Investigating Mass Transfer Relationships in Stereolithography 3D Printed Electrodes for Redox Flow Batteries

Porous electrodes govern the electrochemical performance and pumping requirements in redox ﬂow batteries, yet conventional carbon-ﬁber-based porous electrodes have not been tailored to sustain the requirements of liquid-phase electrochemistry. 3D printing is an eﬀective approach to manufacturing deterministic architectures, enabling the tuning of electrochemical performance and pressure drop. In this work, model grid structures are manufactured with stereolithography 3D printing followed by carbonization and tested as ﬂow battery electrode materials. Microscopy, tomography, spectroscopy, ﬂuid dynamics, and electrochemical diagnostics are employed to investigate the resulting electrode properties, mass transport, and pressure drop of ordered lattice structures. The inﬂuence of the printing direction, pillar geometry, and ﬂow ﬁeld type on the cell performance is investigated and mass transfer vs. electrode structure correlations are elucidated. It is found that the printing direction impacts the electrode performance through a change in morphology, resulting in enhanced performance for diagonally printed electrodes. Furthermore, mass transfer rates within the electrode are improved by helical or triangular pillar shapes or by using interdigitated ﬂow ﬁeld designs. This study shows the potential of stereolithography 3D printing to manufacture customized electrode scaﬀolds, which could enable multiscale structures with superior electrochemical performance and low pumping losses.


Introduction
[8][9] In RFBs, the energy is stored in an electrolyte solution containing dissolved active species, stored in external tanks, which are pumped through the electrochemical stack where the active species undergo electrochemical reactions. [10]The electrochemical stack defines the power density of the system, which is governed by the flow fields, electrodes, and membranes employed.However, current RFBs are unoptimized and remain too costly for widespread deployment. [4,11]One approach to increase their cost competitiveness is to enhance the power density and efficiency of the electrochemical cell, for example, by engineering porous electrodes tailored for application in RFBs.Porous electrodes are performance-and cost-defining components that provide the electrochemically active surfaces for the electrochemical reactions, the porous structure for the electrolyte distribution, and facilitate mass, charge, and heat transport. [10,12]These properties are influenced by the choice of material, electrode structure, and manufacturing technique.
Conventional porous electrodes used in RFBs are fibrous mats, fabricated by the carbonization of polymer precursors, assembled in coherent structures such as papers, cloths, and felts.The electrode structure and thickness are controlled by the manufacturing process, such as weaving, compacting, hydroentangling, and electrospinning, and thus by the arrangement of the micrometric fibers. [4,13]][16][17][18][19] We and others investigated the influence of the electrode structure on the electrochemical performance and pressure drop.We showed that the woven cloth electrode utilizes the highest current density and lowest pressure drop, which we assigned to the bimodal pore size distribution (PSD) and well-defined electrode structure. [8]dditionally, Simon et al. investigated the performance of two cloth and two paper electrodes and suggested that the permeability of fibrous materials strongly correlates to the electrochemical cell behavior under forced convective conditions.Hence, they found that the cloth electrodes with higher permeability, inter-pore connectivity, and mass-transfer coefficients display enhanced RFB performance. [19]Furthermore, Tenny et al. investigated the nuanced relationships between the morphology of various cloth electrodes and their electrochemical performance and pumping requirements and suggested that the 1071 HCB plain weave pattern offers the best performance trade-off. [14]Although these studies gained insights into the requirements of electrodes for RFB application (i.e., well-defined structure, bimodal PSD), the investigated commercial electrodes are repurposed fuel cell gas diffusion electrodes and are not optimized for their use in all-liquid RFBs. [4,20]In addition, the conventional manufacturing and functionalization methods mainly focus on the optimization of the microstructure, but the electrolyte distribution, electrode-electrolyte interface, and electrode conductivity remain unidentified. [13,21,22]Incomplete understanding of the structurefunction-performance relationships and the interplay between the electrode and other RFB components (including the flow field and electrolyte chemistry) challenge the deterministic design of electrode materials.Furthermore, conventional electrodes have limited morphological diversity, constricting the physicochemical properties of the electrode (e.g., low structural control, confined PSD), and thus limiting the electrode permeability.Hence, these limitations motivate the development of new synthesis and manufacturing techniques with large control over the materials' properties, macro-, and microstructure.
Recently, additive manufacturing, or 3D printing, has been employed to fabricate customized electrodes, enabling the finetuning of the fluid transport and electrochemically active surface area. [13,23]In addition, additive manufacturing has great potential for upscaling as the manufacturing can be parallelized and combined with the electrochemical reactor design by e.g., multi-material 3D printing. [23,24]Several additive manufacturing techniques have been employed to fabricate electrodes for electrochemical devices [5,24,25] including material jetting, [26] material extrusion, [13,[27][28][29][30][31][32] powder bed fusion, [33,34] VAT photopolymerization (i.e., stereolithography (SLA), [22,35,36] digital light processing [37,38] ), and two-photon polymerization. [39]The choice of precursor (e.g., metals, plastics, composites, inorganics [24] ) and the manufacturing method control the structural properties of the electrode comprising the feature size, geometry, porosity, size, surface roughness, and mechanical stability, as well as the manufacturing time. [25]Various studies have been conducted on using metals like stainless steel and nickel as electrodes for electrochemical energy storage applications [28,29,33,34] ; however, metal-based electrodes are generally not as viable compared to carbon-based electrodes due to elevated costs and corrosion resistance in relevant electrochemical environments.Moreover, carbonaceous materials have high electrical conductivity and stability and are inexpensive.][42] Therefore, several research groups have shown interest in using polymer precursors [36] followed by carbonization to manufacture carbon-based electrodes, [35] also recently for the fabrication of RFB electrodes. [13,22]Wang et al. presented a novel hybrid method to fabricate porous carbon electrodes with pores spanning the millimeter to nanometer scale by combining SLA, carbonization, and chemical activation.They showed that by tuning the pore diameter and overlap ratio, electrode characteristics such as porosity, thickness, specific surface area, and electrical resistance can be engineered.They additionally tested their 3D printed designs in a supercapacitor and a vanadium RFB and observed that for the RFB a large specific surface area was found to be crucial in achieving enhanced electrochemical performance. [22]Moreover, Beck & Ivanovskaya et al. designed 3D printed carbon-based graphene aerogel electrodes with simple cubic and face-centered cubic lattice structures using the material extrusion method.They revealed that structures with engineered flow enhance mass transfer in flowthrough electrodes as the mass transport properties strongly depend on the flow when operating in the inertial regime. [13]hese studies showed the potential of utilizing 3D printing to manufacture electrodes for RFBs, where the printing resolution, time, and dimensions are the main hurdles in commercially exploiting additive manufacturing for porous electrodes.Furthermore, advances in understanding the role of the electrode structure on both the electrochemical performance and pressure drop should be made to optimize or engineer next-generation porous electrodes. [4,43,44]Nonetheless, utilizing additive manufacturing techniques enables the electrode structures to be manufactured in a rigorous and parametric manner, allowing reactor design-dependent (i.e., flow field geometry, electrolyte chemistry) optimization.
In this work, we focus on understanding the impact of the electrode structure on the mass transport properties of ordered lattice structures in flow cells.Thereby contributing to the understanding of the structure-function-performance relationships in RFBs by exploring novel in-house manufactured electrode architectures.We investigate the influence of the printing direction, pillar geometry, and flow field design on the mass transport in the electrode, and provide insight into the design flexibility [22] and orientation (printing direction) of SLA 3D printing to examine the challenging trade-off between electrochemical performance and pumping requirements.We utilize SLA in combination with carbonization to obtain conductive carbon electrodes which are studied in single electrolyte flow cells containing an organic redox couple with an acetonitrile-based electrolyte, a model electrolyte because of its low surface tension and fast kinetics, [7,11,[45][46][47] and compared the printed structures to commonly used commercial electrodes.
In this study, we first discuss the manufacturing of the 3D printed electrodes (Figure 1a), comprising the thermal treatment steps and structure evaluation.Second, we analyze the physicochemical properties of the 3D printed electrodes including the carbon content, conductivity, and surface area.Third, we examine the pressure drop of the printed electrodes.Fourth, we describe the effect of a horizontal, vertical, and diagonal printing direction on the structure performance (Figure 1b), followed by the influence of distinct flow fields (flow through and interdigitated, Figure 1c), and pillar shapes (square, triangle, cylinder, and helix, Figure 1d).Lastly, we analyze the influence of the printing direction, flow field, and pillar shape on the dimensionless mass transport within the electrode, where we make a comparison between the 3D printed electrodes and two commercial porous electrodes to evaluate their potential for RFB applications.This study shows the capability of 3D printing to manufacture customized structures, enabling the fine-tuning of the electrochemical performance and pressure drop of porous electrodes.We hypothesize that a combination of additive manufacturing with emerging computational approaches in topology optimization [21] could enable the bottom-up design and manufacturing of advanced electrode materials.

