O2 Gases inside Nanobubbles

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A: Kinetics, Dynamics, Photochemistry, and Excited States 2

2

Understanding Combustion of H/O Gases inside Nanobubbles Generated by Water Electrolysis using Reactive Molecular Dynamic Simulations Shourya Jain, and Li Qiao J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b01798 • Publication Date (Web): 27 May 2018 Downloaded from http://pubs.acs.org on May 27, 2018

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The Journal of Physical Chemistry

Understanding Combustion of H2/O2 Gases inside Nanobubbles Generated by Water Electrolysis using Reactive Molecular Dynamic Simulations S. Jain* and L. Qiao* a) *

School of Aeronautics and Astronautics, Purdue University, West Lafayette, Indiana, 47907, USA

a) Corresponding author - Email: [email protected] and Tel.: 765-494-2040.

ABSTRACT: This work explored the mechanism of spontaneous combustion of hydrogen-oxygen mixtures inside nanobubbles (which were generated by water electrolysis) using reactive molecular dynamic simulations based on the first-principles derived reactive force field ReaxFF. The effects of surface-assisted dissociation of H2 and O2 gases which produced H and O radicals were examined. Additionally, the ignition outcome and species evolution as a function of the initial system pressure (or bubble size) were studied. Significant amount of hydrogen peroxide (H2O2), 6-140 times water (H2O), was observed in the combustion products. This was attributed to the low temperature (~300 K) and high pressure (2-80 atm) conditions at which the chemical reactions were being taken place. In addition, the rate of consumption of H2 and O2 molecules was found to increase with an increase in added H and O radical concentrations and initial system pressure. The rate at which heat was being lost from the combustion chamber (nanobubbles) was also compared to the rate at which heat was being released from the chemical reactions. Only a slight rise in the reaction temperature was observed (~68 K), signifying that at such small-scales heat losses dominate. The resulting chemistry was quite different from macroscopic combustion which usually takes place at much higher temperatures of above 1000 K.

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I.

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INTRODUCTION During the past decade, research on combustion at smaller scales (micro- and nanoscales) has

received great interest. A number of applications have been proposed for small-scale combustion devices: micro-thrusters, micro-heaters, actuators, sensors, thermal-to-electrical energy conversion systems, portable power devices and unmanned micro-vehicles1-3. At smaller scales, the surface-tovolume ratio increases and the combustion becomes difficult to be initiated and sustained because of the increased heat loss from the combustion chamber walls and strong wall-flame kinetic interactions4-5. Thus, the successful development of small-scale combustion based power devices continues to face significant challenges. Loyal to the scaling law, combustion should be impossible at nanoscales because the heat loss would profoundly dominate the chemical reactions. However, a few years back, Svetovoy et al.6-7 accidentally discovered that hydrogen and oxygen gases could be ignited spontaneously inside nanobubbles with diameters less than 150 nm. These nanobubbles were produced from short time water electrolysis by applying high frequency alternating sign voltage pulses, which resulted in H2 and O2 gas production above the same electrode. The authors attributed the nanobubble combustion to the fast bubble dynamics achieved through short time electrolysis (1-100 µs) that led to homogenous nucleation of bubbles (high supersaturation, S >1000) and to the bubble surface-assisted chemical processes. In a similar study, performed by Jain et al.8, a 10 nm thick Pt micro-thermal sensor (based on resistance thermometry) was fabricated underneath the combustion electrodes to measure the temperature changes occurring during the combustion of H2/O2 gases inside nanobubbles. The combustion was found to occur only for frequencies greater than 30 kHz and temperature changes up to 1 oC were observed. Moreover, the amount of heat produced was maximized at a duty cycle of 0.5, corresponding to the stoichiometric H2/O2 mixture. These were consistent with the findings of Svetovoy et al.6-7, confirming the occurrence of combustion inside nanobubbles. In another study performed by Svetovoy et al.9, much


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higher temperature changes up to 50 oC were observed. This was because the micro-chamber device that was used had a much lower thermal mass, in contrast to the other works mentioned above6-8. Several other experimental studies have also been conducted to explore the combustion phenomenon inside the nano/micro-bubbles, as have been summarized in a review article by Svetovoy et al10. In contrast to the several experimental works that have been performed6-10, only a few numerical studies have been conducted to understand the mechanism behind the spontaneous combustion process inside nanobubbles. Jain and Qiao11 performed non-reactive molecular dynamic simulations to determine how the surface tension of water is affected by the presence of dissolved external bubble gaseous molecules, which would in turn help to predict pressures inside nanobubbles under supersaturation conditions. The surface tension of water was found to decrease with an increase in the supersaturation value (or an increase in the external bubble gas concentration), thus, the internal pressure inside a nanobubble is much smaller than what would have been predicted using the planar-interface surface tension value of water. Nevertheless, the pressures inside the nanobubbles are still very high, which may provide a suitable environment for spontaneous ignition and combustion to occur. Prokaznikov et al.12 performed a numerical study using the continuum-scale kinetic models to study the combustion process occurring inside nanobubbles. The key mechanism identified was the dissociation of H2 molecules at the surface producing H radicals, which in turn initiated and sustained the combustion process at the room temperature. It was argued that a bubble surface is not neutral but negatively charged13-16 and it is these charged centers at the liquid-vapor interface that leads to the dissociation of H2 and O2 gases into H and O radicals, respectively. These negative charges are related to the V-potential of bubbles and could either be attributed to the adsorption of OH- ions or to the anisotropy of hydrogenbonding (inside water) at the bubble interface17-18.



