Energetic Heterogeneity Research Articles

On the Use of the Multi-Site Langmuir Model for Predicting Methane Adsorption on Shale

Shale gas, mainly consisting of adsorbed gas and free gas, has served a critical role of supplying the growing global natural gas demand in the past decades. Considering that the adsorbed methane has contributed up to 80% of the total gas in place (GIP), understanding the methane adsorption behaviors is imperative to an accurate estimation of total GIP. Historically, the single-site Langmuir model, with the assumption of a homogeneous surface, is commonly applied to estimate the adsorbed gas amount. However, this assumption cannot depict the methane adsorption characteristics due to various compositions and pore sizes of shales. In this work, a multi-site model integrating the energetic heterogeneity in adsorption is derived to predict methane adsorption on shale. Our results show that the multi-site model is capable of addressing the heterogeneity of shales by a wide range of adsorption energy distributions (owing to the complex compositions and different pore sizes), which is different from the single-site model only characterized by single adsorption energy. Consequently, the multi-site model results have better accuracy against the experimental data. Therefore, applying the multi-site Langmuir model for estimating GIP in shales can achieve more accurate results compared with using the traditionally single-site model.

Diffusion-Limited Release of Molecules from Nanocarriers with Appreciable Energetic Heterogeneity

Diffusion-Limited Release of Molecules from Nanocarriers with Appreciable Energetic Heterogeneity

GCMC kernel for analyzing the pore size distribution of porous carbons based on a simplified slit-pore model considering surface energetic heterogeneity

GCMC kernel for analyzing the pore size distribution of porous carbons based on a simplified slit-pore model considering surface energetic heterogeneity

CO2 adsorption on carbonaceous materials obtained from forestry and urban waste materials: a comparative study.

The increasing emissions of gaseous pollutants of anthropogenic origin, such as carbon dioxide (CO2), which causes global warming, have raised great interest in developing and improving processes that allow their mitigation. Among them, adsorption on porous materials has been proposed as a sustainable alternative. This work presents a study of CO2 equilibrium adsorption at low temperatures (0, 10, and 20°C) over a wide range of low pressures, on activated carbon derived from Eucalyptus (ES) and Patula pine (PP) forest waste, and carbonaceous material derived from waste tires (WT). The precursors of these materials were previously prepared, and their physicochemical properties were characterized. ES and PP were thermochemically treated with phosphoric acid, and WT was oxidized with nitric acid. Additionally, these materials were used to obtain monoliths using uniaxial compaction techniques and different binding agents, with better results obtained with montmorillonite. A total of six adsorbent solids had their textural and chemical properties characterized and were tested for CO2 adsorption. The highest specific surface area (1405 m2g-1), and micropore properties were found for activated carbon derived from Eucalyptus whose highest adsorption capacity ranged from 2.27mmolg-1 (at 0°C and 100kPa) to 1.60mmolg-1 (at 20°C and 100kPa). The activated carbon monoliths presented the lowest CO2 adsorption capacities; however, the studied materials showed high potential for CO2 capture and storage applications at high pressures. The isosteric heats of adsorption were also estimated for all the materials and ranged from 16 to 45kJmol-1 at very low coverage explained by the energetic heterogeneity and weak repulsive interactions among adsorbed CO2 molecules.

Two-Dimensional PC-SAFT-DFT Adsorption Models for Carbon Slit-Shaped Pores with Surface Energetical Heterogeneity and Geometrical Corrugation

Two-Dimensional PC-SAFT-DFT Adsorption Models for Carbon Slit-Shaped Pores with Surface Energetical Heterogeneity and Geometrical Corrugation

Adsorption of CO2, CO, H2, and N2 on Zeolites, Activated Carbons, and Metal-Organic Frameworks with Different Surface Nonuniformities

