Chemical potentials and phase equilibria of Lennard-Jones mixtures: a self-consistent integral equation approach

We explore the vapor-liquid phase behavior of binary mixtures of Lennard-Jones-type molecules where one component is supercritical, given the system temperature. We apply the self-consistency approach to the Ornstein-Zernike integral equations to obtain the correlation functions. The consistency checks include not only thermodynamic consistencies (pressure consistency and Gibbs-Duhem consistency), but also pointwise consistencies, such as the zero-separation theorems on the cavity functions. The consistencies are enforced via the bridge functions in the closure which contain adjustable parameters. The full solution requires the values of not only the monomer chemical potentials, but also the dimer chemical potentials present in the zero-separation theorems. These are evaluated by the direct chemical-potential formula [L. L. Lee, J. Chem. Phys. 97, 8606 (1992)] that does not require temperature nor density integration. In order to assess the integral equation accuracy, molecular-dynamics simulations are carried out alongside the states studied. The integral equation results compare well with simulation data. In phase calculations, it is important to have pressure consistency and valid chemical potentials, since the matching of phase boundaries requires the equality of the pressures and chemical potentials of both the liquid and vapor phases. The mixtures studied are methane-type and pentane-type molecules, both characterized by effective Lennard-Jones potentials. Calculations on one isotherm show that the integral equation approach yields valid answers as compared with the experimental data of Sage and Lacey. To study vapor-liquid phase behavior, it is necessary to use consistent theories; any inconsistencies, especially in pressure, will vitiate the phase boundary calculations.     

Modelling Monomer/Disc Composites Phase Behaviour

Summary: A model developed by Balazs' group to explain the phase behaviour of polymer/clay composites is extended to obtain an expression for the free energy of polymer/thin disc mixtures. Phase diagrams for monomer/disc mixtures are built by minimizing the free energy and calculating the chemical potentials of the three system components. Via the comparison of the diagrams, it is studied the effects of nanodisc size and interaction parameters on mixture stability and attained morphology. The performed predictions between monomers and discs give criteria that advance the properties of the mixture. Changes in monomer concentration and interaction parameters provide a means to prevent van der Waals-induced agglomeration. The model takes into account, in only a rather approximate manner, the long-range interactions between clay sheets.     

Solubilities of salts of cobalt(III), chromium(III), and iron(II) complexes in aqueous methanol; transfer chemical potentials of anions

Summary We report solubilities of a variety of salts of cobalt(III), chromium(III), and iron(II) complexes in methanol-water mixtures at 298.2K. From these solubilities and published transfer chemical potentials for the complex cations we are able to derive transfer chemical potentials for such anions as nitrate, thiosulphate, peroxodisulphate, dithionate, thiocyanate, and antimonyl tartrate. Transfer chemical potentials for several hexahalogenometallate anions, and tetrachloroplatinate(II), are derived from published solubilities. A comparative picture of transfer chemical potentials for anions is thus available, with the transition metal complex anions in the overall context of anions and their solvation characteristics in methanol-water mixtures.On leave from the Faculty of Science, Sohag, Egypt.     

Phase-Separation Phenomena of Copolymer Solutions and Fractionation of Copolymers by Chemical Composition

Precipitation temperature-total polymer concentration diagrams for toluene solutions of two styrene-acrylonitrile copolymers different in chemical composition and their mixtures were determined and then triangular phase diagrams of this system were constructed from these diagrams. It is speculated from the triangular phase diagrams and experimentally shown that the copolymer may be effectively fractionated by chemical composition in this system.     

Molecular Thermodynamics for Chemical Process Design

Thermodynamic properties are essential for quantitative process design to produce chemical products. Caloric properties are required for heat balances, but these properties are usually available or estimated easily. More important—and often much more difficult to estimate—are the chemical potentials of components in mixtures; it is these potentials which determine phase equilibria, as required for separation operations, and chemical equilibria, as required for chemical reactors and for separation operations based on chemical reactions. Molecular thermodynamics is an engineering-oriented science for calculating the desired chemical potentials from a minimum of experimental data. This applied science, based on classical and statistical thermodynamics, yields chemical potentials through models that are based on molecular physics and physical chemistry. Selected examples are cited to illustrate the applicability of molecular thermodynamics: group-contribution methods for obtaining chemical potentials in highly nonideal mixtures as required for distillation-column and process-safety design; equation of state for precipitation of uniform-sized crystals from supercritical fluids; molecular-orbital calculations to guide process development for alternatives to environmentally dangerous chlorofluorohydrocarbons; molecular-simulation calculations for separation of gas mixtures with porous adsorbents; equilibria in two-phase aqueous systems for separation of protein mixtures; and, finally, extended polymer-solution thermodynamics to guide synthesis of hydrogels suitable for protein recovery from soybeans and for novel drug-delivery devices.     

