Grand Canonical Ensemble Research Articles

Fleeting-Active-Site-Thrust Oxygen Evolution Reaction by Iron Cations from the Electrolyte.

Oxygen evolution reaction (OER) is key to sustainable energy and environmental engineering, thus necessitating rational design of high-performing electrocatalysts that requires understanding the structure-performance relationship with a possible dynamic nature under working conditions. Herein, we uncover a novel type of OER mechanisms thrust by the fleeting active sites (FASs) dynamically formed on Ni-based layered double hydroxides (Ni-LDHs) by Fe cations from the electrolyte under OER potentials. We employ grand-canonical ensemble methods and microkinetic modeling to elucidate the potential-dependent structures of FASs on Ni-LDHs and demonstrate that the fleeting-active-site-thrust (FAST) mechanism delivers superior OER activity via the FAST intramolecular oxygen coupling pathway, which also suppresses the lattice oxygen mechanism, leading to improved operando stability of Ni-LDHs. We further reveal that introducing only trace-level loadings (10-100 ppm) of FASs on Ni-LDHs can significantly boost and govern the catalytic performance for OER. This underscores the crucial importance of considering the novel FAST mechanism in OER and also suggests the electrolyte as a key part of the structure-performance relationship as well as an effective design strategy via engineering the electrolyte.

Selective methanol production via CO2 reduction on Cu2O revealed by micro-kinetic study combined with constant potential model

High efficiency electrocatalysis of greenhouse gas CO2 to liquid fuel methanol attracts great attentions that allows energy transformation from renewable electric energy to storable chemical energy. Catalytically converting CO2 to methanol using green hydrogen is a promising pathway to achieve carbon neutrality. In this work, the catalytic activity and product selectivity of the electrochemical CO2 reduction reaction on Cu2O were studied using a micro-kinetic model based on Marcus charge transfer theory. The constant potential model under the grand-canonical ensemble enables the accurate description of binding energies and ground-state charge transfer upon surface adsorption as a function of electrode potential. Firstly, the potential-dependent activation energies and rate constants of all possible elementary reactions involved in CO2 reduction are calculated. Then, the surface coverage and its derivative can be obtained in a steady-state approximation. Finally, the total reaction rate and partial reaction rate can be deduced, allowing for direct comparison with catalytic activity (current density) and product selectivity (Faradaic efficiency). It is found that CH3OH is the dominant product on the Cu2O(111) surface, while CO is the main product on the Cu2O(110) surface. Based on the derived total and partial reaction rates under the steady-state approximation, it is demonstrated that Cu2O(111) exhibits the highest electrocatalytic activity and methanol selectivity at U = −0.6 V vs. SHE. This research presents a methodology for predicting apparent electrocatalytic performance from microscopic reaction energy calculations, which can be applied to other important electrocatalytic reaction mechanisms and performance predictions.

Semi-empirical supported, Ab initio derived thermodynamic properties for ClO2 and its sub and extended species, applied in water treatment cycles

This paper describes a group of sixty (60) sub and extended chlorine oxide species with the general formulae of ClxOy (with x ≤ 2, y ≤ 8). Their role in water treatment cycles, behaving as key reactive species, is represented by a complex sequence of chemical inter-dependencies, exposed as a cohesive set of chemical reactions to demonstrate their cyclic role in aqueous media. An empirical/semi-empirical computational approach, supported by Ab Initio simulations, in accordance with open-shell character, has been followed to determine their optimum molecular geometries, to obtain their thermochemical properties. Besides a single molecular analysis, Grand Canonical Ensemble simulations, supported by a revised library of force field parameters, constituted a core component of the computational approach and proved to be invaluable in confirming thermochemical properties. This approach also offered finite estimates of optimum model sizes, a benefit with wider modelling application. Extended molecular species of ClO2 display a complex sequence of bonding character, with a variable charge dissipation (reported as partial charges), which complicates selection of basis sets in optimizing molecular geometries, during Ab Initio analyses.Optimum molecular geometries were obtained using Gaussian and MOPAC, which in turn resulted in reliable Heats of Formation. These correlated well with energies extracted from the open literature. Thermodynamic Analysis of the reaction of selected chlorine oxides with water using FactSage, predicted the production of known and two previously undetected chlorine species, [ClO4]- and [ClOH2]+.

