Theory and Modeling of Fuel Cells: Extravaganza to Panacea? (2016)

This topical issue comprises a collection of articles in the field of theory, modeling and simulation of fuel cells. The editorial provides a brief perspective on the topic: how it emerged, what it currently is about and what it might bring in the future. The guiding thread, alluded to in the title, is the question about the valuation of the field, nested between two extremes: seeing modeling as an overtone (“extravaganza”) to the main acts in materials science, electrochemical characterization and fuel cell engineering, with mere sporadic significance; or regarding modeling – potentially – as the universal remedy (“panacea”) for any challenge related to design, properties, and operation of electrochemical materials and devices. All articles included in this topical issue refer to low-temperature polymer electrolyte fuel cells (PEFCs) which utilize a water-based polymer electrolyte membrane for proton conduction. This seemingly exclusive focus on a specific system was not the result of a narrow bias applied in the selection of invited contributions; it occurred spontaneously and reflects a clear prioritization of interests in theoretical fuel cell research. In terms of methodology, space scales, as well as materials and physico-chemical processes explored, articles in this collection represent a distinguished cross-section of current research in the field. Contributions cover the range from molecular-scale simulations of catalytic surface processes 1 as well as structure formation 2 and transport in ionomer membranes 3, 4, to physical-mathematical models of processes at the scale of individual nanopores 5 and porous membranes 6, and further to theories and models of macroscopic fuel cell components 7, 8 and their operation 9. The discussion of a strategic road map in fuel cell modeling rounds up the collection, striving to provide perspective and guidance to the field 10. The escalating global demand for highly efficient and environmentally benign energy technology drives research on fuel cells and the extended family of electrochemical energy systems. It entails efforts in materials design and fabrication, physico-chemical characterization of structure and function in complex materials, and engineering research to improve power performance, cost-effectiveness, durability, and lifetime of the fuel cell system. In this realm, physi­cal-mathematical theory, modeling and simulation provide increasingly powerful tools to understand, analyze and predict phenomena in electrochemical materials and systems 11. When exploring the frontiers of electrochemistry or crossing lines to neighboring disciplines in physics, chemistry, biology, materials science, or engineering, theoretical research is increasingly expected to provide crucial guidance. Relations between structure, properties and performance of any electrochemical material or system must be consistent with basic theoretical principles that govern transport and reaction phenomena in them. This imperative applies across space and time scales, including: molecular electrocatalytic processes at electrified interfaces; (ii) self-assembly and emergence of structure vs. property relations in polymer electrolytes and porous electrodes; (iii) electrostatic, kinetic and transport phenomena at highly dispersed electrode interfaces in nanostructured materials; (iv) and the interplay of functional materials and components in complete fuel cells and fuel cell stacks. The origins of the field of electrochemistry date back to the time around the year 1800, when Alessandro Volta invented the voltaic pile, the prototype of modern batteries 12. About 40 years later, in the year 1838, Christian Friedrich Schönbein discovered the fuel cell principle 13 and in 1839 William Robert Grove built the first assembly of electrochemical cells based on this principle, his famous gas battery 14. Naturally, the invention of these devices incited the scientific curiosity to theoretically understand their thermodynamic and electrodynamic principles of operation as well as the basic reactions and transport phenomena. Emanating from these origins, the theory of electrified interfaces 15 and charge transfer theory 16 transpired as mainstays in the electrochemical literature and they continually inspire new theoretical forays. More specialized disciplines in theory, modeling, and simulation of electrochemical materials and systems evolved as the commercial prospects of electrochemical devices were being exploited, as in the case of batteries from the early 1960s, or touted heavily as a future prospect, as in the case of fuel cells starting from the late 1980s. Among various disciplines and modeling flavors that have evolved over time, the modeling of porous gas diffusion electrodes has claimed an exceptional status: due to the ubiquitous relevance of porous electrodes for a broad spectrum of electrochemical energy technologies, the theoretical exploration of their structure and operation features a longer history and a more diverse range of seminal contributions than any other topic in theory and modeling of electrochemical systems 17–22. The disciplines that emerged in electrochemical systems modeling amalgamated elements of mechanical engineering, viz. the balances and flows of energy, matter and electricity in confined media, and chemical engineering, viz. the design of chemical reactors, with the