Solution Theory Research Articles

Engineered cellulose-based porous carbon adsorbents for superior gas adsorption and selective separation of CH4/H2 and CH4/N2

Adsorption and separation of methane from turquoise hydrogen and coalbed methane is becoming an important method for using unconventional natural gas. Adsorbent performance determines this technique. In this regard, the cellulose-based (Cell-PC) adsorbents were engineered by a facile process with a one-pot calcination method without solvent and an activating reagent-free like KOH with an economical and green approach for CH4/H2 and CH4/N2 separation. The series of adsorbents were synthesized, such as Cell-100, U-Cell-111, O-Cell-111, O-Cell-112, O-Cell-113, and O-Cell-113-a, from cellulose with urea/oxalic acid and sodium hydrogen carbonate, which helps to create pore structure. All adsorbents were characterized by several techniques, including XRD, SEM, XPS, and BET. All Cell-PC adsorbents were used to systematically investigate adsorption studies for CH4, N2, and H2. The O-Cell-113-a adsorbent demonstrated a superior CH4 uptake capacity of 52.75 cm3/g at 273 K and 37.92 cm3/g at 298 K under 100 kPa. It was attributed to the synergistic role of high surface area, mesopore volume, micropore volume, morphology, and surface functional group. However, the O-Cell-113-a showed lower adsorption for N2 and was unable to adsorb H2 at 298 K, indicating the adsorbent has selective adsorption properties for CH4. Furthermore, the ideal adsorbed solution theory (IAST) model was used to calculate the selectivity of CH4/N2, which was found to be around 13.78 at 273 K and 12.64 at 298 K, which is higher than most previously reported porous carbon. The isosteric heat of adsorption of O-Cell-113-a adsorbent was further calculated for CH4 and N2.

Interaction of saponification products of Robinia pseudoacacia seed oil with cetyltrimethyl ammonium bromide

AbstractThe interaction between novel saponification products (RCOONa or RCOOK) of Robinia pseudoacacia seed oil and cetyltrimethyl ammonium bromide (CTAB) in aqueous solution have been investigated by surface tension method at 25°C. The critical micelle concentration (cmc) of RCOONa/CTAB and RCOOK/CTAB mixture were measured. The surface properties of saponification products, CTAB as well as the mixed system were explored and compared. The composition, activity coefficient of mixed micelle, and the interaction parameters (βσ, βM) between surfactants were estimated according to the Regular Solution Theory, the Clint's model and the Rubingh's model in the framework of pseudophase separation model. The experimental results suggested that both RCOONa and RCOOK have synergism with CTAB in mixed micelle formation and surface tension reduction through calculating of βσ and βM in the mixed system. This could be attributed to the strong interaction between the head groups with opposite charges in the surfactant molecules.

Phase diagrams of oxide system FeO–MnO–MgO–SiO2. Report 1. Binary oxide systems MnO–SiO2 and MgO–SiO2

Manganese and silicon are present in almost any steel, and magnesium can enter the metal from the lining and magnesian slags or be introduced in the form of an alloy, so knowledge of the thermodynamics and phase equilibria of liquid and solid silicate solutions allows to predict the appearance of non-metallic inclusions in steel. The FeO–MnO–MgO–SiO2 system includes six double and four triple phase diagrams of oxide systems. The binary phase diagrams of FeO–MnO, FeO–MgO, FeO–SiO2, and MnO–MgO oxide systems were previously studied. In this work, the phase diagrams of the MnO–SiO2 and MgO–SiO2 systems were considered, the liquidus lines and thermodynamic data on the melting of manganese and magnesium silicates – the enthalpies and entropies of melting of ortho- and metasilicates of manganese (Mn2SiO4 and MnSiO3) and magnesium (Mg2SiO4 and MgSiO3) were calculated. The theory of subregular ionic solutions, which takes into account the dependence of the coordination number on the melt composition, is used to calculate the activities of the components of the oxide melt and accurately describes the diagrams with two immiscible liquids and is consistent with the experimental data presented in the literature. The obtained data on the energy parameters of the theory of subregular ionic solutions for the systems MnO–SiO2 and MgO–SiO2, as well as the thermodynamic data on the formation of manganese and magnesium silicates, make it possible to proceed to the study of ternary oxide systems belonging to the FeO–MgO–MnO–SiO2 system.

