Laser Initiation of Energetic Materials: Selective Photoinitiation

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Laser Initiation of Energetic Materials: Selective Photoinitiation Regime in Pentaerythritol Tetranitrate Edward D. Aluker,† Alexander G. Krechetov,† Anatoliy Y. Mitrofanov,† Denis R. Nurmukhametov,† and Maija M. Kuklja*,‡ † ‡

Department of Physical Chemistry, Kemerovo State University, Kemerovo, 650043 Russia Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742, United States ABSTRACT: We describe and analyze the selective (resonance) laser-induced initiation of chemical decomposition reactions in pentaerythritol tetranitrate (PETN, C5H8N4O12) and propose a potential mechanism for the phenomenon. On the basis of our experiments, the photoinitiation of PETN is a two-stage process that is comprised of a laser-induced optical excitation of the molecule with an activation energy of 1.17 eV (1060 nm) by a neodymium phosphate glass laser followed by the thermal decomposition of the excited state with an energy barrier of 0.4 eV. We also illustrate that the small efficiency of the optical absorption of PETN at this wavelength can be enhanced by the MgO light-scattering additives, which significantly increase the absorption due to multiple scattering incidents in PETN. The resonance photoinitiation clearly demonstrates a possibility for designing tunable explosive material systems and identifies ways to control the sensitivity of the materials to rapid decomposition.

I. INTRODUCTION There are many exciting new opportunities and practical applications for the laser initiation of energetic materials, particularly in solving problems related to security and safety.1-3 We could have successfully used those opportunities had we known how exactly the laser irradiation interacts with the materials and how to control these interactions. The detailed microscale understanding of the laser initiation process and mechanisms that transfer a fairly modest amount of optical energy into a large chemical energy in high energy density materials is far from being complete. In this article, we will shed some light on this issue, and although we will not be able to resolve the challenge, we will describe and analyze new observations, formulate the key questions, and identify a strategy for controlling the sensitivity of highly energetic materials. The overwhelming majority of authors address one property of laser initiation, the impact of the large energy density of the initiating impulse on a sample (target). The most often discussed models of laser initiation, such as hot spots and electric breakdown due to the field of the light wave, etc.,1,2 also focus on analyzing the high energy density of the laser pulse. It is generally believed that the dominating mechanism in the initiation of chemical decomposition is thermal, and the focused energy of the laser serves as a source of heat to stimulate the thermal dissociation of bonds. The wavelength of the laser radiation employed does not appear to be particularly important in these kinds of studies. In the meantime, the fundamental feasibility of photoinitiation had been discussed for many years;4 however, a laser-induced fragmentation of energetic r 2011 American Chemical Society

materials through an excited-state path has been demonstrated only recently for metal azides5 and some organic materials.6,7 In the photoresonance phenomena we explore here, the wavelength and optical absorption play a key role. It is worthwhile to point out that the initiation and the early stages of the chemical reaction of explosive decomposition, i.e., solid-state or pre-explosion stages,3 proceed in the nondestroyed, crystalline lattice of the energetic material. Hence, the solid-state physics approach is the most appropriate approach for studying and describing these phenomena. In particular, by applying the solid-state physics approach to exploring the earliest stages of initiation, sometimes called pre-explosion phenomena, it has been established that in at least some crystalline energetic materials the explosive decomposition reactions are of a chain character, and electronic excitations (quasiparticles) play the role of active chemical radicals in triggering the chemical decomposition.8-10 Therefore, the question arises as to whether it is possible to create conditions in which the active radicals would be directly generated due to photon absorption of the initiating radiation of the crystalline lattice. It is clear that in this case the energy of the initiating photons must fall into an actual absorption band, i.e., in resonance. Hereafter, we will use the term “resonance photoinitiation” in reference to the selective photon absorption by

Received: September 17, 2010 Revised: February 4, 2011 Published: March 17, 2011 6893

dx.doi.org/10.1021/jp1089195 | J. Phys. Chem. C 2011, 115, 6893–6901

The Journal of Physical Chemistry C molecules or local sites (e.g., impurity, point defect), which leads to the generation of active particles (radicals). Further evidence for such selective (or resonance) photoinitiation is very desirable. There is a significant difference in the energy management between selective photoinitiation and other ways of initiation, in which the external energy is pumped up in the entire crystalline lattice where only a small fraction of the energy goes to the generation of active particles, whereas the energy of the initiating pulse absorbed during laser excitation is expended to directly generate active particles. This efficiency coupled with the high selectivity of the process (that is, photoinitiation only in the narrow optical absorption region for a specific material) creates the prerequisite for a significant reduction of the threshold energy of the initiating pulse. There are many potential applications of this method.1 In addition, the enormous experience and vast arsenal of solid-state optics methods can be used to control the photoinitiation process in practical materials, which is, to say the least, very exciting and promising. In the meantime, an experimental observation of resonance photoinitiation is possible only if the wavelength of the initiating laser pulse falls in the range of the optical absorption of the energetic material. Given the limitations of the modern powerful pulse lasers suitable for initiation, a certain amount of luck is required for satisfying this condition. Hence, it is not surprising that the first experiments to evidence a possibility of the resonance photoinitiation regime were performed only recently.11-14 This article presents an extended analysis of these phenomena in the context of the most recent developments in the field. Specifically, we show that the two-stage resonance photothermal decomposition of PETN can be triggered by a neodymium phosphate glass laser with a modest initiation energy (1060 nm) followed by the thermal dissociation of the excited state with a thermal energy at 0.4 eV. Most importantly, we show that the efficiency of the decomposition process can be controlled by light-scattering additives. This opens up an opportunity to optically tune the sensitivity of high energy density material systems to initiation, which leads to a considerably safer and highly reliable use and handling of high explosives and potentially to the elimination of the problem of accidental explosions and fires.

