The penetration depth of atomic radicals in tubes with catalytic surface properties

1.   Introduction

Surface catalysis has attracted significant attention from both the scientific community and the users. Surface catalysis often occurs at elevated temperatures. The temperatures are needed to facilitate surface adhesion and dissociation of different molecules [1]. The surface reactions at low temperatures may be accelerated by pre-dissociation of stable molecules. Molecular fragments such as radicals exhibit a much larger surface adsorption rate than stable molecules [2]. For example, methane will not dissociate on many materials at ambient conditions, but the methane radicals $\mathrm{C}{\mathrm{H}}_{x}$ will readily adsorb on the various solid materials [3]. The formation of molecular radicals in the gas phase could be performed by heating the gas to high temperatures, but such a procedure is energetically unfavorable. Instead, non-equilibrium gaseous plasma is often used for pre-dissociation of stable molecules [4, 5].

In numerous cases, noble metals such as platinum are among the best catalysts [6]. The high cost of such materials, however, suppresses a broad application, so scientists are involved in research on the surface catalysis of cheaper materials, such as nickel [7], cobalt [8], and copper [9].

The increased rate of chemical reactions due to surface catalysis depends on the actual surface area of the catalysts. From this point of view, nanostructured catalysts are preferred [10]. Another preferred option is using arrays of numerous tubes [11‒13], with nanotubes yielding even more impressive results [14]. The gaseous molecules enter the tube on one side and are transferred through the tube by a pressure gradient. Upon passing the tube, the molecules also move by diffusion, so they reach the tube wall, where they can be adsorbed, interact with other adsorbed species, and convert into the desired products, which desorb from the surface and continue their drifting towards the exhaust of the tubes. The molecular radicals will never stick to the surface of the tube at 100% probability, so the penetration depth of such radicals in the tube depends on the sticking probability and probability for chemical reactions [15]. The effectiveness of the gas transformation depends on the diameter of the tube, the probability of surface reactions, the length of the tube, and the gas drift velocity. The sound velocity in the gas limits the latter, which is about 340 m/s. In practical cases, the drift velocities are lower but significant to assure a reasonable throughput.

The optimization of the tubular catalysts should take into account all these effects. Theoretically, the efficiency of the gas conversion upon passing a tube could be calculated by taking into account the gas kinetics, including the diffusion and the surface loss probabilities. Unfortunately, the loss probabilities are often unknown or there is a large scattering of the results reported by different authors [16, 17]. From this point of view, it is more straightforward to measure the gradients of the molecular fragments along the metallic tube to determine the appropriate geometrical dimensions of the tubes. Radicals of high oxidation potential, such as O, OH, F, etc., are of particular interest. Oxidation of hazardous molecules such as CO with atomic oxygen is particularly effective [18]. The oxygen atoms will adhere to the surface of the tube and interact with other molecules arriving from the gas phase by the Eley-Rideal model [19]. The oxygen atoms adsorbed on the catalyst surface, however, do not only interact with radicals such as CO but also with atoms arriving from the gas phase to form ${\mathrm{O}}_{2}$ molecules. Any optimization of the efficiency requires the knowledge of the penetration depth of O atoms in tubes, which are fed on one side and pumped on the opposite side. The penetration depth depends on the atom loss probability, which has been described by many authors with the atom loss coefficient (sometimes equated to the recombination coefficient). The lists of coefficients for nickel, cobalt, and copper are presented in tables 1‒3, respectively. One can observe a large scattering of the results, indicating that the coefficients probably depend on other parameters, not only the type of catalyst. In the present paper, we report the penetration depth of O atoms in the tubes made from these materials.

Table  1.  List of atom loss coefficients ($\gamma$) for nickel determined using various measurement methods at different pressures ($p$) and material temperatures ($T$) from the literature.

