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Results for “Langmuir adsorption isotherm”

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Estimation of isosteric heat of adsorption from generalized Langmuir isotherm

Simulation and design of adsorptive separation units demand accurate estimation of thermodynamic properties. Isosteric heat of adsorption as calculated from generalized Langmuir (gL) isotherm coupled with Clausius-Clapeyron expression for pure component and mixed-gas adsorption equilibria is presented in this work. The estimated isosteric heat of adsorption as functions of surface loading and composition is validated against the experimental data for various adsorption systems. Furthermore, the gL results are compared against classical Langmuir (cL) and Toth isotherm for pure components and with Ideal Adsorbed Solution Theory (IAST) for mixed-gas adsorption equilibria. Furthermore, the comparison highlights that gL outperforms cL and Toth for pure component adsorption and IAST for mixed-gas adsorption, and gL reliably captures the loading dependence and the composition dependence for isosteric heat of adsorption.

42 ENGINEERING↗
DOE OSTI2022

Generalization of thermodynamic Langmuir isotherm for mixed‐gas adsorption equilibria

Abstract This work presents a comprehensive thermodynamic model for both pure component isotherms and mixed‐gas adsorption equilibria. A generalization of thermodynamic Langmuir isotherm, the proposed model assumes competitive adsorption of multiple adsorbates on adsorbent surface for mixed‐gas adsorption equilibria, and it applies an area‐based adsorption nonrandom two‐liquid activity coefficient model in the activity coefficient calculations for the adsorbate phase. The resulting generalized Langmuir isotherm properly captures both surface loading dependence and adsorbate phase composition dependence for mixed‐gas adsorption equilibria. The model is validated with accurate representations of gas adsorption equilibrium data for varieties of unary, binary, and ternary gas systems. The model results are further compared with those calculated from extended Langmuir isotherm and Ideal Adsorbed Solution Theory.

Hamid, Usman↗
DOE OSTI2023

Elucidating the Influence of Metal Surface Composition on Organic Adsorbate Binding Using Active Particle Dynamics

The adsorption strengths of organic compounds on metal surfaces are sensitive to the metal composition, and they play a central role in many catalytic reactions, helping to control the coverage of the reactant and altering the overall reaction rate. While adsorption energies are straightforward to measure and calculate in vacuum and gas-phase environments, adsorption energetics can be dramatically altered by the presence of solvent in liquid-phase reactions. However, the effects of metal composition on binding strengths in a liquid environment are less well understood, primarily due to the difficulty of accurate in situ measurements of organic binding on metal surfaces in the liquid phase. Here, we utilize the motion of active particles in water to probe the adsorption energies of an organic adsorbate (furfural) on a range of metal surfaces (pure Pd, pure Pt, and four PdAu alloy compositions) to elucidate the effect of metal composition. Janus particles with catalytic caps of particular metal compositions all exhibited active motion resulting from consumption of H 2 O 2 ; adsorbate binding was inferred through the decrease in the velocity of active motion and was modeled by a Langmuir adsorption isotherm. The measured adsorption affinities were used to extract the adsorption enthalpy of furfural on the different metals. The Pd surface was found to bind furfural more strongly than the Pt surface by some 10 kJ/mol. Furthermore, the adsorption of furfural on the alloys was found to increase monotonically in magnitude with Pd content. As a result, the data reported herein aid the development of accurate understanding of organic adsorption in the presence of solvent and the role of the metal surface in tuning adsorption strengths to optimize catalytic processes in the liquid phase.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Thiol-Functionalized Adsorbents through Atomic Layer Deposition and Vapor-Phase Silanization for Heavy Metal Ion Removal

The removal of toxic heavy metal ions from water resources is crucial for environmental protection and public health. In this study, we address this challenge by developing a surface functionalization technique for the selective adsorption of these contaminants. Our approach involves atomic layer deposition (ALD) followed by vapor-phase silanization of porous substrates. We utilized porous silica gel powder (similar to 100 mu m particles, 89 m 2 /g surface area, similar to 30 nm pores) as an initial substrate. This powder was first coated with similar to 0.5 nm ALD Al 2 O 3 , followed by vapor-phase grafting of a thiol-functional silane. The modified powder, particularly in acidic conditions (pH = 4), showed high selectivity in adsorbing Cd(II), As(V), Pb(II), Hg(II), and Cu(II) heavy metal ions in mixed ion solutions over common benign ions (e.g., Na, K, Ca, and Mg). Langmuir adsorption isotherms and breakthrough adsorption studies were conducted to assess heavy metal binding affinity and revealed the order of Cd(II) < Pb(II) < Cu(II) < As(V) < Hg(II), with a significantly higher affinity for As(V) and Hg(II) ions. Time-dependent uptake studies demonstrated rapid removal of heavy metal ions from aqueous environments, with Hg(II) exhibiting the fastest adsorption kinetics on thiol-modified surfaces. Finally, these findings highlight the potential of ALD and vapor-phase silanization to create effective adsorbents for the targeted removal of hazardous contaminants from water.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Probing Heterogeneous Charge Distributions at the α-Al 2 O 3 (0001)/H 2 O Interface

