Constant Chemical Potential Research Articles

Polymorph-Specific Solubility Prediction of Urea Using Constant Chemical Potential Molecular Dynamics Simulations.

Molecular dynamics simulations offer a robust approach to understanding the material properties within a system. Solubility is defined as the analytical composition of a saturated solution expressed as a proportion of designated solute in a designated solvent, according to IUPAC. It is a critical property of compounds and holds significance across numerous fields. Various computational techniques have been explored for determining solubility, including methods based on chemical potential determination, enhanced sampling simulation, and direct coexistence simulation, and lately, machine learning-based methods have shown promise. In this investigation, we have utilized Constant Chemical Potential Molecular Dynamics, a method rooted in direct coexistence simulation, to predict the solubility of urea polymorphs in aqueous solution. The primary purpose of using this method is to overcome the limitation of the direct simulation method by maintaining a constant chemical potential for a sufficiently long time. Urea is chosen as a prototypical system for our study, with a particular focus on three of its polymorphs. Our approach effectively discriminates between the polymorphs of urea based on their respective solubility values; polymorph III is found to have the highest solubility, followed by forms IV and I.

Sterol-lipids enable large-scale, liquid-liquid phase separation in bilayer membranes of only 2 components.

A wide diversity of bilayer membranes, from those with hundreds of lipids (e.g., vacuoles of living yeast cells) to those with very few (e.g., artificial vesicles) phase separate into micron-scale liquid domains. The number of components required for liquid-liquid phase separation has been perplexing: only two should be necessary, but more are required except in extraordinary circumstances. What minimal set of molecular characteristics leads to liquid-liquid phase separation in bilayer membranes? This question inspired us to search for single, joined "sterol-lipid" molecules to replace both a sterol and a phospholipid in membranes undergoing liquid-liquid phase separation. By producing phase-separating membranes with only two components, we mitigate experimental challenges in determining tie-lines and in maintaining constant chemical potentials of lipids.

Effect of doping on domain suppression in the presence of hot electrons in semiconducting achiral carbon nanotubes

Effect of doping semiconducting achiral carbon nanotubes on domain suppression prerequisite for potential generation of terahertz radiations in the presence of hot electrons has been theoretically considered. This was done by solving the semiclassical Boltzmann's transport equation in the presence of hot electrons source to derive the current density as a function of constant electric field and chemical potential of semiconducting achiral carbon nanotubes (CNTs). Plots of normalized current density versus electric field strength for semiconducting achiral CNTs as the chemical potential (μ) representing the degree of doping increases from 1.4 eV to 2.0 eV (i.e. heavily doped CNT) revealed an increase in positive differential conductivity (PDC) that results in enhancement of domain suppression prerequisite for generation of terahertz radiations. Also, it has been observed that PDC which is associated with domain suppression increases as the relative thickness and carrier temperature of semiconducting CNTs increase. Therefore, the study predicts heavily doped larger radius semiconducting achiral CNT at a higher carrier temperature as a better candidate for generation of terahertz radiations whose applications are relevant in current-day technology, industry, and research.

Positivity preserving density matrix minimization at finite temperatures via square root.

We present a Wave Operator Minimization (WOM) method for calculating the Fermi-Dirac density matrix for electronic structure problems at finite temperature while preserving physicality by construction using the wave operator, i.e., the square root of the density matrix. WOM models cooling a state initially at infinite temperature down to the desired finite temperature. We consider both the grand canonical (constant chemical potential) and canonical (constant number of electrons) ensembles. Additionally, we show that the number of steps required for convergence is independent of the number of atoms in the system. We hope that the discussion and results presented in this article reinvigorate interest in density matrix minimization methods.

Retrospective rationalization of disparities between the concentration dependence of diffusion coefficients obtained by boundary spreading and dynamic light scattering.

