Equality Of Chemical Potentials Research Articles

On the formulation of the material equilibrium condition for a dissolving solid nanoparticle

Widely known Gibbs' relationship predicting a difference of chemical potentials in a small solid particle and in a surrounding fluid phase at equilibrium is shown to refer to a real or imaginary bulk phase inside the particle. A similar relationship derived for the real surface monolayer of a nanoparticle exhibits the equality of chemical potentials at equilibrium, which allows for experimental measurement of the surface chemical potential of a dissolving solid nanoparticle.

A new surface equation of state: Hydrophobic–hydrophilic contributions to the activity coefficient

A new surface equation of state with two thermodynamic parameters: the critical micellar concentration and the surface compressibility factor is presented, which comes from the experimental evidence and the equality of the Volmer's surface chemical potential and the bulk chemical potential at the diluted region under the symmetric activity coefficients convention. The new surface equation of state contains in its boundaries the exact relationship between the standard Gibbs energy of adsorption and the standard energy of micellization, and additionally allows the interpretation of the activity coefficient at infinite dilution in the light of the hydrophobic effect.

Key Role of the Polarization Anisotropy of Water in Modeling Classical Polarizable Force Fields

We have evaluated the extent to which classical polarizable force fields, based either on the chemical potential equalization principle or on distributed polarizabilities in the framework of the Sum of Interactions Between Fragments Ab initio computed (SIBFA), can reproduce the ab initio polarization energy and the dipole moment of three distinct water oligomers: bifurcated chains, transverse hydrogen-bonded chains, and longitudinal hydrogen-bonded chains of helical shape. To analyze the many-body polarization effect, chains of different size, i.e., from 2 to 12 water monomers, have been considered. Although the dipole moment is a well-defined quantity in both classical polarizable models and quantum mechanical methods, polarization energy can be defined unequivocally only in the former type of approaches. In this study we have used the Kitaura-Morokuma (KM) procedure. Although the KM approach is on the one hand known to overestimate the polarization energy for strongly interacting molecules, on the other hand it can account for the many-body polarization effectively, whereas some other procedures do not. Our data show that, if off-centered lone pair polarizabilities are explicitly represented, classical polarizable force fields can afford a close agreement with the ab initio results, both in terms of polarization energy and in terms of dipole moment.

Study of phase-diagram domains

We propose a novel approach to calculate the thermodynamic phase diagrams. Differing from the conventional method in which the boundaries of the coexisting phases are the ultimate goal, the present work crosshatches the domains of the homogeneous phase and also the phases in coexistence. This was done by treating the separated phases as a composite system whose Helmholtz free energy density is expressed as the sum average of the constituent free energy densities which are weighed by their respective volume proportions. As a result, both the domains of the coexisting phases and the homogeneous single phase can be determined in addition to locating the phase boundaries, customarily obtained by imposing the thermodynamic equilibrium conditions of equal pressure and equal chemical potential. We illustrate the elegance of the theory by studying a thermally responsive microgel system.

Thermal response of a microgel system

Recent experimental studies [Z. Wu, B. Zhou, Z.B. Hu, Phys. Rev. Lett. 90 (2003) 048304] on an uncharged aqueous poly- N-isopropylacrylamide (PNIPAM) dispersion have shown that this microgel system is sensitive to temperature. This system was also experimentally found to be modeled quite well by microgel particles interacting via a hard-sphere repulsive plus an inverse power (temperature-dependent) attractive potential. To understand theoretically this thermally responsive PNIPAM dispersion, we apply a novel approach [G.F. Wang, S.K. Lai, Phys. Rev. E 70 (2004) 051402] to calculate its thermodynamic phase diagram. Differing from the conventional method in which the boundaries of the coexisting phases are the ultimate target, the present work places emphasis on crosshatching colloidal domains which include the homogeneous phase (gas, liquid or solid), two coexisting phases and perhaps also multi-phases in coexistence. Strategically, this was done by treating the coexisting phases as one composite system whose Helmholtz free energy density is written as the sum of constituent free energy densities each of which is weighed by its respective volume proportion. We show here that by minimizing the composite system's free energy density the phase-diagram domains can all be determined in addition to the phase boundaries customarily obtained by imposing the conditions of equal pressure and equal chemical potential. Also, we present the theoretically predicted phase diagram of PNIPAM dispersion and compare it with the one observed experimentally.

