Computational design of microarchitected porous electrodes for redox flow batteries
Graphical abstract
Introduction
Electricity generated from renewable sources is a continually growing component of global energy production and a key driver for a sustainable energy future [1], [2], [3]. Further expansion requires efficient and cost-effective integration into existing power distribution systems but intermittency and curtailment remain a challenge [4], [5], [6]. A number of strategies have emerged to address these issues, including electrochemical energy storage [7] and repurposing otherwise wasted electricity to electrify chemical manufacturing [8], [9], [10], [11]. The direct electrochemical conversion of CO is an especially powerful avenue as it simultaneously combines storage, chemical synthesis, and carbon-removal [12], [13], [14]. As these advances are translated from the laboratory to industrial scale, energy efficient operation will become increasingly important to ensure economic viability [2], [6], [7], [15].
Porous electrodes are routinely used as the core reactor component across these applications and are ubiquitously employed for electrochemical energy storage using redox flow batteries [2], [4]. Flow battery performance is closely tied to the porous electrode properties. The electrode is often a disordered, homogeneous collection of micron-scale, electroactive particles like carbon fibers, felts or spherical substrates, any of which may be further coated with catalyst [4], [16], [17]. These materials seek to maximize the surface reaction while minimizing overpotential and hydraulic losses. However, the material properties needed to meet these requirements are inherently adversarial and present a major challenge in attaining high performance. Open structures are necessary to allow fluid penetration, promote mass transfer, reduce pumping losses and supply reactants to the surface, but permeable geometries will reduce the solid fraction and require low hydrodynamically accessible surface area. In turn, the increasing porosity, decreasing intrinsic surface area, and lower overall conductance lead to greater kinetic and Ohmic losses [4], [17].
Previous demonstrations of high power flow batteries have circumvented these issues by engineering the assembly to enable the use of very thin electrodes in a “flow-by” configuration [18], [19]. The improved performance is attributed in part to the significantly decreased area specific resistances relative to thicker electrodes like uncompressed carbon felts [20], [21]. Controlling electrode thickness and compression becomes an effective bulk parameter to control the gross electrode microstructure, impacting average conductance, permeability, and mass transfer [20], [21], [22], [23].
To further drive performance, these architectures use sophisticated flow fields to appropriately distribute reactants across the electrode surface [24], [25], [26]. This important approach partially externalizes the challenges of balancing mass transport and electrochemical losses from the electrode to the fluid distribution system, providing further design freedom but at the cost of increased complexity. Previous studies have thus employed a combination of numerical [27], [28], [29], [30], [31], [32] and combined numerical and experimental [33] approaches to develop engineering guidelines for flow field channel dimensions and layouts to maximize peak power and efficiency. More recent work has employed X-ray computed tomography to simultaneously assess the impact of non-uniform compression and flow field arrangement, thus connecting bulk engineering parameters to the electrode microstructure and its effective properties [34]. Indeed, a growing body of research has focused on further establishing the connection between microstructure and hydraulic, mass transport, and electrochemical properties [23], [34], [35], [36].
As a complement to developing new assembly architectures, engineering the electrode structure directly is emerging as a viable route for improving performance [15], [17]. Holes made using laser perforation were used to create mass transport channels in carbon paper electrodes and increase peak power [37]. Similarly, slots milled into a large scale carbon felt electrode improved fluid distribution and decreased pumping losses without employing a costly flow field [38]. Dual-scale electrodes created by etching carbon papers [39] or combining electrospun fiber mats with a backing layer [40] have enabled even more granular engineering of the structure. Similar dual-scale concepts have been introduced for lithium-ion electrodes [41], [42] and extended to create continuously variable porosity electrodes [43] which lead to improved rate capability while maximizing energy density [44]. However, to date, this novel idea has not been applied to make porous electrodes for flowing, electrochemical systems.
Additive and advanced manufacturing techniques can be employed to further extend and control the structural complexity of electrode materials [45], [46], [47], [48]. Porous electrodes with superior mass transport have been created from carbon and graphene aerogels using direct ink writing for use in supercapacitors [45]. Porous flow-by electrodes made from metals [46], [48], including nickel and stainless steel [47], have been produced at varying scales with complex, flow-controlling architectures. The resolution of the 3D printed, flow-by electrodes leads to feature sizes that exceed those of conventional electrodes by 1–2 orders of magnitude [17]. However, a number of advanced manufacturing technologies exist with resolution approaching micrometers [49], [50] and tenths of micrometers [51] using materials that are, or can be readily transformed to be, suitable for use as electrodes.
