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Reactive Wave Propagation Mechanismsin Energetic Porous Silicon CompositesVenkata Sharat Parimia, Srinivas A. Tadigadapab & Richard A. Yetteraa Department of Mechanical and Nuclear Engineering, ThePennsylvania State University, University Park, Pennsylvania, USAb Department of Electrical Engineering, The Pennsylvania StateUniversity, University Park, Pennsylvania, USAPublished online: 10 Dec 2014.

To cite this article: Venkata Sharat Parimi, Srinivas A. Tadigadapa & Richard A. Yetter (2015) ReactiveWave Propagation Mechanisms in Energetic Porous Silicon Composites, Combustion Science andTechnology, 187:1-2, 249-268, DOI: 10.1080/00102202.2014.973493

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Combust. Sci. Technol., 187: 249–268, 2015Copyright © Taylor & Francis Group, LLCISSN: 0010-2202 print / 1563-521X onlineDOI: 10.1080/00102202.2014.973493

REACTIVE WAVE PROPAGATION MECHANISMSIN ENERGETIC POROUS SILICON COMPOSITES

Venkata Sharat Parimi,1 Srinivas A. Tadigadapa,2

and Richard A. Yetter11Department of Mechanical and Nuclear Engineering, The PennsylvaniaState University, University Park, Pennsylvania, USA2Department of Electrical Engineering, The Pennsylvania State University,University Park, Pennsylvania, USA

Propagating reactive waves through porous silicon (PS)–sodium perchlorate composites andthe generation of shock waves in the gaseous medium above the PS surface were studiedusing high-speed shadowgraphy. Propagation speeds were varied by changing the PS spe-cific surface area (SSA) and the dopant type and level, and by the addition of organizedmicrostructures along the wave propagation direction. Shadowgraph analysis showed thatupstream permeation of hot gaseous combustion products was responsible for a two order ofmagnitude enhancement in the reactive wave propagation speeds obtained by the presence oforganized microscale patterns on PS samples with low SSA (∼ 300 m2/g), which nominallyexhibit baseline speeds of ∼ 1 m/s. Shadowgraph analysis and sound speed measurementson PS samples with high SSA (∼ 700 m2/g), which exhibit fast reactive wave propagations of∼ 1000 m/s, indicated that neither the strong shock over the PS surface nor detonation of theporous layer were the mechanisms by which the wave propagated. Thermal analysis of PSshowed that the heat release from exothermic reactions between PS and the oxidizer withinthe pores shifted to lower temperatures as the SSA of PS increased, which was accompaniedby a reduction in the activation energy associated with the lowest temperature exothermicreaction between PS and the oxidizer. The combined experiments indicated that a combina-tion of conductive and convective burning, possibly assisted by fast crack propagation withinthe silicon/porous silicon substrate, was responsible for the observed difference in propaga-tion speeds and was the mechanism by which the reactive wave propagated with speeds onthe order of a km/s within the porous layers.

Keywords: Micropyrotechnics; Nanoenergetic materials; Porous silicon; Shadowgraphy

INTRODUCTION

Traditional monomolecular and composite energetic materials (EMs) have been usedfor several decades for a wide variety of civilian and military applications, and significantadvances have been made in terms of understanding and formulating traditional EMs. EMs

Received 15 August 2014; revised 1 October 2014; accepted 2 October 2014.Published as part of the Special Issue in Honor of Professor Forman A. Williams on the Occasion of His

80th Birthday with Guest Editors Chung K. Law and Vigor Yang.Address correspondence to Venkata Sharat Parimi, Department of Mechanical and Nuclear Engineering,

The Pennsylvania State University, University Park, PA 16802, USA. E-mail: [email protected] versions of one or more of the figures in the article can be found online at www.tandfonline.com/

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250 V. S. PARIMI ET AL.

can be classified as propellants or pyrotechnics, which release energy by slow deflagrationprocesses with associated time scales on the order of seconds, and explosives, which releasetheir energy rapidly over microsecond timescales. As a result of extensive research efforts,traditional explosives that are typically organic monomolecular compounds are well under-stood, and significant advances have been made in formulating such materials. However,the energy densities of traditional EMs are limited by the enthalpies of product speciesformed (typically CO2 and H2O), resulting in low volumetric and gravimetric energy den-sities (Dreizin, 2009). Recently, there has been a significant interest in miniaturizationto exploit the increased efficiency and performance and reduced cost of microscale sys-tems. Integration of EMs onto microscale platforms is considered to be a promising meansto power and actuate microelectromechanical systems (MEMS) and overcome the scaleeffects associated with the reduced length scales (Rossi and Estève, 2005). While the lim-itation on energy densities of traditional EMs are not apparent at macroscale applications,the increased heat losses at reduced dimensions render most EMs incapable of sustain-ing a reactive wave propagation at sub-millimeter length scales (Rossi et al., 2007). Whileorganic EMs suffer from limited energy density due to the product species formed, sig-nificantly higher energy densities can be obtained upon combustion of metals (Dreizin,2009). Unlike monomolecular organic EMs whose combustion processes are kineticallycontrolled, the ignition and combustion of metal particles are usually in the diffusion con-trolled regime. Micrometer scale metal particles have large ignition delays and burn timeswhen incorporated into EM formulations, as the oxidizing species or the metal vapor typ-ically need to diffuse through the native oxide layer to initiate and sustain the reaction,resulting in poor combustion efficiencies (Babuk and Vasilyev, 2002; Glassman and Yetter,2008; Price, 1995; Williams, 1997).

