Solution Theory Research Articles

Metal-Organic Framework-Based NF3 Nanotrap for the Separation of NF3 and CF4.

As an electronic specialty gas, nitrogen trifluoride (NF3) has been widely used in the semiconductor, photovoltaic, and display industries. However, NF3 in industrial settings is typically mixed with CF4, and the distillation method commonly used for their separation consumes significant energy. Herein, we propose a novel NF3 nanoadsorber featuring relatively proximal unsaturated metal sites. The potential field overlap between the two unsaturated metal centers creates an NF3-affinitive environment. The adsorption mechanism of NF3 molecules in the metal-organic frameworks (MOFs) was investigated through density functional theory (DFT) optimization. The results from ideal adsorbed solution theory (IAST) calculations and breakthrough experiments reveal that the MOF-based NF3 nanotrap possesses the highest adsorption capacity and excellent NF3/CF4 selectivity among the physically adsorptive materials reported to date. This work presents a novel solution for the separation and purification of NF3, contributing to the field of gas separation technology.

Adsorption of Methane–Nitrogen mixtures with flexible Zeolitic Imidazolate Framework-7 (ZIF-7)

ZIF–7 is a pressure–regulated flexible metal–organic framework with a notably lower admission pressure for CH4 relative to N2, making it highly-prospective for curbing fugitive emissions of methane. Here, the separation of CH4 from N2 by an improved variant of ZIF–7 was studied over a range of pressures, temperatures, and compositions using multiple complementary techniques. Pure gas adsorption isotherms measured from (283 to 323) K at up to 16 MPa reveal this variant of ZIF-7 exhibits 50–60 % higher adsorption capacities for both CH4 and N2 in the large–pore phase than previous ZIF–7 samples. Binary mixture adsorption isotherms from dynamic column breakthrough experiments were consistent with those predicted from pure–gas isotherms using Ideal Adsorbed Solution Theory. Methane uptake increased significantly when the pore phase transition pressure for the mixture was reached, while the uptake of nitrogen remained small. Consequently, the equilibrium CH4-over–N2 selectivity of ZIF-7 is always larger than 5.5 and can increase to around 9, significantly above that of conventional adsorbents. Further characterisation showed the rate of the adsorption on ZIF–7 initially decreases as the pore phase transition begins before it increases significantly. Raman spectra acquired at various pressures along the adsorption isotherms revealed changes in certain vibrational modes associated with the structural change. Collectively, these observations indicate that the conceptually simple gating mechanism often used to describe the pore phase transitions in ZIF-7 in fact depends on interactions between the guest molecules and the adsorbent framework that continue to operate once the material is in the large–pore state.

Parallel (competitive) reactions of micelle formation and cyclodextrin–surfactant inclusion complex formation in aqueous solution: A consequence of the Gibbs–Duhem equation—invariance of the mass action law and the possibility of determining the equilibrium constant of the inclusion complex

The Gibbs–Duhem equation results in the independence between the standard Gibbs free energy of micelle formation and the standard Gibbs free energy of monocomponent surfactant’s and cyclodextrin’s (CD’s) inclusion complex formation in aqueous solution. The experimental data show that the surfactant’s critical micellar concentration increases in the presence of CD. At a constant temperature, the standard Gibbs free energy of micelle formation remains constant, irrespective of the presence of parallel competitive processes such as inclusion complex formation. This indicates that the critical micellar concentration remains unchanged at the corresponding concentration scale. As a result, the equilibrium constant for surfactant–CD inclusion complex formation can be determined by changing the critical micellar concentration in the presence and absence of CD. A graphical method for determining the equilibrium constant of the inclusion complex is also presented. An analytical approach for analyzing the influence of the formation of the inclusion complex with CD on the formation of the binary mixed micellar pseudophase is presented. Suppose that different values exist for the equilibrium constants of the formation of the inclusion complex for two surfactants from their binary mixture. In this case, there is a change in the initial mole fraction from the initial mixture of surfactants, which should be considered when applying the regular solution theory protocol when determining the parameters of a binary mixed micelle in the presence of CD.