Hydrogen Storage via the Hydrolysis of NaBH4 Basic Solution: Optimization of NaBH4 Concentration

Generation of hydrogen via the hydrolysis of sodium borohydride (NaBH4) solution in the presence of metal catalysts is a promising method for hydrogen storage. The concentration of NabH4 should be as high as possible in order to improve energy density. On the other hand, NaBO2 is produced after the hydrolysis of NaBH4. When the NaBH4 concentration is high enough, NaBO2 will precipitate from the solution, which would block the active sites of the catalysts and bring about the complexity of solution transportation. This paper addressed the issue through thermodynamic modeling. A mathematical model was derived first using the equality of chemical potential of the solute in solution and in its solid state. The parameters in the model were determined using phase-diagram analysis and hydration analysis of the NaBH4−NaOH−H2O and NaBO2−NaOH−H2O systems. The optimal concentration of NaBH4 in the hydrogen-generation system was then calculated and a comparison of the modeling results with experimental data, which were in good agreement, was given.

Adsorption Free Energy of Variable-Charge Nanoparticles to a Charged Surface in Relation to the Change of the Average Chemical State of the Particles

Variable-charge nanoparticles such as proteins and humics can adsorb strongly to charged macroscopic surfaces such as silica and iron oxide minerals. To model the adsorption of variable-charge particles to charged surfaces, one has to be able to calculate the adsorption free energy involved. It has been shown that the change in the free energy of variable-charge particles is related to the change in their average chemical state upon adsorption, which is commonly described using surface complexation models. In this work, expressions for the free-energy change in variable-charge particles due to changes in chemical binding are derived for three ion-binding models (i.e., the Langmuir, Langmuir-Freundlich, and NICA models) and for changes due to nonspecific binding for the Donnan model. The expressions for the adsorption free energy of the variable-charge particles to a charged surface are derived on the basis of the equality of the (electro)chemical potential of the particles in the bulk solution and adsorption phase. The expressions derived are general in the sense that they account for the competition between charge-determining ions that bind chemically to the particles, and they also apply in case of the formation of chemical bonds between particle ligands and surface sites. The derived expressions can be applied in the future to model the adsorption of variable-charge nanoparticles to charged surfaces. The results obtained for the NICA-Donnan model make it possible to apply this advanced surface complexation model to describe the adsorption of humics to minerals.

Comparing polarizable force fields to ab initio calculations reveals nonclassical effects in condensed phases

In a recent work [Giese and York J. Chem. Phys. 120, 9903 (2004)] showed that many-body force field models based solely on pairwise Coulomb screening cannot simultaneously reproduce both gas-phase and condensed-phase polarizability limits. In particular, polarizable force fields applied to bifurcated water chains have been demonstrated to be overpolarized with respect to ab initio methods. This behavior was ascribed to the neglect of coupling between many-body exchange and polarization. In the present article we reproduce those results using different ab initio levels of theory and a polarizable model based on the chemical-potential equalization principle. Moreover we show that, when hydrogen-bond (H-bond) forming systems are considered, an additional nonclassical effect, i.e., intermolecular charge transfer, must be taken into account. Such effect, contrarily to that of coupling between many-body exchange and polarization, makes classical polarizable force fields underpolarized. In the case of water at standard conditions, being H-bonded geometries much more probable than the bifurcated ones, intermolecular charge transfer is the dominant effect.

Polarization response of water and methanol investigated by a polarizable force field and density functional theory calculations: Implications for charge transfer

Electronic polarization response in hydrogen-bond clusters and liquid configurations of water and methanol has been studied by density functional theory (DFT) and by a polarizable force field based on the chemical potential equalization (CPE) principle. It has been shown that an accurate CPE parametrization based on isolated molecular properties is not completely transferable to strongly interacting hydrogen-bond clusters with discrepancies between CPE and DFT overall dipole moments as large as 15%. This is due to the lack of intermolecular charge transfer in the standard CPE implementation. A CPE scheme for evaluating the amount of transferred charge has been developed. The charge transfer parameters are determined with the aid of accurate DFT calculations using only hydrogen-bond dimer configurations. The amount of transferred charge is found to be of the order of few hundredths of electrons, as already found in recent studies on hydrogen-bond systems. The parameters of the model are then used, without further adjustment, to different hydrogen-bond clustered forms of water and methanol (oligomer and liquid configurations). In agreement with different approaches proposed in literature for studying charge transfer effects, the transferred charge in hydrogen-bond dimers is found to decrease exponentially with the hydrogen-bond distance. When allowance is made for charge transfer according to the proposed scheme, the CPE dipole moments are found to reproduce satisfactorily the DFT data.

