arXiv subjects

Zachary A. H. Goodwin

Publications and source records attributed to Zachary A. H. Goodwin.

At least 19 recordsLinked to original sources

arXiv2026

Reversible Ionic Aggregation Kinetics in Concentrated Electrolytes

Here we develop a formalism for reversible ionic aggregation kinetics in an example concentrated electrolyte, building on previous equilibrium work of McEldrew and co-workers, and thermoreversible polymers and patchy particle systems. This is achieved through solving a macroscopic rate equation of open/occupied association sites, shown to be a solution of the reversible Smoluchowski aggregation equation, which predicts how ionic associations in electrolytes change subject to a step-change in conditions. We test the derived equations against atomistic molecular dynamics simulations of a salt-in-ionic liquid, where good qualitative agreement is obtained, but quantitative differences are found. This highlights the multiple time scales that exist in concentrated electrolytes, with a fast timescale preceding a longer timescale. We hope this formalism opens new avenues in understanding the dynamics and non-equilibrium behaviour in electrolytes. For example, the formalism can be developed further to investigate the non-Newtonian behaviour of concentrated electrolytes, double layer charging, and the slow dynamics of these electrolytes in confinement.

cond-mat.soft↗

arXiv2026

Duality of Theories for the Electrical Double Layer in Concentrated Electrolytes

Understanding the electrical double layer (EDL), i.e, the distribution of electrolyte at an electrified interface, in concentrated electrolytes is important for various technologies, such as supercapacitors, batteries and electrocatalysis. Atomistic approaches offer unprecedented detail, but are too computationally expensive to exhaustively investigate the EDL of concentrated electrolytes, motivating the development of continuum theories. In these concentrated electrolytes, correlations between ions and solvents are strong, through electrostatic and specific interactions, as well as significant excluded volume effects of the complicated molecular species, making the development of theories challenging. Thus far, there are mainly two distinct \textit{simple} theoretical approaches to understand the EDL of concentrated electrolytes, with account of these correlations beyond mean-field. One is a local-density approximation (LDA) based on treating electrostatic and specific interactions beyond mean-field through the ionic aggregation and solvation; where a simple conceptual understanding can be gained and reasonable agreement with experiments in terms of integrated quantities, but poor agreement for ion profiles and Debye capacitance. The other approach is to treat electrostatic correlations and excluded volume effects more rigorously with beyond LDA approaches, but at the cost of simplifying the chemical interactions between species; where excellent agreement can be obtained for ion profiles, differential capacitance, etc., but mainly for the simplified hard-sphere systems that the theories are based on. Here, we describe the merits and downfalls of these two approaches, how they have contributed to understanding anomalous underscreening, and outline future directions for these theoretical approaches.

cond-mat.soft↗

arXiv2026

Thermodynamic effects of solid electrolyte interphase formation from solvation and ionic association in water-in-salt electrolytes

Water-in-Salt-Electrolytes (WiSEs) are a promising class of next-generation electrolytes. Unlike classical dilute electrolytes or more conventional battery electrolytes, WiSEs are characterised by their super-concentrated salt concentration with only a small amount of water, which gives rise to their expanded electrochemical stability window (ESW). The expansion of the ESW is, in part, due to the formation of an inorganic solid electrolyte interphase (SEI) that passivates the anode; this principle is also important in graphite and Li-metal anodes, and beyond Li-ion technologies. The solvation and ionic associations are key descriptors in understanding the expansion of the ESW. Specifically, as reactions which lead to the SEI (or cathode electrolyte interphase, CEI) must occur at the electrode-electrolyte interface, the distribution of reactants and their various solvation environments are critical. This distribution near the interface is referred to as the electrical double layer (EDL), in the absence of reactions. Here we further develop and analyse a recently proposed thermodynamic theory of hydration and ionic associations in the EDL of WiSEs. We parameterize this theory from bulk molecular dynamics simulations and benchmark it against EDL simulations, finding good qualitative agreement. Using this thermodynamic theory, we rationalise changes in the ESW through: changes in the activity in the bulk electrolyte through the Nernst equation, which directly changes the stability of the electrolytes; and thermodynamic changes to the kinetics of these reactions, from the Butler-Volmer equation and coupled ion electron transfer kinetics, through the concentration of reactant species in the Helmholtz layer.

