Chemical Potentials Of Components Research Articles

Molecular dynamics study of the thermodynamic properties of triglyceride/methanol mixtures in the presence of cosolvent

Biodiesel is a renewable source of energy that has the potential to replace fossil fuel-based resources. It is produced via the transesterification reaction in which a triglyceride reacts with methanol in the presence of a catalyst. Cosolvents are usually added to the reactants in transesterification to improve the mutual solubility of methanol and triglycerides and to create a single phase. The commonly used cosolvents in transesterification include tetrahydrofuran (THF) and diethyl ether (DEE). Understanding the thermodynamic properties of this system is important in the selection of cosolvent. In this study, molecular dynamics simulations were used to study the mixing behavior between the components of ternary mixtures of triolein/methanol/THF and triolein/methanol/DEE via the application of Flory-Huggins theory of solutions. A simple approach to calculation of the Flory-Huggins interaction parameters is used in which the mixing energy is derived from averaged non-bonded pair interaction energies. Apart from pure triolein, these ternary systems resemble the experimentally studied ternary systems employing various plant-based oils. The binary interaction parameters, Gibbs Free energy and chemical potentials of the components were calculated to study the mixing behavior. Our results show that along the experimental phase boundary the binary interaction parameters remain relatively unchanged with a deviation observed at the highest volume fractions of triolein where the highest binary interactions were observed indicating the possibility of phase separation. The Gibbs energy of mixing for the systems changed from positive to negative as one moves from two phase to single phase part of the ternary system as expected and in agreement with experimental data. The chemical potentials of the ternary mixture components were calculated from the partial derivatives of the Gibbs free energy of mixing. The activities calculated from Flory-Huggins chemical potentials were compared to those calculated using the UNIFAC model. There is good agreement between the two, with both able to predict a single and biphasic mixture. However, disagreements are noted at low and high concentrations of triolein.

Cell voltage of mixed conductors under partially frozen conditions

Partially frozen-in states are rather the rule than the exception. Coexistence between equilibrium states and frozen-in states is relevant in view of the diversity and complexity of charge carriers, or sublattices, especially in multinary compounds, but also with respect to differently equilibrated spatial regions. This contribution deals with the open circuit potential of samples where only surface-near regions feel the outer partial pressure, or more generally, the component chemical potentials, established by the electrodes. In view of the significance of such measurements for separating ionic and electronic conductivity contributions, and the kinetic difficulties in getting full equilibration near room-temperature, the value of these considerations is obvious. The necessary relations are derived, or their derivations are sketched within the framework of linear force–flux laws. An account is made of recent emf measurements of hybrid halide perovskites, and a refinement of their standard defect diagram is recommended.

Thermodynamic Analysis of Relaxation Model for Non-Equilibrium Phase Behavior of Hydrocarbon Mixtures

Mathematical models of phase behavior are widely used to describe multiphase oil and gas-condensate systems during hydrocarbon recovery from natural petroleum reservoirs. Previously a non-equilibrium phase behavior model was proposed as an extension over generally adopted equilibrium models. It is based on relaxation of component chemical potentials difference between phases and provides accurate calculations in some typical situations when non-instantaneous changing of phase fractions and compositions in response to variations of pressure or total composition is to be considered. In this paper we present a thermodynamic analysis of the relaxation model. General equations of non-equilibrium thermodynamics for multiphase flows in porous media are considered, and reduced entropy balance equation for the relaxation process is obtained. Isotropic relaxation process is simulated for a real multicomponent hydrocarbon system with different values of characteristic relaxation time using the non-equilibrium model implemented in the PVT Designer module of the RFD tNavigator simulation software. The results are processed with a special algorithm implemented in Matlab to calculate graphs of the total entropy time derivative and its constituents in the entropy balance equation. It is shown that the constituents have different signs, and the greatest influence on the entropy is associated with the interphase flow of the major component of the mixture and the change of the total system volume in the isotropic process. The characteristic relaxation time affects the rate at which the entropy is approaching its maximum value.

Pseudomorphic 9-line silician ferrihydrite and Fe-rich serpentine-group minerals in FeTi oxide-rich ferroan peridotite, Laramie anorthosite complex, Wyoming, U.S.A.

