Computational Insights into Materials and Interfaces for Capacitive Energy Storage

Surface charge-driven sodium-ion migration and secondary desolvation in MXene nanoconfinement

Improving the energy storage and power delivery of layered materials relies heavily on a better understanding of the ultrafast ion intercalation dynamics within nanoconfinement. Here we report a molecular dynamics (MD) simulation that directly probes the effect of surface charge strengths on Na ion transport properties in slit MXene (Ti3C2(OH)2) anodes. We found that at high surface charge strengths, the migration of intercalated Na+ to the MXene surface is the main reason for the significantly increased interlayer Na+ conductivity. More importantly, during the "interlayer-to-surface" process of most intercalated Na+, the H-bonding network of some surface water is disrupted by the Na-ions' electrostatic attraction, causing these water molecules to lose surface affinity and flip away from the MXene surface. This allows further desolvated Na ions to be exposed on the electrode surface, thereby improving the charge transfer between ions and the electrode. This work provides an atomic understanding of Na-ion's secondary desolvation mechanism based on surface water molecular dipole flipping, which may provide new insights into the energy storage mechanism of nanoscale layered materials.

A computational study of the ternary mixtures of NaPF6-EC and choline glycine ionic liquid

This study investigates the structural and dynamic properties of ternary mixtures composed of NaPF6, ethylene carbonate (EC), and the ionic liquid choline glycine (ChGly), with a focus on their potential as electrolytes for supercapacitors. The combination of NaPF6-EC, known for its high ionic conductivity, with the biodegradable and environmentally friendly ChGly offers a promising approach to enhancing electrolyte performance. Through molecular simulations, we analyze how the inclusion of small concentrations of ChGly affects key properties such as density, cohesive energy, and ion mobility. Our findings demonstrate that the NaPF6-EC-ChGly mixture exhibits a complex network of electrostatic interactions and hydrogen bonding, with the glycine anion significantly influencing the liquid structure. In mixtures with small additions of ChGly, we observed an optimal balance of diffusion and ionic mobility. These results highlight the potential of ChGly as a green additive to conventional electrolytes, paving the way for more sustainable and high-performance energy storage devices.

Effects of size and shape of hole defects on mechanical properties of biphenylene: a molecular dynamics study

The distinctive multi-ring structure and remarkable electrical characteristics of biphenylene render it a material of considerable interest, notably for its prospective utilization as an anode material in lithium-ion batteries. However, understanding the mechanical traits of biphenylene is essential for its application, particularly due to the volumetric fluctuations resulting from lithium ion insertion and extraction during charging and discharging cycles. In this regard, this study investigates the performance of pristine biphenylene and materials embedded with various types of hole defects under uniaxial tension utilizing molecular dynamics simulations. Specifically, from the stress‒strain curves, we obtained key mechanical properties, including toughness, strength, Young's modulus and fracture strain. It was observed that various near-circular hole (including circular, square, hexagonal, and octagonal) defects result in remarkably similar properties. A more quantitative scaling analysis revealed that, in comparison with the exact shape of the defect, the area of the defect is more critical for determining the mechanical properties of biphenylene. Our finding might be beneficial to the defect engineering of two-dimensional materials.

Enhancing the supercapacitive performance of a carbon-based electrode through a balanced strategy for porous structure, graphitization degree and N,B co-doping

Regarding carbon-based electrodes, simultaneously establishing a well-defined meso-porous architecture, introducing abundant hetero-atoms and improving the graphitization degree can effectively enhance their capacitive performance. However, it remains a significant challenge to achieve a good balance between defects and graphitization degree. In this study, the porous structure and composition of carbon materials are co-optimised through a 'dual-function' strategy. Briefly, K3Fe(C2O4)3 and H3BO3 were hybridised with a gelatin aqueous solution to form a homogeneous composite hydrogel, followed by lyophilisation and carbonisation. Owing to the dual functionality of raw materials, the graphitization, activation and hetero-atom doping processes can occur simultaneously during a one-step high-temperature treatment. The resultant carbon material exhibits a high graphitization degree (ID/IG = 0.9 ± 0.1), high hetero-atom content (N: 9.0 ± 0.3 at.%, B: 6.9 ± 0.5 at.%) and a large specific area (1754 ± 58 m2/g). The as-prepared electrode demonstrates a superior capacitance of 383 ± 1F g-1 at 1 A/g. Interestingly, the cyclic voltammetry (CV) curves exhibit a distinctive pair of broad redox peaks, which is uncommon in KOH electrolyte. Experiment data and density functional theory (DFT) simulation verify that N-5, B co-doping enhances the activity of the faradic reaction of carbon electrodes in KOH electrolyte. Furthermore, the fabricated Zn-ion hybrid supercapacitor (ZHSC) based on this carbon electrode delivers a high-energy density of 140.7 W h kg-1 at a power density of 840 W kg-1.

Modeling of Nanomaterials for Supercapacitors: Beyond Carbon Electrodes

Capacitive storage devices allow for fast charge and discharge cycles, making them the perfect complements to batteries for high power applications. Many materials display interesting capacitive properties when they are put in contact with ionic solutions despite their very different structures and (surface) reactivity. Among them, nanocarbons are the most important for practical applications, but many nanomaterials have recently emerged, such as conductive metal-organic frameworks, 2D materials, and a wide variety of metal oxides. These heterogeneous and complex electrode materials are difficult to model with conventional approaches. However, the development of computational methods, the incorporation of machine learning techniques, and the increasing power in high performance computing now allow us to tackle these types of systems. In this Review, we summarize the current efforts in this direction. We show that depending on the nature of the materials and of the charging mechanisms, different methods, or combinations of them, can provide desirable atomic-scale insight on the interactions at play. We mainly focus on two important aspects: (i) the study of ion adsorption in complex nanoporous materials, which require the extension of constant potential molecular dynamics to multicomponent systems, and (ii) the characterization of Faradaic processes in pseudocapacitors, that involves the use of electronic structure-based methods. We also discuss how recently developed simulation methods will allow bridges to be made between double-layer capacitors and pseudocapacitors for future high power electricity storage devices.

