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.     

Thermodynamic perturbation theory of simple liquids. A hierarchy of equations for expansion coefficients

The properties of an expansion of the statistical sum of a simple liquid with respect to the potential in thermodynamic perturbation theory are analyzed. The coefficients of this expansion are determined by the unperturbed potential, depend on temperature and density, and can be calculated by means of mathematical modeling. It is shown here that the derivatives of these coefficients with respect to temperature and density are expressed through the higher expansion coefficient (these relations are usually called a hierarchy of equations). These coefficients determine the expansion of the Helmholtz free energy and RDF with respect to the perturbation potential. The thermodynamic characteristics of the system (entropy, internal energy, pressure) are expressed through both the differential relations for the Helmholtz free energy and the integral expressions containing RDF. It is found that the hierarchy of equations obtained in this work makes these different methods equivalent. This is important for the application of thermodynamic perturbation theory because it becomes unnecessary to model any other equilibrium properties of the system apart from the expansion coefficients.     

Solid phase thermodynamic perturbation theory: test and application to multiple solid phases

A simple procedure for the determination of hard sphere (HS) solid phase radial distribution function (rdf) is proposed, which, thanks to its physical foundation, allows for extension to other crystal structures besides the fcc structure. The validity of the procedure is confirmed by comparing (1) the predicted HS solid phase rdf's with corresponding simulation data and (2) the predicted non-HS solid phase Helmholtz free energy by the present solid phase first-order thermodynamic perturbation theory (TPT) whose numerical implementation depends on the HS solid phase rdf's as input, with the corresponding predictions also by the first-order TPT but the required HS solid phase rdf is given by an "exact" empirical simulation-fitted formula. The present solid phase first-order TPT predicts isostructural fcc-fcc transition of a hard core attractive Yukawa fluid, in very satisfactory agreement with the corresponding simulation data and is far more accurate than a recent thermodynamically consistent density functional perturbation theory. The present solid phase first-order TPT is employed to investigate multiple solid phases. It is found that a short-ranged potential, even if it is continuous and differentiable or is superimposed over a long-ranged potential, is sufficient to induce the multiple solid phases. When the potential range is short enough, not only isostructural fcc-fcc transition but also isostructural bcc-bcc transition, simple cubic (sc)-sc transition, or even fcc-bcc, fcc-sc, and bcc-sc transitions can be induced. Even triple point involving three solid phases becomes possible. The multiple solid phases can be stable or metastable depending on the potential parameters.     

Phase equilibria and surface tension of pure fluids using a molecular layer structure theory (MLST) model

This paper presents a new model based on thermodynamic and molecular interaction between molecules to describe the vapour–liquid phase equilibria and surface tension of pure component. The model assumes that the bulk fluid can be characterised as set of parallel layers. Because of this molecular structure, we coin the model as the molecular layer structure theory (MLST). Each layer has two energetic components. One is the interaction energy of one molecule of that layer with all surrounding layers. The other component is the intra-layer Helmholtz free energy, which accounts for the internal energy and the entropy of that layer. The equilibrium between two separating phases is derived from the minimum of the grand potential, and the surface tension is calculated as the excess of the Helmholtz energy of the system. We test this model with a number of components, argon, krypton, ethane, n-butane, iso-butane, ethylene and sulphur hexafluoride, and the results are very satisfactory.     