Author	Method	$p\ \left(\mathrm{P}\mathrm{a}\right)$	$T\left(\mathrm{K}\right)$	$\gamma$	Reference
Greaves	Calorimetry	10	300	0.028	[20]
Šorli	Calorimetry	10–100	500–1100	0.27	[21]
Myerson	Calorimetry, NO titration	750	/	0.0085	[22]
Melin	Wrede–Harteck, NO titration	1–4	300	0.017	[23]
Cvelbar	Calorimetry	10–400	800	0.27	[24]
Mozetič	Calorimetry, NO titration	100	550	0.27	[25]
Drenik	Calorimetry	30–280	300	0.28	[26]
Greaves	Thermocouple probe	10	300	0.0077	[20]
Hartunian	Calorimetry	7–15	300	0.04	[27]
Dickens	Calorimetry	4	295–620	0.0008–0.056	[28]
Rosner	NO titration	4	300	0.1	[29]
Greaves	Wrede–Harteck	650	300	0.00089	[30]

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Table  2.  List of atom loss coefficients ($\gamma$) for cobalt determined using various measurement methods at different pressures ($p$) and material temperatures ($T$) from the literature.

Author	Method	$p\ \left(\mathrm{P}\mathrm{a}\right)$	$T\left(\mathrm{K}\right)$	$\gamma$	Reference
Melin	Wrede–Harteck, NO titration	1–4	300	0.075	[23]
Cvelbar	Calorimetry	10–400	750	0.14–0.08	[24]
Guyon	Actinometry	110	300–473	0.029–0.034	[31]
Dickens	Calorimetry	4	300–625	0.0018–0.25	[28]
Greaves	Wrede–Harteck	650	300	0.00049	[30]

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Table  3.  List of atom loss coefficients ($\gamma$) for copper determined using various measurement methods at different pressures ($p$) and material temperatures ($T$) from the literature.

Author	Method	$p\ \left(\mathrm{P}\mathrm{a}\right)$	$T\left(\mathrm{K}\right)$	$\gamma$	Reference
Greaves	Calorimetry	10	300	0.17	[20]
Donnelly	Mass spectrometry	0.02	300	0.07	[32]
Herdrich	Calorimetry	25620	300	0.00217	[33]
Herdrich	Calorimetry	18400	300	0.00899	[33]
Herdrich	Calorimetry	13410	300	0.0213	[33]
Park	Calorimetry	1400	300	0.016	[34]
Goulard	Calorimetry	1400	300	0.4	[35]
Myerson	Calorimetry, NO titration	760	/	0.031	[22]
Melin	Wrede–Harteck, NO titration	1–4	300–370	0.015–0.024	[23]
Cvelbar	Calorimetry	10–400	800	0.225	[24]
May	Calorimetry, effusion	1–2	298–375	0.070–0.11	[36]
Cauquot	Calorimetry, NO-titration	300	313	0.025	[37]
Wickramanayaka	NO-titration	93	300	0.019, 0.026	[38]
Mozetič	Calorimetry, NO titration	100	550	0.23	[25]
Park	Calorimetry	14000	300	0.0026–0.0032	[34]
Dickens	Calorimetry	4	295–485	0.034–0.18	[28]
Greaves	Wrede–Harteck	650	300	0.043	[30]
Greaves	Calorimetry	10	300	0.02	[20]
Dickens	Calorimetry	4	300–540	0.1–0.34	[28]

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2.   Experimental setup

The penetration depth of oxygen atoms in nickel, cobalt, and copper tubes was determined using appropriately designed metallic tubes with a diameter of 8 mm, which were connected to a source of oxygen atoms. A movable probe for oxygen atoms was mounted into the metallic tubes, and the O-atom density was measured versus the position of the probe. Figure 1 shows the dimensions of the metallic tubes and the position of the probe. The position l = 0 cm corresponds to the entrance of the metallic tube, and l = 10 cm to the exhaust.

Figure  1.  Schematic of the catalytic probe inside the metallic tube, with a marked position ($l$) of the catalytic probe. The catalytic probe was connected to a voltmeter with thermocouple wires enveloped in a glass casing.