Triple Synergism Effect of Ammonium Nitrilotriacetate on the Chemical Mechanical Polishing Performance of Ruthenium Barrier Layers

As the feature size of integrated circuits continues to decrease, ruthenium (Ru) has been suggested as the successor to traditional Ta/TaN bilayers for barrier layer materials due to its unique properties. This research delves into the effects of ammonium nitrilotriacetate (NTA(NH4)3) on the chemical mechanical polishing (CMP) performance of Ru in H2O2-based slurry. The removal rate (RR) of Ru surged from 47 to 890 Å min-1, marking an increase of about 17 times. The essence of this mechanism lies in the triple synergistic effects of NTA(NH4)3 in promoting ruthenium (Ru) removal: 1) The interaction betweenNH 4 + ${\mathrm{NH}}_{\mathrm{4}}^{\mathrm{+}}$ from NTA(NH4)3 and SiO2 abrasives; 2) The chelating action of [(NH4)N(CH2COO)3]2- from NTA(NH4)3 on Ru and its oxides; 3) The ammoniation and chelation of Ru and its oxides byNH 4 + ${\mathrm{NH}}_{\mathrm{4}}^{\mathrm{+}}$ from NTA(NH4)3, which enhance the dissolution and corrosion of oxidized Ru, making its removal during the barrier layer CMP process more efficient through mechanical means. This research introduces a synergistic approach for the effective removal of Ru, shedding light on potential applications of CMP in the field of the integrated circuits.

Electronic structures and quantum capacitance of twisted bilayer graphene with defects based on three-band tight-binding model

Twisted bilayer graphene (tBLG) with C vacancies would greatly improve the density of states (DOS) around the Fermi level (EF) and quantum capacitance; however, the single-band tight-binding model only considering pz orbitals cannot accurately capture the low-energy physics of tBLG with C vacancies. In this work, a three-band tight-binding model containing three p orbitals of C atoms is proposed to explore the modulation mechanism of C vacancies on the DOS and quantum capacitance of tBLG. We first obtain the hopping integral parameters of the three-band tight-binding model, and then explore the electronic structures and the quantum capacitance of tBLG at a twisting angle of θ = 1.47° under different C vacancy concentrations. The impurity states contributed by C atoms with dangling bonds located around the EF and the interlayer hopping interaction could induce band splitting of the impurity states. Therefore, compared with the quantum capacitance of pristine tBLG (∼18.82 μF cm-2) at zero bias, the quantum capacitance is improved to ∼172.76 μF cm-2 at zero bias, and the working window with relatively large quantum capacitance in the low-voltage range is broadened in tBLG with C vacancies due to the enhanced DOS around the EF. Moreover, the quantum capacitance of tBLG is further increased at zero bias with an increase of the C vacancy concentration induced by more impurity states. These findings not only provide a suitable multi-band tight-binding model to describe tBLG with C vacancies but also offer theoretical insight for designing electrode candidates for low-power consumption devices with improved quantum capacitance.

Molecular Understanding of Charging Dynamics in Supercapacitors with Porous Electrodes and Ionic Liquids

Porous electrodes and ionic liquids could significantly enhance the energy storage of supercapacitors. However, they may reduce the charging dynamics and power density due to the nanoconfinement of porous electrodes and the high viscosity of ionic liquids. A comprehensive understanding of the charging mechanism in porous supercapacitors with ionic liquids provides a crucial theoretical foundation for their design optimization. Here, we review the progress of molecular simulations of the charging dynamics in supercapacitors consisting of porous electrodes and ionic liquids. We highlight and delve into the breakthroughs in the ion transport and charging mechanism for electrodes with subnanometer pores and realistic porous structures. We also discuss future directions for the charging dynamics of supercapacitors.

Molecular dynamics study of fluorosulfonyl ionic liquids as electrolyte for electrical double layer capacitors

The development of high-performance supercapacitors is an important goal in the field of energy storage. Ionic liquids (ILs) are promising electrolyte materials for efficient energy storage in supercapacitors, because of the high stability, low volatility, and wider electrochemical stability window than traditional electrolytes. However, ILs-based supercapacitors usually show a relatively lower power density owing to the inherent viscosity-induced low electrical conductivity. Fluorosulfonyl ILs have aroused much attention in energy storage devices due to its low toxicity and excellent stability. Here, we propose that structural modification is an effective way to improve the energy storage performance of fluorosulfonyl ILs through the classical molecular dynamics (MD) method. Four fluorosulfonyl ILs with different sizes and symmetries were considered. Series of properties including conductivity, interface structure, and double-layer capacitance curves were systematically investigated. The results show that smaller size and more asymmetric structure can enhance self-diffusion coefficient and conductivity, and improve the electrochemical performance. Appropriate modification of the electrodes can further enhance the capacitive performance. Our work provides an opportunity to further understand and develop the fluorosulfonyl ILs electrolyte in supercapacitors.

Theoretical investigation of quantum capacitance of Co-doped α-MnO2 for supercapacitor applications using density functional theory

The rapid depletion of fossil fuels and ever-growing energy demand have led to a search for renewable clean energy sources. The storage of renewable energy calls for immediate attention to the fabrication of efficient energy storage devices like supercapacitors (SCs). As an electrode material for SCs, MnO2 has gained wide research interest because of its high theoretical capacitance, variable oxidation state, vast abundance, and low cost. However, the low electric conductivity of MnO2 limits its practical application. The conductivity of MnO2 can be enhanced by tuning the electronic states through substitution doping with cobalt. In the present work, first principles analysis based on density functional theory (DFT) has been used to examine the quantum capacitance (CQC) and surface charge (Q) of Co-doped MnO2. Doping enhanced the structural stability, electrical conductivity, potential window, and quantum capacitance of α-MnO2. The shortened band gap and localized states near the Fermi level improve the CQC of α-MnO2. For the narrow potential range (-0.4 to 0.4 V), the CQC is observed to increase with doping concentration. The highest CQC value at +0.4 V is observed to be 2412.59 μF cm-2 for Mn6Co2O16 (25% doping), five times higher than that of pristine MnO2 (471.18 μF cm-2). Mn6Co2O16 also exhibits better CQC and 'Q' at higher positive bias. Hence, it can be used as an anode material for asymmetric supercapacitors. All these results suggest better capacitive performance of Co-doped α-MnO2 for aqueous SCs and as an anode material for asymmetric supercapacitors.

