Design, imaging and performance of 3D printed open-cell architectures for porous electrodes: Quantification of surface area and permeability

Background: The development of new open-cell porous electrodes for electrochemical flow cells and reactors is demonstrated through the application of 3D printing. The properties of diverse architectures were investigated, including rectangular, circular, hexagonal and triangular cells with linear porosity grades of 10, 20 and 30 pores per inch. Specimens were digitally designed, then 3D printed in stainless steel via selective laser melting. After being examined using scanning electron microscopy, they were characterised in terms of volumetric surface area and porosity with the aid of X-ray computed tomography. Pressure drop measurements were performed over a range of mean linear velocity and Reynolds number, allowing the estimation of Darcy’s friction factor and permeability. Results: Volumetric surface area estimated from tomography scans was up to 36% higher than the nominal values due to surface roughness and post-processing algorithms. In contrast, volumetric porosity obtained by tomography agreed fully with measured values. Triangular architectures afforded additional surface area both digitally and according to tomography. The largest pressure drop was found in circular materials, the triangular ones showing the lowest. The 20 ppi triangular architecture had a volumetric surface area of approximately 44.5 cm -1 and a permeability of 2.31 × 10 -5 cm 2 . Conclusion: Triangular architectures were preferred due to their favourable combination of high surface area and high permeability with low mass and reduced digital complexity. This provides a strategy to initiate the optimization of 3D printed porous electrodes for electrochemical flow cells and reactors in novel and niche applications.


Introduction
Interest in innovative 3D printed electrochemical devices continues to grow. 1,2 One of the most important and promising applications is the development of tailored electrochemical flow reactors with enhanced efficiency for electrochemical processing and energy storage and conversion. 3,4 3D printing already offers the possibility of manufacturing fast prototypes 5 and working models of electrochemical flow reactors 6 and electrolysers, 7 enabling their design through a recently proposed cycle of conceptualization, simulation, rapid prototyping and experimental validation. 8,9 However, it is also important to adequately assess the characteristics of electrodes produced by 3D printing in order to predict their performance realistically and to enable the design of improved electrochemical reactors.
A growing number of 3D printed architectures are based on periodic cellular materials for use as porous electrodes in electrochemical technologies. 10,11 Such electrodes increase the productivity of electrochemical reactors by providing extended active surface area and enhancing mass transfer of reactants compared to planar electrodes. 12 Ideally, porous electrode materials should have good electrical conductivity, high volumetric surface area and high hydraulic permeability, 13 leading to more efficient, compact reactors. The electrode structure can then be modified using a wide diversity of catalysts and hierarchical structures, adding functionality and selectivity. 14,15 3D printing can provide control over pore size and shape, distance between pores, volumetric porosity and surface area of the porous structures within the manufacturing resolution. Such advances could find novel or niche applications for 3D printed electrodes in water treatment, 16,17 electrosynthesis, 18,19 environmental remediation, 20,21 and energy storage. 22,23 In the case of 3D printed metallic electrodes, 15 the technique chosen in this contribution creates tailored architectures by layer-by-layer deposition of a precursor powder through selective laser melting (SLM). 24 Compared to other laser-based techniques, SLM results in better surface morphology, homogeneity and mechanical properties. It permits the production of components not only in ferrous alloys but also in titanium, aluminium and copper. 24 The potential for this concept in electrochemical flow cells has been demonstrated by 3D printed stainless steel electrodes coated with nickel 3 and MoS2 7 and by 3D printed titanium electrodes coated with TiO2 25 and platinum. 26 SLM has also been applied to produce helical electrodes, 27 moulds for sintered electrodes 28 as well as static cells for sensors 29 and oxygen evolution. 30 The analysis of 3D printed porous electrodes can be carried out by X-ray computed tomography (CT) in order to estimate or validate their volumetric porosity, solid volume, physical surface area and derived parameters. 31 These characteristics are essential to assess their performance and to the calculation or simulation of their hydrodynamic, ohmic and kinetic behaviour. 32 The physical surface area of these materials and its comparison to active electrochemical surface area is particularly important in electrochemical studies. 33,34 Examples involving conventional porous electrodes by CT include the tortuosity of carbon felt, 35 the surface area of reticulated vitreous carbon (RVC) 31 and the distribution of metal deposits such as copper and cadmium 36 or platinum. 37,38 Related examples of the analysis of inert porous materials by CT include the determination of pore diameter distribution in SiC-Al2O3 foams 39 and the study of porosity and tortuosity in SiC foams. 40 Similar structural and parametrical analysis would certainly be of interest in non-electrochemical 3D printed flow reactors, such as those recently proposed for the enhancement of heterogeneous reactions and separation processes. 41 Following the characterization of the material, the performance of a porous electrode in an electrochemical flow reactor can be quantified by the volumetric mass transfer coefficient, kmAe, and its relationship to the pressure drop, ∆P, which is caused by frictional losses as the electrolyte flows through the porous structure. 3,42,43 The first is strongly related to the limiting current density and the minimization of overpotentials. 12 The latter depends on the permeability of the material which affects pumping energy demand and energy efficiency. 44 A low pressure drop also facilitates the assembly and operation of leak-free reactors. Electrodes having high volumetric surface area and high permeability are required for an energy efficient electrochemical process. A comparative study of porous electrode architectures can be initiated by seeking such characteristics, before progressing to electrochemical aspects.
After introducing 3D printed porous electrodes for electrochemical flow reactors 3 and applying CT to the analysis of the surface area of porous electrodes, 31 we now turn our attention to the development of diverse 3D printed porous architectures for use in electrochemical flow reactors. This approach is an example of a 'virtuous cycle' in which a rational development for porous electrodes, based on the digital design of tailored structures, is followed by their manufacture, subsequent imaging and analysis of their physical properties then the evaluation of their performance. 8,9 See Figure 1. Up to now, attention has been focused on the achievement of smaller pore sizes or on the increase of mass transfer, neglecting the parameters of surface area (which is directly linked to the electrochemical performance) and hydraulic permeability (which is of utmost importance in a practical flow device.) The novelty of this work lies in the methodology for selecting a 3D printed electrode architecture. We have aimed for maximum surface area and high hydrodynamic permeably, an important step towards the development of advanced electrode materials. Work in progress will utilise the results of this study in the assessment of the electrochemical performance and application of the 3D printed electrodes under mass transfercontrolled conditions.

