Equality Of Chemical Potentials Research Articles

Compaction and Segregation of DNA in Escherichia coli.

Theoretical and experimental approaches have been applied to study the polymer physics underlying the compaction of DNA in the bacterial nucleoid. Knowledge of the compaction mechanism is necessary to obtain a mechanistic understanding of the segregation process of replicating chromosome arms (replichores) during the cell cycle. The first part of this review discusses light microscope observations demonstrating that the nucleoid has a lower refractive index and thus, a lower density than the cytoplasm. A polymer physics explanation for this phenomenon was given by a theory discussed at length in this review. By assuming a phase separation between the nucleoid and the cytoplasm and by imposing equal osmotic pressure and chemical potential between the two phases, a minimal energy situation is obtained, in which soluble proteins are depleted from the nucleoid, thus explaining its lower density. This theory is compared to recent views on DNA compaction that are based on the exclusion of polyribosomes from the nucleoid or on the transcriptional activity of the cell. These new views prompt the question of whether they can still explain the lower refractive index or density of the nucleoid. In the second part of this review, we discuss the question of how DNA segregation occurs in Escherichia coli in the absence of the so-called active ParABS system, which is present in the majority of bacteria. How is the entanglement of nascent chromosome arms generated at the origin in the parental DNA network of the E. coli nucleoid prevented? Microscopic observations of the position of fluorescently-labeled genetic loci have indicated that the four nascent chromosome arms synthesized in the initial replication bubble segregate to opposite halves of the sister nucleoids. This implies that extensive intermingling of daughter strands does not occur. Based on the hypothesis that leading and lagging replichores synthesized in the replication bubble fold into microdomains that do not intermingle, a passive four-excluding-arms model for segregation is proposed. This model suggests that the key for segregation already exists in the structure of the replication bubble at the very start of DNA replication; it explains the different patterns of chromosome arms as well as the segregation distances between replicated loci, as experimentally observed.

Fractional Charge Density Functional Theory and Its Application to the Electro-inductive Effect

We employed the chemical potential equalization principle to demonstrate that fractional electrons are involved in the electro-inductive effect as well as the vibrational Stark effect. By the chemical potential model, we were able to deduce that the frontier molecular orbitals of immobilized molecules can provide valuable insight into these effects. To further understand and quantify these findings, we introduced fractional charge density functional theory (FC-DFT), a canonical ensemble approach for open systems. This method allows for the calculation of electronic energies, nuclear gradients, and the Hessian matrix of fractional electronic systems. To correct the spurious delocalization error commonly found in approximate density functionals for small systems, we imposed the Perdew-Parr-Levy-Balduz (PPLB) condition through linear interpolation of two adjacent integer points (LI-FC-DFT). Although this approach is relatively simple in terms of molecular modeling, the results obtained through LI-FC-DFT calculations predict the same trend seen in experimental reactivity and the frequency change of immobilized molecules.

CALCULATION OF THE MELTING POINTS OF ALKALI HALIDES USING THE THERMODYNAMIC PERTURBATION THEORY

A model for calculating phase equilibria between a liquid and a crystal is proposed, which makes it possible to evaluate the melting points of ionic compounds. The dependence of the melting temperatures of alkali halides on the cation-anion composition can be described in terms of ionic radii and polarizabilities using thermodynamic perturbation theory for the molten phase. The chemical potential of the crystal phase contains the Born-Mayer formula for the electrostatic part of the energy and the Debye formula for the vibration contribution. The full system of equations describing the equilibrium between liquid and solid includes not only the equality of chemical potentials, but also contains the equation of state to calculate the equilibrium density of melts at the crystallization point. One more equation of the system is necessary for the self-consistent computation of the characteristic Blum’s screening parameter within the mean spherical model of the ionic mixture. On this basis, the melting points of fluorides, chlorides, bromides and iodides of lithium, sodium, potassium, rubidium and cesium have been calculated. It has been shown that the combination of the reference mean-spherical model of charged hard spheres with different diameters and the perturbation due to the charge-induced dipoles into the chemical potentials of molten salts is a good basis for quantitative agreement with experimental data on the melting temperatures within a few percent. Moreover, the regularities of the change in the melting temperatures reduced to the Coulomb energy at the maximum contact of the cation and anion, as well as depending on the difference in the ionic radii of the salts, are discussed.

