Electrolyte-UNIQUAC-NRF model for the correlation of the mean activity coefficient of electrolyte solutions

The new electrolyte-UNIQUAC-NRF excess Gibbs function is obtained for calculation of the activity coefficient of the binary electrolyte solutions. The excess Gibbs energy of the model consists of the Pitzer–Debye–Hückel equation, describing the long-range electrostatic contribution and the electrolyte-UNIQUAC-NRF model to account for the short-range contributions. With two adjustable parameters per electrolyte, the new model is applied to correlation of the mean activity coefficients of more than 130 binary aqueous electrolyte solutions at 25 °C. Also the binary parameters, obtaining from regression of mean activity data, are used for prediction of osmotic coefficient data for the same electrolytes. The results are compared with various local composition models such as the electrolyte-NRTL, electrolyte NRF-Wilson, electrolyte-NRTL-NRF, N-Wilson-NRF models. The comparison of the results with experiment demonstrates that the new model can correlate the experimental activity coefficient data and predict the osmotic coefficient data of binary electrolytes accurately.     

Monte Carlo simulation of an inhomogeneous dielectric continuum model for B-DNA

Thermodynamic and structural properties of the counterion atmosphere surrounding B-DNA are calculated by Monte Carlo simulation in a spatially inhomogeneous, but piecewise uniform, dielectric continuum cell model - the "barbarous" model. A boundary element formulation is implemented to study the sensitivity of these properties with respect to perturbations in the location of discontinuous dielectric boundaries relative to fixed and mobile charges. High concentrations are considered corresponding to the liquid crystalline hexagonally ordered phase of DNA. Primitive model results are verified against other simulation reports and a comparison of barbarous model predictions with experimental data is discussed. The internal energy, osmotic coefficient, radial distributions and the population ratio of counterions in the geometrically resolved major and minor grooves are all found to strongly depend on the dielectric boundary position. This suggests that a self-consistent development of the model should consider a free surface problem where the boundary is not specified a priori.     

Optimized Baxter model of protein solutions: electrostatics versus adhesion

A theory is set up of spherical proteins interacting by screened electrostatics and constant adhesion, in which the effective adhesion parameter is optimized by a variational principle for the free energy. An analytical approach to the second virial coefficient is first outlined by balancing the repulsive electrostatics against part of the bare adhesion. A theory similar in spirit is developed at nonzero concentrations by assuming an appropriate Baxter model as the reference state. The first-order term in a functional expansion of the free energy is set equal to zero which determines the effective adhesion as a function of salt and protein concentrations. The resulting theory is shown to have fairly good predictive power for the ionic-strength dependence of both the second virial coefficient and the osmotic pressure or compressibility of lysozyme up to about 0.2 volume fraction.     

Thermodynamic properties of unsymmetrical sticky electrolytes with overlap between ions from Ornstein-Zernike equation

Ornstein-Zernike (OZ) integral equation is solved for unsymmetrical sticky electrolyte solutions with overlap at various distances between ions equal to or less than the collision diameter. Based on the mean-spherical approximation (MSA), all correlation functions and thermodynamic properties can be expressed explicitly in terms of the sticky parameters obtained through a self-consistent procedure. With the reference of an ideal-gas mixture, numerical results of excess internal energy, excess Helmholtz function, osmotic coefficient and activity coefficient for mixtures with stickiness between oppositely charged ions as well as between identically changed ions are presented.     

A model for the Gibbs energy of aqueous solutions of polyelectrolytes

A new model for the excess Gibbs energy of aqueous solutions of polyelectrolytes is presented and applied for the correlation of the activity of water in aqueous solutions of polyelectrolytes without as well as with an added (single) salt. The model considers the phenomenon of counterion condensation, i.e., the partial dissociation of highly charged polyelectrolytes in water. Three parameters (a binary interaction parameter between polymer segments, the equilibrium constant of the dissociation reaction and a parameter which accounts for the polymer configuration) were fitted to the experimental results. The model allows for a reliable correlation of experimental results for the osmotic coefficient of aqueous solutions of a single polyelectrolyte (without as well as with an added salt).     

Thermodynamic behaviour of binary mixture of 1,3-dimethoxyimidazolium bis(trifluoromethyl-sulfonyl)imide and water

The osmotic coefficient value of binary aqueous solution containing ionic liquid was obtained by using vapour-pressure osmometry technique. The change in activity and vapour pressure depression of solvent on addition of 1,3-dimethoxyimidazolium bis(trifluoromethylsulfonyl) imide ((OMe)₂Im:NTf₂) to water have been estimated at two different temperatures (T =313 K and 323 K). The experimental osmotic coefficient values of (OMe)₂Im:NTf₂ at different molality were correlated by extended Pitzer model of Archer and the ion interaction parameters were evaluated. The correlation coefficients obtained from this model were used to estimate the mean molal activity coefficient, and excess Gibbs free energy of this mixture. The osmotic coefficient values were decreased with increase in molality of the ionic liquid within the solution. The osmotic coefficient values were found to be increased with increase in temperature of the system.     

