Chemical Free Energies Research Articles

Combined study of phase transitions in the P2-type NaXNi1/3Mn2/3O2 cathode material: experimental, ab-initio and multiphase-field results

The research of new electrode materials such as sodium intercalation compounds is key to meet the challenges of future demands of sustainable energy storage. For these batteries, the intercalation behavior on the micro-scale is governed by a complex interplay of chemical, electrical and mechanical forces strongly influencing the overall cell performance. The multiphase-field method is a suitable tool to study these multi-physics and bridge the scale from ab-initio methods to the cell level. In this work, we follow a combined approach of experiments, density functional theory (DFT) calculations and multiphase-field simulations to predict thermodynamic and kinetic properties for the P2-type NaXNi1/3Mn2/3O2 sodium-ion cathode material. Experimentally, we obtain the thermodynamic potential and diffusion coefficients at various sodium contents using electrochemical techniques and discuss limitations of the experimentally applied methods. DFT is used to identify stable phases by calculating an energy hull curve. Then, the influence of long-range dispersion interactions and the exchange-correlation functional on the voltage curve is investigated by comparison with experimental results. Finally, multiphase-field simulations are performed based on inputs from experiments and DFT. The fitting of phase-specific chemical free energies from DFT calculations and experimental data is discussed. Our results highlight the thermodynamic consistency of all three approaches close to thermodynamic equilibrium. Furthermore, the phase-field method accurately describes the kinetics of the system including multiple phase transitions, by which we unravel the mechanism of the P2-O2 phase transition in a single crystal under the influence of intercalation reaction, bulk diffusion and elastic deformation. The model is able to predict the kinetic capacity loss depending on charging rate in agreement with C-rate experiments.

Combining particle and field-theoretic polymer models with multi-representation simulations.

Particle-based and field-theoretic simulations are both widely used methods to predict the properties of polymeric materials. In general, the advantages of each method are complementary. Field-theoretic simulations are preferred for polymers with high molecular weights and can provide direct access to chemical potentials and free energies, which makes them the method-of-choice for calculating phase diagrams. The trade-off is that field-theoretic simulations sacrifice the molecular details present in particle-based simulations, such as the configurations of individual molecules and their dynamics. In this work, we describe a new approach to conduct "multi-representation" simulations that efficiently map between particle-based and field-theoretic simulations. Our approach involves the construction of formally equivalent particle-based and field-based models, which are then simulated subject to the constraint that their spatial density profiles are equal. This constraint provides the ability to directly link particle-based and field-based simulations and enables calculations that can switch between one representation to the other. By switching between particle/field representations during a simulation, we demonstrate that our approach can leverage many of the advantages of each representation while avoiding their respective limitations. Although our method is illustrated in the context of complex sphere phases in linear diblock copolymers, we anticipate that it will be useful whenever free energies, rapid equilibration, molecular configurations, and dynamic information are all simultaneously desired.

An effective model for sodium insertion in hard carbons.

Sodium ion batteries (NIBs) are a potential alternative to Lithium ion batteries (LIBs) because of their lower cost and greater availability. As anodes, hard carbons (HCs) seem to be the most promising candidates for NIBs. Previous numerical theoretical research studies have focussed on the general conditions for Na insertion in HCs, while experiments have shown that the properties of Na insertion in HCs depend strongly on specific material properties of HCs. Our target is building an effective model based on experimental data and the volume expansion phenomenon as a base for constructing chemical potentials and free energies efficiently as the starting point for continuum modeling of intercalation in HCs. In our effective model, HC is treated implicitly, while Na is simulated in a confined space, created by the HC. To reproduce the complex intercalation behavior of Na, different intercalation sites at different energy levels must be introduced. The results show good agreement with the experimental data and clarify the contribution of different Na insertion sites and the exchange between different sites of Na to the open circuit voltage as well as their contribution to the reversible and irreversible capacity of Na in HCs.

Multi-Scale Modelling of the Bound Metal Deposition Manufacturing of Ti6Al4V

Nonlinear shrinkage of the metal part during manufacturing by bound metal deposition, both on the ground and under microgravity, is considered. A multi-scale physics-based approach is developed to address the problem. It spans timescales from atomistic dynamics on the order of nanoseconds to full-part shrinkage on the order of hours. This approach enables estimation of the key parameters of the problem, including the widths of grain boundaries, the coefficient of surface diffusion, the initial redistribution of particles during the debinding stage, the evolution of the microstructure from round particles to densely-packed grains, the corresponding changes in the total and chemical free energies, and the sintering stress. The method has been used to predict shrinkage at the levels of two particles, of the filament cross-section, of the sub-model, and of the whole green, brown, and metal parts.