II. SAMPLES AND EXPERIMENTAL METHODS By their nature, explosive experiments are multiscale and multifaceted experiments. Hence a necessary provision for obtaining the unambiguous and reliable physical results is a careful choice of experimental setup, which allows for the exclusion of side effects and uncontrollable factors. The standard methodology of laser initiation experiments is based on initiating samples through an encapsulated pressed tablet of an energetic material. The samples normally do not explode without the encapsulating shell, probably due to a premature shatter of the material in the reaction zone.1,2 Here, the experimental results strongly depend upon the particle size dispersion of the explosive powder, conditions of pressing the powder to make tablets, properties of the encapsulating shell’s material, the size of the irradiated region, and so on.1 To minimize the potential effects of these factors, we use the following restrictions in preparing and initiating the samples. 1. The thermal treatment of samples occurs directly within the measurement cell (Figure 1). Samples are prepared out

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Figure 1. Duration of the induction period: (a) schematic representation of the measurement apparatus: 1 is a photoelectron amplifier (PEA), 2 are light filters, 3 is a photodiode, 4 is a probe laser, 5 is a sample, and 6 is a Cooper heater; (b) electric current measured by PEA registering explosive glowing; and (c) electric current measured by photodiode registering the intensity of the probe laser.

of PETN powder with a grain size of ∼10 μm. Mounted powder (the sample) (20 mg) is placed in the cavity of the copper (Cu) heater in the measurement cell and heated to 450 K. The samples are ignited after cooling to a certain temperature. (The melting temperature of PETN is 414 K, so the samples are melts above 414 K and solids at the lower temperatures.) This procedure affords the possibility to initiate an open sample (with no encapsulating shell) at T > 350 K, and it allows us to avoid using the supporting shell, to exclude uncertainties related to the pressing conditions, and to standardize the content of the products of the thermal decomposition emerging during the thermal treatment. At lower temperatures, the energy of the laser was insufficient for initiating the explosion. To reduce the energy that is necessary for initiation, we modified the 6894

dx.doi.org/10.1021/jp1089195 |J. Phys. Chem. C 2011, 115, 6893–6901

The Journal of Physical Chemistry C

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experimental conditions by covering the sample’s surface with a quartz plate, by using the supporting shell, or by adding 0.1-1% weight powder of MgO with a grain size of ∼10 μm to the samples. The size distribution of MgO particles is well described by a Gaussian with a full width at half-maximum of ∼5 μm. Due to multiple scattering from MgO particles, the photon trajectory in the sample elongates, increasing the absorption probability, and allows for a reduction in the initiation energy. 2. For the initiation, we used the first (1060 nm) and second (530 nm) harmonics of the pulse (10 ns) neodymium phosphate glass laser. The laser beam was focused onto the sample, and the diameter of the beam (4-8 mm) exceeded the sample’s diameter (2 mm). Since both the first and second harmonics fall in the region of the optical transparency of PETN,13 the thickness of the samples (∼2 mm) ensures the homogeneity of initiation by a homogeneous distribution of the absorbed energy in the sample. Under these conditions, the decomposition reactions can be explored without complications introduced by the propagation of the detonation wave.3 Due to the stochastic nature of the initiation process, the energy threshold is commonly used as the main energy characteristic of the laser initiation of energetic materials, that is, the exposure value, or the ratio of the amount of energy, H0.5, deposited onto the sample surface to the surface area that provides a 50% probability explosion.1 To determine the initiation energy threshold, the dependence of the frequency of explosion incidents, p, on the initiation exposure was investigated at different initial temperatures. The measurement of the duration of the induction period at the initiation temperatures is illustrated in Figure 1. In additional experiments, PETN samples were examined using both the first and second harmonics (1064 and 532 nm) of an Nd:YAG pulse (∼30 ps) laser. Measurements of single PETN crystal extinction spectra were performed by means of a Shimadzu UV-3600 spectrophotometer, which was modified in such a way that the vacuum cell with the built-in thermoelectric battery was mounted in the measurement chamber. This modification allowed for variations in sample temperature in the range of 210-370 K.

III. RESULTS III.1. Effect of Temperature on the Initiation Threshold and the Duration of the Induction Period. We observed that

the initiation by the first harmonic (1060 nm) in a rather wide temperature range, 350-450 K, which falls above and below the melting temperature, caused the explosion of open-surface PETN samples. Examples of explosion incident frequency as a function of the initiation exposure are depicted in Figure 2a. The initiation threshold characteristics were obtained from the displayed functions. In particular, we were interested in the energy initiation threshold, H0.5, the initiation exposure that yields an explosion in 50% of incidents, and the extrapolated threshold, Hmin, the value of which was determined by the extrapolation of a linear region of p as a function of H (Figure 2a). Both of these parameters decrease with an increase in temperature (Figure 2b), and the following relationship describes this behavior well within the experimental accuracy (Figure 2c), with an activation energy of E = 0.4 ( 0.05 eV. p ¼ 1 - e-AðH - Hmin Þe

-E=kT

Figure 2. Effect of temperature on the efficiency of laser initiation of PETN with an open surface (1060 nm, 20 ns). (a) Examples of probability of explosion p as a function of initiation exposure H at two temperatures: 1 at 425 K and 2 at 350 K. b correspond to experimental-E/kT data, and the solid line is an approximation by eq 9: p = 1 - e-A(H-Hmin)e , at E = 0.4 eV. Hmin is the extrapolated threshold. (b) Dependence of H0.5 (curve 1) and Hmin (curve 2) upon temperature. (c) ln H as a function of 1000/T.

