Dynamics and Energetics of Ion Adsorption at the Interface between a Pure Ionic Liquid and Carbon Electrodes.

Molecular dynamics simulations have been used extensively to determine equilibrium properties of the electrode-electrolyte interface in supercapacitors held at various potentials. While such studies are essential to understand and optimize the performance of such energy storage systems, investigation of the dynamics of adsorption during the charge of the supercapacitors is also necessary. Dynamical properties are especially important to get an insight into the power density of supercapacitors, one of their main assets. In this work, we propose a new method to coarse-grain simulations of all-atom systems and compute effective Lennard-Jones and Coulomb parameters, allowing subsequently to analyze the trajectories of adsorbing ions. We focus on pure 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide in contact with planar carbon electrodes. We characterize the evolution of the ion orientation and ion-electrode distance during adsorption and show that ions reorientate as they adsorb. We then determine the forces experienced by the adsorbing ions and demonstrate that Coulomb forces are dominant at a long range while van der Waals forces are dominant at a short range. We also show that there is an almost equal contribution from the two forces at an intermediate distance, explaining the peak of ion density close to the electrode surface.

Structural disorder determines capacitance in nanoporous carbons.

The difficulty in characterizing the complex structures of nanoporous carbon electrodes has led to a lack of clear design principles with which to improve supercapacitors. Pore size has long been considered the main lever to improve capacitance. However, our evaluation of a large series of commercial nanoporous carbons finds a lack of correlation between pore size and capacitance. Instead, nuclear magnetic resonance spectroscopy measurements and simulations reveal a strong correlation between structural disorder in the electrodes and capacitance. More disordered carbons with smaller graphene-like domains show higher capacitances owing to the more efficient storage of ions in their nanopores. Our findings suggest ways to understand and exploit disorder to achieve highly energy-dense supercapacitors.

Investigating particle size effects on NMR spectra of ions diffusing in porous carbons through a mesoscopic model.

Characterizing ion adsorption and diffusion in porous carbons is essential to understand the performance of such materials in a range of key technologies such as energy storage and capacitive deionisation. Nuclear Magnetic Resonance (NMR) spectroscopy is a powerful technique to get insights in these systems thanks to its ability to distinguish between bulk and adsorbed species and to its sensitivity to dynamic phenomena. Nevertheless, a clear interpretation of the experimental results is sometimes rendered difficult by the various factors affecting NMR spectra. A mesoscopic model to predict NMR spectra of ions diffusing in carbon particles is adapted to include dynamic exchange between the intra-particle space and the bulk electrolyte surrounding the particle. A systematic study of the particle size effect on the NMR spectra for different distributions of magnetic environments in the porous carbons is conducted. The model demonstrates the importance of considering a range of magnetic environments, instead of a single chemical shift value corresponding to adsorbed species, and of including a range of exchange rates (between in and out of the particle), instead of a single timescale, to predict realistic NMR spectra. Depending on the pore size distribution of the carbon particle and the ratio between bulk and adsorbed species, both the NMR linewidth and peak positions can be largely influenced by the particle size.

Understanding the Chemical Shifts of Aqueous Electrolyte Species Adsorbed in Carbon Nanopores.

Interfaces between aqueous electrolytes and nanoporous carbons are involved in a number of technological applications such as energy storage and capacitive deionization. Nuclear magnetic spectroscopy is a very useful tool to characterize ion adsorption in such systems thanks to its nuclei specificity and the ability to distinguish between ions in the bulk and in pores. We use complementary methods (density functional theory, molecular dynamics simulations, and a mesoscopic model) to investigate the relative importance of various effects on the chemical shifts of adsorbed species: ring currents, ion organization in pores of various sizes, specific ion-carbon interactions, and hydration. We show that ring currents and ion organization are predominant for the determination of chemical shifts in the case of Li+ ions and hydrogen atoms of water. For the large Rb+ and Cs+ ions, the additional effect of the hydration shell should be considered to predict chemical shifts in agreement with experiments.

Elucidating Curvature-Capacitance Relationships in Carbon-Based Supercapacitors.