classical branches of theoretical electrochemistry. Driven by applications, the engineering-focus became a dominant influence in the field of battery modeling. At the same time, fuel cell modeling led an early existence in the shadows with only a few scattered and marginally impactful publications prior to the 1980s. The situation changed dramatically in the late 1980s, when the introduction of new materials and design concepts boosted the power performance of PEFCs. Exponential trend in Pt mass activity (in units of A per mg of Pt) of polymer electrolyte fuel cells. Mond and Langer performed measurements on the first practical fuel cell stack and they coined the term fuel cell in 1889 23. Grubb and Niedrach are credited with the invention of PEFCs, dating back to the late 1950s 24. The year 1989 brought a major performance leap achieved with a completely redesigned catalyst layer by Ian D. Raistrick at Los Alamos National Laboratory 25. The GORE® PRIMEA®cell from 2003 was the industry standard of MEA development in the mid-2000s 26. At about the same time, the company 3M developed a novel MEA concept that utilizes a nanoporous ionomer-free catalyst layer design 27. Figure 1 illustrates this point. As gleaned from a selection of polarization curves, the specific power of PEFCs has grown roughly exponentially since their advent almost 60 years ago, with a doubling seen on average every 5.4 years. Over this period, the mass activity and specific power of PEFCs have increased by a staggering factor of approximately 103. The most dramatic performance leap occurred in 1989, when Ian D. Raistrick at Los Alamos National Laboratory developed an innovative design of the membrane electrode assembly that has survived until today 25. The main improvements involved a scaling down of the catalyst to the size of nanoparticles and a densification of catalyst nanoparticles on a highly porous carbon support; furthermore, impregnation of the active layer with ionomer induced a vital enhancement of the local reaction conditions. The advances achieved with these intuitive modifications triggered an avalanche of publications in fuel cell modeling, with seminal publications by Spinger et al. 28 and Bernardi and Verbrugge 29 leading the way. Fuel cell modeling took off as a blend of engineering and theoretical electrochemistry at the beginning of the 1990s. However, the gold-rush mentality of the fuel cell sector of the time engendered a premature fixation on the development of modeling tools for large-scale engineering-type simulation, with the foremost practical goal to optimize performance at stack and system levels. The electrochemistry was essentially by-passed in these approaches that easily raked up >50 parameters. This prioritization was based on the expectation that the putatively imminent deployment and commercialization of fuel cells would be achieved with already known component materials and cell designs – a formidable misjudgment. As it turned out, none of the complex fuel cell simulation codes developed in the 1990s found their way into technology development efforts pursued in industry today. Interestingly, whilst their practical usefulness has remained questionable, the interest in developing multi-scale and multi-parameter modeling approaches has not withered. In spite of continued efforts in this realm, there is no generally accepted comprehensive fuel cell model, which consistently treats all components, properties, and processes in a cell or stack and agrees reasonably well with a wide range of experimental data. From the foundations of theoretical electrochemistry to applied fuel cell theory, modeling and simulation, showing a spectrum of sub-disciplines in the fusion zone. Important functional materials that had been treated in thin interface approximation or as effective transport media in the early engineering-type models of the 1990s, have been expanded to their full complexity in sophisticated component models that have been developed over the last 25 years. Indeed, polymer electrolyte membrane and catalyst layers have become primary targets for theory and modeling. The thicknesses of these materials have become key parameters in view of optimizing fuel cell power density and overall operation. Advanced fabrication methods with high degree of structural control and rapidly developing characterization tools in spectroscopy, microscopy, imaging, and tomography allow relations between structure and properties of fuel cell materials to be studied with unprecedented accuracy and ever-increasing resolution. Corresponding physical models of electrochemical materials ingest this information to unravel the interplay of self-organization in multiphase composites, nanoscale physics, and interfacial electrochemical kinetics. These advances are vital for modeling to support efforts in design and integration of advanced fuel cell materials. Using a well-devised hierarchy of methods and approaches, fuel cell models drill down all the way from macroscale to the molecular level. Passing information between different levels of the hierarchy should proceed as exemplified here for the case of catalyst layer modeling: density functional theory (DFT) reveals electronic, electrostatic, and catalytic surface properties of catalyst materials; using DFT in combination with thermochemical modeling, the chain of elementary reaction events can be unraveled and rate constants for elementary reaction steps