Non-hard sphere thermodynamic perturbation theory

A non-hard sphere (HS) perturbation scheme, recently advanced by the present author, is elaborated for several technical matters, which are key mathematical details for implementation of the non-HS perturbation scheme in a coupling parameter expansion (CPE) thermodynamic perturbation framework. NVT-Monte Carlo simulation is carried out for a generalized Lennard-Jones (LJ) 2n-n potential to obtain routine thermodynamic quantities such as excess internal energy, pressure, excess chemical potential, excess Helmholtz free energy, and excess constant volume heat capacity. Then, these new simulation data, and available simulation data in literatures about a hard core attractive Yukawa fluid and a Sutherland fluid, are used to test the non-HS CPE 3rd-order thermodynamic perturbation theory (TPT) and give a comparison between the non-HS CPE 3rd-order TPT and other theoretical approaches. It is indicated that the non-HS CPE 3rd-order TPT is superior to other traditional TPT such as van der Waals/HS (vdW/HS), perturbation theory 2 (PT2)/HS, and vdW/Yukawa (vdW/Y) theory or analytical equation of state such as mean spherical approximation (MSA)-equation of state and is at least comparable to several currently the most accurate Ornstein-Zernike integral equation theories. It is discovered that three technical issues, i.e., opening up new bridge function approximation for the reference potential, choosing proper reference potential, and/or using proper thermodynamic route for calculation of f(ex-ref), chiefly decide the quality of the non-HS CPE TPT. Considering that the non-HS perturbation scheme applies for a wide variety of model fluids, and its implementation in the CPE thermodynamic perturbation framework is amenable to high-order truncation, the non-HS CPE 3rd-order or higher order TPT will be more promising once the above-mentioned three technological advances are established.     

Density functional theory study on the structure and capillary phase transition of a polymer melt in a slitlike pore: effect of attraction

A density functional theory is proposed to investigate the effects of polymer monomer-monomer and monomer-wall attractions on the density profile, chain configuration, and equilibrium capillary phase transition of a freely jointed multi-Yukawa fluid confined in a slitlike pore. The excess Helmholtz energy functional is constructed by using the modified fundamental measure theory, Wertheim's first-order thermodynamic perturbation theory, and Rosenfeld's perturbative method, in which the bulk radial distribution function and direct correlation function of hard-core multi-Yukawa monomers are obtained from the first-order mean spherical approximation. Comparisons of density profiles and bond orientation correlation functions of inhomogeneous chain fluids predicted from the present theory with the simulation data show that the present theory is very accurate, superior to the previous theory. The present theory predicts that the polymer monomer-monomer attraction lowers the strength of oscillations for density profiles and bond orientation correlation functions and makes the excess adsorption more negative. It is interesting to find that the equilibrium capillary phase transition of the polymeric fluid in the hard slitlike pore occurs at a higher chemical potential than in bulk condition, but as the attraction of the pore wall is increased sufficiently, the chemical potential for equilibrium capillary phase transition becomes lower than that for bulk vapor-liquid equilibrium.     

Sensitivity analysis of thermodynamic properties of liquid water: a general approach to improve empirical potentials

A sensitivity analysis of bulk water thermodynamics is presented in an effort to understand the relation between qualitative features of molecular potentials and properties that they predict. The analysis is incorporated in molecular dynamics simulations and investigates the sensitivity of the Helmholtz free energy, internal energy, entropy, heat capacity, pressure, thermal pressure coefficient, and static dielectric constant to components of the potential rather than the parameters of a given functional form. The sensitivities of the properties are calculated with respect to the van der Waals repulsive and the attractive parts, plus short- and long-range Coulomb parts of three four site empirical water potentials: TIP4P, Dang-Chang and TTM2R. The polarization sensitivity is calculated for the polarizable Dang-Chang and TTM2R potentials. This new type of analysis allows direct comparisons of the sensitivities for different potentials that use different functional forms. The analysis indicates that all investigated properties are most sensitive to the van der Waals repulsive, the short-range Coulomb and the polarization components of the potentials. When polarization is included in the potentials, the magnitude of the sensitivity of the Helmholtz free energy, internal energy, and entropy with respect to this part of the potential is comparable in magnitude to the other electrostatic components. In addition similarities in trends of observed sensitivities for nonpolarizable and polarizable potentials lead to the conclusion that the complexity of the model is not of critical importance for the calculation of these thermodynamic properties for bulk water. The van der Waals attractive and the long-range Coulomb sensitivities are relatively small for the entropy, heat capacity, thermal pressure coefficient and the static dielectric constant, while small changes in any of the potential contributions will significantly affect the pressure. The analysis suggests a procedure for modification of the potentials to improve predictions of thermodynamic properties and we demonstrate this general approach for modifying potentials for one of the potentials.     