Nanoscale surface curvatures, either convex or concave, strongly influence the charging behavior of supercapacitors. Rationalizing individual influences of electrode atoms to the capacitance is possible by interpreting distinct elements of the charge-charge covariance matrix derived from individual charge variations of the electrode atoms. An ionic liquid solvated in acetonitrile and confined between two electrodes, each consisting of three undulated graphene layers, serves as a demonstrator to illustrate pronounced and nontrivial features of the capacitance with respect to the electrode curvature. In addition, the applied voltage determines whether a convex or concave surface contributes to increased capacitance. While at lower voltages capacitance variations are in general correlated with ion number density variations in the double layer formed in the concave region of the electrode, for certain electrode designs a surprisingly strong contribution of the convex part to the differential capacitance is found both at higher and lower voltages.

Carbon-carbon supercapacitors: Beyond the average pore size or how electrolyte confinement and inaccessible pores affect the capacitance.

Carbon-carbon supercapacitors are high power electrochemical energy storage systems, which store energy through reversible ion adsorption at the electrode-electrolyte interface. Due to the complex structure of the porous carbons used as electrodes, extracting structure-property relationships in these systems remains a challenge. In this work, we conduct molecular simulations of two model supercapacitors based on nanoporous electrodes with the same average pore size, a property often used when comparing porous materials, but different morphologies. We show that the carbon with the more ordered structure, and a well defined pore size, has a much higher capacitance than the carbon with the more disordered structure and a broader pore size distribution. We analyze the structure of the confined electrolyte and show that the ions adsorbed in the ordered carbon are present in larger quantities and are also more confined than for the disordered carbon. Both aspects favor a better charge separation and thus a larger capacitance. In addition, the disordered electrodes contain a significant amount of carbon atoms, which are never in contact with the electrolyte, carry a close to zero charge, and are thus not involved in the charge storage. The total quantities of adsorbed ions and degrees of confinement do not change much with the applied potential, and as such, this work opens the door to computationally tractable screening strategies.

NMR studies of adsorption and diffusion in porous carbonaceous materials.

Porous carbonaceous materials have many important industrial applications including energy storage, water purification, and adsorption of volatile organic compounds. Most of their applications rely upon the adsorption of molecules or ions within the interior pore volume of the carbon particles. Understanding the behaviour and properties of adsorbate species on the molecular level is therefore key for optimising porous carbon materials, but this is very challenging owing to the complexity of the disordered carbon structure and the presence of multiple phases in the system. In recent years, NMR spectroscopy has emerged as one of the few experimental techniques that can resolve adsorbed species from those outside the pore network. Adsorbed, or "in-pore" species are shielded with respect to their free (or "ex-pore") counterparts. This shielding effect arises primarily due to ring currents in the carbon structure in the presence of a magnetic field, such that the observed chemical shift differences upon adsorption are independent of the observed nucleus to a first approximation. Theoretical modelling has played an important role in rationalising and explaining these experimental observations. Together, experiments and simulations have enabled a large amount of information to be gained on the adsorption and diffusion of adsorbed species, as well as on the structural and magnetic properties of the porous carbon adsorbent. Here, we review the methodological developments and applications of NMR spectroscopy and related modelling in this field, and provide perspectives on possible future applications and research directions.

Mesoscopic simulations of the in situ NMR spectra of porous carbon based supercapacitors: electronic structure and adsorbent reorganisation effects.

In situ NMR spectroscopy is a powerful technique to investigate charge storage mechanisms in carbon-based supercapacitors thanks to its ability to distinguish ionic and molecular species adsorbed in the porous electrodes from those in the bulk electrolyte. The NMR peak corresponding to the adsorbed species shows a clear change of chemical shift as the applied potential difference is varied. This variation in chemical shift is thought to originate from a combination of ion reorganisation in the pores and changes in ring current shifts due to the changes of electronic density in the carbon. While previous Density Functional Theory calculations suggested that the electronic density has a large effect, the relative contributions of these two effects is challenging to untangle. Here, we use mesoscopic simulations to simulate NMR spectra and investigate the relative importance of ion reorganisation and ring currents on the resulting chemical shift. The model is able to predict chemical shifts in good agreement with NMR experiments and indicates that the ring currents are the dominant contribution. A thorough analysis of a specific electrode/electrolyte combination for which detailed NMR experiments have been reported allows us to confirm that local ion reorganisation has a very limited effect but the relative quantities of ions in pores of different sizes, which can change upon charging/discharging, can lead to a significant effect. Our findings suggest that in situ NMR spectra of supercapacitors may provide insights into the electronic structure of carbon materials in the future.

