2017 Volume 58 Issue 5 Pages 782-789
In the present work, we investigated the alternating current (AC) etching of aluminum wires with the aim of fabricating catalyst supports. This support material was found to possess a spongy surface layer that could be subsequently filled with γ-alumina by a combination of hydration and calcination. These support wires are easily fabricated at low cost, and could be mass produced continuously. The integrated structure of the catalyst produces a strong interconnection between the wire substrate and a thick catalyst layer on the wire. This work also demonstrated that the diffusion inside the catalyst layer can be controlled by varying the etched structure of the support layer. A micro-structured catalytic wall reactor concept was developed using these wires, situated parallel to one another within a tubular device, such that microchannels were present between the wires. The steam-reforming of methanol was assessed in this type of microreactor.
Electrochemical etching has been previously employed to obtain aluminum foils with high surface areas for use as electrolytic capacitor electrodes1–5). This etching is characterized by the creation of rough metal surfaces. In our prior work, an anisotropic etching technique was used to produce tunnel-shaped etching pits6). When this technique is employed to fabricate electrode foils for electrolytic capacitors, an initial etching step forms tunnel-shaped pits that penetrate the aluminum foil, after which a second etching step increases the diameter of these pits. The resulting pits can be applied as reaction channels.
In the present study, we investigated electrochemical etching with an alternating current (AC) to generate catalyst support layers. This etching is characterized by the creation of rough metal surfaces with numerous cubic etching pits1,2). The walls of the cubic etching pits are covered with an etching film that is deposited during the cathodic half-cycle immediately after pit formation. Secondary pits are typically initiated at weak points in the etching film at the base pits. These new pits degrade the preexisting etching film and grow until the end of the anodic half-cycle. During the subsequent cathodic half-cycle, this metal surface becomes covered with a new etching film, thus completing the sequence. Repeated sequences involving weak points in the etching film on different pit faces give rise to multidirectional cube-by-cube pit propagation. AC etching thus generates a residual sponge-structured aluminum layer containing a high density of cubic etching pits. The surface area of 100-µm-thick aluminum foil, etched on both sides to a depth of 30 µm to generate sponge-like layers, has been shown to increase by two orders of magnitude.
Process innovation is essential to ensuring that the efficiency and productivity of chemical industry continues to increase, thus maintaining a competitive advantage. There has been a growing interest in the use of process intensification (PI) as a means of achieving this goal, and micro-structured catalytic wall reactors are recognized as an important tool for PI7). Microreactors are devices employed to promote chemical reactions, and the synthesis of various compounds based on microspatial phenomena and micro-fabrication technology is currently used to manufacture reactor microchannels for this purpose8–10). Microreactors are known to have important advantages over conventional reactor types, including significantly higher surface-to-volume ratios and superior heat transfer coefficients. It is also expected that high rates of heat transfer, high efficiency mixing, narrow residence time distributions and short diffusive lengths will all be achievable in the microchannels. As a consequence, microreactors should allow precise control over chemical reactions, leading to high efficiency and selectivity. Catalysts are, of course, important in many synthetic chemical reactions, and so methods are required to deposit catalysts on surfaces of microreactor for the catalyst reaction, because the techniques traditionally used with conventional bead-type reactors lead to pressure loss and catalyst outflow when applied to microreactors. The deposition of catalysts on microchannel surfaces remains a major challenge, and the development of useful materials and efficient methods for depositing catalysts on structured surfaces is a frequent requirement11). It remains difficult to fabricate materials with microchannels supporting catalyst metals in a cost-effective manner. In addition, the stability of catalyst coatings on such substrates and the mechanical strength of the supports are important factors affecting practical applications.
Our own research group has examined the use of an anodized alumina layer as a catalyst support and has published details regarding the application of this material12–15). Anodic oxidation is often used as a pretreatment for wall coating methods, and anodized porous alumina layers can be formed on aluminum plate surfaces by anodization. These layers have many advantages over conventional catalysts, including high thermal conductivity and the ready formation of various shapes and structures. In this study, the performance of reactors based on etched wires was compared with that of a device based on anodized wires.