Co-Based superalloy morphology evolution: A phase field study based on experimental thermodynamic and kinetic data

Cobalt-based superalloys with two phase γ/γ′ microstructures offer great promise as candidates for next-generation high-temperature alloys for applications, such as turbine blades. It is essential to understand the thermodynamic and kinetic factors that influence the microstructural evolution of these alloys in order to optimize the alloy compositions and processing steps with a goal to improve their coarsening, creep and rafting behavior. We are using a continuum phase field approach to study the diffusion process and to predict the equilibrium shapes of Co-Al-W γ′ precipitates. In order to obtain quantitatively predictive capabilities, we extract chemical free energies for the γ/γ′ phases based on CALculation of PHAse Diagrams (CALPHAD) thermodynamic data and diffusion mobilities for Co alloys based on CALPHAD kinetic data. We also use experimental or first-principles data for other quantities, such as misfit strain and interface information, for the parameterization of our model. A particular focus of our study is to understand how different energy balances, misfit strain and kinetics affect the coarsening and rafting behavior of γ′ precipitates, and the sensitivity of the final precipitate shape to materials parameters. We find that the equilibrium shape of the precipitate results from a delicate competition between chemical, interfacial, and elastic energies, and it is very sensitive to changes in model parameters. We examine how modeling input parameters affect the equilibrium shape of precipitates and relate these parameters to experimentally available values.

A consistent formation free energy definition for multicomponent clusters in quantum thermochemistry

Quantum chemical calculations have proven to describe the thermodynamics of sub-nanometre clusters more accurately than the liquid drop model used in classical nucleation theory (CNT). However, the standard quantum chemical free energies of multicomponent clusters are fundamentally incompatible with the quantity appearing in the exponential of the CNT expression for the nucleation rate. The origin of this incompatibility is known to be in the statistical thermochemistry, but it is also connected to a much debated issue of self-consistency within CNT. Although these issues do not affect the main results of previous theoretical studies of nucleation, a thorough analysis and discussion about the nature of free energy in quantum chemistry of cluster formation has been missing. In this study, we present a consistent definition for the formation free energy using the law of mass action and a general equilibrium cluster distribution function, and apply this definition to gas-phase quantum thermochemical calculations. This internal consistency allows us to integrate the high-level thermochemical data to the basic framework of CNT and the liquid drop model contained therein. Moreover, based on our analysis, we derive a simple analytical expression for the steady-state nucleation rate compatible with the widely used numerical acdc model. As an illustrative example, the consistent formation free energies and nucleation rates are presented and analysed for atmospherically relevant H2SO4–NH3 clusters at various temperature and monomer vapour pressure conditions.

The formulation of chemical potentials and free energy changes in biochemical reactions

In 1994, an IUBMB-IUPAC joint committee recommended a revised formulation for standard chemical potentials and reaction free energies motivated by the fact that, in biochemistry, the reactants and products often exist in multiple charge states depending on the pH and pMg of the solution environment. The recommendation involved both the use of (1) a mathematical transform with the intent to hold the pH constant, and (2) the formulation of reference chemical potentials of ionized isomeric species based on the log sum of the individual standard chemical potentials of each isomeric species. Recently, several reports including a 2020 IUPAC report have appeared that challenged the need for such summary formulations, arguing that the standard chemical potentials were sufficient with full accounting of each of the different charge state isomers involved in a biochemical reaction. This work critically evaluates both the use of thermodynamic transforms and the different chemical potential formulations. It is shown that (1) transforms are not necessary to hold the pH constant and (2) demonstrates that the two chemical potential formulations are not equivalent. Which formulation is appropriate depends on what species are measured experimentally or whether an assumption of equilibrium among the charge state isomers is reasonable and desirable.

On the interactions of the receptor-binding domain of SARS-CoV-1 and SARS-CoV-2 spike proteins with monoclonal antibodies and the receptor ACE2

A new betacoronavirus named SARS-CoV-2 has emerged as a new threat to global health and economy. A promising target for both diagnosis and therapeutics treatments of the new disease named COVID-19 is the coronavirus (CoV) spike (S) glycoprotein. By constant-pH Monte Carlo simulations and the PROCEEDpKa method, we have mapped the electrostatic epitopes for four monoclonal antibodies and the angiotensin-converting enzyme 2 (ACE2) on both SARS-CoV-1 and the new SARS-CoV-2 S receptor binding domain (RBD) proteins. We also calculated free energy of interactions and shown that the S RBD proteins from both SARS viruses binds to ACE2 with similar affinities. However, the affinity between the S RBD protein from the new SARS-CoV-2 and ACE2 is higher than for any studied antibody previously found complexed with SARS-CoV-1. Based on physical chemical analysis and free energies estimates, we can shed some light on the involved molecular recognition processes, their clinical aspects, the implications for drug developments, and suggest structural modifications on the CR3022 antibody that would improve its binding affinities for SARS-CoV-2 and contribute to address the ongoing international health crisis.