AbstractLow-temperature hydrous alteration of FeTi oxide-rich ferroan peridotite, Laramie anorthosite complex, Wyoming, produced silician ferrihydrite, cronstedtite, greenalite, hisingerite, and talc. Ferrihydrite occurs as nanocrystals in ~50 nm diameter granules that form monomineralic masses up to 300 μm across. It is inferred to have formed by the replacement of an igneous sulfide such as pyrrhotite. Electron diffraction shows the ferrihydrite to be a 9-line variety. Si-rich cronstedtite formed thin rims around the ferrihydrite, and talc grew patchily around the cronstedtite. Greenalite formed in ~10 μm cracks through all the above minerals and olivine, and hisingerite microveinlets partially replaced olivine. Igneous minerals remaining include olivine Fa46, magnetite, ilmenite, hornblende, biotite, and trace clinopyroxene. Correlations among the constituents of ferrihydrite determined by electron microprobe, including anhydrous totals, indicate progress during the growth of two charge-balanced exchanges involving silica enrichment: an inverse cronstedtite substitution (MgFe2+,Si) (Fe3+Mn3+)–2 and an inverse hydrogarnet substitution SiH–4. The cronstedtite exchange requires charge and size balance across nearest-neighbor T and O crystal sites, suggesting crystal-interior rather than crystal-surface control. Ferrihydrite’s composition reflects time- and space-related variations in the chemical potentials of components in the hydrous fluid at the site of alteration. An upper limit for SiO2 of 14–15 wt%, or ≈1.0 Si per 5-cation formula unit, would seem to correspond to the limit of availability in ferrihydrite of tetrahedral sites open to the entry of Si. Our EPMA data, projected to zero SiO2, indicate an anhydrous total of ≈83 wt% for end-member ferrihydrite, a number that matches the formula: Fe10O15·9H2O. The geochemical properties of Laramie ferrihydrite are shared by some samples of altered chondritic and Martian meteorites. Ferrihydrite on Earth commonly occurs as a surface deposit; unlike the Laramie occurrence, these lack the microspatial coherence of replacements/pseudomorphs to show systematic, structure-related element variations. The superior crystal quality of the Laramie ferrihydrite likely contributed to its unique compositional variability.

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).

Teaching Nano-Thermodynamics: Gibbs Energy of Single-Component Nanoparticles

Much attention has been paid to thermodynamic modeling of nanosystems. A common approach consists in addition of a surface/interface term to the Gibbs energy of bulk materials and application of general conditions of equilibrium. Some discrepancy still remains dealing with the expression for surface contribution to molar Gibbs energy and chemical potential of components. It is shown, that due to the nonextensive nature of the surface area, these contributions are different for molar and partial molar quantities. The consistent expressions for the molar Gibbs energy and chemical potential of a single-component spherical nanoparticle are put forward along with the simple derivation of the Kelvin and Gibbs-Thomson equations.

Statistical thermodynamics of material transport in nonisothermal suspensions.

An approach to the transport of material in a temperature gradient is outlined using nonequilibrium thermodynamics theory. The model is applicable to the thermophoresis of colloids and nanoparticles in systems with limited miscibility. Component chemical potentials in binary systems are calculated using statistical mechanics. The local pressure distribution is obtained using the condition of local thermodynamic equilibrium around the suspended particle. The Laplace contribution of the local pressure distribution within the layer of liquid surrounding the particle leads to a size dependence that is consistent with empirical data. The contribution of Keezom interaction to the thermodiffusion coefficient is calculated using empirical values of the thermodiffusion coefficient for silica particles in water and acetonitrile. The resulting interaction energies are consistent with those found in the literature.

Mass spectrometric study of thermodynamic properties in the Yb2O3‐ZrO2 system at high temperatures

Materials based on the Yb2O3-ZrO2 system have many industrial applications such as high-temperature solid electrolytes, ceramics with special properties and most importantly for thermal barrier coatings. As their synthesis and use take place at high temperatures, information on the vaporization processes, thermodynamic properties and phase equilibria of this system at high temperatures is of great importance. Measurements were performed by high-temperature Knudsen effusion mass spectrometry with a MS-1301 mass spectrometer. Vaporization was carried out using two tungsten effusion cells containing the sample under study and pure Yb2O3. The values of component activities in the Yb2O3-ZrO2 system were also calculated using the CALPHAD approach. The Yb and O vapor species were identified over the samples studied at 2400 K. Using these data the ZrO2 activities, chemical potentials of components and the Gibbs energies of the solid solution formation were calculated in this system. The thermodynamic values were also obtained as the result of modeling of the Yb2O3-ZrO2 system based on the CALPHAD approach using the data available on the phase diagram of this system and calorimetric measurements only. The thermodynamic functions found in the Yb2O3-ZrO2 system at 2400 K, such as the activities of components and the Gibbs energy of formation, displayed negative deviation from ideality. Mutual agreement was observed between the experimental thermodynamic values and the results of calculations based on the CALPHAD approach.

Electric-Field Induced Degradation of Ionic Solids

Degradation of performance and life time of a functional material or device thereof is induced, to a great extent, by mass transfer in the material that is driven by various thermodynamic forces imposed intentionally or accidentally during its operation or service. The forces are any gradient of intensive thermodynamic variables, component chemical potentials, electrical potential, temperature, stresses, and the like. This paper reviews electric-field induced degradation phenomena in ionic solid compounds including insulation resistance degradation, crystal shift, microstructural alterations, compositional unmixing, and compound decomposition. Their inner workings are also discussed qualitatively.