Performance evaluation of third-order thermodynamic perturbation theory and comparison with existing liquid state theories

To evaluate the performance of a recently proposed third-order thermodynamic perturbation theory (TPT), we employ the third TPT for calculation of thermodynamic properties such as compressibility factor, internal energy, excess chemical potential, gas-liquid coexistence curve, and critical properties of several fluids. By comparing the third-order TPT results with corresponding simulation data available in literature and supplied in the present report and theoretical results from several other theoretical approaches, one concludes that the third-order TPT is, in general, more accurate than other approaches such as Barker-Henderson second-order TPT using a macroscopic compressibility approximation (MCA-TPT), self-consistent Ornstein-Zernike approach, Monte Carlo perturbation theory, and a specially devised equation of state. Specifically, the third-order TPT can predict quantitatively a double critical phenomena of gas-liquid transition and a low-density liquid (LDL)-high-density liquid (HDL) transition associated with a soft core (SC) potential fluid very satisfactorily, but the predictions for the LDL-HDL transition based on the second-order MCA-TPT are quantitatively very bad or qualitatively incorrect. The failure of the second-order MCA-TPT for the SC fluid can be ascribed to the facts that for the SC potential the second-order and third-order terms of the perturbation expansion are not small quantities and that the second-order term is underestimated by the MCA. It is concluded that the present third-order version of the TPT is reliable for varying model fluids.     

Prenematic behavior of the electric-field-induced increment of the basic thermodynamic quantities of isotropic mesogenic liquids of different polarity

Temperature dependences of the static dielectric permittivity and its derivative, obtained for isotropic mesogenic liquids composed of the molecules of different polarity in relation to the basic thermodynamic quantities (internal energy, entropy, and Helmholtz free energy), are analyzed. A role of the molecular polarity in the dielectric behavior of the liquids in the vicinity of the isotropic to nematic phase transition is discussed.     

Communication: Thermodynamics of water modeled using ab initio simulations

We regularize the potential distribution framework to calculate the excess free energy of liquid water simulated with the BLYP-D density functional. Assuming classical statistical mechanical simulations at 350 K model the liquid at 298 K, the calculated free energy is found in fair agreement with experiments, but the excess internal energy and hence also the excess entropy are not. The utility of thermodynamic characterization in understanding the role of high temperatures to mimic nuclear quantum effects and in evaluating ab initio simulations is noted.     

Accurate and local formulation for thermodynamic properties directly from integral equation method

A local formulation for determination of excess chemical potential is derived out by applying an assumption of linear dependence of correlation function and bridge function on the charging parameter to the Kirkwood charging formula and scaling the bridge function, the scaling parameter is specified by a Gibbs–Duhem relation. The local formulation for the excess chemical potential only requires the correlation function and bridge function of the investigated state as input and is therefore free of an unwieldy thermodynamic integration. A comprehensive comparison between the presently calculated thermodynamic quantities for a Lennard–Jones (LJ) fluid including two key quantities, i.e. the excess chemical potential and excess entropy, corresponding simulation data available in literature, and corresponding calculated results by several other global and local formulations, indicates that the present formulation is the only one capable of predicting locally and excellently all of the thermodynamic properties of the LJ fluid. The GCMC simulation is carried out for a core-softened potential fluid and the LJ fluid near critical state and at subcritical state near the gas–liquid coexistence line to obtain the excess chemical potential which is also in excellent agreement with the theoretical prediction from the present formalism; this indicates that the present formalism is of general interest in fluid statistical mechanics and applicable to parameter space covering over the entire phase diagram.     

