Solution Theory Research Articles

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

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.

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.

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.

Integrated spectral based monitoring, optimization and control of the combined ozonation and powdered activated carbon adsorption process to remove organic micropollutants from secondary effluent

In this study, an innovative approach for the integrated monitoring, optimization and control of the combined ozonation (O3) and powdered activated carbon (PAC) adsorption process is introduced making use of spectral surrogates (UVA254 and EEM-PARAFAC components). The combined O3-PAC process is designed to remove organic micropollutants (µP) from secondary effluent. Therefore, the removal of 6 µP with varying ozone reactivity was systematically studied in both O3 and PAC as stand-alone systems and in the combined O3-PAC system. For the latter, adsorption experiments were performed with µP spiked into ozonated secondary effluent (sequential system) and with µP spiked into the initial secondary effluent before ozonation (integrated system). In accordance with Swiss standards, the goal was to achieve 80% atrazine removal (as a model O3 recalcitrant compound) at optimized O3 and PAC doses. An ozone dose ranging from 0.45 to 0.65 mg O3/mg DOC was more cost-effective in promoting subsequent PAC adsorption (less than 40%), particularly at low PAC doses (1-2 mg PAC/mg (initial (DOC))). The classical ideal adsorbed solution theory (IAST) model could not be used to predict the subsequent PAC dose after ozonation in the integrated system. Therefore, correlation models were established between (i) the reduction of spectral surrogates during both O3 and PAC dosing and µP removal, (ii) the reduction of spectral surrogates during ozonation and the related PAC dose of the subsequent adsorption process and (iii) between the reduction of spectral surrogates during ozonation and the integrated process. Based on these correlation models, an online spectral control strategy was developed and implemented. Finally, the optimal dosing strategy for 80% atrazine removal was determined as 0.5 mg O3/mg DOC and 1.4 mg PAC/mg (initial) DOC.

Influence of flexoelectricity on coupled electromechanical response of 2D MXene/graphene-based hybrid piezocomposites.

This study investigates the influence of flexoelectricity on the coupled electromechanical behavior of MXene/graphene-based hybrid piezocomposite (MGHPC) plates. We developed an analytical model based on Navier's solution and Kirchhoff's plate theory, as well as an approximate model based on the Ritz method for validation purposes. A three-phase micromechanical modeling is developed for determining the effective properties of MGHPC composed of 2D MXene and graphene nano-reinforcements embedded in an epoxy matrix. These micromechanical models were implemented to predict the static and dynamic electromechanical response of MGHPC plates subject to various edge support and loading conditions. Both the analytical and approximate solutions provided unequivocal evidence of the profound impact of the flexoelectric effect on the bending and modal analysis of MGHPC nanoplates. The flexoelectric effect enhanced the stiffness of the nanoplate, irrespective of the support condition. This implies that MGHPC plates can be tailored for precise resonance frequencies and static deflection within nanoelectromechanical systems. This can be achieved by manipulating parameters such as boundary conditions and geometric attributes, including plate thickness/aspect ratio and graphene/MXene nano-reinforcements volume fractions.

A novel Al-based MOF with straight channel and pocket pore structure for trace benzene adsorption and benzene/cyclohexane separation

Benzene (Bz) vapor poses significant health risks to humans, even at trace concentrations. Additionally, the separation and recycling of Bz and cyclohexane (Cy) is challenging due to their similar kinetic diameters and boiling points. Developing an adsorption-separation material with stronger interactions with Bz than with Cy could serve as a viable strategy for trace Bz adsorption and Bz/Cy separation. In this study, we present a novel aluminum-based metal–organic framework, ZJU-521(Al), composed of tetrakis (4-carboxyphenyl)methane and a helical chain [Al5(OH)7(−COO)8]∞, featuring a simple network of one-way rods and tetrahedra. This framework exhibited a uniform micropore size of 7.23 Å and a specific surface area of 1,248 m2 g−1, demonstrating excellent trace Bz adsorption (4.18 mmol g−1) at P/P0 = 0.01, attributed to its straight channel and orthogonal-array pocket pore structure. The ideal adsorbed solution theory selectivity and separation factor values of ZJU-521(Al) for Bz/Cy were 22.50 and 6.20, respectively, indicating its potential as a material for Bz/Cy separation. Multicomponent simulations showed that Bz molecules were preferentially adsorbed in the pocket due to stronger interactions, such as Al–π interactions. Thus, ZJU-521(Al) exhibits stronger interactions with Bz than with Cy, facilitating effective Bz/Cy separation.

