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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 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 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 OSTI2022

Thermodynamic modeling of adsorption at the liquid-solid interface

Adsorptive separation techniques are significantly energy efficient in comparison to conventional thermal separation techniques such as distillation. Despite extensive research and development activities undertaken for mixed-gas adsorption, the use of adsorption techniques for the separation of multicomponent liquid mixtures is still limited. A major barrier is the lack of accurate adsorption thermodynamic models, which form the scientific foundation of process simulation of such systems, making the translation to industrial scale challenging. In this work, we have rigorously computed the surface excess of adsorption for six binary liquid mixtures on silica gel at 303 K using the frameworks of the generalized Langmuir isotherm (gL) and the adsorbed solution theory (AST). The six binary liquid mixtures were formed by the pair-wise combinations of four components: benzene, 1,2-dichloroethane, cyclohexane, and n-heptane. We have based our calculations by considering simultaneous equilibria of three phases: saturated vapor phase, bulk liquid phase, and adsorbed phase. Further, the composition of the corresponding saturated vapor phase was estimated by the Nonrandom Two-Liquid activity coefficient model and experimental vapor-liquid equilibria data. The activity coefficients of the adsorbed phase, the central issue of multicomponent adsorption thermodynamics, were calculated using the adsorption Nonrandom Two-Liquid activity coefficient model. Devoid of simplifying assumptions, gL and AST provide rigorous thermodynamic frameworks for adsorption equilibria of multicomponent liquid mixtures.

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

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. Here, 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.

09 BIOMASS FUELS↗
DOE OSTI2023

Comparison of Heterogeneous Langmuirian Models for Mixed-Gas Adsorption Equilibria

Mixed-gas adsorption remains a very active area of research, where newly proposed adsorption equilibrium models need to be compared to standards in the field. The generalized Langmuir (gL) isotherm, proposed by Hamid et al. to address adsorption of different size molecules on heterogeneous adsorbents without requiring evaluation of the Gibbs isotherm, has thus far been tested mainly against the adsorbed solution theory (AST). The gL isotherm was shown to be thermodynamically consistent and gave either better or similar representation than AST models. Here, the gL isotherm is contrasted with the Dual-Process Langmuir isotherm popularized by Ritter and his co-workers and the Loading Ratio Correlation popularized for simple mixtures, both of which are considered the “standard” models for process simulation. Furthermore, the comparison is based on their theoretical roots, interpretations, and representation of the equilibrium loading and the isosteric enthalpy of adsorption of unary, binary, and ternary mixtures of various gaseous adsorbates on different adsorbents over a range of experimental pressures and temperatures.

42 ENGINEERING↗
DOE OSTI2022

Isotherm Model for Moisture-Controlled CO 2 Sorption

Moisture-controlled sorption of CO 2 , the basis for moisture-swing CO 2 capture from air, is a novel phenomenon observed in strong-base anion exchange materials. Prior research has shown that Langmuir isotherms provide an approximate fit to moisture-controlled CO 2 sorption isotherm data. However, this fit still lacks a governing equation derived from an analytic model. As such, in this paper we derive an analytic form for an isotherm equation from a bottom-up approach, starting with a fundamental theory for an alkali liquid. In the range of interest relevant to CO 2 capture from air, an isotherm equation for an alkali liquid reduces to a simple analytic form with a single parameter, $K_{\text{eq}}$. In the limit $K_{\text{eq}} \gg 1$, a 2nd order approximation simplifies to a Langmuir isotherm that, however, deviates from experimental data. The isotherm theory for an alkali liquid has been generalized to a strong-base anion exchange material. In a strong-base anion exchange material, water concentration inside a sorbent, [H 2 O], is not large enough to be regarded as constant, which allows us to extend $K_{\text{eq}}$ to $K_{\text{eq(AEM)eff}} = K_{\text{eq(AEM)}} \times$ [H 2 O]$^{–n}$ according to the law of mass action. The final isotherm formula has been validated by experimental data from the literature. For a moisture-controlled CO 2 sorbent, $K_{\text{eq(AEM)eff}}$ varies significantly with moisture content of the sorbent. Depending on moisture level, the observed $K_{\text{eq(AEM)eff}}$ in a specific sorbent ranges from a few times to a few thousand times the value of $K_{\text{eq}}$ of a 2 mol L –1 alkali liquid.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Uranium Retardation Capacity of Lithologies from the Negev Desert, Israel—Rock Characterization and Sorption Experiments

A series of batch experiments were performed to assess the uranium sorption capacity of four mineralogically distinct lithologies from the Negev Desert, Israel, to evaluate the suitability of a potential site for subsurface radioactive waste disposal. The rock specimens consisted of an organic-rich phosphorite, a bituminous marl, a chalk, and a sandstone. The sorption data for each lithology were fitted using a general composite surface complexation model (GC SCM) implemented in PHREEQC. Sorption data were also fitted by a non-mechanistic Langmuir sorption isotherm, which can be used as an alternative to the GC SCM to provide a more computationally efficient method for uranium sorption. This is because all the rocks tested have high pH/alkalinity/calcium buffering capacities that restrict groundwater chemistry variations, so that the use of a GC SCM is not advantageous. The mineralogy of the rocks points to several dominant sorption phases for uranyl (UO 2 2+ ), including apatite, organic carbon, clays, and iron-bearing phases. The surface complexation parameters based on literature values for the minerals identified overestimate the uranium sorption capacities, so that for our application, an empirical approach that makes direct use of the experimental data to estimate mineral-specific sorption parameters appears to be more practical for predicting uranium sorption.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
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 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↗