Chemical potential perturbation: a method to predict chemical potentials in periodic molecular simulations

A new method, called chemical potential perturbation (CPP), has been developed to predict the chemical potential as a function of density in periodic molecular simulations. The CPP method applies a spatially varying external force field to the simulation, causing the density to depend upon position in the simulation cell. Following equilibration the homogeneous (uniform or bulk) chemical potential as a function of density can be determined relative to some reference state after correcting for the effects of the inhomogeneity of the system. We compare three different methods of approximating this correction. The first method uses the van der Waals density gradient theory to approximate the inhomogeneous Helmholtz free energy density. The second method uses the local pressure tensor to approximate the homogeneous pressure. The third method uses the Triezenberg-Zwanzig definition of surface tension to approximate the inhomogeneous free energy density. If desired, the homogeneous pressure and Helmholtz free energy can also be predicted by the new method, as well as binodal and spinodal densities of a two-phase fluid region. The CPP method is tested using a Lennard-Jones (LJ) fluid at vapor, liquid, two-phase, and supercritical conditions. Satisfactory agreement is found between the CPP method and an LJ equation of state. The efficiency of the CPP method is compared to that for Widom's method under the tested conditions. In particular, the new method works well for dense fluids where Widom's method starts to fail.     

Modeling of phase equilibrium and vapor adsorption on carbon black based on a combination of a lattice theory and equation of state

A thermodynamic approach is developed in this paper to describe the behavior of a subcritical fluid in the neighborhood of vapor-liquid interface and close to a graphite surface. The fluid is modeled as a system of parallel molecular layers. The Helmholtz free energy of the fluid is expressed as the sum of the intrinsic Helmholtz free energies of separate layers and the potential energy of their mutual interactions calculated by the 10-4 potential. This Helmholtz free energy is described by an equation of state (such as the Bender or Peng-Robinson equation), which allows us a convenient means to obtain the intrinsic Helmholtz free energy of each molecular layer as a function of its two-dimensional density. All molecular layers of the bulk fluid are in mechanical equilibrium corresponding to the minimum of the total potential energy. In the case of adsorption the external potential exerted by the graphite layers is added to the free energy. The state of the interface zone between the liquid and the vapor phases or the state of the adsorbed phase is determined by the minimum of the grand potential. In the case of phase equilibrium the approach leads to the distribution of density and pressure over the transition zone. The interrelation between the collision diameter and the potential well depth was determined by the surface tension. It was shown that the distance between neighboring molecular layers substantially changes in the vapor-liquid transition zone and in the adsorbed phase with loading. The approach is considered in this paper for the case of adsorption of argon and nitrogen on carbon black. In both cases an excellent agreement with the experimental data was achieved without additional assumptions and fitting parameters, except for the fluid-solid potential well depth. The approach has far-reaching consequences and can be readily extended to the model of adsorption in slit pores of carbonaceous materials and to the analysis of multicomponent adsorption systems.     

Resummed thermodynamic perturbation theory for central force associating potential. Multi-patch models

A resummed thermodynamic perturbation theory for associating fluids with multiply bondable central force associating potential is extended for the fluid with multiple number of multiply bondable associating sites. We consider a multi-patch hard-sphere model for associating fluids. The model is represented by the hard-sphere fluid system with several spherical attractive patches on the surface of each hard sphere. Resummation is carried out to account for blocking effects, i.e., when the bonding of a particle restricts (blocks) its ability to bond with other particles. Closed form analytical expressions for thermodynamical properties (Helmholtz free energy, pressure, internal energy, and chemical potential) of the models with arbitrary number of doubly bondable patches at all degrees of the blockage are presented. In the limiting case of total blockage, when the patches become only singly bondable, our theory reduces to Wertheim's thermodynamic perturbation theory (TPT) for polymerizing fluids. To validate the accuracy of the theory we compare to exact values, for the thermodynamical properties of the system, as determined by Monte Carlo computer simulations. In addition we compare the fraction of multiply bonded particles at different values of the density and temperature. In general, predictions of the present theory are in good agreement with values for the model calculated using Monte Carlo simulations, i.e., the accuracy of our theory in the case of the models with multiply bondable sites is similar to that of Wertheim's TPT in the case of the models with singly bondable sites.     

