Equality Of Chemical Potentials Research Articles

Chemical potential of an antiferromagnetic magnon gas

Understanding the statistics of quasi-particle excitations in magnetic systems is essential for exploring new magnetic phases and collective quantum phenomena. While the chemical potential of a ferromagnetic gas has been extensively investigated both theoretically and experimentally, its antiferromagnetic counterpart remains uncharted. Here, we derive the statistics of a two-component U(1)-symmetric Bose gas and apply our results to an axially-symmetric antiferromagnetic insulator. We find that the two magnon eigenmodes of the system are described by an equal and opposite chemical potential, in analogy with a particle-antiparticle pair. Furthermore, we derive the thermomagnonic torques describing the interaction between the coherent and incoherent antiferromagnetic spin dynamics. Our results show that the magnitude and sign of the chemical potential can be tuned via an AC magnetic field driving resonantly one of the magnon modes. Finally, we propose NV-center relaxometry as a method to experimentally test our predictions.

Surface tension and interfacial compositions of binary glycerol/alcohol mixtures

The main aim of this research was to study the surface tension and interfacial composition of different binary mixtures of glycerol and alcohols. To achieve this aim, mixtures of glycerol and ethanol, 1-propanol, 2-propanol, and 1-butanol were prepared. By using the Du-Nouy ring method, surface tensions were experimentally measured as a function of composition in the temperature range of (293–333) K. The equality of chemical potentials of components at the surface layer and bulk liquid was considered for simultaneous prediction of surface tension and composition. The model was employed by using different approaches, including an activity based and a fugacity-based method. The UNIFAC activity model and PSRK EOS were used to calculate the activity and fugacity coefficients, respectively. The results of this study showed that the ability of the activity-based approach is limited (overall AADσ = 26.78%) while the fugacity-based method successfully predicted the surface tensions of the studied mixtures (overall AADσ = 1.84%). Our hypothesis is that the fugacity-based method was more accurate because it accounted for the partial molar area of the components.

Eliminating symmetry problems in electronegativity equalization and correcting self-interaction errors in conceptual DFT.

The chemical potential is by definition constant in molecules, and electronic charge is in principle equilibrated by bonding. Does electronegativity offer the best scale to unify these principles? According to conceptual density functional theory (c-DFT), the electronegativity equalization (ENE) and chemical potential equalization (CPE) principles seem rigorous and identical. However, the operational formulations of CPE and ENE fail to validate this claim, and frequently dramatic deviations from equalization are reported. We here eliminate the deviations to a very large extent. The problems originate from (i) c-DFT's exclusive reference to ground states and violations of the Wigner-Witmer symmetry constraints for bonding, (ii) electron self-interaction and delocalization errors. The problems are solved, and much more accurate ENE and bond polarities are obtained by replacing the ground-state electronegativity (χGS ) by the valence-state electronegativity (χVS ) and its generalization, the valence-pair-affinity (VPA, αVP ). The VPA is a charge dependent pair-sharing potential connected to Ruedenberg's bond theory that emphasizes the role of electron pair-density. The performances of the valence-pair equilibration (VPEq) and c-DFT's operational CPE are compared for 89 molecules with very diverse bond characters, including the "exotic" dimers Be2 , Mg2 , B2 , C2 , and Mn2 . The accuracy of VPEq is about 9 times better than that of operational CPE. Without requiring ad hoc calibrations, the VPEq bond polarities agree very well with results of state-of-the-art population analyses, and charges derived from vibrational spectra. A paradigm shift emphasizing valence states seems in order for c-DFT. Electronegativity and the chemical potential should be regarded as separate properties. Copyright © 2018 Wiley Periodicals, Inc.

A simulation method for the phase diagram of complex fluid mixtures.