We note that this temperature dependence is characteristic only for the laser initiation, as the threshold dependence upon temperature was not observed in shock initiation control experiments. An increase of the initiation energy density and an increase of the sample’s temperature lead to a reduction in the duration of the induction period ti (Figure 3). It is noteworthy that the dependence of ti upon temperature is much weaker than the temperature dependence of the initiation threshold (Figures 2 and 3). To extend the temperature range and to reduce the initiation threshold, we, as mentioned above, had to modify the experimental conditions in two ways. The first way is a well-known method of covering the sample surface with a quartz plate; the 6895



Figure 3. Effect of temperature T and exposure of initiation H on the duration of the induction period ti. (a) Example dependencies correspond to different temperatures: 1, measurements are made at 400 K, 2-440 K. (b) Example dependencies correspond to different exposures of initiation: 1, measurements are made at 1.5 J/cm2 and 2, at 18 J/cm2. b, 2 show experimental data, while the solid line is an approximation by eq 15, ti = τ(ln(Nmax/(R0H)) þ (E/kT)), at τ = 0.7 μs and E = 0.4 eV.

formation of the supporting shell1,2 allows us to reduce the low temperature limit to 300 K. The second way represents the method developed here that utilizes the introduction of lightscattering additives into the sample. This effectively increases the trajectory of a photon within the sample and significantly enhances the absorption of the energy of the initiating light. This method proved to be quite effective (Figure 4a) and allowed us to decrease the lower limit of the temperature range to 300 K even for initiating the open-surface samples. We emphasize that the considerable change in the initiation threshold caused by the introduction of light-scattering additives (Figure 4a) applies only to laser initiation. This is illustrated in Figure 4b, which shows the probability of explosion as a function of MgO particle concentration in the PETN/MgO mixture samples. The control experiments on shock initiation fall short in supporting any noticeable effect of MgO powder additives on the initiation threshold. The initiation threshold values, H0.5, obtained under various experimental conditions, such as the open or closed surface and the presence or absence of light-scattering additives, significantly differ from each other. Hence, it is convenient to introduce the normalized threshold as Hn ¼

H0:5 ðTÞ H0:5 ðT0 Þ

where H0.5(T) and H0.5(T0) denote the values of H0.5 under the

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Figure 4. Effect of light-scattering additives on the efficiency of laser initiation (1060 nm, 20 ns) of PETN is illustrated by: (a) experiments with PETN with an open surface at 350 K. 1 represents pure PETN; 2 stands for the PETN þ 0.5% MgO mixture; p is the probability of initiation; and H is the exposure of initiation and (b) the probability of explosion of PETN þ MgO mixtures as a function of MgO particle concentration at H = 30 J/cm2 and T = 300 K. Note that in the PETN þ MgO samples there are three different types of interfaces, PETN/air, PETN/MgO, and MgO/air. Light scattering occurs at each of those interfaces.

current, T, and initial, T0, temperatures, respectively (Figure 5). Figure 5 shows that with more complicated conditions of initiation (such as the closed surface or in the presence of the lightscattering additives) the temperature dependence is preserved only at sufficiently high temperatures. The decrease in temperature leads to a significant change in the nature of this dependence. III.2. Initiation Selectivity and Absorption Spectra. Unexpectedly, from the energetic point of view, attempts at laser initiation of PETN by the second harmonics (530 nm) failed even at an energy density of ∼10 J/cm2 and temperatures of ∼450 K. Recall that at 450 K the initiation threshold of the first harmonic does not exceed 0.5 J/cm2 (Figure 2b). Hence, there is a clear difference between the efficiency of initiation at wavelengths of 1060 and 530 nm, which is evidence in favor of a selectivity of the initiation process. Consequently, the question of what portion of the energy deposited by various harmonics can be absorbed by the sample arises. On the basis of the optical absorption spectra measurements of PETN performed with the spectrophotometer (Shimadzu UV-3600), we found a weak band with the maximum around ∼1020 nm and the extinction coefficient of æ e 0.1 cm-1 (Figure 6). Control experiments showed that when the temperature of the sample varies in the range 210-370 K this band remains practically unchanged. We underline here that the first harmonic falls in the region of the observed band, which suggests 6896



Figure 5. Normalized initiation threshold as a function of temperature: open circles correspond to pure PETN with an open surface, filled circles show PETN covered with a quartz plate, and stars show PETN with an open surface and 0.5% MgO additives. The solid line shows an approximation with eq 14, Hn = De(E/kT), at E = 0.4 eV.

Figure 6. Extinction spectrum of a PETN single crystal at 300 K is shown. (1) shows the full spectrum and (2) represents the spectrum at an enlarged scale.

that the differences in the effectiveness of initiation of the first and second harmonics are due to the selective absorption in this band.