With recent advances in material sciences, nanoscale and/or nanostructured metalparticles can be produced in a controlled manner and can be accurately characterized. Oneof the obvious advantages of using nanoscale metal particles in EM formulations is thegreatly reduced transport length scales, which translates into smaller reaction time scalesresulting in increased combustion efficiencies. In addition, the shrinking dimensions resultin enhanced surface-to-volume ratios, and as the dimensions of metal particles approach afew nanometers, the behavior of the nanoparticles starts to deviate significantly from thebulk material. Since the coordination number for the atoms at the surface is always lesserthan the bulk atoms, and the proportion of surface atoms increases significantly at smalldimensions (Klabunde et al., 1996), the behavior of nanoscale metal particles approachesthe behavior of the surface atoms. In terms of EMs, the increased reactivity and reducedmelting temperatures are particularly attractive, as these affect the ignition and combus-tion time scales. Significant progress has been made on incorporating nanoscale metalparticles in EM formulations, and the EMs containing nanoscale metal particles, termednanoenergetic materials (nEMs). Detailed reviews of the state of the art of nEMs can befound elsewhere (Piercey and Klapötke, 2010; Rossi et al., 2007; Yetter et al., 2009; Zhouet al., 2014). Thermites consisting of nanoscale aluminum and molybdenum trioxide mixedby ultrasonic agitation have already been shown to sustain reactive wave propagations inmicroscale channels (Son et al., 2007), and the successful implementation of novel self-assembly methods to create an ordered fuel-oxidizer matrix (Malchi et al., 2009) can furtherreduce the transport length scales and increase the combustion performances.

Aluminum nanoparticles have been extensively used as additives in EMs and innanothermite formulations, the different regimes of aluminum combustion have beendescribed, and several mechanisms have been proposed to explain the high-speed reactive

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REACTIVE WAVE PROPAGATION IN PS COMPOSITES 251

wave propagations, as described elsewhere (Yetter et al., 2009). Another nanostructuredmetal-based reactive composition of interest is porous silicon (PS), which is essentiallycrystalline silicon with highly developed internal surfaces formed by selective dissolutionof silicon atoms in hydrofluoric acid (HF) based electrolytes (Canham, 1997). PS can havespecific surface areas (SSAs) as high as 1000 m2/g, and the high reactivity of the sur-face atoms can be exploited to form energetic composites with various oxidizers rangingfrom liquid oxygen at cryogenic temperatures (Kovalev et al., 2001) to common inorganicsolid oxidizers (Clément et al., 2005). One significant advantage of PS-based energeticmaterials over nanoaluminum is that the PS surfaces are hydrogen terminated, and despitethe small feature sizes (∼ 1 nm), only a small amount of the silicon is oxidized (Parimiet al., 2014b). The hydrogen terminated surfaces make PS an attractive EM capable ofhydrogen storage, and also avoid the incorporation of significant mass fraction of non-energetic oxide layers, as is the case with nanoaluminum particles. Much of the researchon PS is driven by the fact that its base material is silicon, which is the base material ofchoice for MEMS. While many nEMs are capable of sustaining reactive wave propaga-tions at micrometer length scales, the increased reactivity of nEMs generally renders themmore sensitive, which make integration of the nEM and exploitation of the energy released(known as micropyrotechnics) difficult. Since PS can be formed by simple electrochemical,stain (Canham, 1997), or galvanic (Ashruf et al., 1999) etch processes, PS is expected to becompatible with standard microfabrication processes, making its integration onto MEMSeasier. Simple monolithic MEMS with PS-based energetic composites have already beensuccessfully demonstrated (Currano and Churaman, 2009). For micropyrotechnic applica-tions, the performance of EMs is quantified by their volumetric energy density, also knownas the actuation pressure parameter (Rossi and Estève, 2005). Bomb calorimeter studiesby Becker et al. (2010) indicate that energy densities as high as 10 MJ/kg(Si) have beenobtained for non-optimized PS-NaClO4 systems itself, placing PS based composites amongthe most energy dense EMs.

While the reactive wave propagation in PS–oxidizer composites has been describedpreviously, the purpose of this article is to identify the different reactive wave propagationregimes in porous silicon combustion, and elucidate the effect of the interaction between thecondensed and gas phases on the reactive wave propagation within the porous layers. Thereactive wave propagation speeds reported previously range from the order of 1 m/s (Parimiet al., 2012, 2014a) to several hundreds of m/s (Churaman et al., 2010; Parimi et al., 2012,2014a; Plummer et al., 2011) to several thousands of m/s (Becker et al., 2010; Churamanet al., 2010; Piekiel et al., 2014). Reactive wave propagation speeds of 3660 m/s reportedby Piekiel et al. (2014) are among the highest speeds reported for nEMs. The slow speedsless than 10 m/s were typically obtained on PS etched on heavily doped P- or N-type sili-con substrates (resistivity between 0.001 to 0.005 �-cm), and were attributed to conductiveburning. Faster propagation speeds ∼100 m/s were observed by Parimi et al. (2012, 2014a)in PS samples etched on low doped N-type silicon substrates (phosphorus doped, resistiv-ity between 2 to 5 �-cm), which developed random micrometer scale crack patterns duringthe electrochemical etch process. Similar high speeds ∼ 100 m/s were observed by Parimiet al. (2012) on PS etched from heavily doped P-type silicon substrates that were patternedusing microfabrication techniques to create microscale structures. These trends indicate thatthe micro-crack patterns are one mechanism for high-speed propagations, and the enhance-ment in the reactive wave propagation speed was attributed to gas permeating ahead of theflame front (convective burning) or damage to the nanoporous structure ahead of the flamefront, resulting in localized ignition spots. Kovalev et al. (2001) identified that PS is very

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efficient at utilizing mechanical energy to break Si–Si bonds and create free radicals, dueto the mechanically discontinuous nature of the porous layer. Some of the highest speedsobtained by Piekiel et al. (2014) were found to be comparable, and in some cases, slightlygreater than the speed of sound in PS measured by Brillouin spectroscopy (Fan et al., 2002),indicating that the high-speed reactive wave propagation might be a detonation.