Thermodynamics of the Laminar Donnan System

Thermodynamic quantities of a polyelectroyte immersed in salt solution are derived modeling the polyelectrolyte by a sequence of charged parallel flat plates. The starting point for the analysis is the derivation of the Gibbs free enthalpy in its canonic variables pressure (p) and temperature (T), i.e., as a thermodynamic potential. From this, further thermodynamic quantities such as Helmoltz free energy, entropy, internal energy, compressibility, isobar and isochor heat capacities, and expansive force are derived in analytical expressions by differentiation. All these formulas contain the parameter plate surface charge density (sigma) that provides a measure of the discontinuity of the polymer charge distribution that can be used to fit the theory to experimental data. Thermodynamic quantities are also known from the classical Donnan equilibrium that treats the polyelectroyte charge network as a charge continuum. A limiting process is used to perform the transition from the laminar Poisson- Boltzmann model to the continuous Donnan equilibrium. In general, the expressions of the Donnan system are recovered for plate charge density sigma-->0, number of plates Z-->infinity, and sigma Z=constant. Copyright 2000 Academic Press.     

Density-functional theory and Monte Carlo simulation for the surface structure and correlation functions of freely jointed Lennard-Jones polymeric fluids

We present a nonlocal density-functional theory of polymeric fluids consisting of freely jointed Lennard-Jones chains with explicit consideration of the segment size, van der Waals attraction, and structural correlations due to chain connectivity. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the short-ranged repulsion and the first-order thermodynamic perturbation theory for chain connectivity. The contribution of the long-ranged attraction to the Helmholtz energy functional is taken into account using a quadratic density expansion with the direct correlation function obtained from the first-order mean-spherical approximation. The numerical performance of the density-functional theory is compared well with the simulation results from this work as well as those from the literature for the segment-level density profiles and correlation functions of Lennard-Jones chains in slit pores, near isolated nanoparticles, or in bulk.     

Thermodynamic and structural properties of methanol-water solutions using nonadditive interaction models

We study bulk structural and thermodynamic properties of methanol-water solutions via molecular dynamics simulations using novel interaction potentials based on the charge equilibration (fluctuating charge) formalism to explicitly account for molecular polarization at the atomic level. The study uses the TIP4P-FQ potential for water-water interactions, and the CHARMM-based (Chemistry at HARvard Molecular Mechanics) fluctuating charge potential for methanol-methanol and methanol-water interactions. In terms of bulk solution properties, we discuss liquid densities, enthalpies of mixing, dielectric constants, self-diffusion constants, as well as structural properties related to local hydrogen bonding structure as manifested in radial distribution functions and cluster analysis. We further explore the electronic response of water and methanol in the differing local environments established by the interaction of each species predominantly with molecules of the other species. The current force field for the alcohol-water interaction performs reasonably well for most properties, with the greatest deviation from experiment observed for the excess mixing enthalpies, which are predicted to be too favorable. This is qualitatively consistent with the overestimation of the methanol-water gas-phase interaction energy for the lowest-energy conformer (methanol as proton donor). Hydration free energies for methanol in TIP4P-FQ water are predicted to be -5.6 +/- 0.2 kcal/mol, in respectable agreement with the experimental value of -5.1 kcal/mol. With respect to solution microstructure, the present cluster analysis suggests that the microscale environment for concentrations where select thermodynamic quantities reach extremal values is described by a bipercolating network structure.     

Adsorption Equilibrium of Binary Mixtures in Zeolites and State of Adsorbed Phase

The criterion of ideal behavior of a mixture of a few molecules within a separate zeolite cavity is formulated on the basis of the statistical thermodynamics. The criterion determines the dependence of the Helmholtz free energy, internal energy, and entropy of a molecular aggregate on the ratio of the number of molecules of components 1 and 2. The similarity between this criterion and the criterion of ideal behavior for bulk solutions is shown. Expressions of excess thermodynamic functions of the molecular mixture in a cavity are obtained. The negative magnitude of these excess functions is proposed to be due to rearrangement of molecules under influence of energetic heterogeneity. The calculation procedure of the excess functions has been demonstrated for the system CO₂-C₂ H₆-zeolite NaX, the information of both isotherms and isosteric adsorption heats being used simultaneously. The approach offered allows the state of adsorbed mixture in a separate cavity to be analyzed from pure-component and multicomponent experimental data.     

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.