Probing and Interpreting the Porosity and Tortuosity Evolution of Li-O2 Cathodes on Discharge through a Combined Experimental and Theoretical Approach.

Li-O2 batteries offer a high theoretical discharge capacity due to the formation of light discharged species such as Li2O2, which fill the porous positive electrode. However, in practice, it is challenging to reach the theoretical capacity and completely utilize the full electrode pore volume during discharge. With the formation of discharge products, the porous medium evolves, and the porosity and tortuosity factor of the positive electrode are altered through shrinkage and clogging of pores. A pore shrinks as solid discharge products accumulate, the pore clogging when it is filled (or when access is blocked). In this study, we investigate the structural evolution of the positive electrode through a combination of experimental and computational techniques. Pulsed field gradient nuclear magnetic resonance results show that the electrode tortuosity factor changes much faster than suggested by the Bruggeman relation (an equation that empirically links the tortuosity factor to the porosity) and that the electrolyte solvent affects the tortuosity factor evolution. The latter is ascribed to the different abilities of solvents to dissolve reaction intermediates, which leads to different discharge product particle sizes: on discharging using 0.5 M LiTFSI in dimethoxyethane, the tortuosity factor increases much faster than for discharging in 0.5 M LiTFSI in tetraglyme. The correlation between a discharge product size and tortuosity factor is studied using a pore network model, which shows that larger discharge products generate more pore clogging. The Knudsen diffusion effect, where collisions of diffusing molecules with pore walls reduce the effective diffusion coefficients, is investigated using a kinetic Monte Carlo model and is found to have an insignificant impact on the effective diffusion coefficient for molecules in pores with diameters above 5 nm, i.e., most of the pores present in the materials investigated here. As a consequence, pore clogging is thought to be the main origin of tortuosity factor evolution.

Local Distortions and Dynamics in Hydrated Y-Doped BaZrO3.

Y-doped BaZrO3 is a promising proton conductor for intermediate temperature solid oxide fuel cells. In this work, a combination of static DFT calculations and DFT based molecular dynamics (DFT-MD) was used to study proton conduction in this material. Geometry optimizations of 100 structures with a 12.5% dopant concentration allowed us to identify a clear correlation between the bending of the metal-oxygen-metal angle and the energies of the simulated cells. Depending on the type of bending, two configurations, designated as inward bending and outward bending, were defined. The results demonstrate that a larger bending decreases the energy and that the lowest energies are observed for structures combining inward bending with protons being close to the dopant atoms. These lowest energy structures are the ones with the strongest hydrogen bonds. DFT-MD simulations in cells with different yttrium distributions provide complementary microscopic information on proton diffusion as they capture the dynamic distortions of the lattice caused by thermal motion. A careful analysis of the proton jumps between different environments confirmed that the inward and outward bending states are relevant for the understanding of proton diffusion. Indeed, intra-octahedral jumps were shown to only occur starting from an outward configuration while the inward configuration seems to favor rotations around the oxygen. On average, in the DFT-MD simulations, the hydrogen bond lengths are shorter for the outward configuration which facilitates the intra-octahedral jumps. Diffusion coefficients and activation energies were also determined and compared to previous theoretical and experimental data, showing a good agreement with previous data measuring local proton motion.

Efficient prediction of nucleus independent chemical shifts for polycyclic aromatic hydrocarbons.

Nuclear Magnetic Resonance (NMR) is one of the most powerful experimental techniques to characterize the structure of molecules and confined liquids. Nevertheless, the complexity of the systems under investigation usually requires complementary computational studies to interpret the NMR results. In this work we focus on polycyclic aromatic hydrocarbons (PAHs), an important class of organic molecules which have been commonly used as simple analogues for the spectroscopic properties of more complex systems, such as porous disordered carbons. We use Density Functional Theory (DFT) to calculate 13C chemical shifts and Nucleus Independent Chemical Shifts (NICS) for 34 PAHs. The results show a clear molecular size dependence of the two quantities, as well as the convergence of the 13C NMR shifts towards the values observed for graphene. We then present two computationally cheap models for the prediction of NICS in simple PAHs. We show that while a simple dipolar model fails to produce accurate values, a perturbative tight-binding approach can be successfully applied for the prediction of NICS in this series of molecules, including some non-planar ones containing 5- and 7-membered rings. This model, one to two orders of magnitude faster than DFT calculations, is very promising and can be further refined in order to study more complex systems.

