Lattice Fluid Research Articles

A crossover lattice fluid equation of state for pure fluids

A lattice fluid model is one of the most versatile, molecular-based engineering equations of state (EOS) but, in common with all analytic equations of state, the lattice fluid (LF) EOS exhibits classical behaviour in the critical region rather than the non-analytical, singular behaviour seen in real fluids. In this research, we use the LF EOS and develop a crossover lattice fluid (xLF) equation of state near to and far from the critical region which incorporates the scaling laws valid asymptotically close to the critical point while reducing to the original classical LF EOS far from the critical point. We show that, over a wide range of states, the xLF EOS yields the saturated vapour pressure data and the density data with much better accuracy than the classical LF EOS.

Correlations between Penetrant Properties and Infinite Dilution Gas Solubility in Glassy Polymers: NELF Model Derivation

An analysis of the empirical correlations that relate the solubility coefficient of gases at infinite dilution in glassy polymers to penetrant properties has been performed, by considering gas sorption as a succession of three steps: condensation of the penetrant, dissolution in the equilibrium polymeric phase, and departure of the system from equilibrium. The infinite dilution solubility coefficient is obtained from the contributions of the three steps, the first two of which involve standard equilibrium thermodynamics, while the latter requires nonequilibrium considerations and is described by using the nonequilibrium lattice fluid (NELF) model. The various terms have been evaluated for several gases in polycarbonate, polysulfone, poly(phenylene oxide), and poly(methyl methacrylate). It has been found that the largest term in the expression of solubility is due to condensation, which explains the observed correlation between solubility and critical temperature, while the out of equilibrium contribution to solubility, which generally gives numerical values lower than the condensation term, is in turn more strongly correlated to the penetrant critical volume.

Calculating the Equation of State Parameters and Predicting the Spinodal Curve of Isotactic Polypropylene/Poly(ethylene-co-octene) Blend by Molecular Dynamics Simulations Combined with Sanchez−Lacombe Lattice Fluid Theory

Molecular dynamics simulations are adopted to calculate the equation of state characteristic parameters P*, rho*, and T* of isotactic polypropylene (iPP) and poly(ethylene-co-octene) (PEOC), which can be further used in the Sanchez-Lacombe lattice fluid theory (SLLFT) to describe the respective physical properties. The calculated T* is a function of the temperature, which was also found in the literature. To solve this problem, we propose a Boltzmann fitting of the data and obtain T* at the high-temperature limit. With these characteristic parameters, the pressure-volume-temperature (PVT) data of iPP and PEOC are predicted by the SLLFT equation of state. To justify the correctness of our results, we also obtain the PVT data for iPP and PEOC by experiments. Good agreement is found between the two sets of data. By integrating the Euler-Lagrange equation and the Cahn-Hilliard relation, we predict the density profiles and the surface tensions for iPP and PEOC, respectively. Furthermore, a recursive method is proposed to obtain the characteristic interaction energy parameter between iPP and PEOC. This method, which does not require fitting to the experimental phase equilibrium data, suggests an alternative way to predict the phase diagrams that are not easily obtained in experiments. As an example, in the framework of SLLFT, the spinodal curve for the iPP/PEOC blend is predicted at the low molecular weights that are used in the simulations.

Vapor−Liquid Equilibrium for Carbon Dioxide + Isopropyl, Isobutyl, and Isoamyl Acetates

Vapor−liquid equilibrium of three acetates (isopropyl, isobutyl, and isoamyl acetate) + carbon dioxide were measured using a circulating-type equilibrium cell at temperature ranging from (313.2 to 333.2) K and pressure up to 10 MPa. The measured experimental data were correlated by the Peng−Robinson with conventional mixing rule and nonrandom lattice fluid with hydrogen bonding equations of state with a single binary interaction parameter.

Nonrandom Hydrogen-Bonding Model of Fluids and Their Mixtures. 2. Multicomponent Mixtures

Nonrandom hydrogen bonding (NRHB) lattice theory is extended here to multicomponent fluid mixtures rigorously. The model accounts for nonideal thermodynamic behavior of mixtures due to molecular connectivity of nonspherical molecules, weak van der Waals forces between first-neighbor molecular segments, and hydrogen-bonding interactions. The random distribution of molecules in the lattice is calculated using the generalized Staverman theory, while for the nonrandom correction, the Guggenheim quasi-chemical theory is adopted. Finally, the hydrogen-bonding contribution is based on Veytsman statistics as implemented in lattice fluid theory by Panayiotou and Sanchez. The equation of state is coupled with the mass action law due to hydrogen bonding, and both are solved simultaneously. The model is applied for the calculation of vapor−liquid, liquid−liquid, and vapor−liquid−liquid equilibria at low and high pressures of binary mixtures of fluids with large molecular size differences and/or different types of int...