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Chemical reactions, in general, cannot be initiated at room temperature without a stimulation such as an ignition source. In practical macroscale combustion devices, once the ignition takes place, the combustion drives up the temperatures (generally over 1000 K). However, at nanoscales, the surface to volume ratio increases, which in turn increases the heat loss and as a result, the temperature of the gases will not increase significantly due to the fast heat diffusion. The ignition and combustion process inside a nanobubble is believed to be distinctively different from macroscopic high-temperature combustion that has been studied widely. The present study used reactive molecular dynamic simulations to explore the mechanism for the spontaneous combustion of H2/O2 gases inside nanobubbles for several reasons. Firstly, due to the constraints of dimensions (since the nanobubbles were restricted to a few hundred nanometers), conventional modeling, numerical simulations, or kinetic studies were not suitable. Secondly, many of the physical and chemical processes taking places inside the nanobubbles were unknown and hence, couldn't be modeled. For example, the heat diffusion rates, bi- and tri-molecular reaction rate constants and bubble pressures, were all unknown. Thirdly, the surface-assisted dissociation process at the gas/liquid interface was unclear; although it was believed to be due to the dissociation of H2 molecules at the bubble surface12, the exact mechanism causing this dissociation was not well understood. Thus, using MD simulations, the various different ways through which the H radicals could be produced were examined and compared. Motivated by the above, the effects of surface-assisted dissociation of H2 and O2 gases and the initial system pressure on the ignition and reaction kinetics of the H2/O2 system were studied. Moreover, in contrast to the work of Prokaznikov et al.12, which explored the spontaneous combustion of H2/O2 gases from the chemical kinetics perspective, no assumptions regarding bi- and tri-molecular reaction rate constants were made as the combustion process was simulated using the first-principles derived reactive force field, ReaxFF, which includes both the physical changes such as thermal/mass transport


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and the chemical changes such as bond breaking and forming. In addition, the temperature of the H2/O2 system was not held constant at 300 K but was allowed to be varied in order to compare the rate at which the heat was being lost vs. the rate at which the heat was being produced from the exothermic reactions. II.

COMPUTATIONAL METHOD The simulations were performed using LAMMPS19, an open source molecular dynamic

simulation code developed by Sandia National Labs. The interactions between the atoms were calculated using the ReaxFF interaction potential, which was initially developed by van Duin et al.20 and was implemented within LAMMPS using the USER-REAXC module21. The bond order was determined between a pair of atoms from their interatomic distance. Table 1 lists the minimum bond order values used to identify the species produced during the combustion process. Pair of atoms that had the bond order value greater than the listed threshold bond order value were considered to be bonded. The particular ReaxFF force-field used in this study was developed by Agrawalla22, which was designed to investigate the reaction kinetics of the H2/O2 system at high pressures and low temperatures and thus, contains information on different pathways leading to the formation and consumption of HO2 and H2O2 molecules, which will play a key role in understanding the reaction kinetics of nanobubbles. Moreover, the force-field developed by Agrawalla22 has also been validated with the predictions of existing continuum-scale kinetic models for H2/O2 combustion at high temperatures and low pressures22. Table 1. Minimum bond order values23 Atom type

Atom type

Bond order

H

H

0.55

H

O

0.40

O

O

0.65



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Table 2. Simulation matrix Case

Initial % of H

Initial % of O

System size

Method

No.

radical added

radical added

(nm)

type

1

3

0

30 x 30 x 30

I

2

1

0

50 x 50 x 50

I

3

3

0

50 x 50 x 50

I

4

6

0

50 x 50 x 50

I

5

0

3

50 x 50 x 50

I

6

-

0

50 x 50 x 50

II

7

3

0

70 x 70 x 70

I

8

3

0

100 x 100 x 100

I

9

3

0

120 x 120 x 120

I

For the simulations, cubic boxes were used to represent the nanobubbles. Since, the main goal of this work was to understand the mechanism behind the spontaneous combustion of H2/O2 gases at room temperature, a good qualitative understanding of the initial and boundary conditions (pressure, temperature and H/O radical concentrations) could be obtained with the cubic boxes. Moreover, the cubic boxes reduce the computational cost and complexity considerably. Initially, H2 (124,200) and O2 (62,100) molecules were randomly added to the simulation box in a stoichiometric proportion, which was because during the experiments8, the electrolysis was conducted at a duty cycle of 0.5 that generated H2 and O2 gases in a stoichiometric proportion of 2:1. The simulation box size was based on the desired initial pressure and was varied from 30 nm to 120 nm, corresponding to the initial pressure ranging from 2 to 80 atm, respectively. After the initial set-up of the computational domain, temperature equilibration under the NVT (constant number of particles (N), temperature (T), and volume (V)) conditions to 300 K was performed using the Nose-Hoover thermostat. The NVT equilibration was performed for 0.5 ns with the time step and the relaxation time 6 ACS Paragon Plus Environment