can be determined; reaction scenario and rate constants, obtained from DFT, can then be used to establish and parameterize time-dependent mass balance equations for adsorbed intermediate species; steady-state solution of surface coverage equations provides the conversion function for relevant electrochemical reactions like the oxygen reduction reaction, which can be used in the simplified current conservation equation needed to build a comprehensive catalyst layer (CL) performance model; solution of the catalyst layer performance model yields the CL polarization curve, which can be used as input in fuel cell or stack models. This chain of information transfer constitutes a bottom-up approach in the modeling and design of electrocatalytic materials. A sound grounding on the foundations of charge transfer theory, the theory of electrified interfaces, and theoretical electrocatalysis is vital for the success of this approach. Over time, new blends of theoretical electrochemistry and electrochemical engineering with polymer chemistry, statistical physics, condensed and soft matter physics, surface science, and heterogeneous catalysis have brought to fruition new disciplines in the modeling of electrochemical materials and devices, some of which are featured in Figure 2. To advance the design and integration of functionally optimized materials, guide the development of a comprehensive set of diagnostic tools, and enable the optimization of performance and durability of fuel cells, theoretical research has to embrace the full cycle in Figure 3. The goals are to understand, how complex fuel cell materials come to live during fabrication and self-assembly; how they live, e.g., by breathing oxygen in and water vapour out and by transporting electrons and protons across; and how they degrade during normal use cycles and die due to failure. Fuel cell modeling and simulation from cradle to grave. Approaches employ a broad inventory of methods and tools to study how materials form, operate, degrade, and fail; using examples from on-going research for illustration. In fuel cell electrocatalysis, the development of a self-consistent methodology for first principles electrochemical simulations will remain a foremost goal 30; the challenge is to employ the metal-phase potential as the control variable and obtain its functional relations to dependent variables that represent surface charging, adsorbate formation, solvent effects, ion density distributions, and the electrostatic potential profile of the solution phase. Density functional theory calculations and the development of self-consistent methods in first principles electrochemistry should identify viable descriptors of electrocatalytic activity for the reactions at fuel cell electrodes, desired energy-converting reactions or undesired side reactions. The ambivalent role of oxide formation for stability and activity of catalyst materials needs to be tackled. The fusion of first principles electrochemical simulations and kinetic modeling should yield a general methodology for deciphering multi-step reaction mechanisms and calculating effective kinetic parameters to pass on to electrode performance models. Understanding transport processes of ions, protons and water in phase-separated nanoporous electrolytes will remain a foremost goal of molecular modeling and concomitantly developed physical theories. The water environment, consisting of free bulk-like and strongly bound surface water, will determine the transport mechanisms and the overall rates of transport. Understanding these effects will be essential for the design of membranes, in which the sensitivity of proton conductivity to external conditions is suppressed or eliminated. Theory and molecular modeling of structural organization in complex materials will be essential to study the self-assembly of ionomer molecules into bundles and bundle networks. This structural information is a prerequisite to rationalize structure-dependent transport properties, e.g., using percolation theory and random network simulations. Structural, electrostatic and mechanical properties of ionomer networks and membranes are needed to theoretically explore stability, durability, and lifetime of polymer electrolyte membranes, e.g., employing kinetic Monte Carlo simulations for studies of crack formation in ionomer bundle networks. Structure formation in catalyst layer inks is a keenly pursued topic, which can be approached with coarse-grained molecular dynamics studies. Of particular interest is the ionomer structure in the catalyst layer and its impact on porous structure, wettability, water sorption and all related physico-chemical properties of the layer. Understanding this aspect will help assessing the following question: How critical is ionomer impregnation for catalyst layer function and operation? Knowing the structure of a polymer electrolyte membrane or a catalyst layer, attention should turn towards dynamic water phenomena in these media, rationalizing the distribution and transport of water as well as the effective materials properties that are sensitive to the water distribution. At this point, comprehensive modeling approaches must account for the coupled water fluxes in different fuel cell layers and across interfaces. Ionomer and water distributions in the catalyst layer are essential for the local distribution of the reaction conditions at the dispersed catalyst surface. Knowing these