The single-component adsorption of CO2, CO, N2, and H2 at 25 and 35 °C was studied using microporous faujasite-framework zeolites (NaY and NaX), activated carbons (GCN and MSP), and metal–organic frameworks (A100 and Z1200) as starting points for the separation of CO2 from syngases produced by gasifying biomass-based solid wastes. The indicated adsorption isotherms and uptake of the adsorbates strongly depended on the adsorbates themselves as well as on the adsorbents because of significant differences in the surface features, such as surface nonuniformity, and in the molecular properties. The selectivity of CO2 to the other gases also varied with the adsorbents due to the distinctive energetic characteristics. The surfaces of the zeolites were the most energetically heterogeneous ones, yielding higher CO2 uptake at low pressures, while the two activated carbons and A100 had moderate surface heterogeneities, and MSP showed the highest CO2 uptake at high pressures, such as 6 bar, at which the micropore volume and surface area are important. Z1200, which has highly homogeneous surfaces and no high-affinity-binding sites, exhibited the lowest CO2 adsorption capacity regardless of equilibrated pressure. The surface nonuniformities of the six sorbents were consistent with the calculated isosteric heats of CO2 adsorption. CO2 could be reversibly adsorbed on NaY and MSP but not on GCN, with some metal impurities, although all these adsorbents showed a fully reversible process for CO adsorption. The estimated working capacity for CO2 adsorption at 25 °C was 0.78–6.50 mmol/g, depending on the sorbents used. The highest value was disclosed for MSP, the surface energetic heterogeneity of which was between that of zeolites and Z1200. Such a high working capacity bodes well for use in our later applications.

Quasi-isothermal (Q-TG), cryoporometric (DSC) and adsorption characterization of activated carbons

In the presented paper, the structural and energetic heterogeneities of the activated carbons (ACs) surfaces were investigated. The ACs of well-developed microporosity were obtained from the spent coffee grounds as a result of pyrolysis (N2 or CO2) with the chemical activation of H3PO4 (I = 1, 1.5 or 2 w/w). The low-temperature N2 adsorption, the quasi-isothermal thermogravimetry as well as the low-temperature differential scanning calorimetry were employed. Moreover, the selected materials adsorption properties were studied in relation to methylene blue (MB). The micro/mesoporous structure of the carbons was proved. The different types of water clusters on the surface indicated the carbons surface heterogeneity. The activated carbons are characterized by the high sorption capacity (qe,exp = 200.3–237.67 mg g−1) as for MB. The adsorption process was described by means of the Radke–Prausnitz isotherm model.Graphical abstract

Insights into the statistical physics modeling and fractal like kinetic approach for the adsorption of As(III) on coordination polymer gel based on zirconium(IV) and 2-thiobarbituric acid

A novel coordination polymer gel based on zirconium(IV) and 2-thiobarbituric (ZrTBA) was synthesized and explored its potential to remediate As(III) from water. Box-Behnken design with desirability function and genetic algorithm yielded the optimized conditions (initial concentration=194 mg L-1, dosage = 42.2 mg, time= 95 min and pH = 4.9) for maximum removal efficiency (99.19 %). The experimental saturation capacity for As(III) was 178.30 mg g-1. The steric parameter n > 1 of the best fitted statistical physics model: monolayer with two energies (R2 = 0.987–0.992) suggested multimolecular mechanism with vertical orientation of As(III) molecules onto the two active sites. XPS and FTIR confirmed the two active sites being zirconium and oxygen. The adsorption energies (E1 = 35.81–37.63 kJ/mol; E2 = 29.50–36.49 kJ/mol) and isosteric heat of adsorption indicated that physical forces governed the As(III) uptake. DFT calculations implied that the weak electrostatic interaction and hydrogen bonding were involved. The best fitted (R2>0.99) fractal like pseudo first order model established energetic heterogeneity. ZrTBA showed excellent removal efficiency in the presence of potential interfering ions and could be used up to 5 cycles of adsorption-desorption with < 8 % loss in the efficiency. ZrTBA removed ≥96.06 % As(III) from real water samples spiked at different levels of As(III).

Towards the determination of carbon dioxide retention in earthen materials

Thanks to its hygroscopic properties, raw earth can passively buffer indoor humidity. The high sorption properties of clay minerals present in earth also attract other molecules, such as carbon dioxide (CO2), this can potentially lead to indoor CO2 buffering. It would improve air quality in buildings and their resilience towards mechanised ventilation systems. However, there is currently no protocol to evaluate this potential. This paper aims to present a innovative methodology based on thermogravimetric (TG) and calorimetric (DSC) analysis to characterise the interactions between clay and CO2 at the microscopic scale by focusing on the dry state. Results show a CO2 adsorption capacity of 134 mg/kg at 5000 ppm at 35 °C associated with a reversible physisorption process and provides first evidence of a passive CO2 regulation capacity of the indoor air. Determination of the adsorption enthalpies as a function of the amount adsorbed revealed high values (from −74 kJ/mol to −40 kJ/mol) which are characteristic of a strong energetic heterogeneity of the material.