Phase diagrams of oxide system FeO–MnO–MgO–SiO2. Report 1. Binary oxide systems MnO–SiO2 and MgO–SiO2

Manganese and silicon are present in almost any steel, and magnesium can enter the metal from the lining and magnesian slags or be introduced in the form of an alloy, so knowledge of the thermodynamics and phase equilibria of liquid and solid silicate solutions allows to predict the appearance of non-metallic inclusions in steel. The FeO–MnO–MgO–SiO2 system includes six double and four triple phase diagrams of oxide systems. The binary phase diagrams of FeO–MnO, FeO–MgO, FeO–SiO2, and MnO–MgO oxide systems were previously studied. In this work, the phase diagrams of the MnO–SiO2 and MgO–SiO2 systems were considered, the liquidus lines and thermodynamic data on the melting of manganese and magnesium silicates – the enthalpies and entropies of melting of ortho- and metasilicates of manganese (Mn2SiO4 and MnSiO3) and magnesium (Mg2SiO4 and MgSiO3) were calculated. The theory of subregular ionic solutions, which takes into account the dependence of the coordination number on the melt composition, is used to calculate the activities of the components of the oxide melt and accurately describes the diagrams with two immiscible liquids and is consistent with the experimental data presented in the literature. The obtained data on the energy parameters of the theory of subregular ionic solutions for the systems MnO–SiO2 and MgO–SiO2, as well as the thermodynamic data on the formation of manganese and magnesium silicates, make it possible to proceed to the study of ternary oxide systems belonging to the FeO–MgO–MnO–SiO2 system.

Thermodynamics of multi-sublattice battery active materials: from an extended regular solution theory to a phase-field model of LiMnyFe1-yPO4

Phase separation during the lithiation of redox-active materials is a critical factor affecting battery performance, including energy density, charging rates, and cycle life. Accurate physical descriptions of these materials are necessary for understanding underlying lithiation mechanisms, performance limitations, and optimizing energy storage devices. This work presents an extended regular solution model that captures mutual interactions between sublattices of multi-sublattice battery materials, typically synthesized by metal substitution. We apply the model to phospho-olivine materials and demonstrate its quantitative accuracy in predicting the composition-dependent redox shift of the plateaus of LiMnyFe1-yPO4 (LFMP), LiCoyFe1-yPO4 (LFCP), LiCoxMnyFe1-x-yPO4 (LFMCP), as well as their phase separation behavior. Furthermore, we develop a phase-field model of LFMP that consistently matches experimental data and identifies LiMn0.4Fe0.6PO4 as a superior composition that favors a solid solution phase transition, making it ideal for high-power applications.

Method of Stress Field and Stability Analysis of Bedding Rock Slope Considering Excavation Unloading

The stress state of a slope and its analytical solution are prerequisites for stability analysis. Currently, the limit equilibrium method cannot consider the stress state of slopes, and the solution of bedding slope stress remains in numerical simulations for a long time. In this paper, based on the theory of the elastic stress solution of the wedge top under a concentrated load, the analytical solution of the stress field was obtained using Matlab programming. Unloading stress analysis method (USAM) for determining the sliding surface of the bedding rock slope, safety factor (Fs), and reinforcement forces (Fr) were proposed. The USAM is compared with the Limit Equilibrium Method (LEM) and Finite Element Method (FEM) in terms of the Fs, Fr, sliding surface position, and sliding surface stress. The results show: 1) The analytical stress of the slope can be obtained quickly and conveniently using the USAM, while subsequent programming helps in faster completion of the stability evaluation of the bedding rock slope. Fs, Fr, sliding surface position, and sliding surface stress are all close to the results obtained by the FEM. 2) The USAM is more suitable for analyzing slopes when the angle between the slope surface and structural plane is greater than 20° (θ > 20°) and the slope angle is greater than 45° (β > 45°). 3) Through the analysis of specific engineering cases, the safety factor calculated by USAM are 0.06 and 0.02 larger than those obtained by LEM and FEM, respectively, and the required reinforcement force for the slope is closer to that obtained by FEM. The novel stress and stability analysis method allows for the rapid evaluation and optimal engineering design of bedding rock slope.