Cu-trimesate and mesoporous silica composite as adsorbent showing enhanced CO2/CH4 and CO2/N2 selectivity for biogas and flue gas separation

Due to their diverse structure, high porosity, and tunable functionality, Metal-Organic Frameworks (MOFs) hold great potential as materials for diverse applications, including gas separation. Material science researchers are focusing on creating flexible materials that have special properties. Most of the latest research mainly concentrates on fabricating composite materials of MOFs and other functional materials. These MOF-based composites can mitigate the limitations of pure MOFs and may even perform better than the individual components. Here, we present a systematic study on the effect of solvent in synthesising a composite (Cu-BTC@SBA-15) of Cu-trimesate MOF (aka CuBTC) and ordered mesoporous silica SBA-15, showing considerable improvement in selectivity for CO2 adsorption from the flue gas and biogas. The pristine Cu-BTC, SBA-15 and the composites with different content of Cu-BTC were characterized by PXRD, BET, FT-IR, SEM, TEM and TGA techniques. The pure gas adsorption isotherms were measured for CO2, CH4, and N2 gases. Ideal Adsorbed Solution Theory (IAST) is used for the binary selectivity calculations for gas systems such as CO2/CH4 and CO2/N2 in the context of biogas and flue gas separation. The composite exhibited an increase in CO2/CH4 selectivity by 39 % compared to pure Cu-BTC and 85 % compared to pure SBA-15. For the CO2/N2 system, the composite showed 38 % higher selectivity than Cu-BTC. The work has significance in the design of effective MOF-based composites for CO2 separation. Our work might open up a new route to design multifunctional materials for worldwide applications through an adsorptive and or mixed matrix membrane route.

Synthesis of Research on Science Learning Management Affecting Problem Solving Skills: Meta-Analysis

The rapidly changing world of the 21st century is complex and unpredictable. The researcher aimed to study the findings from a meta-analysis of 42 research studies related to the learning management of science that affects problem-solving skills during 2012–2022 from a database in Thailand called ThaiLIS. The findings revealed the variables that cause different mean effect sizes and the influence of research quality on the effect size. The instruments of this research were the research quality assessment form and the research characteristics assessment form. Statistics for data analysis were mean, standard deviation, one-way analysis of variance, and multiple regression analysis. The directional research hypothesis, multi-stage sampling, randomized control group post-test only design, PBL, and Weir's solution theory were discovered in the study to be the variables that caused the mean effect sizes to differ at the statistical significance level of .05. In addition, research quality had a positive influence on the effect size. The findings of this study will be useful to teachers who want to provide learning management of science that helps students develop problem-solving skills. This will develop skills more effective than traditional teaching.

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.

The Poisson–Boltzmann equation in micro- and nanofluidics: A formulary

The Poisson–Boltzmann (PB) equation provides a mean-field theory of electrolyte solutions at interfaces and in confinement, describing how ions reorganize close to charged surfaces to form the so-called electrical double layer (EDL), with numerous applications ranging from colloid science to biology. This formulary focuses on situations of interest for micro- and nanofluidics, and gathers important formulas for the PB description of a Z:Z electrolyte solution inside slit and cylindrical channels. Different approximated solutions (thin EDLs, no co-ion, Debye–Hückel, and homogeneous/parabolic potential limits) and their range of validity are discussed, together with the full solution for the slit channel. Common boundary conditions are presented, the thermodynamics of the EDL is introduced, and an overview of the application of the PB framework to the description of electrokinetic effects is given. Finally, the limits of the PB framework are briefly discussed, and Python scripts to solve the PB equation numerically are provided.

Preparation of highly graphitized porous carbon and its ethane/ethylene separation performance

The efficient separation of ethane (C2H6) and ethylene (C2H4) is crucial for the preparation of polymer-grade C2H4, necessitating the development of highly selective and stable C2H6/C2H4 adsorbents. Highly graphitized porous carbon, denoted GC-800, was synthesized by polymerization at room temperature followed by carbonization at 800 °C using phenolic resin as the precursor and FeCl3 as the iron source. Vienna Ab-initio Simulation Package (VASP) calculations confirmed a higher binding energy between C2H6 molecules and graphitized porous carbon surfaces, so that a high degree of graphitization increased the adsorption capacity of porous carbon for C2H6. However, catalytic graphitization using Fe at high temperatures disrupted the microporous structure of the carbon, thereby reducing its ability to separate C2H6/C2H4. By controlling the carbonization temperature, the degree of graphitization and pore structure of the porous carbon could be changed. Raman spectra and XPS spectra showed that the GC-800 had a high degree of graphitization, with a sp2 C content as high as 73%. Low-temperature N2 physical adsorption measurements estimated the specific surface area of GC-800 to be as high as 574 m2·g−1. At 298 K and 1 bar, it had an equilibrium adsorption capacity of 2.16 mmol·g−1 for C2H6, with the C2H6/C2H4 (1:1 and 1:9, v/v) ideal adsorbed solution theory selectivity respectively reaching 2.4 and 3.8, significantly higher than the values of most reported high-performance C2H6 selective adsorbents. Dynamic breakthrough experiments showed that GC-800 could produce high-purity C2H4 in a single step from a mixture of C2H6 and C2H4. Dynamic cycling tests confirmed its good cyclic stability, and that it could efficiently separate C2H6/C2H4 even under humid conditions.