Concerns regarding limited supplies of petroleum have stimulated intensive development of fuel cell technology. Due to the current limitations of hydrogen storage methods, fuel processors that can convert liquid fuel into hydrogen have attracted significant interest, and methanol has often been studied as a potential hydrogen storage medium owing to its many advantages16). For this reason, the present work demonstrates the application of our new catalyst support structure to methanol stream-reforming (MSR) using a Cu catalyst17,18). We report herein the first-ever use of micro-structured materials containing a catalyst support layer to form parallel channels with catalytic walls in a reactor for the generation of hydrogen.
Figure 1 summarizes the catalyst preparation process. To produce the catalytic etched wires, aluminum wires (A9999W, 0.8 mm φ, Nikkei Sangyo Co., Ltd., Shizuoka, Japan) were subjected to electrochemical AC etching to generate spongy surface layers19,20). This etching was carried out at 348 K at a frequency of 75 Hz for 60 sec in an aqueous solution of 10 mass% hydrochloric acid and 0.1 mass% sulfuric acid. The treated wires were subsequently washed with 0.25 mass% sulfuric acid to remove residual chlorine ions and then washed with purified water. The metal wire supports were fabricated by forming a coating over the etched layer through consecutive hydration and calcination. Two hydration treatments were performed at 353 K in purified water and calcination was carried out by first heating the wires at 623 K for 2 min and then at 823 K for 2 min. The boehmite formed by the hydration step was crystallized to give γ-alumina during the calcination21). During these processes, the residual sponge-structured aluminum was consumed in the etched layer, and this etched layer was subsequently filled with the hydrated alumina, including a γ-alumina phase containing mesopores. Lastly, these catalyst supports were impregnated twice with a Cu solution containing 0.50 mol/dm3 Cu ions over 3 hours at pH 9.5 and 303 K, and then calcined at 623 K for 1 hour. Figure 2 presents a schematic image of the wire catalyst support with an enlarged view showing the cross-section view of the catalyst layer formed by the hydrated alumina. The etched wires described above are termed “S-type.”
Flow charts showing the procedures for the preparation of (a) the catalytic etched wires, (b) the catalytic anodized wires, and (c) the granular catalyst.
Schematic image of the catalytic etched wire with an enlarged view showing the cross-section view of the catalyst layer formed by the hydrated alumina.
A second type of etched wire was also prepared by varying both the etching temperature and frequency, in an attempt to improve the internal diffusion. The etching was carried out at 323 K at a frequency of 10 Hz over a time span of either 60 or 120 sec, employing the same etching solution. The resulting specimens are termed “G-type wire-1” and “G-type wire-2,” respectively. The thickness of the etched layer was found to vary with changes in the etching time, such that etched layers on the G-type wire-1 and -2 samples were approximately 36 and 60 µm deep, as determined by scanning electron microscopy (SEM) observations.
To prepare the catalytic anodized wires, the same aluminum wires (A9999W) were treated so as to generate an anodized alumina layer. These wires were first cleaned with a NaOH solution as a pretreatment in preparation for anodization. After this, the aluminum wire was anodized in a 4 mass% oxalic acid solution at 40 V (DC) and 307 K over 4.5 hour to form an anodized porous alumina support layer. The thickness of the anodized porous alumina layer was adjusted to equal that of the etched catalyst layer by varying the anodizing time. In the case of the anodized wires, longer time spans were required to generate the same thickness of support layer as on the etched wires. Subsequently, a pore-widening treatment (PWT) was conducted at 307 K for 3 hours to enlarge the alumina pores. The primary reason for this PWT was to enlarge the pore diameter and improve the internal diffusion. Next, hydration was carried out at 353 K for 1 hour in purified water, followed by calcination at 773 K for 3 hours. Lastly, the catalyst support was impregnated twice with a Cu solution (0.50 mol/dm3 Cu ions) for 3 hours at pH 9.5 and 303 K, and then calcined at 623 K for 1 hour.
In our work, these specially treated wires were situated parallel to one another within tubular reactors, such that microchannels were formed between the wires. It is possible to employ such wire-loaded tubes as micro-structured catalytic wall reactors because the catalyst layers consist of γ-alumina, a catalytic substance.
A granular catalyst was also produced using commercially available alumina beads (AA300, Nippon Light Metal Co. Ltd., Tokyo, Japan) with diameters in the range of 1.4–2 mm. These beads were crushed and sieved to 0.5–1.0 mm and impregnated twice using the same method as applied to the wires, over a time span of 3 hours. These catalyst preparation processes are summarized in the flow charts shown in Figs. 1(a) to (c).