Eliminating solution singularity of variably distributed-order time-fractional diffusion equation via strongly singular initial distribution

We investigate a distributed-order time-fractional diffusion equation with a time-dependent density function and its support. The well-posedness and regularity of the equation are analyzed. In particular, by proposing appropriate assumptions on the density function, which may lead to a strongly singular initial distribution instead of smooth distributions that are usually imposed in the literature, we prove smoothing properties of the solutions and eliminate their nonphysical initial singularities without affecting the memory and hereditary properties of the model, i.e. the current state of the model depends on its states at previous time instants, away from the initial time. The results generalize the solution theory of distributed-order equations and provide a model correction for problems that do not exhibit initial singularities.

A Microporous Zn(bdc)(ted)0.5 with Super High Ethane Uptake for Efficient Selective Adsorption and Separation of Light Hydrocarbons.

Separating light hydrocarbons (C2H6, C3H8, and C4H10) from CH4 is challenging but important for natural gas upgrading. A microporous metal-organic framework, Zn(bdc)(ted)0.5, based on terephthalic acid (bdc) and 1,4-diazabicyclo[2.2.2]octane (ted) ligands, is synthesized and characterized through various techniques, including powder X-ray diffraction (PXRD), scanning electron microscopy (SEM), thermogravimetric analysis (TGA), and porosity analysis. The adsorption isotherms of light hydrocarbons on the material are measured and the isosteric adsorption heats of CH4, C2H6, C3H8, and C4H10 are calculated. The prediction of C2-4/C1 adsorption selectivities is accomplished using ideal adsorbed solution theory (IAST). The results indicate that the material exhibits exceptional characteristics, including a Brunauer-Emmett-Teller (BET) surface area of 1904 m2/g and a pore volume of 0.73 cm3/g. Notably, the material demonstrates remarkable C2H6 adsorption capacities (4.9 mmol/g), while CH4 uptake remains minimal at 0.4 mmol/g at 298 K and 100 kPa. These findings surpass those of most reported MOFs, highlighting the material's outstanding performance. The isosteric adsorption heats of C2H6, C3H8, and C4H10 on the Zn(bdc)(ted)0.5 are higher than CH4, suggesting a stronger interaction between C2H6, C3H8, and C4H10 molecules and Zn(bdc)(ted)0.5. The molecular simulation reveals that Zn(bdc)(ted)0.5 prefers to adsorb hydrocarbon molecules with richer C-H bonds and larger polarizability, which results in a stronger dispersion force generated by an adsorbent-adsorbate induced polarization effect. Therefore, the selectivity of C4H10/CH4 is up to 180 at 100 kPa, C3H8/CH4 selectivity is 67, and the selectivity of C2H6/CH4 is 13, showing a great potential for separating C2-4 over methane.

Abstraction of Continuous-Time Systems Based on Feedback Controllers and Mixed Monotonicity

In this paper, we consider the problem of the computation of efficient symbolic abstractions for continuous-time control systems. The new abstraction algorithm builds symbolic models with the same number of states but fewer transitions in comparison to the one produced by the standard algorithm. At the same time, the new abstract system is at least as controllable as the standard one. The proposed algorithm is based on the solution of a region-to-region control synthesis problem. This solution is formally obtained using the theory of viscosity solutions of the dynamic programming equation and the theory of differential equations with discontinuous righthand side. In the new abstraction algorithm, the symbolic controls are essentially the feedback controllers that solve this control synthesis problem. The improvement in the number of transitions is achieved by reducing the number of successors for each symbolic control. For a certain class of control systems, with a suitable set of discretization parameters, the new algorithm may even produce deterministic abstract systems or systems with a singleton input alphabet. The approach is illustrated by examples that compare the two abstraction algorithms.