Phosphorus diffusion model in surrounding rock from phosphogypsum-based cemented paste backfill under multifactor coupling effect

Abstract Phosphogypsum (PG) is filled in the solidified filling body formed in the goaf of underground mines, and its leaching of toxic and harmful ions infiltrates and spreads to the groundwater in the surrounding rock, and there is a potential risk of environmental pollution. In order to grasp the diffusion law of pollutant ions in surrounding rock from phosphogypsum-based cemented paste backfill (PCPB), the diffusion coefficient equation of P ions in surrounding rock was established based on the electrolyte solution theory, taking phosphorus (P) ions leached from PCPB as the research object. Adopting Fick’s second law, the diffusion model of P ions in the surrounding rock from PCPB under multi-factor coupling was established by comprehensively considering the effects of multiple factors such as P ion binding capacity in the surrounding rock, time dependence of P ions diffusion coefficients, structural defects of the surrounding rock, stress level, temperature, and so on, and the effects of different factors on the diffusion of P ions in the surrounding rock were analysed. The results show that the larger the concentration of P ions in the surrounding rock, the larger the diffusion coefficient is. The larger the diffusion distance is, the smaller the concentration of P ions in the surrounding rock is. P ions binding capacity and time are negatively correlated with the diffusion coefficient, and the coefficient of deterioration effect of the surrounding rock, the coefficient of stress influence and temperature are positively correlated with the diffusion coefficient. Temperature is the most significant factor affecting the diffusion coefficient of P ions, and after a temperature of 40 °C, the diffusion coefficient of P ions increases rapidly.

Separation of sticker-spacer energetics governs the coalescence of metastable condensates.

A key conundrum of biological condensates is the coexistence of multiple droplets, in direct variance with classical predictions of mean-field theories of polymer solutions. Our current study uncovers that the merging of sticker-spacer condensate is an entropy driven process, as opposed to the surface energy driven fusion that are observed for canonical liquid droplets. This entropy, stemming from the inter-condensate polymer exchange, makes the droplet merging process dependent on inter-sticker dissociation kinetics. Stronger inter-sticker interaction triggers a kinetic arrest, preventing the condensate merger even at a low density. Our prediction starkly correlates with recent experimental findings on protein-RNA condensates in vitro and in vivo, highlighting the biological relevance of the interplay of kinetics and thermodynamics.

CO2 selectivity and adsorption performance of K2CO3-modified zeolite: a temperature-dependent study.

High-performing zeolite materials for carbon dioxide capture are promising for applications such as flue gas CO2 capture. Potassium carbonate-loaded zeolites can offer a plethora of benefits. In this work, for the first time, zeolite-Y impregnated with K2CO3 was studied as a gas adsorbent (CO2, CH4, and N2) and characterized using TGA (thermogravimetric analyzer), XRD, BET, FTIR, FETEM (Field-Emission Transmission Electron Microscope), and XPS. The effect of carbonate loading, temperature, and pressure was particularly targeted and assessed. Accordingly, for a variation in K2CO3 loading from 5 to 15 wt.%, the CO2 adsorption capacity reduced from 3.61 to 1.73mmolg-1 in the synthesized adsorbents. Among all the cases, KYZC10 exhibited very good cyclic adsorption-desorption performance and thermal stability. Further equilibrium modeling studies indicate that the stable and optimally K2CO3-loaded adsorbent (KYZC10) demonstrates effective adsorption isotherm behavior, making it suitable for different temperature variation processes in commercial carbon dioxide capture applications. The KYZC10 adsorbent's stable performance at varying temperatures contributes to its enhanced economic feasibility. This study also used the ideal adsorbed solution theory (IAST) to predict CO2 selectivity over other gases (CH4 and N2).

A Novel kgd-Topological Covalent Organic Framework with Optimum Pore Size for Efficient Benzene/Cyclohexane Separation.

Separation of benzene and cyclohexane is essential for obtaining high-purity cyclohexane in the chemical industry and for resource recovery from exhaust gas, but is one of the most challenging separation processes due to their highly similar boiling points and kinetic diameters. Herein, based on the isoreticular contraction strategy, a novel covalent organic framework (i.e., HFPB-TAB-COF) with kgd topological structure and average pore size of 5.70 Å, between the kinetic diameters of benzene (5.60 Å) and cyclohexane (6.10 Å), is synthesized for benzene/cyclohexane separation by pore confinement effect. HFPB-TAB-COF has the highest ideal adsorbed solution theory (IAST) selectivity of 36.0 for benzene/cyclohexane separation, and can produce 0.48mmol g-1 cyclohexane with purity of +99% from 50:50 (v:v) benzene/cyclohexane mixture under dynamic condition, higher than reported separation materials. Optimizing the pore size of COFs by isoreticular contraction strategy can trigger the pore confinement effect for better meeting the separation challenge in industry.