Hydrate Production Philosophy and Thermodynamic Calculations

The amount of energy in the form of natural gas hydrates is huge and likely substantially more than twice the amount of worldwide conventional fossil fuel. Various ways to produce these hydrates have been proposed over the latest five decades. Most of these hydrate production methods have been based on evaluation of hydrate stability limits rather than thermodynamic consideration and calculations. Typical examples are pressure reduction and thermal stimulation. In this work we discuss some of these proposed methods and use residual thermodynamics for all phases, including the hydrate phase, to evaluate free energy changes related to the changes in independent thermodynamic variables. Pressures, temperatures and composition of all relevant phases which participate in hydrate phase transitions are independent thermodynamic variables. Chemical potential and free energies are thermodynamic responses that determine whether the desired phase transitions are feasible or not. The associated heat needed is related to the first law of thermodynamics and enthalpies. It is argued that the pressure reduction method may not be feasible since the possible thermal gradients from the surroundings are basically low temperature heat that is unable to break water hydrogen bonds in the hydrate–water interface efficiently. Injecting carbon dioxide, on the other hand, leads to formation of new hydrate which generates excess heat compared to the enthalpy needed to dissociate the in situ CH4 hydrate. But the rapid formation of new CO2 hydrate that can block the pores, and also the low permeability of pure CO2 in aquifers, are motivations for adding N2. Optimum mole fractions of N2 based on thermodynamic considerations are discussed. On average, less than 30 mole% N2 can be efficient and feasible. Thermal stimulation using steam or hot water is not economically feasible. Adding massive amounts of methanol or other thermodynamic inhibitors is also technically efficient but far from economically feasible.

Precipitation of γ′ in the γ binder phase of WC-Al-Co-Ni cemented carbide: A phase-field study

High-temperature properties of WC-Co cemented carbides can be greatly improved by introducing ordered γ′ precipitates (L12 structure) into disordered γ Co-binder matrix (fcc structure). The microstructure evolution of γ′ precipitates in γ matrix was investigated by using multi-phase-field (MPF) method. In order to avoid indistinguishable miscibility during MPF simulations, a phenomenon caused by mistaking the chemical free energies of γ and γ′ phase for each other, the thermodynamic driving force and diffusivities were taken from CALPHAD databases with the Gibbs energies of ordered and disordered phases separated according to a single Gibbs energy expression in a thermodynamic database. The interfacial energy between γ and γ′ phases was estimated based on a thermodynamic model applied to coherent interfaces. The elastic strain energy was introduced to reproduce the cuboidal shape of the ordered γ′ precipitates. Specially, the MPF approach was applied to study the morphological evolution of γ + γ′ microstructure as a function of concentration, temperature and aging time. It was shown that with increasing of Al concentration the cuboidal shape of precipitates appears at early stages of growth. After long term aging at 1373K the γ′/γ interface becomes semi-coherent and some γ-channels are formed. The simulation results are in good agreement with experimental data and have demonstrated the ability of the model to capture the major structural characteristics of microstructural evolution in Al–Co–Ni binder system during long-term heat treatment. Based on the knowledge of microstructure evolution, it is possible to design the optimal process parameters efficiently instead of expensive and time-consuming experiments.

Machine learning models for hydrogen bond donor and acceptor strengths using large and diverse training data generated by first-principles interaction free energies

We present machine learning (ML) models for hydrogen bond acceptor (HBA) and hydrogen bond donor (HBD) strengths. Quantum chemical (QC) free energies in solution for 1:1 hydrogen-bonded complex formation to the reference molecules 4-fluorophenol and acetone serve as our target values. Our acceptor and donor databases are the largest on record with 4426 and 1036 data points, respectively. After scanning over radial atomic descriptors and ML methods, our final trained HBA and HBD ML models achieve RMSEs of 3.8 kJ mol−1 (acceptors), and 2.3 kJ mol−1 (donors) on experimental test sets, respectively. This performance is comparable with previous models that are trained on experimental hydrogen bonding free energies, indicating that molecular QC data can serve as substitute for experiment. The potential ramifications thereof could lead to a full replacement of wetlab chemistry for HBA/HBD strength determination by QC. As a possible chemical application of our ML models, we highlight our predicted HBA and HBD strengths as possible descriptors in two case studies on trends in intramolecular hydrogen bonding.