A nonelectrolyte local composition model and its application in the correlation of the mean activity coefficient of aqueous electrolyte solutions

The local composition models have been widely used for the correlation of activity coefficient of nonelectrolyte and electrolyte solutions. A new equation for the excess Gibbs energy function is developed based on the local composition expression of Wilson and the random reference state. This new function, the nonelectrolyte Wilson nonrandom factor (N-Wilson-NRF) model, is presented in the form of a molecular framework so that it can be used for both nonelectrolyte and electrolyte solutions. Without any particular assumptions for ionic solutions, the new function is used to described the short-range contribution of the excess Gibbs energy of electrolyte solutions. The long-range contribution is represented by Pitzer–Debye–Hückel model. With two adjustable parameters per electrolyte, the new model is applied to correlate the mean activity coefficients of more than 150 binary aqueous electrolyte solutions at 25 °C. The results are compared with various local composition models such as the electrolyte-NRTL, electrolyte NRF-Wilson and electrolyte-NRTL-NRF models. The comparison of the results with experiment demonstrates that the new model can correlate the experimental data accurately. Moreover, the model shows high precision of predictability for the osmotic coefficient of binary electrolyte solutions.     

Miniaturized Salinity Gradient Energy Harvesting Devices

Harvesting salinity gradient energy, also known as “osmotic energy” or “blue energy”, generated from the free energy mixing of seawater and fresh river water provides a renewable and sustainable alternative for circumventing the recent upsurge in global energy consumption. The osmotic pressure resulting from mixing water streams with different salinities can be converted into electrical energy driven by a potential difference or ionic gradients. Reversed-electrodialysis (RED) has become more prominent among the conventional membrane-based separation methodologies due to its higher energy efficiency and lesser susceptibility to membrane fouling than pressure-retarded osmosis (PRO). However, the ion-exchange membranes used for RED systems often encounter limitations while adapting to a real-world system due to their limited pore sizes and internal resistance. The worldwide demand for clean energy production has reinvigorated the interest in salinity gradient energy conversion. In addition to the large energy conversion devices, the miniaturized devices used for powering a portable or wearable micro-device have attracted much attention. This review provides insights into developing miniaturized salinity gradient energy harvesting devices and recent advances in the membranes designed for optimized osmotic power extraction. Furthermore, we present various applications utilizing the salinity gradient energy conversion.     

Confinement free energy of flexible polyelectrolytes in spherical cavities

A weakly charged flexible polyelectrolyte chain in a neutral spherical cavity is analyzed by using self-consistent field theory within an explicit solvent model. Assuming the radial symmetry for the system, it is found that the confinement of the chain leads to creation of a charge density wave along with the development of a potential difference across the center of cavity and the surface. We show that the solvent entropy plays an important role in the free energy of the confined system. For a given radius of the spherical cavity and fixed charge density along the backbone of the chain, solvent and small ion entropies dominate over all other contributions when chain lengths are small. However, with the increase in chain length, chain conformational entropy and polymer-solvent interaction energy also become important. Our calculations reveal that energy due to electrostatic interactions plays a minor role in the free energy. Furthermore, we show that the total free energy under spherical confinement is not extensive in the number of monomers. Results for the osmotic pressure and mean activity coefficient for monovalent salt are presented. We demonstrate that fluctuations at one-loop level lower the free energy and corrections to the osmotic pressure and mean activity coefficient of the salt are discussed. Finite size corrections are shown to widen the range of validity of the fluctuation analysis.     

Density functional study on the structural and thermodynamic properties of aqueous DNA-electrolyte solution in the framework of cell model

A density functional theory (DFT) in the framework of cell model is proposed to calculate the structural and thermodynamic properties of aqueous DNA-electrolyte solution with finite DNA concentrations. The hard-sphere contribution to the excess Helmholtz energy functional is derived from the modified fundamental measure theory, and the electrostatic interaction is evaluated through a quadratic functional Taylor expansion around a uniform fluid. The electroneutrality in the cell leads to a variational equation with a constraint. Since the reference fluid is selected to be a bulk phase, the Lagrange multiplier proves to be the potential drop across the cell boundary (Donnan potential). The ion profiles and electrostatic potential profiles in the cell are calculated from the present DFT-cell model. Our DFT-cell model gives better prediction of ion profiles than the Poisson-Boltzmann (PB)- or modified PB-cell models when compared to the molecular simulation data. The effects of polyelectrolyte concentration, ion size, and added-salt concentration on the electrostatic potential difference between the DNA surface and the cell boundary are investigated. The expression of osmotic coefficient is derived from the general formula of grand potential. The osmotic coefficients predicted by the DFT are lower than the PB results and are closer to the simulation results and experimental data.     

