Simulated Adsorption Isotherms Research Articles

Use of molecular simulation to design modification of a chromium‐based MOF for adsorptive removal of inhalation anaesthetic agents

AbstractMIL‐101‐Cr‐X (X = OH−, F−) has been reported to be the most suitable material so far for adsorptive removal of inhalation anaesthetic agents (IAA) sevoflurane and desflurane at the working conditions in hospital operation rooms. To further enhance its affinity and uptake capacity towards IAA, several structural modifications were proposed, and their isotherms were predicted using our molecular simulation approach adopted in our previous publication for the case of the pristine MIL‐101‐Cr (X = F−, OH−) structure. The proposed modifications include (1) grafting the metal‐cluster site with coordinated NH3 ligands to produce MIL‐101‐Cr@NH3 (X = F−, OH−), (2) anion exchange of the fluorine atom bonded to chromium with chlorine to synthesize MIL‐101‐Cr (X = Cl−), and (3) functionalization of the benzene rings of the ligand linkers in the MOFs with amino‐ and nitro‐ groups in order to form NH2‐MIL‐101‐Cr (X = Cl−) and NO2‐MIL‐101‐Cr (X = Cl), respectively. Simulated adsorption isotherms of IAA on these modifications were verified by the experimental results using the standard volumetric technique and they clearly demonstrated that MIL‐101‐Cr@NH3 (X = F−, OH−) possesses the highest equilibrium capacity for IAA. This observation can be attributed to the electron‐transfer contribution of the coordinated ammonium molecules to the unsaturated coordinated sites of the MOF while doing away with steric hindrance inside the pore cages. The new compound can significantly enhance the economy of adsorptive removal of IAA from vented gas mixtures.

Quantifying the Uncertainty of Force Field Selection on Adsorption Predictions in MOFs.

Comparisons between simulated and experimental adsorption isotherms in MOFs are fraught with challenges. On the experimental side, there is significant variation between isotherms measured on the same system, with a significant percentage (∼20%) of published data being considered outliers. On the simulation side, force fields are often chosen "off-the-shelf" with little or no validation. The effect of this choice on the reliability of simulated adsorption predictions has not yet been rigorously quantified. In this work, we fill this gap by systematically quantifying the uncertainty arising from force field selection on adsorption isotherm predictions. We choose methane adsorption, where electrostatic interactions are negligible, to independently study the effect of the framework Lennard-Jones parameters on a series of prototypical materials that represent the most widely studied MOF "families". Using this information, we compute an adsorption "consensus isotherm" from simulations, including a quantification of uncertainty, and compare it against a manually curated set of experimental data from the literature. By considering many experimental isotherms measured by different groups and eliminating outliers in the data using statistical analysis, we conduct a rigorous comparison that avoids the pitfalls of the standard approach of comparing simulation predictions to a single experimental data set. Our results show that (1) the uncertainty in simulated isotherms can be as large as 15% and (2) standard force fields can provide reliable predictions for some systems but can fail dramatically for others, highlighting systematic shortcomings in those models. Based on this, we offer recommendations for future simulation studies of adsorption, including high-throughput computational screening of MOFs.

Effect of layer bending on montmorillonite hydration and structure from molecular simulation

Abstract Conceptual models of smectite hydration include planar (flat) clay layers that undergo stepwise expansion as successive monolayers of water molecules fill the interlayer regions. However, X-ray diffraction (XRD) studies indicate the presence of interstratified hydration states, suggesting non-uniform interlayer hydration in smectites. Additionally, recent theoretical studies have shown that clay layers can adopt bent configurations over nanometer-scale lateral dimensions with minimal effect on mechanical properties. Therefore, in this study we used molecular simulations to evaluate structural properties and water adsorption isotherms for montmorillonite models composed of bent clay layers in mixed hydration states. Results are compared with models consisting of planar clay layers with interstratified hydration states (e.g. 1W–2W). The small degree of bending in these models (up to 1.5 Å of vertical displacement over a 1.3 nm lateral dimension) had little or no effect on bond lengths and angle distributions within the clay layers. Except for models that included dry states, porosities and simulated water adsorption isotherms were nearly identical for bent or flat clay layers with the same averaged layer spacing. Similar agreement was seen with Na- and Ca-exchanged clays. While the small bent models did not retain their configurations during unconstrained molecular dynamics simulation with flexible clay layers, we show that bent structures are stable at much larger length scales by simulating a 41.6×7.1 nm2 system that included dehydrated and hydrated regions in the same interlayer.