Partial molar volumes of 1–1 electrolytes at high T and P: correlations and predictions

Knowledge of the partial molar volumes of aqueous ions allows accurate calculation of the pressure dependence of equilibrium constants, solubility of minerals, etc., thus being useful for thermodynamic modeling of hydrothermal processes. This study analyzed methods to correlate and predict the values of the partial molar volumes at infinite dilution, V2o, for 1–1 electrolytes and singly charged ions at elevated T and P. Since the precise experimental values of the dielectric constant of water are measured only up to 873 K, we were interested only in non-electrostatic ways to correlate V2o data. First of all, we compiled the V2o values at T > 373 K for the following 1–1 electrolytes: HCl, LiCl, LiI, LiNO3, LiOH, NaF, NaCl, NaBr, NaI, NaNO3, NaOH, NaHCO3, NaClO4, NaH2PO4, NaTr (Tr stands for triflate), KF, KCl, KBr, KI, KNO3, KOH, CsBr, and NH4Cl. Relations, following from the “density” model and from the Fluctuation Solution Theory (FST) were employed to analyze data. It was concluded that at the current state of knowledge of V2o the FST-relations for electrolytes are recommended mainly to reject strongly deviating experimental outliers. However, the “density” model provides a simple and fairly accurate way to describe the compiled set of data with only two parameters for each ion, n and Vhc, values of which were evaluated for the following singly-charged ions: H+, Li+, Na+, K+, Cs+, NH4+, F-, Cl-, Br-, I-, OH–, NO3–, H2PO4-, HCO3–, ClO4-, Tr- (Tr = triflate). Following Mesmer et al. (1988), we consider the fitting parameters Vhc and n to be related to the intrinsic volume of the ion and to the number of water molecules transferred from the bulk water to a hydration shell around the ion, respectively.Although the values of n and Vhc were fitted from data at temperatures from 373 to 673 K and water densities, do, from 0.5 to 1.1 g cm−3, apparently, they predict realistic V2o values at temperatures up to 1600 K and do ranges from 0.2 to 1.6 g cm−3.

Utilizing molecular simulation, ideal adsorbed solution theory and ensemble learning algorithms to investigate adsorption and separation of sulfides on amorphous nanoporous materials

Using grand canonical Monte Carlo method, we investigated the adsorption of pure H2S and SO2 gases on amorphous materials, and the separation of CH4-H2S and CO2-SO2 mixtures. At 303 K, the optimal adsorbent for both gases was found to be HCP-Colina-id016, with 16 mmol/g. For CH4-H2S mixture, despite aCarbon-Marks-id002 exhibiting the highest selectivity (approximately 80), the H2S adsorption was low (around 1 mmol/g), while Kerogen-Coasne-id013 demonstrated a high H2S adsorption of 12 mmol/g with a selectivity of 20. In the case of CO2-SO2, HCP-Colina-id018 exhibited a SO2 selectivity exceeding 30, with a high SO2 adsorption of 12 mmol/g. The Ideal Adsorbed Solution Theory underestimated the adsorption and selectivity of both mixtures, particularly evident in CO2-SO2. Molecular simulations revealed that, for the CO2-SO2 system, CO2 underwent condensation, resulting in a sudden drop in the SO2 adsorption isotherm. However, IAST accurately predicted this abrupt change. Based on the adsorption data obtained from molecular simulations, we compared the predictive performance of four ensemble learning algorithms, namely Random Forest (RF), Gradient Boosted Decision Trees (GBDT), Extreme Gradient Boosting (XGBoost), and CatBoost, for H2S and SO2 pure gases in amorphous porous materials. The rankings were observed to be XGBoost > GBDT > RF > CatBoost.