The phase behavior of complex fluid mixtures is of continuing interest, but obtaining the phase diagram from computer simulations can be challenging. In the Gibbs ensemble method, for example, each of the coexisting phases is simulated in a different cell, and ensuring the equality of chemical potentials of all components requires the transfer of molecules from one cell to the other. For complex fluids such as polymers, successful insertions are rare. An alternative method is to simulate both coexisting phases in a single simulation cell, with an interface between them. The challenge here is that the interface position moves during the simulation, making it difficult to determine the concentration profile and coexisting concentrations. In this work, we propose a new method for single cell simulations that uses a spatial concentration autocorrelation function to (spatially) align instantaneous concentration profiles from different snapshots. This allows one to obtain average concentration profiles and hence the coexisting concentrations. We test the method by calculating the phase diagrams of two systems: the Widom-Rowlinson model and the symmetric blends of freely jointed polymer molecules for which phase diagrams from conventional methods are available. Excellent agreement is found, except in the neighborhood of the critical point where the interface is broad and finite size effects are important. The method is easy to implement and readily applied to any mixture of complex fluids.

Investigation on the interfacial behavior of aqueous solutions of cetyltrimethyl ammonium bromide in the presence of polyethylene glycols

The surface tensions of aqueous cetyltrimethyl ammonium bromide and four polyethylene glycols were measured experimentally at the temperature of 298.15 K and the pressure of 1 atm. Then the surface tensions of aqueous (cetyltrimethyl ammonium bromide + polyethylene glycols) were measured at different concentrations. These measurements were conducted with the pendant drop method. The surface tensions of these aqueous solutions were described by using the equality of chemical potentials at the interface and bulk liquid. The calculated results showed a good agreement with experimental measurements, so the model was successfully applied to aqueous cetyltrimethyl ammonium bromide, polyethylene glycols, and their mixtures. Moreover, the surface coverage, molar surface area, and surface-to-solution distributions were determined by this model. The values of critical micelle concentration were obtained through surface tension measurements for each aqueous solution. The presence of polyethylene glycols increased the values of the critical micelle concentration and decreased the surface coverages of cetyltrimethyl ammonium bromide.

On the improvement of computational performance of a vapor-liquid equilibria solver for mixtures

This work deals the computational performance improvement of vapor–liquid equilibria solver for fluids mixtures. The code here developed is based on the chemical potential equality (expressed in terms of fugacity) and implements Soave–Redlich–Kwong and Peng–Robinson equations of state with classical van der Waals mixing rules. To reduce the bulk of the computational effort required by the solver we propose the following approaches: (i) exploit high-order methods for the solution of Rachford–Rice equation; (ii) develop an efficient programming methodology for the sub-routines devoted to the fugacity coefficients computation in order to reduce their overall impact on the CPU-time exploiting the parallelism at CPU level, i.e. CPU pipelining, and cache blocking. In this paper we have carefully evaluated the effectiveness of the aforementioned approaches performing a suite of computations of the equilibrium properties of several literature mixtures. The pros and cons of the strategies here suggested are outlined and discussed.

Modelling interfacial properties of binary and ternary liquid mixtures of tetrahydrofuran, 2-propanol and 2,2,4-trimethylpentane

ABSTRACTThe present modelling study has been dedicated to determining the interfacial properties of binary and ternary liquid mixtures made up of tetrahydrofuran, 2-propanol and 2,2,4-trimethylpentane. The variation of the temperature is from 288 to 308 K. By using both UNIFAC activity model and the fugacity model based on the cubic plus association (CPA) equation of state (EOS), a model based on the equality of chemical potentials in the liquid and the surface layer is utilised to describe the liquid–vapour interface of these liquid mixtures. The surface tension, composition and density are simultaneously predicted. The results of this model show that experimental surface tension data are in a good agreement with the predicted ones. The model using CPA EOS and molar volume has a better performance than the one uses the UNIFAC activity model.