Reparameterization of the chemical-potential equalization model with DFTB3: A practical balance between accuracy and transferability.

To improve the performance of the third-order density-functional tight-binding method (DFTB3) for non-covalent interactions involving organic and biological molecules, a chemical-potential equalization (CPE) approach was introduced [J. Phys. Chem. A, 116, 9131 (2012)] and parameterized for the H, C, N, O, and S chemical elements [J. Chem. Phys., 143, 084123 (2015)]. Based largely on equilibrium structures, the parameterized DFTB3/CPE models were shown to exhibit improvements in molecular polarizabilities and intermolecular interactions. With more extensive analyses, however, we observe here that the available DFTB3/CPE models have two critical limitations: (1) they lead to sharply varying potential energy surfaces, thus causing numerical instability in molecular dynamics (MD) simulations, and (2) they lead to spurious interactions at short distances for some dimer complexes. These shortcomings are attributed to the employed screening functions and the overfitting of CPE parameters. In this work, we introduce a new strategy to simplify the parameterization procedure and significantly reduce free parameters down to four global (i.e., independent of element type) ones. With this strategy, two new models, DFTB3/CPE(r) and DFTB3/CPE(r†) are parameterized. The new models lead to smooth potential energy surfaces, stable MD simulations, and alleviate the spurious interactions at short distances, thus representing consistent improvements for both neutral and ionic hydrogen bonds.

Equilibrium structure of a dense trimesic acid monolayer on a homogeneous solid surface: from atomistic simulation to thermodynamics.

A general methodology for determining the thermodynamic characteristics of rigid organic crystals on the atomistic level is presented. The proposed approach is based on a combination of grid interpolation of the precalculated intermolecular potential and kinetic Monte Carlo simulation of the gas-crystal system with an explicit interphase. The two-phase system is stabilized in a wide range of external parameters with an imposed external potential and damping field. The damping field reduces the intermolecular potential at the edges of the crystals and turns it off in the gas phase. To determine the thermodynamic characteristics of a crystal the conditions of equality of chemical potentials in coexisting phases are used. The intermolecular pairwise potential can be calculated on the atomistic or quantum level. In the kinetic Monte Carlo simulations, a grid interpolation of the precalculated potential is performed on each iteration of the algorithm. We have applied the approach to the thermodynamic analysis of a dense monolayer of trimesic acid on a homogeneous surface. The calculated free energy and entropy for the dense "superflower" and filled chicken-wire phases obey the Gibbs-Duhem equation, which confirms the thermodynamic consistency of our approach. Using the proposed approach, we have revealed that the dense "superflower" phase becomes metastable at zero pressure and 470-500 K. Under these conditions, the filled chicken-wire structure with partially released hexagonal cages is thermodynamically favourable. The proposed approach is a potentially universal tool for the thermodynamic analysis of crystals formed by "rigid" organic molecules of any complexity on the atomistic level.

Unified polarizable electrode models for open and closed circuits: Revisiting the effects of electrode polarization and different circuit conditions on electrode-electrolyte interfaces.

A precise understanding of the interfacial structure and dynamics is essential for the optimal design of various electrochemical devices. Herein, we propose a method for classical molecular dynamics simulations to deal with electrochemical interfaces with polarizable electrodes under the open circuit condition. Less attention has been given to electrochemical circuit conditions in computation despite being often essential for a proper assessment, especially comparison between different models. The present method is based on the chemical potential equalization principle, as is a method developed previously to deal with systems under the closed circuit condition. These two methods can be interconverted through the Legendre transformation so that the difference in the circuit conditions can be compared on the same footing. Furthermore, the electrode polarization effect can be correctly studied by comparing the present method with conventional simulations with the electrodes represented by fixed charges, since both of the methods describe systems under the open circuit condition. The method is applied to a parallel-plate capacitor composed of platinum electrodes and an aqueous electrolyte solution. The electrode polarization effects have an impact on the interfacial structure of the electrolyte solution. We found that the difference in circuit conditions significantly affects the dynamics of the electrolyte solution. The electric field at the charged electrode surface is poorly screened by the nonequilibrium solution structure in the open circuit condition, which accelerates the motion of the electrolyte solution.