A multi-fluid nonrandom associating lattice fluid model

A lattice fluid theory valid from pure fluids to multi-component mixtures of molecules having any number of associating donor and acceptor groups formulated. Under the fundamental assumption that the intermolecular forces are divided into physical and chemical forces, the Veytsman statistics for associating contribution was combined with the multi-fluid nonrandom lattice fluid (MLF) equation of state developed recently by the present authors. The physical contribution is characterized by temperature independent molecular parameters representing close packed volumes of a mer, segment numbers and energy parameters of a pure fluid, and a binary interaction parameter for a binary mixture. The chemical part is represented by internal energy and entropy of associating system. The resulting multi-fluid nonrandom associating lattice fluid (MALF) equation of state was applied to describe thermodynamic properties of pure fluids and phase equilibrium of mixtures. The results for alkane–alcohol and alcohol–alcohol mixtures were found satisfactory for most systems when compared with the MLF and the statistical associating fluid theory (SAFT) model.

A quasi-chemical nonrandom lattice fluid model for phase equilibria of associating systems

The contribution from Veytsman statistics for associating is combined with the quasi-chemical nonrandom lattice fluid (QLF) equation of state developed by the present authors. The physical contribution is characterized by temperature independent molecular parameters, representing close packed volume of a mer, segment numbers and energy parameters of a pure fluid, and a binary interaction parameter for a mixture. The chemical part is represented by the internal energy and entropy of the associating system. The resulting quasi-chemical nonrandom associating lattice fluid equation of state was applied to describe thermodynamic properties of pure fluids and phase equilibria of mixtures. The absolute chemical potentials which are derived from the canonical partition function are presented by using the fundament thermodynamic relations to consistently calculate phase equilibrium properties. The results for alkane–alkanol and alcohol–alkanol mixtures were found satisfactory for most systems when compared with the quasi-chemical nonrandom lattice fluid model and the statistical associating fluid theory model.

Solubility of mixed gases containing carbon dioxide in ionic liquids: Measurements and predictions

Solubilities of pure carbon dioxide and propane and those of the mixed gases carbon dioxide + nitrogen and carbon dioxide + propane in 1-hexyl-3-methylimidazolium tri(bisfluoromethylsulfonyl)imide were experimentally studied at 298.15 K and up to 1 MPa. A group-contribution lattice fluid equation of state was applied for the prediction of the solubility of pure and mixed gases with ionic liquids. Predicted results were found in reasonably good agreements with experimental data.

High Pressure Phase Behavior of Carbon Dioxide + 2,2,2-Trifluoroethyl Methacrylate and + Poly(2,2,2-trifluoroethyl methacrylate) Systems

Pressure−composition isotherms for binary mixtures of carbon dioxide (CO2) + 2,2,2-trifluoroethyl methacrylate (TFEMA) were investigated in a variable volume view cell at temperature from (323.2 to 353.2) K and pressure up to about 12 MPa. Phase behavior of these binary experimental data were correlated with Peng−Robinson equation of state using a van der Waals one fluid mixing rule with two adjustable parameters. The cloud points of CO2 + poly(2,2,2-trifluoroethyl methacrylate) (poly(TFEMA)) were investigated at temperature up to 450 K and pressure up to 59.4 MPa. The CO2 + poly(TFEMA) system showed LCST pressure behavior. The Sanchez−Lacombe lattice fluid equation of state is used to correlate the experimental cloud point data.

New Travelling Wave Solutions for an Asymmetric Model of a Rod in a Lattice Fluid with Nonlinear Advection

Based on the modified extended tanh-function method, we consider the continuum problem of the driven diffusive flow of particles behind an impenetrable obstacle (rod) of the length L. The results show that the presence of an obstacle, whether stationary or moving, in a driven diffusive flow with nonlinear drift will distort the local concentration profile to a state which divided the (x,y)-plane into two regions. The concentration is relatively higher in one side than the other side, apart from the value of , where D is the diffusion coefficient and v is the drift velocity. This problem has relevance for the size segregation of particulate matter which results from the relative motion of different-size paricles induced by shaking. The obtained soultions include soliton, periodical, rational and singular solutions.