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being 0.1 fs and 100 fs, respectively. After the NVT equilibration, the desired amount of H and O radicals were added to the simulation box. Since, the details of the process through which the radicals are produced at the bubble surface is not well understood, two different methods were used to add the radicals. In the first method, the radicals were added only initially, during the start of the combustion process, whereas in the second method, the radicals were added continuously at regular intervals of 0.01 ns. Moreover, for both the methods, the radicals were added only near the surface of the simulation box (at distance < 3% of the box length). For the first method, the initial H and O radical concentrations were varied from 1% to 6% (of the total number of initial H2 and O2 moles present in the system), whereas for the second method, the amount of H radicals added at each interval of 0.01 ns was based on the estimated reaction rate constant, as given by Prokaznikov et al.12. Table 2 lists the different cases that were simulated.

FIG. 1. Snapshot of the simulation box. H/O radicals were added only in the green shaded area. To simulate the combustion process, a non-thermostatted dynamics was used. Since, during the experiments6-8, nanobubbles were produced inside the water droplet, which was at 300 K, an isothermal 7 ACS Paragon Plus Environment


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boundary of 300 K was assumed for the cubic boxes. Thus, for atoms near the surface of the box (at distance < 3% of the box length), the NVT ensemble at 300 K was used. This enforced the isothermal boundary condition required. However, for atoms in the interior of the box, the NVE ensemble was used, allowing the temperature to rise due to the heat produced during the combustion process. A time step of 0.1 fs was used with the relaxation time (for the NVT ensemble) being 100 fs. Moreover, special precautions were made to make sure that the NVT boundary was set on a group of atoms defined as dynamic. The atoms were allowed to move in and out of the boundary but the NVT condition was applied only to the atoms near the boundary. The dynamic group was updated at every time step of 0.1 fs and the atoms were assigned to or removed from the group depending on their respective locations. Thus, the NVT boundary never collapsed and remained valid throughout the simulation. Fig. 1 shows a snapshot of the simulation box.


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III.

RESULTS AND DISCUSSION

A.

H2/O2 reaction characteristics at high pressures and low temperatures

FIG. 2. Species mole fraction as a function of time for 3% initial H radical concentration. The initial system pressure was set to 30 atm with the box size fixed at 50 nm. Mole fraction is defined as the number of moles of a species per total number of initial moles of H2 and O2.

Fig. 2 shows the species distribution as a function of time during the combustion of H2/O2 gases. The initial H radical concentration and system pressure were set to 3% and 30 atm, respectively. No O radicals were added initially but during the combustion process, the formation of O radicals was observed. In a combustion process at high temperature conditions (> 1000 K), H2O is the dominant stable species formed. However, for the present conditions of low temperatures (~300 K), instead of H2O, H2O2 was the dominant stable species, as can be seen from Fig. 2. Moreover, for combustion at macroscales, whenever an ignition is provided, chain branching reactions are initiated and a significant rise in the temperature is observed. However, in the present case, due to the large surface to volume ratio, most of the energy released from the exothermic reactions was lost from the walls of the



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combustion chamber and as a result, only a slight rise in the temperature of the reaction products was obtained, around 50 K. Thus, to initiate the combustion process at low temperatures, high pressure and a certain amount of H/O radicals are required initially, as will be discussed later in sections III. B-D. Next, the reaction mechanism at high pressures and low temperatures is explained in detail: Chain initiating step: The added H radicals reacted with the H2 and O2 molecules through the following 3 reactions:

H + O% + M → HO% + M (R1) H + O% → O + OH (R2) O + H% → H + OH (R3) In the reaction R1, M is the concentration of the third body and represents the overall system concentration, which in turn can be expressed in terms of the pressure and temperature of the system using the ideal gas law. Thus, the reaction rate for R1 is pressure dependent and increases with an increase in the system pressure. Moreover, the reaction R1 has a much lower activation energy as compared to the reaction R222. Thus, at high temperatures and low pressures, the reaction R2 dominates but at low temperatures and high pressures, the reaction R1 dominates. Chain propagating step: Reactions in which at least one radical was produced:

HO$ + H → OH + OH (R4) HO$ + H → H$ O + O (R5) HO$ + O → OH + O$ (R6) O + H + M → OH + M (R7) H# + OH → H# O + H (R8) 10 ACS Paragon Plus Environment

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O + H% O → OH + OH (R9) O + OH → H + O& (R10) HO$ + H$ → H$ O$ + H (R11) OH + OH → H& O + O (R12) As can be seen from Fig. 2, HO2 was the dominant intermediate product obtained, as expected. H (except during the initial part), OH and O radicals, however, were present in much smaller amounts with their concentrations quickly reaching steady state values i.e. these radicals were being consumed as soon as they were produced. The OH radicals were produced through reactions R4, R6, R7 and R9 whereas, the H and O radicals were produced through reactions R5, R8, R10, R11 and R12. Chain terminating step: Reactions with either H2O or H2O2 in the products:

OH + OH + M → H' O' + M (R13) HO$ + HO$ → H$ O$ + O$ (R14) HO$ + H$ → H$ O$ + H (R15) H# + OH → H# O + H (R16) H# O# + OH → H# O + HO# (R17) HO$ + OH → H$ O + O$ (R18) OH + OH → H& O + O (R19) H + OH + M → H' O + M (R20) HO$ + H → H$ O + O (R21)



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FIG. 3. Relative concentration of H2O2 to H2O as a function of time for 3% initial H radical concentration. The initial system pressure was set to 30 atm with the box size fixed at 50 nm.

Next, the intermediate radicals, according to reactions R13-21, combined to form the stable species: H2O and H2O2. Fig. 3 plots the relative amount of H2O2 to H2O as a function of time. As can be seen, significant amount of H2O2, up to 32 times that of H2O, was produced. The reactions R14-15 uses the reactants HO2 and H2, which were available in abundance, to produce H2O2. On the other hand, for the H2O production, the main intermediate product required was OH, which was present in much smaller quantities as compared to HO2 and H2. Thus, although the rate constants for the reactions R18 and R20 (required for H2O production) were much larger as compared to the rate constants for the reactions R1315 (required for H2O2 production)12, the concentration of reactants available limited the rate of reactions, resulting in much greater H2O2 production. Other chain terminating reactions requiring H and O radicals as reactants are not listed as they have very small rate constant values at room temperature.


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B.


Effect of initial H radical concentration

FIG. 4. Effect of initial H radical concentration. The initial system pressure was set to 30 atm with the box size fixed at 50 nm. Left: zoomed-out and right: zoomed-in images.

FIG. 5. Relative concentration of H2O2 to H2O as a function of time for various H radical concentrations. The initial system pressure was set to 30 atm with the box size fixed at 50 nm.



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Fig. 4 shows the effect of H radical concentration on the reactivity of the H2/O2 system. In the figure, the species reactivity is defined as the rate of change of a given species quantity per unit time i.e. dNs/dt (1/ns), where Ns is the number of particles of a given species. The initial H radical concentration was varied from 1 to 6% to represent the different probabilities of hydrogen dissociation at the bubble surface. Moreover, the initial system pressure was set to 30 atm with the box size being kept fixed at 50 nm. As can be seen, the reactivity of the system (formation of H2O2) was found to increase with an increase in the H radical concentration. This was expected, since, the greater the amount of H radicals added, the greater would be the number of HO2 radicals produced through the reaction R1. For 3% and 6% initial H radical concentrations, a significant amount of initial boost in the H2O2 reaction rate was observed but then due to the heat loss, an exponential decay was obtained thereafter. However, for 1% H radical concentration, no significant initial boost in the H2O2 reaction rate was observed but instead the reaction rate increased only slightly before falling down to the steady state value. Thus, for the case of 30 atm initial pressure, at least 3% H radical concentration was required to observe any significant H2O2 formation. Moreover, as can be seen from Fig. 5, the relative amount of H2O2 to H2O was found to decrease with an increase in the initial H radical concentration. This could be attributed to the competition of H radicals towards the formation of H2O2 and H2O. With an increase in the H radical concentration, the number of HO2 and OH radicals produced in the system increases, which in turn increases both the H2O2 and H2O production. But since, the reactions R18 and R20 have much larger rate constant values as compared to the reactions R13-1512, the amount of increase observed in H2O production was much more as compared to the amount of increase observed in H2O2 production.


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C.


Effect of initial system pressure

FIG. 6. Effect of initial system pressure. The initial H radical concentration was kept fixed at 3%. Left: zoomed-out and right: zoomed-in images.

FIG. 7. Relative concentration of H2O2 to H2O as a function of time for various initial system pressure. The initial H radical concentration was kept fixed at 3%.