IV. DISCUSSION IV.1. Initiation Energy and Light Scattering. The observed differences in the effectiveness of initiation of the first and second harmonics fall short in finding an explanation within the traditional mechanisms of laser initiation (hot spots or light-induced breakdown1,2). Note that the observed selectivity of initiation at 1060 nm is consistent with the data15 on the initiation by a ruby laser (693 nm). The authors report that even with an exposure of 30 J/cm2 they could not ignite open-surface PETN melt samples, whereas according to our data, the initiation threshold at 1060 nm does not exceed 5 J/cm2 (Figure 2c). On the other hand, the observed selectivity finds its natural explanation in terms of the resonance photoinitiation mechanism: only the first harmonic of the neodymium phosphate glass (1060 nm) falls into the actual absorption band (Figure 6), which leads to the much more economical mode of photoinitiation. To test this assumption, it is useful to compare the energy of the laser initiation and the electron beam initiation. The fact is that in the case of the electron beam initiation the energy is

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pumped up into the entire crystalline lattice; a large fraction of it dissipates in heating the lattice; and nonselective excitation takes place.16 Unlike this, in the case of photoinitiation, the selective excitation of specific chemical bonds takes place, which has to affect the overall initiation efficiency. According to electron beam experiments,17 the threshold of the total density of the absorbed energy in the initiation of open-surface PETN at 300 K was found to be on the order of 1000 J/cm3. In contrast, the data extrapolation in Figure 2 at 300 K shows that the first harmonic initiation within the same conditions leads to an exposure threshold not exceeding 100 J/cm2. Taking into account the absorption coefficient of æ < 0.1 cm-1 (Figure 6), the total density of the absorbed energy is æH e 10 J/cm3, 2 orders of magnitude smaller than that of the electron beam initiation. Hence, based on energetic considerations, laser initiation with λ = 1060 nm happens to be much more efficient than the electron beam initiation. We would like to reiterate that the high efficiency of the first harmonic initiation is most likely due to the economic character of resonance photoinitiation, in which almost all of the absorbed energy is directed to the formation of electronic excitations. In contrast, electronic beam initiation suffers significant losses of the absorbed energy due to heat dissipation in the crystalline lattice.18 Thus, we obtained two important arguments in favor of the hypothesis that the first harmonic initiation with the neodymium phosphate glass laser (1060 nm) induces the resonance photoinitiation regime in PETN. These include (a) the energetic analysis of the initiation process, illustrating the dramatic differences in the efficiency of initiation with λ = 1060 nm, λ = 530 nm, and λ = 693 nm and (b) the discovery of an absorption band with a maximum around 1020 nm in the optical absorption spectra of PETN (Figure 6). However, despite the high efficiency of the resonance photoinitiation of PETN at λ = 1060 nm, practical applications of this initiation regime are limited due to the small absorption coefficient in the actual absorption band (æ < 0.1 cm-1), which causes a large fraction of the initiating light to transmit through the sample without being absorbed. An increase in absorption can be achieved by increasing the photon free path in the sample. Simply increasing the sample’s thickness was not particularly helpful, as the critical parameter of initiation is not the total number of molecules, but a local concentration of excited molecules.18Thus, not just the absorbed energy but rather the total energy density is important. In other words, we have to increase the photon pathway in the samples without changing the sample volume. The simplest way to solve the problem is to extend the photon free path due to multiple scattering by incorporating the light-scattering additives. Now, we perform a simple mathematical analysis to estimate the feasibility of the effect. Following the Bouguer-Beer law, the absorbed fraction of the energy deposited onto the pure PETN sample that is consumed to generate electronically excited states can be expressed as η0 = 1 - exp[-æd], where æ < 0.1 cm-1 (λ = 1060 nm, Figure 6), and taking d ∼ 1 mm (d is the thickness of the sample) and æd , 1, one can set η0 ≈ æd. The photon free path in the sample, L, will play the role of the d parameter. Taking into account the multiple light-scattering events, the fraction of the absorbed energy would be ηs = 1 - exp(-æL), which becomes ηs ≈ æL at æL , 1. The efficiency of the proposed method may be quantified by the amplification coefficient Ks = ηs/η0. Taking æd , 1 and æL , 1 Ks ¼ 6897

L d

ð1Þ



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The value of Ks can be linked to the concentration and the cross section of the light-scattering additives. The movements of a photon in a sample can be described by a random walk.19 Then rffiffiffi n ð2Þ L ¼ nl, d ¼ l 3 where l is the photon free path length relative to the light scattering, and n is the average number of scattering incidents. By substituting the relationship l = 1/σN, where σ is the scattering cross section and N is the concentration of the scattering centers, into (1) and (2), we get Ks ¼ 3σdN

ð3Þ

By using the σ parameter, the geometric cross section of the lightscattering particles,20 σ ∼ 10-6 cm2 at r ∼ 10 μm, the sample thickness of ∼1 mm, and the concentration of the light-scattering particles N ∼ 106 cm-3 (the corresponding weight concentration of the additives here is ∼1%), eq 3 yields the values of Ks equal to a few units. This estimate is well-supported by experiments, as illustrated in Figure 4. Qualitatively similar results were also obtained using Al, Si, and Ag as light-scattering particles. We note that MgO is one of the best diffusive reflector materials, and therefore, an initiation-induced heating of the MgO particles is not an issue. The analysis described above is valid for an ideal scattering, while a nonideal scattering leads to some radiation absorption by the scattering centers, which can be described as follows æ ¼ æ0 þ æa and q ¼ q0 þ qa

shock, electric spark, etc., which, in fact, vividly illustrates the possibility of designing a tunable energetic material system. IV.2. Effect of Temperature and Energy on the Initiation Processes. In this section, we attempt to build a phenomenological model of the early stages of initiation reactions. Our experimental investigations have established that while the explosion probability is a strong function of the energy of the initiating pulse and the initial temperature of the sample (Figure 2) the dependence of the duration of the induction period on these parameters is fairly weak (Figure 3). Also, the strong dependence of the initiation efficiency on the sample’s initial temperature is characteristic only for laser initiation as in impact or shock experiments, the initial temperature of the sample barely makes any difference in the efficiency. The simple explanation for these observations lays in the fact that the revealed temperature dependences are determined by the influence of temperature on the primary act of photoinitiation (formation of active radicals upon the absorption of photons). The temperature dependence of the subsequent stages of the process, multiplication of radicals, can be neglected in the first approximation. Now, consider the following assumptions: 1. At the early reaction stage, multiplication of active particles, e.g., NO2 moieties,9 is described by an exponential dependence characteristic of chain reactions21 N ¼ N0 et=τ