Ultra-High Cycling Stability of 3D Flower-like Ce(COOH)3 for Supercapacitor Electrode via a Facile and Scalable Strategy

An electrode material with high performance, long durability, and low cost for supercapacitors has long been desired in academia and industry. Among all the factors that affect the electrochemical performance and cycling stability of electrode materials, the morphology and intrinsic structure characteristics are the most important. In this study, a novel 3D flower-like Ce(COOH)3 electrode material was designed by taking advantage of the Ce3+ and -COOH groups and fabricated by a one-pot microwave-assisted method. The morphology and structure characteristics of the sample were examined by SEM, EDS, TEM, XRD, FT-IR, XPS, N2 adsorption/desorption techniques, and the electrochemical behaviors were investigated in a three-electrode configuration. The Ce(COOH)3 electrode presents an excellent specific capacitance of 140 F g-1 at 1 A g-1, higher than many other previously reported Ce-based electrodes. In addition, it delivers high rate capability that retains 60% of its initial capacitance when the current density is magnified 20 times. Dramatically, the Ce(COOH)3 electrode exhibits an ultra-high cycling stability with capacitance retention of 107.9% after 60,000 cycles, which is the highest durability among reported Ce-organic compound electrodes to the best of our knowledge. The excellent electrochemical performance is ascribed to its intrinsic crystal structure and unique morphology. This work indicates that the 3D flower-like Ce(COOH)3 has significant potential for supercapacitor applications and the facile and scalable synthesis strategy can be extended to produce other metal-organic composite electrodes.

PiNNwall: Heterogeneous Electrode Models from Integrating Machine Learning and Atomistic Simulation

Electrochemical energy storage always involves the capacitive process. The prevailing electrode model used in the molecular simulation of polarizable electrode-electrolyte systems is the Siepmann-Sprik model developed for perfect metal electrodes. This model has been recently extended to study the metallicity in the electrode by including the Thomas-Fermi screening length. Nevertheless, a further extension to heterogeneous electrode models requires introducing chemical specificity, which does not have any analytical recipes. Here, we address this challenge by integrating the atomistic machine learning code (PiNN) for generating the base charge and response kernel and the classical molecular dynamics code (MetalWalls) dedicated to the modeling of electrochemical systems, and this leads to the development of the PiNNwall interface. Apart from the cases of chemically doped graphene and graphene oxide electrodes as shown in this study, the PiNNwall interface also allows us to probe polarized oxide surfaces in which both the proton charge and the electronic charge can coexist. Therefore, this work opens the door for modeling heterogeneous and complex electrode materials often found in energy storage systems.

Energy Storage Mechanism in Supercapacitors with Porous Graphdiynes: Effects of Pore Topology and Electrode Metallicity

Porous graphdiynes are a new class of porous 2D materials with tunable electronic structures and various pore structures. They have potential applications as well-defined nanostructured electrodes and can provide platforms for understanding energy storage mechanisms underlying supercapacitors. Herein, the effect of stacking structure and metallicity on energy storage with such electrodes is investigated. Simulations reveal that supercapacitors based on porous graphdiynes of AB stacking structure can achieve both higher double-layer capacitance and ionic conductivity than AA stacking. This phenomenon is ascribed to more intense image forces in AB stacking, leading to a breakdown of ionic ordering and the formation of effective "free ions". Macroscale analysis shows that doped porous graphdiynes can deliver outstanding gravimetric and volumetric energy and power densities due to their enhanced quantum capacitance. These findings pave the way for designing high-performance supercapacitors by regulating pore topology and metallicity of electrode materials.

Theory and Simulations of Ionic Liquids in Nanoconfinement

Room-temperature ionic liquids (RTILs) have exciting properties such as nonvolatility, large electrochemical windows, and remarkable variety, drawing much interest in energy storage, gating, electrocatalysis, tunable lubrication, and other applications. Confined RTILs appear in various situations, for instance, in pores of nanostructured electrodes of supercapacitors and batteries, as such electrodes increase the contact area with RTILs and enhance the total capacitance and stored energy, between crossed cylinders in surface force balance experiments, between a tip and a sample in atomic force microscopy, and between sliding surfaces in tribology experiments, where RTILs act as lubricants. The properties and functioning of RTILs in confinement, especially nanoconfinement, result in fascinating structural and dynamic phenomena, including layering, overscreening and crowding, nanoscale capillary freezing, quantized and electrotunable friction, and superionic state. This review offers a comprehensive analysis of the fundamental physical phenomena controlling the properties of such systems and the current state-of-the-art theoretical and simulation approaches developed for their description. We discuss these approaches sequentially by increasing atomistic complexity, paying particular attention to new physical phenomena emerging in nanoscale confinement. This review covers theoretical models, most of which are based on mapping the problems on pertinent statistical mechanics models with exact analytical solutions, allowing systematic analysis and new physical insights to develop more easily. We also describe a classical density functional theory, which offers a reliable and computationally inexpensive tool to account for some microscopic details and correlations that simplified models often fail to consider. Molecular simulations play a vital role in studying confined ionic liquids, enabling deep microscopic insights otherwise unavailable to researchers. We describe the basics of various simulation approaches and discuss their challenges and applicability to specific problems, focusing on RTIL structure in cylindrical and slit confinement and how it relates to friction and capacitive and dynamic properties of confined ions.

