Impedance of nanocapacitors from molecular simulations to understand the dynamics of confined electrolytes.

Nanoelectrochemical devices have become a promising candidate technology across various applications, including sensing and energy storage, and provide new platforms for studying fundamental properties of electrode/electrolyte interfaces. In this work, we employ constant-potential molecular dynamics simulations to investigate the impedance of gold-aqueous electrolyte nanocapacitors, exploiting a recently introduced fluctuation-dissipation relation. In particular, we relate the frequency-dependent impedance of these nanocapacitors to the complex conductivity of the bulk electrolyte in different regimes, and use this connection to design simple but accurate equivalent circuit models. We show that the electrode/electrolyte interfacial contribution is essentially capacitive and that the electrolyte response is bulk-like even when the interelectrode distance is only a few nanometers, provided that the latter is sufficiently large compared to the Debye screening length. We extensively compare our simulation results with spectroscopy experiments and predictions from analytical theories. In contrast to experiments, direct access in simulations to the ionic and solvent contributions to the polarization allows us to highlight their significant and persistent anticorrelation and to investigate the microscopic origin of the timescales observed in the impedance spectrum. This work opens avenues for the molecular interpretation of impedance measurements, and offers valuable contributions for future developments of accurate coarse-grained representations of confined electrolytes.

Electrical noise in electrolytes: a theoretical perspective.

Seemingly unrelated experiments such as electrolyte transport through nanotubes, nano-scale electrochemistry, NMR relaxometry and surface force balance measurements, all probe electrical fluctuations: of the electric current, the charge and polarization, the field gradient (for quadrupolar nuclei) and the coupled mass/charge densities. The fluctuations of such various observables arise from the same underlying microscopic dynamics of the ions and solvent molecules. In principle, the relevant length and time scales of these dynamics are encoded in the dynamic structure factors. However, modelling the latter for frequencies and wavevectors spanning many orders of magnitude remains a great challenge to interpret the experiments in terms of physical processes such as solvation dynamics, diffusion, electrostatic and hydrodynamic interactions between ions, interactions with solid surfaces, etc. Here, we highlight the central role of the charge-charge dynamic structure factor in the fluctuations of electrical observables in electrolytes and offer a unifying perspective over a variety of complementary experiments. We further analyze this quantity in the special case of an aqueous NaCl electrolyte, using simulations with explicit ions and an explicit or implicit solvent. We discuss the ability of the standard Poisson-Nernst-Planck theory to capture the simulation results, and how the predictions can be improved. We finally discuss the contributions of ions and water to the total charge fluctuations. This work illustrates an ongoing effort towards a comprehensive understanding of electrical fluctuations in bulk and confined electrolytes, in order to enable experimentalists to decipher the microscopic properties encoded in the measured electrical noise.

Frequency-Dependent Impedance of Nanocapacitors from Electrode Charge Fluctuations as a Probe of Electrolyte Dynamics.

The frequency-dependent impedance is a fundamental property of electrical components. We show that it can be determined from the equilibrium dynamical fluctuations of the electrode charge in constant-potential molecular simulations, extending in particular a fluctuation-dissipation relation for the capacitance recovered in the low-frequency limit and provide an illustration on water-gold nanocapacitors. This Letter opens the way to the interpretation of electrochemical impedance measurements in terms of microscopic mechanisms, directly from the dynamics of the electrolyte, or indirectly via equivalent circuit models as in experiments.

Ranking the synthesizability of hypothetical zeolites with the sorting hat.

Zeolites are nanoporous alumino-silicate frameworks widely used as catalysts and adsorbents. Even though millions of siliceous networks can be generated by computer-aided searches, no new hypothetical framework has yet been synthesized. The needle-in-a-haystack problem of finding promising candidates among large databases of predicted structures has intrigued materials scientists for decades; yet, most work to date on the zeolite problem has been limited to intuitive structural descriptors. Here, we tackle this problem through a rigorous data science scheme-the "Zeolite Sorting Hat"-that exploits interatomic correlations to discriminate between real and hypothetical zeolites and to partition real zeolites into compositional classes that guide synthetic strategies for a given hypothetical framework. We find that, regardless of the structural descriptor used by the Zeolite Sorting Hat, there remain hypothetical frameworks that are incorrectly classified as real ones, suggesting that they might be good candidates for synthesis. We seek to minimize the number of such misclassified frameworks by using as complete a structural descriptor as possible, thus focusing on truly viable synthetic targets, while discovering structural features that distinguish real and hypothetical frameworks as an output of the Zeolite Sorting Hat. Further ranking of the candidates can be achieved based on thermodynamic stability and/or their suitability for the desired applications. Based on this workflow, we propose three hypothetical frameworks differing in their molar volume range as the top targets for synthesis, each with a composition suggested by the Zeolite Sorting Hat. Finally, we analyze the behavior of the Zeolite Sorting Hat with a hierarchy of structural descriptors including intuitive descriptors reported in previous studies, finding that intuitive descriptors produce significantly more misclassified hypothetical frameworks, and that more rigorous interatomic correlations point to second-neighbor Si-O distances around 3.2-3.4 Å as the key discriminatory factor.

Quasiequilibrium multistate cellular automata.

In our effort to tackle the problem of letting nontrivial interactions, thermodynamic equilibrium, and full synchronicity coexist, and in the hope of reviving interest in cellular automata as promising tools for the quantitative, large-scale investigation of multiparticle systems, we built a fully synchronous cellular automaton rule for the simulation of occupancy-based lattice systems with multistate cells and neighboring interactions. The core of this rule, which constitutes an actual synchronous sampling scheme, is a negotiation stage; it produces cell occupancy distributions in very good agreement with their sequential Monte Carlo counterparts, and it satisfies a cellwise detailed balance principle thanks to the use of "mixed" intermediate states that allow for the computation of locally averaged acceptance probabilities. We took a square lattice (but the rule itself is not bound by dimensionality) as a basis for comparison with sequential Monte Carlo for showing that this synchronous rule leads to quasiequilibrium; the fulfillment of cellwise detailed balance is shown through results obtained for a small one-dimensional system, where the transition matrix could be computed exactly.