Capillary condensation of a binary mixture in slit-like pores

We investigate the capillary condensation of two model fluid mixtures in slit-like pores, which exhibit different demixing properties in the bulk phase. The interactions between adsorbate particles are modeled by using Lennard-Jones (12,6) potentials and the adsorbing potentials are of the Lennard-Jones (9,3) type. The calculations are performed for different pore widths and at different concentrations of the bulk gas, by means of density functional theory. We evaluate the capillary phase diagrams and discuss their dependence on the parameters of the model. Our calculations indicate that a binary mixture confined to a slit-like pore may exhibit rich phase behavior.     

Solvent-free model for self-assembling fluid bilayer membranes: stabilization of the fluid phase based on broad attractive tail potentials

We present a simple and highly adaptable method for simulating coarse-grained lipid membranes without explicit solvent. Lipids are represented by one head bead and two tail beads, with the interaction between tails being of key importance in stabilizing the fluid phase. Two such tail-tail potentials were tested, with the important feature in both cases being a variable range of attraction. We examined phase diagrams of this range versus temperature for both functional forms of the tail-tail attraction and found that a certain threshold attractive width was required to stabilize the fluid phase. Within the fluid-phase region we find that material properties such as area per lipid, orientational order, diffusion constant, interleaflet flip-flop rate, and bilayer stiffness all depend strongly and monotonically on the attractive width. For three particular values of the potential width we investigate the transition between gel and fluid phases via heating or cooling and find that this transition is discontinuous with considerable hysteresis. We also investigated the stretching of a bilayer to eventually form a pore and found excellent agreement with recent analytic theory.     

Determination of fluid-phase behavior using transition-matrix Monte Carlo: binary Lennard-Jones mixtures

We present a novel computational methodology for determining fluid-phase equilibria in binary mixtures. The method is based on a combination of highly efficient transition-matrix Monte Carlo and histogram reweighting. In particular, a directed grand-canonical transition-matrix Monte Carlo scheme is used to calculate the particle-number probability distribution, after which histogram reweighting is used as a postprocessing procedure to determine the conditions of phase equilibria. To validate the methodology, we have applied it to a number of model binary Lennard-Jones systems known to exhibit nontrivial fluid-phase behavior. Although we have focused on monatomic fluids in this work, the method presented here is general and can be easily extended to more complex molecular fluids. Finally, an important feature of this method is the capability to predict the entire fluid-phase diagram of a binary mixture at fixed temperature in a single simulation.     

Field induced gradient simulations: a high throughput method for computing chemical potentials in multicomponent systems

We present a simulation method for direct computation of chemical potentials in multicomponent systems. The method involves application of a field to generate spatial gradients in the species number densities at equilibrium, from which the chemical potential of each species is theoretically estimated. A single simulation yields results over a range of thermodynamic states, as in high throughput experiments, and the method remains computationally efficient even at high number densities since it does not involve particle insertion at high densities. We illustrate the method by Monte Carlo simulations of binary hard sphere mixtures of particles with different sizes in a gravitational field. The results of the gradient Monte Carlo method are found to be in good agreement with chemical potentials computed using the classical Widom particle insertion method for spatially uniform systems.     

Application of one-particle Green functions technique for calculation of vertical ionization potentials of closed-shell molecules described by CNDO/2 semiempirical Hamiltonian

A simple method of infinite summations of some dominant diagrams in the framework of the one-particle Green functions technique is suggested. This method for the calculation of the lowlying vertical ionization potentials of some simple closed-shell molecules described by CNDO/2 semiempirical Hamiltonian is applied. The obtained results are in quite-satisfactory agreement with the experimental values of the vertical ionization potentials measured by the photo-electron spectroscopy technique.     