In the present work, we study the reactive wave propagation in PS samples usinghigh-speed shadowgraphy to provide further mechanistic insight into the wave propagationmechanisms. PS samples etched on heavily doped P-type substrates (resistivity between0.001 to 0.005 �-cm) with different configurations of organized microscale structuresexhibiting reactive wave propagation speeds up to 150 m/s, and PS samples etched onlow doped P-type substrates (resistivity between 10 to 20 �-cm) exhibiting reactive wavepropagation speeds up to 1500 m/s are studied. Also, we combine the observations fromhigh-speed shadowgraphy with ultrasonic speed of sound measurements and kinetic anal-ysis using differential scanning calorimetry (DSC) to provide further understanding of theorigins of the high-speed reactive wave propagation and the factors that influence it.

SAFETY

Energetic composites prepared by impregnating oxidizers within PS can be very sen-sitive, and appropriate care must be taken while handling these samples. Researchers areurged to work with small samples until they are familiar with PS–solid oxidizer compos-ites. Furthermore, hydrofluoric acid used to etch PS is extremely toxic and corrosive, andappropriate precautions must be taken to ensure safety.

EXPERIMENTAL METHODS

Porous silicon was prepared by an electrochemical etch process using an electrolyteconsisting of a 1:1 (by volume) solution of 30% aqueous HF and ethyl alcohol in a custometch cell as described elsewhere (Parimi et al., 2012). The etched PS was characterized bymeans of scanning electron microscope (SEM) images and gas adsorption measurements(Brunauer et al., 1938). The etched silicon wafers were scribed and cleaved into test sam-ples 5 mm wide, and with lengths between 30 mm and 50 mm. Sodium perchlorate wasimpregnated within the nanoscale pores to create energetic composites as described previ-ously (Parimi et al., 2014a). For the PS etched on heavily doped silicon substrates, the testsamples were soaked in saturated sodium perchlorate/methanol solutions for several hours(12–16 h), and then mounted on a glass slide using a double-sided adhesive tape. For PSsamples etched on low doped P-type substrates, the samples were mounted on a glass slide,and then several drops of the saturated oxidizer solution were applied on the PS surface.The PS samples were then dried by heating them in a vacuum chamber, and then ignited byan electric spark, or a 10 ms pulse from a 200 W continuous wave CO2 laser.

To study the effect of microscale structures on the reactive wave propagation, squarepillars (10 µm × 10 µm base) and microchannels with different channel widths (5, 15, and25 µm) with a fixed silicon wall thickness (15 µm) were etched on the silicon substrates.The fabrication was accomplished by coating the silicon wafers with a thick positive pho-toresist (Megaposit SPR-955) followed by photolithography and deep reactive ion etch(DRIE) to create the microscale patterns. The aspect ratio of the microscale patterns wasvaried by changing the duration of DRIE. The photoresist was then stripped from the sili-con substrates (using an acetone/isopropyl alcohol bath followed by heating the wafers to

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80 ◦C for 1 h in Remover-PG), and was followed by an electrochemical etch to create PS.The photolithography, DRIE, and the scribing and cleaving of the test samples were carriedout such that the PS samples consisted of an unpatterned section and a patterned section.The reactive wave was initiated in the unpatterned PS and allowed to propagate into thepatterned PS. This allowed the unpatterned PS to be used as a baseline, and also separatedthe effect of ignition transients from the effect of microscale features on the reactive wavepropagation.

Due to the surface hydrogen termination, combustion of PS produces a large volumeof gaseous products (Churaman et al., 2010; Currano et al., 2009). The behavior of the hotgaseous products during the reactive wave propagation was studied by igniting the samplesin a focused shadowgraph system (Settles, 2001). A schematic of the experimental setupused for high-speed shadowgraphy is shown in Figure 1. The illumination was providedusing a 300 W Xe arc lamp, and the collimated beam for the test section was created usingtwo 100 mm diameter plano-convex lenses with a focal length of 300 mm. The shadow-gram was focused onto the image sensor of a high-speed camera (Vision Research PhantomV310) using a focusing lens (Nikon 28mm f/2.8) and was recorded at frame rates between80000–250000 fps.

The longitudinal speed of sound in PS (LA) was measured by microechography usinga scanning acoustic microscope, similar to the method previously used to measure the speedof sound in PS (Fonseca et al., 1995). The PS samples were placed in water below animmersion-type ultrasound resonator with a central frequency of 75 MHz, and the timetaken for the reflections from the PS/water and the PS/Si interfaces to return to the trans-ducer was measured. The thickness of the PS layer measured from SEM images was usedto calculate the longitudinal wave speed in PS.

The activation energy for the chemical reaction between PS and sodium perchloratewas estimated from DSC experiments using a Netzsch STA 449 F1 Jupiter TGA/DSC andthe method proposed by Kissinger (1957). Kissinger’s analysis can be used to estimatethe activation energy for solid–solid reactions regardless of the reaction order, based onthe shift in the temperature of exothermic peaks as a function of heating rates. The DSCtraces for PS treated with sodium perchlorate indicate a low temperature exothermic reac-tion occurring significantly below the temperatures at which oxidizer starts to decompose.