Exploring the catalytic activity of graphene-based TM-NxC4-x single atom catalysts for the oxygen reduction reaction via density functional theory calculation

Electrocatalysts for the oxygen reduction reaction (ORR) are extremely crucial for advanced energy conversion technologies, such as fuel cell batteries. A promising ORR catalyst usually should have low overpotentials, rich catalytic sites and low cost. In the past decade, single-atom catalyst (SAC) TM-N₄ (TM = Fe, Co, etc.) embedded graphene matrixes have been widely studied for their promising performance and low cost for ORR catalysis, but the effect of coordination on the ORR activity is not fully understood. In this work, we will employ density functional theory (DFT) calculations to systematically investigate the ORR activity of 40 different 3d transition metal single-atom catalysts (SACs) supported on nitrogen-doped graphene supports, ranging from vanadium to zinc. Five different nitrogen coordination configurations (TM-N_xC_4-x with x = 0, 1, 2, 3, and 4) were studied to reveal how C/N substitution affects the ORR activity. By looking at the stability, free energy diagram, overpotential, and scaling relationship, our calculation showed that partial C substitution can effectively improve the ORR performance of Mn, Co, Ni, and Zn-based SACs. The volcano plot obtained from the scaling relationship indicated that the substitution of N by C could distinctively affect the potential-limiting step in the ORR, which leads to the enhanced or weakened ORR performance. Density of states and d-band center analysis suggested that this coordination-tuned ORR activity can be explained by the shift of the d-band center due to the coordination effect. Finally, four candidates with optimal ORR activity and dynamic stability were proposed from the pool: NiC₄, CoNC₃, CrN₄, and ZnN₃C. Our work provides a feasible designing strategy to improve the ORR activity of graphene-based TM-N₄ SACs by tuning the coordination environment, which may have potential implication in the high-performance fuel cell development.

An AI-Based Newly Developed Analytical Formulation for Discharging Behavior of Supercapacitors with the Integration of a Review of Supercapacitor Challenges and Advancement Using Quantum Dots

A supercapacitor is a type of electrical component that has larger capacitance, due to asymmetric behavior with better power density, and lower ESR (effective series resistance) than conventional energy-storage components. Supercapacitors can be used with battery technology to create an effective energy storage system due to their qualities and precise characterization. Studies have shown that the use of quantum dots as electrodes in supercapacitors can significantly increase their effectiveness. In this research article, we have used a Drude model based on free electrons (asymmetric nature) to describe the supercapacitor’s discharging characteristics. Commercially available Nippon DLA and Green-cap supercapacitors were used to verify the Drude model by discharging them through a constant current source using a simple current mirror circuit. The parameters of both the fractional-order models and our suggested method were estimated using the least-squares regression fitting approach. An intriguing finding from the Drude model is the current-dependent behavior of the leakage-parallel resistance in the constant current discharge process. Instead of using the traditional exponential rule, supercapacitors discharge according to a power law. This work reflects the strong symmetry of different aspects of designing a hybrid supercapacitor with high efficiency and reliability.

Predictive Molecular Models for Charged Materials Systems: From Energy Materials to Biomacromolecules

Electrostatic interactions play a dominant role in charged materials systems. Understanding the complex correlation between macroscopic properties with microscopic structures is of critical importance to develop rational design strategies for advanced materials. But the complexity of this challenging task is augmented by interfaces present in the charged materials systems, such as electrode-electrolyte interfaces or biological membranes. Over the last decades, predictive molecular simulations that are founded in fundamental physics and optimized for charged interfacial systems have proven their value in providing molecular understanding of physicochemical properties and functional mechanisms for diverse materials. Novel design strategies utilizing predictive models have been suggested as promising route for the rational design of materials with tailored properties. Here, an overview of recent advances in the understanding of charged interfacial systems aided by predictive molecular simulations is presented. Focusing on three types of charged interfaces found in energy materials and biomacromolecules, how the molecular models characterize ion structure, charge transport, morphology relation to the environment, and the thermodynamics/kinetics of molecular binding at the interfaces is discussed. The critical analysis brings two prominent field of energy materials and biological science under common perspective, to stimulate crossover in both research field that have been largely separated.

Confinement Effects on Distribution and Transport of Neutral Solutes in a Small Hydrophobic Nanopore

Molecular dynamics simulations are used to study confinement effects in small cylindrical silica pores with extended hydrophobic surface functionalization as realized, for example, in reversed-phase liquid chromatography (RPLC) columns. In particular, we use a 6 nm cylindrical and a 10 nm slit pore bearing the same C₁₈ stationary phase to compare the conditions inside the smaller-than-average pores within an RPLC column to column-averaged properties. Two small, neutral, apolar to moderately polar solutes are used to assess the consequences of spatial confinement for typical RPLC analytes with water (W)-acetonitrile (ACN) mobile phases at W/ACN ratios between 70/30 and 10/90 (v/v). The simulated data show that true bulk liquid behavior, as observed over an extended center region in the 10 nm slit pore, is not recovered within the 6 nm cylindrical pore. Instead, the ACN-enriched solvent layer around the C₁₈ chain ends (the ACN ditch), a general feature of hydrophobic interfaces equilibrated with aqueous-organic liquids, extends over the entire pore lumen of the small cylindrical pore. This renders the entire pore a highly hydrophobic environment, where, contrary to column-averaged behavior, neither the local nor the pore-averaged sorption and diffusion of analytes scales directly with the W/ACN ratio of the mobile phase. Additionally, the solute polarity-related discrimination between analytes is enhanced. The consequences of local ACN ditch overlap in RPLC columns are reminiscent of ion transport in porous media with charged surfaces, where electrical double-layer overlap occurring locally in smaller pores leads to discrimination between co- and counterionic species.

Assessing the impact of valence asymmetry in ionic solutions and its consequences on the performance of supercapacitors

Molecular dynamics simulations were performed to describe the properties of hypothetical salt electrolytic solutions. The main focus of this work is the valence asymmetry, which in recent years has been considered an important aspect in the physical chemistry of aqueous electrolytes. In general, our results show that the structural, energetic, and dynamic properties respond differently to the asymmetry of ionic solutions, but in all cases, appreciable changes were observed. Graphene supercapacitors based on the investigated electrolytes were studied in light of their electrostatic properties. We observed that the electrode capacitances, positive and negative, were greatly influenced by the presence of cations in the electrical double layer of the negative electrode and by the absence of these cations, in the double layer of the positive electrode. In general, we assess that quantitative variations due to valence asymmetry may indeed be an important factor for the development of new and more efficient electrolytes.