Grand-potential-based phase-field model of dissolution/precipitation: Lattice Boltzmann simulations of counter term effect on porous medium

Most of the lattice Boltzmann methods simulate an approximation of the sharp interface problem of dissolution and precipitation. In such studies the curvature-driven motion of interface is neglected in the Gibbs–Thomson condition. In order to simulate those phenomena with or without curvature-driven motion, we propose a phase-field model which is derived from a thermodynamic functional of grand-potential. Compared to the free energy, the main advantage of the grand-potential is to provide a theoretical framework which is consistent with the equilibrium properties such as the equality of chemical potentials. The model is composed of one equation for the phase-field ϕ coupled with one equation for the chemical potential μ. In the phase-field method, the curvature-driven motion is always contained in the phase-field equation. For canceling it, a counter term must be added in the ϕ-equation. For reason of mass conservation, the μ-equation is written with a mixed formulation which involves the composition c and the chemical potential. The closure relationship between c and μ is derived by assuming quadratic free energies for the bulk phases. The anti-trapping current is also considered in the composition equation for simulations with null solid diffusion. The lattice Boltzmann schemes are implemented in LBM_saclay, a numerical code running on various High Performance Computing architectures. Validations are carried out with analytical solutions representative of dissolution and precipitation. Simulations with or without counter term are compared on the shape of porous medium characterized by microtomography. The computations have run on a single GPU-V100.

On the thermodynamics of curved interfaces and the nucleation of hard spheres in a finite system.

We determine, for hard spheres, the Helmholtz free energy of a liquid that contains a solid cluster as a function of the size of the solid cluster by means of the formalism of the thermodynamics of curved interfaces. This is done at the constant total number of particles, volume, and temperature. We show that under certain conditions, one may have several local minima in the free energy profile, one for the homogeneous liquid and others for the spherical, cylindrical, and planar solid clusters surrounded by liquid. The variation of the interfacial free energy with the radius of the solid cluster and the distance between equimolar and tension surfaces are inputs from simulation results of nucleation studies. This is possible because stable solid clusters in the canonical ensemble become critical in the isothermal-isobaric ensemble. At each local minimum, we find no difference in chemical potential between the phases. At local maxima, we also find equal chemical potential, albeit in this case the nucleus is unstable. Moreover, the theory allows us to describe the stable solid clusters found in simulations. Therefore, we can use it for any combination of the total number of particles, volume, and global density as long as a minimum in the Helmholtz free energy occurs. We also study under which conditions the absolute minimum in the free energy corresponds to a homogeneous liquid or to a heterogeneous system having either spherical, cylindrical, or planar geometry. This work shows that the thermodynamics of curved interfaces at equilibrium can be used to describe nucleation.

Embedding Quantum Statistical Excitations in a Classical Force Field.

Quantum-mechanically driven charge polarization and charge transfer are ubiquitous in biomolecular systems, controlling reaction rates, allosteric interactions, ligand-protein binding, membrane transport, and dynamically driven structural transformations. Molecular dynamics (MD) simulations of these processes require quantum mechanical (QM) information in order to accurately describe their reactive dynamics. However, current techniques-empirical force fields, subsystem approaches, ab initio MD, and machine learning-vary in their ability to achieve a consistent chemical description across multiple atom types, and at scale. Here we present a physics-based, atomistic force field, the ensemble DFT charge-transfer embedded-atom method, in which QM forces are described at a uniform level of theory across all atoms, avoiding the need for explicit solution of the Schrödinger equation or large, precomputed training data sets. Coupling between the electronic and atomistic length scales is effected through an ensemble density functional theory formulation of the embedded-atom method originally developed for elemental materials. Charge transfer is expressed in terms of ensembles of ionic state basis densities of individual atoms, and charge polarization, in terms of atomic excited-state basis densities. This provides a highly compact yet general representation of the force field, encompassing both local and system-wide effects. Charge rearrangement is realized through the evolution of ensemble weights, adjusted at each dynamical time step via chemical potential equalization.

Controlling potential difference between electrodes based on self-consistent-charge density functional tight binding.