Stability analysis for multicomponent mixtures including capillary pressure

Despite the large potential of unconventional resources, many unknowns still exist regarding the physics controlling the extraction processes in these settings. These include accurate representation of phase equilibrium in tight formations and effective implementation of relevant models in simulation tools.When a fluid is confined in pore spaces of nanometer size, significant interfacial curvatures may occur that can result in large capillary pressures between the liquid and vapor phases: The pressure difference between the two phases will likely affect the vapor-liquid equilibrium state. Previous efforts have shown that this effect is negligible for conventional reservoirs (with pores in the micron range) and current commercial reservoir simulators commonly ignore the effect of capillary pressure in the VLE calculations. However, experimental and modeling efforts have shown that ignoring capillary pressure in the VLE calculations will not be a valid approximation for unconventional (tight) reservoirs.In this work, we analyze the numerical aspects of including capillarity phenomena in VLE calculations in an effort to arrive at robust and efficient algorithms for stability analysis that can be used in compositional modeling/simulation of unconventional reservoirs. While the equality of chemical potentials is a necessary condition for equilibrium, it is not a sufficient one. A sufficient condition for equilibrium is the minimization of Gibbs energy, and the latter can be tested using the tangent plane distance (TPD) criteria. We show that stability analysis based on the TPD criteria remains valid for systems with large capillary pressures and propose effective/robust algorithms for stability testing. The proposed algorithms are tested for multicomponent reservoir fluid systems over a range of relevant temperatures, pressures and pore radii.

A Generalized Statement of Highest-Entropy Principle for Stable Equilibrium and Non-Equilibrium in Many-Particle Systems

Among all statements of Second Law, the existence and uniqueness of stable equilibrium, for each given value of energy content and composition of constituents of any system, have been adopted to define thermodynamic entropy by means of the impossibility of Perpetual Motion Machine of the Second Kind (PMM2) which is a consequence of the Second Law. Equality of temperature, chemical potential and pressure in many-particle systems are proved to be necessary conditions for the stable equilibrium. The proofs assume the stable equilibrium and derive, by means of the Highest-Entropy Principle, equality of temperature, chemical potential and pressure as a consequence. A first novelty of the present research is to demonstrate that equality is also a sufficient condition, in addition to necessity, for stable equilibrium implying that stable equilibrium is a condition also necessary, in addition to sufficiency, for equality of temperature potential and pressure addressed to as generalized potential. The second novelty is that the proof of sufficiency of equality, or necessity of stable equilibrium, is achieved by means of a generalization of entropy property, derived from a generalized definition of exergy, both being state and additive properties accounting for heat, mass and work interactions of the system underpinning the definition of Highest-Generalized-Entropy Principle adopted in the proof.

Discussion on Thermodynamic Criterion of Equal Chemical Potential for Phase Equilibrium between Gas and Liquid in Curved Interface

Discussion on Thermodynamic Criterion of Equal Chemical Potential for Phase Equilibrium between Gas and Liquid in Curved Interface

Precipitation of Non-Spherical Particles in Aluminum Alloys Part I: Generalization of the Kampmann–Wagner Numerical Model

Particles precipitated during aging treatments often have non-spherical shapes, e.g., needles or plates, while in the classical Kampmann–Wagner Numerical (KWN) precipitation model, it is assumed that the particles are of spherical shape. This model is here generalized resulting in two correction factors accounting for the effects induced by the particles’ non-spherical shape on their growth kinetics. The first one is for the correction of the growth rate. It is derived from the approximate solution of the diffusion problem on spheroidal coordinate and verified by the three-dimensional numerical solutions for cuboid particles. The second factor is for the energetic correction due to the particle surface curvature. It is derived from chemical potential equality (or Gibbs energy minimization principle) at equilibrium for non-spherical particles and provides a correction factor for the Gibbs–Thomson effect. In the accompanying paper, the two correction factors are implemented into a multi-component KWN modeling framework, and the resulting improvements on the model’s predictive power are demonstrated.

Improving intermolecular interactions in DFTB3 using extended polarization from chemical-potential equalization.