Electrochemical Capacitors with Confined Redox Electrolytes and Porous Electrodes

Electrochemical capacitors (ECs), including electrical-double-layer capacitors and pseudocapacitors, feature high power densities but low energy densities. To improve the energy densities of ECs, redox electrolyte-enhanced ECs (R-ECs) or supercapbatteries are designed through employing confined soluble redox electrolytes and porous electrodes. In R-ECs the energy storage is based on diffusion-controlled faradaic processes of confined redox electrolytes at the surface of a porous electrode, which thus take the merits of high power densities of ECs and high energy densities of batteries. In the past few years, there has been great progress in the development of this energy storage technology, particularly in the design and synthesis of novel redox electrolytes and porous electrodes, as well as the configurations of new devices. Herein, a full-screen picture of the fundamentals and the state-of-art progress of R-ECs are given together with a discussion and outlines about the challenges and future perspectives of R-ECs. The strategies to improve the performance of R-ECs are highlighted from the aspects of their capacitances and capacitance retention, power densities, and energy densities. The insight into the philosophies behind these strategies will be favorable to promote the R-EC technology toward practical applications of supercapacitors in different fields.

Microscopic Simulations of Electrochemical Double-Layer Capacitors

Electrochemical double-layer capacitors (EDLCs) are devices allowing the storage or production of electricity. They function through the adsorption of ions from an electrolyte on high-surface-area electrodes and are characterized by short charging/discharging times and long cycle-life compared to batteries. Microscopic simulations are now widely used to characterize the structural, dynamical, and adsorption properties of these devices, complementing electrochemical experiments and in situ spectroscopic analyses. In this review, we discuss the main families of simulation methods that have been developed and their application to the main family of EDLCs, which include nanoporous carbon electrodes. We focus on the adsorption of organic ions for electricity storage applications as well as aqueous systems in the context of blue energy harvesting and desalination. We finally provide perspectives for further improvement of the predictive power of simulations, in particular for future devices with complex electrode compositions.

Electric-field-induced oscillations in ionic fluids: a unified formulation of modified Poisson-Nernst-Planck models and its relevance to correlation function analysis

We theoretically investigate an electric-field-driven system of charged spheres as a primitive model of concentrated electrolytes under an applied electric field. First, we provide a unified formulation for the stochastic charge and density dynamics of the electric-field-driven primitive model using the stochastic density functional theory (DFT). The stochastic DFT integrates the four frameworks (the equilibrium and dynamic DFTs, the liquid state theory and the field-theoretic approach), which allows us to justify in a unified manner various modifications previously made for the Poisson-Nernst-Planck model. Next, we consider stationary density-density and charge-charge correlation functions of the primitive model with a static electric field. We predict an electric-field-induced synchronization between emergences of density and charge oscillations. We are mainly concerned with the emergence of stripe states formed by segregation bands transverse to the external field, thereby demonstrating the following: (i) the electric-field-induced crossover occurs prior to the conventional Kirkwood crossover without an applied electric field, and (ii) the ion concentration dependence of the decay lengths at the onset of oscillations bears a similarity to the underscreening behavior found by recent simulation and theoretical studies on equilibrium electrolytes. Also, the 2D inverse Fourier transform of the correlation function illustrates the existence of stripe states beyond the electric-field-induced Kirkwood crossover.

Understanding the Electric Double-Layer Structure, Capacitance, and Charging Dynamics

Significant progress has been made in recent years in theoretical modeling of the electric double layer (EDL), a key concept in electrochemistry important for energy storage, electrocatalysis, and multitudes of other technological applications. However, major challenges remain in understanding the microscopic details of the electrochemical interface and charging mechanisms under realistic conditions. This review delves into theoretical methods to describe the equilibrium and dynamic responses of the EDL structure and capacitance for electrochemical systems commonly deployed for capacitive energy storage. Special emphasis is given to recent advances that intend to capture the nonclassical EDL behavior such as oscillatory ion distributions, polarization of nonmetallic electrodes, charge transfer, and various forms of phase transitions in the micropores of electrodes interfacing with an organic electrolyte or ionic liquid. This comprehensive analysis highlights theoretical insights into predictable relationships between materials characteristics and electrochemical performance and offers a perspective on opportunities for further development toward rational design and optimization of electrochemical systems.

Simulating the charging of cylindrical electrolyte-filled pores with the modified Poisson-Nernst-Planck equations

Understanding how electrolyte-filled porous electrodes respond to an applied potential is important to many electrochemical technologies. Here, we consider a model supercapacitor of two blocking cylindrical pores on either side of a cylindrical electrolyte reservoir. A stepwise potential difference $2\Phi$ between the pores drives ionic fluxes in the setup, which we study through the modified Poisson-Nernst-Planck equations, solved with finite elements.We focus our discussion on the dominant timescales with which the pores charge and how these timescales depend on three dimensionless numbers.Next to the dimensionless applied potential $\Phi$, we consider the ratio $R/R_b$ of the pore's resistance $R$ to the bulk reservoir resistance $R_b$ and the ratio $r_{p}/\ld$ of the pore radius $r_p$ to the Debye length $\ld$.We compare our data to theoretical predictions by Aslyamov and Janssen ($\Phi$), Posey and Morozumi ($R/R_b$), and Henrique, Zuk, and Gupta ($r_{p}/\ld$).Through our numerical approach, we delineate the validity of these theories and the assumptions on which they were based.