Accurate Quantum Chemical Free Energies at Affordable Cost

Free energy sampling methods allow studying the full dynamics of activated processes. Unfortunately, the affordable accuracy of the potential describing the energy and forces of the system is usually rather low. Here we introduce a new method that by combining metadynamics and free energy perturbation allows calculating accurate quantum chemical free energies for chemical reactions. To prove the effectiveness of this new approach we study the SN2 reaction of CH3F + Cl- → CH3Cl + F- in vacuo and solvated by water. Comparisons are made with harmonic transition-state theory to show how this method could provide accurate equilibrium and rate constants for complex systems.

Phase-field model for growth and dissolution of a stoichiometric compound in a binary liquid.

We propose a simple formulation of the phase-field model for a stoichiometric compound growing in a binary liquid. In previous models, chemical free energies of stoichiometric compounds have been approximated by parabolic functions of composition; however, the curvature has been determined arbitrarily in spite of the fact that the stoichiometric composition was undesirably modified depending on the curvature. To avoid this uncertainty, we supposed that the chemical free energy of the stoichiometric compound is represented by a single value at a given temperature and derived the phase-field equations without the parabolic free-energy approximation. The phase mobility was derived both for diffusion- and interface-controlled solidification based on a thin interface limit analysis. We carried out numerical simulations of one-dimensional calculations both in diffusion-controlled and interface-controlled cases and found that the growth velocities agreed with the analytic predictions. We also examined two-dimensional solidification of a circular crystal and confirmed that the equilibrium state was shifted, as suggested by the Gibbs-Thomson effect. This study is an important step for phase-field modeling that includes stoichiometric compounds with their accurate thermodynamic properties.

The effect of Mn/Ni on thermodynamic properties of critical nucleus in Fe-Cu-Mn (Ni) ternary alloys

The aging- or radiation-induced hardening of Cu/Mn/Ni precipitates in Fe alloys is one of property degradation mechanisms in structural materials in nuclear reactors. Experiments show that aging or radiation leads the formation of Cu-rich precipitates, and the addition of Mn or Ni elements enhances the precipitation kinetics. In this work, the phase-field model coupled with the constrained string method have been applied to investigate the thermodynamic properties of critical nuclei such as the minimum energy path of Cu/Mn/Ni precipitation in Fe-Cu-Mn and Fe-Cu-Ni ternary alloys. The chemical free energies used in the model are taken from CALPHAD. The simulation results show that the formation of Cu/Mn/Ni clusters needs to overcome an energy barrier, and the precipitate has a Core-Shell structure. The thermodynamic properties of the critical nucleus are influenced by temperature and Cu/Mn/Ni overall concentrations, which are in accordance with the simulation results as well as the experimental observations.

Effect of Hydration and Base Contaminants on Sulfuric Acid Diffusion Measurement: A Computational Study

We used quantum chemical formation free energies of hydrated sulfuric acid-containing molecular clusters and a dynamic model to simulate a flow tube measurement, and determined the effective diffusion coefficient of sulfuric acid as a function of relative humidity. This type of measurement was performed by Hanson and Eisele, who presented and applied a fitting method to obtain equilibrium constants K1 and K2 for the formation of sulfuric acid mono- and dihydrates, respectively, from the experimentally determined diffusion coefficients. The fit is derived assuming that only H2SO4 molecules hydrated by up to two water molecules are present. To study the sensitivity of the results to this assumption, we implemented the same fit to the modeled diffusion coefficient data, computed including also larger H2SO4 hydrates with more than two waters. We show that according to quantum chemical equilibrium constants, the larger hydrates are likely to be present in nonnegligible amounts, which affects the effective diff...

Temporal Variation of a Protein Folding Energy Landscape in the Cell

Chemical reaction rate coefficients and free energies are usually time-independent quantities. Protein folding in vitro is one such reaction with a fixed energy landscape. However, in the milieu of the cell, the energy landscape can be modulated in space and time by fluctuations in the intracellular environment such as cytoskeletal rearrangements, changes in biomolecule concentrations, and large scale cellular reorganization. We studied the time dependence of the folding landscape of a FRET-labeled enzyme, yeast phosphoglycerate kinase (PGK-FRET). Living U2OS cells served as our test tube, and the mammalian cell cycle, a process strictly regulated in time, served as our clock. We found that both the rate of folding and the thermodynamic stability of PGK-FRET are cell cycle-dependent. We also assayed folding rates of PGK-FRET in spatial proximity to and far away from mitotic chromosomes. Our results show that expedited folding in DNA-rich regions cannot account for the faster rate of PGK-FRET folding in mitotic cells.