Ionic Liquids under Confinement: From Systematic Variations of the Ion and Pore Sizes toward an Understanding of the Structure and Dynamics in Complex Porous Carbons.

We use molecular simulations of an ionic liquid in contact with a range of nanoporous carbons to investigate correlations between the ion size, pore size, pore topology, and properties of the adsorbed ions. We show that diffusion coefficients increase with the anion size and, surprisingly, with the quantity of adsorbed ions. Both findings are interpreted in terms of confinement: when the in-pore population increases, additional ions are located in less-confined sites and diffuse faster. Simulations in which the pores are enlarged while keeping the topology constant support these observations. The interpretation of properties across structures is more challenging. An interesting point is that smaller pores do not necessarily lead to a larger confinement. In this work, the highest degrees of confinement are observed for intermediate pore sizes. We also show a correlation between the quantity of adsorbed ions and the ratio between the maximum pore diameter and the pore limiting diameter.

Carbons with Regular Pore Geometry Yield Fundamental Insights into Supercapacitor Charge Storage.

We conduct molecular dynamics simulations of electrical double-layer capacitors (EDLCs) using a library of ordered, porous carbon electrode materials called zeolite templated carbons (ZTCs). The well-defined pore shapes of the ZTCs enable us to determine the influence of pore geometry on both charging dynamics and charge storage mechanisms in EDLCs, also referred to as supercapacitors. We show that charging dynamics are negatively correlated with the pore-limiting diameter of the electrode material and display signatures of both progressive charging and ion trapping. However, the equilibrium capacitance, unlike charging dynamics, is not strongly correlated to commonly used, purely geometric descriptors such as pore size. Instead, we find a strong correlation of capacitance to the charge compensation per carbon (CCpC), a descriptor we define in this work as the average charge of the electrode atoms within the coordination shell of a counterion. A high CCpC indicates efficient charge storage, as the strong partial charges of the electrode are able to screen counterion charge, enabling higher ion loading and thus more charge storage within the electrode at a fixed applied voltage. We determine that adsorption sites with a high CCpC tend to be found within pockets with a smaller radius of curvature, where the counterions are able to minimize their distance with multiple points on the electrode surface, and therefore induce stronger local partial charges.

Towards an atomistic understanding of disordered carbon electrode materials.

Disordered nanoporous and "hard" carbons are widely used in batteries and supercapacitors, but their atomic structures are poorly determined. Here, we combine machine learning and DFT to obtain new atomistic insight into carbonaceous energy materials. We study structural models of porous and graphitic carbons, and Na intercalation as relevant for sodium-ion batteries.

Stochasticity of Pores Interconnectivity in Li-O2 Batteries and its Impact on the Variations in Electrochemical Performance.

While large dispersions in electrochemical performance have been reported for lithium oxygen batteries in the literature, they have not been investigated in any depth. The variability in the results is often assumed to arise from differences in cell design, electrode structure, handling and cell preparation at different times. An accurate theoretical framework turns out to be needed to get a better insight into the mechanisms underneath and to interpret experimental results. Here, we develop and use a pore network model to simulate the electrochemical performance of three-dimensionally resolved lithium-oxygen cathode mesostructures obtained from TXM nanocomputed tomography. We apply this model to the 3D reconstructed object of a Super P carbon electrode and calculate discharge curves, using identical conditions, for four different zones in the electrode and their reversed configurations. The resulting galvanostatic discharge curves show some dispersion, (both in terms of capacity and overpotential) which we attribute to the way pores are connected with each other. Based on these results, we propose that the stochastic nature of pores interconnectivity and the microscopic arrangement of pores can lead, at least partially, to the variations in electrochemical results observed experimentally.

Tracking Ionic Rearrangements and Interpreting Dynamic Volumetric Changes in Two-Dimensional Metal Carbide Supercapacitors: A Molecular Dynamics Simulation Study.