3D Printing
The four 3D printed electrode designs (30 × 30 × 1.5 mm 3 , Figure 1d) were drawn using the AUTOCAD (LT 2023) software.The void space of one repeating unit of the square and helical designs, hereafter referred to as pores, was 0.9 × 0.9 × 0.9 mm 3 in size with a pillar thickness of 0.3 mm, the triangular design pores of 0.81 × 0.81 × 0.81 mm 3 with pillars of 0.48 mm, and the cylindrical design pores of 0.72 × 0.72 × 0.72 mm 3 with pillars of 0.48 mm, resulting in a calculated porosity of ≈77% for all designs.The AUTOCAD designs were loaded into the 3D printing software PreForm (Formlabs) where the 3D designs were translated to printable structures by adding a baseplate and support pillars using the auto-generate option (density of 1.00 and a touchpoint size of 0.50 mm), connecting the baseplate to the 3D design (Figure S1, Supporting Information).The designs were orientated parallel to the printing platform for the horizontal printing direction, whereas, for the vertical and diagonal printing directions, the designs were orientated with a 90°and 45°a ngle to the printing platform, respectively (Figure 1b, Figure S1, Supporting Information).The stereolithography 3D printer Form 3 (Formlabs) was used with the clear acrylate-based UV-curing High Temp V2 (Formlabs) resin.The 3D printer was equipped with a 405 nm laser, a power of 120 mW, a laser spot size of 85 μm, an XY motor resolution of 25-300 μm (based on the printer settings), and a Z motor resolution of 25 μm, provided by Formlabs, where the X/Y/Z resolution refers to the laser step size in the specified direction.The total printing time was ≈1 h per structure.Finally, the 3D prints were washed using Form Wash (Formlabs) for 5 min in isopropanol to rinse off the excess resin.

Thermal Treatment
To understand the thermal response of the resin in terms of its thermal stability and degradation, thermogravimetric analysis (PerkinElmer TGA 4000 apparatus) was performed.The thermogravimetric analysis was performed from room temperature to 1000 °C using a ramp rate of 10 °C min −1 and an oxygen or nitrogen gas flow of 20 mL min −1 .After printing the structures, the polymeric scaffolds were thermally treated to form conductive electrodes.First, the 3D printed material was oxidized in a muffle oven (Naberthem model P300) under atmospheric air at 250 °C for 5 h at the peak temperature with a ramp rate of 1 °C min −1 which functioned as a stabilization step in obtaining the 3D structure with minimal deformation. [48]Subsequently, the material was carbonized in a tubular oven (Carbolite so.3/96/782, TZF 12/75/700) under a nitrogen atmosphere (0.2 mPa) for 1 h at a peak temperature of 850 °C with a ramp rate of 5 °C min −1 for all structures, except for the cylindrical pillar design.The cylindrical pillar design was carbonized with a ramp rate of 1 °C min −1 to prevent structure deformation because of the slightly reduced porosity.Volume shrinkage and thickness decrease occur during carbonization because of the out-gassing of gaseous products, which could lead to structure deformation, including curling due to compressive forces during volume shrinkage. [40]Therefore, the structures (six at once) were placed in a perforated metal framework consisting of stainless-steel plates separated by 2 mm bolts (Figure S2, Supporting Information) to constrict the samples whilst allowing gas release (Figure S3c, Supporting Information).

Microscopy, Spectroscopy, and Tomography
The 3D printed surfaces and cross-sections after printing, oxidation, and/or carbonization were examined with a scanning elec-tron microscope (SEM, JEOL JSM-IT100) using a secondary electron imaging (SEI) detector with a 10 kV acceleration voltage.The elemental composition, carbon, oxygen, and nitrogen content of the 3D printed structures were examined with the energydispersive X-ray spectroscopy (EDS) detector.To eject more electrons out of the sample, the acceleration voltage was increased to 16 kV.The non-carbonized samples were sputter coated in an argon environment with platinum at 40 mA for 60 s before imaging, using a Jeol JFC-2300HR high-resolution fine coater.The equivalent pore diameter was obtained from the SEM images by measuring the pore area using the median filter, threshold, and measuring tools of ImageJ.The pore area was used to calculate the equivalent pore diameter assuming the pore is a perfect circle with the measured pore area, see the inset of Figure 2b for a visual representation.The electrode thickness was measured using a micrometer at five different locations on the electrodes for all manufactured electrodes (six electrodes per investigated system, n = 6).
The elemental analysis of the samples was additionally performed using X-ray Photoelectron Spectroscopy (XPS) using a Thermo Scientific K-alpha X-ray photo-electron spectrometer equipped with a monochromatic small-spot X-ray source and a 180°double-focusing hemispherical analyzer with a 128-channel detector.The spectra were obtained using an aluminum anode (Al K = 1486.6eV) source operating at 72 W with a spot size of 400 μm.Survey scans were measured at a constant energy pass of 200 eV, whereas the region scans for carbon, oxygen, and nitrogen were measured at 50 eV.The background pressure was set to 2 × 10 −8 mbar argon and rose to 4 × 10 −7 mbar argon during the measurement because of the charge compensation.
The 3D printed electrodes were scanned using a laboratory micro-CT (Scanco Medical μCT 100 cabinet microCT scanner, holder type U50822 with a diameter of 9 mm and a height of 78 mm) at an isotropic resolution of 3.3 μm per voxel.The scans were carried out using a peak potential of 55 kVp, a current of 72 μA, 4 W, and a 0.1 mm aluminum filter to acquire 580 projection images over 360 degrees.The gray-scale X-ray tomographic microscopy (XTM) images were subsequently processed using ImageJ by applying a 2D median filter with a radius of 2.0 pixels to reduce the noise in the images.Thereafter, each voxel was assigned to either the solid or void phase using a K-means cluster segmentation filter.A 3.3 × 3.3 mm 2 selection was made and imported in Paraview to extract the internal surface area, limited by the imported image size, XTM sample size, resolution, imaging time, and by the selection of an area without defects and curvature.For the visual representation of the samples in 3D, a smaller 1.7 × 1.7 mm 2 area selection was used.