Lagrangian Manifolds in the Theory of Wave Beams and Solutions of the Helmholtz Equation

Lagrangian Manifolds in the Theory of Wave Beams and Solutions of the Helmholtz Equation

A dynamic entanglement model for adaptive networks in amorphous polymers with pH-responsive dual-shape memory effect

The pH-responsive shape memory polymers (pH-SMPs) have recently attracted significant attention due to their unique and spontaneous actuation capabilities. However, there are few constitutive models developed to explore the working principles behind these complex shape memory behaviors. In this study, a dynamic entanglement model was developed for describing the pH-responsive shape memory effect (SME) in SMPs, in which the crosslinking points in polymer networks underwent reversible entanglements and disentanglements. Susceptible-Infected-Susceptible (SIS) model was firstly employed to formulate an entanglement probability function, which was used to identify the working principles for entanglements of polymer networks and shape recovery of the pH-SMPs. An entanglement free-energy function was further formulated to characterize the pH-responsive dual-SMEs based on the Flory-Huggins solution theory. Phase transition theory was then used to characterize glass transition behaviors and recovery strains of the pH-SMPs, by combining Gordon-Taylor and Kohlrausch-Williams-Watts (KWW) equations. Finally, the proposed model was verified using experimental results reported in the literature. This study provides a fundamental approach to explore the working principle and constitutive relationship between reversible entanglement and pH-responsive SME in SMPs.

Modified Debye-Hückel-Onsager theory for electrical conductivity in aqueous electrolyte solutions: Account of ionic charge nonlocality.

This paper presents a mean field theory of electrolyte solutions, extending the classical Debye-Hückel-Onsager theory to provide a detailed description of the electrical conductivity in strong electrolyte solutions. The theory systematically incorporates the effects of ion specificity, such as steric interactions, hydration of ions, and their spatial charge distributions, into the mean-field framework. This allows for the calculation of ion mobility and electrical conductivity, while accounting for relaxation and hydrodynamic phenomena. At low concentrations, the model reproduces the well-known Kohlrausch's limiting law. Using the exponential (Slater-type) charge distribution function for solvated ions, we demonstrate that experimental data on the electrical conductivity of aqueous 1:1, 2:1, and 3:1 electrolyte solutions can be approximated over a broad concentration range by adjusting a single free parameter representing the spatial scale of the nonlocal ion charge distribution. Using the fitted value of this parameter at 298.15K, we obtain good agreement with the available experimental data when calculating electrical conductivity across different temperatures. We also analyze the effects of temperature and electrolyte concentration on the relaxation and electrophoretic contributions to total electrical conductivity, explaining the underlying physical mechanisms responsible for the observed behavior.

A novel dimension reduction model based on POD and two-grid Crank–Nicolson mixed finite element methods for 3D nonlinear elastodynamic sine–Gordon problem

Earthquake, petroleum and gas extraction, and underground nuclear test all could cause nonlinear tectonic deformation. It is of great significance to effectively predict and evaluate the disasters and impacts of these geological structure deformation. In this end, a three-dimension (3D) nonlinear elastodynamic sine–Gordon model that can be used to describe nonlinear tectonic deformation including 3D displacement vector, 3 × 3 symmetric stress tensor matrix, nonlinear sin term, and singular initial value functions is first proposed. Then, a new time semi-discrete mixed Crank–Nicolson (TSDMCN) scheme for the 3D nonlinear elastodynamic sine–Gordon model is developed, and the existence, stability, and error estimates of the TSDMCN solutions are proved. Next, a new two-grid mixed finite element Crank–Nicolson (TGMFECN) method with unconditional stability for the 3D nonlinear elastodynamic sine–Gordon model is developed, and the existence, stability, and error estimates of the TGMFECN solutions are proved. Thenceforth, it is the most important thing is that a novel reduced-dimensional iterative TGMFECN (RDITGMFECN) method in matrix form is established by resorting to proper orthogonal decomposition only to lower the unknown TGMFECN solution coefficient vectors and keep TGMFECN basis functions unchanged, which can ensure that the RDITGMFECN method has the same accuracy as the usual TGMFECN method, but can greatly lower the dimension of the unknown TGMFECN solution coefficient vectors so as to mitigate calculated workload, save CPU operating-time, improve computing efficiency, and improve real-time calculating accuracy. In theory, the existence, stability, and error estimates of RDITGMFECN solutions are demonstrated by matrix analysis such that the theoretical analysis becomes very intuitive and easy to be understood by the public, which is a new attempt of theoretical analysis. In application, two numerical examples are used to simulate the 3D nonlinear tectonic deformation caused by earthquake and to verify the correctness of our theoretical results and the effectiveness of the RDITGMFECN method.