Monte Carlo simulation of polarizable systems: Early rejection scheme for improving the performance of adiabatic nuclear and electronic sampling Monte Carlo simulations

An early rejection scheme for trial moves in adiabatic nuclear and electronic sampling Monte Carlo simulation (ANES-MC) of polarizable intermolecular potential models is presented. The proposed algorithm is based on Swendsen–Wang filter functions for prediction of success or failure of trial moves in Monte Carlo simulations. The goal was to reduce the amount of calculations involved in ANES-MC electronic moves, by foreseeing the success of an attempt before making those moves. The new method was employed in Gibbs ensemble Monte Carlo (GEMC) simulations of the polarizable simple point charge-fluctuating charge (SPC-FQ) model of water. The overall improvement in GEMC depends on the number of swap attempts (transfer molecules between phases) in one Monte Carlo cycle. The proposed method allows this number to increase, enhancing the chemical potential equalization. For a system with 300 SPC-FQ water molecules, for example, the fractions of early rejected transfers were about 0.9998 and 0.9994 at 373 and 423 K, respectively. This means that the transfer moves consume only a very small part of the overall computing effort, making GEMC almost equivalent to a simulation in the canonical ensemble.

Surface tension of a Lennard-Jones liquid under supersaturation

A formally exact Kirkwood-Buff virial formula for the surface tension of a supersaturated interface is derived. A modified Gibbs ensemble method is given that allows the creation of interacting supersaturated phases of equal chemical potential, and which enables the Kirkwood-Buff formula to be applied. The methods are tested by Monte Carlo simulation of a supersaturated Lennard-Jones fluid with a planar liquid-vapor interface. The Kirkwood-Buff results for the supersaturated surface tension are found to be in reasonable agreement with new results obtained here using the recently developed, formally exact, ghost interface method, [M. P. Moody and P. Attard, J. Chem. Phys., 2002, 117, 6705]. The surface tension is obtained as a function of supersaturation at four temperatures, and it is found to decrease with increasing supersaturation, and to vanish at the vapor spinodal. The relevance of the present results to the nucleation of droplets in a supersaturated vapor is discussed.

Molecular Orbital and Density Functional Study of the Formation, Charge Transfer, Bonding and the Conformational Isomerism of the Boron Trifluoride (BF3) and Ammonia (NH3) Donor-Acceptor Complex

The formation of the F3B–NH3 supermolecule by chemical interaction of its fragment parts, BF3 and NH3, and the dynamics of internal rotation about the ‘B–N’ bond have been studied in terms of parameters provided by the molecular orbital and density functional theories. It is found that the pairs of frontier orbitals of the interacting fragments have matching symmetry and are involved in the charge transfer interaction. The donation process stems from the HOMO of the donor into the LUMO of the acceptor and simultaneously, back donation stems from the HOMO of acceptor into the LUMO of the donor. The density functional computation of chemical activation in the donor and acceptor fragments, associated with the physical process of structural reorganization just prior to the event of chemical reaction, indicates that BF3 becomes more acidic and NH3 becomes more basic, compared to their separate equilibrium states. Theoretically it is observed that the chemical reaction event of the formation of the supermolecule from its fragment parts is in accordance with the chemical potential equalization principle of the density functional theory and the electronegativity equalization principle of Sanderson. The energetics of the chemical reaction, the magnitude of the net charge transfer and the energy of the newly formed bond are quite consistent, both internally and with the principle of maximum hardness, PMH. The dynamics of the internal rotation of one part with respect to the other part of the supermolecule about the ‘B–N’ bond mimics the pattern of the conformational isomerism of the isostructural ethane molecule. It is also observed that the dynamics and evolution of molecular conformations as a function of dihedral angles is also in accordance with the principle of maximum hardness, PMH. Quite consistent with spectroscopic predictions, the height of the molecule’s barrier to internal rotation is very small. A rationale for the low height of the barrier has been put forward in terms of the energy partitioning analysis. On the question of origin of the barrier to internal rotation, we conclude that the conformational barrier to internal rotation does not originate from a particular region of the molecule, but rather it is a result of the subtle conjoint interplay of a number of opposing effects of one- and two-center bonded and nonbonded energy terms involving the entire skeleton of the molecule.