The near arbitrary controlled provided by these techniques cannot be fully exploited without advanced analysis and design tools to guide the electrode architecture. Simulation has been used extensively and effectively to develop a more detailed understanding of the transport and electrochemical processes in flow batteries [52], [53]. The computational efforts have additionally provided design guidance, identified key control variables, and provided useful heuristics highlighting the importance of flow uniformity when engineering the electrode assembly [54], [55], [56], [57].
The current design methodology begins with an initial system architecture, analyzes the system, and then improves it through human-driven iteration. This process can be laborious and, crucially, explores only a limited portion of the design-space. A novel, alternative technique is to use automatic design algorithms, like topology optimization [58], to invert the design process and aid in the design-space exploration. Instead of evaluating the performance of a proposed architecture, a performance target is specified and the algorithm iterates over permissible architectures to meet the target. This can lead to intriguing, non-intuitive designs which are nevertheless high performance, as have been recently demonstrated for flow field design in flow batteries [59] and fuel cells [60]. Similar inverse design concepts have also been used to optimize the porosity of lithium ion batteries [43] but have never been applied to design the structure of porous flow-through nor flow-by electrodes.
We introduce the concept of algorithmically designed, microarchitected variable porosity 3D porous electrodes for electrochemical flow reactors. As a specific application, we focus on energy storage by designing porous electrodes for vanadium redox flow batteries. We begin by describing our modeling, simulation and optimization methodology, including using high resolution continuum simulation to develop a homogenized description of the constituent microstructure unit cell. High performance computing is then employed to determine optimal distributions of the spatially varying unit cell porosities to maximize power efficiency across operating conditions. The resultant architectures are evaluated for their power performance and compared to bulk, porous electrodes. The mechanisms leading to improved power efficiency are identified and connected to the underlying electrode structure. Finally, we demonstrate how this computational design methodology can be used to scale-up electrodes to larger areas while minimizing power efficiency losses. The design methodology provides a framework for automatically generating high performance, architected 3D electrodes which can fully exploit the design freedom resulting from advanced and additive materials manufacturing techniques.
Section snippets
Computational design of electrode architecture
A combination of modeling, simulation and computational design optimization is used to generate the 3D, architected porosity electrodes presented in this work. The techniques described here are generally applicable to dilute, single-phase, porous electrochemical flow reactors. Here, this methodology is applied to determine optimal electrode architectures for electrochemical energy storage applications. Specifically, we model the electrode when used in the negative half-cell of a vanadium redox
Results and discussion
The ultimate power efficiency of the flow cell is engineered by balancing the losses arising from insufficient mass transport to the reactive surfaces against the hydraulic power necessary to drive fluid to those surfaces while maintaining effective charge conduction pathways. Below we characterize the power losses in porous electrodes composed of isotrusses and apply design optimization to a three-dimensional model of coupled fluid flow, species transport, and current distribution, to address
Conclusions
This work has introduced the concept of algorithmically designed, microarchitected 3D porous electrodes for electrochemical flow reactors. The technique was used to design electrodes for the negative half-cell of a vanadium redox flow battery. Across a range of flow rates, the optimized architected electrodes led to power efficiency gains of 13.5%–310% over optimized uniform porosity, bulk electrodes. Decomposing the power losses into flow losses, internal electric losses, and concentration
CRediT authorship contribution statement
Victor A. Beck: Conceptualization, Methodology, Software, Validation, Writing - original draft, Writing - review & editing, Visualization, Supervision, Project administration, Funding acquisition. Jonathan J. Wong: Software, Validation, Writing - review & editing, Visualization. Charles F. Jekel: Software, Validation, Writing - review & editing, Visualization. Daniel A. Tortorelli: Methodology, Writing - review & editing. Sarah E. Baker: Supervision, Project administration, Funding acquisition.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07-NA27344 and was supported by the LLNL-LDRD program under project numbers 16-ERD-051, 19-SI-005, and 19-ERD-035. LLNL Release Number LLNL-JRNL-819457.
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