Effective CO2/N2 adsorptive separation by fluorinated CAG zeolitic imidazolate frameworks in humid environments

Designing and synthesizing stable porous materials for selective carbon dioxide (CO2) capture in humid environments is a paramountly important challenge. In this study, we introduce and present a new hydrophobic fluorinated structure for tetrahedral imidazolate framework-4 (TIF-4) with CAG topology, TIF-4-F. Single-component gas adsorption performance reveals that the CO2 adsorption capacity of TIF-4-F exceeds that of TIF-4 by a dramatic 118.7 % at 298 K and 1 bar. The Langmuir isotherm was utilized to describe the pure CO2 and N2 equivalence, demonstrating that the Ideal adsorbed solution theory (IAST) selectivity for CO2/N2 increased by a remarkable value of 18.9 % that of TIF-4, thereby achieving superior performance among various ZIFs. Grand Canonical Monte Carlo (GCMC) simulations elucidate the adsorption mechanism of CO2 on both materials, with TIF-4-F significantly enhancing its recognition capabilities for CO2. The separation efficacy of two materials was evaluated in a dry CO2/N2 mixture (15/85, v/v), with TIF-4-F showing a significantly prolonged separation time. Furthermore, TIF-4-F maintained its original separation performance over three cycles in a CO2/N2 mixture (15/85, v/v) at 75 % relative humidity (RH). These findings underscore potential applications of TIF-4-F in flue gas and present a viable approach for fluorinated MOFs in CO2/N2 separation.

Synthesis of discrete SSZ-39 zeolite nanosheets by solvent-free seed-assisted route for efficient CO2 capture

Efficient CO2 capture from flue gas and natural gas is highly desirable to reduce greenhouse gas emissions. Discrete SSZ-39 zeolite nanosheets are prepared by the solvent-free seed-assisted route for the first time to capture CO2. Synthesis parameters such as H2O/SiO2 ratio and synthesis time are optimized and the formation mechanism of the SSZ-39 zeolite nanosheets is studied. The nanosheets have a thickness of 30 nm and an aspect ratio of 10. The HR-TEM characterization shows that the base face of the nanosheet corresponds to its (001) plane with a pore size of 3.8 Å × 3.8 Å. The CO2/N2 and CO2/CH4 selectivities of SSZ-39 zeolite nanosheets are as high as 1092 and 136 by Ideal Adsorption Solution Theory (IAST), respectively. Furthermore, breakthrough results indicate that SSZ-39 zeolite nanosheets have great application potential for separating CO2 from flue gas and natural gas.

Two-step preparation of asphalt-based porous carbon adsorbent with superior C2H6/CH4 selectivity for ethane recovery from natural gas

Efficient recovery of ethane (C2H6) from natural gas is of industrial importance, yet it poses considerable challenges. Herein, we report the two-step green preparation of asphalt-based carbon adsorbent Asphalt-based Carbon adsorbents (AsCs) with exceptional C2H6/CH4 selectivity and high capacity, where the KOH usage can be significantly reduced by 75% than conventional chemical activation processes. More importantly, the resulting AsC-0.75-900 exhibits exceptional C2H6/CH4 separation performance with the ideal adsorbed solution theory (IAST) selectivity of 30.74 and C2H6 capacity of 4.53 mmol/g at 298 K and 100 kPa. Notably, even at the low pressure of 10 kPa, its C2H6 uptake remains high at 2.25 mmol/g, comparable to many advanced metal-organic frameworks (MOFs). Molecular simulation was used to elucidate the adsorption mechanism. Fixed-bed experiments further demonstrate dynamic separation performance, achieving complete separation of a C2H6/CH4 binary mixture (10:90, v/v) at ambient condition. In addition to superior separation performance, AsC-0.75-900 offers inherent structural stability and cost-effectiveness, positioning it a highly promising candidate for C2H6 recovery from natural gas.