A study of a nonprimitive model for electrolyte solutions based on perturbation theory

The equation for the Helmholtz free energy for systems of small anisotropic molecules and ions is deduced by substituting the complete expression for various potential energies (including repulsive, dispersive, electrostatic, and induced energies) into the perturbation expansion. The equation is applied to pure water. The relative dielectric constant is set at unity. Based on the equal chemical potentials of equilibrated vapor and liquid phases, the molecular parameters of water are regressed from the densities of saturated vapor in the temperature range of 0 to 370°C. The ARD of regression is 1.16%. These parameters are used to predict the heat of vaporization and densities of saturated vapor and liquid phases of water in the same temperature range. The ARDs of prediction are 4.5% and 9.8%, respectively. The equation is used to correlate the osmotic coefficients of twelve 1:1 electrolyte solutions. The relative dielectric constant is set at unity. The parameters (Soft-sphere diameter and dispersive constant) of seven ions (Na⁺, K⁺, Rb⁺, Cs⁺, Cl^–, Br^–, and I^–) are obtained. The total average absolute deviation between calculated and experimental values of the osmotic coefficient is 0.041. The parameters of ions can keep constant in different systems.     

广义渗透系数

本文将Bjerrum渗透系数概念推广到混合溶剂体系中,提出了广义渗透系数的概念及其一般定义式,并导出了广义渗透系数与电解质活度系数之间的相互关系式,从而可以借助于广义渗透系数较易实现混合溶剂体系中溶质与溶剂热力学性质之间的相互推算,同时,混合溶剂作为一个整体的非理想性亦可得到具体度量.因此引入广义渗透系数概念具有理论与实际意义.     

盐-水体系溶解平衡计算的自由能最小化及溶度积方法

根据电解质溶液的基本物理化学原理和近代电解质溶液理论的Pitzer离子相互作用模型,通过计算浓电解质溶液的活度系数和水的活度,研究了盐-水体系溶解平衡的计算方法.结果表明,体系Gibbs自由能最小化方法是计算盐-水体系溶解平衡的一种有效方法,其计算结果与溶度积法一致.     

Thermodynamic studies of molecular interactions in aqueous alpha-cyclodextrin solutions: application of McMillan-Mayer and Kirkwood-Buff theories

Osmotic vapor pressure and density measurements were made for aqueous alpha-cyclodextrin (alpha-CD) solutions in the temperature range between 293.15 and 313.15 K. The experimental osmotic coefficient data were used to determine the corresponding activity coefficients and the excess Gibbs free energy of solutions. Further, the activity data obtained at different temperatures along with the enthalpies of dissolution (reported in the literature) were processed to obtain the excess enthalpy and excess entropy values for the solution process. The partial molar entropies of water and of alpha-cyclodextrin were calculated at different temperatures and also at different concentrations of alpha-CD. Using the partial molar volume data at infinite dilution, the solute-solvent cluster integrals were evaluated which yielded information about solute-solvent interactions. The application of McMillan-Mayer theory of solutions was made to obtain osmotic second and third virial coefficients which were decomposed into attractive and repulsive contributions to solute-solute interactions. The second and third osmotic virial coefficients are positive and show minimum at 303.15 K. The Kirkwood-Buff (KB) integrals G(ij), defined by the equation G(ij) = f(infinity)0 (g(ij)- 1)4pir(2) dr, have been evaluated using the experimental osmotic coefficient (and hence activity coefficient) and partial molar volume data. The limiting values of KB integrals, G(ij)(0) are compared with molecular interaction parameters (solute-solute i.e., osmotic second virial coefficient) obtained using McMillan-Mayer theory of solutions. We found an excellent agreement between the two approaches.     

The osmotic second virial coefficient and the Gibbs–McMillan–Mayer framework

The osmotic second virial coefficient is a key parameter in light scattering, protein crystallisation, self-interaction chromatography, and osmometry. The interpretation of the osmotic second virial coefficient depends on the set of independent variables. This commonly includes the independent variables associated with the Kirkwood–Buff, the McMillan–Mayer, and the Lewis–Randall solution theories. In this paper we analyse the osmotic second virial coefficient using a Gibbs–McMillan–Mayer framework which is similar to the McMillan–Mayer framework with the exception that pressure rather than volume is an independent variable. A Taylor expansion is applied to the osmotic pressure of a solution where one of the solutes is a small molecule, a salt for instance, that equilibrates between the two phases. Other solutes are retained. Solvents are small molecules that equilibrate between the two phases. The independent variables of the solvents are temperature, pressure, and chemical potentials. The derivatives in the Gibbs–McMillan–Mayer framework are transformed into derivatives in the Gibbs framework. This offers the possibility for an interpretation and correlation of the osmotic second virial coefficient using activity coefficient models.     