Figure 1 Schematic of the focused shadowgraphy system used in this work.

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This low temperature oxidation reaction is called the “back-bond oxidation,” and involvesthe oxidation of Si–Si bonds of the Si atoms attached to the surface hydrogen terminatedsilicon atoms (Salonen et al., 1997). Since the low temperature back-bond oxidation occursbefore the oxidizer decomposes, it is a solid–solid reaction similar to the ones considered byKissinger, and the activation energy for the low temperature back-bond oxidation reactionscan be calculated from

d ln(

φ

T2p

)d

(1Tp

) = −EaR

(1)

where φ is the heating rate, Tp is the temperature of the exothermic peak, R is the universalgas constant, and Ea is the activation energy. To obtain the temperatures of the peaks as afunction of heating rates, samples containing 1–2 mg of PS were treated with a dilute 0.4 Msodium perchlorate/methanol solution, and heated in the DSC with an inert environmentat several different heating rates (10 K/min, 20 K/min, and 40 K/min). The maximumobtainable heating rates were limited by the equipment.

RESULTS AND DISCUSSION

Effect of Microscale Structures on Reactive Wave Propagation

In our previous work, we have shown that for PS etched on heavily doped P-typesubstrates, the reactive wave propagation speeds obtained were below 10 m/s. The lowspeeds observed were consistent with the hypothesis that the reactive wave propagationwas driven by conductive heat transfer, as predicted by thermochemical equilibrium cal-culations and a proposed reaction model (Parimi et al., 2014a). The addition of an arrayof square pyramidal pillars that were 8 µm square base and 35 µm tall was found toresult in an enhancement of the reactive wave propagation speeds by up to two ordersof magnitude. This geometry was revisited here using high-speed shadowgraphy to exam-ine the effect of the microscale pillars on the gaseous product flow. Figure 2 illustratesthe square pillars created. A series of high-speed shadowgraph images from a single videodepicting several phenomena that occur as the sample is ignited in the unpatterned region,with the reactive wave being allowed to propagate into the patterned region, is shown inFigure 3.

The sample is ignited on the unpatterned PS by means of an electrical spark, andthe transient ignition process results in the formation of a weak spherical shock as seenin Figures 3a and 3b. During the reactive wave propagation in the unpatterned region, asseen in Figures 3a–3f, it can be seen that the plume comprising the hot gaseous productsis directed away from the direction in which the reactive wave propagates. However, whenthe reactive wave enters the patterned region, there is a clear permeation of the hot gasesahead of the luminous flame front, as shown in Figures 3g–3l. The permeation of the hotgaseous products ahead of the luminous flame front indicates that the reactive wave prop-agation is occurring by means of convective heat transfer, and that the enhancement of thereactive wave propagation speed is by transition from a conductive burning mechanism toconvective burning. For the sample shown in Figure 1, the reactive wave propagation speedin the nonpatterned and patterned regions was 4.3 m/s and 137 m/s, respectively. Further,

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Figure 2 SEM images of the square cylindrical pillars etched on heavily doped P-type substrates. (a) Top viewshowing 12 µm × 12 µm square bases separated by 7 µm. (b) The silicon–PS interface. (c) Side view of thesquare cylindrical pillars and the PS layer etched on the silicon substrate. The PS layer below the pillars is 133µm thick, and the initial thickness of the silicon wafer was 525 µm. (d) Side view of a pillar showing the sidewallprofile arising due to the plasma etch process (DRIE). The pillars are 57 µm tall. The curvature in the side wallprofile is due to the isotropic component of the DRIE.

it can be seen from Figures 3g–3k that the shock and the luminous front are decoupled.The spherical shock front expands with a nearly constant speed of 419 m/s, whereas theluminous zone only moves at 137 m/s. The decoupling of the shock and the luminous zonealso indicates that the enhancement is due to convective heat transfer by the gaseous prod-ucts, and not the interaction of the shock front, with the PS resulting in the formation oflocalized ignition fronts due to mechanical damage to the PS.

This directionality of the plume arises from the fact that the combustion of PS occursheterogeneously at the surface and the gaseous reaction products are generated at a solidsurface. The solid boundary forces the gases to be ejected in a direction away from thereactive wave propagation direction, as shown in Figure 4. However, in the case of thesmall pillars protruding above the PS surface, it can be expected that they disintegrateand burn rapidly, that is, explode, causing the hot gaseous products to be ejected in alldirections. This process is believed to be the mechanism responsible for the permeation ofthe gases ahead of the luminous reaction zone. Plummer et al. (2011) attributed the erraticand infrequent “flame jump” observed in Figures 3c and 3d to the detachment of the PSfilm from the silicon substrate due to the pressure build up within the porous layer. Suchskipping has been observed at speeds ranging from < 10 m/s in our work to speeds above3000 m/s in Piekiel et al.’s (2014) work. While the mechanism for the flame skippingmight be different between the vastly different propagation speeds, the crystalline nature ofPS and the underlying silicon substrate makes it possible for the PS film to crack and ignitedue to mechanical stresses generated from temperature gradients near the reaction zone andthe thrust experienced by the sample.