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Fig. 6 shows how the initial system pressure (or the box size) effects the reactivity of the H2/O2 system. The initial H radical concentration was kept fixed at 3% and no O radicals were added initially. As expected, the reactivity of the system (formation of H2O2) increases with an increase in the system pressure (or a decrease in the box size). This could be attributed to the chain initiation reaction R1. With an increase in the system pressure, the concentration of the third body M also increases, which in turn increases the rate of formation of HO2 radicals. This increase in the HO2 concentration then translates to greater H2O2 and H2O production, as can be seen from the reaction mechanism. For the 30 atm and 80 atm initial pressure cases, a significant amount of initial boost in the H2O2 production was observed but for the 12 atm initial pressure case, no initial boost was obtained but instead the H2O2 reaction rate was increased only slightly, thus, for the 3% initial H radical concentration, the initial system pressure must be greater than 12 atm to observe combustion. In the nanobubble experimental study, faradaic currents up to 0.28 mA were observed for 20 x 20 µm2 electrodes8. Then using the diffusion length and faradaic current equation, for a frequency of 30 kHz (frequency above which substantial temperature rise was obtained), a supersaturation ratio value of 175 was obtained along with a diffusion length of 270 nm, which using non-reactive MD simulations roughly corresponds to a pressure value of 8 atm11. Thus, the nanobubble experimental studies performed by Svetovoy et al.6-7 and Jain8 and the present reactive MD simulations predicted similar threshold pressure values for the combustion to occur. Fig. 7 shows how the relative amount of H2O2 to H2O produced is affected by changing the initial system pressure. As can be seen, a decrease in the relative concentration was obtained with a decrease in the system pressure. This can again be attributed to the reaction R1. With a decrease in the system pressure, the third body concentration, M, also decreases, which in turn causes a decrease in HO2 formation. Since, the reactions R14-15 are directly dependent on the HO2 concentration, in contrast to the reactions R18 and R20, the decrease observed in the H2O2 production was much more as compared 16 ACS Paragon Plus Environment

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to the decrease observed in the H2O production, resulting in the relative amount of H2O2 to H2O to be lowered with a decrease in the system pressure. D.

Effect of O radical concentration

FIG. 8. H radical addition vs. O radical addition. The initial system pressure was set to 30 atm with the box size fixed at 50 nm. Left: zoomed-out and right: zoomed-in images.

FIG. 9. Relative concentration of H2O2 to H2O produced for H radical addition vs. O radical addition. The initial system pressure was set to 30 atm with the box size fixed at 50 nm.



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Fig. 8 shows how the reactivity of the H2/O2 system is affected when, instead of H radicals, only O radicals were added. The initial concentration of the respective radicals added was kept fixed at 3%. Moreover, the initial system pressure was set to 30 atm with the box size being kept fixed at 50 nm. As can be seen, for the case of O radical addition, a slight increase in the system reactivity was obtained. However, for both the cases, H2O2 was dominant stable species formed. The reaction mechanism observed in the case of O radical addition was slightly different from the H radical addition reaction mechanism. For the chain initiation step, the reaction R3 now dominates, since initially, significant amount of O radicals was added, which in turn produced the required H and OH radicals. H radicals were then consumed via the reaction R1 producing the main intermediate species, the HO2 radical. This mechanism could be further confirmed by looking at the rate of consumption of H2 and O2 species in Fig. 8. For the case of O radical addition, significantly more H2 molecules were consumed as compared to the O2 molecules, which was in contrast to the case of H radical addition where, an opposite trend was obtained. Thus, for the O radical addition, the main initiation was provided by the reaction R3, whereas for the H radical addition, the main initiation was provided by the reaction R1. Fig. 9 shows how the relative amount of H2O2 to H2O produced is affected when instead of H radicals, only O radicals were added. As can be seen, the relative concentration of H2O2 to H2O decreases for the case of O radical addition, which is mostly due to an increase in the H2O production. The rise obtained in the H2O production could be attributed to the reaction R3, via which significant amount of OH radicals were produced. Since, the amount of H2O molecules produced is strongly dependent on the H and OH radical concentrations, as can be seen from the reactions R16-21, a significant rise in the H2O production was observed. In contrast, for the H2O2 production, only a slight increase was observed. This was because HO2 radicals, instead of H and OH radicals, controlled the amount of H2O2 molecules being produced, as can be seen from the reactions R13-15. Moreover, since,


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the rate constants for the reactions R18 and R20 were much larger as compared to the rate constants for the reactions R13-15, the increased H and OH radical concentrations effect was even much more enhanced, and thus, a decrease in the relative concentration of H2O2 to H2O was observed for the O radical addition as compared to the H radical addition. E.