The Cu in these catalysts was reduced prior to the catalytic trials, because the catalytic metal was oxidized during the calcination step that followed impregnation. Catalytic activity trials were performed employing a specific mass of catalytic Cu per methanol feed rate (W/F [g·h/mol]). In this study, MSR was carried out as a means of assessing the catalyst's activity, just as we tested Cu/ZnO catalysts in our prior research6). In the present work, however, we elected to use a catalyst containing Cu but not Zn, so as to limit the number of variables. In prior work, the Cu-to-Zn ratio was found to vary between catalysts having different support structures, and the presence of Zn was also determined to degrade the performance of the Cu. Hence, because the activity of this type of catalyst evidently depends on the dispersion and distribution of both Cu and Zn in the material, trials were performed using a catalyst impregnated with only Cu.
2.2 CharacterizationSEM was performed using a JSM-7401F instrument (JEOL Ltd., Tokyo, Japan). Replicate images of the etched layers were obtained by encasing wire samples in resin and then dissolving the aluminum and observing the sample from the aluminum side. Cross-section polishing of wire samples after hydration was carried out using an SM-09010 instrument (JEOL Ltd.). The pore sizes of the catalyst supports were measured by nitrogen adsorption with a Belsorp-mini II (MicrotracBEL Corp., Osaka, Japan) together with calculations based on the Brunauer–Emmett–Teller (BET) method and the Barrett-Joyner-Halenda (BJH) method. The amount of catalytic metal loaded onto each catalyst support was determined by inductively coupled plasma spectroscopy (ICP; Vista-Pro, Agilent Inc., Santa Clara, CA, USA).
2.3 Catalyst testingAs noted, the MSR reaction was carried out as a means of assessing the catalytic activity. The catalyst test conditions were the same as those reported previously6). In these trials, a methanol/water feed was introduced into the reactor, using nitrogen as the carrier gas. The outlet gas flow rate was calculated based on the nitrogen gas flow entering the reactor. These trials employed a steam-to-carbon ratio of 1.5, and the molar ratios in the gas flow were N2:H2O:MeOH = 5:3:2. Reactions were performed at temperatures between 473 and 593 K. During each activity test, the material feed rate was used to calculate the specific W/F values.
The W/F values were calculated as in eq. 1.
| \[ W/F [{\rm g \cdot h/mol}] = \frac{Cu\ Catalyst\ Weight[{\rm g}]}{MeOH\ Feed\ Rate[{\rm mol}/{\rm h}]} \] | (1) |
The reactor employed in this work consisted of a stainless steel tube in which catalytic wires having diameters of 0.8 mm were situated in parallel, such that reactant gases flowed between the wires.
The initial experiment was intended to establish whether multiple wires could be situated in the reactor. These activity tests were carried out using the catalytic S-type etched wires, with three wires positioned in a tubular reactor having a 2.17 mm internal diameter, and 20 wires positioned in a tubular reactor having a 4.35 mm internal diameter (Fig. 3). Activity trials were performed at a specific ratio of catalytic metal mass to methanol feed rate (W/F) of 0.04 g·h/mol, and the resulting hydrogen production rates were measured. The effluent gases during these trials consisted of H2 and CO2 generated by the MSR reaction, C2H6O (dimethyl ether, DME) from the methanol dehydration reaction, CO from the reverse water-gas shift reaction and unreacted CH4O (methanol, MeOH) and H2O from the original feed.
Photographic images of reactors packed with (a) three and (b) 20 wires.
During the second test, the performance of the S-type etched wires was compared with that of the anodized wires. In these trials, three wires were loaded into the 2.17 mm reactor and the test was performed at a W/F of 0.04 g·h/mol.
We subsequently assessed G-type etched wire-1 and -2 specimens, generated using different etching conditions, at a W/F of 0.04 g·h/mol. Again, three wires were positioned in the 2.17 mm device.
Last, the S-type etched wire catalyst was compared with the granular catalyst at a W/F of 0.04 g·h/mol. In this trial, 20 wires were positioned in the 4.35 mm reactor and the granular catalyst was packed in the same reactor.