We present a molecular dynamics simulation study achieved on two-dimensional (2D) Ti3 C2 Tx MXenes in the ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([EMIM]+ [TFSI]- ) electrolyte. Our simulations reproduce the different patterns of volumetric change observed experimentally for both the negative and positive electrodes. The analysis of ionic fluxes and structure rearrangements in the 2D material provide an atomic scale insight into the charge and discharge processes in the layer pore and confirm the existence of two different charge-storage mechanisms at the negative and positive electrodes. The ionic number variation and the structure rearrangement contribute to the dynamic volumetric changes of both electrodes: negative electrode expansion and positive electrode contraction.

New Perspectives on the Charging Mechanisms of Supercapacitors.

Supercapacitors (or electric double-layer capacitors) are high-power energy storage devices that store charge at the interface between porous carbon electrodes and an electrolyte solution. These devices are already employed in heavy electric vehicles and electronic devices, and can complement batteries in a more sustainable future. Their widespread application could be facilitated by the development of devices that can store more energy, without compromising their fast charging and discharging times. In situ characterization methods and computational modeling techniques have recently been developed to study the molecular mechanisms of charge storage, with the hope that better devices can be rationally designed. In this Perspective, we bring together recent findings from a range of experimental and computational studies to give a detailed picture of the charging mechanisms of supercapacitors. Nuclear magnetic resonance experiments and molecular dynamics simulations have revealed that the electrode pores contain a considerable number of ions in the absence of an applied charging potential. Experiments and computer simulations have shown that different charging mechanisms can then operate when a potential is applied, going beyond the traditional view of charging by counter-ion adsorption. It is shown that charging almost always involves ion exchange (swapping of co-ions for counter-ions), and rarely occurs by counter-ion adsorption alone. We introduce a charging mechanism parameter that quantifies the mechanism and allows comparisons between different systems. The mechanism is found to depend strongly on the polarization of the electrode, and the choice of the electrolyte and electrode materials. In light of these advances we identify new directions for supercapacitor research. Further experimental and computational work is needed to explain the factors that control supercapacitor charging mechanisms, and to establish the links between mechanisms and performance. Increased understanding and control of charging mechanisms should lead to new strategies for developing next-generation supercapacitors with improved performances.

NMR Study of Ion Dynamics and Charge Storage in Ionic Liquid Supercapacitors.

Ionic liquids are emerging as promising new electrolytes for supercapacitors. While their higher operating voltages allow the storage of more energy than organic electrolytes, they cannot currently compete in terms of power performance. More fundamental studies of the mechanism and dynamics of charge storage are required to facilitate the development and application of these materials. Here we demonstrate the application of nuclear magnetic resonance spectroscopy to study the structure and dynamics of ionic liquids confined in porous carbon electrodes. The measurements reveal that ionic liquids spontaneously wet the carbon micropores in the absence of any applied potential and that on application of a potential supercapacitor charging takes place by adsorption of counterions and desorption of co-ions from the pores. We find that adsorption and desorption of anions surprisingly plays a more dominant role than that of the cations. Having elucidated the charging mechanism, we go on to study the factors that affect the rate of ionic diffusion in the carbon micropores in an effort to understand supercapacitor charging dynamics. We show that the line shape of the resonance arising from adsorbed ions is a sensitive probe of their effective diffusion rate, which is found to depend on the ionic liquid studied, as well as the presence of any solvent additives. Taken as whole, our NMR measurements allow us to rationalize the power performances of different electrolytes in supercapacitors.

Lattice simulation method to model diffusion and NMR spectra in porous materials.

A coarse-grained simulation method to predict nuclear magnetic resonance (NMR) spectra of ions diffusing in porous carbons is proposed. The coarse-grained model uses input from molecular dynamics simulations such as the free-energy profile for ionic adsorption, and density-functional theory calculations are used to predict the NMR chemical shift of the diffusing ions. The approach is used to compute NMR spectra of ions in slit pores with pore widths ranging from 2 to 10 nm. As diffusion inside pores is fast, the NMR spectrum of an ion trapped in a single mesopore will be a sharp peak with a pore size dependent chemical shift. To account for the experimentally observed NMR line shapes, our simulations must model the relatively slow exchange between different pores. We show that the computed NMR line shapes depend on both the pore size distribution and the spatial arrangement of the pores. The technique presented in this work provides a tool to extract information about the spatial distribution of pore sizes from NMR spectra. Such information is difficult to obtain from other characterisation techniques.