A general thermodynamic analysis and treatment of phases and components in the analysis of phase assemblages in multicomponent systems

Systematic thermodynamic analysis reveals that an essential condition for the thermodynamically valid chemographic projections proposed by Greenwood is completely excessive. In other words, the phases or components from which the projection is made need not be pure, nor have their chemical potentials fixed over the whole chemographic diagram. To facilitate the analysis of phase assemblages in multicomponent systems, all phases and components in the system are divided into internal and external ones in terms of their thermodynamic features and roles, where the external phases are those common to all assemblages in the system, and the external components include excess components and the components whose chemical potentials (or relevant intensive properties of components) are used to define the thermodynamic conditions of the system. This general classification overcomes the difficulties and defects in the previous classifications, and is easier to use than the previous ones. According to the above classification, the phase rule is transformed into a new form. This leads to two findings: (1) the degree of freedom of the system under the given conditions is only determined by the internal components and phases; (2) different external phases can be identified conveniently according to the conditions of the system before knowing the real phase relations. Based on the above results, a simple but general approach is proposed for the treatment of phases and components: all external phases and components can be eliminated from the system without affecting the phase relations, where the external components can be eliminated by appropriate chemographic projections. The projections have no restriction on the states of the phases or the chemical potentials of components from which the projections are made. The present work can give a unified explanation of the previous treatments of phases and components in the analysis of phase assemblages under various specific conditions. It helps to avoid potential misunderstandings or errors in the topological analysis of phase relations.

Second-Order Derivatives of the Gibbs Energy for Liquid Mixtures of Alcohol + Heptane at Pressures up to 100 MPa

Second-order thermodynamic derivative properties, such as isobaric thermal molar expansions, isothermal and adiabatic molar compressibilities, and isochoric molar heat capacities of (ethanol, decan-1-ol, 2-methyl-2-butanol) + heptane mixtures at pressures up to 100 MPa and in the temperature range from 293.15 K to 318.15 K were derived from experimental speed-of-sound u(T, p), density ρ(T, p = 0.1 MPa), and isobaric heat-capacity Cp(T, p = 0.1 MPa) data using appropriate thermodynamic relations. Excess values for the given properties were calculated according to the criterion of thermodynamic ideality of a mixture (Douheret et al., Chem. Phys. Chem. 2, 148 (2001)), i.e., assuming that the chemical potential of component i in the ideal liquid mixture is equal to the chemical potential of component i in the mixture of perfect gases. The deviations from ideality for the mixtures under test have been explained in terms of the self-association of alcohols in solution which produces a strong departure from random mixing, the change in the non-specific interactions during mixing, and the packing effects.

Evaluation of the Component Chemical Potentials in Analytical Models for Ordered Alloy Phases

The component chemical potentials in models of solution phases with a fixed number of sites can be evaluated easily when the Helmholtz energy is known as an analytical function of composition. In the case of ordered phases, however, the situation is less straightforward, because the Helmholtz energy is a functional involving internal order parameters. Because of this, the chemical potentials are usually obtained numerically from the calculated integral Helmholtz energy. In this paper, we show how the component chemical potentials can be obtained analytically in ordered phases via the use of virtual cluster chemical potentials. Some examples are given which illustrate the simplicity of the method.

On the reality of the residual entropy of glasses and disordered crystals: The entropy of mixing

We have previously shown that the assumption that the configurational entropy of a supercooled liquid vanishes at T g leads to a non-trivial violation of the second law. Here we consider the example of the entropy of mixing. We use as a model system two similar chemical substances which form an ideal solution in a mixed phase. We apply the reasoning of our earlier paper to show that this vanishing would lead to a dilemma; either it violates the second law of thermodynamics, or else it cannot be demonstrated by any conceivable experiment. We show further that the vanishing of the entropy of mixing on kinetic arrest leads to the counter-intuitive result that the chemical potential of each component in an infinitely dilute kinetically arrested (or glassy) solution can equal or the chemical potential of the pure component. The most parsimonious conclusion from these results is that residual entropies are real.

Thermodynamic models of liquid multicomponent metallic solutions

Thermodynamic models for regular, pseudo-regular, subregular, and pseudosubregular metallic solutions are considered. It is shown that the transition from the excess Gibbs energy of a solution to the excess chemical potentials of the components in the subregular solution model leads to more complex dependences of the activity coefficients on the solution composition than those in the regular and pseudoregular solution models. Equations for the excess chemical potentials of components obtained by these models are presented for binary, ternary, and multicomponent solutions. The energy of mixing of components in binary solutions are calculated and estimated using experimental data obtained by various authors for the last half a century. The zero-order and first-order interaction parameters are estimated from the energy parameters for dilute solutions.