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The source of oxygen atoms was weakly ionized oxygen plasma sustained by a microwave discharge in the surfatron mode. A quartz tube was immersed into a microwave cavity, which was powered with a microwave generator operating at the standard frequency of 2.45 GHz and a power of 180 W (GMS200WSM by Sairem, Décines-Charpieu, France). Details about such sources were disclosed in earlier papers [39‒42]. A high electric field causes gas breakdown and formation of gaseous plasma, whose critical electron density is $3\times10^{17}\mathrm{\ m}^{-3}$ [43]. Gaseous plasma is moderately conductive, so the electromagnetic fields cannot penetrate deep into the plasma due to the skin effect. Instead, the microwaves propagate within a sheath between the plasma and the quartz tube, where the electric conductivity is optimal for the absorption of the microwaves by plasma electrons. The electrons accelerate in the sheath and then transfer their energy to slower plasma electrons at elastic collisions, so the plasma is sustained at the electron temperature of a few eV [44]. The dissociation fraction of oxygen molecules passing through the quartz tube is several percent, depending on the discharge power, the pressure, and the gas speed [18]. Gaseous plasma only propagates along the quartz tube as long as the critical electron density is ensured. Further, along the quartz tube, the concentration of charged particles becomes negligible, but the dissociation fraction remains practically the same because of the very low probability of loss of oxygen atoms on the quartz surface, which is roughly 10⁻⁴ [28, 45, 46]. Therefore, the gas entering the metal tube is practically free from charged particles but rich in neutral radicals. As a side note, ozone production in our experimental system was negligible, as it only becomes noticeable at very specific experimental conditions [47].

The probability for surface loss of oxygen atoms on metals such as nickel, cobalt, and copper is much larger, as shown in tables 1‒3. The O-atom density along the metallic tube will likely decrease with increasing distance from the quartz tube. The density was measured with a calibrated catalytic probe, which is explained in detail elsewhere [48]. The probe tip is very small so that the probe itself does not influence the kinetics of the gas inside the metallic tube. The exhaust of the metallic tube was connected to a vacuum system, and pumped with a two-stage rotary pump with a nominal pumping speed of $80\;{\mathrm{m}}^{3}/\mathrm{h}$ (E2M80 by Edwards Vacuum, Burgess Hill, UK). The schematic of the entire experimental setup is shown in figure 2. All tubes were made from 0.05 mm thin foils of 99.99% purity nickel, cobalt, and copper (purchased from Goodfellow, Huntingdon, UK). Before conducting the experiments, all tubes were immersed in oxygen plasma for an hour to stabilize the oxide layer.

Figure  2.  Schematic of the microwave plasma reactor, with gaseous oxygen entering the system on the right-hand side and exiting on the left-hand side. Two pressure gauges ($p$) were installed at each end of the experimental setup.

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The density of neutral oxygen atoms along the tubes made from nickel, cobalt, and copper was measured systematically at a fixed discharge power of 180 W and 3 different flow rates: 50, 300, and 600 sccm, which equated to pressures of 10, 35, and 60 Pa. At those conditions, the metallic tubes were heated to 360, 390, and 450 K at the flow rates of 50, 300, and 600 sccm, respectively. The pressure gradient along the tubes appeared because of the constant introduction of oxygen on one side of the experimental system, and pumping on the other side (figure 3). By measuring the pressures at both sides of the experimental system, the following gradients were obtained by taking into account a linear decrease of 17, 54, and 80 Pa/cm for the flow rates of 50, 300, and 600 sccm, respectively.

Figure  3.  Pressure ($p$) profile along the length ($l$) of the metallic tubes at the given gas flow rates.

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3.   Results and discussion

The behavior of the O-atom density versus the length of the tube is shown in figures 4‒6 for nickel, cobalt, and copper respectively, with position 0 marked in figures 1 and 2. The curves exhibit a gradual decrease in the O-atom density. Two effects explain the decreasing atom density: (i) loss of atoms on the surface by heterogeneous association to parent molecules, and (ii) the pressure gradient along the tube. The error bars represent the statistic error of repeated measurements.

Figure  4.  Neutral oxygen atom density ($n$) along the length ($l$) of the nickel tube.

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Figure  5.  Neutral oxygen atom density ($n$) along the length ($l$) of the cobalt tube.

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Figure  6.  Neutral oxygen atom density ($n$) along the length ($l$) of the copper tube.

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The pressure gradient in the metallic tube was determined from measured pressures on both sides of the experimental setup shown in figure 2 as explained above. By considering the linear dependence of the pressure gradient, the decrease of O-atom density should be also linear in the absence of the surface effects. The curves in figures 4–6, however, are not linear, indicating that the surface effects are the major cause of the decreasing O-atom density. The O-atom density at the exhaust from all three metallic tubes is at the detection limit of our probe (approximately ${10}^{19}\;{\text{m}}^{-3}$), taking into account the probe accuracy, which is about $\pm$10%. Still, the densities as revealed in figures 4–6 do not drop to zero. This effect will be explained later.