cond-mat.soft↗

arXiv2026

Tailoring spontaneous symmetry breaking in engineered van der Waals superlattices

Superlattice engineering in van der Waals heterostructures (e.\,g.\ by moiré engineering) provides a powerful platform for designing electronic bands and realising correlated and topological quantum phenomena. Here, we pioneer a scheme to tailor superpotentials based on intrinsic substrate electronic orders. We show that this establishes a robust, self-aligned, and highly versatile route to band-structure control as we demonstrate in graphene by engineering two distinct, nearly commensurate superlattices using the charge density waves of 1T-NbSe$_2$. In these superlattices the graphene's Dirac cones are folded either to the $Γ$-point or to the K-points of the mini-Brillouin zone. Using scanning tunnelling microscopy, we observe that the $Γ$-folded system preserves C$_3$ symmetry, while the K-folded system exhibits spontaneous symmetry breaking. Combining density functional theory with an interlayer interaction model, we reveal that this difference is not electronically driven but originates from a structural instability. Our work establishes superlattice engineering for designer quantum states and unveils a structural mechanism for controlled emergent symmetry breaking.

cond-mat.mes-hall↗

arXiv2025

Magnetic Ordering in Moiré Graphene Multilayers from a Continuum Hartree+U Approach

Recently, symmetry-broken ground states, such as correlated insulating states, magnetic order and superconductivity, have been discovered in twisted bilayer graphene (tBLG) and twisted trilayer graphene (tTLG) near the so-called magic-angle. Understanding the magnetic order in these systems is challenging, however, as atomistic methods become extremely expensive near the magic angle and continuum approaches fail to capture important atomistic details. In this work, we develop an approach to incorporate short-ranged Hubbard interactions self-consistently in a continuum model. In addition, we include long-ranged Coulomb interactions, which are known to be important when doping the flat bands of tBLG and tTLG. Therefore, for the first time, magnetic order in moiré graphene multilayers is self-consistently explored in a continuum model with atomistic detail. With this approach, we perform a systematic analysis of the magnetic phase diagram of tBLG as a function of doping level and twist angle, near the magic angle. Our results are consistent with previous perturbative atomistic Hartree+U calculations. Furthermore, we investigated magnetic order of tTLG, which were found to be similar to those in tBLG. In the future, the developed continuum model can be utilized to investigate magnetic ordering tendencies from short-range exchange interactions in other moiré graphene multilayers as a function of doping, twist angle, screening environment, among other variables.

cond-mat.mtrl-sci↗

arXiv2025

Exploring Charge Density Waves in two-dimensional NbSe2 with Machine Learning

Niobium diselenide (NbSe$_2$) has garnered significant attention due to the coexistence of superconductivity and charge density waves (CDWs) down to the monolayer limit. However, realistic modeling of CDWs-capturing effects such as layer number, twist angle, and strain-remains challenging due to the high computational cost of first-principles methods. Here, we develop a physically informed workflow for training machine-learning interatomic potentials (MLIPs) based on the E(3)-equivariant Allegro architecture, tailored to capture the subtle structural and dynamical signatures of CDWs in mono- and bilayer NbSe$_2$.We find that while CDW lattice distortions are relatively easy to learn, modeling vibrational properties remains more challenging. It requires targeted dataset design and careful hyperparameter tuning, pushing the boundaries and testing the extensibility of current MLIP frameworks. Our MLIPs enable reliable simulations of commensurate and incommensurate CDW phases, including their sensitivity to dimensionality and stacking, as well as CDW dynamics, phonons, and transition temperatures estimated via the stochastic self-consistent harmonic approximation. This work opens new possibilities for studying and tuning CDWs in NbSe$_2$ and other two-dimensional systems, with implications for electron-phonon coupling, superconductivity, and advanced materials design.