Flow Cell Configuration
Symmetric flow cell experiments were conducted in a laboratoryscale flow cell platform [8,49,50] inside a nitrogen-filled glovebox (MBraun, LABstar, O 2 < 1 ppm, H 2 O < 1 ppm).The electrolyte solution was pumped through the flow cell using a Masterflex L/S Easy-Load II pump and LS-14 tubing, where the cell in-and outlets were connected to a single solution reservoir with separate tubing to ensure a constant state of charge at the cell inlets.Custom-made flow cells were used with machined polypropylene (McMaster-Carr) flow diffusers.Graphite current collectors (G347B graphite, 3.18 mm thick, MWI, Inc.) were used and milled with the desired flow field design: flow-through (two 13 × 1 × 0.5 mm 3 flow channels perpendicular to the electrolyte flow) or interdigitated (seven 16 × 1 × 0.5 mm 3 channels parallel to the electrolyte flow, of which four inlet and three outlet channels), to distribute the electrolyte to and through the porous electrode (Figure 1c).On each half cell, one printed electrode with a geometric area of 2.55 cm 2 (1.7 cm × 1.5 cm) was confined within a 1 mm incompressible polytetrafluoroethylene gasket (ERIKS).The commercial electrodes, Freudenberg H23 and ELAT Cloth, with the same geometrical area, were confined within 165 or 375 μm thickness gaskets, respectively.One electrode was used per half-cell.A Daramic 175 (SLI Flatsheet Membrane, 175 μm) porous separator was used to separate both half-cells, and the cell was tightened to 2.2 N m.To account for differences in electrode thickness, the performance was compared at similar inlet velocities, where the 3D printed electrodes with a flow-through flow field (FTFF) were measured at 10, 5.0, 1.5, and 0.5 cm s −1 for the polarization experiments (based on previous work [15] ) and at 10, 5.0, 2.5, 1, and 0.5 cm s −1 for the limiting current density experiments, the 3D printed electrode with the interdigitated flow field (IDFF) at 4, 2.3, 1.5, and 0.5 cm s −1 for both experiments (limited by the upper limit of the peristaltic pump and tubes used), and the Freudenberg H23 and ELAT Cloth at 20, 10, 5, and 1.5 cm s −1 for the polarization experiments and at 20, 10, 5, 2.5, and 1 cm s −1 for the limiting current density experiments (limited by the lower limit of the peristaltic pump and tubes used).All experiments were performed with electrolyte velocities in descending order to enhance electrode wetting by the removal of residual gas bubbles in the cell.2) where Q FTFF and Q IDFF are the volumetric flow rate for the flowthrough flow field and interdigitated flow field, respectively.

Electrical Conductivity
The electrical conductivity of the carbonized 3D printed electrode was obtained by measuring the electrical resistance of the electrode in a flow cell configuration without flow, where one electrode (with a 1 mm gasket) was located between the two current collectors.The electrical resistance was measured using the Biologic VMP-300 potentiostat with electrochemical impedance spectroscopy at open circuit voltage with an amplitude of 10 mV and a frequency range of 10 kHz -50 Hz, 8 points per decade, 8 measurements per frequency, and a waiting time of 0.10 period before each frequency, where the high-frequency intercept was identified as the value of the electrode resistance, corrected for the high-frequency intercept of a cell without electrodes (i.e., only flow fields).The measurements were repeated two times for new assemblies (n = 2).The electrical conductivity,  e [S m −1 ], can be obtained from the electrode resistance according to where A e is the electrode area [m 2 ], (2.55 cm 2 ), and R e the electrode resistance [Ω].The electrical conductivity of commercial electrodes was measured with the appropriate gasket thickness (165 μm for the Freudenberg H23 and 375 μm for the ELAT Cloth) as characteristic length.Because of the nature of this measurement, the electrical conductivity was likely underestimated as contact resistances were not corrected for but could play a significant role.

Pressure Drop Measurements
The pressure drop measurements were performed with acetonitrile (MeCN, Acros Organics 99.9+%) as it had similar density, viscosity, and surface tension as the organic electrolyte due to the low species concentration used in this work.The difference between inlet and outlet pressures was measured when stabilized using pressure sensors (Stauff SPG-DIGI-USB, −1 -16 bar) over a range of flow rates depending on the pressure drop (3D printed electrode between 239.4 -89.8 mL min −1 , carbonized 3D printed electrodes between 180 -67.5 mL min −1 , Freudenberg H23 between 29.7 -1.5 mL min −1 , and the ELAT Cloth between 67.5 -16.9 mL min −1 ).For the pressure drop measurement, an altered cell design was used consisting of only one flow field, electrode, and gasket.The membrane in this configuration was replaced with a 3D printed backing plate (High Temp V2, Formlabs) and only one side of the cell was connected to the solution reservoir.The pressure drop of the cells with the electrode was corrected for a cell without an electrode to isolate the pressure drop through the electrode without piping and cell elements.All measurements were repeated twice for new cell assemblies (n = 2), and the pump was calibrated for different gasket thicknesses and flow fields used.The Darcy-Forchheimer equation was used to fit the pressure drop data to extract the permeability,  [m 2 ], of the electrodes according to the following equation: with ΔP the pressure drop [Pa m], L e the electrode length [m] (17 mm), μ the electrolyte viscosity [Pa s] (3.4 × 10 −4 Pa s [15] ),  the non-Darcy or Forchheimer coefficient [m −1 ], and  the electrolyte density [kg m −3 ] (852 kg m −3 [15] ).The Forchheimer coefficient accounts for inertial effects in the fluid flow. [8]The permeability and Forchheimer coefficients were extracted using a secondary polynomial fit of Equation (4).

Electrolyte Preparation
The oxidized form of the redox couple 2,2,6,6-Tetramethyl-1-piperidinyloxy-oxo hexafluorophosphate (TEMPO + PF 6 − ) was synthesized inside a nitrogen-filled glove box (MBraun, LABstar, O 2 < 1 ppm, H 2 O < 1 ppm) by chemical oxidation of 2,2,6,6-Tetramethylpiperidin-1-yl)oxyl (TEMPO, Sigma Aldrich 98%, 20.52 g) dissolved in acetonitrile by slowly adding 1.1 molar equivalents of nitrosonium hexafluorophosphate (NOPF 6 , Thermo Scientific, 95%, 25.28 g) during 3 h to prevent NO x build-up. [8]Afterward, a rotary evaporator (40 °C, gradual decrease from atmospheric pressure to vacuum) was used to recover the TEMPO + PF 6 − .Stock solutions of 750 mL were prepared and stored inside the glovebox for both the polarization and limiting current density experiments.The stock solution for the polarization experiments consisted of 0.1 M TEMPO, 0.1 M TEMPO + PF 6 − , and 1 M tetrabutylammonium hexafluorophosphate (TBAPF 6 , Sigma Aldrich >99%) dissolved in MeCN.For the limiting current density experiments, the concentration was lower and asymmetric where the concentration of the reduced species was five times higher, hence the limiting current was determined by the oxidation reaction.This solution consisted of 28.9 mM TEMPO, 5.78 mM TEMPO + PF 6 − , and 1 M TBAPF 6 dissolved in MeCN.For each experiment, 20 mL of the stock solutions were used per cell.