The MOBH35 Metal–Organic Barrier Heights Reconsidered: Performance of Local-Orbital Coupled Cluster Approaches in Different Static Correlation Regimes

We have revisited the MOBH35 (Metal–Organic Barrier Heights, 35 reactions) benchmark [Iron, Janes, J. Phys. Chem. A, 2019, 123 ( (17), ), 3761−378130973722; ibid. 2019, 123, 6379–6380] for realistic organometallic catalytic reactions, using both canonical CCSD(T) and localized orbital approximations to it. For low levels of static correlation, all of DLPNO-CCSD(T), PNO-LCCSD(T), and LNO-CCSD(T) perform well; for moderately strong levels of static correlation, DLPNO-CCSD(T) and (T₁) may break down catastrophically, and PNO-LCCSD(T) is vulnerable as well. In contrast, LNO-CCSD(T) converges smoothly to the canonical CCSD(T) answer with increasingly tight convergence settings. The only two reactions for which our revised MOBH35 reference values differ substantially from the original ones are reaction 9 and to a lesser extent 8, both involving iron. For the purpose of evaluating density functional theory (DFT) methods for MOBH35, it would be best to remove reaction 9 entirely as its severe level of static correlation makes it just too demanding for a test. The magnitude of the difference between DLPNO-CCSD(T) and DLPNO-CCSD(T₁) is a reasonably good predictor for errors in DLPNO-CCSD(T₁) compared to canonical CCSD(T); otherwise, monitoring all of T₁, D₁, max|t_i^A|, and 1/(ε_LUMO – ε_HOMO) should provide adequate warning for potential problems. Our conclusions are not specific to the def2-SVP basis set but are largely conserved for the larger def2-TZVPP, as they are for the smaller def2-SV(P): the latter may be an economical choice for calibrating against canonical CCSD(T). Finally, diagnostics for static correlation are statistically clustered into groups corresponding to (1) importance of single excitations in the wavefunction; (2a) the small band gap, weakly separated from (2b) correlation entropy; and (3) thermochemical importance of correlation energy, as well as the slope of the DFT reaction energy with respect to the percentage of HF exchange. Finally, a variable reduction analysis reveals that much information on the multireference character is provided by T₁, I_ND/I_tot, and the exchange-based diagnostic A₁₀₀[TPSS].

Understanding of Bulk and Interfacial Structures Ternary and Binary Deep Eutectic Solvents with a Constant Potential Method: A Molecular Dynamics Study

In the last decade, deep eutectic solvents (DESs) emerge as promising electrolytes in supercapacitors and rechargeable batteries due to their unique properties, wide electrochemical window, low viscosity, and high ionic...

Salt-in-water and water-in-salt electrolytes: the effects of the asymmetry in cation and anion valence on their properties

We investigated the structural, dynamic, energetic, and electrostatic properties of electrolytes based on the ion pairs LiCl and Li₂SO₄. Atomistic molecular dynamics simulations were used to simulate these aqueous electrolytic solutions at two different concentrations 2 M (normal) and 21 M (superconcentrated, WiSE). The effects of the valence asymmetry of the Li₂SO₄ electrolyte were also discussed for both salt concentrations. Our results differ in the physical aspect of pure electrolytes, showing the drastic effect of high concentration, in particular on the viscosity, which is dramatically increased in WiSE. This is a consequence of their reduced ionic mobility and has a direct effect on ionic conductivity. Also, our results for graphene-based supercapacitors, as indicated by some experimental work, do not indicate any better performance of WiSEs over normal electrolytes. In fact, the differences in the total capacitance, due to the concentration of ions, presented by both electrolytes are negligible. The valence asymmetry can be clearly observed in some properties but for most of them its effects could not be quantified or isolated.

Quantum Capacitance through Molecular Infiltration of 7,7,8,8-Tetracyanoquinodimethane in Metal-Organic Framework/Covalent Organic Framework Hybrids

Metal-organic frameworks (MOFs) and covalent organic frameworks (COFs) have been extensively investigated during the last two decades. More recently, a family of hybrid materials (i.e., MOF@COF) has emerged as particularly appealing for gas separation and storage, catalysis, sensing, and drug delivery. MOF@COF hybrids combine the unique characteristics of both MOF and COF components and exhibit peculiar properties including high porosity and large surface area. In this work, we show that the infiltration of redox-active 7,7,8,8-tetracyanoquinodimethane (TCNQ) molecules into the pores of MOF@COF greatly improves the characteristics of the latter, thereby attaining high-performance energy storage devices. Density functional theory (DFT) calculations were employed to guide the design of a MOF@COF-TCNQ hybrid with the TCNQ functional units incorporated in the pores of MOF@COF. To demonstrate potential application of our hybrids, the as-synthesized MOF@COF-TCNQ hybrid has been employed as an active material in supercapacitors. Electrochemical energy storage analysis revealed outstanding supercapacitor performance, as evidenced by a specific areal capacitance of 78.36 mF cm^-2 and a high stack volumetric energy density of 4.46 F cm^-3, with a capacitance retention of 86.4% after 2000 cycles completed at 0.2 A cm^-2. DFT calculation results strongly indicate that the high capacitance of MOF@COF-TCNQ has a quantum capacitance origin. Our liquid-phase infiltration protocol of MOF@COF hybrids with redox-active molecules represents a efficacious approach to design functional porous hybrids.

Separation of Rare-Earth Ions from Mine Wastewater Using B12S Nanoflakes as a Capacitive Deionization Electrode Material

In this study, nanoflakes of B₁₂S were fabricated by plasma-assisted reaction of sulfur dichloride in an ionic liquid at room temperature using europium boride as a hard template. The nanoflakes had an average width and thickness of about 3 ₁urn and 9.6 nm, respectively, and a large specific surface area of 1197.2 m² g ¹. They behaved like typical electric double-layer capacitors with a capacitance of 201.2 F g ¹ at 0.2 mA cm ² During capacitive deionization to recover rare-earth ions, the nanoflakes had higher adsorption selectivity for Sm³⁺ than for other competing ions present in real mine waste water. This is due to the strong interaction of the electron-concentered S-groups (S''') of the nanoflakes with S m³⁺. This provides an alternative to construct efficient systems to specifically remove Sm³⁺ from aqueous solution using B₁₂S nanoflakes. This process demonstrates that other boron sulfide compounds can be used to recover valuable ions by capacitive deionization.

Investigating the Accuracy of Water Models through the Van Hove Correlation Function

We present molecular-simulation-based calculations of the Van Hove correlation function (VHF) of water using multiple modeling approaches: classical molecular dynamics with simple three-site nonpolarizable models, with a polarizable model, and with a reactive force field; density functional tight-binding molecular dynamics; and ab initio molecular dynamics. Due to the many orders of magnitude difference in the computational cost of these approaches, we investigate how small and short the simulations can be while still yielding sufficiently accurate and interpretable results for the VHF. We investigate the accuracy of the different models by comparing them to recently published inelastic X-ray scattering measurements of the VHF. We find that all of the models exhibit qualitative agreement with the experiments, and in some models and for some properties, the agreement is quantitative. This work lays the foundation for future simulation approaches to calculating the VHF for aqueous solutions in bulk and under nanoconfinement.