Two metal-organic frameworks based on tetracarboxylic ligand exhibiting high performance for gas adsorption and separation

Developing porous materials for purification of acetylene is of great significance, but remains challenging. Currently, the use of metal-organic frameworks (MOFs) for gas adsorption separation has received substantial research interest. Herein, based on the tetracarboxylic acid ligand H4TPTA ([1,1':3′,1″-terphenyl]-4,4′,4″,6′-tetracarboxylic acid), two MOFs (ErTPTA and CdTPTA) constructed by trinuclear cluster secondly building units (SBUs) have been successfully synthesized. They are three dimensional (3D) framework with 1D rhomboid channels, demonstrating a (4,8)-connected scu network. A series of gas adsorption tests were performed and the both compounds exhibited outstanding gas selective adsorption performance. Accordingly, the ideal adsorption solution theory (IAST) is used to simulate the adsorption selectivity, the selectivity of CdTPTA for CO2/CH4 is 11.85 (0.5:0.5) and 17.02 (0.05:0.95), and for C2H2/CH4 is 11.81 (0.5:0.5); the selectivity of ErTPTA for C2H2/CO2 is 4.45 (0.5:0.5).

CO2-Induced Gate-Opening Adsorption on a Chabazite/Phillipsite Composite Zeolite Transformed from a Faujasite Zeolite Using Organic Structure-Directing Agent-Free Steam-Assisted Conversion.

Organic structure-directing agent-free steam-assisted conversion and Cs+ ion exchange were used to transform the faujasite (FAU)-type zeolite to the Cs+-type chabazite/phillipsite (CHA/PHI) composite zeolite. Compared with the pure PHI-type zeolite, the Cs+-type CHA/PHI zeolite showed gate-opening CO2 adsorption behavior and good thermal stability. In situ powder X-ray diffraction (PXRD) of the CO2 adsorption was measured to elucidate the mechanism for the gate-opening adsorption on the CHA/PHI zeolite. The Na+-type CHA/PHI zeolite did not show such adsorption behavior, and the PXRD pattern of the Na+-type CHA/PHI zeolite did not change with increasing CO2 partial pressure, which suggests that this unique adsorption behavior was caused by the PHI framework transition or Cs+ ions moving in both the CHA and PHI frameworks. Furthermore, in situ Fourier-transform infrared spectra of CO2 adsorption and CO2 breakthrough measurement on the Cs+-type CHA/PHI zeolite suggest that the CHA and PHI frameworks in the CHA/PHI zeolite shared eight-membered-ring windows and that CO2 molecules could easily diffuse from a CHA cage to a PHI framework. The ideal adsorbed solution theory was used to calculate the CO2/N2 separation selectivity for the Cs+-type CHA/PHI zeolite. At 298 and 318 K, the Cs+-type CHA/PHI composite zeolite showed a high CO2/N2 separation coefficient of >10,000 compared with other zeolites with high CO2 adsorption capacity. Furthermore, the CO2 working capacity was calculated for the Cs+-type CHA/PHI zeolite in both the pressure- and temperature-swing processes, and the results showed that the CHA/PHI composite zeolite could selectively separate CO2 from the CO2/N2 gas mixtures released from power generation plants operating using these processes.