As mentioned earlier, the decreasing density is also a consequence of the pressure gradient. To clarify this, we used the measured O-atom densities from figures 4‒6 to calculate the dissociation fractions ($\eta$) of oxygen molecules, which are defined as:

where $n$ is the oxygen atom number density, $k$ is the Maxwell-Boltzmann constant, $T$ is the gas temperature, and $p$ is the gas pressure. The dissociation fractions along the metallic tubes are shown in figures 7–9. The dissociation fractions first decrease almost exponentially with increasing depth, but then stabilize at a finite value. The curves in figures 7–9 were fitted with an exponential curve in the form of:

Figure  7.  The dissociation fraction ($\eta$) of oxygen molecules along the length ($l$) of the nickel tube.

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Figure  8.  The dissociation fraction ($\eta$) of oxygen molecules along the length ($l$) of the cobalt tube.

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Figure  9.  The dissociation fraction ($\eta$) of oxygen molecules along the length ($l$) of the copper tube.

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where ${\eta }_{0}$ and $A$ are the fitting parameters and ${l}_{0}$ is the penetration depth.

The exponential curves fit the measured data very well, taking into account the accuracy of our probe. The fitting curves plotted in figures 7–9 enable the calculation of the penetration depth, i.e. the depth at which the dissociation fraction of oxygen molecules drops to 1/e of the initial value at the entrance to the metallic tube. The penetration depths are summarized in table 4. The penetration depths depend on the gas flow and increase monotonously with the flow. This effect is explained by the decreasing flux of O atoms on the catalyst surface, which is due to the decreasing mean free path of O atoms with increasing pressure. Namely, the mean free path decreases linearly with increasing pressure. Another explanation would be the pressure dependence of the atom loss probability. The results in tables 1–3 do not allow for drawing the pressure dependence, because different authors used different experimental setups and different methods for the determination of the atom loss coefficient. Still, some recent studies reported that the atom loss coefficient for some materials decreases with increasing pressure [49‒51]. The pressure dependence of the atom loss coefficient for oxygen atoms on nickel and cobalt was studied systematically previously, and the results were published recently [52, 53]. Still, any differences between the effects of the mean free path and the pressure dependence of the atom loss coefficient are impossible to distinguish from the results summarized in table 4.

Table  4.  The penetration depth of oxygen atoms in metallic tubes with a diameter of 8 mm made from nickel, cobalt, and copper at three different gas flows and pressures in the glow chamber.

Flow rate (sccm)	p (Pa)	Nickel	Cobalt	Copper
50	10	1.2 cm	1.0 cm	1.1 cm
300	35	1.7 cm	1.3 cm	1.3 cm
600	60	2.4 cm	1.7 cm	1.6 cm

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Table 4 gives guidelines about the penetration depth of radicals, which associate to stable molecules by heterogeneous surface recombination. Knowing the penetration depth, one can calculate the depth at which the degree of dissociation drops to any value using equation (2). If the goal is total consumption of radicals, the metallic tubes would be long. If the diameter is 8 mm, as in our case, 90% consumption of the radicals is achieved at a depth of a couple of centimeters, depending on the gas flow and tube material. If the goal is efficiency in terms of the length of the tubes, the tubes should be much shorter than in our case. The conductance of the tubes decreases with increasing length, so it is obsolete to use long metallic tubes, because they suppress the gas throughput.

The constant value of the dissociation fraction along the tube from about 5–10 cm is highly unexpected and cannot be explained by surface effects. A feasible explanation of the finite O-atom density in the range between about 5 and 10 cm is the accuracy of our probes. As explained in the classical paper [48], the probe calculates the O-atom density from the power dissipated on the catalytic tip due to the heterogeneous surface recombination. While this power is by far the most important contribution to the catalyst heating, other channels will also contribute to the probe heating. Among them is the accommodation of gaseous molecules. The gas kinetic temperature in gaseous plasma exceeds the ambient temperature due to the abundance of super elastic collisions in the ionized gas. Another explanation is offered up by examining equation (1): since pressure decreases along the length of the metallic tubes, this seemingly increases the dissociation fraction towards the exhaust of the metallic tubes. Instead of a slow decline, we therefore get a constant value of the dissociation fraction near the exhaust of the metallic tubes.