Semi-empirical quantum mechanical methods traditionally expand the electron density in a minimal, valence-only electron basis set. The minimal-basis approximation causes molecular polarization to be underestimated, and hence intermolecular interaction energies are also underestimated, especially for intermolecular interactions involving charged species. In this work, the third-order self-consistent charge density functional tight-binding method (DFTB3) is augmented with an auxiliary response density using the chemical-potential equalization (CPE) method and an empirical dispersion correction (D3). The parameters in the CPE and D3 models are fitted to high-level CCSD(T) reference interaction energies for a broad range of chemical species, as well as dipole moments calculated at the DFT level; the impact of including polarizabilities of molecules in the parameterization is also considered. Parameters for the elements H, C, N, O, and S are presented. The Root Mean Square Deviation (RMSD) interaction energy is improved from 6.07 kcal/mol to 1.49 kcal/mol for interactions with one charged species, whereas the RMSD is improved from 5.60 kcal/mol to 1.73 for a set of 9 salt bridges, compared to uncorrected DFTB3. For large water clusters and complexes that are dominated by dispersion interactions, the already satisfactory performance of the DFTB3-D3 model is retained; polarizabilities of neutral molecules are also notably improved. Overall, the CPE extension of DFTB3-D3 provides a more balanced description of different types of non-covalent interactions than Neglect of Diatomic Differential Overlap type of semi-empirical methods (e.g., PM6-D3H4) and PBE-D3 with modest basis sets.

Enhanced Lithium-Sulfur Battery By Amine-Functionalized Cathode and Kinetic Study of Polysulfides Dissolution

Lithium-Sulfur battery is very attractive due to its high energy density of 2500 Wh/kg or 2800 Wh/L. The low cost of Sulfur ($0.02/g) provides a significant driving force to obtain a commercial Li-S battery. But their practical use is still hindered by several issues including capacity fading, short lifespan, and low efficiency. The dissolution of long-chain lithium polysulfides (Li2Sx, 2 < x < 8) (LiPS) into the electrolyte and the shuttling of polysulfides between cathode and anode have been generally considered responsible for the capacity degradation. A variety of methods have been applied to prevent the dissolution of LiPS, most of which focus on physical trapping by using carbon matrix as barrier materials. However, the effect of barrier materials is kinetics; LiPS physically trapped in carbon host will eventually leach into the electrolyte. Also, the nonpolar carbon matrix will facilitate the detachment of LiPS, which is highly polar, from the cathode, resulting in loss of active materials. Thus thermal sequestering of LiPS via chemical binding and a polar cathode surface is desired. Herein, we report a facile approach towards high-performance sulfur-carbon cathodes by stabilizing LiPS on amine-functionalized cathode. Specifically, Polyethylenimine (PEI) is chosen for the reason that it possesses a large amount of amine groups within a molecular. PEI is attached to the cathode by reacting with hydroxyl functionalized carbon nanotubes (Figure 1). The strong affinity of LiPS to PEI-functionalized CNT is verified by DFT calculation, showing high binding energy of 1.23 eV, while it is 0.34eV between LiPS and graphene and 0.83eV between LiPS and PVDF. The interaction is also confirmed by FTIR, XPS, and other characterization techniques. With the merits of CNT such as good conductivity and robust mechanical properties, the nanocomposite of amine-functionalized CNT and sulfur exhibits stable cycling performance with high capacities (Figure 1). Furthermore, the kinetic study of polysulfides dissolution is carefully carried out. The dissolution constant k is determined by the method described in Figure 2. k is obtained for cathodes with various compositions: (1) Li2S4 without PEI; (2) Li2S4 with PEI; (3) Li2S9 without PEI; (4) Li2S9 with PEI. By comparing dissolution constants in each case, the much stronger affinity of PEI with the LiPS can be observed with smaller k. Also, the higher solubility and dissolution rate are found with increasing chain length of LiPS. The equilibrium concentration (ceq) of LiPS in the electrolyte is found, where LiPS has equal chemical potential in the electrolyte and cathode. This guides us in adding LiPS with concentration of ceqto the electrolyte when designing Li-S batteries. In this case, LiPS will not leach into the electrolyte since there is no driving force in the condition of equilibrium. The battery performance will be presented in the talk. In summary, the new method takes advantage of the numerous amine groups in PEI and the strong affinity with LiPS to realize a high performance Li-S battery. The systematical kinetic study also reveals the working mechanism and paves the way to further rational design of Li-S battery. Figure 1