Based on the observations from the shadowgraph images presented here and thefour different configurations of the samples with microstructures tested in our previouswork (Parimi et al., 2012), the parameters controlling the reactive wave propagation speedenhancement by convective burning can be summarized as follows:

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Figure 3 Series of images from the high-speed side view shadowgram captured for samples in which the non-patterned PS was ignited and the reactive wave was allowed to propagate into the patterned region. The high-speedvideo was recorded at a frame rate of 80590 fps, with an exposure of 1.02 µs. Note the nonlinear time scales used.The dark strip seen on the left side in each of the images in the panel is the side view of the silicon wafer and themounting block placed in the shadowgraph system depicted in Figure 1. (a) and (b) Consecutive images acquiredfollowing the ignition of the PS sample by a spark. The arrows point to the location of the weak shock that wasgenerated upon ignition. (c) and (d) depict the formation and growth of a localized ignition front resulting in a“flame jump.” (e) and (f) show the steady state propagation, and (f) is the frame right before the reactive waveencounters the patterned region. In (a)–(f), the plume containing the hot gaseous products is directed away from thedirection the reactive wave propagates. (g) shows the shock formation when the reactive wave enters the patternedregion. (h), (i), and (j) show that the shock and the reactive wave are decoupled. In (g)–(l), gas permeation aheadof the luminous flame front can be seen.

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Figure 4 Schematic explaining the directionality of the gaseous product plume seen in Figure 3. In the nonpat-terned region, the gaseous products formed at the reaction zone are confined in the upstream direction by thesilicon substrate and the PS layer, forcing the gases to be ejected in a direction away from the reactive wave prop-agation. However, the small micrometer sized pillars are expected to disintegrate and burn, or explode, resultingin the gaseous products being ejected ahead of the reaction zone, resulting in convective burning.

1. The permeability of the microscale structure: The permeability depends on the geometryof the microscale patterns etched, and provides the resistance to the flow of the gaseousreaction products in the upstream direction.

2. The spacing between the microscale features: An enhancement in the burning rate isobserved as long as the convective heat transfer to the adjacent microscale PS ele-ment from the reaction zone occurs faster than the time taken for the purely conductivereactive wave in the underlying PS film to cover the same distance. When the spac-ing between the microscale structures is too large or too small, it can be expected thatthere will be no convective burning, and the reactive wave propagation will approachthe purely conductive burning attained in unpatterned PS.

3. The height of the microscale features above the PS base, which controls the surface areaand the volume of the microscale feature: This controls the heat transfer by convectionand also the volume of gas phase reaction products generated. The height and spacingalso affect the permeability of the microscale patterns.

In case of the square pillars, the three parameters cannot be independently varied. To obtainbetter control over the three parameters described, PS samples with a different geometryof microscale pattern, that is, microchannels, were prepared. Reactive wave propagationperpendicular to the microchannels restricts the upstream gas flow, as any gases generatedat the reaction zone cannot travel any further than the next side wall they encounter. Thespacing and the height can thus be varied independently by changing the feature size onthe mask and changing the DRIE duration. When the reactive wave propagates along thedirection of the microchannels, a fraction of the gases generated from the reaction zonecan travel along the microchannel and heat the side walls. This provides a pathway withhigh permeability for the gaseous products. A representative image of the microchannelsis shown in Figure 5. Test samples were ignited on nonpatterned PS, and the reactive wavewas allowed to propagate into the region patterned with the microchannels. The reactive

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Figure 5 Representative SEM image of the microchannels etched on PS samples. For the PS sample shown inthis figure, the spacing between the sidewalls is 8 µm, and the thickness of the sidewalls is 12 µm. The height ofthe sidewalls is 82 µm, and the thickness of the PS layer below is 118 µm. The curvature in the side wall profileis due to the isotropic component of the DRIE.

wave propagation speed observed in the nonpatterned region was 4.6 ± 0.5 m/s (average± standard deviation) between the several samples tested. The effect of the microchannelson the reactive wave propagation was as follows:

1. When the reactive wave propagation was perpendicular to the microchannels, a slightincrease in the reactive wave propagation speeds was observed, and the maximumobserved speed was 15.1 m/s.

2. When the reactive wave propagation was parallel to the microchannels, a larger enhance-ment in the reactive wave propagation speeds was observed. The maximum observedspeed was 51.2 m/s.

3. No specific dependence of the reactive wave propagation speed on just the depth or thewidth of the microchannels was observed.

However, when the reactive wave propagation speeds in the patterned region were plot-ted as a function of the channel aspect ratio (distance between the sidewalls/height of theside walls), they show a dependence on the aspect ratio, as shown in Figure 6, indicatingthat the higher propagation speeds were observed at lower aspect ratios. The low enhance-ment of the reactive wave propagation speeds in the perpendicular configuration indicatesthat the gas permeation has the strongest effect on the enhancement. The pillar structures inwhich the gases could permeate ahead of the reaction zone exhibited speeds above 100 m/s,whereas the maximum speed observed in the perpendicular configuration was limited to15.1 m/s. Further, the parallel configuration showed higher enhancements than the perpen-dicular configuration, despite only a fraction of the gas being driven ahead of the reactionzone. The aspect ratio of the microchannels is phenomenologically the inverse of the ratio

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Figure 6 Reactive wave propagation speeds parallel and perpendicular to the microchannels etched on heavilydoped P-type PS as a function of the void aspect ratio. No specific dependence of the reactive wave propagationspeed on the channel width or height was observed. The highest speeds were obtained when the reactive wavepropagation was along the microchannels, and at low void aspect ratios.

of the flow resistance to the gas flow to escape through the top opening and to be driven inthe upstream direction. Thus, as the aspect ratio reduces, a higher fraction of the gaseousproducts can be expected to be driven along the microchannels (especially in the paral-lel configuration), resulting in higher reactive wave propagation speeds. This interpretationis consistent with the observations on pressure driven flow in Al/CuO nanothermites bySullivan et al. (2012, 2013).