A molecular perspective on induced charges on a metallic surface.

Understanding the response of the surface of metallic solids to external electric field sources is crucial to characterize electrode-electrolyte interfaces. Continuum electrostatics offer a simple description of the induced charge density at the electrode surface. However, such a simple description does not take into account features related to the atomic structure of the solid and to the molecular nature of the solvent and of the dissolved ions. In order to illustrate such effects and assess the ability of continuum electrostatics to describe the induced charge distribution, we investigate the behavior of a gold electrode interacting with sodium or chloride ions fixed at various positions, in a vacuum or in water, using all-atom constant-potential classical molecular dynamics simulations. Our analysis highlights important similarities between the two approaches, especially under vacuum conditions and when the ion is sufficiently far from the surface, as well as some limitations of the continuum description, namely, neglecting the charges induced by the adsorbed solvent molecules and the screening effect of the solvent when the ion is close to the surface. While the detailed features of the charge distribution are system-specific, we expect some of our generic conclusions on the induced charge density to hold for other ions, solvents, and electrode surfaces. Beyond this particular case, the present study also illustrates the relevance of such molecular simulations to serve as a reference for the design of improved implicit solvent models of electrode-electrolyte interfaces.

Scaling-Up Simulations of Diffusion in Microporous Materials.

We introduce and demonstrate the coarse-graining of static and dynamical properties of host-guest systems constituted by methane in two different microporous materials. The reference systems are mapped to occupancy-based pore-scale lattice models. Each coarse-grained model is equipped with an appropriate coarse-grained potential and a local dynamical operator, which represents the probability of interpore molecular jumps between different cages. Coarse-grained thermodynamics and dynamics are both defined based on small-scale atomistic simulations of the reference systems. We considered two host materials: the widely studied ITQ-29 zeolite and the LTA-zeolite-templated carbon, which was recently theorized. Our method allows for representing with satisfactory accuracy and a considerably reduced computational effort the reference systems while providing new interesting physical insights in terms of static and diffusive properties.

A new kind of atlas of zeolite building blocks.

We have analyzed structural motifs in the Deem database of hypothetical zeolites to investigate whether the structural diversity found in this database can be well-represented by classical descriptors, such as distances, angles, and ring sizes, or whether a more general representation of the atomic structure, furnished by the smooth overlap of atomic position (SOAP) method, is required to capture accurately structure-property relations. We assessed the quality of each descriptor by machine-learning the molar energy and volume for each hypothetical framework in the dataset. We have found that a SOAP representation with a cutoff length of 6 Å, which goes beyond near-neighbor tetrahedra, best describes the structural diversity in the Deem database by capturing relevant interatomic correlations. Kernel principal component analysis shows that SOAP maintains its superior performance even when reducing its dimensionality to those of the classical descriptors and that the first three kernel principal components capture the main variability in the dataset, allowing a 3D point cloud visualization of local environments in the Deem database. This "cloud atlas" of local environments was found to show good correlations with the contribution of a given motif to the density and stability of its parent framework. Local volume and energy maps constructed from the SOAP/machine learning analyses provide new images of zeolites that reveal smooth variations of local volumes and energies across a given framework and correlations between the contributions to volume and energy associated with each atom-centered environment.

Molecular QCA embedding in microporous materials.

We propose an environment for information encoding and transmission via a nanoconfined molecular Quantum Dot Cellular Automata (QCA) wire, composed of a single row of head-to-tail interacting 2-dots molecular switches. While most of the research in the field refers to dots-bearing molecules bound on some type of surface, forming a bidimensional array of square cells capable of performing QCA typical functions, we propose here to embed the information bearing elements within the channels of a microporous matrix. In this way molecules would self-assemble in a row as a consequence of adsorption inside the pores of the material, forming an encased wire, with the crystalline environment giving stability and protection to the structure. DFT calculations on a diferrocenyl carborane, previously proposed and synthesized [J. A. Christie, R. P. Forrest, S. A. Corcelli, N. A. Wasio, R. C. Quardokus, R. Brown, S. A. Kandel, Y. Lu, C. S. Lent and K. W. Henderson, Angew. Chem., Int. Ed., 2015, 54, 15448], were performed both in vacuum and inside the channels of zeolite ITQ-51, indicating that information encoding and transmission is possible within the nanoconfined environment.

Local free energies for the coarse-graining of adsorption phenomena: The interacting pair approximation.

We investigate the coarse-graining of host-guest systems under the perspective of the local distribution of pore occupancies, along with the physical meaning and actual computability of the coarse-interaction terms. We show that the widely accepted approach, in which the contributions to the free energy given by the molecules located in two neighboring pores are estimated through Monte Carlo simulations where the two pores are kept separated from the rest of the system, leads to inaccurate results at high sorbate densities. In the coarse-graining strategy that we propose, which is based on the Bethe-Peierls approximation, density-independent interaction terms are instead computed according to local effective potentials that take into account the correlations between the pore pair and its surroundings by means of mean-field correction terms without the need for simulating the pore pair separately. Use of the interaction parameters obtained this way allows the coarse-grained system to reproduce more closely the equilibrium properties of the original one. Results are shown for lattice-gases where the local free energy can be computed exactly and for a system of Lennard-Jones particles under the effect of a static confining field.