A Method to Derive the Definition of Generalized Entropy from Generalized Exergy for Any State in Many-Particle Systems

The literature reports the proofs that entropy is an inherent property of any system in any state and governs thermal energy, which depends on temperature and is transferred by heat interactions. A first novelty proposed in the present study is that mechanical energy, determined by pressure and transferred by work interactions, is also characterized by the entropy property. The second novelty is that a generalized definition of entropy relating to temperature, chemical potential and pressure of many-particle systems, is established to calculate the thermal, chemical and mechanical entropy contribution due to heat, mass and work interactions. The expression of generalized entropy is derived from generalized exergy, which in turn depends on temperature, chemical potential and pressure of the system, and by the entropy-exergy relationship constituting the basis of the method adopted to analyze the available energy and its transfer interactions with a reference system which may be external or constitute a subsystem. This method is underpinned by the Second Law statement enunciated in terms of existence and uniqueness of stable equilibrium for each value of energy content of the system. The equality of chemical potential and equality of pressure are assumed, in addition to equality of temperature, to be necessary conditions for stable equilibrium.

Symmetry laws improve electronegativity equalization by orders of magnitude and call for a paradigm shift in conceptual density functional theory.

The strict Wigner-Witmer symmetry constraints on chemical bonding are shown to determine the accuracy of electronegativity equalization (ENE) to a high degree. Bonding models employing the electronic chemical potential, μ, as the negative of the ground-state electronegativity, χ(GS), frequently collide with the Wigner-Witmer laws in molecule formation. The violations are presented as the root of the substantially disturbing lack of chemical potential equalization (CPE) in diatomic molecules. For the operational chemical potential, μ(op), the relative deviations from CPE fall between -31% ≤ δμ(op) ≤ +70%. Conceptual density functional theory (cDFT) cannot claim to have operationally (not to mention, rigorously) proven and unified the CPE and ENE principles. The solution to this limitation of cDFT and the symmetry violations is found in substituting μ(op) (i) by Mulliken's valence-state electronegativity, χ(M), for atoms and (ii) its new generalization, the valence-pair-affinity, α(VP), for diatomic molecules. Mulliken's χ(M) is equalized into the α(VP) of the bond, and the accuracy of ENE is orders of magnitude better than that of CPE using μ(op). A paradigm shift replacing the dominance of ground states by emphasizing valence states seems to be in order for conceptual DFT.

Chemical potentials and phase equilibria of Lennard-Jones chain fluids

Computer simulations (molecular dynamics) were performed for ensembles of flexible tangent Lennard-Jones chains consisting of n sites (n = 1, 2, 4, 8, and 16). From these simulations, the orthobaric liquid and vapour densities were calculated not only with the traditional method of simulating a liquid film in coexistence with vapour, but also using the rigorous thermodynamic condition of satisfying the chemical potential equality between the phases in equilibrium. The agreement with literature data, as far as such exist, is excellent.

Fermi Level Pinning and Orbital Polarization Effects in Molecular Junctions: The Role of Metal Induced Gap States

Understanding the alignment of molecular orbitals and corresponding transmission peaks with respect to the Fermi level of the electrodes is a major challenge in the field of molecular electronics. In order to design functional devices, it is of utmost importance to assess whether controlled changes in the electronic structure of isolated compounds are preserved once they are inserted in the molecular junctions. Here, light is shed on this central issue by performing density functional theory calculations on junctions including diarylethene‐based molecules. It is demonstrated that the chemical potential equalization principle allows to rationalize the existence or not of a Fermi level pinning (i.e., same alignment in spite of a varying ionization potential in the isolated compounds), pointing to the essential role played by metal induced gap states (MIGS). It is further evidenced that the degree of level pinning is intimately linked to the degree of orbital polarization when a bias is applied between the two electrodes.