Electrochemical Performance
All electrochemical measurements, performed with a Biologic VMP-300 potentiostat, were repeated three times for new cell assemblies (n = 3) and new electrolyte solutions for each flowrate in descending order.Polarization and limiting current density measurements were performed by employing constant voltage steps of 0.05 V for 1 min and measuring the steady-state current over a voltage range of 0.0 -1.0 V. Electrochemical impedance spectroscopy measurements were performed at open circuit voltage with an amplitude of 10 mV and a frequency range of 2 Hz -200 kHz or 20 mHz -200 kHz, 8 points per decade, six measurements per frequency, and a waiting time of 0.10 period before each frequency, where the high-frequency intercept was identified as the value of the total cell resistance and was used to obtain the iR Ω -corrected potential data.Each cell was first stabilized by flowing the solution for the limiting current density experiments through the cell at the highest flow rate for ≈10 min.Thereafter, the limiting current density experiment was performed (impedance measurement to evaluate the resistance of the cell (2 Hz -200 kHz), polarization, and impedance (20 mHz -200 kHz)), after which the electrolyte was replaced, and the regular polarization experiment was performed (impedance, polarization, and impedance).

Limiting Current Measurements
The limiting current can be obtained by diminishing the active species concentration such that at an applied potential the surface concentration can be assumed zero.The limiting current was defined as [10,14,29,51] : where where C1 represents the dimensionless prefactor and C2 the dimensionless exponent.

Surface Area Determinations
The internal surface area of the 3D printed electrode was determined by three different methods.1) The first method was by algebraic calculations of the internal geometrical surface area by the set pillar and pore sizes for the 3D print (AUTOCAD), and by the measured pillar and pore sizes using SEM and ImageJ for the resulting carbonized structure, considering the geometry of spheres, cuboids, cylinders, and triangular prisms.
2) The second method was by measuring the ratio in exchange current densities between the 3D printed electrodes and the commercial Freudenberg H23 with known internal surface area (7.2 × 10 4 m −2 m −3 [8] ), as the exchange current density can be defined as: where j 0 is the exchange current density per electrode volume [A m −3 ], k 0 the standard rate constant [m s −1 ] that was assumed comparable for the different electrodes for the estimation of the surface area, C i/j the concentration [mol m −3 ] of the reduced and oxidized species (100 mol m −3 ), and  the charge transfer coefficient [−] of the reduced or oxidized species (we assumed 0.5 for both TEMPO and TEMPO + PF 6 − [52] ).The exchange current density was obtained from the polarization data by fitting the low current density region (<100 mA cm −2 ) to the Butler-Volmer equation [15] : ) [ exp where i is the current density per volume [A m −3 ] obtained from the polarization curve, C i,s the surface concentration of species i [mol m −3 ], C i,b the bulk concentration of species i [mol m −3 ], and  act the activation overpotential [V] obtained after iR Ω -correction of the experimental data and assuming the mass transfer overpotential to be negligible, thus the surface concentration being equal to the bulk concentration.
3) The third method used the XTM images, where a 3.3 × 3.3 mm 2 selection was made from the center of the processed image to prevent boundary effects from sample cutting.This image was imported in Paraview to extract the internal surface area by applying the threshold (0.5 -255), contour, extract surface, and integrate variables (cell data) filters.
The algebraic approach (method (1)) was also used to obtain the porosity of the electrode by dividing the void volume by the total volume of the electrode, based on the pore and pillar dimensions set by AUTOCAD, or obtained from the equivalent diameter using the SEM images in combination with ImageJ (as described in Section 2.3).

Thermal Sequence and Manufacturing Fidelity
Designed ordered lattice structures were manufactured by 3D printing of a resin, consisting of acrylate monomers, urethane dimethacrylate, and a photoinitiator, with an SLA printer.To obtain a well-defined conductive electrode that can be used in flow batteries, the 3D printed structures need to be carbonized (Figure 1a).We find that, to carbonize acrylic structures without large structural deformation, the 3D prints should have a porosity of at least 70% after printing (determined experimentally), and should be placed in a perforated metal framework (Figures S2  and S3a,c, Supporting Information).In addition, the curing of the resin must be investigated depending on the type of resin and 3D printer used. [53]In this study, it was found that for the High Temp V2 resin, the printing resolution was impacted by significant resin spreading and curing of excess resin into the pores, resulting in a 150 ± 50 μm smaller pore diameter than the input geometry (Figure S4, Supporting Information).Therefore, it was chosen, considering the porosity of the print, to manufacture square pillar designs with pores of 0.9 × 0.9 × 0.9 mm 3 and a pillar thickness of 0.3 mm.
First, a thermographic analysis must be performed (Figure 2a) to investigate if the material can withstand carbonization.Then, the appropriate thermal sequence must be selected, which is material-dependent (i.e., resin formulation and material geometry). [42]The carbonization temperature impacts the carbon content, carbon structure (amorphous to crystalline carbon), carbonization phase (polyaddition, pyrolysis, dehydrogenation, or annealing), and thus the conductivity of the material.The ramp rate impacts the gas release rate which can drastically influence the resulting structure by impacting the carbon atom rearrangement, carbon content, and surface area. [40,42,54,55]Carbonization sequences used in the literature [22,35] resulted in significant structure deformation and were thus not suited for the resin used in this work (Figure S3b, Supporting Information).Therefore, the thermal sequence was selected based on the thermogravimetric analysis performed (Figure 2a), which showed that the main mass loss for this material, due to dehydrogenation, polymer degradation, and the out-gassing of gaseous products, [40,42] is between 300 -450 °C in a nitrogen atmosphere and thus the oxidation step should be <300 °C and the carbonization step >450 °C.It was found that oxidation at 250 °C for 5 h with a ramp rate of 1 °C min −1 before carbonization at 850 °C for 1 with a ramp rate of 5 °C min −1 resulted in a stable carbonized 3D printed structure.The oxidation step before carbonization acts as a stabilization step and involves chemical reactions such as crosslinking, [48,56] which is crucial in obtaining 3D structures with minimal deformation.Literature studies have shown that the carbonization temperature should be >1100 °C to obtain highly conductive structures [55][56][57] ; yet, in this work, the structures were carbonized at 850 °C because of the upper limit of the carbonization oven used, which resulted in conductive electrodes (Table 1, 85 S m −1 for the 3D printed electrode compared to 82 S m −1 for the Freudenberg H23 and 122 S m −1 for the ELAT Cloth).
SEM was used to visualize the structures after printing, oxidation, and carbonization (Figure 2c,d), for which ImageJ was used to extract the equivalent diameters (Figure 2b) to assess the pore shrinkage due to dehydrogenation, polymer degradation, and the out-gassing of gaseous products [40,42] after thermal treatment.To quantify the shrinkage of the horizontally printed structure, we elect to visualize the pores from the top (top layer after printing), bottom, and side.Upon oxidation, the pore sizes shrunk by 11% in an isotropic manner as shown in Figure 2b, whereas after carbonization the total pore shrinkage was 45% and anisotropic, as the pores at the top shrunk more (52%) than the pores at the side (40%).We hypothesize that this anisotropic shrinkage is a result of the printing line direction, as these printing lines are in the through-plane direction (perpendicular to the flow with an FTFF, Figure 2c), and partially retain their features after carbonization.Interestingly, for the vertical printing direction, the pores at the side shrunk more (45%) than the top and bottom pores (39%) because of the printing lines in the in-plane direction.The diagonal case lies in between, where an isotropic shrinkage of 50% is observed in all directions.The pore diameters of all systems are shown in Tables S1 and S2 (Supporting Information).Furthermore, the shrinkage caused a porosity decrease for all tested electrodes (from 77% to 59% for the horizontally printed electrode, see Table 1, based on the pillar and pore geometry, assuming a smooth electrode surface).
When comparing the 3D printed carbonized structures to the SEM images before carbonization (Figures 2 and 4a  (Figure 1d), it is observed that the distinct pillar shapes remain mainly present upon carbonization, especially for the square and triangular designs.The cylinder and helical structures however show deviations from the input geometry which is partially a result of the 3D printing accompanied by resin spreading and curing into the pores.Although the SEM images before and after carbonization show similar structural properties (Figure S7, Supporting Information), both electrodes expanded on the highest density regions (pillar connections) after carbonization, altering the surface curvature at the top side for both designs, as well as the pore shape of the cylindrical design.Overall, these results show the versatility of SLA 3D printing in combination with carbonization to obtain porous electrodes with geometrical (electrode design) and orientational (printing direction) flexibility.