Statistical Thermodynamic Description of Self-Assembly of Large Inclusions in Biological Membranes.

Recent studies revealed anomalous underscreening in concentrated electrolytes, and we suggest that the underscreened electrostatic forces between membrane proteins play a significant role in the process of self-assembly. In this work, we assumed that the underscreened electrostatic forces compete with the thermodynamic Casimir forces induced by concentration fluctuations in the lipid bilayer, and developed a simplified model for a binary mixture of oppositely charged membrane proteins with different preference to liquid-ordered and liquid-disordered domains in the membrane. In the model, like macromolecules interact with short-range Casimir attraction and long-range electrostatic repulsion, and the cross-interaction is of the opposite sign. We determine energetically favored patterns in a system in equilibrium with a bulk reservoir of the macromolecules. Different patterns consisting of clusters and stripes of the two components and of vacancies are energetically favorable for different values of the chemical potentials. Effects of thermal flutuations at low temperature are studied using Monte Carlo simulations in grand canonical and canonical ensembles. For fixed numbers of the macromolecules, a single two-component cluster with a regular pattern coexists with dispersed small one-component clusters, and the number of small clusters depends on the ratio of the numbers of the molecules of the two components. Our results show that the pattern formation is controlled by the shape of the interactions, the density of the proteins, and the proportion of the components.

Discharging of Ramsdellite MnO2 Cathode in a Lithium-Ion Battery.

We report an application of our unbiased Monte Carlo approach to investigate thermodynamic and electrochemical properties of lithiated manganese oxide in the ramsdellite phase (R-MnO2) to uncover the mechanism of lithium intercalation and understand charging/discharging of R-MnO2 as a cathode material in lithium-ion batteries. The lithium intercalation reaction was computationally explored by modeling thermodynamically significant distributions of lithium and reduced manganese in the R-MnO2 framework for a realistic range of lithium molar fractions 0 < x < 1 in Li x MnO2. We employed interatomic potentials and analyzed the thermodynamics of the resultant grand canonical ensemble. We found ordered or semiordered phases at x = 0.5 and 1.0 in Li x MnO2, verified by configurational entropy changes and simulated X-ray diffraction patterns of partially lithiated R-MnO2. The radial distribution functions show the preference of lithium for homogeneous distributions across the one-dimensional 2 × 1 ramsdellite channels accompanied by alternating reduced/oxidized manganese ions. The occupation of the interstitial sites in the channels is correlated with the calculated voltage profile, showing a sharp voltage drop at x = 0.5, which is explained by the energy penalty of shifting lithium ions from stable tetrahedral to unstable octahedral sites. To facilitate this work, our in-house software, Knowledge Led Master Code (KLMC) was extended to support massive parallelism on high-performance computers.

Partition function zeros of zeta-urns

We discuss the distribution of partition function zeros for the grand-canonical ensemble of the zeta-urn model, where tuning a single parameter can give a first or any higher order condensation transition. We compute the locus of zeros for finite-size systems and test scaling relations describing the accumulation of zeros near the critical point against theoretical predictions for both the first and higher order transition regimes.

Plasma-Plasma Third Order Phase Transition from Type IIB Supergravity.

We show that the planar, charged black hole in asymptotically anti-de Sitter spacetime, dual to the strongly coupled quark-gluon plasma thermal state of large N, SU(N), N=4 super Yang-Mills at finite chemical potential undergoes a third-order phase transition in the grand canonical ensemble to a hairy black hole of type IIB supergravity. The hairy phase is another strongly coupled fluid with a conformal equation of state and can be interpreted as another kind of quark-gluon plasma. This new quark-gluon plasma has less entropy and, therefore, seems to characterize some form of smooth hadronization. The locus of the transition in terms of the critical values of the "baryon" chemical potential μ_{c} and the temperature T_{c} is μ_{c}=2πT_{c}.