A proper understanding and description of the electronic response of the electrode surfaces in electrochemical systems are quite important because the interactions between the electrode surface and electrolyte give rise to unique and useful interfacial properties. Atomistic modeling of the electrodes requires not only an accurate description of the electronic response under a constant-potential condition but also computational efficiency in order to deal with systems large enough to investigate the interfacial electrolyte structures. We thus develop a self-consistent-charge density functional tight binding based method to model a pair of electrodes in electrochemical cells under the constant-potential condition. The method is more efficient than the (ab initio) density functional theory calculations so that it can treat systems as large as those studied in classical atomistic simulations. It can also describe the electronic response of electrodes quantum mechanically and more accurately than the classical counterparts. The constant-potential condition is introduced through a Legendre transformation of the electronic energy with respect to the difference in the number of electrons in the two electrodes and their electrochemical potential difference, through which the Kohn-Sham equations for each electrode are variationally derived. The method is applied to platinum electrodes faced parallel to each other under an applied voltage. The electronic response to the voltage and a charged particle is compared with the result of a classical constant-potential method based on the chemical potential equalization principle.

Hydrogen and Deuterium Molecular Escape from Clathrate Hydrates: "Leaky" Microsecond-Molecular-Dynamics Predictions.

It is predicted herewith that the leakage of both hydrogen (H2) and deuterium (D2) from sII clathrate hydrates, borne of guest chemical-potential equalization driving enhanced nonequilibrium intercage hopping, should be observable experimentally. To this end, we have designed simulations to realize and study this process by microsecond molecular dynamics within the temperature range of 150–180 K—for which the hydrate lattice was found to be stable. In this pursuit, we considered initial large-cage (51264) guest occupancies of 1–4, with single occupation of 512 cavities. Examining transient, nonequilibrium intercage hopping, we present a lattice-escape activation energy for the four nominal large-cage occupancies (1–4), by fitting to the hydrate-leakage rate. The intercage hopping of H2 and D2 was studied using Markov-chain models and expressed at different temperatures and large-cage occupancies. The free energy of guest “binding” in the large and small cages was also computed for all of the occupancies. Toward equilibrium, following the majority of H2/D2 escape via leakage, the percentage of occupancies was calculated for both H2 and D2 for all of the systems for all initial nominal large-cage occupancies; here, not unexpectedly, double occupancies occurred more favorably in large cages and single occupancies dominated in small cages.

Polarizability relaxation in water/ethanol mixtures

Molecular dynamics simulations are used to investigate structural and dynamical properties of liquid mixtures of water and ethanol over the entire range of compositions from neat liquid water to neat liquid ethanol. Particular emphasis is given to the time relaxation of the anisotropic collective polarizability and the low-frequency part of the depolarized Raman spectra. While the dynamics was carried out using simulations with standard force fields for water and ethanol, the post-analysis was performed employing the chemical potential equalization (CPE) method. For comparison purposes, the CPE results are compared to those obtained with the traditional interaction-induced model. Both methods are able to capture the basic shape and position of the Raman bands. Polarizability response in time and frequency domains is disentangled in permanent, interaction-induced and induced-permanent (cross) terms. Our findings suggest that the polarizability relaxation of water is more sensitive to environmental fluctuations. Once water signal remains covered by the ethanol contribution even in water-rich concentrations, some water polarizability features were unveiled and correlated with H-bond dynamics. The permanent term, representative of the reorientational dynamics, captures the short-time oscillations and responds for a part of the total relaxation, while the long-range interaction-induced contribution is responsible for great part of the total polarizability relaxation.

The unhappy chaperone.