The S-type etched wires were examined by SEM. Figure 4(a) presents a surface image of the S-type etched wire after etching while Fig. 4(b) shows a BE mode compositional image of the cross-section of the same wire after etching. Some remaining surface was observed after the etching process, as the result of intrusion of the sponge-structured layer into the interior of the base wire material. Figure 4(c) shows a replicate image of the pits taken from the region indicated in Fig. 4(b). This image demonstrates that the aluminum core was uneven. Figure 4(d) presents a high magnification BE mode compositional image of the cross-section after the etching. It is evident that the electrochemical etching of the aluminum generated pits to form a spongy surface layer approximately 40 µm deep. Figure 4(e) provides an SEM image of a cross-section of the S-type etched wire after hydration. From Fig. 4(e), it can be seen that the sponge-structured aluminum was consumed during the hydration process, such that etched layer filled with the hydrated alumina. Figure 4(f) shows a compositional image in the BE mode of a cross-section of an S-type etched wire after impregnation. This image demonstrates that both the quantity of cracks and the separation of the alumina layer were greatly reduced in the catalyst layer, compared with the anodized wire.
(a) An SEM image of the surface of an S-type etched wire, (b) a BE mode compositional image of a cross-section of the S-type etched wire after etching, showing the sponge-like surface layer, (c) SEM image of a replica of the etched pits, (d) a high-magnification BE mode compositional image of the cross-section of the S-type etched wire after etching, (e) an SEM image of a cross-section of the S-type etched wire after hydration, and (f) a BE mode compositional image of a cross-section of the S-type etched wire after impregnation.
The anodized wire was also examined by SEM, and Fig. 5(a) presents a surface image acquired after the PWT. After hydration, the pores of the anodized porous alumina were filled with alumina, and the surface was also covered with this material. The boehmite formed by hydration evidently crystallized to γ-alumina containing mesopores during the calcination. Figure 5(b) and (c) show BE mode compositional image of a cross-section of the anodized wire acquired before and after impregnation. Both cracks and separation of the alumina layer are evident in these figures, in addition to dissolution of the anodized porous alumina after impregnation. It is apparent that the impregnation process dissolved the anodized alumina but not the highly crystalline hydrated alumina. The anodized alumina, incorporating anions from the electrolytic bath, was less crystalline than the hydrated alumina. Therefore, the anodized alumina readily dissolved in the impregnation solution containing ammonia. In addition, the aluminum substrate could be dissolved to a significant extent by the ammonia. The presence of cracks that are not covered by the hydrated alumina in the catalyst coating layer suggests dissolution of the exposed anodized alumina and the aluminum substrate during impregnation. These cracks are believed to result from the difference in the extent of thermal expansion of the smooth aluminum substrate and the anodized alumina. These images also demonstrate that the anodized alumina layer was approximately 40 µm deep.
(a) An SEM image of the surface of the anodized wire after PWT, (b) and (c) a BE mode compositional image of a cross-section of the anodized wire before and after impregnation.
In contrast, the etched wire is covered with a highly crystalline hydrated alumina layer over top of an uneven aluminum substrate. The integrated structure of this catalyst system, together with the reduction in stress resulting from lowering the difference in the coefficients of thermal expansion of the constituent materials, produces a strong interconnection between the etched wire substrate and the catalyst layer. This approach avoids problems associated with planar substrates, such as the formation of cracks and separation of the alumina layer after heat treatment and impregnation. Thick anodized alumina layers on flat substrates often suffer from such issues. SEM observations offer further evidence that the integrated structure of the catalyst results in a strong interconnection between the etched wire substrate and the thick catalyst layer.
Lastly, a G-type etched wire was also examined by SEM, and Fig. 6(a) shows a BE mode compositional image of a cross-section of the wire. The pits generated by etching are seen to be quite large compared with those in Fig. 4(d). Figure 6(b) presents a cross-section of the G-type etched wire after hydration, from which it can be seen that the etched layer were filled with the hydrated alumina. It is also obvious that, in the case of these wires, the residual sponge-structured aluminum was consumed by hydration. Because the etched pits were large in these wires, a significant quantity of aluminum was dissolved. As a result, the amount of remaining aluminum in the etched layer was insufficient to fill the etched layer with alumina. Therefore, we believe that there were voids in the hydrated alumina. Figure 6(c) shows a BE mode compositional image of a cross-section of the G-type etched wire after impregnation. In Fig. 6(c), few cracks and separations can be seen. Because of its internal structure, the catalyst layer on the G-type etched wires had not almost cracks and a stronger connection with the aluminum substrate relative to the S-type etched wires.