Calculating the chemical potential of components of a binary solution in a plane-parallel pore

The chemical potential of components of a binary solution is calculated using the expansion of the external field potential in a Taylor series. An expansion of the chemical potential in terms of concentration-concentration direct correlation functions of all orders is obtained. For a plane-parallel pore with an exponential near-wall potential, a solution to the obtained differential equation is constructed in the smooth-inhomogeneity approximation.

Models and calculations of liquid metallic solutions

The thermodynamic models of liquid metallic solutions, namely, regular, pseudoregular, subregular, and pseudosubregular models, are described. The transition from the excess Gibbs energy of a solution to the excess chemical potentials of components in the subregular solution model is shown to lead to more complex dependences of the activity coefficients on the solution composition as compared to the regular and pseudoregular solution models. The energies of mixing of the components in the binary solutions from the eightcomponent Fe-Cr-Ni-Si-Mn-C-O-S system are calculated and estimated using the experimental data reported in the last five decades.

Bilayer Edge and Curvature Effects on Partitioning of Lipids by Tail Length: Atomistic Simulations

The partitioning of lipids among different microenvironments in a bilayer is of considerable relevance to characterization of composition variations in biomembranes. Atomistic simulation has been ill-suited to model equilibrated lipid mixtures because the time required for diffusive exchange of lipids among microenvironments exceeds typical submicrosecond molecular dynamics trajectories. A method to facilitate local composition fluctuations, using Monte Carlo mutations to change lipid structures within the semigrand-canonical ensemble (at a fixed difference in component chemical potentials, Δμ), was recently implemented to address this challenge. This technique was applied here to mixtures of dimyristoylphosphatidylcholine and a shorter-tail lipid, either symmetric (didecanoylphosphatidylcholine (DDPC)) or asymmetric (hexanoyl-myristoylphosphatidylcholine), arranged in two types of structure: bilayer ribbons and buckled bilayers. In ribbons, the shorter-tail component showed a clear enrichment at the highly curved rim, more so for hexanoyl-myristoylphosphatidylcholine than for DDPC. Results on buckled bilayers were variable. Overall, the DDPC content of buckled bilayers tended to exceed by several percent the DDPC content of flat ones simulated at the same Δμ, but only for mixtures with low overall DDPC content. Within the buckled bilayer structure, no correlation could be resolved between the sign or magnitude of the local curvature of a leaflet and the mean local lipid composition. Results are discussed in terms of packing constraints, surface area/volume ratios, and curvature elasticity.

Mass transfer and replacement of minerals in the course of infiltration metasomatism

The direction of Na, K, Ca, Mg, and Fe transfer was determined in the granite-chloride solution system during the metasomatic replacement of granite in response to a temperature and pressure change. The analysis of modeled metasomatic zoning (metasomatic columns) indicates that metasomatic processes of alkaline/acidic and basification/debasification types are controlled by differences in the chemical potentials of components in the solution and rock and by the addition/removal of material due to its excess/deficit in the solution. The former are manifested in the mineralogy of the rear zones of metasomatic columns, while the latter control the total variations in the contents of components in all zones. One of the consequences of this difference is the occurrence of extrema in the distribution of components in zones. Information on the chemical composition of rocks in any given zone does not provide a clue to either the character of the metasomatic processes or the proportions of component concentrations in the solution. In contrast to isobaric-isothermal columns, their thermogradient analogues are characterized by the continuous replacement of minerals and mass transfer in all zones. This predetermines the possibility of the identification of the gradient character of certain columns.

Determination of the critical parameters of polymer solutions

The contribution of short-range orientation order to the chemical potentials of components in a polymer-solvent system was determined. The temperature dependence of the degree of orientation of solvent molecules relative to polymer chains in a polyisobutylene-benzene system was obtained. It was shown that the short-range order in the polymer-solvent system fails with temperature to a much lesser extent than in the pure solvent. The expressions for the upper and lower critical solution temperatures with allowance for the contribution of short-range order to the entropy and the free energy of solution, as well as to the chemical potentials of components, were found. It was demonstrated that, in the polymer-solvent system, two upper and two lower critical solution temperatures can exist.

“Chessboard” effect and mass transfer in interfacial media of organic and inorganic nature

The paper reviews our previous research work on the origin of mass transfer through interfaces of solids and biological membranes. Using the thermodynamic approach of physical mesomechanics we conclude that the propagation of transport flows through interfaces and membranes in organic and inorganic nature is based on structural phase transformations in nanostructural states at interfaces of heterogeneous media. Such states arise at interfaces and in membranes under a chessboard-like distribution of stresses, strains and chemical potentials of components of conjugated dissimilar media. The practical applications of the developed approach in biology and modern materials science are considered.