Physicochemical Analysis
Following the manufacturing of the 3D printed electrodes, the carbon content, conductivity, and surface area should be analyzed.The carbon content was obtained with EDS and XPS (the carbon, oxygen, and nitrogen contents are shown in Table S3, Supporting Information) and increased upon carbonization (from 71 to 94 atom% measured by EDS and from 77 to 82 atom% measured by XPS) accompanied by a decrease in oxygen content (from 27 to 5.0 atom% measured by EDS and from 20 to 12 atom% measured by XPS).Deconvoluted carbon signals obtained by XPS show the increase in carbon sp2/sp3 bonds relative to the carbon-oxygen bonds upon carbonization and can be found in Section S2.2 (Supporting Information).Moreover, the material is moderately conductive after carbonization, Table 1 (85 S m −1 for the 3D printed electrode compared to 82 S m −1 for the Freudenberg H23 and 122 S m −1 for the ELAT Cloth).The conductivity is however lower compared to the 3D printed electrode of Niblett et al., [35] who obtained a conductivity of 150 S m −1 after carbonization at 900 °C.This is because the electrical conductivity in this work is underestimated as a result of contact resistances (the electrical conductivity of commercial electrodes is ≈300 S m −1 [51] ).Nevertheless, carbonization at higher temperatures (e.g., >1100 °C) enables the formation of highly conductive graphitic structures, [55][56][57] which should be the focus of future work.
Table 1.Material characteristics of the 3D print with a square pillar shape and horizontal printing direction after printing and carbonization, where the internal surface area was obtained with three different methods: *1 by algebraic calculations of the pillar and pore sizes, *2 by the exchange current density ratio between the 3D printed electrode and a commercial (paper) electrode with known internal surface area, and *3 by extracting the internal surface area from the XTM images using Paraview.‡ The 3D printed material swells and partially dissolves upon contact with acetonitrile, thus a reliable permeability value could not be obtained.The available surface area and the surface density of electroactive sites of the electrode dictate the number of reaction sites present for the electrochemical reactions.Yet, in this work the available surface area was estimated based on the geometry defined by the input structure before carbonization and by three different methods after carbonization (by geometrical calculations, by the ratio between exchange current densities, and by using XTM images), see Table 1.It was found that the internal surface area per volume increases by a factor of two after carbonization.Moreover, the internal surface area is further increased for the vertical and diagonal designs as a result of the printing lines that induce surface roughness (Table 2), where the diagonal orientation has the highest internal surface area.Regarding the pillar structure analysis, the internal surface area was slightly impacted by the design choice of evaluating at constant porosity, affecting the pillar and pore dimensions and thus the internal surface area (Table S4 and S5, Supporting Information).Consequently, the helical design has the highest internal surface area, and the triangular design has the lowest.Nonetheless, the final porosity and surface area remain notably low for the 3D printed electrodes compared to commercially available electrodes with a porosity of 66-90%, [8,15,19,58] and an internal surface area of 7.2 × 10 4 m 2 m −3 [8] for the paper electrode and 1.4 × 10 4 m 2 m −3 for the cloth electrode. [4,15]This is a result of the big pores and narrow PSD (490 -530 μm), resulting from the printer resolution, compared to the PSD of commercial electrodes with significantly smaller pores.
Moreover, care must be taken with the interpretation of the internal surface area values where in the first and third calculation methods the surface roughness was not considered (not considered in the geometrical calculations and not considered in the extracted images as a result of the XTM imaging resolution), although present as a result of the printing lines (Figure 2c,d), increasing the internal surface area of the designs. [35]Furthermore, in the second method, the kinetic rate constant of the 3D printed electrode systems was assumed constant to use the ratio between the exchange current densities of the commercial paper electrode, with known internal surface area, and the 3D printed electrodes.Based on the cyclic voltammetry measurements (Section S2.4,Supporting Information), this second method can only be used to compare the 3D printed designs amongst themselves, as the redox reactions on the 3D printed electrode surface are not fully reversible, potentially related to the limited electronic conductivity of the 3D printed electrodes. [42]This was observed by the correlation between the peak current and scan rate, where electrochemical quasi-reversibility is observed for the 3D printed electrode by the shift in peak-to-peak separation with scan rate, showing a different correlation compared to that of the commercial electrode (Figure S12b, Supporting Information). [59]Rezaei et al. found that the carbonization conditions of the High Temp V1 resin (Formlabs, an older version of the High Temp V2 used in this study) affect the reversibility of the redox reactions, supporting the need to carbonize 3D printed materials at elevated temperatures. [42]Besides the crude assumptions made in determining the internal surface area of the 3D printed electrodes, the obtained values are in a small range of 4600 -6600 m 2 m −3 and are significantly lower than that of the commercial electrodes.

Pressure Drop
To assess the pumping losses through the electrochemical cell, pressure drop measurements were performed.The permeability, acquired from the Darcy-Forchheimer equation (Equation ( 4)), and pressure drop before and after carbonization of the 3D printed electrodes can be compared to two commercial electrodes with distinct electrode geometries: the binder-free Freudenberg H23 paper electrode with a narrow PSD and the highly ordered ELAT Cloth woven electrode with a bimodal PSD.It was found that the pressure drop of the 3D printed electrodes is reduced by a factor of ≈14 compared to the cloth electrode and by a factor of ≈65 compared to the paper electrode at a constant electrolyte velocity (at 10 cm s −1 , Figure 3a).Hence, resulting in a higher permeability (47 × 10 −10 m 2 for the 3D printed electrode compared to 0.16 × 10 −10 m 2 and 0.89 × 10 10 m 2 for the paper and cloth electrodes, respectively), which is a remnant of the big pore sizes in the 3D printed electrode ordered as highly connected transport pathways in both the in-plane and through-plane directions. [21]The large pores in the 3D printed electrode additionally affect the inertial effects in the electrodes, captured by the Forchheimer coefficient that describes the deviation of the pressure drop from Darcy's law, which is significantly lower than for the commercial electrodes (0.32 × 10 4 m −1 for the 3D printed electrode compared to 2.8 × 10 4 m −1 and 1.4 × 10 4 m −1 for the paper and cloth electrodes, respectively).
Compared to the horizontal orientation, the pressure drop is lower for both the vertical and diagonal printed systems (Figure 3b).Furthermore, the inertial effects in the vertical and diagonal printed systems were reduced compared to the horizontal system (Table S5, Supporting Information) which is a remnant of the through-plane surface roughness in this system, that enhances electrolyte mixing by inertial effects.Moreover, the flow field impacts the pressure drop in the system. [60]Compared to the FTFF, the IDFF electrolyte pathway through the electrode is reduced (over a 1 mm rib instead of over the 17 mm electrode length from the inlet to the outlet channel(s)).Therefore, for fibrous paper electrodes with a small and narrow PSD (e.g., Freudenberg H23), the pressure drop is greatly decreased when using an IDFF; however, for structures with large pores in the in-plane direction (e.g., 3D printed electrodes or cloth electrodes) the pressure drop can be higher. [60]This is observed for the 3D printed electrode, where the pressure drop is larger because of the fluid pathway in this flow field (Figure 1c), which is both in the in-plane and through-plane directions from the inlet channel, over the rib, to the outlet channel.Thus, the electrolyte is forced through the structure and cannot follow a straight fluid pathway from the inlet to the outlet channel as is the case for the FTFF.Furthermore, the pillars partially block the inlet and outlet channels of the IDFF, increasing the pressure drop, resulting in a higher inertial contribution (2.4 × 10 4 m −1 ) and a lower permeability (24 × 10 −10 m 2 ).Lastly, the pressure drop through the electrode is affected by the pillar shape.Utilizing a triangular design increases the pressure drop, whereas the pressure drop could be slightly reduced by using a helical pillar shape.Nonetheless, the permeabilities follow a diverse trend as a result of the inertial contributions, where the highest permeability can be achieved by using a square pillar design (Table S5, Supporting Information).