Influence of structural and interfacial properties of microemulsion eluent on chromatographic separation of simvastatin and its impurities

In order to calculate the structural and compositional characteristics of microemulsions, used as eluents in the investigation of HPLC separation of simvastatin and its six impurities, predictive molecular thermodynamic approach is developed. For calculating fundamental interfacial properties of microemulsions, from pure component properties, the lattice fluid self-consistent field theory (SCF), in conjunction with new classical thermodynamic expressions, was applied. Calculation of predicted radii (PR), area per surfactant (ApS) and film thickness (FT), as well as is interfacial tension and bending moment enabled better understanding of separation of such a complex mixture. The microemulsion, which contained 1% (w/w) of diisopropyl ether, 2% (w/w) of sodium dodecyl sulphate (SDS), 6.6% (w/w) of co-surfactant such as n-butanol and 90.4% (w/w) of aqueous 25 mM disodium phosphate pH 7.0 enabled appropriate chromatographic separation between investigated compounds. It has been proved that this microemulsion had the smallest droplet radii and film thickness, which enabled optimal separation. Also the interfacial tension is the smallest, so the free energy change associated with dispersing the drops favoured a large number of small droplets. Hydrophobic interactions between solutes and stationary phase, as well as the microstructural characteristics of microemulsion eluents had a significant influence on chromatographic behavior of simvastatin and its six impurities.

Enhanced, mass-conserving closure scheme for lattice Boltzmann equation hydrodynamics

We derive and demonstrate a practical and accurate algorithm designed to impose Dirichlet boundary conditions (specified boundary velocity) on the edge nodes of a lattice Boltzmann fluid simulation space. The current algorithm models the lattice fluid on boundary and bulk nodes to identical accuracy and in a demonstrably equivalent manner. Whilst this new method applies to rectangular geometries, it adds to our previous method [2] (i) the condition of mass conservation and (ii) the ability to treat with unimpaired accuracy both internal and external corners.

A quasi-chemical nonrandom lattice fluid model: General derivation and application to pure fluids and mixtures

A quasi-chemical nonrandom lattice fluid model without temperature dependence of the close packed volumes of a mer, segment numbers and energy parameters of pure systems is presented. The explicit nonrandom lattice fluid (NLF) model with quasi-chemical approach was capable of describing properties for complex systems, but this model had strong the temperature dependence of energy parameters and segment numbers of pure systems. In this work, a quasi-chemical nonrandom lattice fluid model with no temperature dependence of close packed volumes of a mer, segment numbers and energy parameters of pure systems is proposed. And the model was extended to mixtures by using consistent method for phase equilibrium calculation with fugacity coefficients derived from the present equation of state. We tested consistently the present model on 17 phase equilibrium data sets of vapor–liquid equilibria and compared with the NLF model and the SAFT model. The present model (three pure parameters for pure component and one binary interaction parameter) showed better results for most systems than the NLF model (six adjustable pure parameters and one binary interaction parameter) and the SAFT model (three pure parameters and one binary interaction parameter).

Athermal lattice chains compared with hard-sphere chains

The Guggenheim–Huggins–Miller approximation of athermal lattice fluids has been a basis for lattice fluid equations of state. For better understanding of GHM solution, it was compared with molecular simulation data of hard-sphere chains. Relations were developed between parameters of lattice and off-lattice chain fluids for the comparison. The Guggenheim–Huggins–Miller approximation was found in good agreements with molecular simulation data of fused-hard-spheres when compared using the developed relations. But the agreements of GHM solution with tangent-hard-sphere chain data were found less satisfactory and deviations increased as segment number increased. Average deviations of GHM solution from mixed tangent-hard-sphere chain data were found similar to those of pure components. Real fluid parameters fitted to a GHM-based lattice fluid equation of state and the first order thermodynamic perturbation theory-based SAFT were found optimized to give similar repulsive contributions.

A multi-fluid nonrandom lattice fluid model: General derivation and application to pure fluids

A multi-fluid nonrandom lattice fluid model with no temperature dependence of close packed volumes of a mer, segment numbers and energy parameters of pure systems is presented. The multi-fluid nonrandom lattice fluid (MF-NLF) model with the local composition concept was capable of describing properties for complex systems. However, the MF-NLF model has strong temperature dependence of energy parameters and segment numbers of pure systems; thus empirical correlations as functions of temperature were represented for reliable and convenient use in engineering practices. The MF-NLF model without temperature dependence of pure parameters could not predict thermodynamic properties accurately. It was found that the present model with three parameters describes quantitatively the vapor pressure and the saturated density for the pure fluid.

