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Diglyme co-intercalation with sodium ion (Na + ) into graphite can enable the use of graphite as a potential anode for sodium-ion batteries (NIBs). However, the presence of diglyme molecules in Na + intercalated graphite limits Na + storage capacity and increases volume changes. In this work, the effect of functionalising diglyme molecules with fluoro and hydroxy groups on Na + storage properties in graphite were computationally studied. It was found that the functionalisation can significantly alter the binding between sodium and the solvent ligand as well as between the sodium-solvent complex and the graphite. The hydroxy-functionalised diglyme exhibits the strongest binding to the graphite of the other functionalised diglyme compounds considered. The calculations also reveal that the graphene layer affects the electron distribution on the diglyme molecule and Na, so the diglyme complexed Na binds more strongly to the graphene layer than the Na alone. We also propose a mechanism for the early stages of the intercalation mechanism that involves a reorientation of the sodium-diglyme complex and suggest how the solvent can be designed to optimise the co-intercalation process.

Expanded graphite (EG) has been shown to be able to store a significant amount of sodium ions. Understanding the alkali metal ion storage in EG is of importance for improving EG electrode performance. In this work, the effect of interlayer distance of pure EG on sodium ion storage was investigated using the density functional theory calculation method. EG structure models with interlayer distances ranging from 3.4 Å to 10.0 Å were simulated. It was found that EG can store a fairly large amount of sodium ions through an intercalation mechanism without any contributions from the co-intercalation mechanism or adsorption mechanism if the interlayer distance is larger than 4.4 Å and smaller than 6.0 Å. It was also found that an interlayer distance of 6.0 Å gives strong binding energy of sodium ions with EG forming thermodynamically stable sodium-graphite intercalation compound (Na-GIC). However, when the interlayer distance becomes larger than 6.0 Å, the binding energy between sodium ions and EG becomes weaker. Computational results have also shown that the enthalpy of formation of the Na-GIC of EG is energetically more favourable when the interlayer distance is increased. An optimal d-spacing of EG for sodium ion storage was identified in this work. These findings provide atomistic insights into sodium ion storage in EG, providing guidelines for the design of graphite-based anode materials for sodium-ion batteries.

Accurate models of the free energies of ions in solution are crucially important. They can be used to predict and understand the properties of electrolyte solutions in the huge number of important applications where these solutions play a central role such as electrochemical energy storage. The Born model, developed to describe ion solvation free energies, is widely considered to be critically flawed as it predicts a linear response of water to ionic charge, which fails to match water's supposed intrinsic preference to solvate anions over cations. Here, we demonstrate that the asymmetric response observed in simulation is the result of an arbitrary choice of the oxygen atom to be the centre of a water molecule. We show that an alternative and reasonable choice, which places the centre 0.5 Å towards the hydrogen atoms, results in a linear and charge symmetric response of water to ionic charge for a classical water model consistent with the Born model. Therefore, this asymmetry should be regarded as a property of the specific short-range repulsive interaction not an intrinsic electrostatic property of water and so the fact that the Born model does not reproduce it is not a limitation of this approach. We also show that this new water centre results in a more reasonable surface potential contribution to the solvation free energies.

The ability to reproduce the experimental structure of water around the sodium and potassium ions is a key test of the quality of interaction potentials due to the central importance of these ions in a wide range of important phenomena. Here, we simulate the Na + and K + ions in bulk water using three density functional theory functionals: (1) the generalized gradient approximation (GGA) based dispersion corrected revised Perdew, Burke, and Ernzerhof functional (revPBE-D3) (2) the recently developed strongly constrained and appropriately normed (SCAN) functional (3) the random phase approximation (RPA) functional for potassium. We compare with experimental X-ray diffraction (XRD) and X-ray absorption fine structure (EXAFS) measurements to demonstrate that SCAN accurately reproduces key structural details of the hydration structure around the sodium and potassium cations, whereas revPBE-D3 fails to do so. However, we show that SCAN provides a worse description of pure water in comparison with revPBE-D3. RPA also shows an improvement for K + , but slow convergence prevents rigorous comparison. Finally, we analyse cluster energetics to show SCAN and RPA have smaller fluctuations of the mean error of ion-water cluster binding energies compared with revPBE-D3.

The calculation of ion-ion interactions in water is a problem of long standing importance. Modelling these interactions is a prerequisite to explaining Hofmeister (specific ion) effects. We here generalize our solvation model of ions to calculate the free energy of two ions in water as a function of separation. The same procedure has previously been applied to calculate ion interactions with the air-water interface successfully. The Conductor like Screening Model (COSMO) is used. This treats the ions on a quantum mechanical level and calculates numerically the electrostatic response of the surrounding solvent. Estimates of the change in the cavity formation energy and the change in the ion-water dispersion energy as the ions approach are included separately. The calculated interaction potentials are too attractive and this is a significant issue. However, they do reproduce the affinity of similarly sized ions for each other, which is a crucial property of these potentials. They are also oscillatory, another important property. We normalize the potentials to reduce the over-attraction, and good correlation with experimental values is achieved. We identify the driving contributions to this like-prefers-like behaviour. We then put forward a plausible hypothesis for the over-attraction of the potentials. An agreeable feature of our approach is that it does not rely on salt specific parameters deliberately adjusted to reproduce experimental values.