (Phenoxyl Radicals), Kiev: Naukova Dumka, 1969. 8. Faber, R.J. and Fraenkel, G.K., J. Chem. Phys., 1967, vol. 47, no. 8, p. 2462. 9. Makarevich, G.G., Pak, V.Kh., and Ryabykh, S.M., Materialy 10-oi Mezhdunarodnoi konferentsii po radiatsionnoi fizike i khimii neorganicheskikh materialov

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15. Makarevich, G.G., Pak, V.Kh., and Ryabykh, S.M., Abstracts of Papers, 2 Mezhdunarodnaya konferentsiya “Radiatsionno-termicheskie effekty i protsessy v neorganicheskikh materialakh” (2nd Int. Conf. on Radiation-Thermal Effects and Processes in Inorganic Materials), Tomsk, 2000, p. 112. 16. Makarevich, G.G., Pak, V.Kh., Pugachev, V.M., and Ryabykh, S.M., Khim. Vys. Energ., 1999, vol. 33, no. 4, p. 314 [High Energy Chem. (Engl. transl.) 1999, vol. 33, no. 4, p. 269]. 17. Semenov S.V., Makarevich G.G., Pak V.Kh., and Ryabykh S.M., Abstracts of Papers, 8 Mezhdunarodnaya konferentsiya “Fiziko-khimicheskie protsessy v neorganicheskikh materialakh” (8th Int. Conf. on Physicochemical Processes in Inorganic Materials), Kemerovo, 2001, p. 100.

HIGH ENERGY CHEMISTRY

Vol. 38

No. 5

2004