MoSDeF Cassandra: A complete Python interface for the Cassandra Monte Carlo software

We introduce a new Python interface for the Cassandra Monte Carlo software, molecular simulation design framework (MoSDeF) Cassandra. MoSDeF Cassandra provides a simplified user interface, offers broader interoperability with other molecular simulation codes, enables the construction of programmatic and reproducible molecular simulation workflows, and builds the infrastructure necessary for high-throughput Monte Carlo studies. Many of the capabilities of MoSDeF Cassandra are enabled via tight integration with MoSDeF. We discuss the motivation and design of MoSDeF Cassandra and proceed to demonstrate both simple use-cases and more complex workflows, including adsorption in porous media and a combined molecular dynamics - Monte Carlo workflow for computing lateral diffusivity in graphene slit pores. The examples presented herein demonstrate how even relatively complex simulation workflows can be reduced to, at most, a few files of Python code that can be version-controlled and shared with other researchers. We believe this paradigm will enable more rapid research advances and represents the future of molecular simulations.

Efficient Parametrization of Force Field for the Quantitative Prediction of the Physical Properties of Ionic Liquid Electrolytes

The prediction of transport properties of room-temperature ionic liquids from nonpolarizable force field-based simulations has long been a challenge. The uniform charge scaling method has been widely used to improve the agreement with the experiment by incorporating the polarizability and charge transfer effects in an effective manner. While this method improves the performance of the force fields, this prescription is ad hoc in character; further, a quantitative prediction is still not guaranteed. In such cases, the nonbonded interaction parameters too need to be refined, which requires significant effort. In this work, we propose a three-step semiautomated refinement procedure based on (1) atomic site charges obtained from quantum calculations of the bulk condensed phase; (2) quenched Monte Carlo optimizer to shortlist suitable force field candidates, which are then tested using pilot simulations; and (3) manual refinement to further improve the accuracy of the force field. The strategy is designed in a sequential manner with each step improving the accuracy over the previous step, allowing the users to invest the effort commensurate with the desired accuracy of the refined force field. The refinement procedure is applied on N,N-diethyl-N-methyl-N-(2-methoxyethyl)ammonium bis(trifluoromethanesulfonyl)imide (DEME-TFSI), a front-runner as an electrolyte for electric double-layer capacitors and single-molecule-based devices. The transferability of the refined force field is tested on N,N-dimethyl-N-ethyl-N-methoxyethoxyethylammonium bis(trifluoromethanesulfonyl)imide (N_112,2O2O1-TFSI). The refined force field is found to be better at predicting both structural and transport properties compared to the uniform charge scaling procedure, which showed a discrepancy in the X-ray structure factor. The refined force field showed quantitative agreement with structural (density and X-ray structure factor) and transport properties-diffusion coefficients, ionic conductivity, and shear viscosity over a wide temperature range, building a case for the wide adoption of the procedure.

Theories and models of supercapacitors with recent advancements: impact and interpretations

Supercapacitors provide remarkable eco-friendly advancement in energy conversion and storage with a huge potential to control the future economy of the entire world. Currently, industries focus on the design and engineering aspects of supercapacitors with high performance (high energy), flexibility (by the use of composite polymer based electrolytes), high voltage (ionic liquid) and low cost. The paper reviews the modelling techniques like Empirical modelling, Dissipation transmission line models, Continuum models, Atomistic models, Quantum models, Simplified analytical models etc. proposed for the theoretical study of Supercapacitors and discusses their limitations in studying all the aspects of Supercapacitors. It also reviews the various software packages available for Supercapacitor (SC) modelling and discusses their advantages and disadvantages. The paper also reviews the Experimental advancements in the field of electric double layer capacitors (EDLCs), pseudo capacitors and hybrid/asymmetric supercapacitors and discusses the commercial progress of supercapacitors as well.

Demystifying the Stern layer at a metal-electrolyte interface: Local dielectric constant, specific ion adsorption, and partial charge transfer

Electric double layer (EDL) represents one of the most basic concepts in electrochemistry and is pertinent to diverse engineering applications ranging from electrocatalysis to energy storage. Whereas phenomenological and coarse-grained models have been long established to describe ionic distributions in the diffuse layer, a faithful prediction of the physicochemical properties of the electrode-electrolyte interface from a molecular perspective remains a daunting challenge. In this work, we investigate the charging behavior of an Ag (111) electrode in NaF aqueous solutions leveraging experimental results and theoretical calculations based on the classical density functional theory for ion distributions in the diffuse layer and on the joint density functional theory (JDFT) for the electronic structure. When the Ag electrode is applied with a negative voltage, the surface charge density can be reasonably described by assuming a neutral Stern layer with the dielectric constant dependent on the local electric field as predicted by the Kirkwood equation. However, the specific adsorption of F^- ions must be considered when the electrode is positively charged and the fluoride adsorption can be attributed to both physical and chemical interactions. Qualitatively, F^- binding and partial charge transfer are supported by JDFT calculations, which predict an increased binding energy as the voltage increases. Our findings shed insight on the molecular characteristics of the Stern layer and the charge behavior of adsorbed species not specified by conventional EDL models.

Breaking the Controversy of the Electropolymerization of Pyrrole Mechanisms by the Effective Screening Medium Quantum Charged Model Interface

Several mechanisms for the electropolymerization of pyrrole have been proposed since the first report 40 years ago. However, none of them were consensual despite a range of assumptions. We simulated and explained the preliminary steps governing the electropolymerization of pyrrole in a charged model interface using first-principles molecular dynamics calculations to solve the problem. We have shown under these conditions that adjacent pyrrole molecules in water can react together, causing their electropolymerization at the interface with a biased platinum electrode in anodic oxidation. In this work, the effective screening medium method that prevents energy divergence of the system was applied to different configurations of pyrrole, water, and electrolyte molecules to best screen the phase space. Furthermore, we worked on a Pt(100) electrode surface in an aqueous electrolyte to be as close as possible to the experimental conditions, MD taking the average of their different orientations.