CRAFTED: An exploratory database of simulated adsorption isotherms of metal-organic frameworks

Grand Canonical Monte Carlo is an important method for performing molecular-level simulations and assisting the study and development of nanoporous materials for gas capture applications. These simulations are based on the use of force fields and partial charges to model the interaction between the adsorbent molecules and the solid framework. The choice of the force field parameters and partial charges can significantly impact the results obtained, however, there are very few databases available to support a comprehensive impact evaluation. Here, we present a database of simulations of CO2 and N2 adsorption isotherms on 690 metal-organic frameworks taken from the CoRE MOF 2014 database. We performed simulations with two force fields (UFF and DREIDING), six partial charge schemes (no charges, Qeq, EQeq, MPNN, PACMOF, and DDEC), and three temperatures (273, 298, 323 K). The resulting isotherms compose the Charge-dependent, Reproducible, Accessible, Forcefield-dependent, and Temperature-dependent Exploratory Database (CRAFTED) of adsorption isotherms.

Exploring the Potential of a Highly Scalable Metal-Organic Framework CALF-20 for Selective Gas Adsorption at Low Pressure.

In this study, the ability of the highly scalable metal-organic framework (MOF) CALF-20 to adsorb polar and non-polar gases at low pressure was investigated using grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations. The results from the simulated adsorption isotherms revealed that the highest loading was achieved for SO2 and Cl2, while the lowest loading was found for F2 molecules. The analysis of interaction energies indicated that SO2 molecules were able to form the strongest adsorbent-adsorbate interactions and had a tight molecular packing due to their polarity and angular structure. Additionally, Cl2 gas was found to be highly adsorbed due to its large van der Waals surface and strong chemical affinity in CALF-20 pores. MD simulations showed that SO2 and Cl2 had the lowest mobility inside CALF-20 pores. The values of the Henry coefficient and isosteric heat of adsorption confirmed that CALF-20 could selectively adsorb SO2 and Cl2. Based on the results, it was concluded that CALF-20 is a suitable adsorbent for SO2 and Cl2 but not for F2. This research emphasizes the importance of molecular size, geometry, and polarity in determining the suitability of a porous material as an adsorbent for specific adsorbates.

Molecular Dynamics Simulation of Pore-Size Effects on Gas Adsorption Kinetics in Zeolites

AbstractStrong gas-mineral interactions or slow adsorption kinetics require a molecular-level understanding of both adsorption and diffusion for these interactions to be properly described in transport models. In this combined molecular simulation and experimental study, noble gas adsorption and mobility is investigated in two naturally abundant zeolites whose pores are similar in size (clinoptilolite) and greater than (mordenite) the gas diameters. Simulated adsorption isotherms obtained from grand canonical Monte Carlo simulations indicate that both zeolites can accommodate even the largest gas (Rn). However, gas mobility in clinoptilolite is significantly hindered at pore-limiting window sites, as seen from molecular dynamics simulations in both bulk and slab zeolite models. Experimental gas adsorption isotherms for clinoptilolite confirm the presence of a kinetic barrier to Xe uptake, resulting in the unusual property of reverse Kr/Xe selectivity. Finally, a kinetic model is used to fit the simulated gas loading profiles, allowing a comparison of trends in gas diffusivity in the zeolite pores.

Effects of surfactant adsorption on the wettability and friction of biomimetic surfaces.

The properties of solid-liquid interfaces can be markedly altered by surfactant adsorption. Here, we use molecular dynamics (MD) simulations to study the adsorption of ionic surfactants at the interface between water and heterogeneous solid surfaces with randomly arranged hydrophilic and hydrophobic regions, which mimic the surface properties of human hair. We use the coarse-grained MARTINI model to describe both the hair surfaces and surfactant solutions. We consider negatively-charged virgin and bleached hair surface models with different grafting densities of neutral octadecyl and anionic sulfonate groups. The adsorption of cationic cetrimonium bromide (CTAB) and anionic sodium dodecyl sulfate (SDS) surfactants from water are studied above the critical micelle concentration. The simulated adsorption isotherms suggest that cationic surfactants adsorb to the surfaces via a two-stage process, initially forming monolayers and then bilayers at high concentrations, which is consistent with previous experiments. Anionic surfactants weakly adsorb via hydrophobic interactions, forming only monolayers on both virgin and medium bleached hair surfaces. We also conduct non-equilibrium molecular dynamics simulations, which show that applying cationic surfactant solutions to bleached hair successfully restores the low friction seen with virgin hair. Friction is controlled by the combined surface coverage of the grafted lipids and the adsorbed CTAB molecules. Treated surfaces containing monolayers and bilayers both show similar friction, since the latter are easily removed by compression and shear. Further wetting MD simulations show that bleached hair treated with CTAB increases the hydrophobicity to similar levels seen for virgin hair. Treated surfaces containing CTAB monolayers with the tailgroups pointing predominantly away from the surface are more hydrophobic than bilayers due to the electrostatic interactions between water molecules and the exposed cationic headgroups.