RASPA3: A Monte Carlo code for computing adsorption and diffusion in nanoporous materials and thermodynamics properties of fluids.

We present RASPA3, a molecular simulation code for computing adsorption and diffusion in nanoporous materials and thermodynamic and transport properties of fluids. It implements force field based classical Monte Carlo/molecular dynamics in various ensembles. In this article, we introduce the new additions and changes compared to RASPA2. RASPA3 is rewritten from the ground up in C++23 with speed and code readability in mind. Transition-matrix Monte Carlo is added to compute the density of states and free energies. The Monte Carlo code for rigid molecules is based on quaternions, and the atomic positions needed in the energy evaluation are recreated from the center of mass position and quaternion orientation. The expanded ensemble methodology for fractional molecules, with a scaling parameter λ between 0 and 1, now also keeps track of analytic expressions of dU/dλ, allowing independent verification of the chemical potential using thermodynamic integration. The source code is freely available under the MIT license on GitHub. Using this code, we compare four Monte Carlo (MC) insertion/deletion techniques: unbiased Metropolis MC, Configurational-Bias Monte Carlo (CBMC), Continuous Fractional Component MC (CFCMC), and CB/CFCMC. We compare particle distribution shapes, acceptance ratios, accuracy and speed of isotherm computation, enthalpies of adsorption, and chemical potentials, over a wide range of loadings and systems, for the grand canonical ensemble and for the Gibbs ensemble.

Accelerated convergence via adiabatic sampling for adsorption and desorption processes.

Under isothermal conditions, phase transitions occur through a nucleation event when conditions are sufficiently close to coexistence. The formation of a nucleus of the new phase requires the system to overcome a free energy barrier of formation, whose height rapidly rises as supersaturation decreases. This phenomenon occurs both in the bulk and under confinement and leads to a very slow kinetics for the transition, ultimately resulting in hysteresis, where the system can remain in a metastable state for a long time. This has broad implications, for instance, when using simulations to predict phase diagrams or screen porous materials for gas storage applications. Here, we leverage simulations in an adiabatic statistical ensemble, known as adiabatic grand-isochoric ensemble (μ, V, L) ensemble, to reach equilibrium states with a greater efficiency than its isothermal counterpart, i.e., simulations in the grand-canonical ensemble. For the bulk, we show that at low supersaturation, isothermal simulations converge slowly, while adiabatic simulations exhibit a fast convergence over a wide range of supersaturation. We then focus on adsorption and desorption processes in nanoporous materials, assess the reliability of (μ, V, L) simulations on the adsorption of argon in IRMOF-1, and demonstrate the efficiency of adiabatic simulations to predict efficiently the equilibrium loading during the adsorption and desorption of argon in MCM-41, a system that exhibits significant hysteresis. We provide quantitative measures of the increased rate of convergence when using adiabatic simulations. Adiabatic simulations explore a wide temperature range, leading to a more efficient exploration of the configuration space.

Exploring the UV and IR of a type-II holographic superconductor using a dyonic black hole

In this study, we investigate a type-II holographic superconductor with a perturbative scalar field over a (3 + 1)-dimensional electric and magnetically charged planar AdS black hole. We review the thermodynamical properties of the background relevant for the dual description of the Ginzburg–Landau density of superconducting states, showing that the adoption of a London gauge allows a consistent description of the Abrikosov vortex lattices, typical of type-II superconductors. We further derive a new expression for the upper critical magnetic field as a function of temperature in the grand canonical ensemble, supplementary to the one previously obtained in the canonical ensemble setup. These results confirm that our perturbative scalar field model consistently reproduces the well-known temperature behavior of the upper critical magnetic field according to the Ginzburg–Landau theory and other Abelian–Higgs holographic developments for type-II superconductors. We then continue with an original analysis of the scalar field equation in terms of a Schrödinger potential that led to the observation of bound states, a signal for the condensation of Cooper pairs. These results provide robust evidence for the existence of an IR order parameter near extremality. In view of this, we performed a closer inspection of the IR effective scalar equation in which the geometry adopts a Schwarzschild AdS2×R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {AdS}_{2}\ imes {\\mathbb {R}}^{2}$$\\end{document} structure, finding novel condensed bound states in the IR regime.