Surface area
The volumetric surface area, Ae, is an important property of a porous electrode material and is the ratio of its total surface area, A, to its volume VR (in a specimen or inside an electrochemical reactor): Ae, can then be used to rationalize the performance factor kmAe via the estimation of a limiting current, IL, or mass transfer coefficient, km, during electrochemical characterization of the material. 34,45,46 The electrode area per unit solid volume, Asv, is related to Ae and the volumetric porosity of the material, ε : 47 Asv can also be determined using the Ergun equation in the case of materials with relatively small pore sizes, 39,48 facilitating comparison with other porous electrodes. The value of Asv is particularly useful as an indicator of how well a porous body can maximise its surface area. A similar parameter is the specific surface area, which relates surface area and mass of material.

Pressure drop
Regarding pressure drop through the porous electrodes, a normalization is useful, in terms of the fluid flow regime, to enable comparisons. A simple approach can consider the mean linear velocity of the fluid, v as it passes through the porous material. It is given by the expression: 49 where Q is volumetric flow rate and Ax is the cross-sectional area of the porous material.
where ρ is density and µ is dynamic viscosity. The experimental value of ∆P can be conveniently fitted to an empirical power law involving Re: 50 ∆8 = 323 9 (5) where e and h are empirical constants; their values define this relationship, which is specific to each porous material.
∆P can be used to calculate Darcy's friction factor, fD, as an indicator of the intensity of frictional losses. This friction factor can be plotted as a function of v or Re allowing a comparison of different porous media: where L is the length of the porous material experiencing the flow. Darcy's friction factor, fD has been employed to characterize rough electrodes, 51 mesh spacers 52,53 and porous electrodes. 42,54 Similarly, Darcy's permeability, KD can be used to characterise the influence of electrode geometry on the fluid flow. 55 From Darcy's law, this property defines how fast fluid passes through a volume of porous material per unit of differential pressure and is an indicator of how well the pores are interconnected. 48 It is calculated from the expression: KD has been used to describe the suitability of electrode materials in electrochemical reactors, 56 for instance in redox flow batteries. 54 Figure 3. The arrangement of the pores was such that they formed rectilinear grids in the horizontal direction which were staggered in the vertical direction. The characteristic lengths of the void, interconnected cells ranged from 0.7 mm to 2.6 mm. Table 1 provides a list of their nominal characteristic lengths, linear and volumetric porosity and surface areas according to the CAD program.

3D printing of porous materials
The complex porous geometries, which would have been very problematic to manufacture using traditional machining methods, were printed layer-by-layer using a M2 Cusing (ConceptLaser GmbH, Germany) SLM metal printer with a maximum resolution of 20 micrometres and a power of 200 W under a N2 gas environment. The precursor powder was a 316L (CL20 ES) austenitic stainless-steel (Fe base containing 17.5% Cr, 11.5% Ni, 2.3% Mo) with particle sizes between 20 and 40 µm in diameter. The 3D printed electrode materials are shown in the Supplementary Material; Figure S6a). The mass, diameter and height of the specimens were measured in order to determine their volumetric porosity, ε, and compare it with CAD values. Assuming that the internal microporosity of the material was negligible, ε was calculated from the expression: where Vbulk is the bulk volume of the specimen and Vsolid is the volume of the metal. These values were calculated using the following equations: where D and H are the measured diameter and height of the specimen, respectively, m is the mass of the material and ρ is the density of stainless steel (7.98 g cm -3 for austenitic grade 316L material). 59 Mass was measured in an analytical balance (Mettler-Toledo Inc., USA) to an accuracy of ±1 mg. Dimensions of the 3D printed samples were taken with a digital calliper (Mitutoyo Corp., Japan).