Semiclassical approach to form factors in the sinh-Gordon model

Form factors in the sinh-Gordon model are studied semiclassically for small values of the parameter b ~ ħ1/2 in the background of a radial classical solution, which describes a heavy exponential operator placed at the origin. For this purpose we use a generalization of the radial quantization scheme, well known for a massless boson field. We introduce and study new special functions which generalize the Bessel functions and have a nice interpretation in the Tracy-Widom theory of the Fredholm determinant solutions of the classical sinh-Gordon model. Form factors of the exponential operators in the leading order are completely determined by the classical solutions, while form factors of the descendant operators contain quantum corrections even in this approximation. The construction of descendant operators in two chiralities requires renormalizations similar to those encountered in the conformal perturbation theory.

Pore engineering in cost-effective and stable Al-MOFs for efficient capture of the greenhouse gas SF6

The capture and separation of the greenhouse gas sulfur hexafluoride (SF6) from nitrogen (N2) holds significant potential for mitigating the greenhouse effect and yielding economic advantages for the semiconductor industry. In this study, a pair of isoreticular cost-effective and stable metal–organic frameworks (MOFs) with slightly different pore environments (CAU-10-H and CAU-10-Py) were prepared at >10 g scale for SF6/N2 separation. CAU-10-Py exhibited a remarkable improvement in SF6 uptake capacity at both low pressure (1.13 mmol/g at 0.1 bar and 298 K, compared to 0.68 mmol/g) and elevated pressure (2.11 mmol/g at 1 bar and 278 K, compared to 1.07 mmol/g). The ideal adsorbed solution theory (IAST) selectivity of SF6/N2 (10/90) was found to be 204 for CAU-10-Py and 123 for CAU-10-H. These enhanced capacities and selectivity endow CAU-10-Py a highly promising candidate for SF6 capture. Single crystal structural analysis, 77 K N2 adsorption data and theoretical calculations indicated that the substitution of benzene by pyridine slightly expand the pore diameter, facilitating more efficient accommodation of SF6 within the channel pores. The SF6 molecule is adsorbed around four benzene rings in CAU-10-H but trapped by two pyridine rings in CAU-10-py, resulting in one fold increase in adsorption capacity. Intriguingly, time-dependant adsorption experiments revealed that CAU-10-Py exhibited a higher SF6 adsorption rate and a lower N2 adsorption rate compared to CAU-10-H, further highlighting the benefit of CAU-10-Py for SF6/N2 separation. Dynamic breakthrough experiments conducted under simulated working conditions further confirmed the outstanding SF6/N2 separation performance of CAU-10-Py. Considering its excellent regeneration ability and cycling performance, this cost-effective and easily scalable MOF demonstrates great promise for SF6/N2 separation.

Theory of electrolyte solutions in a slit charged pore: Effects of structural interactions and specific adsorption of ions.

In this paper, we present a continuation of our research on modeling electrolyte solutions within charged pores. We make use of the model developed by Blossey et al. [Phys. Rev. E 95, 060602 (2017)], which takes into account the structural interactions between ions through a bilinear form over the gradients of local ionic concentrations in the grand thermodynamic potential, as well as their steric interactions through the lattice gas model. The structural interactions may describe the effects of the molecular structure of ions at a phenomenological level. For example, these effects include steric effects due to non-spherical shapes of ions, their conformational lability, and solvent effects. In addition, we explore their specific interactions with the pore walls by incorporating external attractive potentials. Our primary focus is on observing the behavior of ionic concentration profiles and the disjoining pressure as the pore width changes. By starting with the local mechanical equilibrium condition, we derive a general expression for the disjoining pressure. Our findings indicate that considering the structural interactions of ions leads to a pronounced minimum on the disjoining pressure profiles at small pore widths. We attribute this minimum to the formation of electric double layers on the electrified surfaces of the pore. In addition, our results demonstrate that the inclusion of the attractive interactions of ions with the pore walls enhances this minimum and shifts it to smaller pore thicknesses. Our theoretical discoveries may be useful for those involved in supercapacitor electrochemical engineering, particularly when working with porous electrodes that have been infused with concentrated electrolyte solutions.