Unlike metal or semiconductor electrodes, the surface charge resulting from the protonation or deprotonation of insulating mineral oxides is highly localized and heterogeneous in nature. In this work the Stark active C≡N stretch of potassium thiocyanate is used as a molecular probe of the heterogeneity of the interfacial electrostatic potential at the α-Al 2 O 3 (0001)/H 2 O interface. Vibrational sum frequency generation (vSFG) measurements performed in the OH stretching region suggest that thiocyanate species organize interfacial water similarly to halide ions. Changes in the electrostatic potential are then tracked via Stark shifts of the vibrational frequency of the thiocyanate stretch. Our vSFG measurements show that we can simultaneously measure the vSFG response of SCN – ions experiencing charged and neutral surface sites. We assign local potentials of +308 and -154 mV to positively and negatively charged aluminol groups that are present at pH = 4 and pH = 10, respectively. Thiocyanate anions at positively charged surface sites and negatively charged surface sites and those participating in contact ion pairing adopt similar orientations and are oppositely oriented relative to thiocyanate ions near neutral surface sites. All four species followed Langmuir adsorption isotherms. Density functional theory–molecular dynamics (DFT-MD) simulations of SCN – near the neutral α-Al 2 O 3 (0001)/H 2 O interface show that the vSFG response in the C≡N stretch region originates from a SCN–H–O–Al complex, suggesting the surface site specificity of these experiments. To our knowledge this is the first spectroscopic measurement of local potentials associated with a heterogeneously charged surface. The ability to probe the evolution of local charges in situ could provide vital insight into many industrial, electrochemical, and geochemically relevant interfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Quantum sensing of paramagnetic analytes by nanodiamonds in levitated microdroplets and aqueous solutions

Nanodiamonds (ND) hosting negatively charged nitrogen-vacancy (NV-) color centers have received attention for applications in magnetic field, electric field, chemical, and bio-sensing. The versatility of these probes is their excellent room-temperature optical and spin properties, along with their small size, functionalized surfaces and resistance to bleaching, making them ideal as nanoscopic sensors in picoliter volumes (e.g. single cells, but also microcompartments and aerosols). For quantitative ND-NV- sensing of paramagnetic analytes in such contexts, however, there remains an incomplete understanding of how factors related to the aqueous phase environment control detection efficiency. To address this, optically detected magnetic resonance (ODMR) is measured in bulk macroscale solutions and single levitated microdroplets as a function of Gd+3 concentration (340 nM to 1.5 mM), nanodiamond size, pH, competitor ions, and ligands. The ODMR response to [Gd+3] is found to be nonlinear, and pH, ND and sample volume dependent; indicating the detection of Gd+3 requires efficient adsorption of the analyte to the diamond surface. Langmuir adsorption isotherms embedded in a quantitative photophysical model links the ODMR response to adsorption thermodynamics of Gd+3. The equilibrium constant for Gd+3 adsorption to a carboxylated ND surface is determined to be (1 ± 0.5) x 105 M-1 corresponding to a free energy of adsorption of (-28 ± 1) kJ mol-1. These results provide general insight into how complex aqueous and microscale environments impact nanodiamond based quantum sensing modalities, and portend their application as quantitative chemical sensors in microenvironments.

Brown, Emily K↗
DOE OSTI2021

From Langmuir isotherm to Brunauer–Emmett–Teller isotherm

Abstract Developed for multilayer adsorption, the Brunauer–Emmett–Teller ( BET) isotherm considers the adsorption of the first layer as an equilibrium chemical reaction between adsorbate molecules and adsorption sites and the adsorption of the second and subsequent layers as a condensation–evaporation process. Following the recent development of an activity‐based formulation for the Langmuir isotherm for monolayer adsorption, we present an activity‐based formulation for the BET isotherm in which species concentrations are replaced with species activities. Capturing the adsorbent surface heterogeneity for the adsorption of the first layer, the resulting thermodynamic BET isotherm is shown to accurately represent pure component adsorption isotherms over the relative pressure range of zero to unity or prior to the onset of capillary condensation. The thermodynamic BET isotherm should facilitate accurate estimation of monolayer adsorption capacity and the corresponding adsorbent surface area.