where N0 and N are the initial and the current concentration of the active particles, respectively; τ is the characteristic time of the reaction build up; and t is the time from the moment of initiation. 2. The critical parameters to determine the reaction initiation, described by eq 6, and its termination are the average concentrations of active particles,19 Nmin and Nmax. In particular, Nmin is the threshold concentration (minimal) induced by the initiating pulse (note that eq 6 is valid only at N0 g Nmin because the reaction decays at N0 < Nmin); Nmax is the limiting concentration (maximal) for the sample to explode, i.e., the sample breaking point leading to a termination of active particle multiplication by eq 6.22,23 Both Nmin and Nmax are assumed not to depend upon temperature and the initiation energy. 3. The initial concentration of active particles is proportional to the exposure H

ð4Þ

where æ, æ0, and æa are the initiation absorption coefficients of the light-scattering enhanced PETN sample, pure PETN, and the light-scattering additives, respectively, and q, q0, and qa are the total absorption energy density of the enhanced PETN, pure PETN, and the light-scattering additives, respectively. In the case of nonideal scattering, from eq 4, and the Bouguer-Beer law for the amplification coefficient, we obtain KR ¼

æ0 1 - expð- æLÞ æ 1 - expð- æ0 dÞ

Further, taking into account eq 2 and the æ = σN relationship, we get Ka ¼

C1 f1 - exp½-ðC3 N þ C4 N 2 Þg, 1 þ C2 N

ð6Þ

N0 ¼ RH and Nmin ¼ RHmin

ð5Þ

ð7Þ

where R is a coefficient and Hmin is the minimal initiation exposure. Within these assumptions, the duration of the induction period, ti, is the time during which the concentration reaches its maximum Nmax. In other words, from eqs 6 and 7, we derive

where C1 = [1 - exp(-æ0d)]-1, C2 = σR/æ0, C3 = 3d2σsæ0, C4 = 3d2σsσR, and σs and σR are the cross sections of light scattering and photon absorption, respectively. Equation 5 shows that the optimal concentration of light-scattering centers corresponds to a maximum in KR, which is in good agreement with the data shown in Figure 4b. We think that the experiments with the light-scattering additives can be regarded as yet another rather significant argument in support of the validity of the resonance mode of photoinitiation. The effect of light-scattering additives creates an array of novel, interesting opportunities of practical applications of the photoinitiation regime. Not only is the initiating energy pulse selective, but this also brings about a chance to significantly reduce the energy of the initiating pulse without changing the sensitivity of the energetic material to other perturbations, such as impact,

ti ¼ τ ln

Nmax RH

ð8Þ

Now, let us consider how to obtain the probability of explosion, p, as a function of initiation exposure. At an increase dN0 in the concentration of active particles N0, induced by an initiating impulse, a reduction of the probability of “survival” of the sample, dr, i.e., that it will not explode, is proportional to the probability that it “has survived” earlier (at concentration N0) and to the size of the increment in concentration dN0, dr = βrdN0, where β is 6898



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a coefficient. By integrating this expression with r = 1 and N0 < Nmin and taking into account relationships 7 and the probability of explosion p = 1 - r, we obtain p ¼ 1 - e-RβðH - Hmin Þ

ð9Þ

Equation 9 describes the experimental data well in the working range of p = 0.2-0.8 (Figure 2a). The initiation threshold, H0.5, can be obtained from eqs 7 and 9 H0:5 ¼

A ln 2 where A ¼ Nmin þ R β

ð10Þ

If the necessary stage of the initiation process is a thermally activated transition into a dissociative state, for example, the thermally activated dissociation of the photoexcited PETN molecule, leading to the NO2 radical formation, then R ¼ R0 e-E=kT

ð11Þ

In this case, eqs 8-11 provide a direct comparison with the experimental curves shown in Figures 2 and 3 -E=kT

p ¼ 1 - e-BðH - Hmin Þe

, where B ¼ R0 β

ð12Þ

Hmin ¼ C 3 eE=kT , where C ¼ Nmin =R0

ð13Þ

1 ln 2 Nmin þ H0:5 ¼ D 3 eE=kT , where D ¼ ð14Þ R0 β and

Nmax E þ ti ¼ τ ln R0 H kT

ð15Þ

Expressions 12-15 accurately describe the whole set of experimental results presented in Figures 2 and 3 at the same value of the activation energy, 0.4 ( 0.05 eV. This is a vital illustration of the adequacy of the proposed model. It is also necessary to emphasize that if the initiating pulse instantly creates a concentration of active particles equal to or greater than the critical concentration (N0 > Nmax) the pre-explosive process is absent, i.e., ti = 0, and thus, the area of the existence of pre-explosive processes is: Nmin e N0 e Nmax. IV.3. Photoactivated Decomposition of the PETN Molecule. We would like to note here that the exact nature of the photoactivated decomposition of PETN as well as of the absorption band detected in the experiments is not yet established; therefore, we only suggest and discuss some possible interpretations. There are several observations we attempt to comprehend and interpret: 1. The decomposition is a two-step process that includes photo- and thermally stimulated phases as only the joint action of a laser pulse and temperature initiates explosion. At T g 350 K, a thermally activated phase of the photoinduced decomposition requires an activation energy of 0.4 eV (Figure 2c). There are, in principle, two variants that differ by a sequence of events. They are: (a) a photothermal process (a photostimulated transition from the ground state to an excited state (hν = 1.17 eV) and the subsequent thermally activated (0.4 eV) fragmentation of the excited state) and (b) a thermo-optical process (a thermally activated