Predicting thermophysical properties of biodiesel fuel blends using the SAFT-VR approach

Modeling of thermophysical properties and phase equilibria of long-chain methylesters mixtures are presented, using the SAFT-VR approach for mixtures. Molecules are represented as chains of spherical segments that can associate due to the presence of short-ranged attractive sites, using previous molecular parameters obtained for pure fatty acid methyl esters. These attractive sites as well as the intermolecular interactions between monomers segments are modeled via variable-ranged square-well potentials. The cross-energy binary-interaction parameter of the extended Berthelot combining rule was fitted to liquid densities and speed of sound. Very good predictions are obtained for isochoric heat capacities and for binary and ternary phase diagrams.     

A modification of Newton-Raphson algorithm for phase equilibria calculations using numerical differentiation of the gibbs energy

Deiters, U.K., 1985. A modification of Newton-Raphson algorithm for phase equilibria calculations using numerical differentiation of the Gibbs energy. Fluid Phase Equilibria, 19: 287-293.For the solution of the system of nonlinear equation describing the phase equilibrium conditions in fluid mixtures a modified Newton-Raphson method is proposed, which uses numerical differentiation to obtain the chemical potentials. For binary mixtures the new algorithm a little faster, because the same intermediate results that are required for the chemical potentials are also used for the construction of the Jacobian matrix.     

Analyzing the composition-property diagrams of multicomponent liquid mixtures

We consider the local regularities of the composition-intensive/specific property diagrams of multicomponent mixtures in which composition is a scalar function of a vector argument. A topographical method used in differential geometry is used to produce one-dimensional, two-dimensional, and three-dimensional scalar fields. The scalar field gradient is used to study the composition-property diagrams of five-component mixtures (producing four-dimensional scalar fields).     

Multicomponent adsorption on activated carbons under supercritical conditions

Adsorption of binary mixtures onto activated carbon Norit R1 for the system nitrogen-methane-carbon dioxide was investigated over the pressure range up to 15 MPa. A new model is proposed to describe the experimental data. It is based on the assumption that an activated carbon can be characterized by the distribution function of elements of adsorption volume (EAV) over the solid-fluid potential. This function may be evaluated from pure component isotherms using the equality of the chemical potentials in the adsorbed phase and in the bulk phase for each EAV. In the case of mixture adsorption a simple combining rule is proposed, which allows determining the adsorbed phase density and its composition in the EAV at given pressure and compositions of the bulk phase. The adsorbed concentration of each adsorbate is the integral of its density over the set of EAV. The comparison with experimental data on binary mixtures has shown that the approach works reasonably well. In the case of high-pressure binary mixture adsorption, when only total amount adsorbed was measured, the proposed model allows reliably determining partial amounts of the adsorbed components.     

Transfer Chemical Potentials,Solubility and Reactivity of Psoralen and 8-Hydroxypsoralen in Binary Aqueous Methanol Mixtures

Solubilities are reported for psoralen and 8-hydroxypsoralen in binary aqueous mixtures at ambient pressure and 298 K, with organic cosolvent methanol. Gibb's energies of transfer of there two compounds are calculated from their solubilities. Transfer chemical potentials of both compounds are stabilised by increasing prapartion of organic cosolvent because of their markedly hydrophobic character. Basic hydrolysis of psoralen and 8-hydroxypsoralen in aqueous methanol mixtures was examines kinetically, yielding Gibb's energies of activation. Derived transfer parameters are used in analysis of kinetic data to describe the influence of solvent composition on initial and transition states. Derived transfer chemical potentials for a single ion such as hydroxide ion lead to an interesting comparison of the effects of extrathermodynamic assumptions, Wells estimates and TATB assumption, on the initial and transition states. The analysis comfirm the important role played by the choice of extrathermodynamic assumption in determining the overall kinetic pattern. We describe misgivings concerning procedures used by wells to derive transfer chemical potential for single ions.     