Vyawahare, Pradeep↗
DOE OSTI2026

Opportunities and challenges in process modeling and simulation of electrochemical systems

Electrochemical technologies have garnered intense interest in both academic research and industrial applications due to their potential to increase energy efficiency and reduce carbon footprint. However, electrochemical process fundamentals have been absent from the chemical process simulators available to millions of chemical engineers worldwide. To expedite process research and development of electrochemical technologies in the chemical industry, it is imperative that essential electrochemical process fundamentals be incorporated into process simulators to support modeling and simulation of electrochemical processes. Here, this study examines three process fundamentals key to the research and development of electrochemical processes: electrochemical reaction kinetics, electrolyte thermodynamics, and heat and mass transfer. It further illustrates application of these process fundamentals with a case study modeling an electrochemical process for the conversion of acrylonitrile to adiponitrile. The modeling example highlights the roles of applied voltage on reaction rates, and electron flow rates on the performance of electrochemical processes. It suggests that the applied voltage and electron flow rates are two unique concepts that should be included in simulators for electrochemical processes.

09 BIOMASS FUELS↗
DOE OSTI2023

On the Thermodynamic Condition for Adsorption Azeotropes

Adsorption azeotropy is a common phenomenon in mixed-gas adsorption equilibria. Since the first literature report of binary adsorption azeotropes in 1933, numerous studies investigated the thermodynamic conditions for adsorption azeotropes but failed to reach definitive conclusions. Based on the generalized Langmuir isotherm model for multicomponent adsorption equilibria which takes into account the vacant site as part of the adsorbed phase, this study presents the thermodynamic condition for adsorption azeotropes as derived from the generalized Langmuir isotherm to be the equality of the ratios of adsorbed phase activity coefficient γi and adsorption equilibrium constant $K$$^{o}_{i}$ for the two adsorbates in the binary 1–2 adsorption system, i.e., γ 1 /$K$$^{o}_{1}$ = γ 2 /$K$$^{o}_{2}$. This adsorption azeotropic condition is analogous to the vapor–liquid equilibrium azeotropic condition, i.e., the equality of the products of liquid phase activity coefficient and saturation vapor pressure Pisat for the two components, i.e., γ 1 $P$$^{sat}_{1}$ = γ 2 $P$$^{sat}_{2}$. We validated the thermodynamic condition for adsorption azeotropes with 14 azeotrope-forming adsorption systems in this study. As a result, we investigated the effects of the pressure, temperature, and adsorbed phase nonideality on azeotrope formation.

42 ENGINEERING↗
DOE OSTI2023

Addressing spreading pressure dependence of real adsorbed solution theory with generalized Langmuir isotherm

This work addresses spreading pressure dependence of Real Adsorbed Solution Theory (RAST) for mixed-gas adsorption equilibria using generalized Langmuir (gL) isotherm. Considering vacant sites as an integral part of competitive multicomponent adsorption on a constant adsorbent surface area, the gL isotherm properly accounts for surface heterogeneity and loading, adsorbate composition, and temperature dependence. We show the spreading pressure dependence of adsorbate activity coefficient expression in the RAST framework can be generated from the gL isotherm. The procedure is illustrated with a spreading pressure dependent adsorption Nonrandom Furthermore, two-Liquid activity coefficient model, and the results are validated for ten binary mixed-gas adsorption equilibria systems including two highly nonideal azeotropic systems.

42 ENGINEERING↗
DOE OSTI2022

Advance modification of polyacrylonitrile nanofibers for enhanced removal of hexavalent chromium from water