Cerofolini’s Model and the Fractal Adsorption Isotherms

The close link between the roughness of a surface and its adsorptive properties in Cerofolini’s model yields, with an adequate choice of adsorption energy, the well-known Dubinin-Radushkevich or Freundlich adsorption isotherms. Assuming fractal behavior concerning both energetic and geometric surface heterogeneities described by the power-law expressions and fractal dimensions, the paper will develop some fractal adsorption isotherms. Using our theoretical approach, fractal isotherms will provide insights not only into the fractal behavior of the surface geometry but also into the fractal energetic heterogeneities, implying that a sorbent does not need to be porous to apply a fractal isotherm: adsorption on “flat” surfaces can also be described by fractal isotherms and fractal dimensions related to energetic disorders. For example, the theory will be applied to computing the energetic fractal dimensions of some nanoparticle catalysts, Rh/Al2O3, Rh/TiO2, and Rh/WO3.

Release of molecules from nanocarriers.

Release of drugs or vaccine molecules from macro-, micro-, and nano-sized carriers is usually considered to be limited by diffusion and/or carrier dissolution and/or erosion. The corresponding experimentally observed kinetics are customarily fitted by using the empirical Weibull and Korsemeyer-Peppas expressions. With decreasing size of carriers down to about 100 nm, the timescale of diffusion decreases, and accordingly the release can be kinetically limited, i.e., controlled by jumps of molecules located near the carrier-solution interface. In addition, nanocarriers (e.g., lipid nanoparticles) are often structurally heterogeneous so that the absorption of molecules there can be interpreted in terms of energetic heterogeneity, i.e., distribution of energies corresponding to binding sites and activation barriers for release. Herein, I present a general kinetic model aimed at such situations. For illustration, the deviation of the molecule binding energy from the maximum value was considered to be about 4-8 kcal mol-1. With this physically reasonable (for non-covalent interaction) scale of energetic heterogeneity, the predicted kinetics (i) are linear in the very beginning and then, with increasing time, become logarithmic and (ii) can be nearly perfectly fitted by employing the Weibull or Korsmeyer-Peppas expressions with the exponent in the range from 0.6 to 0.75. Such values of the exponent are often obtained in experiments and customarily associated with non-Fickian diffusion. My analysis shows that the energetic heterogeneity can be operative here as well.

Use of shear sensitive coloured guest component to track powder mixing in adhesive binary mixtures

The mixing performance in binary powder blends with components exhibiting guest and host type interactions was assessed by tracking the colour change of the mixture. . The operation parameters like mixing time and speed were studied in compositions containing lactose monohydrate as host and iron oxide nanoparticle as coloured guest components . The mixing characteristics were analysed through visual imaging and colorimetric estimations. Furthermore, surface analytical techniques like scanning electron microscope (SEM) for surface area coverage (SAC) determination and Finite Dilution Inverse Gas chromatography (FD-IGC) for surface energy heterogeneity characterisation were employed. The mixing sensitivity of the coloured tracer and the consequent colour transitions under different conditions helped in validating the mixing performance and operation conditions. The FD-IGC results showed lowering of the energetic heterogeneity for better quality mixtures. Thus, a shear sensitive coloured nano-tracer can be utilised for a simple, quick and cost-effective estimation of the mixture quality and for the validation of mixing process. • Binary powders with guest-host interactions studied. • Mixing performance was tracked using iron oxide guest. • Binary mixtures examined through colorimetric, FD-IGC and SEM analysis. • A simple, quick and cost-effective approach for mixing process validation reported.

Atomistic-Scale Energetic Heterogeneity on a Membrane Surface.