distributions makes it possible – at least, in principle – to calculate a catalyst activity (or “heat”) map, quantifying to what extent catalyst particles at different locations contribute to the overall rate of current conversion. Polarization curves fitted with steady state performance models to yield key parameters of processes in fuel cell components. Impedance spectra treated with transient performance models to complement and markedly enhance the analytical information extracted from polarization curves. A modeling-derived catalyst activity map that displays active and inactive regions in a catalyst layer and reveals the potential for improvements in composition and structure. An overall effectiveness factor of catalyst utilization as a descriptor to compare catalyst layer designs. Modeling-based degradation analyses with a breakdown of different degradation mechanisms and capabilities to determine parameters of underlying mechanisms. Modeling based analyses of materials failure and an overall lifetime assessment considering relevant degradation mechanisms and failure modes. Moving forward with the field of fuel cell theory and modeling, it will be essential to realize misapprehensions and potential pitfalls looming along the way. Multi-scale and multi-parameter models of fuel cell operation are appealing from a practical point of view, due to their inherent promise to reduce or eliminate tedious steps in experimental materials design, integration, and testing and further down the road enable a computer-aided design of an optimal fuel cell system and stack. The term multi-scale modeling does not describe a new modeling strategy or flavor. It is something that researchers have done over many decades in fields at the cross-section of materials science and engineering. However, the multi-scale model does not replace the need for a justification of assumptions made, or a validation of parameters incorporated at different levels of the space-scale hierarchy. In fact, the validation of a multi-scale model is a nightmare and therefore it is often only done in a cursory fashion, undermining the very purpose of the exercise. Besides, the accuracy of a multi-scale model could not be better than the accuracy of its weakest parts – the weaknesses must be identified and weeded out, demanding extensive parameter sensitivity studies and careful evaluation of limiting cases. The understanding of structure vs. function relations in fuel cell materials hugely benefits from the rapidly progressing capabilities of high-resolution microscopy, imaging, and tomography. However, this progress in experimentation should not misguide the modeling community towards ever more detailed structural models, ultimately attempting to carve out an exact structural replica. Such a replica would not have any value for the field of fuel cell R&D. The value of modeling increases with the degree of abstraction achieved, and the reduction of structural information to a level that captures pivotal trends in structure vs. function relations, whilst preserving predictive capabilities. For instance, the development of advanced heterogeneous media models and refined percolation laws would be an intriguing prospect of this field. In the bigger scheme of things, fuel cell modeling can assume a key role in strategic planning of research forays, exploring new options and opportunities in materials design and the layout of fuel cell systems. Assuming that models live up to the highest standards of scientific consistency and originality, their adoption by experimentalists and fuel cell practitioners will hinge on other factors: model implementations developed as practical tools for data analytics should be clear, transparent, and well-documented; models should be provided together with algorithms explaining how to use them in materials design, fabrication, and property characterization as well as fuel cell assembly, testing, and optimization. Modeling connects primary data on structure and properties of materials with practical goals in view of performance, durability, and lifetime. Thus, modeling enterprises are ideally positioned to fulfill coordinating roles in data handling and analytics, promoting data-driven evolutionary approaches to learning and advancement in fuel cell science and technology. This will accelerate the materials design cycle. Moreover, fuel cell modeling will make an important contribution to the standardization and harmonization of fuel cell testing and diagnostics. Modeling-derived tools in virtual design and demonstration will pave the way for new ways in student training, education of the public, as well as demonstration of safety and reliability of fuel cell and hydrogen technologies. Using model-based demonstrations, educators will be able to take students/customers virtually to functional structures of materials, chemical processes, transport phenomena in complex media, and fuel cell dynamics. They will be able to virtually demonstrate fuel cells as components of future energy systems and infrastructures. To sum this up, fuel cell modeling comes along as a delicate balancing act of simplicity and complexity. Thus, it is fitting to conclude this editorial with an aphorism credited to Albert Einstein (who in an original statement from 1933 worded it more elaborately): “Everything should be made as simple as possible, but not simpler.” Michael Eikerling, Simon Fraser University, British Columbia, Canada