Chaperones protect other proteins against misfolding and aggregation, a key requirement for maintaining biological function. Experimental observations of changes in solubility of amyloid proteins in the presence of certain chaperones are discussed here in terms of thermodynamic driving forces. We outline how chaperones can enhance amyloid solubility through the formation of heteromolecular aggregates (co-aggregates) based on the second law of thermodynamics and the flux towards equal chemical potential of each compound in all phases of the system. Higher effective solubility of an amyloid peptide in the presence of chaperone implies that the chemical potential of the peptide is higher in the aggregates formed under these conditions compared to peptide-only aggregates. This must be compensated by a larger reduction in chemical potential of the chaperone in the presence of peptide compared to chaperone alone. The driving force thus relies on the chaperone being very unhappy on its own (high chemical potential), thus gaining more free energy than the amyloid peptide loses upon forming the co-aggregate. The formation of heteromolecular aggregates also involves the kinetic suppression of the formation of homomolecular aggregates. The unhappiness of the chaperone can explain the ability of chaperones to favour an increased population of monomeric client protein even in the absence of external energy input, and with broad client specificity. This perspective opens for a new direction of chaperone research and outlines a set of outstanding questions that aim to provide additional cues for therapeutic development in this area.

A polarizable molecular dynamics method for electrode-electrolyte interfacial electron transfer under the constant chemical-potential-difference condition on the electrode electrons.

Electron transfer (ET) at an electrode-electrolyte interface is a crucial step in electrochemical reactions. Computational simulations play an important role in unraveling the effects of the interfacial structure of the electrolyte solution and the applied voltage on the energetics and kinetics. In such simulations, it is important to know the chemical potentials of the electrons in the cathode and the anode and the nonequilibrium response of the interface to the abrupt change in the charge distribution in the system. We have developed a classical fully polarizable molecular dynamics method to deal with the interfacial nonadiabatic ET processes in which both the metal electrodes and the solvent molecules are electronically polarizable. The chemical potential of the electrons in each electrode is introduced based on the chemical potential equalization principle, and their difference between the cathode and the anode is kept equal to the applied voltage. We have investigated the effects of the electronic polarization of the solvent molecules on the interfacial structure of the electrolyte solution and the Marcus free energy curves. The effects are non-negligible for the accurate evaluation of the reorganization energies but become less significant as the redox species comes closer to the electrode surface, where the electronic polarization of the metal electrode plays a more dominant role.

A model based on the equality of chemical potentials for describing the liquid-liquid interfaces of water-hydrocarbons up to high pressures

A reliable model was used to describe the interfacial tension, composition, and density of the liquid-liquid interfaces of water-hydrocarbons. The parachor model was combined with the equality of the chemical potential of components at the interface and the bulk liquid. The fugacity coefficient was used for computing chemical potentials. To compute the fugacity coefficients of the components, various types of equations of state (The Valderrama Patel-Teja, cubic plus association, and the simplified Perturbed-Chain Statistical Association Fluid Theory) were utilized. These models were applied to the temperature and the pressure range of (285.65–423) K and (1–3000) bar, respectively. The adjustable parameters of these models were regressed based on the experimental interfacial tensions of (water/hydrocarbon) binary systems at the pressure of 1 bar. These adjustable parameters were used to predict the interfacial tension, composition, and density of (water/hydrocarbon) binary systems at high pressures. It was found that Valderrama Patel-Teja (AAD% = 1.49) and cubic plus association (AAD% = 2.33) equations of state had the best results for ternary and quaternary systems, respectively.

Spin transfer and proximity effects in case of FePt (L1) nanoparticles coated with P3HT

Nanocomposites based on half-metallic FePt (L10) magnetic nanoparticles coated with the semiconducting conjugated polymer poly(3-hexylthiophene-2,5-diyl) (P3HT) show a significant reduction in the magnetic coercivity. This study adopts a physical approach based on chemical potential equalization at the interface. The underlying charge/spin transfer mechanism unveils an imbalance: only spin-down polarized electrons are allowed to be transferred from the semiconductor to the half-metal (spin-down) conduction band, while spin-up states remain blocked at the interface. This process determines an excess of spin-up states on the P3HT side, and due to a RKKY mechanism, this effective spin system becomes ferromagnetic polarized. Due to this proximity effect, the conjugate polymer becomes exchange coupled to the hard magnetic FePt (L10) phase, thus reducing the coercivity of the half-metal. These processes make this type of composite suitable for magnetic recording applications.