Effect of the H radical concentration and system pressure on the system temperature

FIG. 10. Core system temperature as a function of time for various H radical concentrations and box sizes Fig. 10 shows how the core system temperature changes as a function of the simulation time. The effects of both the initial H radical concentration and system pressure (or box size) were considered. The core of the system represents the interior of the simulation box in which the NVE ensemble was used to simulate the combustion process and thus, allowing for the system temperature to increase. As can be seen, for all the cases, initially a slight rise in the core temperature was obtained but then because of the significant amount of heat being lost to the atoms near the isothermal boundary, a quick drop in the temperature was observed. The amount of temperature rise obtained was found to increase with an increase in the initial H radical concentration or a decrease in the box size. This could be attributed to the reaction R1, which was the main initiation reaction producing radicals into the system. Among all



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the cases simulated (method I), the maximum temperature rise obtained was only 68 K. Thus, the first major conclusion that can be made is that the heat losses dominate i.e. the rate at which the heat is lost is much greater than the rate at which the heat is released from the chemical reactions. Secondly, the heat loss rate was found to be a much stronger function of the simulation box size as compared to the initial H radical concentration. As can be seen, for the 50 nm box, similar asymptotic temperature profiles were obtained for both 3% and 6% H radical addition. However, for the 30 nm box, a much steeper asymptotic slope was obtained. Similar conclusions were made by Prokaznikov et al.12, in which a simple heat diffusion equation was used to predict the thermalization time, which was then found to be on the order of 0.1 ns, much faster than the chemical reaction rates. Moreover, the heat diffusion time was also found to be directly proportional to the box size, again being consistent with the results given in Fig. 10. F.

Effect of adding H radicals continuously during the combustion process

FIG. 11. Mole fraction of H2, O2, H2O2 and H2O as a function of time. The initial system pressure was set to 30 atm with the box size fixed at 50 nm.


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FIG. 12. Core system temperature as a function of time. The initial system pressure was set to 30 atm with the box size fixed at 50 nm. In contrast to the previous method I, where the H radicals were added only at the beginning of the simulation, in this method II, the H radicals were added continuously at regular intervals of 0.01 ns, according to the reaction rate constant given by Prokaznikov et al.12 to duplicate a H2 surface dissociation reaction:

K =

ϵv& S (E1) 4V

In the above equation, e represents the probability of H2 dissociation, vi is the thermal velocity and S and V are the surface area and volume of the simulation box, respectively. Using a dissociation probability (e) of 10-2, 210 H radicals were added every 0.01 ns. Moreover, the H radicals were added only near the surface of the simulation box (at distance < 3% of the box length). Fig. 11 compares the rate of formation of H2O2 and H2O obtained using the two methods (for the method I - 6% H). The simulation box size was kept fixed at 50 nm. As can be seen, for both the methods, H2O2 was the dominant final product formed. For the method I, initially, due to the large amount of H radicals added, a huge spike in both H2O and H2O2 formation was observed but after that the molecules were produced at a much slower rate. This is in contrast to the method II, where both H2O 21 ACS Paragon Plus Environment


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and H2O2 species were formed at a much steadier rate. At 0.47 ns (corresponding to 11,000 H radicals added in both the methods), more H2O2 and H2O molecules were produced using the method II. The H2O2 production was increased slightly but a much greater rise was observed in the H2O production. After 0.47 ns, however, one to one comparison between the two methods is not possible as the total number of H radicals added in the method II would be much greater than the total number of H radicals added initially in the method I. The greater H2O production observed using the method II could be attributed to the core system temperature, as shown in Fig. 12. As can be seen, for the method II, a greater rise in the temperature was observed (395 K for the method II vs 340 K for the method I) at 0.47 ns, which in turn led to more H2O2 and H2O molecules being produced. The greater temperature rise observed in the method II could be due to the fact that every time the 210 H radicals were added, not all were consumed via the initiation reactions R1 and R2. Some of these H radicals also combined with other radicals that were already present in the system via the chain propagating and terminating reactions producing more OH and H2O. For the method I, however, since all the H radicals were added instantly at the beginning, the reactions R1 and R2 dominated as there were not any other radicals present in the system for the H radicals to react with. Moreover, since the chain terminating and propagating reactions produce more heat in general as compared to the chain initiation reactions, a greater rise in the temperature was observed at the end of 0.47 ns using the method II.


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FIG. 13. Mole fraction of HO2, H, O and OH as a function of time. The initial system pressure was set to 30 atm with the box size fixed at 50 nm. a) zoomed-out and b) zoomed-in images.

Fig. 13 shows the different intermediate species formed using the two methods. As can be seen for the method I, as expected, initially a huge rise in the HO2 concentration was observed. However, for the method II, since the H radicals were added periodically, the concentrations of both OH and HO2 radicals were observed to increase much more steadily. In the HO2 concentration, however, above 0.2 ns, a decrease was obtained, which could be attributed to the reaction R4. Because of the increased core temperature (Fig. 12, at 0.2 ns, method II), the rate of reaction R4 was also enhanced and as a result, more HO2 radicals were being converted to OH radicals. Moreover, for the method II at 0.47 ns, much more OH and HO2 radicals were produced as compared to the method I. The greater HO2 production in the method II could again be attributed to the higher core temperature observed, whereas the greater OH production could be attributed to the reaction R4 as explained earlier and to the fact that every time the 210 H radicals were added, some of the H radicals reacted with the other intermediates already present in the system, which in turn generated more OH radicals. Another interesting observation that could be made from Fig. 13 is that for both methods,



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H radicals were being consumed as soon as they were added/produced. A similar behavior in O radicals was observed and thus, a rise in the O radical concentration was never detected during the two methods. IV.