Coupling HPLC to on-line, post-column (bio)chemical assays for high-resolution screening of bioactive compounds from complex mixtures

It is challenging to screen and identify bioactive compounds from complex mixtures. We review a recently developed technique that couples high-performance liquid chromatography (HPLC) to on-line, post-column (bio)chemical assays and parallel chemical analysis to screen and identify bioactive compounds from complex mixtures without the need for cumbersome purification and subsequent screening. In this system, HPLC separates complex mixtures and a post-column (bio)chemical assay determines the activity of the individual compounds present in the mixtures. Parallel chemical-detection methods (e.g., diode-array detection, mass spectrometry and nuclear magnetic resonance) identify and quantify the active compounds simultaneously. We focus on relatively widely used on-line, post-column assays for antioxidant screening and less widely used hyphenated systems involving assays based on enzymes and receptors. These strategies have proved to be very useful for rapid profiling and identification of individual active components in mixtures to provide a powerful method for natural product-based drug discovery.     

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.     

Interfacial tension and interfacial profiles: an equation-of-state approach

A quasi-thermodynamic approach of inhomogeneous systems is used for modeling the fluid-fluid interface. It is based on the recently introduced QCHB (quasi-chemical hydrogen bonding) equation-of-state model of fluids and their mixtures, which is used for the estimation of the Helmholtz free energy density difference, Deltapsi(0), between the system with interface and another system of the same constitution but without interface. Consistent expressions for the interfacial tension and interfacial profiles for various properties are presented. The interfacial tension is proportional to the integral of Deltapsi(0) along the full height of the system, the proportionality constant being equal to 1, when no density gradient contributions are taken into consideration, 2, when the Cahn-Hilliard approximation is adopted, and 4, when the full density gradient contributions are taken into consideration. A satisfactory agreement is obtained between experimental and calculated surface tensions. Extension of the approach to mixtures is examined along with the associated problems for the numerical calculations of the interfacial profiles. A new equation is derived for the chemical potentials in the interfacial region, which facilitates very much the calculation of the composition profiles across the interface.     

Density-functional study of model bidisperse ferrocolloids in an external magnetic field

We present phase diagrams of a model bidisperse ferrocolloid consisting of a binary mixture of dipolar hard spheres (DHSs) under the influence of an external magnetic field. The dipole moments of the particles are chosen proportional to the particle volume to mimic real ferrocolloids, and we focus on dipole-dominated systems where isotropic attractive interactions are absent. Our results are based on density-functional theory in the modified mean-field (MMF) approximation. For one-component DHS fluids in external fields, and for corresponding mixtures dominated by one of the components, MMF theory predicts the tricritical point of the transition between an isotropic gas and a ferromagnetic liquid occurring at zero field to be changed into a critical point separating two magnetically ordered phases of different density. The corresponding critical temperature displays a nonmonotonic dependence on the field strength. Completely different behavior is found for the critical temperature related to the demixing phase transitions appearing in strongly asymmetric mixtures [G. M. Range and S. H. L. Klapp, Phys. Rev. E 70, 061407 (2004)]. For such systems, we find a monotonic decrease of the demixing critical temperature with increasing field. The field strength dependence of the critical temperature can therefore be tuned between nonmonotonic and monotonic behaviors just by changing the composition of the mixture--e.g., by adjusting the chemical potentials. This allows us to efficiently control the influence of external magnetic fields on the phase behavior over a large temperature interval.     

Influence of Partition Function and Interaction Potential on Transport Properties of Thermal Plasmas

This paper, divided into two parts, is devoted to the transport properties at local thermodynamic equilibrium: the first part shows the influences of partition functions through the plasma composition and the second part the influence of interaction potentials. In the first part, for complex chemical mixtures the determination of the partition functions of different species is considered: monatomic, diatomic and polyatomic. In the plasmas the monatomic species are important; we study thoroughly the partition functions of monatomic neutrals and ions. We introduce two cut-off criteria. We test the influence of the two criteria on the partition functions and consequently onto the plasma composition and transport properties. We applied the study to Ar–Cu mixtures. In the second part, an historic study shows that the collision integrals used in calculating the transport properties become more accurate leading to more reliable values of the transport coefficients: application to N₂ plasma. Now we have to calculate transport properties of complex mixtures and in these cases, for numerous interactions, a lack of data means that model potentials have to be used to determine collision integrals. In this paper, we have used two potential models: the first, for neutral–neutral and ion–neutral interactions, is an improvement of the Lennard-Jones function and the second is developed, from Stockmayer potential, for polar gases. We compare, for the collision integrals, the results obtained by these two models with those determined with more accurate potentials: applications to CO₂ plasma and H₂–N₂ mixtures.