Influence of Printing Direction
To evaluate the potential of using 3D printed electrodes for RFB applications, the electrochemical performance in a symmetric flow cell is analyzed by performing polarization and electrochemical impedance spectroscopy measurements.The electrochemical performance is analyzed using iR Ω -corrected polarization curves to investigate the effect of the internal surface area and mass transfer in the 3D printed electrode designs.In this study, a non-aqueous electrolyte was used to ensure complete wetting of the carbonaceous structure. [8]Hence, pretreatment or functionalization of the electrode to improve wetting can be omitted because of the low surface tension of the solvent.To employ the 3D prints in aqueous systems, the hydrophilicity should be improved through modifications of the carbon electrode surfaces by, for example, post-thermal treatment of the carbonized structure, [61] but this is beyond the scope of this work.
First, the influence of the printing direction on the electrode performance was investigated.SLA is a point-based, layer-bylayer technique resulting in high geometrical and orientational (printing direction) design flexibility.The orientation of the designs impacts the electrode performance because of resin curing of individual layers, affecting the internal surface area, conductivity, shrinkage upon carbonization, and the resin spreading that is additionally affected by gravity.The printing orientation regarding the printing platform is therefore of interest to optimize the performance of 3D printed electrodes in future work.In this work, the 3D prints were orientated with a 0°, 90°, and 45°angle regarding the printing platform to manufacture designs with a horizontal, vertical, and diagonal printing direction, respectively (Figures 1b, and 4a,b; Figure S9, Supporting Information).
Enhanced performance is observed for the vertical and diagonal systems in Figure 4c.The increase in surface area can directly be connected to an increase in electrochemical performance, as the attainable current density linearly correlates to the internal surface area by the charge transfer overpotential. [10]n addition, the convoluted charge and mass transfer resistances are lower for these systems (Figure 4d) because of the increased surface area.Unfortunately, these resistances are convoluted in the impedance plots, most likely due to distributed ohmic on account of electronic resistances [62,63] caused by the carbonization at a relatively low temperature and lack of sufficient solid phase conductivity. [40,55]Nevertheless, the differences between the impedance spectra of the three systems are velocitydependent, highlighting that the printing direction additionally impacts the mass transfer overpotential.A note must be made on the high-frequency intercept of the three different systems, as this value, which includes the membrane resistance and contact resistances, is 1.4 times higher for the diagonal system (Figure S17, Supporting Information) as a result of higher contact resistances because of a reduced electrode thickness (Table S5, Supporting Information).
The impact of the printing direction on the mass transport in the electrode can be assessed by measuring the limiting current over a range of superficial velocities (Figure 4e).The prefactors and exponents of the different systems can be found in Table 2.At increased electrolyte velocities, the mass transfer is enhanced in the horizontal system compared to the vertical and diagonal systems.This is a result of the stronger dependency on the electrolyte velocity by a higher exponent (Table 2) potentially caused by the through-plane surface roughness (Figure 4a,b) leading to increased turbulence and thus mixing, as was observed by the higher inertial contribution to the pressure drop (Table S5, Supporting Information).Thus, whereas the diagonal system has a higher electrochemical performance, the mass transfer can be enhanced with horizontal systems.
Table 2.The internal surface area of the different 3D printed electrodes after carbonization, where the internal surface area was obtained with two methods: *2 by the exchange current density ratio between the 3D printed electrode and a commercial electrode with known internal surface area, and *3 by extracting the internal surface area from the XTM images using Paraview.Together with the constants (C1 and C2) of the volume-specific surface area mass transfer coefficient (a • k m ) as a function of the electrolyte velocity, and the constants (C3 and C4) of the Sherwood number as a function of the Peclet number, where the exponential factors (C2 and C4) are the same for both mass transfer expressions.
Printing direction -pillar shape -flow field

Influence of the Flow Field Type
The interplay between the flow field design and electrode structure has proven to be crucial in the selection of electrode types for RFBs. [60]Therefore, we investigate two commonly used flow field designs, the FTFF (used throughout this study as a reference flow field) and the IDFF, both with distinct flow distributions through the electrode.Compared to the FTFF, the IDFF electrolyte pathway length through the electrode is reduced, impacting the mass transfer and thus the electrochemical performance (Figure 5a).The flow distribution in the IDFF reduces the mass transfer overpotential [50,51] at all measured electrolyte velocities (Figure 5b, Figure S14b, Supporting Information) by providing a shorter electrolyte transport path, potentially by an improved ac-tive species mass transfer of the bulk to the electrode surface, and by increased inertial effects and mixing (Section S3.3, Supporting Information).The mass transfer coefficient through the electrode is greatly enhanced when utilizing an IDFF compared to an FTFF (Figure 5c), [50,51] resulting in a twice as high prefactor (Table 2).Although the prefactor is significantly higher for the IDFF, the dependency on the electrolyte velocity is reduced.This is because the effect on the exponent in Equation ( 7) depends on the electrode-flow field combination.IDFFs are anticipated to reduce this exponent significantly compared to flow-through designs for electrodes with a uniformly narrow PSD of pores in the submicrometer range (e.g., paper electrodes [51] ), and only slightly impact the exponent for electrodes with a bimodal PSD (e.g., woven electrodes [58] ) spanning a larger pore size range, as also observed in this work (Table 2).