cond-mat.mtrl-sci↗

arXiv2025

Theory of Cation Solvation in the Helmholtz Layer of Li-ion Battery Electrolytes

The solvation environments of Li$^+$ in conventional non-aqueous battery electrolytes, such as LiPF$_6$ in mixtures of ethylene carbaronate (EC) and ethyl methyl carbonate (EMC), are often used to rationalize the transport properties of electrolytes and solid electrolyte interphase (SEI) formation. In the SEI, the solvation environments in the compact electrical double layer (EDL) next to the electrode, also known as the Helmholtz layer, determine (partially) what species can react to form the SEI, with bulk solvation environments often being used as a proxy. Here we develop and test a theory of cation solvation in the Helmholtz layer of non-aqueous Li-ion battery electrolytes. First, we validate the theory against bulk and diffuse EDL atomistic molecular dynamics (MD) simulations of LiPF$_6$ EC/EMC mixtures as a function of surface charge, where we find the theory can capture the solvation environments well. Next we turn to the Helmholtz layer, where we find that the main effect of the solvation structures next to the electrode is an apparent reduction in the number of binding sites between Li$^+$ and the solvents, again where we find good agreement with our developed theory. Finally, by solving a simplified version of the theory, we find that the probability of Li$^+$ binding to each solvent remains equal to the bulk probability, suggesting that the bulk solvation environments are a reasonable place to start when understanding new battery electrolytes. Our developed formalism can be parameterized from bulk MD simulations and used to predict the solvation environments in the Helmholtz layer, which can be used to determine what could react and form the SEI.

cond-mat.stat-mech↗

arXiv2025

Room-temperature decomposition of the ethaline deep eutectic solvent

Environmentally-benign, non-toxic electrolytes with combinatorial design spaces are excellent candidates for green solvents, green leaching agents, and carbon capture sources. Here, we examine one particular green solvent, ethaline, a 2:1 molar ratio of ethylene glycol and choline chloride. Despite its touted green credentials, we find partial decomposition of ethaline into toxic chloromethane and dimethylaminoethanol at room temperature, limiting its sustainable advantage. We experimentally characterize these decomposition products and computationally develop a general, quantum chemically-accurate workflow to understand decomposition. We find that fluctuations of the hydrogen bonds bind chloride near reaction sites, initiating the reaction between choline cations and chloride anions. In summary, in the design of green solvents, we do not recommend the use of choline chloride due to its susceptibility to undergo decomposition in strongly hydrogen-bound mixtures.

physics.chem-ph↗

arXiv2025

Ionic Associations and Hydration in the Electrical Double Layer of Water-in-Salt Electrolytes

Water-in-Salt-Electrolytes (WiSEs) are an exciting class of concentrated electrolytes finding applications in energy storage devices because of their expanded electrochemical stability window, good conductivity and cation transference number, and fire-extinguishing properties. These distinct properties are thought to originate from the presence of an anion-dominated ionic network and interpenetrating water channels for cation transport, which indicates that associations in WiSEs are crucial to understanding their properties. Currently, associations have mainly been investigated in the bulk, while little attention has been given to the electrolyte structure near electrified interfaces. Here, we develop a theory for the electrical double layer (EDL) of WiSEs, where we consistently account for the thermoreversible associations of species into Cayley tree aggregates. The theory predicts an asymmetric structure of the EDL. At negative voltages, hydrated Li$^+$ dominate and cluster aggregation is initially slightly enhanced before disintegration at larger voltages. At positive voltages when compared to the bulk, clusters are strictly diminished. Performing atomistic molecular dynamics (MD) simulations of the EDL of WiSE provides EDL data for validation and bulk data for parameterization of our theory. Validating the predictions of our theory against MD showed good qualitative agreement. Furthermore, we performed electrochemical impendence measurements to determine the differential capacitance of the studied LiTFSI WiSE and also found reasonable agreement with our theory. Overall, the developed approach can be used to investigate ionic aggregation and solvation effects in the EDL, which amongst other properties, can be used to understand the pre-cursers for solid-electrolyte interphase formation.

physics.chem-ph↗

arXiv2024

Transferability and Accuracy of Ionic Liquid Simulations with Equivariant Machine Learning Interatomic Potentials

Ionic liquids (ILs) are an exciting class of electrolytes finding applications in many areas from energy storage to solvents, where they have been touted as ``designer solvents'' as they can be mixed to precisely tailor the physiochemical properties. As using machine learning interatomic potentials (MLIPs) to simulate ILs is still relatively unexplored, several questions need to be answered to see if MLIPs can be transformative for ILs. Since ILs are often not pure, but are either mixed together or contain additives, we first demonstrate that a MLIP can be trained to be compositionally transferable, i.e., the MLIP can be applied to mixtures of ions not directly trained on, whilst only being trained on a few mixtures of the same ions. We also investigate the accuracy of MLIPs for a novel IL, which we experimentally synthesize and characterize. Our MLIP trained on $\sim$200 DFT frames is in reasonable agreement with our experiments and DFT.