Hexavalent chromium [Cr(VI)] is a known carcinogenic and mutagenic heavy metal. Its level in drinking water is regulated worldwide to protect public health. This work presents a novel chemical method to modify the polyacrylonitrile (PAN) nanofibers for efficient Cr(VI) removal from water. The PAN nanofibers with an average diameter of 165 nm are produced using the electrospinning technique. Through a 2-step chemical modification process, the amidine polyacrylonitrile (APAN) nanofibers are synthesized by the conversion of nitrile groups [—C≡N] in PAN nanofibers into amidines [—C(N=NH)(NH 2 )]. The attenuated total reflectance Fourier transform (ATR-FTIR) spectroscopy revealed the successful conversion of nitrile groups into amidoximes, resulting in amidoximated polyacrylonitrile nanofibers, and subsequent conversion into amidine functional groups, forming the APAN nanofibers. Greater concentration of hydroxylamine hydrochloride, increased reaction time and temperature yielded higher conversion of nitrile groups into amidoximes to a maximum of 37%. The Cr(VI) uptake by APAN nanofibers was found as a multilayer adsorption process modeled by Freundlich isotherm. The maximum Langmuir Cr(VI) adsorption capacity for APAN nanofibers was found as 225 mg g -1 at pH = 3.0 after 4.0 h exposure duration. The regeneration study revealed the excellent reusability of APAN nanofibers after five adsorption/desorption cycles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Characterizing cobalt sequestration in manganese-rich coal mine drainage treatment solids

This study investigates Co adsorption on synthesized birnessites over a wide pH range and in sulfate-rich solution to simulate CMD treatment conditions. Langmuir and Freundlich adsorption isotherms of Co at pH values of 3.5, 4.5, and 6.5 at 25°C onto Na-and H-birnessite were generated. Cobalt concentrations in supernatants were determined by ICP-MS and chelation ion chromatography. Mineralogy and morphology of pre- and post-adsorption experiment solids characterization by X-ray diffraction and scanning electron microscopy will be presented. These experiments suggest that cobalt sulfate complexes and pH of CMD, as well as the Mn-oxide mineral structures present in treatment beds, will impact cobalt adsorption in CMD solids, and can be used as calibration points for equilibrium and kinetic modeling approaches that are critical for developing effective and implementable remediation processes and to better inform future Co recovery efforts from CMD solids.

Schaffer, Camille↗
DOE OSTI2024

Adsorption Equilibrium, Kinetics, and Column Breakthrough Data of Acetic Acid, Butyric Acid, and Lactic Acid on IRN-78 Ion-exchange Resin at Initial pH ~3 – 7 and Temperature 25 – 55 °C

This work presents systematic aqueous-phase adsorption equilibrium, kinetics, and column breakthrough measurements with three key biointermediates that are common compounds in many bioprocesses. Adsorption equilibrium experiments were carried out with acetic acid, butyric acid, and lactic acid on a commercial ion-exchange resin, Amberlite IRN-78, at wide ranges of acid concentration (8-500 mmol/L), initial pH (similar to 3-7), and temperature (25-55 degrees C), simulating the effluent characteristics from different fermenter operations. The kinetics and column breakthrough experiments were conducted at an initial pH of 6 and a concentration of 200 mmol/L. The equilibrium study shows a higher loading at the initial pH < pK(a) and a lower loading at the initial pH > pK(a). Overall removal varies between 16 and 99% depending on the initial pH, temperature, and organic acid concentration and type. The study further indicates monolayer adsorption at the equilibrium pH > 10 and multilayer adsorption at the equilibrium pH < 6. The thermodynamic modeling of adsorption isotherm data was carried out using Langmuir and Freundlich isotherms. IRN-78 presents fast adsorption kinetics as the maximum loading was attained in <= 10 min and nearly the same breakthrough time for all three organic acids involved in this study.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

The Temperature Dependence of the Langmuir Adsorption Model for a Single-Site Metal–Organic Framework

The single-site Langmuir adsorption model, also known as the Langmuir isotherm equation, is one of the simplest possible descriptions of adsorption phenomena, and yet finds widespread applicability across a range of disciplines. In its simplest form, it is deployed to treat adsorption equilibria at constant temperature (i.e., along isotherms); however, at the heart of its derivation is a more general class of models that each incorporate an explicit temperature dependence, subject to assumptions about the spatial/translational degrees of freedom of the adsorbed species. In this work, measurements of the temperature dependence of supercritical adsorption of H 2 on a single-site metal-organic framework (MOF) are presented, and fitted using a range of Langmuir models with distinct treatments of degrees of freedom in the adsorbed phase. Surprisingly, all of the models can be used to adequately represent the measured data, despite yielding significantly different values for binding energy and the temperature dependence of the isosteric enthalpy of adsorption (i.e., the isosteric heat, qst). Furthermore, a critical finding is that the mean-temperature isosteric enthalpy of adsorption remains consistent across all models within experimental error, highlighting its reliability for evaluating adsorption thermodynamics.