Knowing the energetic topology of a surface is important, especially with regard to membrane fouling. In this study, molecular computations were carried out to determine the energetic topology of a polyvinylidene fluoride (PVDF) membrane with different surface wettability and three representative probe molecules (namely argon, carbon dioxide and water) of different sizes and natures. Among the probe molecules, water has the strongest interaction with the PVDF surface, followed by carbon dioxide and then argon. Argon, which only has van der Waals interactions with PVDF, is a good probing molecule to identify crevices and the molecular profile of a surface. Carbon dioxide, which is the largest probing molecule and does not have dipole moment, exhibits similar van der Waals and electrostatic interactions. As for water, the dominant attractive interactions are electrostatics with fluorine atoms of the intrinsically hydrophobic PVDF membrane, but the electrostatic interactions are much stronger for the hydroxyl and carboxyl groups on the hydrophilic PVDF due to strong dipole moment. PVDF only becomes hydrophilic when the interaction energy is approximately doubled when grafted with hydroxyl and carboxyl groups. The energetic heterogeneity and the effect of different probe molecules revealed here are expected to be valuable in guiding membrane modifications to mitigate fouling.

Binding of Proteins to Copolymers of Varying Charges and Hydrophobicity: A Molecular Mechanism and Computational Strategies.

Because of their ability to selectively bind to a target protein, copolymer nanoparticles (NPs) containing a selected combination of hydrophobic and charged groups have been frequently reported as potent antibody-like analogues. However, due to the intrinsic disorder of the copolymer NP in terms of its random monomer sequence and the cross-linked copolymer matrix, the copolymer NP is indeed strikingly different from a well-folded protein antibody and the complexation between the copolymer NP and a target protein is likely not due to a lock-key type of interaction but possibly due to a novel and unexplored molecular mechanism. Here, we study a key biomarker protein, vimentin, interacting with a set of random copolymer chains using implicit-water explicit-ion coarse-grained (CG) molecular dynamics (MD) simulations along with biolayer interferometry (BLI) analysis. Due to the charge and hydrophobicity anisotropy on the vimentin dimer (VD) surface, a set of bound copolymers are found inhomogenously adsorbed on the VD, with energetic heterogeneity for different binding sites and cooperative effect in the adsorption. Increasing the charge or hydrophobicity of the copolymer may have different consequences on the adsorption. In this study, we found that with more copolymer charges, the protein coverage increases for copolymers of low hydrophobicity and decreases of high hydrophobicity, which is explained by the distribution and size of various functional patches on the VD in loading those copolymers. Employing a coverage-dependent Langmuir model, we propose a simulation protocol to address the full profile of the copolymer binding free energy through the fit to the simulated binding isotherm. The obtained results correlate well with those from the BLI experiment, indicating the significance of this method for the rational design of the copolymer NP with engineered protein binding affinity.

Effect of Energetical and Geometrical Heterogeneity of Kerogen on BET Surface Area Characterization and Methane Adsorption

Effect of Energetical and Geometrical Heterogeneity of Kerogen on BET Surface Area Characterization and Methane Adsorption

Quantitative analysis of framework Al at channel intersections of HZSM-5 zeolite by toluene adsorption–desorption

Precise analysis of the framework Al (AlF) at channel intersections of HZSM-5 zeolite is the basis of fine tuning of the spatial distribution of active sites within different pores which is critical to promote the catalytic performance in various applications. However, existing technologies cannot provide reliable quantitative results either in theory or practice due to the co-existence of Al pair and single Al. Here we report a new method based on toluene adsorption–desorption. As a promising probe, toluene can be preferentially adsorbed on AlF at channel intersection under low loading (≤4 molecules/unit cell) due to spatial matching and energetic heterogeneity. After strengthening the toluene/AlF affinity through replacing H+ by Na+ and designing a new stepwise TPD technique (toluene-STPD), the contents of AlF atoms at channel intersections of HZSM-5 samples were successfully calculated by counting the desorbed toluene molecules based on the 1:1 stoichiometric relationship between adsorbed toluene and AlF.

Contact angle of water on a model heterogeneous surface. A density functional approach

We use a density functional approach to calculate the contact angle of the water model on a heterogeneous, graphite-like surface. The surface heterogeneity results from the pre-adsorption of a layer of spherical species. The pre-adsorbed molecules can also be a mixture of molecules of different sizes. The presence of pre-adsorbed layer causes geometrical and energetical heterogeneity of the surfaces. Two cases are considered. The pre-adsorbed molecules can either behave like hard-sphere obstacles, or they can also attract the molecules of water. In the first case, an increase of the amount of pre-adsorbed species leads to an increase of the wetting temperature, but this increase does not depend linearly on the amount of obstacles. In the case of obstacles exerting attractive forces on water molecules, the curves describing the dependence between the amount of pre-adsorbed species and the contact angle can exhibit a maximum. In addition, we have also studied how the pre-adsorbed species influence the local densities of gaseous and liquid phases in contact with a modified solid surface.