Local Chemical Potential Equalization Model for Cosolvent Effects on Biomolecular Equilibria

A simple model for describing the effects of cosolvents on biomolecular equilibria in solution is presented. The model is developed using the Kirkwood−Buff theory of solutions and relates changes in the chemical potential of the cosolvent, due to the presence of the solute, to changes in the cosolvent (and water) concentrations in the vicinity of the biomolecule. The model is then used to determine the dependence of changes in the free energy for protein denaturation on cosolvent concentration. The experimentally observed linearity for urea, and small deviation from linear behavior for guanidinium chloride denaturation, are reproduced. In addition, the model is also predicted to provide a good description of the helix-inducing effects of TFE solutions.

Comparative analysis of the Si dangling bonds saturation by H or D in gas and liquid phases

A theoretical consideration is carried out of the dangling bond saturation on the Si(111) surface both in atomic or molecular gas of hydrogen (deuterium) and in hydrogenated (deuterated) electrolyte solution. The isotope effect originating from the difference in the vibrational behavior between D- and H-adatoms is analyzed. The isotope ratios of D- to H-adatom concentrations were calculated for the thermodynamical equilibrium between the Si surface and the relevant gas phase, and for the steady state in the electrolytic systems. The adatom concentrations were obtained from the conditions of equality of the adatom chemical potential to the chemical potential of the atoms in the gas phase or from the conditions of equality of relevant electrochemical reactions rates, respectively. It is shown that the adatom concentrations are affected by the adatom vibration frequencies both in the gas systems and in the electrolytic systems. The numerical evaluations of the isotope ratios were obtained in technologically important temperature ranges from 300K to 700K for the gas systems, and from 272K to 373K for the liquid systems. For the D or H atomic gas phases, the enhancement of the D- to H-adatom concentrations is shown to occur. The ratio is 3.2 at 300K and 1.2 at 700K. On the other hand, the ratio is reduced to 0.8 for the molecular D2 or H2 gases, and to about 0.9 for the hydrogenated or deuterated electrolytes. The both ratios decrease slowly with increasing temperature.

Multiphase Equilibria Calculation by Direct Minimization of Gibbs Free Energy Using the Tunnelling Global Optimization Method

Abstract In this paper, we advocate the use of the Tunnelling global optimization method for phase stability analysis and for multiphase equilibria calculations. The method had been successfully used for solving a variety of phase-equilibrium problems. The Tunnelling method has two steps. First, a minimum (which may not be the putative global minimum) of the objective function is found by a local bounded minimization algorithm. In a second step, the method checks for global optimality. If the minimum found in the first step is only a local minimum, a feasible initial estimate for a new minimization is generated in another valley of the objective function. Cubic equations of state are used, but any thermodynamic model for the Gibbs free energy can be used (the method being model-independent). The proposed method has proven to be an efficient and reliable tool for multiphase equilibrium calculation. Introduction The methods for multiphase equilibria calculation based on the equality of chemical potentials cannot guarantee the convergence to the correct solution since the problem is non-convex (i.e., several local minima exist), and such methods can find only one minimum for a given initial guess. Moreover, the global optimization methods currently available are generally very time consuming. A global optimization method(1, 2), called Tunnelling, able to escape from local minima and saddle points, is used in this work for the direct minimization of the Gibbs free energy and of the tangent plane distance function (TPD). The Tunnelling method has two phases. In phase one, a local bounded optimization method is used to minimize the objective function. In phase two (tunnelization), either global optimality is ascertained or a feasible initial estimate for a new minimization is generated. The Tunnelling method has shown its ability in efficiently solving difficult non-convex, highly non-linear problems. Different kinds of phase equilibrium problems were solved using Tunnelling(3–6). The problems addressed here are vapour-liquid and liquid-liquid two-phase equilibria, three-phase vapour-liquid-liquid equilibria, and three-phase vapour-liquid-solid equilibria for a variety of representative systems. We use in this work a general form of cubic equation of state (EOS), incorporating the Soave-Redlich-Kwong (SRK) and Peng- Robinson (PR) EOS. Multiphase Equilibrium Equations Phase Splitting According to the second law of thermodynamics, at the equilibrium state, a system of nc components of composition z = (z1, z2,...,znc)T has the lowest possible Gibbs free energy from all possible states. The dimensionless Gibbs free energy is expressed as:

Poisson-Boltzmann theory of the charge-induced adsorption of semi-flexible polyelectrolytes.