This study establishes the existence of substantial agreement between published results from traditional boundary spreading measurements (including synthetic boundary measurements in the analytical ultracenrifuge) on two globular proteins (bovine serum albumin, ovalbumin) and the concentration dependence of diffusion coefficient predicted for experiments conducted under the operative thermodynamic constraints of constant temperature and solvent chemical potential. Although slight negative concentration dependence of the translational diffusion coefficient is the experimentally observed as well as theoretically predicted, the extent of the concentration dependence is within the limits of experimental uncertainty inherent in diffusion coefficient measurement. Attention is then directed toward the ionic strength dependence of the concentration dependence coefficient ([Formula: see text]) describing diffusion coefficients obtained by dynamic light scattering, where, in principle, the operative thermodynamic constraints of constant temperature and pressure preclude consideration of results in terms of single-solute theory. Nevertheless, good agreement between predicted and published experimental ionic strength dependencies of [Formula: see text] for lysozyme and an immunoglobulin is observed by a minor adaptation of the theoretical treatment to accommodate the fact that thermodynamic activity is monitored on the molal concentration scale because of the constraint of constant pressure that pertains in dynamic light scattering experiments.

Non-constancy of the bulk resistance of ionophore-based ion-selective membranes within the Nernstian response range: A semi-quantitative explanation

The non-constancy of the bulk resistance of solvent-polymeric ion-selective membranes containing ionophores is semi-quantitatively explained in view of micro-heterogeneity of membranes due to water uptake. Membranes are considered containing a dispersed aqueous sub-phase (water droplets) within the organic sub-phase (plasticized polymer). It is assumed that charged species in the membrane (ion-ionophore complexes and ion-exchanger ions) are confined in the organic sub-phase owing to their lipophilicity. This entails two inferences: (1) part of the membrane volume is excluded from the transportation of charged species, and (2) the average path length of the charged species transfer across membranes increases because these species have to circumvent water droplets. Because of this, the membrane bulk resistance increases along with the increase of water uptake. The presented results of the theoretical account based on this conjecture are consistent with experimental data. The increase of water uptake alongside the dilution of the external aqueous solution is considered thermodynamically. It is shown that the increase of water uptake from diluted solutions with almost constant chemical potential of water is caused by an interplay between the osmotic pressure, surface tension at the water - polymer matrix curved interface and the elasticity of the membrane matrix.

Analysis of the Conditions of Mechanical Equilibrium on the Curved Surface of a Vapor–Liquid System in a Gravitational Field

A thermodynamic analysis of mechanical equilibrium conditions is performed for the curved interface of a vapor–liquid system in the gravitational field potential with regard to ratios of experimental times of relaxation of thermodynamic parameters (momentum, energy, and mass). In a kinetic analysis of the relaxation stage of reaching the equilibrium state, it is revealed that it is important to consider the physical nature of the boundary of separating phases. The mechanical model of the boundary is one with an intermediate foreign film preventing the attainment of chemical equilibrium between the neighboring phases. The real boundary of coexisting phases has a variable density profile corresponding to the condition of the constant chemical potential throughout the region of transition and in the neighboring coexisting phases. The absence of an intermediate film excludes the priority of the mechanical equilibrium over the chemical equilibrium and results in pressure being the function of local temperature and chemical potential values (excluding the application of the Laplace equation). Considering times of relaxation is found to change the familiar Gibbs expression for the pressure jump between coexisting vapor and fluid as functions of the boundary in the gravitational field potential. A consequence of considering the correct ratio of momentum and mass times of relaxation is discussed: the phase equilibrium conditions of a separating vapor–liquid system in combined gravitational and surface force fields must be analyzed in order to solve problems of the capillary theory.

Axial-Vector Form Factor of Nucleons in the Isospin Medium from the Hard-Wall AdS/QCD Model

We study the axial-vector form factor of the nucleons in a constant and homogenous isospin chemical potential using holographic QCD. Nucleon mass splitting in such an isospin medium is taken into account. According to AdS/CFT correspondence, the critical value of the isospin chemical potential equals to UV- boundary value of the time component of the bulk gauge field. We calculate the axial-vector form factor of the proton and neutron in such background in the framework of the hard-wall model and plot the form factors for the isospin chemical potential critical value.