Well-posedness and stability of a stochastic neural field in the form of a partial differential equation

A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously derived from a stochastic particle system and its noise-driven pattern-forming bifurcations have been characterised. However, due to its nonlinear and non-local nature, standard well-posedness theory for smooth time-dependent solutions of parabolic equations does not apply. In this article, we transform the problem through a suitable change of variables into a nonlinear Stefan-like free boundary problem and use its representation formulae to construct local-in-time smooth solutions under mild hypotheses. Then, we prove that fast-decaying initial conditions and globally Lipschitz modulation functions imply that solutions are global-in-time. Last, we improve previous linear stability results by showing nonlinear asymptotic stability of stationary solutions under suitable assumptions.

Adsorption Thermodynamics for Process Simulation.

Adsorption has rapidly evolved in recent decades and is an established separation technology extensively practiced in gas separation industries and others. However, rigorous thermodynamic modeling of multicomponent adsorption equilibrium remains elusive, and industrial practitioners rely heavily on expensive and time-consuming trial-and-error pilot studies to develop adsorption units. This article highlights the need for rigorous adsorption thermodynamic models and the limitations and deficiencies of existing models such as the extended Langmuir isotherm, dual-process Langmuir isotherm, and adsorbed solution theory. It further presents a series of recent advances in the generalization of the classical Langmuir isotherm of single-component adsorption by deriving an activity coefficient model to account for the adsorbed phase adsorbate-adsorbent interactions, substituting adsorbed phase adsorbate and vacant site concentrations with activities, and extending to multicomponent competitive adsorption equilibrium, both monolayer and multilayer. Requiring a minimum set of physically meaningful model parameters, the generalized Langmuir isotherm for monolayer adsorption and the generalized Brunauer-Emmett-Teller isotherm for multilayer adsorption address various thermodynamic modeling challenges including adsorbent surface heterogeneity, isosteric enthalpies of adsorption, BET surface areas, adsorbed phase nonideality, adsorption azeotrope formation, and multilayer adsorption. Also discussed is the importance of quality adsorption data that cover sufficient temperature, pressure, and composition ranges for reliable determination of the model parameters to support adsorption process simulation, design, and optimization.

Discretization of Fractional Fully Nonlinear Equations by Powers of Discrete Laplacians

AbstractWe study discretizations of fractional fully nonlinear equations by powers of discrete Laplacians. Our problems are parabolic and of order $$\sigma \in (0,2)$$ σ ∈ ( 0 , 2 ) since they involve fractional Laplace operators $$(-\Delta )^{\sigma /2}$$ ( - Δ ) σ / 2 . They arise e.g. in control and game theory as dynamic programming equations – HJB and Isaacs equation – and solutions are non-smooth in general and should be interpreted as viscosity solutions. Our approximations are realized as finite-difference quadrature approximations and are 2nd order accurate for all values of $$\sigma $$ σ . The accuracy of previous approximations of fractional fully nonlinear equations depend on $$\sigma $$ σ and are worse when $$\sigma $$ σ is close to 2. We show that the schemes are monotone, consistent, $$L^\infty $$ L ∞ -stable, and convergent using a priori estimates, viscosity solutions theory, and the method of half-relaxed limits. We also prove a second order error bound for smooth solutions and present many numerical examples.

Understanding the Enhanced Separation Mechanism of C2H4/C2H6 at Low Pressure by HKUST−1