An Inverse Cluster Expansion for the Chemical Potential

Interacting particle systems in a finite-volume in equilibrium are often described by a grand-canonical ensemble induced by the corresponding Hamiltonian, i.e. a finite-volume Gibbs measure. However, in practice, directly measuring this Hamiltonian is not possible, as such, methods need to be developed to calculate the Hamiltonian potentials from measurable data. In this work, we give an expansion of the chemical potential in terms of the correlation functions of such a system in the thermodynamic limit. This is a justification of a formal approach of Nettleton and Green from the 50’s, that can be seen as an inverse cluster expansion.

Topology of charged AdS black hole in restricted phase space* *Supported by the National Natural Science Foundation of China (12075143, 12375050), and the Natural Science Foundation of Shanxi Province, China (202203021221209, 202303021211180)

The local topological properties of black hole systems can be expressed through winding numbers as defects. To date, AdS black hole thermodynamics are often depicted by the dual parameters of in the extended phase space, while there have been several studies on the black hole thermodynamics in the restricted phase space. In this paper, we analyze the topological properties of charged AdS black holes in the restricted phase space under the higher-dimension and higher-order curvature gravity frame. The results show that the topological number of the charged black hole in the same canonical ensembles is a constant and is independent of the concrete dual thermodynamical parameters. However, the topological number in the grand canonical ensemble is different from that in the canonical ensemble for the same black hole system. Furthermore, these results are independent of dimension d and highest order k of the Lanczos-Lovelock densities.

Hyperdensity Functional Theory of Soft Matter.

We present a scheme for investigating arbitrary thermal observables in spatially inhomogeneous equilibrium many-body systems. Extending the grand canonical ensemble yields any given observable as an explicit hyperdensity functional. Associated local fluctuation profiles follow from an exact hyper-Ornstein-Zernike equation. While the local compressibility and simple observables permit analytic treatment, complex order parameters are accessible via simulation-based supervised machine learning of neural hyperdirect correlation functionals. We exemplify efficient and accurate neural predictions for the cluster statistics of hard rods, square-well rods, and hard spheres. The theory allows one to treat complex observables, as is impossible in standard density functional theory.

Theory and Monte Carlo simulation of the ideal gas with shell particles in the canonical, isothermal-isobaric, grand canonical, and Gibbs ensembles.

Theories of small systems play an important role in the fundamental understanding of finite size effects in statistical mechanics, as well as the validation of molecular simulation results as no computer can simulate fluids in the thermodynamic limit. Previously, a shell particle was included in the isothermal-isobaric ensemble in order to resolve an ambiguity in the resulting partition function. The shell particle removed either redundant volume states or redundant translational degrees of freedom of the system and yielded quantitative differences from traditional simulations in this ensemble. In this work, we investigate the effect of including a shell particle in the canonical, grand canonical, and Gibbs ensembles. For systems comprised of a pure component ideal gas, analytical expressions for various thermodynamic properties are obtained. We also derive the Metropolis Monte Carlo simulation acceptance criteria for these ensembles with shell particles, and the results of the simulations of an ideal gas are in excellent agreement with the theoretical predictions. The system size dependence of various important ensemble averages is also analyzed.