Boundary-Monte Carlo Method for Neutral and Charged Confined Fluids

In this work, we describe a new Monte Carlo (MC) simulation method to investigate highly coupled fluids in confined geometries at a constant chemical potential. This method is based on so-called multi-scale Hamiltonian methods, wherein the chemical potential is determined using a more amenable Hamiltonian for a fluid in an "outer" region, which facilitates standard methods, such as grand canonical MC simulations or Widom's particle insertion method. The (inner region) fluid of interest is placed in diffusive contact with the simpler outer fluid via a boundary zone wherein the Hamiltonian is transformed. The current method utilizes an ideal fluid for the outer regions, which allows for implicit rather than explicit simulations. Only the boundary and inner region need explicit consideration; hence, the nomenclature used is boundary-Monte Carlo. We illustrate the utility of the method for simple neutral and charged fluids in cylindrical and planar pores. In the latter case, we use a dense room-temperature ionic liquid model and illustrate how the boundary zone establishes a proper Donnan equilibrium between inner and outer fluids in the presence of charged planar electrodes. Thus, the method allows direct calculation of properties such as the differential capacitance, without the need for additional difficult calculations of the requisite Donnan potential.

Giant compliance and spontaneous buckling of beams containing mobile solute atoms

Recent experiments have shown that the elastic compliance of a porous metal can be substantially enhanced when mobile solute is alloyed into interstitial sites of the crystal lattice. The observations agree with predictions – due to Gorsky and to Larché and Cahn – for the elasticity of open systems in which the elastic responses is probed at constant chemical potential. The underlying mechanism involves an exchange of solute between tensile and compressive fibers in beam-like elements of the microstructure. Here, we analyze the elastic deformation of such elements in a continuum approach, accounting explicitly for the coupling between chemistry and mechanics. We consider a regular solution with linear elasticity in the limit of constant composition and with a linear composition-strain coupling. Materials parameters are matched to experiments on Pd-H, so as to realistically account for the balance between chemical and mechanical energies. At constant chemical potential, the elastic response can be strongly nonlinear. With decreasing temperature, the bending goes from a monotonic moment-curvature relation to one including a horizontal tangent and, hence, a state of giant bending compliance. Reducing the temperature further brings first a temperature interval with a simple bistability and finally one with degeneracy including – depending on the chemical potential or on the mean solute fraction – the possibility of finite curvature at zero moment. Quenching the uniform solution into a two-phase region of the alloy phase diagram can lead to spontaneous buckling at no load. Furthermore, degenerate moment-curvature relations allow for bending states in which the radius is not a constant along the beam axis. Intervals of lar ge strain at constant load are similar to superelasticity, but the underlying phase transformation is here not martensitic.

Improved well-balanced free-energy lattice Boltzmann model for two-phase flow with high Reynolds number and large viscosity ratio

Spurious velocities and inaccurate density properties arising from the imbalance of discretized forces at discrete level are frequently observed in numerical simulation of multiphase flows based on lattice Boltzmann equation (LBE) models. In this paper, an improved well-balanced free-energy LBE model is proposed for two phase flows with high Reynolds numbers and large viscosity differences based on the well-balanced LBE [Guo et al., Phys. Fluids 33, 031709 (2021)]. To this end, a free parameter associated with the shear rate is introduced into the equilibrium distribution function. This results in a fluid viscosity that is dependent not only on the relaxation time but also on the introduced parameter. The relaxation time can be chosen to improve the numerical stability and accuracy, while the viscosity is mainly determined by the new parameter. To test the capability of the present model in capturing discrete equilibrium states, both one-dimensional flat interface and two-dimensional stationary droplet are simulated. Numerical results show that the present model is capable of eliminating spurious velocities and maintaining a constant chemical potential when the system reaches an equilibrium state. To further validate the performance of the present LBE for dynamic problems, both binary droplet collision and single bubble rising are performed, which demonstrates that the present model has the capability to deal with two phase flows with high Reynolds number and large viscosity ratio.

Statistical study of thermoradiative and photovoltaic cells based on a two-level model

We use a two-level energy model to understand the conversion process that takes place in thermoradiative cells and to compare it with the conversion process that happens in photovoltaic cells. In this way, we show that in both kinds of converters the conversion process can be studied as the succession of a change in the populations of the levels that occur at constant chemical potential and a change in the value of the chemical potential of the two levels that happens while keeping their populations constant. As an application of the model, we will discuss why in thermoradiative cells the open-circuit voltage is negative while it is positive in photovoltaic cells. We also show that the expression for the open-circuit voltage is the same in both kinds of cells but that due to the values of the temperatures it is negative in thermoradiative cells and positive in photovoltaic ones.