Geometry of the energy input of a shockwave generated by a nanosecond laser-induced breakdown

The spatio-temporal evolution of the shock wave generated by a laser induced breakdown is often investigated and interpreted in the framework of the theory of shock similarity solutions. This work is a discussion about the choice of the most relevant geometry (spherical or cylindrical) to be used in the Jones modelling to track the intermediate-strength shockwave trajectory coming from a laser-induced non-resonant breakdown in argon. Laser incident energies ranging from 10 to 200 mJ with initial pressure of argon from 250 to 2500 mbar are investigated using a Q-switched Nd:YAG laser operating at a wavelength of 532 nm with a 6 ns pulse duration. Experimental results show that using the radial component of the ellipsoidal shape of the shockwave with a cylindrical geometry best describes the shockwave trajectory over time. Moreover, the deduced characteristic length allows us to observe a shockwave shape similarity for all tested laser energies at a given pressure.

Effect of Carbon Nanoparticles on the Porous Texture of ι-Carrageenan-Based N-Doped Nanostructured Porous Carbons and Implications for Gas Phase Applications

S and N double-doped high surface area biomass-derived carbons were obtained from marine biomass-derived ι-carrageenan. Adding carbon nanoparticles (CNPs), namely graphene oxide (GO) or carbon nanotubes (CNTs), in the early stage of the synthesis leads to a modified porous texture and surface chemistry. The porous textures were characterized by N2 (−196.15 °C) and CO2 (0 °C) isotherms. The best GO- and CNT-added carbons had an apparent surface area of 1780 m2/g and 1170 m2/g, respectively, compared to 1070 m2/g for the CNP-free matrix. Analysis of the Raman spectra revealed that CNT was more efficient in introducing new defects than GO. Based on XPS, the carbon samples contain 2–4.5 at% nitrogen and 1.1 at% sulfur. The Dubinin–Radushkevich (DR) and Henry models were used to assess the strength of the interactions between various gases and the surface. The N2/H2 and CO2/CH4 selectivities were estimated with ideal adsorbed solution theory (IAST). While the CNPs, particularly GO, had a remarkable influence on the porous texture and affected the surface chemistry, their influence on the separation selectivity of these gases was more modest.

Robust Fluorine-Functionalized {Ln5}-Organic Frameworks for Excellent Catalytic Performance on Cycloaddition of CO2 with Epoxides and Knoevenagel Condensation.

Lanthanide-organic frameworks (LnOFs) are a class of promising catalysts on a large number of organic reactions because of the higher coordination number of Ln3+ ions, inspired by which exploratory preparation of cluster-based LnOFs was carried out by us. Herein, the exquisite combination of spindly [Ln5(μ3-OH)6(CO2)6(H2O)6] clusters (abbreviated as {Ln5}) and fluorine-functionalized tetratopic ligand of 2',3'-difluoro-[p-terphenyl]-3,3″,5,5″-tetracarboxylic acid (F-H4PTTA) engendered two highly robust isomorphic nanoporous frameworks of {[Ln5(FPTTA)2(μ3-OH)6(H2O)6](NO3)}n (NUC-61, Ln = Ho and Dy). NUC-61 compounds are rarely reported {Ln5}-based 3D frameworks with nano-caged voids (19 Å × 17 Å), which are shaped by twelve [Ln5(μ3-OH)6(COO)8] clusters and eight completely deprotonated F-PTTA4- ligands. Activated NUC-61a compounds are characterized by plentiful coexisted Lewis acid-base sites of open LnIII sites, capped μ3-OH, and -F. Judged by the ideal adsorbed solution theory (IAST), activated NUC-61Ho-a had a high CO2/CH4 adsorptive selectivity with the value of 12.7 (CO2/CH4 = 50/50) and 9.1 (CO2/CH4 = 5/95) at 298 K, which could lead to high-purity CH4 (≥99.9996%). Furthermore, catalytic experiments exhibited that NUC-61Ho-a, as a representative, could efficiently catalyze the cycloaddition reactions of CO2 with epoxides as well as the Knoevenagel condensation reactions of aldehydes and malononitrile. This work proves that the {Ln5}-based skeletons of NUC-61 with chemical stability, heterogeneity, and recyclability are an excellent acid-base bifunctional catalyst for some organic reactions.