Reactive Wave Propagation in Low Doped P-Type Substrates

High speeds on the order of ∼ 1000 m/s have been reported on PS etched on lowdoped P-type substrates with resistivity > 1 �-cm. In this section, we present an exam-ination of the reactive wave propagation in low doped P-type substrates etched using anelectrochemical process with the same parameters as reported previously (Churaman et al.,2010). The etched porous layers were 35 µm thick, and gas adsorption measurementsindicated a SSA of 730 m2/g and a porosity of 0.67. The samples were impregnated bysodium perchlorate by drop-casting the saturated oxidizer solution on the sample surface,and were ignited by an electric spark. The samples exhibited reactive wave propagationspeeds on the order of 1000 m/s. The reactive wave propagation speed was supersonicwith respect to the air surrounding the sample, and a shock driven by the reactive wavefront was observed in the shadowgrams. At the surface of the PS sample, the shock orien-tation was normal to the surface, and the static temperature and pressure jump conditionsacross the shock are

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P2P1

= 2γ M2s

γ + 1 −γ − 1γ + 1 (2)

T2T1

=(

1 + γ−12 M2s) (

2γγ−1 M

2s − 1

)M2s

(2γ

γ−1 + γ−12) (3)

Ms = ϑ/√

γ RT1 (4)

where Ms is the Mach number of the shock, P2 and T2 are the static pressure and tempera-ture behind the shock, P1 and T1 are the static pressure and temperature ahead of the shock,γ is the ratio of specific heats of the gas, R is the specific gas constant, and ν is the speedof the reactive wave front. A small stand-off distance (∼ 1 mm) was observed betweenthe luminous reactive wave front and the location where the shock touches the PS surface,as shown in Figure 7. The stand-off distance indicates the possibility of the reactive wavefront in the condensed phase being coupled to the shock observed in the gas phase in twoways:

1. The high static temperature behind the shock can heat the PS and cause thermal ignition.2. The high pressure behind the shock can cause mechanical damage to PS and result in

the formation of localized ignition fronts as described previously (Kovalev et al., 2001).

The interaction between the condensed phase reactions and the gas phase compress-ible flow phenomena was investigated by preparing samples with a section in the middle

Figure 7 Side view shadowgram image of the reactive wave propagation in low doped P-type PS samples impreg-nated with sodium perchlorate. The reactive wave front moves supersonic with respect to the air, and drives theshock. A small stand-off distance was observed between the shock-PS surface and the luminous reactive wavefront on the PS surface.

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that was not filled with the oxidizer. This sample fabrication was accomplished by mask-ing a section of the PS (10 mm long) in the middle of the test sample with a tape anddrop-casting the oxidizer solution on the other two halves. A section of the masked regionremained unfilled with the oxidizer, as seen by the unburned PS remaining on the sam-ple strips after the combustion experiments. When the samples were ignited, the shockremained coupled with the luminous zone, while the reactive wave front propagated inthe first reactive PS region. When the reactive wave front reached the inert PS region, theshock decoupled from the luminous zone and began to decay as it propagated over the inertregion. In a small number of experiments (2 of >10), the decayed shock was capable ofigniting the second reactive PS region, as shown in Figure 8. Since the decayed shock wascapable of igniting PS, and the shock appeared coupled to the reactive wave for propaga-tion speeds greater than ∼ 1000 m/s as indicated by the relative positions of shock andluminous zone, the interaction between the shock and the reactive wave was examined fur-ther. From Eqs. (2), (3), and (4), the jump conditions across the shock depend on the ratioof specific heats of the gas around the sample and the strength of the moving shock. Themoving shock itself was observed to be coupled to the reactive wave front, and the strengthof the shock depends on the shock Mach number, which is affected by the speed of soundof the gas. Thus, the reactive wave propagation was studied in air at ambient pressure anda lower pressure (0.1 atm), and in helium at a pressure of 1 atm. Between the experimentsin air at different pressures, the strength of the shock, and thus, the ratio of static pressuresand temperatures across the shock, remain the same. While the static temperature behindthe shock remains the same, heat transfer to the sample is different due to the difference indensity of air over the surface of the sample. Also, the actual pressure behind the shock andthe resulting force on the PS sample are lesser than in the experiments conducted at 1 atm.For experiments conducted in helium, the Mach number of the shock coupled with thereactive wave front is significantly smaller, as the speed of sound in helium is much higher(1008 m/s in helium vs 343 m/s in air at 293 K), and consequently, the temperature andpressure jumps across the shock are smaller compared to air. The reactive wave propaga-tion speeds in air and helium are shown in Table 1. Because the reactive wave propagationspeeds did not slow down in air at low pressure or in helium, it can be concluded that the

Figure 8 (a) Schematic (not to scale) of the test samples prepared to study the interaction of the gas phase shockwith PS. The PS in the top and bottom regions of the test sample is impregnated with sodium perchlorate, while thePS in the middle is not. (b), (c), (d), and (e) are a series of images from a high speed shadowgraph recording, andthe time delay between each image is 12.5 µs. (b) shows the reactive wave front in the first PS region impregnatedwith the oxidizer. In this image, the shock is driven by the reactive wave front. (c) shows the propagation of thedecaying shock upon the complete combustion of the reactive PS in the first filled region. (d) and (e) show theignition and combustion of the second reactive PS region as the shock from the first region passes over it.