physics.chem-ph↗

arXiv2024

In-plane staging in lithium-ion intercalation of bilayer graphene

The ongoing efforts to optimize Li-ion batteries led to the interest in intercalation of nanoscale layered compounds, including bilayer graphene. Its lithium intercalation has been demonstrated recently but the mechanisms underpinning the storage capacity remain poorly understood. Here, using magnetotransport measurements, we report in-operando intercalation dynamics of bilayer graphene. Unexpectedly, we find four distinct intercalation stages that correspond to well-defined Li-ion densities. We refer to these stages as 'in-plane', with no in-plane analogues in bulk graphite. The fully intercalated bilayers represent a stoichiometric compound C14LiC14 with a Li density of 2.7x10^{14} cm^{-2}, notably lower than fully intercalated graphite. Combining the experimental findings and DFT calculations, we show that the critical step in bilayer intercalation is a transition from AB to AA stacking which occurs at a density of 0.9x10^{14} cm^{-2}. Our findings reveal the mechanism and limits for electrochemical intercalation of bilayer graphene and suggest possible avenues for increasing the Li storage capacity.

cond-mat.mtrl-sci↗

arXiv2024

Coexisting charge density waves in twisted bilayer NbSe2

Twisted bilayers of two-dimensional materials have emerged as a highly tunable platform for studying broken symmetry phases. While most interest has been focused on emergent states in systems whose constituent monolayers do not feature broken symmetry states, assembling monolayers that exhibit ordered states into twisted bilayers can also give rise to interesting phenomena. Here, we use large-scale first-principles density-functional theory calculations to study the atomic structure of twisted bilayer $\mathrm{{N}b{S}e_2}$ whose constituent monolayers feature a charge density wave. We find that different charge density wave states coexist in the ground state of the twisted bilayer: monolayer-like $3\times 3$ triangular and hexagonal charge density waves are observed in low-energy stacking regions, while stripe charge density waves are found in the domain walls surrounding the low-energy stacking regions. These predictions, which can be tested by scanning tunneling microscopy experiments, highlight the potential to create complex charge density wave ground states in twisted bilayer systems and can serve as a starting point for understanding superconductivity occurring at low temperatures.

cond-mat.mtrl-sci↗

arXiv2024

Electric Field Induced Associations in the Double Layer of Salt-in-Ionic-Liquid Electrolytes

Ionic liquids (ILs) are an extremely exciting class of electrolytes for energy storage applications because of their unique combination of properties. Upon dissolving alkali metal salts, such as Li or Na based salts, with the same anion as the IL, an intrinsically asymmetric electrolyte can be created for use in batteries, known as a salt-in-ionic liquid (SiIL). These SiILs have been well studied in the bulk, where negative transference numbers of the alkali metal cation have been observed from the formation of small, negatively charged clusters. The properties of these SiILs at electrified interfaces, however, have received little to no attention. Here, we develop a theory for the electrical double layer (EDL) of SiILs where we consistently account for the thermoreversible association of ions into Cayley tree aggregates. The theory predicts that the IL cations first populate the EDL at negative voltages, as they are not strongly bound to the anions. However at large negative voltages which are strong enough to break the alkali metal cation-anion associations, these IL cations are exchanged for the alkali metal cation because of their higher charge density. At positive voltages, we find that the SiIL actually becomes $\textit{more aggregated while screening the electrode charge}$ from the formation of large, negatively charged aggregates. Therefore, in contrast to conventional intuition of associations in the EDL, SiILs appear to become more associated in certain electric fields. We present these theoretical predictions to be verified by molecular dynamics simulations and experimental measurements.