The surface chemical potential from a surface equation of state versus Butler's equation

In the last years, our research group has been committed to the development of bulk–surface equilibrium models that relate surface tension, bulk composition, and bulk activity coefficients; in this paper, we focus on two of them. The starting premise is the equality of bulk and surface chemical potentials. Instead of the common practice of expressing the surface chemical potential analogously to the bulk, in the first model, surface chemical potential is obtained from the integration of Gibbs adsorption equation coupled to Volmer's equation of state, and written as a function of surface pressure shown to be a measure of surface activity. In the second model, Gibbs adsorption equation was evaluated in the surface saturated region and then coupled to the bulk chemical potential avoiding the use of an explicit expression for the surface. Both models are equivalent in meaning and structure to the widely accepted Sprow and Prausnitz equation (Trans. Faraday Soc. 62 (1966) 1105), originally derived by Butler (Proc. R. Soc. A 138 (1932) 348), where it is necessary to introduce non-thermodynamic approximations for the calculation of partial molar areas, surface activity coefficients and surface composition. On the contrary, the parameters of the two proposed models are attained from the fitting to the experimental data. Obeying a monolayer model, Butler arrived to the conclusion that bulk and surface chemical potentials are not equal, but it is demonstrated that in Gibbs adsorption equation, the equality of chemical potentials is valid and that the models are thermodynamically consistent.

Communication: Thermodynamic analysis of critical conditions of polymer adsorption

Polymer adsorption to solid surfaces is a ubiquitous phenomenon, which has attracted long-lasting attention. Dependent on the competition between the polymer-solid adsorption and polymer-solvent solvation interactions, a chain may assume either 3d solvated conformation when adsorption is weak or 2d adsorbed conformation when adsorption is strong. The transition between these conformations occurring upon variation of adsorption strength is quite sharp, and in the limit of "infinite" chain length, can be treated as a critical phenomenon. We suggest a novel thermodynamic definition of the critical conditions of polymer adsorption from the equality of incremental chemical potentials of adsorbed and free chains. We show with the example of freely jointed Lennard-Jones chains tethered to an adsorbing surface that this new definition provides a link between thermodynamic and geometrical features of adsorbed chains and is in line with classical scaling relationships for the fraction of adsorbed monomers, chain radii of gyration, and free energy.

Effect of capillary term parameters on the thermodynamic modeling of methane hydrate formation in porous media

According to the solid-solution theory, the stability of gas hydrates is related to the activity of water. Geometrical constraints decrease the activity of water. Therefore, differences in phase behavior calculations of gas hydrates in porous media from gas hydrates in the bulk, stem from activity of water calculations. In this work, the effects of different parameters describing capillary forces on the results of methane-hydrate formation modeling are studied. Two different thermodynamic models are applied for calculations. The first model assumes a single-size porous media and the equality of chemical potential. The second model considers the pore size distribution and the equality of water fugacity as the equilibrium criteria. It is shown that the value of surface tension proposed by Uchida and co-workers yields the most accurate predictions compared to experimental results. In addition, values of shape factors (assuming a fixed wetting angle) are optimized using experimental data. The optimized values are correlated to the hydrate formation temperature. To validate the optimized shape–factor parameters, the correlated values are used for an additional set of experimental data, which leads to reduced errors. If the single-size pore modeling is used, percent of average absolute deviation (AAD%) decreases from 7.83% to 4.59% in LW–H–V region and from 19.58% to 15.71% and 7.03% in the I–H–V region for perfect wetting contact and complete non-wetting contact, respectively. If the model which considers the pore size distribution (PSD) is used, AAD% decreases from 9.98% to 5.79%. The results of this study show that at temperatures below the temperature of quadruple point, assumption of a cylindrical contact leads to much more accurate predictions in the I–H–V region even when the pore size distribution is not considered.