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Table 1 Reactive wave propagation speeds in air and helium

Reactive wave propagation speed (m/s)

Test conditions Average Standard deviation

Air (1 atm) 1162 94Air (0.1 atm) 1324 125Helium (1 atm) 1279 177

compressible flow phenomena above the PS surface are not the mechanisms responsiblefor the high speed of the reactive wave. Further, these results indicate that the high-speedreactive wave propagation depends on what happens within the PS sample.

Piekiel et al. (2014) obtained reactive wave propagation speeds slightly greater thanthe estimated speed of sound in their PS samples, and concluded that a detonation wasresponsible for the high speeds observed. Since the speed of sound in PS strongly dependson the pore morphology, the speed of sound for the PS used in this study was measuredusing an acoustic microscope. The speed of sound measured for the samples used in thiswork and the values found in the literature for the speed of sound in low doped P-type PS(Aliev et al., 2011; Fan et al., 2002; Fonseca et al., 1995) are shown in Figure 9. It mustbe noted that the longitudinal velocity measured was for the sound wave propagating ina direction perpendicular to the reactive wave propagation in the PS samples. Due to theslightly anisotropic nature of the porous layer, as seen in Figure 1b, the speed of sound

Figure 9 Longitudinal speed of sound in low doped P-type PS from literature and the values measured by acousticmicroscopy. For the low doped P-type PS samples used in this work, the measured speed of sound was between2169 m/s and 2479 m/s, while the reactive wave propagation speeds measured were below 1500 m/s, indicatingthat the reactive wave propagation was subsonic.

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can be expected to depend on the direction of propagation. The anisotropy in the structurearises from the fact that the pore growth during the electrochemical etch process is fastest inthe direction (Canham, 1997; Guendouz et al., 2000). However, the measurements by Alievet al. (2011) on PS etched on differently oriented silicon substrates show that the measuredspeed of sound for a given porosity between (100), (110), and (111) oriented substrates arevery similar, despite the differences in the orientation of the pores within the porous layer.Thus, the experimentally measured sound speeds can be assumed to be similar to the speedof sound along the direction of the reactive wave propagation within the porous layers. Thereactive wave propagation speeds measured are smaller than the measured speed of soundin PS, indicating that the high-speed propagations are not detonations. Since compressibleflow phenomena above the PS surface or within the PS sample (detonations) are not themechanisms for the high-speed reactive wave propagations, other mechanisms internal tothe porous layers are responsible for the high-speed reactive wave propagations observed.Possible mechanisms responsible are a combination of conductive and convective burn-ing within the porous layer, which could be assisted by other mechanisms unique to thismaterial.

Conductive and convective burning. High-speed reactive wave propagationsin most conventional EMs and nEMs are a consequence of convective burning (for example,nanothermites) or detonations (RDX, HMX, etc.). The slow deflagration processes in EMstypically involve combustion in the gas phase, and the reactive wave propagates by heattransfer from the gas to the solid, such as in low-speed propellant combustion. However, theoxidation of silicon takes place heterogeneously (Yetter et al., 2009), and the heat releaseoccurs at the solid surface. Further, while PS has poor thermal transport properties com-pared to bulk crystalline silicon, the thermal diffusivity of PS is higher (0.02–0.09 cm2/s)(Shen and Toyoda, 2002) than that of nanothermite formulations (0.001–0.005 cm2/s)(Pantoya et al., 2009) or typical composite propellants (∼ 10−4–10−3 cm2/s) (Kuo andAcharya, 2012). Since the reactive wave propagation speed scales with the thermal diffu-sivity for a purely conductive propagation, and the heat release in PS occurs directly atthe solid surface, PS can be expected to have a higher purely conductive component of thereactive wave propagation speed than most EM/nEMs.

DSC traces of different PS samples with different SSA are shown in Figure 10. At afixed heating rate, the first exothermic peak, which is associated with a solid–solid reaction,as well as the overall exothermicity, are observed to shift to lower temperatures, indicatingincreased reactivity of the PS. Following Semenov’s analysis, assuming the transport prop-erties remain the same, the reactive wave propagation speed for a purely conductive wavescales as

ϑ ∼√

A

Eaexp

(−EaRT

)(5)

where Ea is the activation energy and A is the pre-exponential factor. Using Kissinger’smethod, the activation energy was estimated for the heavily doped P-type substrates andthe low doped P-type substrates. The first exothermic peak was used to determine the acti-vation energy for the purely solid–solid reaction, and the data presented in Table 2 showthat the low doped P-type PS/sodium perchlorate reaction has the lower activation energy.However, assuming that the pre-exponential factor scales with the SSA, the difference inthe activation energies measured at low heating rates itself cannot explain the difference in

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Figure 10 DSC traces of PS samples with different SSA treated with a dilute (0.4 M) NaClO4 solution and heated20 K/min in an inert helium environment. The temperature of the first exothermic peak was found to shift to lowertemperatures as the SSA increases, with most of the heat release from the PS samples with the highest SSA usedin this work (730 m2/g) being associated with the lowest temperature exothermic peak.

Table 2 Estimated activation energies for the first exothermic reaction between PS and sodium perchlorate forPS etched from heavily doped and low doped P-type substrates

SSA (m2/g) Average pore diameter (nm) Activation energy (kJ/mol)

284 18.9 124.5730 4.8 72.1

the reactive wave propagation speeds observed, and falls short by an order of magnitude.The activation energies for the reaction pathways associated with the high heating ratesexperienced by PS in the preheat zone during combustion could be significantly differentthan the low heating rates used in the DSC, or they could indicate coupling with a differentmechanism such as convective burning.