physics.chem-ph↗

arXiv2023

Short vs. long range exchange interactions in twisted bilayer graphene

We discuss the effect of long-range interactions within the self-consistent Hartree-Fock (HF) approximation in comparison to short-range atomic Hubbard interactions on the band structure of twisted bilayer graphene (TBG) at charge neutrality for various twist angles. Starting from atomistic calculations, we determine the quasi-particle band structure of TBG with Hubbard interactions for various magnetic orderings: modulated anti-ferromagnetic (MAFM), nodal anti-ferromagnetic (NAFM) and hexagonal anti-ferromagnetic (HAFM). Then, we develop an approach to incorporate these magnetic orderings along with the HF potential in the continuum approximation. Away from the magic angle, we observe a drastic effect of the magnetic order on the band structure of TBG compared to the influence of the HF potential. Near the magic angle, however, the HF potential seems to play a major role on the band structure compared to the magnetic order. These findings suggest that the spin-valley degenerate broken symmetry state often found in HF calculations of charge neutral TBG near the magic angle should favour magnetic order, since the atomistic Hubbard interaction will break this symmetry in favour of spin polarization.

cond-mat.mes-hall↗

arXiv2023

Theory of Cation Solvation and Ionic Association in Non-Aqueous Solvent Mixtures

Conventional lithium-ion batteries, and many next-generation technologies, rely on organic electrolytes with multiple solvents to achieve the desired physicochemical and interfacial properties. The complex interplay between these properties can often be elucidated via the coordination environment of the cation. We develop a theory for the coordination shell of cations in non-aqueous solvent mixtures that can be applied with high fidelity, up to super-concentrated electrolytes. Our theory can naturally explain simulation and experimental values of cation solvation in ''classical'' non-aqueous electrolytes. Moreover, we utilise our theory to understand general design principles of emerging classes of non-aqueous electrolyte mixtures, such as high entropy electrolytes. It is hoped that this theory provides a systematic framework to understand simulations and experiments which engineer the solvation structure and ionic associations of concentrated non-aqueous electrolytes.

cond-mat.soft↗

arXiv2023

Effect of Coulomb impurities on the electronic structure of magic angle twisted bilayer graphene

In graphene, charged defects break the electron-hole symmetry and can even give rise to exotic collapse states when the defect charge exceeds a critical value which is proportional to the Fermi velocity. In this work, we investigate the electronic properties of twisted bilayer graphene (tBLG) with charged defects using tight-binding calculations. Like monolayer graphene, tBLG exhibits linear bands near the Fermi level but with a dramatically reduced Fermi velocity near the magic angle (approximately 1.1°). This suggests that the critical value of the defect charge in magic-angle tBLG should also be very small. We find that charged defects give rise to significant changes in the low-energy electronic structure of tBLG. Depending on the defect position in the moiré unit cell, it is possible to open a band gap or to induce an additional flattening of the low-energy valence and conduction bands. Our calculations suggest that the collapse states of the two monolayers hybridize in the twisted bilayer. However, their in-plane localization remains largely unaffected by the presence of the additional twisted layer because of the different length scales of the moiré lattice and the monolayer collapse state wavefunctions. These predictions can be tested in scanning tunnelling spectroscopy experiments.

cond-mat.mtrl-sci↗

arXiv2023

Spectroscopic signatures of tetralayer graphene polytypes

Tetralayer graphene has recently become a new addition to the family of few-layer graphene with versatile electronic properties. This material can be realised in three distinctive stacking configurations, for which we determine spectroscopic signatures in angle-resolved photoemission spectroscopy (ARPES), dynamical optical conductivity, and Raman spectra of inter-band excitations. The reported library of spectral features of tetralayer graphenes can be used for the non-invasive identification of the stacking order realised in a particular film.

cond-mat.mes-hall↗

arXiv2022

Imaging gate-induced molecular melting on a graphene field-effect transistor

Solid-liquid phase transitions are fundamental physical processes, but atomically-resolved microscopy has yet to capture both the solid and liquid dynamics for such a transition. We have developed a new technique for controlling the melting and freezing of 2D molecular layers on a graphene field-effect transistor (FET) that allows us to image phase transition dynamics via atomically-resolved scanning tunneling microscopy. Back-gate voltages applied to a F4TCNQ-decorated graphene FET induce reversible transitions between a charge-neutral solid phase and a negatively charged liquid phase. Nonequilibrium molecular melting dynamics are visualized by rapidly heating the graphene surface with electrical current and imaging the resulting evolution toward new equilibrium states. An analytical model has been developed that explains the observed equilibrium mixed-state phases based on spectroscopic measurement of both solid and liquid molecular energy levels. Observed non-equilibrium melting dynamics are consistent with Monte Carlo simulations.

cond-mat.mes-hall↗