SEM and CT imaging
SEM images of the 3D printed specimens were obtained at 15 kV using a JSM-6500F field emission electron microscope (Jeol Inc, USA). X-ray CT scans were performed in a modified (Volume Graphics GmbH, Germany). Volume and surface area were established using the 'ISO50%' threshold condition.

Pressure drop measurements
Pressure drop measurements were carried out with distilled water in a tubular, circular section flow cell with internal and external diameters of 30 mm and 40 mm, respectively. The clear acrylic polymer flow cell consisted of two threaded tube segments; see Figure S6b). The entry segment had a length of 30.0 cm, which is ten times larger than the internal diameter, to achieve a fully developed flow in the test section. 60 The outlet segment had a length of 10.0 cm and part of it had a wider internal diameter (3.02 cm) to hold the electrode samples. In order to prevent any bypassing of flow, waterproof adhesive tape was placed between the samples and the tube by compression; see Figure S6c). Pressure drop was measured with a HT-1890 digital manometer (Risepro, China) at pressure taps drilled in the flow cell as close to the porous material as the arrangement allowed, using two polypropylene tubes (2 mm internal diameter) sealed with epoxy resin; see Figure S6d).
During the experiments, the flow cell was mounted horizontally, having first removed air bubbles   Indeed, in previous work on the study of RVC by CT, 62 it was found that this technique was useful in determining properties derived from a 3D volume (such as porosity), whereas those derived from 2D surfaces required ad hoc image post processing and calibration in order to achieve sufficient accuracy.

SEM and CT characterisation
The estimation of the surface area of 3D printed porous materials from CT scans was also explored.
As seen in Table 2, the CT values are higher than the nominal CAD values due to the roughness of the manufactured samples. In the case of the rectangular pores, the difference in the surface area increases along linear porosity grade but the opposite is true in the case of the samples with triangular pores. Given the limited number of specimens, a clear trend cannot be established in relation to surface area vs. porosity at this point. However, it can be safely assumed that the real surface area of these porous geometries is larger than in the CAD drawings. As mentioned above, surface area properties are less accurate than the CT-determined volumetric porosity. 31 A validation of the surface area of the 3D printed specimens as estimated by CT would require demanding work and careful consideration of the resolution and thresholding algorithms used to process the CT rendering of the specimens, 63 as it is known that the ISO50% algorithm is not always accurate. 64 These tasks are outside the scope of this work but such dependencies have been discussed in the case of RVC. 31 The values of Ae and Asv can be calculated from the surface area values for the 3D printed electrode architectures using Eqs. (1) and (2), respectively. The results are shown in Table 3 can still be presented cautiously for comparison purposes. Indeed, as shown in Table 3, Ae values are up to 35% larger while As is underestimated with a large dispersion between 3 and 38%. The fact that CT surface area properties are not accurate for the 3D printed specimens in this work is reinforced by the fact that the linear relationship of Asv vs. Ae intersects the y axis at a positive value. See Figure 5b). |Similar behaviour was observed when surface areas were calculated for RVC from CT scans with insufficient resolution in disagreement with direct methods. 31 Clearly, there are research opportunities in studying the metrology of open-cell 3D printed porous materials and improving software approaches to the computation of surface area-related characteristics.

Pressure drop
The pressure drop taking place across the 20 mm-long 3D printed porous samples is shown in Figure 6a) as a function of mean linear velocity and in Figure 6b The relationship between pressure drop and Reynolds can be described in a practical manner by a log-log plot, as shown in Figure 7. Here, the pressure drop over the 3D printed porous materials follows a linear power law (see Eq. 5). Thus, a set of two empirical coefficients can characterize their behaviour. These values are given in Table 4, along values found in the literature for Pt/Ti felt (ε = 0.80), mesh (ε = 0.71), micromesh (ε = 0.53) and a polypropylene turbulence promoter (TP) mesh (ε = 0.78) in a rectangular flow channel, 73 the FM01-LC electrochemical reactor, 50 and a rectangular channel reactor with a small interelectrode gap. 74 It can be seen that, for these 3D More recently, porosity and tortuosity of SiC foams obtained from CT scans were used to predict the pressure drop across these materials. 40 The application of these strategies to the architectures here presented for electrochemical flow reactors can be expected.