The high speeds associated with nanothermite formulations are attributed to con-vective burning. A recent study has highlighted the issues with reactive wave speedmeasurements following the luminous zone in nanothermite formulations (Densmore et al.,2014), which found that the luminous front propagation could be affected strongly by dis-persion of the reactive material and does not necessarily correspond with a propagatingreactive wave. However, the structural integrity of PS can be expected to prevent this sortof erroneous measurement, as evident from Figure 8. The increased structural integrity ofPS also makes gas permeation difficult in PS compared to nanothermites, as the reactive

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material cannot be dispersed as easily and the gas permeation has to occur through thenanometer scale pores. Interconnectivity within the porous layers is by very small poreswith diameter ∼ 2 nm (Teschke et al., 1993), which makes effective gas permeation dif-ficult, and the hot gaseous products can be expected to permeate only short distances.Increasing the SSA also increases the amount of hydrogen present in the sample in the formof surface hydrides, and a threefold increase in the SSA results in a threefold increase inthe gas production. The increased gas production and pressure generated within the porescan result in improved permeation through the pores in the pressure driven flow, which,in conjunction with the change in activation energies, could explain the difference in thereactive wave propagation speeds between the heavily doped and the low doped P-type PSsamples.

Other mechanisms. In addition to the classical conductive and convective reac-tive wave propagation mechanisms described in the previous section, the unique physicalproperties of PS can result in other mechanisms. Despite its nanoscale structure, poroussilicon retains its crystallinity, and remains as single-crystal silicon with missing siliconatoms. Thus, cracks along crystallographic directions can be easily initiated in the PS sam-ple, and can propagate at very high speeds (Buehler et al., 2006). The oxidation of siliconatoms in the nanoporous structure results in a volume expansion, which can initiate cracks.Also, the enhanced gas production in low doped P-type PS due to higher SSA can increasethe stresses experienced by the PS, which can also result in initiation and growth of cracks.The cracks can generate free radicals, which act as localized ignition fronts. Furthermore,the openings created by the cracks can also act as conduits for the permeation of the hotgaseous products, which offer significantly lesser flow resistance and higher permittivitythan the nanoscale pores within the porous layers, contributing to the high-speed reactivewave propagation speeds observed.

CONCLUSIONS

This work presents an examination of the effect of phenomena occurring withinthe porous layers and in the gas above the PS surface on the reactive wave propagationin PS/NaClO4 composites. The mechanism for the enhancement of the reactive wavepropagation speeds in heavily doped P-type substrates on which organized microscalestructures were etched was studied by high-speed shadowgraphy. These experimentsrevealed upstream permeation of hot gaseous products ahead of the luminous reactionfront in the patterned region, indicating that the observed enhancement in the reactive wavepropagation speeds is due to convective burning. The parameters expected to affect theenhancement in the reactive wave propagation speeds, the permeability of the microscalestructure, the spacing between the microscale features, and the height of the microscalestructures were examined by studying the reactive wave propagation parallel and perpendic-ular to microchannels. Experimental results indicated that the permeability of the structurehas the strongest effect on the enhancement obtained, and the reactive wave propagationspeed depends on the aspect ratio of the microchannels etched.

The high speed reactive wave propagations in low doped P-type PS/NaClO4 com-posites drive a shock along the surface of the sample, which was found to be capable ofigniting the PS sample even after decaying in strength. However, examining the reactivewave propagation in helium revealed that the high speed reactive wave propagations are notdue to ignition of PS by the shock above the surface, as high speeds were observed even in

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a helium environment wherein the shock is significantly weaker. Speed of sound measure-ments obtained by ultrasonic microechography indicated that the reactive wave propagationis subsonic, and the observed high speeds are not due to detonation phenomenon. Thermalanalysis of the PS impregnated with NaClO4 shows that the heat release from the exother-mic solid–solid reactions shifts to lower temperatures as the SSA increases. The activationenergy measured at heating rates between 10–40 K/min for the first exothermic peak corre-sponding to the solid–solid reaction was also lower for the low doped P-type PS comparedto the high doped P-type PS. However, following Semenov’s analysis for purely conductivereactive wave propagation, the difference in the activation energy is insufficient to explainthe three order of magnitude difference in the reactive wave propagation speeds observed.Thus, a combination of conductive and convective burning, which could be assisted withmaterial specific phenomena such as crack propagation, is believed to be the mechanismresponsible for the observed high-speed reactive wave propagations.

ACKNOWLEDGMENTS

The authors wish to thank Julie Anderson and Lymaris Ortiz Rivera from theMaterials Characterization Laboratory (MCL) for help with gas adsorption measurements,and Prof. Bernhard Tittmann and Andrew Suprock from the Engineering Science andMechanics Department at The Pennsylvania State University for help with the sound speedmeasurements.

FUNDING

The authors gratefully acknowledge the support and funding from the U.S. Air ForceOffice of Scientific Research (AFOSR) under grant number AFOSR FA9550-13-1-0004.This publication was supported by the Pennsylvania State University Materials ResearchInstitute Nanofabrication Lab and the National Science Foundation Cooperative AgreementNo. ECS-0 335 765.

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ABSTRACTINTRODUCTIONSafetyExperimental MethodsResults and DiscussionEffect of Microscale Structures on Reactive Wave PropagationReactive Wave Propagation in Low Doped P-Type SubstratesConductive and convective burningOther mechanisms

ConclusionsAcknowledgmentsFundingREFERENCES

reactive wave propagation mechanisms department of ......tion of conductive and convective burning,...

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