Other authors have measured the kinetic temperature of gaseous molecules in plasmas sustained by microwave discharge in the surfatron mode [54]. The measurements are not feasible for oxygen because of the peculiarities of rovibrational states, but it was determined rather precisely for nitrogen [55]. The gas kinetic temperature in such plasma depends on the discharge power and the gas pressure and is roughly between 700 and 1000 K [56]. The gas cools down on its way from gaseous plasma to the metallic tubes by adiabatic expansion and accommodation on the surfaces of both quartz and metallic tubes. The gas speed, however, is large, so the accommodation is not complete. The artefact of the method used for measuring the O-atom density therefore explains the finite dissociation fraction along the metallic tubes between 5 and 10 cm. The actual dissociation fraction is probably very low at the exhaust from the metallic tube.

The metals always oxidize upon exposure to the air, so that a native layer of oxide is formed. In our case, however, the catalytic metals are not exposed only to molecular oxygen, but also to oxygen atoms. The oxidation of copper upon treatment with oxygen plasma was studied by several authors, including Ooi and Goh [57], and Tang et al [9]. In a recent paper, Xia and Sautet [58] reported a systematic study of copper oxidation upon treatment with atomic oxygen and found that a few nanometer-thick oxide film forms even at room temperature. A recent experimental report by Kuo and Su [59] showed that the oxide films could be much thicker and it includes the penetration of the native oxide film, and transportation of precursors through the oxide film, leading to much thicker films than forecasted from theoretical works [58]. Various oxides are formed on the copper surface, which further complicates the oxidation kinetics and thus the mechanisms of the oxygen atom loss on copper tubes. The same applies to cobalt. Different authors reported various methods for cobalt oxidation and agreed that at least two oxides are formed upon exposure to atomic oxygen, i.e. CoO and $\mathrm{C}{\mathrm{o}}_{3}{\mathrm{O}}_{4}$ [60‒62]. Nickel oxide behaves similarly, but only has one known form of oxide: NiO [63, 64]. This oxide tends to be structured in a simple cubic crystal lattice [65].

In any case, the treatment of nickel, cobalt, or copper tubes with oxygen atoms causes oxidation and the oxides are rarely in the form of a smooth film of uniform thickness. Many authors reported very rich morphology after treating metallic samples with oxygen plasma [66‒68]. The evolution of surface morphology depends on numerous parameters, but it is clear that the morphology evolves with increasing treatment times. To avoid the effect of unpredictable evolution of surface morphology and thus increase the actual surface area, we pre-treated all three metallic tubes in oxygen plasma at elevated temperatures. The metallic tubes were mounted in a radiofrequency plasma reactor and exposed to oxygen plasma at the temperature of about 700 K for 20 min. This treatment caused the formation of a rather thick oxide film, which was not supposed to change during our experiments because the experiments disclosed in this article were performed at much lower temperatures of the metallic tubes. The metallic tubes did not heat over 100 °C during our experiments. The heating is, of course, predominantly due to the exothermic surface association of oxygen atoms to ${\mathrm{O}}_{2}$ molecules. The pre-treatment of the metallic tubes in oxygen plasma therefore assured for formation of a stable oxide film before conducting our experiments, and thus reliability of our results.

4.   Conclusions

Systematic measurements of the O-atom density inside metallic tubes, which were connected to a source of O atoms on one side and pumped on the other side, enabled the determination of the penetration depths for O atoms. The O-atom density decreased monotonously along the metallic tubes, which was an effect of both the pressure gradient and the loss of atoms by heterogeneous surface recombination. The dissociation fraction of oxygen molecules along the metallic tubes was calculated from measured O-atom density and measured pressure drop along the narrow tubes. The dissociation fraction decreased exponentially along the length of the tubes. The penetration depth in 8 mm wide metallic tubes depended on the type of metal and the gas flow. At the lowest flow probed in our experiments, i.e. 50 sccm, the penetration depth was about 1 cm. At the highest flow of 600 sccm, the penetration depth was about 2 cm. These data are useful in any attempt to estimate the loss of molecular fragments along tubes, which serve as catalysts for the association of various radicals to stable molecules.