Friction factor, fD
The normalized frictional losses across the porous materials were determined using Darcy's friction factor. Figure 8 shows

Darcy's permeability, KD
Darcy's permeability was also calculated based on the pressure drop readings. This coefficient is independent of the viscosity of the fluid and density, therefore, KD of porous electrodes determined in different liquids (or electrolytes) can be compared. Figure 9 shows the permeability of the 3D The average values of Darcy's permeability for each porous architecture are listed in Table 5 in increasing order. The 3D printed structure with circular pores, grade 20 ppi is the least permeable, and therefore not the best option in terms of increasing the efficiency of an electrochemical reactor.
It is followed by the 30 ppi rectangular electrode. Interestingly, the 10 ppi rectangular and 10 ppi rectangular (2 mm pore size) specimens as well as the 20 ppi rectangular and 20 ppi rectangular (1 mm pore size) specimens show very close values for all the evaluated mean linear flow velocities. One could argue that, in these cases, the size of the pores affects the permeability coefficient to a greater extent than their shape. Therefore, it could be stated that the electrodes with rectangular and hexagonal pores could be used interchangeably. However, when considering its greater volumetric surface area, see Table 3, the rectangular 20 ppi material should be chosen for an electrochemical application over the hexagonal equivalent.
Triangular porous structures are the most permeable, having higher KD values than those of the other geometrical shapes for both 10 ppi and 20 ppi materials; see Table 5. Moreover, the 10 ppi triangular 3D printed material also produced the lowest pressure gradient and frictional losses.
This means that, as a flow-through or flow-across porous electrode, it would require the least electrolyte pumping power among the specimens evaluated in this study (as long as the same flow direction relative to the structure is kept). This is seen more clearly in a plot of KD vs. Ae (as given by CAD). Such relationships, shown in Figure 10a) for all the evaluated porous architectures, indicate the ideal trade-off between electrode surface area and hydraulic permeability, i.e.
resistance to the fluid flow of an electrolyte. (The same plot taking the Ae values estimated from uncalibrated CT can be seen in Figure S8 in the Supplementary Material. In it, the triangular architectures also perform better the other pore geometries.) Continuing with Figure 10, the Ae of the CAD 10 ppi triangular specimen was between approximately 1.2 and 1.7 times larger than the surface areas of the electrodes of the same grade but different geometries; see Table 3. It also has close to 25% less mass; see Table 2. This could be a beneficial factor in terms of minimizing the net size, mass and cost of the electrochemical reactor. Furthermore, the 20 ppi triangular specimen has about twice the Ae of its 10 ppi grade equivalent, being also approximately 30% superior to the rectangular and hexagonal geometries.
This, suggests that the 20 ppi triangular structure could be advantageous as a porous electrode in an electrochemical flow reactor, having the best combination of high permeability and high surface area among the materials designed in this work. A plot of KD vs. Asv, seen in Figure 10b), shows essentially the same trends.
These KD values of the 3D printed porous materials can be put in perspective when compared to those reported in the literature; see Table 6. KD decreases with decreasing pore diameter of opencell foams. 75 The reason for this is that for decreasing pore diameter there are more struts in the same volume which obstructs fluid flow. 39 Materials with similar volumetric porosity display close values. Among those previously reported, porous SiC-Al2O3 (ε = 0.85) 39 and alumina foams (ε = 0.80) 55 have permeability values of 5.1 × 10 -5 cm 2 and 6.2 × 10 -5 cm 2 , respectively, being close to the triangular 10 ppi design. Meanwhile, 0.70 porous aluminium foam has a permeability of 1.2 × 10 -5 cm 2 , 76 being quite close to the 20 ppi hexagonal and rectangular pore architectures.
Additionally, the latter is just under the 1.7 × 10 -5 cm 2 values reported for Pt/Ti micromesh electrodes. 73 As expected, the permeabilities of materials having significantly larger volumetric porosity or much larger pore sizes are at least one order of magnitude higher than the values presented in the current work. This is the case of aluminium foams with a porosity of 0.92 (108.9 × 10 -5 cm 2 ), 68 and expanded metal mesh (71.0 × 10 -5 cm 2 ). 73 The opposite is true for materials with very small pores, such as carbon felt (0.2 × 10 -5 cm 2 ), or titanium felt (0.1 × 10 -5 cm 2 ), which are less permeable than the circular 20 ppi geometry. In summary, the 3D printed porous architectures display a wide range of hydrodynamic permeability and can be made analogous to conventional porous materials. • CT revealed irregularities in the 3D printed materials due to laser movement tolerances, although this could be avoided with the optimization of printing parameters. Volumetric porosity values obtained from CT corresponded to the ones calculated from the measured mass and volume of the specimens. On the other hand, CT surface area estimations turned out to be between 10% and 36% higher than the CAD surface areas. However, our results indicate the importance of surface area metrology in 3D printed porous materials for better accuracy in these estimations.