A multi-fluid nonrandom lattice fluid model: Mixtures

A multi-fluid nonrandom lattice fluid model with no temperature dependence of close packed volumes of a mer, segment numbers and energy parameters of pure systems and its consistent method for phase equilibrium calculation were presented in the previous paper. In this work, the model was extended to mixtures by using consistent method for phase equilibrium calculation with fugacity coefficients derived from the present equation of state and it was applied to vapor-liquid equilibrium. We consistently tested the present model on 17 phase equilibrium data sets of vapor-liquid equilibria and compared it with the MF-NLF model and the SAFT model. The present model (3 pure parameters for pure component and one binary interaction parameter) showed better results for most systems than the MF-NLF model (6 adjustable pure parameters and one binary interaction parameter) and the SAFT model (3 pure parameters and one binary interaction parameter).

Solubility of gases and vapors in glassy polymers modelled through non-equilibrium PHSC theory

Well established equation-of-state (EoS) models from Perturbed Hard Sphere Chain Theory have been adopted within the framework of non-equilibrium thermodynamics for glassy polymers (NET-GP) to describe the solubility of small penetrants in glassy polymers. The procedure presented here parallels the one already applied to the Lattice Fluid EoS, obtaining the Non-Equilibrium Lattice Fluid (NELF) model. The solubility is calculated as pseudo-equilibrium solute content in the glassy polymeric phase at fixed temperature and solute fugacity, and is compared to the experimental data. The NE-PHSC model predictions require pure component and binary EoS parameters, together with the value of the glassy polymer density during sorption. Several common glassy polymers, as well as a high free volume fluoropolymer, have been considered to test the model ability to represent the thermodynamic properties of glassy gas–polymer mixtures. A comparison between the performance of two NE-PHSC models, endowed with different expressions for the interaction potential, is also presented, offering interesting conclusions on their accuracy in the representation of the thermodynamic properties of relatively high-density systems. The results obtained in this work show that the NET-GP approach provides a reliable description of the properties of homogeneous glassy mixtures.

Intra- and Intermolecular Hydrogen-Bonding Model and Its Application to 2-Alkoxyethanol Systems

Intramolecular hydrogen bonding is known to be responsible for unusual phase behaviors such as liquid−liquid equilibria in polymer solutions and protein folding in biological systems. Results of experimental intra- and interbonded fraction data and molecular simulation have been interpreted using lattice statistics and perturbation theories. So far, however, few quantitative comparisons are reported with physical properties and phase equilibrium data of real systems. In this study, a more general derivation of statistics was developed for intra- and interbonding contributions based on Veytsman statistics, which was incorporated in physical contributions of a nonrandom lattice fluid theory to obtain a free energy model for real systems. The proposed model was applied to vapor pressures and densities of pure 2-alkoxyethanols and intra- and interbonded mole fractions and phase equilibria of 2-alkoxyethanol containing mixtures. Calculated results were found in close agreement with property data in the constraint of correlating inter- and intrabonded mole fractions, and deviations of calculated results with data were found similar to those without an intrabonding consideration.

New miscible blends composed of polysulfone and poly(1-vinylpyrrolidone- co-acrylonitrile) copolymers and their phase behavior

The miscibility of polysulfone, PSf, blend with poly(1-vinylpyrrolidone), PVP, and that of PSf blend with poly(1-vinylpyrrolidone- co-acrylonitrile) copolymers, P(VP–AN), containing various amount of VP were explored. Even though PSf did not formed miscible blends with PVP when both components had high molecular weight, it formed miscible blend with PVP by decreasing molecular weight of PVP. PSf also formed homogeneous mixtures with P(VP–AN) containing AN from 2 to 16 wt%. These miscible blends underwent phase separation on heating caused by LCST-type (lower critical solution temperature-type) phase behavior. The phase separation temperature of miscible blends first increases with AN content, goes through a maximum centered at about 8 wt% AN. Interaction energies of binary pairs involved in blends were evaluated from the observed phase boundaries using the lattice–fluid theory. The decline of the contact angle between water and blend film by increasing P(VP–AN) content in blend indicated that the hydrophobic properties of PSf could be improved by blending with P(VP–AN) copolymers.

Hydration of an apolar solute in a two-dimensional waterlike lattice fluid

In a previous work, we investigated a two-dimensional lattice-fluid model, displaying some waterlike thermodynamic anomalies. The model, defined on a triangular lattice, is now extended to aqueous solutions with apolar species. Water molecules are of the "Mercedes Benz" type, i.e., they possess a D3 (equilateral triangle) symmetry, with three equivalent bonding arms. Bond formation depends both on orientation and local density. The insertion of inert molecules displays typical signatures of hydrophobic hydration: large positive transfer free energy, large negative transfer entropy (at low temperature), strong temperature dependence of the transfer enthalpy and entropy, i.e., large (positive) transfer heat capacity. Model properties are derived by a generalized first order approximation on a triangle cluster.