08 HYDROGEN↗
DOE OSTI2026

CMPO-Functionalized Silica Sorbents for pH-Tunable Separation and Enrichment of Rare-Earth Elements from Environmental Matrices

Rare-earth elements (REEs) are crucial in many applications, yet mutual separation is challenging due to their similar chemical behavior. Octylphenyl- N,N-diisobutyl carbamoyl methyl phosphine oxide (CMPO) is an organophosphorus ligand originally developed for extracting actinides and lanthanides from spent nuclear fuel. Here, we report a pH-tunable CMPOfunctionalized silica sorbent for selective REE separation from complex aqueous matrices. A CMPO-associated silica gel sorbent was synthesized and characterized by Brunauer−Emmett−Teller (BET) surface area, scanning electron microscopy, and X-ray photoelectron spectroscopy to confirm the surface functionalization and binding behavior. Sorbent performance was evaluated by using a synthetic 46- element solution and a real phosphate rock fertilizer leachate. Notably, REEs were successfully eluted with ultrapure water, demonstrating reversible desorption controlled by pH adjustment. Packed-bed column studies increased the REE mass fraction from 3.6% to 64% (20-fold enrichment), with up to 30-fold enrichment of neodymium. The adsorption process follows the Langmuir isotherm behavior and follows pseudo-second-order kinetics. The uptake capacity of 1 μmol of REEs per 4.2 μmol of CMPO supports the formation of a predominantly 4:1 ligand:rare earth element(III) pseudocomplex. These results demonstrate CMPO-functionalized silica as a selective, water-elutable, and low-chemical-input platform for sustainable REE recovery from environmental and industrial sources.

chelating ligands↗
DOE OSTI2025

Facet-Dependent Adsorption of Pb(II) on Hematite (001), (116), and (104) Surfaces

Hematite’s common (001) and (012) facets are frequently used in model studies of lead (Pb) adsorption behavior, but there is a lack of research on the high-energy facets, e.g. (104), present in nature. Also, few studies have attempted to connect the molecular details of facet-specific Pb adsorption to macroscopic uptake behavior. Here, to address these knowledge gaps, we investigated Pb(II) adsorption behaviors on facet-engineered hematite nanoparticles dominated by (001), (104), and (116). Adsorption experiments revealed significant variations in Pb(II) uptake among the three samples, with (001) demonstrating the highest capacity and (116) showing the best adsorption efficiency when normalized to specific surface area. Adsorption kinetics followed the pseudo-second-order model, indicating the adsorption process is governed mostly by chemisorption. Adsorption isotherms were well fitted by the Langmuir model, indicating uptake proceeds until roughly monolayer adsorption. Detailed characterization revealed Pb(II) was adsorbed as single atoms with complex inner-sphere binding modes that varied across different facets, indicating adsorption is both structurally and energetically facet-dependent. Co-adsorption experiments further demonstrated Cu 2+ , Zn 2+ , and humic acid significantly promoted Pb(II) adsorption. This study advances the understanding of hematite surface reactivity in controlling macroscopic wet adsorption behaviors, providing valuable insights into the environmental fate of Pb(II).

Contaminant removal↗
DOE OSTI2020

X-ray and Neutron Reflectivity Studies of Styrene-Maleic Acid Copolymer Interactions with Galactolipid-Containing Monolayers

Styrene-maleic acid (SMA) copolymers have recently gained attention for their ability to facilitate the detergent-free solubilization of membrane protein complexes and their native boundary lipids into polymer-encapsulated, nanosized lipid particles, referred to as SMALPs. However, the interfacial interactions between SMA and lipids, which dictate the mechanism, efficiency, and selectivity of lipid and membrane protein extraction, are barely understood. Our recent finding has shown that SMA 1440, a chemical derivative of the SMA family with a functionalized butoxyethanol group, was most active in galactolipid-rich membranes, as opposed to phospholipid membranes. In the present work, we have performed X-ray reflectometry (XRR) and neutron reflectometry (NR) on the lipid monolayers at the liquid–air interface followed by the SMA copolymer adsorption. XRR and Langmuir Π–A isotherms captured the fluidifying effect of galactolipids, which allowed SMA copolymers to infiltrate easily into the lipid membranes. NR results revealed the detailed structural arrangement of SMA 1440 copolymers within the membranes and highlighted the partition of butoxyethanol group into the lipid tail region. In conclusion, this work allows us to propose a possible mechanism for the membrane solubilization by SMA.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