A model is suggested for the structure of an adsorbed layer of a highly charged semi-flexible polyelectrolyte on a weakly charged surface of opposite charge sign. The adsorbed phase is thin, owing to the effective reversal of the charge sign of the surface upon adsorption, and ordered, owing to the high surface density of polyelectrolyte strands caused by the generally strong binding between polyelectrolyte and surface. The Poisson-Boltzmann equation for the electrostatic interaction between the array of adsorbed polyelectrolytes and the charged surface is solved for a cylindrical geometry, both numerically, using a finite element method, and analytically within the weak curvature limit under the assumption of excess monovalent salt. For small separations, repulsive surface polarization and counterion osmotic pressure effects dominate over the electrostatic attraction and the resulting electrostatic interaction curve shows a minimum at nonzero separations on the Angstrom scale. The equilibrium density of the adsorbed phase is obtained by minimizing the total free energy under the condition of equality of chemical potential and osmotic pressure of the polyelectrolyte in solution and in the adsorbed phase. For a wide range of ionic conditions and charge densities of the charged surface, the interstrand separation as predicted by the Poisson-Boltzmann model and the analytical theory closely agree. For low to moderate charge densities of the adsorbing surface, the interstrand spacing decreases as a function of the charge density of the charged surface. Above about 0.1 M excess monovalent salt, it is only weakly dependent on the ionic strength. At high charge densities of the adsorbing surface, the interstrand spacing increases with increasing ionic strength, in line with the experiments by Fang and Yang [J. Phys. Chem. B 101, 441 (1997)].

DFT Based Atomic Softness and Its Application in Site Selectivity

AbstractActive site of a complex molecule and mechanism of chemical reaction has been studied with the help of atomic softness values derived from calculation based on Density functional theory. The quantum mechanical equation of Klopman has been solved with the help of AM1 calculation by using Win MOPAC7.21 software. On the basis of chemical potential equalization principle, and Koopmans theorem for frontier orbitals a formalism has been developed for the calculation of electron affinity of an atom in a molecule EA. The reliability of the EA values have been tested with electron density (obtained from AM1 calculation) and Fukui function values taken from literature.

Mixed-phase description of colossal magnetoresistive manganites

In view of recent experiments, indicating the spatial coexistence of conducting and insulating regions in the ferromagnetic metallic phase of doped manganites, we propose a refined mixed-phase description. The model is based on the competition of a double-exchange driven metallic component and a polaronic insulating component, whose volume fractions and carrier concentrations are determined self-consistently by requiring equal pressure and chemical potential. The resulting phase diagram as well as the order of the phase transition are in very good agreement with measured data. In addition, modelling the resistivity of the mixed, percolative phase by a random resistor network, we obtain a pronounced negative magnetoresistance in the vicinity of the Curie temperature $T_C$.

An algebraic method that includes Gibbs minimization for performing phase equilibrium calculations for any number of components or phases

The most widely used technique for performing phase equilibria calculations is the K-value method (equality of chemical potentials). This paper proposes a more efficient algorithm to achieve the results that includes Gibbs minimization when we know the number of phases. Using the orthogonal derivatives, the tangent plane equation and mass balances, it is possible to reduce the Gibbs minimization procedure to the task of finding the solution of a system of non-linear equations. Such an operation is easier and faster than finding tangents or areas, and appears to converge as fast as the K-value method. Examples illustrate application of the new technique to two and three phases in equilibrium for binary and ternary mixtures.

Simulation of the coexistence of a shearing liquid and a strained crystal

The coexistence between a strained crystal and its shearing melt is studied using nonequilibrium molecular dynamics simulations of Lennard-Jones particles. The coexistence is found to be independent of initial conditions, boundary effects, and the details of the thermostat. The nonequilibrium phase diagram is presented. The shear stress at coexistence is found to be significantly smaller than the yield stress of the crystal. It is demonstrated that there exists no physically reasonable prescription for a nonequilibrium analogue of chemical potential for the shearing liquid by which the coexistence could be attributed to an equality of chemical potentials between the two phases. We conclude that the nonequilibrium coexistence is determined by the stability of the interface.