Influence of Pillar Geometry
Turbulence promotors or electrode mixers are used in many research fields to enhance mass transfer by inducing turbulence or mixing in the system. [13,28,29,64,65]Consequently, the mass transfer at the electrode surface is enhanced resulting in an increased limiting current density (Figure S18, Supporting Information).The importance of the electrode microstructure (e.g., pillar shape or mixer unit cell) on the mass transport was shown by Hereijgers et al. in their structured 3D electrodes derived from static mixer unit cell designs.They showed that similar mass transfer coefficients and electrochemical output can be obtained whilst reducing the pressure drop substantially. [29]Furthermore, de Rop et al., showed with Computational Fluid Dynamics simulations that, by changing the pillar shape in electrochemical reactors from cylindrical to diamond, the mass transfer coefficient can be increased by a factor of two as a result of significant mixing effects. [66]Hence, in this work we investigate the influence of the electrode pillar shape on the electrochemical performance, focusing on mass transport.To this end, our ordered cubic lattice structures with distinct pillar geometries (square, triangular, cylindrical, and helical, Figure 6a) were investigated.To compare the different structures, the porosity was kept constant,  impacting the pillar and pore dimensions slightly for the different structures (Section S2.1, Supporting Information).
We found that the triangular and cylindrical pillar shapes do not significantly affect the electrochemical performance (Figure 6b) compared to the square pillar shape.The combined charge and mass transfer resistances in these structures are similar to that of the square system but slightly lower at enhanced electrolyte velocities and higher at reduced electrolyte velocities (Figure 6c).This is a result of the lower internal surface area of the triangular and cylindrical systems (Table 2), increasing the charge transfer overpotential, in combination with the distinct mass transfer relationships for these electrodes (Figure 6d), impacting the dependency of the mass transfer overpotential on the electrolyte velocity.The helical pillar shape, however, especially impacts the current density and resistance compared to the other designs, Figure 6b,c.This is hypothesized to be related to the higher internal surface area and improved mass transfer through the electrode (Figure 6d), which indicates a relationship between the pillar geometry and the mass transfer through the electrode.Based on the literature, [66] it is anticipated that the pillar geometry presented in this work influences the mass transport through the electrode by affecting the electrolyte distribution around the pillars.The helical pillar shape shows an increased mass transfer coefficient with a 1.4 times higher prefactor compared to the square pillar shape (Figure 6d and Table 2) where the helical twist in the pillar structure (Figure 6a) is expected to induce local mixing of the electrolyte, improving the active species mass transfer of the bulk to the electrode surface. [28,29,33,66]Future work could focus on visualizing the concentration distribution around the pillars in ordered structures, for example using fluorescence [67] or confocal microscopy, to better understand the mixing phenomenon in porous electrodes.

Mass Transfer Correlations
Typically, the mass transfer relation is extended to compute nondimensional numbers such as the Sherwood (Sh) and the Peclet (Pe) numbers to correct for the differences in internal surface area and porosity between electrode structures.Using this approach, the manufactured structures can be compared to commercial electrodes in terms of their mass transfer coefficient, corrected for differences in porosity and internal surface area.The Sherwood number describes the correlation between the convective and diffusive mass transport, defined as  couple [14,68] ).The Peclet number relates the convective velocity to the diffusive velocity as follows: By plotting the Sherwood number over the Peclet number, a power law relationship can be determined in the following form where C3 is the prefactor and C4 the exponent.By fitting the experimental data to this relationship, the mass transfer can be analyzed by dimensionless numbers, where a larger exponent results in a stronger velocity dependency of the mass transfer coefficient. [13]Figure 7 shows this relation and the prefactors and exponents are listed in Table 2.
For the printing direction study (Figure 7a) no noticeable differences were observed compared to Figure 4e as only the contrast between the distinct printing directions becomes more pronounced at higher Peclet numbers.Furthermore, as the IDFF is investigated with the same electrode design (identical porosity and surface area), the differences between the flow fields remain the same, where the IDFF outperforms the FTFF with a significantly higher prefactor but a reduced velocity dependency (Figure 7b).For the various pillar shapes when corrected for the internal surface area and porosity (Figure 7c), we find that the square design features the lowest prefactor compared to the other structures, showing the dependency of different morphologies on the mass transfer rates.Furthermore, the triangular design has a greater dependency on the electrolyte velocity, and the cylindrical design a smaller, resulting in differences in mass transfer at larger Peclet numbers.The corrected mass transfer relations confirm the higher activation overpotential contribution to the polarization and impedance curves for the cylindrical and triangular designs (Figure 6b,c) and hint that these structures, like the helical structure, could enhance the mass transfer around the pillars compared to the square design. [66]This study shows that by slightly affecting the electrode geometry by altering the pillar shape or printing direction, the mass transfer in the electrode can be enhanced.Hence, future work should focus on diverse pillar or fiber shapes and their orientation [16] to enhance the mass transport in porous electrodes for RFBs.
Even though the printing resolution was limited and therefore the electrode feature sizes, which strongly impact the internal surface area, SLA 3D printed carbonized electrodes can be promising for flow cell applications.To investigate their potential, a comparison is made with a paper and a cloth electrode, which have been shown to be among the best-performing electrodes in non-aqueous redox flow batteries. [8]These electrodes are well studied, [8,14,15] but remain unoptimized for all-liquid RFBs.The main advantage of these commercial electrodes over 3D printed electrodes is their superior internal surface area, resulting in a better volume-specific surface area mass transfer coefficient (a • k m ) as a function of the electrolyte velocity (Figure S19, Supporting Information).However, when corrected for the internal surface area, Figure S20d (Supporting Information), their mass transfer coefficients appear lower than that of the 3D printed electrode, particularly at low electrolyte velocities.Although the prefactor is significantly lower for the commercial electrodes, also for the Sherwood over Peclet number plots (Figure 7d), the sensitivity of the mass transfer relation to the electrolyte velocity as defined by the exponent is larger as a result of forced convection through the dense fiber structure. [14,51]As a result of the superior internal surface area of the commercial electrodes, their electrochemical power output outperforms the 3D printed designs, see Figure 4c and Figure S14 (Supporting Information).The 3D printed designs, however, outperform the commercial electrodes in terms of pumping requirements (Figure 3a).When evaluating the trade-off between electrochemical performance and pumping requirements in terms of flow cell efficiency, the cloth electrode performs best in terms of both electrochemical and pumping power requirements. [8,15,60]or the 3D printed electrodes to compete with commercial electrodes for application in RFBs, their design must be optimized.First and foremost, their internal surface area needs to be increased by designing electrodes with smaller feature sizes by using advanced 3D printing technologies (e.g., two-photon lithography), combined with highly porous surfaces obtained through e.g., etching, thermal treatments, coatings, or addition of porogen in the printing resin. [69]A higher internal surface area enhances the electrochemical current density but generally results in structures with a smaller and narrower PSD, reducing the electrode permeability.Thus, high electrolyte permeabilities should be attained by considering the flow fieldelectrode interplay in the designs to maintain a low-pressure drop in the reactor.To this end, a bimodal PSD could be beneficial for the design of next-generation RFB electrodes. [15,21]urthermore, tailored resins should be investigated where the resin formulation (i.e., monomers and photoinitiator) should be optimized to reduce resin spreading and control shrinkage during carbonization.Lastly, mass transport within porous electrodes needs to be optimized on all length scales to enhance the electrolyte distribution, internal mixing, and mass transport toward the electrode surface, for which the electrode thickness is an important optimization parameter.After implementing the above-mentioned properties, the 3D printed electrodes should be compared to state-of-the-art electrodes where their mechanical stability, cycling performance, and cost of manufacturing should additionally be considered to investigate the practical applicability of 3D printed electrodes for RFB applications.