Predicting the surface tension of mixtures of fatty acid ethyl esters and biodiesel fuels using UNIFAC activity coefficients

This work presents the use of a formal thermodynamic model together with UNIFAC activity coefficients model, without any further adjustable parameter, to predict the surface tension of biodiesel fuels based on the equality of chemical potentials between the vapor-liquid interface and liquid bulk. The biodiesel samples included in this work were reported previously in the open literature. They were produced from vegetable oils such as: canola, coconut, corn, cottonseed, hazelnut, lard, palm, peanut, rapeseed, safflower, soybean, sunflower, and Walnut. Surface tension values for 18 samples of binary, ternary and quaternary mixtures of fatty acid ethyl esters (FAEEs) at T = 298.15 were predicted with an average absolute relative deviation (AARD) = 1.39%. Surface tension values for 31 biodiesel samples composed by fatty acid methyl esters (FAMEs) were also predicted at temperatures from 303.15 K to 353.15 K. The AARD value obtained for the 78 experimental points of biodiesel samples was 1.86% which shows a very good agreement with experimental measurements. In the UNIFAC method, predictions of surface tension values for the mixtures are based on the knowledge of the values of the surface tension for the pure components; these values were obtained from different sources. Also, two simple mixing rules on mass and mole fraction basis were used to predict the surface tension of biodiesel fuels. The AARD value obtained from the comparison between experimental and calculated values were: 2.77% and 2.91% for mixing rules on mass and mole fractions, respectively.

Comment on “Surface properties of ethanol/water mixture: Thickness and composition”

A controversial discussion regarding the estimation of surface thickness in aqueous ethanol as calculated by Phan and co-workers (2019) from neutron reflectivity experiments and by Bagheri et al. (2016) and Santos and Reis (2018) from surface tension data and equality of chemical potentials is addressed. The theoretical link among equilibrium mole fractions, Gibbs excess concentration, surface molar volume and interfacial thickness developed by Phan and co-workers is rearranged into an explicit expression for the calculation of thickness, which is shown to be inconsistent with their Gibbs excess concentration estimating equation from neutron reflectivity experiments. A correction is proposed, and the recalculated equivalent thickness values present an increase, with increasing ethanol contents, in fair agreement with the values reported by Santos and Reis (2018).

Numerical Simulation of Non-Equilibrium Isochoric Phase Transitions in Hydrocarbon Mixtures

Numerical simulations of phase behavior in multicomponent hydrocarbon mixtures is an essential part of petroleum reservoir engineering practice. Almost all industry-adopted models are based on equilibrium assumptions. The condition of Gibbs energy minimum, or equality of chemical potentials, combined with the equation of state (EoS), e.g. the Peng-Robinson EoS, for each phase and with balance conditions for concentrations are used to compute phase mole fractions and compositions (component concentrations in the phases). However, experimental and field data show that in a number of important real situations equilibrium assumptions are not valid. In the previous study of Indrupskiy et al. (Computational Geosciences, 21(5), 2017) a unified model and numerical algorithms were presented for isothermal non-equilibrium phase behavior simulations in petroleum engineering applications. The model is based on the relaxation equation for the component chemical potentials difference between phases. It was verified on field data; however, only integral behavior of the system (a gas-condensate reservoir) was available to be matched. In the current study, we extended the non-equilibrium model to isochoric processes and developed a numerical algorithm which allowed to perform direct simulation of laboratory experiments with a multicomponent hydrocarbon mixture and validate the non-equilibrium model. The experimental data were successfully matched with the model simulations. The model and algorithm are suitable for equilibrium and non-equilibrium isochoric phase behavior simulations with synthetic and real multicomponent hydrocarbon mixtures (oils and gas-condensates).

A chemical potential equalization approach to constant potential polarizable electrodes for electrochemical-cell simulations.

Atomistic modeling of electrochemical systems is one of the most challenging topics in the field of molecular simulations. We derive the equations for modeling constant potential polarizable electrodes in electrochemical-cell simulations based on the chemical potential equalization principle. They reduce to those derived by Siepmann and Sprik [J. Chem. Phys. 102, 511 (1995)], later arranged by Reed, Lanning, and Madden [J. Chem. Phys. 126, 084704 (2007)] under some assumptions. The present approach clarifies the physical meaning of the total energy of a system that includes classical polarizable electrodes, which is important in order to analyze the energetics of chemical phenomena at electrode-electrolyte interfaces. The effects of the Hubbard U parameter of an electrode atom are discussed in connection with the perfect conductor limit for a metal electrode.