Corrections of Electron–Phonon Coupling for Second‐Order Structural Phase Transitions

Structural phase transitions are accompanied by a movement of one nucleus (or a few) in the crystallographic unit cell. If the nucleus movement is continuous, a second‐order phase transition without latent heat results, whereas an abrupt nucleus displacement indicates a first‐order phase transition with accompanying latent heat. Herein, a Hamiltonian including electron–phonon coupling (EPC) as proposed by Kristoffel and Konsel is taken. Contrary to their treatment, both the kinetic energy of the nucleus and its position are treated. The interaction of the many‐electron system with the single nucleus is taken into account by the Born–Oppenheimer approximation and perturbative expressions for the free energies are derived. The nuclei corrections due to the entangled electrons are found to be minor, but highlight the importance of the symmetry breaking at low temperature. Furthermore the free energy for a canonical ensemble is computed, whereas Kristoffel and Konsel use a grand canonical ensemble, which allows to derive more stringent bounds on the free energy. For the zero‐order nucleus correction, the shift of the phase transition temperature by evaluating the free energy is deduced.

Droplet dynamics in a two-dimensional rarefied gas under Kawasaki dynamics

This is the second in a series of three papers in which we study a lattice gas subject to Kawasaki conservative dynamics at inverse temperature β>0 in a large finite box Λβ⊂Z2 whose volume depends on β. Each pair of neighboring particles has a negative binding energy−U<0, while each particle has a positive activation energyΔ>0. The initial configuration is drawn from the grand-canonical ensemble restricted to the set of configurations where all the droplets are subcritical. Our goal is to describe, in the metastable regime Δ∈(U,2U) and in the limit as β→∞, how and when the system nucleates, i.e., grows a supercritical droplet somewhere in Λβ. In the first paper we showed that subcritical droplets behave as quasi-random walks. In the present paper we use the results in the first paper to analyze how subcritical droplets form and dissolve on multiple space–time scales when the volume is moderately large, namely, |Λβ|=eΘβ with Δ<Θ<2Δ−U. In the third paper we consider the setting where the volume is very large, namely, |Λβ|=eΘβ with Δ<Θ<Γ−(2Δ−U), where Γ is the energy of the critical droplet in the local model, i.e., when Λβ has a fixed volume not depending on β and particles can be created and annihilated at the boundary, and use the results in the first two papers to identify the nucleation time. We will see that in a very large volume critical droplets appear more or less independently in boxes of moderate volume, a phenomenon referred to as homogeneous nucleation. Since Kawasaki dynamics is conservative, i.e., particles move around and interact but are preserved, we need to control non-local effects in the way droplets are formed and dissolved. This is done via a deductive approach: the tube of typical trajectories leading to nucleation is described via a series of events, whose complements have negligible probability, on which the evolution of the gas can be captured by a coarse-grained Markov chain on a space of droplets, which we refer to as droplet dynamics.

The Impact of Metal Centers in the M-MOF-74 Series on Formic Acid Production.

The confinement effect of porous materials on the thermodynamical equilibrium of the CO2 hydrogenation reaction presents a cost-effective alternative to transition metal catalysts. In metal-organic frameworks, the type of metal center has a greater impact on the enhancement of formic acid production than the scale of confinement resulting from the pore size. The M-MOF-74 series enables a comprehensive study of how different metal centers affect HCOOH production, minimizing the effect of pore size. In this work, molecular simulations were used to analyze the adsorption of HCOOH and the CO2 hydrogenation reaction in M-MOF-74, where M = Ni, Cu, Co, Fe, Mn, Zn. We combine classical simulations and density functional theory calculations to gain insights into the mechanisms that govern the low coverage adsorption of HCOOH in the surrounding of the metal centers of M-MOF-74. The impact of metal centers on the HCOOH yield was assessed by Monte Carlo simulations in the grand-canonical ensemble, using gas-phase compositions of CO2, H2, and HCOOH at chemical equilibrium at 298.15-800 K, 1-60 bar. The performance of M-MOF-74 in HCOOH production follows the same order as the uptake and the heat of HCOOH adsorption: Ni > Co > Fe > Mn > Zn > Cu. Ni-MOF-74 increases the mole fraction of HCOOH by ca. 105 times compared to the gas phase at 298.15 K, 60 bar. Ni-MOF-74 has the potential to be more economically attractive for CO2 conversion than transition metal catalysts, achieving HCOOH production at concentrations comparable to the highest formate levels reported for transition metal catalysts and offering a more valuable molecular form of the product.