On the thermodynamics of the McMillan–Mayer state function

The osmotic second virial coefficient is a key parameter in light scattering, protein crystallisation, self-interaction chromatography, and osmometry. The interpretation of the osmotic second virial coefficient depends on the solution theory. On the macroscopic level an expansion of the osmotic pressure is employed. A common statistical interpretation of the osmotic second virial coefficient of the expansion employs the McMillan–Mayer framework and the potential of mean force to characterise the solute–solute interaction. Supplementary to the statistical interpretation, it may be advantageous to develop the McMillan–Mayer framework in a classical thermodynamic context for which we develop the relationship between the state function of the McMillan–Mayer framework and the Helmholtz state function.     

A transport model for swelling of polyelectrolyte gels in simple and complex geometries

A model for the swelling of polyelectrolyte gels in salt solutions is developed and solved numerically. The model accounts for the effect of network stress, osmotic pressure, and electrical potential on the species diffusive flux. The osmotic pressure and the network stress are derived from the Helmholtz free energy of the system that is the sum of mixing, elastic, and electrostatic components. One- and two-dimensional swelling in unconstrained and constrained geometries are simulated for a salt–solvent–polymer system. The transient and equilibrium fields of electrical potential, concentrations, deformation, and stress are obtained. Transient overshoots and non-uniformities in the residual profiles are predicted.     

Statistical associating fluid theory coupled with restrictive primitive model extended to bivalent ions. SAFT2: 2. Brine/seawater properties predicted

Statistical associating fluid theory coupled with restricted primitive model (SAFT2) represents the properties of aqueous multiple-salt solutions, such as brine/seawater. The osmotic coefficients, densities, and vapor pressures are predicted without any additional parameters using the salt hydrated diameters obtained for single-salt solutions. For a given ion composition of brine, the predicted vapor pressure, osmotic coefficient, activity of water, and density are found to agree with the experimental data.     

A New Gibbs Energy Model for Obtaining Thermophysical Properties of Aqueous Electrolyte Solutions

In this paper, a new Gibbs energy model is proposed to study the thermophysical properties of aqueous electrolyte solutions at various temperatures. The proposed model assumes that the electrolytes completely dissociate in solution. The model also has two temperature-independent adjustable parameters that were regressed using experimental values of the mean ionic activity coefficients (MIAC) for 87 electrolyte solutions at 298.15 K. Results from the proposed model for the MIAC were compared with those obtained from the E-Wilson, E-NRTL, Pitzer and the E-UNIQUAC models, and the adjustable model parameters were used directly to predict the osmotic coefficients at this temperature. The results showed that the proposed model can accurately correlate the MIAC and predict the osmotic coefficients of the aqueous electrolyte solutions better on the average than the other models studied in this work at 298.15 K. Also, the proposed model was examined to study the osmotic coefficient and vapor pressure for a number of aqueous electrolyte solutions at high temperatures. It should be stated that in order to calculate the osmotic coefficients for the electrolyte solutions, the regressed values of parameters obtained for the vapor pressure at high temperatures were used directly. The results obtained for the osmotic coefficients and vapor pressures of electrolyte solutions indicate that good agreement is attained between the experimental data and the results of the proposed model. In order to unequivocally compare the results, the same experimental data and same minimization procedure were used for all of the studied models.     

Osmotic swelling behavior of globules of W/O/W emulsion liquid membranes

The osmotic swelling behavior of water-in-oil-in-water (W/O/W) type emulsion liquid membranes (ELMs) was investigated. Using an optical microscope equipped with a camera, the changes in the size of the W/O/W globules were monitored over a long period of time (up to about 4 h). The osmotic pressure gradient between the internal and external aqueous phases was induced by creating a concentration difference of d-glucose between the two aqueous phases. The results indicate that the swelling ratio, defined as the ratio of globule diameter at time t to globule diameter at t=0, decreases with the increase in ϕ_W/O(0) (initial volume fraction of internal aqueous phase droplets). The swelling ratio generally increases with the increase in the concentration of surfactant present in the membrane (oil) phase. The permeation coefficient of water also increases with the increase in the surfactant concentration. With the increase in ϕ_W/O(0) up to about 0.42, the permeation coefficient decreases only slightly. However, with further increase in ϕ_W/O(0), a sharp reduction in the permeation coefficient occurs. The mechanism of water transfer in ELMs of the present work is reasoned to be the diffusion of hydrated surfactants.