CONCLUSION

In this work, using reactive MD simulations, the possibilities of spontaneous ignition of H2/O2 gases under low temperature and high-pressure conditions were explored. The results obtained qualitatively explained as why spontaneous combustion has taken place inside nanobubbles with diameters smaller than 150 nm (corresponding to a bubble pressure of 13 atm for a supersaturation value of 400), as was observed in the nanobubble experimental studies performed by Svetovoy et al.6-7 and Jain8. In macroscale combustion, whenever an ignition is provided, a huge rise in the temperature is observed with H2O as the final product being formed. However, in the present nanoscale combustion process, due to the large surface to volume ratio, most of the energy released from the exothermic chemical reactions was lost to the walls of the combustion chamber and thus, only a slight rise in the temperature was observed (~68 K, using method I). Moreover, instead of H2O, H2O2 was the final product formed. This was attributed to the low-temperature and high-pressure conditions under which the chemical reactions were being taken place. The system reactivity (or the rate of H2O2 formation) was found to increase with an increase in either the initial H radical concentration or the system pressure. In addition, the effect of only O radical addition was also studied and similar to the H radical addition, H2O2 was the dominant final product formed. The system reactivity, however, was slightly increased but the overall species evolution of the intermediates remained unchanged. Moreover, since the exact mechanism through which the H radicals are produced at the bubble surface is not known, the effect of continuous addition of H radicals (method II) vs. adding H radicals only at the beginning of the simulation (method I) was also studied. And again, similar to all the previous cases simulated, H2O2 was the final product formed. However, using the method II, slightly higher temperature and H2O production was observed. 24 ACS Paragon Plus Environment

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REFERENCES 1. Jain, S.; Yehia, O.; Qiao, L., Flame Speed Enhancement of Solid Nitrocellulose Monopropellant Coupled with Graphite at Microscales. J. Appl. Phys. 2016, 119, 094904. 2. Jain, S.; Park, W.; Chen, Y. P.; Qiao, L., Flame Speed Enhancement of a Nitrocellulose Monopropellant Using Graphene Microstructures. J. Appl. Phys. 2016, 120, 174902. 3. Jain, S.; Mo, G.; Qiao, L., Molecular Dynamics Simulations of Flame Propagation Along a Monopropellant Petn Coupled with Multi-Walled Carbon Nanotubes. J. Appl. Phys. 2017, 121, 054902. 4. Sitzki, L.; Borer, K.; Wussow, S.; Maruta, E.; Ronney, P., Combustion in Microscale Heat-Recirculating Burners. In 39th Aerospace Sciences Meeting and Exhibit, American Institute of Aeronautics and Astronautics: 2001. 5. Norton, D. G.; Vlachos, D. G., Combustion Characteristics and Flame Stability at the Microscale: A Cfd Study of Premixed Methane/Air Mixtures. Chem. Eng. Sci. 2003, 58, 4871-4882. 6. Svetovoy, V. B.; Sanders, R. G. P.; Lammerink, T. S. J.; Elwenspoek, M. C., Combustion of Hydrogen-Oxygen Mixture in Electrochemically Generated Nanobubbles. Phys. Rev. E 2011, 84, 035302. 7. Svetovoy, V. B.; Sanders, R. G. P.; Elwenspoek, M. C., Transient Nanobubbles in Short-Time Electrolysis. J. Phys.: Condens. Matter 2013, 25, 184002. 8. Jain, S.; Mahmood, A.; Qiao, L. In Quantifying Heat Produced During Spontaneous Combustion of H2/O2 Nanobubbles, 2016 IEEE SENSORS, Oct. 30 2016-Nov. 3 2016; 2016; pp 1-3. 9. Svetovoy, V. B.; Sanders, R. G. P.; Ma, K.; Elwenspoek, M. C., New Type of Microengine Using Internal Combustion of Hydrogen and Oxygen. Sci Rep. 2014, 4, 4296. 10. Svetovoy, V.; Postnikov, A.; Uvarov, I.; Sanders, R.; Krijnen, G., Overcoming the Fundamental Limit: Combustion of a Hydrogen-Oxygen Mixture in Micro- and Nano-Bubbles. Energies 2016, 9, 94. 11. Jain, S.; Qiao, L., Molecular Dynamics Simulations of the Surface Tension of Oxygen-Supersaturated Water. AIP Adv. 2017, 7, 045001. 12. Prokaznikov, A.; Tas, N.; Svetovoy, V., Surface Assisted Combustion of Hydrogen-Oxygen Mixture in Nanobubbles Produced by Electrolysis. Energies 2017, 10, 178. 13. Li, C.; Somasundaran, P., Reversal of Bubble Charge in Multivalent Inorganic Salt Solutions—Effect of Magnesium. J. Colloid Interface Sci. 1991, 146, 215-218. 14. Graciaa, A.; Morel, G.; Saulner, P.; Lachaise, J.; Schechter, R. S., The Zeta-Potential of Gas Bubbles. J. Colloid Interface Sci. 1995, 172, 131-136. 15. Takahashi, M., Zeta Potential of Microbubbles in Aqueous Solutions: Electrical Properties of the Gas−Water Interface. J. Phys. Chem. B 2005, 109, 21858-21864. 16. Creux, P.; Lachaise, J.; Graciaa, A.; Beattie, J. K., Specific Cation Effects at the Hydroxide-Charged Air/Water Interface. J. Phys. Chem. C 2007, 111, 3753-3755. 17. Beattie, J. K.; Djerdjev, A. M.; Warr, G. G., The Surface of Neat Water Is Basic. Faraday Discuss. 2009, 141, 3139. 18. Vácha, R.; Marsalek, O.; Willard, A. P.; Bonthuis, D. J.; Netz, R. R.; Jungwirth, P., Charge Transfer between Water Molecules as the Possible Origin of the Observed Charging at the Surface of Pure Water. J. Phys. Chem. Lett. 2012, 3, 107111. 19. Plimpton, S., Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, 1-19. 20. van Duin, A. C. T.; Dasgupta, S.; Lorant, F.; Goddard, W. A., Reaxff: A Reactive Force Field for Hydrocarbons. J. Phys. Chem. A 2001, 105, 9396-9409. 21. Aktulga, H. M.; Fogarty, J. C.; Pandit, S. A.; Grama, A. Y., Parallel Reactive Molecular Dynamics: Numerical Methods and Algorithmic Techniques. Parallel Comput. 2012, 38, 245-259. 22. Agrawalla, S.; van Duin, A. C. T., Development and Application of a Reaxff Reactive Force Field for Hydrogen Combustion. J. Phys. Chem. A 2011, 115, 960-972. 23. Budzien, J.; Thompson, A. P.; Zybin, S. V., Reactive Molecular Dynamics Simulations of Shock through a Single Crystal of Pentaerythritol Tetranitrate. J. Phys. Chem. B 2009, 113, 13142-13151.