SEM images showing a cross-section of a G-type etched wire after (a) etching and (b) hydration, and (c) a BE mode compositional image of a cross-section of a G-type etched wire-2 specimen (60 µm) after impregnation.
Pore sizes were calculated based on the BJH method and using nitrogen sorption isotherms. Figure 7 compares the catalyst supports of the catalytic S-type etching wires, the catalytic anodized wires and the granular catalyst after impregnation. In this figure, mesopores approximately 10 nm in size are indicated by the circle. The volume of these mesopores in the etched wire was lower than in the other materials, and this sample also generated a sharper distribution peak. In the case of the granular catalyst, the volume per catalyst mass is shown on the right hand vertical axis, because the masses of the other materials included the non-functioning aluminum core.
Pore size analysis of the catalyst after impregnation as calculated by the BJH method.
Figure 8 shows a comparison based on the etching treatments of the wires. Again, 10 nm mesopores are indicated within the circle. We prepared improved G-type etched wires by modifying the etching conditions so as to improve the internal diffusion. From a comparison of the S-type and G-type etched wires after impregnation, the volume of the 10 nm mesopores in the G-type etched wires was greater than in the S-type etched wires. The G-type etched wires contained a low density of hydrated alumina because the amount of residual aluminum was insufficient. We therefore believe that the density of the internal hydrated alumina layer affects the volume of 10 nm mesopores. It is inferred from this result that there was resistance to diffusion inside the catalyst layer on the S-type etched wires.
Pore size analysis of S-type and G-type etched wires after impregnation as calculated by the BJH method.
We calculated the BET surface areas of the S-type etched wires without metal cores, so as to remove the effect of the mass of the aluminum core from the nitrogen adsorption isotherm of the wire catalyst supports before impregnation. This was done because the aluminum core was not impregnated with the catalytic metal. Assuming that the etched layer had a depth of 40 µm and represented the catalyst support layer, we calculated the BET surface area by removing the mass of an aluminum core having a 720 µm diameter. The wire catalyst (without metal core) had a surface area of 322.5 m2/g. The catalytic wires without metal cores were found to have approximately equal surface areas to that of the commercial alumina catalyst (100–350 m2/g). Additional data indicated that the surface area of the etched wires was increased after hydration, which is in keeping with previous observations that etched microstructures are transformed to nanostructures by hydration.
3.3 ICP analysesThe amounts of catalytic metal loaded onto the catalyst supports were determined by ICP, with the results provided in Table 1. The activity trial feed rates were calculated using these results. The compositions of the catalysts were different as a result of the different structures of the catalyst layers. In addition, the Cu contents of the G-type etched wire -1 and -2 specimens were found to increase with increasing thickness of the catalyst layer.
| Catalyst | Cu weight, mcu/(mg/g-cat) |
|---|---|
| S-type etched wire | 8.87 |
| Anodized wire | 11.9 |
| G-type etched wire-1 | 6.88 |
| G- type etched wire -2 | 14.7 |
| Granular alumina | 57.3 |
Comparative data from MSR trials using microreactors filled with either three or 20 wires are presented in Fig. 9. It is evident that the hydrogen production rate per catalyst weight was almost unchanged upon increasing the number of wires. These data also demonstrate that reactors loaded with multiple wires are effective for MSR. In other words, the quantity of hydrogen generated hydrogen increased as the number of wires increased.
Hydrogen production rates per mass of catalytic Cu during MSR using microreactors packed with 3 or 20 wires.
In subsequent trials, the S-type etched wires were compared with anodized wires, and the resulting hydrogen production rates are summarized in Fig. 10. These data show that the hydrogen production rate using the anodized wires was higher than that obtained from the S-type etched wires. BJH analysis demonstrated the presence of fewer 10 nm mesopores in the S-type etched wires compared with the anodized wires, and we contend that this difference affects the diffusion resistance inside the catalyst layer. It is also inferred from this result that there was diffusive resistance inside the catalyst layer on the etched wires.
Hydrogen production rates per mass of catalytic Cu during MSR using microreactors packed with S-type etched wires or anodized wires.