Sorption of Carbon Dioxide and Nitrogen on Porous Hyper-Cross-Linked Aromatic Polymers: Effect of Textural Properties, Composition, and Electrostatic Interactions.

Porous hyper-cross-linked aromatic polymers are one of the emerging classes of porous organic polymers with the potential for industrial application. Four different porous polymeric materials have been prepared using different precursors (indole, pyrene, carbazole, and naphthalene), and the composition and textural properties were analyzed. The materials were characterized in detail using different physicochemical techniques like scanning electron microscopy, transmission electron microscopy, nitrogen adsorption at 77 K, Fourier transform infrared spectroscopy, X-ray diffraction, etc. The effect of textural properties and nitrogen species on carbon dioxide and nitrogen adsorption capacities and selectivity was studied and discussed. The carbon dioxide and nitrogen adsorption capacities were measured using a volumetric gas adsorption system. The adsorption data were fitted into different adsorption models, and the ideal absorbed solution theory was used to calculate adsorption selectivity. Among the studied samples, POP-4 shows the highest carbon dioxide and nitrogen adsorption capacities. While POP-1 shows maximum CO2/N2 selectivity of 78.0 at 298 K and 1 bar pressure. It is observed that ultra-micropores, which are present in the prepared materials but not measured during conventional surface area measurement via nitrogen adsorption at 77 K, play a very important role in carbon dioxide adsorption capacity and determining the carbon dioxide selectivity over nitrogen. Surface nitrogen also increases the CO2 selectivity in the dual mode by increasing carbon dioxide adsorption via the acid-base interaction as well as by decreasing nitrogen adsorption due to N-N repulsion.

Preparation of Cu-BTC MOF extrudates for CH4 separation from CH4/N2 gas mixture

Metal-Organic Frameworks (MOF) are promising materials for gas separation and storage. The shaping of MOFs is an essential step for their practical industrial application. In this work, Cu-BTC MOF extrudates (B-5, B-10, and B-15) were prepared by using 5, 10, and 15 wt% of carboxymethyl cellulose as a binder and well characterized by powder X-ray diffraction (PXRD), N2 adsorption-desorption at 77 K, FTIR, TGA, and Scanning Electron Microscopy (SEM). The equilibrium adsorption isotherms of CH4 and N2 with Cu-BTC extrudates were measured at 298, 313, and 328 K and up to 10 bar pressure and compared with zeolite 13X and 5A. The isotherm data of both adsorbates were fitted in Dual Site Langmuir equations, and adsorption selectivity of methane over nitrogen was predicted using Ideal Adsorbed Solution Theory (IAST) method for 20:80, 30:70, and 50:50 (mol%/mol%) CH4/N2 feed gas mixtures representing nitrogen bearing coal bed methane. The CH4/N2 selectivity of Cu-BTC extrudates B-5, B-10, and B-15 was higher than commercial zeolite 13X and 5A. For example, for the 20:80 CH4/N2 feed mixture, the CH4/N2 selectivity of Cu-BTC extrudates B-5, B-10, and B-15 was 3.21, 3.24, and 3.25, respectively, which are about 38 & 34% higher than zeolite 13X and 5A which makes them potential adsorbent for further dynamic studies for the said separation application.

Delay Ait-Sahalia-type interest rate model with jumps and its strong approximation

Abstract In this paper, we study the analytical properties of the true solution to the generalised delay Ait-Sahalia-type interest rate model with Poisson-driven jumps. Since this model does not have a closed-form solution, we employ several new truncated Euler-Maruyama (EM) techniques to investigate the finite-time strong convergence theory of the numerical solution under the local Lipschitz condition plus the Khasminskii-type condition. We justify the strong convergence result for Monte Carlo calibration and valuation of some debt and derivative instruments.