The production of ethylene (C2H4) is typically accompanied by the formation of impurities like ethane (C2H6), making the separation of C2H4 and C2H6 crucial in industrial processes. Here, we investigated the S-shaped adsorption phenomenon of C2H6 on the metal–organic framework HKUST−1. The virial equation is used to fit the C2H6 and C2H4 adsorption isotherms under low coverage. The results showed that the repulsion energy between neighboring C2H6 molecules was significantly higher than that between neighboring C2H4 molecules, which was an important reason for the lower adsorption of C2H6 by HKUST−1 at low coverage. As more molecules are adsorbed, gas molecules aggregate within pores, leading to more hydrogen bonds formed between HKUST−1 and larger-sized C2H6 under high coverage conditions. This phenomenon plays a crucial role in the S-shaped adsorption behavior of HKUST−1 on C2H6. Additionally, this unique adsorption behavior allows for the efficient separation of C2H4/C2H6 mixtures at low pressures. The ideal adsorbed solution theory (IAST) selectivity of HKUST−1 for C2H4/C2H6 mixtures was 3.78 at 283 K and 1 bar, but increased significantly to 7.53 under low pressure. This unique mechanism provides a theoretical basis for the low-pressure separation of C2H4/C2H6 by HKUST−1 and establishes a solid foundation for future practical research applications.

How reliable is the Real Adsorbed Solution Theory (RAST) for estimating ternary mixture equilibrium in microporous host materials?

Microporous crystalline adsorbents such as zeolites, and metal-organic frameworks (MOFs) have potential use in a wide variety of separations applications. In applications such as CO2 capture, the Ideal Adsorbed Solution Theory (IAST) often fails to provide a quantitative description of mixture adsorption equilibrium especially in cation-exchanged zeolites. The failure of the IAST is ascribable to non-compliance with one or more tenets mandated by the IAST such as (a) homogeneous distribution of adsorbates within the pore landscape, (b) no preferential location of guest species, and (c) absence of molecular clustering due to say hydrogen bonding. The focus of this article is on the reliability of the Real Adsorbed Solution Theory (RAST) models for quantitative estimation of adsorption equilibrium. Configurational-Bias Monte Carlo (CBMC) simulations are undertaken to determine the adsorption equilibrium for ternary CO2/CH4/N2, CO2/CH4/C3H8, CO2/CH4/H2, and water/methanol/ethanol mixtures in NaX, LTA-4A, CHA, DDR, and MFI zeolites. Additionally, CBMC simulations of the constituent binary pairs are used to determine the Wilson or NRTL parameters, taking due account of the dependence of the activity coefficients on the spreading pressure. Use of the binary pair Wilson or NRTL parameters allows the estimation of ternary mixture adsorption equilibrium, that is tested against the CBMC data on component loadings. In all investigated guest/host combinations, the RAST provides a good estimation of ternary mixture adsorption equilibrium.

Measuring the solubility of tacrolimus in supercritical carbon dioxide (binary and ternary systems), comparing the performance of machine learning models with conventional models

The solubility of tacrolimus in a supercritical carbon dioxide (SC-CO2) with and without co-solvent (ternary and binary system) was investigated. The experimental conditions include the temperatures of 308 to 338 K and the pressures of 12 to 30 MPa were considered. The values of tacrolimus solubilization in SC-CO2 in binary and ternary systems were from 0.416 × 10−5 to 1.589 × 10−5 and from 0.389 × 10−4 to 0.875 × 10−4, respectively. The obtained results presented that adding a co-solvent (ethanol) could affect tacrolimus solubility significantly, the mole fraction of tacrolimus in SC-CO2/co-solvent under all experimental conditions was at least 4.9 more than that of SC-CO2 alone. The correlation of the solubility data was achieved by three distinct methods: (1) SRK EoS with van der Waals (vdW2) and Wong-Sandler (WS) as mixing rules, (2) solution theory, (3) empirical and (4) machine learning based models. The analysis of variance (ANOVA) results showed that Sparks et al. (AIC −817.05, and AARD 5.08 %) and Bian et al. (AIC −815.77 and AARD 5.17 %) models could correlate the experimental data of tacrolimus in SC-CO2 with more accuracy, as compared to the other empirical models. Sodeifian and Sajadian model with AARD% and AIC of 2.99 and −726.22, respectively, has acted as the most accurate empirical model in ternary system. The solution theory was able to calculate the solubility for the tacrolimus-SC-CO2-ethanol system with high accuracy (AARD, % 4.85, AIC −701.41, F value 169.70 and Radj 0.9622). Also, the Gradient Boosting model (AARD accurately predicted the outcomes with perfect accuracy for binary and ternary systems. Finally, total (ΔHtotal, 23.21 cal/mol), solvation (ΔHsol, −19.47 cal/mol) and vaporization (ΔHvap, 42.68 cal/mol) enthalpies were obtained by using an energy term in Chrastil and Bartle models.