In a third series of trials, we changed the etched structure to improve the diffusion inside the catalyst layer. The improved G-type etched wires contained a low density of hydrated alumina because there was little aluminum remaining in the etched layer. In contrast, the catalyst layer on the S-type etched wires was filled with the hydrated alumina. Consequently, the G-type etched wires contained voids and numerous mesopores with sizes of approximately 10 nm in the hydrated alumina. The resulting hydrogen production rates are shown in Fig. 11. The rates obtained from the G-type etched wire-1 and -2 samples were increased compared with that of the S-type etched wires, and these G-type specimens exhibited performances very similar to that of the anodized wires. The catalyst layers on the G-type etched wires were evidently highly efficient because the G-type etched wire-2 sample maintained high performance even when the thickness of its catalyst layer was greater than that of the S-type etched wires.
Hydrogen production rates per mass of catalytic Cu during MSR using microreactors packed with S-type etched wires or G-type etched wires-1 and -2.
Comparative results obtained from the MSR reaction using the microreactor filled with wires and the granular-type catalysts are shown in Fig. 12. It can be seen that the output of the S-type etched wires was more than 30% greater than that of the granular catalyst at 593 K. It should also be noted that these two materials exhibit distinct trends with regard to the increasing conversion as the temperature is raised. The Arrhenius plots obtained from these data are provided in Fig. 13; these plots were used to calculate activation energies based on their slopes. The activation energies for the MSR reaction are summarized in Table 2. As can be seen, the granular reactor exhibits diffusive resistance at high temperatures, because the activation energy of the granular catalyst is lower at elevated temperatures. From these data, we conclude that the wire-filled reactor does not show problematic external diffusive resistance at any temperature, because the diffusion length in the microchannels between wires is minimal. Additionally, we believe that the catalyst in the etched wires was used more effectively in the reaction than that in the granular material because the external diffusion distance in the microchannels of the reactor filled with the catalytic wires was shorter than that of the reactor containing the granular catalyst having particle sizes of 0.5–1.0 mm.
Hydrogen production rates per mass of catalytic Cu during MSR using microreactors packed with catalytic S-type etched wires or the granular catalyst.
Arrhenius plots for the MSR reaction over catalytic S-type etched wires and the granular catalyst.
| Catalyst | Activation energy, E/(kJ/mol) |
|---|---|
| S-Type Etched Wire | 96.9 |
| Granular (high temp.) | 50.1 |
| Granular (low temp.) | 85.6 |
This study successfully developed a novel catalyst support based on sponge-structured etched aluminum that appears to be effective. The combination of AC electrochemical etching, hydration and calcination demonstrated herein should allow the simple, low-cost fabrication of catalyst supports while allowing for continuous mass production. This process also produces a strong interconnection between the etched wire substrate and the catalyst layer, because of the uneven aluminum structure, and avoids the formation of cracks and separation of the alumina support layer after heat treatment and impregnation. Etched wires made using this technique were compared with anodized wires that had cracks in the catalyst layer but exhibited high performance. This work also demonstrated that the diffusion inside the catalyst layer can be controlled by varying the etched structure of the support layer. To investigate this effect, we produced G-type etched wires by changing the etching conditions to improve both internal diffusion and catalytic performance. These G-type wires were also compared with anodized wires and demonstrated almost the same level of efficiency. Additionally, as a result of the internal structure, the catalyst layers on the G-type etched wires had fewer cracks and a stronger connection with the aluminum substrate compared with the S-type etched wires.
We also designed and constructed a micro-structured catalytic wall tubular reactor, using wires situated parallel to one another within the device. In this configuration, microchannels were formed between wires on which catalytic layers had been generated by etching and hydration. Reactors loaded with multiple wires were found to be effective. We confirmed that the microchannels in these wire reactors did not generate problematic external diffusive resistance at any temperature, because of the minimal diffusion lengths in the microchannels between the wires. In addition, the external diffusion distance of the catalytic wire reactor was shorter than that of the granular catalyst reactor. For these reasons, the etched wire reactors showed higher performance that that of a reactor containing granular catalyst particles with diameters of 0.5 to 1.0 mm.
It should be possible to increase the hydrogen production rate of such reactors by using longer catalytic wires and increasing the number of wires. Additionally, the volume efficiency could be improved by optimizing the etched layer structure and thickness as well as the wire diameter.