Chiral magnetic effect and three-point function from AdS/CFT correspondence

The chiral magnetic effect with a fluctuating chiral imbalance is more realistic in the evolution of quark-gluon plasma, which reflects the random gluonic topological transition. Incorporating this dynamics, we calculate the chiral magnetic current in response to space-time dependent axial gauge potential and magnetic field in AdS/CFT correspondence. In contrast to conventional treatment of constant axial chemical potential, the response function here is the AVV three-point function of the mathcal{N} = 4 super Yang-Mills at strong coupling. Through an iterative solution of the nonlinear equations of motion in Schwarzschild-AdS5 background, we are able to express the AVV function in terms of two Heun functions and prove its UV/IR finiteness, as expected for mathcal{N} = 4 super Yang-Mills theory. We found that the dependence of the chiral magnetic current on a non-constant chiral imbalance is non-local, different from hydrodynamic approximation, and demonstrates the subtlety of the infrared limit discovered in field theoretic approach. We expect our results enrich the understanding of the phenomenology of the chiral magnetic effect in the context of relativistic heavy ion collisions.

Bias-dependent diffusion of a H2O molecule on metal surfaces by the first-principles method under the grand-canonical ensemble

We investigate the process by which a water molecule diffuses on the surface of an Al(111) electrode under constant bias voltage by first-principles density functional theory. To understand the diffusion path of the water on the Al(111), we calculated the minimum energy path (MEP) determined by the nudged elastic band method in combination with constant electron chemical potential (constant-$\mu_{\rm e}$) methods. The simulation shows that the MEP of the water molecule, its adsorption site, and the activation barrier strongly depend on the applied bias voltage. This strong dependence of the water diffusion process on the bias voltage is in good agreement with the result of a previous scanning tunneling microscopy (STM) experiment. The agreement between the theoretical and experimental results implies that accurate treatment of bias voltage plays a significant role in understanding the interaction between the electric field and the surface of the material. Comparative studies of the diffusion process with the constant total number of electrons (constant-$N_\mathrm{e}$) scheme show that the absence of strong interaction between the molecular dipole and the electric field leads to a different understanding of how water diffuses on a metal surface. The proposed constant-$\mu_{\rm e}$ scheme is a realistic tool for the simulation of reactions under bias voltage not only using STM but also at the electrochemical interface.

The density-of-States and equilibrium charge dynamics of redox-active switches

The density-of-states of redox-active molecular scale switches is the origin of a measurable pseudo-capacitance that possesses an intrinsic quantum capacitive nature with applications that spans nanoscale electronics, molecular sensing, field-effect devices and so on. In the present work, we demonstrate that the equilibrium occupancy and shape of this density-of-states, which is associated with the energy state of the interface, can be accurately simulated using statistical mechanics, particularly by applying computational methods based on a constant (electro)chemical potential. This permits the simulation of experimental current-voltage responses and, consequently, the prediction and design of the properties of derived nanoscale devices.

Well-balanced lattice Boltzmann model for two-phase systems

The standard two-phase lattice Boltzmann equation (LBE) method usually fails to capture the physical equilibrium state (zero velocity and constant chemical potential). Consequently, spurious velocities and inconsistent thermodynamic density properties are frequently encountered in LBE simulations. In this work, based on a rigorous analysis of the discrete balance equation of LBE, the structure of force imbalance due to discretization errors is identified. Then, a well-balanced LBE model is proposed, which can achieve the discrete equilibrium state. The well-balance properties of the model are confirmed by simulating a flat interface problem and a droplet system.

First-principles description of electrocatalytic characteristics of graphene-like materials.