formation of a starting state and the subsequent photoinduced fragmentation of this state). 2. The temperature dependence of the threshold of initiation and the duration of the induction period does not change behavior during the melting of the sample, and any features of the dependence near the melting temperature are not observed (Figures 2 and 3), which is evidence in favor of an intramolecular process rather than a crystalline process. 3. The photoinitiation process is connected, apparently, with the absorption band at λ = 1020 nm (Figure 6). The independence of this band with respect to temperature is indicative of the fact that the corresponding optical transition occurs from the ground state, the population of which does not depend on temperature. We argue that the activation energy of PETN decomposition determined in this study, 1.17 þ 0.4 = 1.57 eV (36.11 kcal/mol), is a sum from the two decomposition steps that occur sufficiently close in time; therefore, a single activation energy can be used here as a meaningful quantity. We note that the energy of 1.57 eV is in remarkable agreement with the activation energy 1.58 eV (36.33 kcal/mol) found in spectroscopic and thermal experiments,24 in which the same product, the NO2 moiety, resulted from a onestage thermoactivated process. This energy falls slightly below the range of energies reported based on theoretical calculations, 1.64 eV (37.75 kcal/mol),25 1.74 eV (39.95 kcal/mol),26 and 1.9 eV (43.71 kcal/mol),27 and also attributed to O-NO2 bond fission. We suggest the following scenario to interpret our observations. The initiating pulse excites and breaks the chemical bond(s) in the PETN molecule, which leads to the formation of the active radical(s)28 and triggers the explosive decomposition chain reaction.10 The rupture of the O-NO2 bond with the formation of the NO2 radical appears as the most probable initial decomposition step, which is also the most supported by experiments24 and calculations.31 For definiteness, we will concentrate on this version, although, strictly speaking, the nature of the resulting radical does not have to be specified as only the fact that it has formed is important at this point. An immediate question comes up: how can the initiating pulse of 1.17 eV (1060 nm) trigger the photodecomposition, while the optical band gap of PETN is calculated to fall into the range from 4.2 eV [ref 29] to 5.96 eV [ref 30], depending on the level of theory used? The discrepancy dictates that a dramatic reduction of the splitting between ground and excited-state terms should take place for the optical transition to occur. According to the excitonic mechanism,9 this can happen similarly to the suggested band gap narrowing near edge dislocations in PETN31 and RDX,9,31 shear-strain-induced deformations in DADNE,32-35 or bond-bending in TATB.36 Such a local band gap reduction is now considered to be well established. On one hand, it is recognized that the probability of the band gap narrowing is considerably enhanced for the fast processes when the system is far from equilibrium (under extreme conditions, such as high pressure, high shear strain, or high temperature).33 On the other hand, the reduction required in our case (factor of 4) appears large and needs to be carefully justified. Also, while the band gap narrowing due to dislocations or shear deformations is an essentially solidstate effect and would contradict the intramolecular nature of the process (see 2), the molecular bond-bending does not. Hence, if bond-bending occurs in PETN, an appreciably lower excitation energy [than from the ground-state equilibrium minimum] is able to drive the molecule to the excited-state potential energy 6899


The Journal of Physical Chemistry C surface.37 This model, although appealing, appears problematic to us as it is expected that such a process would require sufficiently elevated temperatures and be deactivated under cooling.38 Further, the role of the lowest singlet-triplet intersystem crossing in molecular nitric acid, the simplest model of O-NO2 bonded PETN, has been illustrated using ab initio complete active space self-consistent field (CAS SCF) wave functions.39 It was found that in the lowest triplet state equilibrium structure of the nitric acid molecule the nitro group is no longer coplanar with the O atom, in contrast to the equilibrium geometry of the ground-state singlet. Furthermore, the CAS SCF fully optimized triplet potential energy curve confirms that the triplet is adiabatically bound with respect to the O-NO2 bond dissociation pathway, with an energy barrier of 15 kcal/mol (0.65 eV).39 Note this is in good agreement with 10 kcal/mol (0.4 eV), the activation energy of the thermal phase from our measurements on PETN. A counterargument for this scenario is that this process has to be strongly dependent upon temperature, while the optical absorption band discovered here does not change with a temperature increase. Furthermore, we suggest that the decomposition of PETN observed in our experiments is defined by a combined two-step process, the photostimulated transition from a deformed configuration singlet to the excited triplet state (with an activation energy of 1.17 eV, λ = 1060 nm) and the thermally stimulated dissociation of this state with the splitting off of the NO2 radical (with an activation energy of 0.4 eV).28 This process is dominant in the purest experimental conditions on the initiation of pure open-surface PETN (Figure 2). With the increasing complexity of the initiation conditions that involve a closed surface or the introduction of additives, the photothermal process dominates only at high temperatures as evidenced by the changing character of the temperature dependence of the initiation threshold (Figure 5). Most likely, the reason for this change is the presence of another, possibly competing mechanism of initiation, which begins to play a significant role only when the photothermal mechanism is deactivated at sufficiently low temperatures.