Conclusion
In this study, we manufactured electrode structures using SLA 3D printing followed by carbonization to investigate the impact of the electrode structure on mass transport properties and pressure drop in electrochemical flow cells.The goal of this study is to contribute to the understanding of structure-functionperformance relationships applicable to redox flow batteries by exploring novel in-house manufactured electrode structures with diverse 3D features.Using single electrolyte flow cells as diagnostic platforms, we employed a reversible and facile redox couple (TEMPO/TEMPO + PF 6 − ) in a non-aqueous electrolyte as a method to deconvolute the influence of the mass transfer overpotentials on the flow cell performance.With this systematic methodology, we studied the influence of the printing direction, pillar geometry, and flow field on the mass transfer rates in ordered lattice structures.
The investigated electrodes impact cell performance through variations in internal surface area, pressure drop, and mass transport.It was found that the printing orientation (with respect to the printing platform) impacts the electrode performance through a change in electrode microstructure, affecting the shrinking direction upon carbonization, internal surface area, and thus the charge transfer resistance, mass transfer resistance, and pressure drop.A horizontal printing direction shows low in-plane surface roughness but enhanced mass transfer, whereas a diagonal printing direction features a higher internal surface area and lower pressure drop, but a reduced mass transfer coefficient.Furthermore, we find that the mass transfer in the electrode can be enhanced by improving the electrolyte mixing by altering the pillar shape to a helical or triangular design, and by using an interdigitated flow field.By comparing the printed structures to commercial electrodes, we show the potential of using 3D printing as a viable manufacturing method to enhance mass transport in RFBs.However, for the 3D printed electrodes to compete with commercial electrodes, their design must be optimized by increasing the internal surface area, which could be achieved by printing electrode structures with smaller feature sizes with advanced 3D printing technologies or by incorporating high surface area materials onto the electrode surfaces.We hypothesize that the combination of a macroporous electrode architecture with finer, nanoscale porosity, surface roughness, and mixing elements can provide the seemingly contradictory requirements of high permeability, mass transfer rates, and electrochemically available surface area.
This study shows the potential of 3D printing to manufacture customized electrodes with high geometrical and orientational (printing direction) flexibility, which have a measurable impact on the electrochemical performance and pressure drop.Furthermore, manufacturing guidelines to enhance the mass transport in porous electrodes are provided and can be translated to other advanced manufacturing techniques.Looking forward, we propose to fine-tune the resin formulation and carbonization steps (e.g., carbonization at elevated temperatures >1100 °C), and explore additional thermal treatment steps or coatings aiming to obtain porous electrodes with higher carbon content, conductivity, and internal surface area.Additionally, future work should focus on alternative pillar or fiber geometries and their orientation to enhance the mass transport in porous electrodes.Owing to the design flexibility, 3D printing can be combined with topology optimization of the porous electrode to realize the manufacturing of computationally optimized structures.

Figure 1 .
Figure 1.Schematic representation of the outline of this manuscript, with: a) the process workflow to obtain a conductive electrode from a nonconductive 3D print to be tested in a flow cell, and b-d) the different systems tested for their performance in a flow cell consisting of studies on: b) the printing direction, c) the flow field, and d) the pillar shape.
The volumetric flow rate, Q [m 3 s −1 ], was calculated for the flowthrough flow field by multiplying the electrolyte velocity, v [m s −1 ], by the geometrical inlet area of the electrode, A geo [m 2 ] (thickness multiplied by the width of the electrode), see Equation (1).Whereas the flow rate of the interdigitated flow field was calculated by multiplying the electrolyte velocity by the number of inlet channels, n c [−] (4 channels), the length of the channel, L c [m] (16 mm), and the incompressible gasket thickness, L [m] (1 mm for the 3D printed electrodes), see Equation ( lim is the limiting current per electrode volume [A m −3 ], n the number of electrons transferred [−] (n = 1 for the TEMPO/TEMPO + PF 6 − system), a the internal surface area of the electrode [m 2 m −3 ], F Faraday's constant [C mol −1 ], C i,b the bulk concentration of the oxidized species i [mol m −3 ], and k m the mass transfer coefficient [m s −1 ].From the limiting current density, the volume-specific surface area mass transfer coefficient (a • k m ) can be estimated as follows a ⋅ k m = I lim nFC i,b V (6) with I lim the current [A] measured by the polarization experiment with fixed potential steps and V the electrode volume [m 3 ].Using Equation (6), the resulting a • k m values for the different electrodes at a range of superficial velocities can be found and plotted on a double-log scale.The slope represents a power law relationship in the following form: , and FiguresS6 and S7, Supporting Information) and the input geometry

Figure 2 .
Figure 2. a) The mass loss with temperature of the 3D print in air or nitrogen atmosphere, and that of the oxidized 3D print in a nitrogen atmosphere, extracted from thermogravimetric analysis.The dashed lines display the chosen oxidation and carbonization temperatures of 250 and 850 °C, respectively.b-d) To quantify the pore shrinkage, we elect to visualize the pores from the top, bottom, and side.b) The pore sizes of the top, bottom, and side view of the horizontal 3D print after printing, oxidation, and carbonization (n = 6), where the pore size was extracted using ImageJ by assuming the pore to be a perfect circle with the pore size being the equivalent pore diameter, visualized by the figure inset.c,d) Scanning electron microscope images of the 3D prints of the top, bottom, and side view (from left to right) at 50× magnification for the horizontal 3D structure after c) printing, and d) carbonization.

Figure 3 .
Figure 3.The pressure drop values (n = 2) over a range of electrolyte velocities for: a) the 3D printed, paper, and cloth electrode, b) the horizontal, vertical, and diagonal printing directions, c) the flow through and interdigitated flow fields, and d) the square, triangular, cylindrical, and helical pillar shapes.The horizontal, FTFF, square, and 3D printed refer to the same 3D printed electrode.The permeability and Forchheimer coefficients were obtained with a secondary polynomial fit of Equation (4).

Figure 4 .
Figure 4. a,b) Scanning electron microscope images of the 3D prints of the horizontal, vertical, and diagonal printing direction (from left to right) at 50 × magnification, for the 3D structure after printing a) from the top, and b) from the side.c-e) Electrochemical data (n = 3) of the horizontal, vertical, and diagonal printing directions, with: c) the iR Ω -corrected polarization curves at 10 and 0.5 cm s −1 , d) the electrochemical impedance spectroscopy data corrected for the high-frequency intercept at 10, 5, 1.5, and 0.5 cm s −1 , and e) the a • k m values for different superficial velocities with the best-fit lines (solid lines) and the slope of the fit (next to the system label), plotted on a double-log scale.

Figure 5 .
Figure 5. Electrochemical data (n = 3) of the 3D printed electrode with a flow through and interdigitated flow field, with: a) the iR Ω -corrected polarization curves at 1.5 and 0.5 cm s −1 , b) the electrochemical impedance spectroscopy data corrected for the high-frequency intercept at 1.5 and 0.5 cm s −1 , and c) the a • k m values for different superficial velocities with the best-fit lines (solid lines) and the slope of the fit (next to the system label), plotted on a double-log scale.

Figure 6 .
Figure 6.a) Subsection of the X-ray tomographic images of the 3D prints after carbonization with a square, triangular, cylindrical, and helical pillar structure.b-d) Electrochemical data (n = 3) of the square, triangular, cylindrical, and helical pillar shapes, with: b) the iR Ω -corrected polarization curves at 10 and 0.5 cm s −1 , c) the electrochemical impedance spectroscopy data corrected for the high-frequency intercept at 10, 5, 1.5, and 0.5 cm s −1 , and d) the a • k m values for different superficial velocities with the best-fit lines (solid lines) and the slope of the fit (next to the system label), plotted on a double-log scale.
) with  being the electrode porosity [−], a the internal surface area of the electrode [m −2 m −3 ], k m the mass transfer

Figure 7 .
Figure 7.The mass transfer relations for different superficial velocities (n = 3) represented by the Sherwood over the Peclet number with the best-fit lines (solid lines) and the slope of the fit (next to the system label), plotted on a double-log scale for: a) the horizontal, vertical, and diagonal printing direction, b) the flow through and interdigitated flow field, c) the square, triangular, cylindrical, and helical pillar shapes, and d) the 3D print and commercial paper and cloth electrodes.The horizontal, FTFF, square, and 3D print refer to the same 3D printed electrode.