An in-situ setup for simultaneous electro-chemo-mechanical characterization of electrode materials for lithium-ion battery

The electro-chemo-mechanical (ECM) coupling effects are nontrivial in alloying electrode materials, whose applications are hindered by the severe volume change during cycling. However, due to the difficulty in the in-situ application of mechanical load onto the active materials, these effects in many emerging lithium-ion battery (LIB) chemistries are largely unknown. Herein, we report a new setup for the in-situ characterizing ECM coupling effects in alloying electrode materials, and the coupling effects in aluminum (Al) foil electrode is studied. The elastic moduli of the Al foil show an increasing then slightly decreasing trend with the lithiation. Meanwhile, electrochemical impedance spectroscopy spectra of the Al foil imply an increasing surface atomistic energetic heterogeneity of the Al foil with the growing tensile force. Furthermore, the stress relaxation phenomena of the Al foil electrode during lithiation are observed. The newly developed setup opens a valuable window into investigating complicated ECM coupling effects in LIBs.

Pore size analysis of carbons with heterogeneous kernels from reactive molecular dynamics model and quenched solid density functional theory

We presented a new kernel of heterogenous carbon surfaces constructed using the reactive molecular dynamics model (rMD). The rMD model explicitly incorporates edges and corrugations resulting from the oxidative etching of graphene walls. The rMD model eliminates the computational artifacts characteristic to the homogeneous pore wall models. In ultramicropores, early uptake is guided by the competition between central energetic adsorption sites and heterogeneities of the wall. In the larger pores, the central energy diminishes and the preferential adsorption sites are located in the pore wall. Comparisons between the rMD model, which mimics the surface roughness explicitly, and the quenched solid density functional theory (QSDFT) model are performed. The rMD model performs similarly to the QSDFT in the reproduction of the carbon experimental isotherms, indicating that it is a viable alternative to the implicit models for carbon characterization. In calculated PSDs, the rMD model attributes higher volumes to the ultramicropores than the QSDFT model due to enhanced adsorption on the surface defects. Finally, we tested the influence of the N2 molecular probe models on adsorption isotherms. It is found that the discrepancies between the nitrogen probe models on heterogeneous wall surfaces are smaller than those for the homogeneous models.

Silanization of siliceous materials, part 3: Modification of surface energy and acid-base properties of silica nanoparticles determined by inverse gas chromatography (IGC)

Surface modified silica nanoparticles are well-established composite materials. To improve their embedding and application behavior, surface energy analysis has been performed before and after silanization with mercaptopropyltrimethoxysilane (MPTMS) using inverse gas chromatography technique (IGC). Experiments with two silica materials have been conducted at infinite dilution to determine the dispersive component of the surface energy (γsd) as well as the specific component (γssp) using the van Oss theory and a least-squares procedure evaluating the IGC data of 8 polar probe molecules collectively (instead of evaluating only the data of a pair of monopolar probes as is often the case in IGC studies). After surface silylation, the total surface energy (γst) of pyrogenic silica nanoparticles decreased from 225 mJ/m2 to 149 mJ/m2 referring to both a reduced wettability and an increased hydrophobicity of the MPTMS-modified sample. Moreover, the acidity/basicity parameters according to the van Oss and the Gutmann approach indicated that the acidity of the silica surface decreases by MPTMS grafting. In addition, IGC at finite concentration (using isopropanol as probe molecule) was applied to obtain the energetic heterogeneity of the silica surface. The results showed a bimodal energy distribution with maxima at about 18 and 25 kJ/mol and a reduction of the higher energetic sites from 65% to only 35% after MPTMS treatment. Overall, it can be seen that the dominance of specific interactions on silica surfaces is maintained even after extensive silanization. These findings are in agreement with the results of 29Si CP MAS NMR measurements which confirm the assignment of higher energetic sites to silanol groups. For the interpretation of the IGC results, quantum chemical calculations proved the preferred interaction of isopropanol onto silica surfaces via hydrogen bridging.