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Snapshot of the simulation box. H/O radicals were added only in the green shaded area. 361x270mm (135 x 135 DPI)

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Species mole fraction as a function of time for 3% initial H radical concentration. The initial system pressure was set to 30 atm with the box size fixed at 50 nm. Mole fraction is defined as the number of moles of a species per total number of initial moles of H2 and O2. 343x130mm (135 x 135 DPI)


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Relative concentration of H2O2 to H2O as a function of time for 3% initial H radical concentration. The initial system pressure was set to 30 atm with the box size fixed at 50 nm. 361x270mm (135 x 135 DPI)



Effect of initial H radical concentration. The initial system pressure was set to 30 atm with the box size fixed at 50 nm. Left: zoomed-out and right: zoomed-in images. 353x139mm (135 x 135 DPI)


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Relative concentration of H2O2 to H2O as a function of time for various H radical concentrations. The initial system pressure was set to 30 atm with the box size fixed at 50 nm. 361x270mm (135 x 135 DPI)



Effect of initial system pressure. The initial H radical concentration was kept fixed at 3%. Left: zoomed-out and right: zoomed-in images. 353x144mm (135 x 135 DPI)


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Relative concentration of H2O2 to H2O as a function of time for various initial system pressure. The initial H radical concentration was kept fixed at 3%. 361x270mm (135 x 135 DPI)



H radical addition vs. O radical addition. The initial system pressure was set to 30 atm with the box size fixed at 50 nm. Left: zoomed-out and right: zoomed-in images. 345x142mm (135 x 135 DPI)


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Relative concentration of H2O2 to H2O produced for H radical addition vs. O radical addition. The initial system pressure was set to 30 atm with the box size fixed at 50 nm. 361x270mm (135 x 135 DPI)



Core system temperature as a function of time for various H radical concentrations and box sizes 361x270mm (135 x 135 DPI)


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Mole fraction of H2, O2, H2O2 and H2O as a function of time. The initial system pressure was set to 30 atm with the box size fixed at 50 nm. 361x270mm (135 x 135 DPI)



Core system temperature as a function of time. The initial system pressure was set to 30 atm with the box size fixed at 50 nm. 361x270mm (135 x 135 DPI)


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Mole fraction of HO2, H, O and OH as a function of time. The initial system pressure was set to 30 atm with the box size fixed at 50 nm. a) zoomed-out and b) zoomed-in images. 361x270mm (135 x 135 DPI)



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O2 Gases inside Nanobubbles

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