V. SUMMARY AND CONCLUSIONS A series of laser initiation experiments were performed for several types of PETN samples including open-surface samples, confined samples, and samples with light-scattering additives. We found that the initiation with the neodymium phosphate glass laser first harmonic (1060 nm, energy density not exceeding 0.5 J/cm2) is fundamentally different from that with the second harmonic (530 nm), which fails to initiate explosion even at the initiation density of ∼10 J/cm2 and temperature of ∼450 K. The first harmonic initiation induces a selective photoexcitation of PETN molecules, which leads to the formation of active radicals and originates the explosive decomposition reaction. This selective photoinitiation is a two-stage decomposition process, which includes the photoexcitation of PETN molecules (possibly deformed by the out-of-plane bending of the NO2 group) and the subsequent thermally stimulated (0.4 eV) dissociation of the molecule from its excited triplet state with the formation of active particles (most likely, the NO2 radicals). The effectiveness of the resonance photoinitiation is significantly higher than that of the nonselective mode of initiation (e.g., electron beam) due to the fact that in the case of resonance photoinitiation almost all of the absorbed energy is spent on the formation of relevant excited states of the molecules. In the

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nonselective modes of initiation, a large portion of the energy dissipates by heating the lattice, and only a small part of it is spent on the formation of the relevant excited states. The practical use of the resonance photoinitiation of PETN is limited by the small absorption coefficient at λ = 1060 nm. This causes the vast majority of the initiating radiation to pass through the sample without interaction. Therefore, a convenient method for improving the energy efficiency of the initiating radiation is the introduction of light-scattering additives into the sample. The multiple scattering of photons occurring in this case leads to a lengthening of their trajectories in the sample and increases the probability of the light absorption. While the introduction of light-scattering additives can significantly reduce the laser initiation threshold, it does not affect the magnitude of the threshold for shock initiation, which opens up attractive prospects for the practical use of the resonance photoinitiation methodology. In conclusion, the considered mechanism of resonance photoinitiation by no means excludes the widely discussed nonselective initiation scenarios (hot spots, light-induced breakdown, etc.). Depending on the conditions of the photoinitiation regime in a real experiment, the dominant role is played by one mechanism or another. It is in this sense that we are investing in the phrase “mode of initiation”, as used in this article. The advantage of and, perhaps, the most intriguing uniqueness of the resonance photoinitiation regime lies in a fundamental plausibility of the realization of a tunable threshold for initiation of PETN samples. It is extremely important that such a tuning of the threshold and, in turn, tuning of the sensitivity of the energetic material system to detonation initiation is related only to the resonance photoinitiation regime without affecting the thresholds of the nonselective mechanisms of initiation (impact, shock, etc.). This is crucial in improving the safety of explosives and in the design of new energetic materials. We also emphasize that the proposed method of increasing the efficiency of the resonance photoinitiation by introduction of light-scattering additives is a special case of the method of sensitizing additives widely used in studies of phosphors and photographic materials.40 Therefore, an extensive experience in this field can be applied to the studies of resonance photoinitiation of energetic materials.

’ REFERENCES (1) Fast Initiation of Explosives. Special Regimes of Detonation: A Collection of Articles; Tarzhanov, V. I., Ed.; RFYaTs VNIITF: Snezhinsk, 1998; p 168 [in Russian]. (2) Bourne, N. K. On the fast ignition and initiation of explosives. R. Soc. London A 2001, 457, 1401–1426. (3) Aluker, Ed. D.; Aduev, B. P.; Zakharov, Yu. A.; Mitrofanov, A. Yu; Krechetov, A. G. Early Stages of Explosive Decomposition of Energetic Materials. Focus Combust. Res. 2006, 55–88. (4) Evans, B. L.; Yoffe, A. D. Proc. R. Soc. London, Ser. A 1959, 250, 346–366. (5) Zakharov, Yu. A.; Aluker, 0 E. D.; Aduev, B. P., et al. Preexplosion Phenomena in Heavy Metal Azides; Khimmash: Moscow, 2002; [in Russian]. (6) Bernstein, E. R. Overviews of Recent Research on Energetic materials; Thompson, D., Brill, T., Shaw, R., Eds.; World Scientific: NJ, 2004. (7) Kunz, A. B.; Kuklja, M. M.; Botcher, T. R.; Russel, T. P. Thermochim. Acta. 2002, 384, 279–284. . D.; Belokurov, G. M.; Zakharov, Yu. A.; (8) Aduev, B. P.; Aluker, E Krechetov, A. G. JETP 1999, 89 (5), 906–923. (9) Kuklja, M. M.; Stefanovich, E. V.; Kunz, A. B. J. Chem. Phys. 2000, 112, 3417–3423. 6900