Graphene-like materials (GLMs) have received much attention as a potential alternative to precious metal-based electrocatalysts. However, the description of their electrocatalytic characteristics may still need to be improved, especially under constant chemical potential. Unlike the case of conventional metal electrodes, the potential drop across the electrical double layer (ϕD) at the electrode-electrolyte interface can deviate substantially from the applied voltage (ϕapp) due to a shift of the Dirac point (eϕG) with charging. This may in turn significantly alter the interfacial capacitance (CT) and the relationship between ϕapp and free-energy change (ΔF). Hence, accurate evaluation of the electrode contribution is necessary to better understand and optimize the electrocatalytic properties of GLMs. In this work, we revisit and compare first-principles methods available to describe the ϕapp-∆F relation. Grand-canonical density functional theory is used to determine ΔF as a function of ϕapp or electrode potential (ϕq), from which the relative contribution of eϕG is estimated. In parallel, eϕG is directly extracted from a density functional theory analysis of the electronic structure of uncharged GLMs. The results of both methods are found to be in close agreement for pristine graphene, but their predictions deviate noticeably in the presence of adsorbates; the origin of the discrepancy is analyzed and explained. We then evaluate the application of the first-principle methods to prediction of the electrocatalytic processes, taking the reduction (hydrogenation) and oxidation (hydroxylation) reactions on pristine graphene as examples. Our work highlights the vital role of the modification of the electrode electronic structure in determining the electrocatalytic performance of GLMs.

Variational Principle for Eigenmodes of Reactivity in Conceptual Density Functional Theory.

In conceptual density functional theory, reactivity indexes as the Fukui function, the global hardness/softness, and hardness/softness kernels are fundamental linear responses extensively studied to predict the nucleophilic and electrophilic propensities of atoms in molecules. We demonstrate that the hardness/softness kernels of an isolated system can be expanded in eigenmodes, solutions of a variational principle. These modes are divided into two groups: the polarization modes and the charging modes. The eigenvectors of the polarization modes are orthogonal to the Fukui function and can be interpreted as densities induced at a constant chemical potential. The charging modes of an isolated system are associated with virtual charge transfers weighted by the Fukui function and obey an exact nontrivial sum rule. The exact relation between these charging eigenmodes and those of the polarizability kernel is established. The physical interpretation of the modes is discussed. Applications of the present findings to the Thomas–Fermi and von Weizacker kinetic energy functionals are presented. For a confined free quantum gas, described by the von Weizacker kinetic energy functional, we succeed to derive an approximate analytical solution for the Fukui function and for hardness/softness and polarizability kernels. Finally, we indicate how numerical calculations of the hardness kernel of a molecule could be performed from the Kohn–Sham orbitals.

Growth rate of lithium filaments in ceramic electrolytes

Lithium-ion batteries with single ion-conductor ceramic electrolytes short-circuit when subjected to charging currents above a critical current density. Here, we analyse the rate at which a lithium (Li) filament (sometimes referred to as a dendrite) will grow from the cathode towards the anode during charging of such batteries. The filament is modelled as a climbing edge dislocation with its growth occurring by Li+ flux from the electrolyte into the filament tip at constant chemical potential. The growth rate is set by a balance between the reduction of free-energy at the filament tip and energy dissipation associated with the resistance to the flux of Li+ through the filament tip. For charging currents above the critical current density, the filament growth rate increases with decreasing filament tip resistance. Imperfections, such as voids in the Li cathode along the electrolyte/cathode interface, decrease the critical current density but filament growth rates are also lower in these cases as filament growth rates scale with the charging currents. The predictions of the model are in excellent quantitative agreement with measurements and confirm that above the critical current density a filament can traverse the electrolyte in minutes or less. This suggests that initiation of filament growth is the critical step to prevent short-circuiting of the battery.

Molecular dynamics simulations of polymerisation and crystallisation at constant chemical potential

ABSTRACT To investigate the complex process of polymer crystallisation during polymerisation, we develop a molecular dynamics (MD) simulation method with dynamic insertion and removal of comonomers in the simulation box. This method is based on Constant Chemical Potential Molecular Dynamics (CμMD) method [J Chem Phys. 2015; 142: 144113], but there is no need to store large amounts of molecules in the reservoir, thus this new method is effective for complex molecular systems. With the validation of this method through MD simulations of polymerisation and crystallisation of polymeric molecules at different temperatures, this new simulation scheme demonstrates great potential in the studies of complex chain-like systems with chemical reactions.