One of the main issues when simulating supercapacitors is the generation of realistic three-dimensional porous carbon models. Indeed, due to their disordered nature, it is a challenge to determine their structure in a precise manner. The models we use are of two types: atomistic structures (for molecular simulations) and pore network models (for mesoscopic simulations). The most common method to generate atomistic models is to conduct quench molecular dynamics simulations using interaction potentials, parameterised on experimental data, which sometimes exaggerate certain characteristics (e.g. bonds or angles too rigid). With the progress of machine learning, it is possible to generate interaction potentials with a precision equivalent to Density Functional Theory (DFT). Following such methodology, we generated porous carbon structures of various densities. For the pore network models, we followed a strategy to extract pore networks directly from tomography images.
Regarding the systematic study at the molecular scale, simulations of several electrolytes in contact with a set of ordered and disordered porous carbons were conducted. In total, around 50 carbon/electrolyte systems were simulated to investigate the effects of pore size, topology and ion size on various properties. We demonstrated that diffusion coefficients increase with the anion size and, surprisingly, with the quantity of adsorbed ions. Both findings were interpreted in terms of confinement: when the in-pore population increases, additional ions are located in less-confined sites and diffuse faster. The interpretation of properties across structures is more challenging. The effects of the carbon structure flexibility and the presence of functional groups were also explored. The most promising carbons were used in simulations of model supercapacitors showing that porous carbons with equal average pore sizes but different topologies can have very different capacities and related this observation to the amount of carbon atoms isolated from the liquid and the quantity of adsorbed ions in the pores.
Regarding mesoscopic simulations, we adapted an existing program suitable for the calculation of NMR spectra of adsorbed species to the calculation of properties relevant to the project. The mesoscopic model, available publicly, is approximately 10,000 times faster than classical molecular simulations and is able to predict i) quantities of adsorbed ions and capacitances compatible with experiments and ii) a strong dependency of the properties on the pore size and the solvation. Future implementations are needed to improve the description of the diffusion before realising an extensive screening of porous carbons.
Regarding the development of a new method to determine accurately the structure of disordered carbons, we focused on Nuclear Magnetic Resonance (NMR) parameters as a constraint to improve the accuracy of existing methods. We built a database of chemical shifts for molecules and solids having similarities with the porous carbons of interest and for species in the vicinity of such structures. We proposed a tight-binding model which is very successful in predicting chemical shifts for molecules close to polycylic aromatic hydrocarbons and is orders of magnitude faster than conventional DFT. This model, too simplistic for disordered solids, is still being refined. Other parameters which can impact the measured NMR spectra (e.g. ion concentration, particle size) can also be explored using the mesoscopic model.