The Journal of Physical Chemistry C (10) Kuklja, M. M.; Aduev, B. P.; Aluker, E. D.; Krasheninin, V. I.; Krechetov, A. G.; Mitrofanov, A. Yu. J. Appl. Phys. 2001, 89, 4156–4166. (11) Aluker, E. D.; Krechetov, A. G.; Loboiko, B. G.; Nurmukhametov, D. R.; Filin, V. P.; Kazakova, E. A. Russ. J. Phys. Chem. B, Focus Phys. 2008, 2 (3), 375–377. (12) Aluker, E. D.; Aluker, N. L.; Belokurov, G. M.; Krechetov, A. G.; Loboiko, B. G.; Nurmukhametov, D. R.; Tupitsyn, A. V.; Filin, V. P. Russ. J. Phys. Chem. B, Focus Phys. 2010, 4 (1), 63–65. . D.; Krechetov, A. G.; Yu., A.; Mitrofanov, D. R.; (13) Aluker, E Nurmukhametov, A. V.; Tupitsyn Tech. Phys. Lett. 2009, 35 (11), 1051–1053. . D.; Belokurov, G. M.; Krechetov, A. G.; Mitrofanov, (14) Aluker, E A. Yu.; Nurmukhametov, D. R. Tech. Phys. Lett. 2010, 36 (3), 285–287. (15) Ng, W. L.; Field, J. E.; Hauser, H. M. J. Appl. Phys. 1986, 59, 3945–3952. (16) Lehman, Chr. Interaction of Radiation with Solids and Elementary Defect Production; North-Holland Publishing Company: Amsterdam and New York, 1977; p 296. (17) Korepanov, V. I.; Lisitsyn, V. M.; Oleshko, V. I.; Tsypilev, V. P. Tech. Phys. Lett. 2003, 29 (8), 669–671. (18) A vivid analogy with the photo- and radioluminescence immediately comes to mind. A direct photoexcitation of luminescent centers (photoluminescence) is known to be much more efficient than the radiation-induced excitation of the crystalline lattice (radioluminescence); see, for example: Aluker, E. D.; Lusis, D. Y.; Chernov, S. A. Electronic Excitation and Radioluminescence of Alkali Halide Crystals; Zinatne: Riga, 1979; p 251 [in Russian]. (19) Heer, C.V. Statistical Mechanics. Kinetic Theory and Stochastic Processes; Academic Press: New York, 1972; p 600. (20) van de Hulst, H. C. Light Scattering by Small Particles; John Wiley & Sons, Inc.: New York; Chapman & Hall, Ltd.: London, 1957. (21) Semenov, N.N. Some problems of chemical kinetics and reactivity; Pergamon Press: London, 1958; p 685. (22) Aluker, E. D.; Belokurov, G. M.; Krechetov, A. G.; Aduev, B. P.; Loboyko, B. G.; Filin, V. P. Two Stages of the Energy Release of Explosive Decomposition of Heavy Metals Azides. AIP Conf. Proc. 2006, 849, 196-200 (Zababakhin Scientific Talks - 2005: International Conference on High Energy Density Physics). As was shown, the fragmentation of the heavy metal azide samples occurs already at a sufficiently low temperature (∼200 K), and most of the energy release and heating (∼3500 K) occur at the stage of expansion of explosion products. Perhaps, something similar can also take place in PETN. See also ref 3. (23) It is also possible that the fracture of the sample is caused by the gaseous reaction products that destroy the crystalline lattice due to their high kinetic energy rather than due to heating. The analogy with radiation blistering is appropriate here; see, for example: Thompson, M.W. Defects and radiation damage in metals; Cambridge Univ. Press: New York, 1969; p 384. (24) Makashir, P. S.; Kurian, E. M. Propellants, Explos., Pyrotech. 1999, 24, 260–265. (25) Wu, C. J.; Ree, F. H.; Yoo, C. S. Propellants, Explos., Pyrotech. 2004, 29, 296. (26) Fried, L. E.; Manaa, M. R.; Pagoria, P. F.; Simpson, R. L. Annu. Rev. Mater. Res. 2001, 31, 291. (27) Landerville, A. C.; Oleynik, I. I.; White, C. T. J. Phys. Chem. A 2009, 113, 12094–12104. (28) Attention is drawn to the sufficiently deep analogy between this process and a well-known process in radiation physics of solid state, an exciton decay into a pair of Frenkel defects (see ref 18). (29) Conroy, M. W.; Oleynik, I. I.; Zybin, S. V.; White, C. T. Phys. Rev. B 2008, 77, 094107. (30) Perger, W. F. Chem. Phys. Lett. 2003, 368, 319–323. (31) Kuklja, M. M.; Kunz, A. B. J. Appl. Phys. 2001, 89, 4962–4970. (32) Kuklja, M. M.; Rashkeev, S. N.; Zerilli, F. J. Appl. Phys. Lett. 2006, 89, 071904. (33) Kuklja, M. M.; Rashkeev, S. N. Phys. Rev. B 2007, 75, 104111. (34) Kuklja, M. M.; Rashkeev, S. N. Appl. Phys. Lett. 2007, 90, 151913.

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(35) Kuklja, M. M.; Rashkeev, S. N. Modeling of defect induced phenomena in energetic materials. In Hydrostatic Compression of Energetic Materials; Peiris, S., Piermarini, G., Eds.;Springer-Verlag: New York, 2008; Chapter 8, pp 322-361. (36) Manaa, M. R.; Fried, L. E.; Reed, E. J. J. Comput.-Aided Mater. Des. 2003, 10, 75–97.KLUWER/ESCOM; Kluwer Academic Publishers: Netherlands, 2004. (37) Since PETN absorption spectra in the near-infrared region are insufficiently studied, it is difficult to propose a well-justified model of the nature of this state at this time. (38) We would like to reiterate that the idea of a pronounced correlation between the observed absorption band at 1020 nm and the band gap narrowing of an ideal PETN molecule is hypothetical and requires complex and computationally demanding ab initio calculations to refine and accept or reject this model. We are grateful to a reviewer of this manuscript who suggested an alternative explanation based on a possible extrapolation of the vibrational overtone sequence as partially observed in: Paisley, D.L. 9th Symposium on Detonation Proceedings; Portland; Office of Naval Research: Washington, DC, 1989; pp 11101117, Figure 3. A difficulty with this model is the lack of a reasonable explanation of why there is a dramatic difference in absorption caused by overtone(s) near 1020 nm and other overtones in the sequence. (39) Manaa, M. R.; Fried, L. E. J. Phys. Chem. A 1999, 103, 9349–9354. (40) Gurvich, A. M. Introduction to the Physical Chemistry of Crystal Phosphors; Vysshaya Shkola: Moscow, 1982; p 375 [in Russian].

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Laser Initiation of Energetic Materials: Selective Photoinitiation

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