Self-Assembly of Model Three- and Four-Patch Colloidal Particles in Two Dimensions.

A coarse-grained effective solvent model of two-patch particles is extended to study the self-assembly of three- and four-patch particles to two-dimensional honeycomb and square lattices, respectively. Employing this model, grand canonical ensemble simulations are done to calculate vapor-liquid equilibria and the critical temperatures for patchy particles of various patch widths. The range of stability of the liquid, although very limited compared to isotropic particles, which interact through a longer-range potential, depends on the patch width and on the number of patches. Biased sampling and unbiased simulations are also done to investigate the mechanism of nucleation and crystal growth for honeycomb and square lattices, self-assembled from three- and four-patch particles, respectively. A two-step mechanism governs the nucleation of both lattices. In the first step, the particles form a dense amorphous network, and in the second step, the particles inside the amorphous network reorient to form crystalline nuclei. Barrier heights for the nucleation of honeycomb and square lattices are 7.8 kBT and 7.4 kBT, which are close to the reported values for the nucleation of the kagome lattice. In agreement with confocal microscopy experiments, the self-assembly in a honeycomb lattice involves the formation of 5- to 7-membered rings. The 5- and 7-membered rings hamper the nucleation of the honeycomb lattice, through defect formation and rotation of the symmetry planes of crystals that form at their surfaces. With the progress of self-assembly, a substantial amount of restructuring of the defects and crystals in their vicinity is needed to heal the defects.

Thermodynamic topology of phantom AdS black holes in massive gravity

In this work, we explore the thermodynamic topology of phantom AdS black holes in the context of massive gravity. To this end, we evaluate these black holes in two distinct ensembles: the canonical and grand canonical ensembles (GCE). We begin by examining the topological charge linked to the critical point and confirming the existence of a conventional critical point (CP1) in the canonical ensemble (CE), this critical point has a topological charge of −1 and acts as a point of phase annihilation, this situation can only be considered within the context of the classical Einstein–Maxwell (CEM) theory (η=1), while no critical point is identified in the GCE. Furthermore, we consider black holes as a topological defect within the thermodynamic space. To gain an understanding of the local and global topological configuration of this defect, we will analyze its winding numbers, and observe that the total topological charge in the CE consistently remains at 1. When the system experiences a pressure below the critical threshold, it gives rise to the occurrence of annihilation and generation points. The value of electric potential determines whether the total topological charge in the GCE is zero or one. As a result, we detect a point of generation point or absence of generation/annihilation point. Based on our analysis, it can be inferred that ensembles significantly impact the topological class of phantom AdS black holes in massive gravity.

Exploring critical behavior of thermodynamic variables of the Kerr-Newman-AdS black hole in the restricted phase space

The present work investigates the thermodynamic properties of the four-dimensional Kerr-Newmann-AdS black hole, utilizing the recently proposed framework of restricted phase space thermodynamics. This approach introduces a novel set of paired thermodynamic variables; the central charge (C) of the corresponding dual conformal field theory and the chemical potential (μ). Through rigorous analysis, we establish fundamental relationships, including the Euler relation, Gibbs-Duhem relation, and the zeroth-order homogeneity of intensive variables. Furthermore, numerical techniques are employed to explore thermodynamic processes between the conjugate variables in canonical and grand canonical ensembles. Our investigation reveals first-order and second-order phase transitions across various macroscopic processes. Despite the absence of complete analytical expressions, our findings unveil striking similarities in behavior between Reissner-Nordström-Anti-de Sitter and Kerr-anti–de Sitter, underscoring the presence of underlying universality within the restricted phase space thermodynamics formalism. Published by the American Physical Society 2024