Quantum Chemical Free Energies: Structure Optimization and Vibrational Frequencies in Normal Modes.

A computational protocol is presented that uses normal mode coordinates for structure optimization and for obtaining harmonic frequencies by numerical differentiation. It reduces numerical accuracy problems encountered when density functional theory with plane wave basis sets is applied to systems with flat potential energy surfaces. The approach is applied to calculate Gibbs free energies for adsorption of methane, ethane, and propane on the Brønsted acidic sites of zeolite H-CHA. The values obtained (273.15 K, 0.1 MPa,), -0.25, -5.95, and -16.76 kJ/mol, respectively, follow the trend of the experimental values, which is not the case for results obtained with the standard approach (Cartesian optimization, frequencies from Cartesian distortions). Anharmonicity effects have been approximately taken into account by solving one-dimensional Schrödinger equations along each normal mode. This leads to a systematic increase of the Gibbs free energy of adsorption of 4.5, 5.0, and 3.1 kJ/mol for methane, ethane, and propane, respectively, making adsorption at a given pressure and temperature less likely. This is due to an increase of low vibrational frequencies associated with hindered translations and rotations of the adsorbed molecules and the floppy modes of the zeolite framework.

Calculation of Chemical Potentials and Occupancies in Clathrate Hydrates through Monte Carlo Molecular Simulations

The flexibility of the water lattice in clathrate hydrates and guest-guest interactions has been shown in previous studies to significantly affect the values of the thermodynamic properties, such as chemical potentials and free energies. Here we describe methods for computing occupancies, chemical potentials, and free energies that account for the flexibility of water lattice and guest-guest interactions in the hydrate phase. The methods are validated for a wide variety of guest molecules, such as methane, ethane, carbon dioxide, and tetrahydrodfuran by comparing the predicted occupancy values of guest molecules with those obtained from isothermal isobaric semigrand Monte Carlo simulations. The proposed methods extend the van der Waals and Platteuw theory for clathrate hydrates, and the Langmuir constant is calculated based on the structure of the empty hydrate lattice. These methods in combination with development of advanced molecular models for water and guest molecules should lead to a more thermodynamically consistent theory for clathrate hydrates.

Free energy barrier in the growth of sulfuric acid–ammonia and sulfuric acid–dimethylamine clusters

The first step in atmospheric new particle formation involves the aggregation of gas phase molecules into small molecular clusters that can grow by colliding with gas molecules and each other. In this work we used first principles quantum chemistry combined with a dynamic model to study the steady-state kinetics of sets of small clusters consisting of sulfuric acid and ammonia or sulfuric acid and dimethylamine molecules. Both sets were studied with and without electrically charged clusters. We show the main clustering pathways in the simulated systems together with the quantum chemical Gibbs free energies of formation of the growing clusters. In the sulfuric acid-ammonia system, the major growth pathways exhibit free energy barriers, whereas in the acid-dimethylamine system the growth occurs mainly via barrierless condensation. When ions are present, charged clusters contribute significantly to the growth in the acid-ammonia system. For dimethylamine the role of ions is minor, except at very low acid concentration, and the growing clusters are electrically neutral.

Revival of martensitic instability in Ga doped Ni–Mn–In alloys

We report here the results of transport and dc magnetization studies of Ga-doped Ni2Mn1.32In0.68 (Ni2Mn1.32In0.68−xGax, x = 0, 0.04, 0.08, 0.16, 0.20, and 0.28) alloys. The parent sample (x = 0) does not show any structural instability, however small Ga substitution at the In site (x = 0.08) suddenly induces martensitic transition in it. The studied alloys are all found to be ferromagnetic below about room temperature and the martensitic transition temperatures are found to be in the range between 175 K and 240 K depending upon x. Samples showing thermally driven maretnsitic transition (x≥ 0.08) are also found to be susceptible to the applied magnetic field, and both magnetization and magnetoresistance indicate the signature of field-induced transition. Upon cooling under a magnetic field, we observe kinetically arrested state which is particularly prominent in low Ga containing samples (x = 0.08, 0.16). It clearly demonstrate that these Ga doped samples posses all the properties of metamagnetic shape memory alloys. We argue that the magnetically arrested state in the alloys is closely connected to the competition between chemical and magnetic free energies associated with the martensitic and austenitic phases.