Carbon-Based Quantum Dots for Supercapacitors: Recent Advances and Future Challenges

Carbon-based Quantum dots (C-QDs) are carbon-based materials that experience the quantum confinement effect, which results in superior optoelectronic properties. In recent years, C-QDs have attracted attention significantly and have shown great application potential as a high-performance supercapacitor device. C-QDs (either as a bare electrode or composite) give a new way to boost supercapacitor performances in higher specific capacitance, high energy density, and good durability. This review comprehensively summarizes the up-to-date progress in C-QD applications either in a bare condition or as a composite with other materials for supercapacitors. The current state of the three distinct C-QD families used for supercapacitors including carbon quantum dots, carbon dots, and graphene quantum dots is highlighted. Two main properties of C-QDs (structural and electrical properties) are presented and analyzed, with a focus on the contribution to supercapacitor performances. Finally, we discuss and outline the remaining major challenges and future perspectives for this growing field with the hope of stimulating further research progress.

Current State and Future Prospects for Electrochemical Energy Storage and Conversion Systems

Electrochemical energy storage and conversion systems such as electrochemical capacitors, batteries and fuel cells are considered as the most important technologies proposing environmentally friendly and sustainable solutions to address rapidly growing global energy demands and environmental concerns. Their commercial applications individually or in combination of two or more devices are based on their distinguishing properties e.g., energy/power densities, cyclability and efficiencies. In this review article, we have discussed some of the major electrochemical energy storage and conversion systems and encapsulated their technological advancement in recent years. Fundamental working principles and material compositions of various components such as electrodes and electrolytes have also been discussed. Furthermore, future challenges and perspectives for the applications of these technologies are discussed.

Selectivity of nitrate and chloride ions in microporous carbons: the role of anisotropic hydration and applied potentials

Understanding ion transport in porous carbons is critical for a wide range of technologies, including supercapacitors and capacitive deionization for water desalination, yet many details remain poorly understood. For instance, an atomistic understanding of how ion selectivity is influenced by the molecular shape of ions, morphology of the micropores and applied voltages is largely lacking. In this work, we combined molecular dynamics simulations with enhanced sampling methods to elucidate the mechanism of nitrate and chloride selectivity in subnanometer graphene slit-pores. We show that nitrate is preferentially adsorbed over chloride in the slit-like micropores. This preferential adsorption was found to stem from the weaker hydration energy and unique anisotropy of the ion solvation of nitrate. Beside the effects of ion dehydration, we found that applied potential plays an important role in determining the ion selectivity, leading to a lower selectivity of nitrate over chloride at a high applied potential. We conclude that the measured ion selectivity results from a complex interplay between voltage, confinement, and specific ion effects-including ion shape and local hydration structure.

Structural and thermodynamic properties of the electrical double layer in slit nanopores: A Monte Carlo study

Grand canonical Monte Carlo (GCMC) simulation techniques at a constant electrode-electrolyte potential drop are employed to study the differential capacitance of a planar electric double layer in slit nanopores. According to the technique, a single randomly selected ion is exchanged between a simulation box and a reservoir. The probability of this step is given by the GCMC algorithm. To preserve the electroneutrality of the system after the ion exchange, the electrode charge is adequately modified, which produces electrode charge fluctuations. The charge fluctuations are used to calculate the differential capacitance of the double layer. Results for the ion distributions, electrode surface charge density, and differential capacitance in slit nanopores are reported for a symmetric system of +1:-1 ionic valences with a common ionic diameter of 0.4 nm at electrolyte concentrations of 0.2M, 1.0M, and 2.5M, pore widths of 0.6 nm, 0.8 nm, and 1.2 nm, a potential drop of 0.05 V, a relative permittivity of 78.5, and a temperature of 298.15 K. These results are compared with the corresponding data for a +1:-2 valence asymmetric system and a size asymmetric system with ionic diameters of 0.4 nm and 0.3 nm. The results show that with increasing electrolyte concentration, the range of confinement effects decreases. For divalent anions, the width dependence of electrode charge and differential capacitance reveals a maximum. The differential capacitance curves show a camel shape to bell shape transition as the electrolyte concentration increases. Asymmetry in both ionic valences and diameters leads to asymmetric capacitance curves.

Porous organic materials offer vast future opportunities

In light of the surging research on porous organic materials, we herein discuss the key issues of their porous structures, surface properties, and end functions. We also present an outlook on emerging opportunities, new applications, and data science-assisted materials discovery.

Transport and Durability of Energy Storage Materials Operating at High Temperatures

Temperature is a state variable that significantly affects thermodynamic and kinetic performances and performance degradation of energy storage materials. In this Perspective, we address our recent progress in the energy storage performance and transporting phenomena of supercapacitors when temperatures are elevated to >100 °C. Electrodes include reduced graphene oxide film and foam and conductive metal organic frameworks; electrolytes include phosphoric-acid-doped polybenzimidazole and double networked ionogels. The electrochemical, thermal, and mechanical properties of electrodes and electrolytes are correlated with energy storage performance and degradation at high temperatures. We also address the fundamental understanding of ion transport of polymeric electrolytes and the emergence of nanoscale-confined fast mobile protons at elevated temperatures.

Electric double layer formation and storing energy processes on graphene-based supercapacitors from electrical and thermodynamic perspectives

Atomistic molecular dynamics simulations were used to investigate the processes of electrical double layer formation and electrolyte confinement in graphene-based supercapacitors. For both processes, free energy calculations were used to analyze the thermodynamics involved in the electrolyte confinement and its re-arrangement in a double layer on the electrode surface. The value of the free energy of the formation of the double electric layer was related to the energy required to charge the supercapacitor, i.e., the energy density stored, and compared with values obtained using Poisson's electrostatic formalism, which is the conventionally employed approach. Both analyzes were consistent with each other, presenting compatible values for the stored energy.