Simulation of surfactant adsorption at liquid-liquid interface: What we may expect from soft-core models?

The present work attempts to systematically explore the surfactant sorption at liquid-liquid interfaces with coarse-grained models targeting thermodynamic properties of reference liquid solutions. We employ dissipative particle dynamics with soft-core forcefield tested against experimental data on micellization of surfactants in water, and the previous results are reproduced in this work. We consider three different nonionic surfactants: hexaethylene glycol monododecyl ether (C12E6), 2-[4-(2,4,4-trimethylpentan-2-yl)phenoxy]ethanol) known as Triton X-100 (TX-100), and two alkyl glucoside surfactants (CnG1) with n-alkane tail fragments and a saccharide hydrophilic head at decane-water and toluene-water interfaces. For TX-100, we composed a model based on the literature forcefield and found good agreement with the experimental critical micelle concentrations (CMCs). The head-head interactions are of different origins for different surfactant groups: entropic repulsion between ethylene oxide chains of C12E6 and TX-100, and more chemically specific and complex interactions between the maltose heads of alkyl glucosides. We interpret our results with the Redlich-Peterson equation of monolayer adsorption in order to relate the adsorption to the bulk concentration of the surfactant and the interfacial tension. The densities of the adsorbed monolayer at CMC mostly agree with the experimental data, and a reasonable agreement was obtained for the interfacial tension at CMC. At the same time, we found significant discrepancies between the simulated and experimental adsorption isotherms. We explain them by the oversimplified forcefield: when the parameters are fitted to the free energies of bulk solutions, they may not correctly reproduce the interfacial free energies.

Modeling adsorption of simple fluids and hydrocarbons on nanoporous carbons

Predicting adsorption on nanoporous carbonaceous materials is important for developing various adsorption and membrane separations, as well as for oil and gas recovery from shale reservoirs. Here, we explore the capabilities of 3D molecular models of disordered carbon structures to reproduce the morphological and adsorption features of practical adsorbents. Using grand canonical Monte Carlo simulations, we construct a series of adsorption isotherms of simple fluids (N2, Ar, CO2, and SO2) and a series of alkanes from methane to hexane on two model 3D structures, purely microporous structure A and micro-mesoporous structure B. We show that structure A reproduces the morphological properties of commercial Norit R1 Extra activated carbon and demonstrates outstanding agreement between the simulated and experimental adsorption isotherms reported in the literature for all adsorbates considered. Good agreement is also found for simulated and measured isosteric heats. Taking into account inherent variability of structural properties of commercial carbons and experimental adsorption data from different literature sources, the correlations with experiments are truly amazing. This work provides a new insight into the specifics of structural and adsorption properties of nanoporous carbons and demonstrates the advantages of using 3D molecular models for predicting adsorption hydrocarbons and other chemicals by MC simulations.

Discrepancy quantification between experimental and simulated data of CO2 adsorption isotherm using hierarchical Bayesian estimation

To quantitatively analyze the inconsistencies commonly observed between experimental and simulated adsorption isotherms, parameter estimation of adsorption isotherm models was conducted by hierarchical Bayesian estimation with parameter uncertainties being quantified as probability distributions. The estimation method was implemented using Markov Chain Monte Carlo (MCMC) to analyze multiple data sets obtained from different sources, including a publicly available database. To describe the discrepancies of experimental and simulated adsorption data, the simulation data was set as the reference to which experimental measurements were compared. We applied the proposed approach to analyze CO2 adsorption isotherms that are measured and simulated on zeolite 13X and MIL-101(Cr). In these case studies, the discrepancy of CO2 adsorption isotherm was successfully quantified between experimental measurements and predictions given by molecular simulations using Grand Canonical Monte Carlo (GCMC), where uncertainties were quantified as probability distributions. Furthermore, experimental data sets that agree well with the GCMC simulation have been identified, providing insights into experimental and measurement methods as well as choosing the right assumptions in the molecular simulation.

Influence of layer slipping on adsorption of light gases in covalent organic frameworks: A combined experimental and computational study

Sorption of gases in micro- and mesoporous materials is typically interpreted on the basis of idealized structural models where real structure effects such as defects and disorder are absent. For covalent organic frameworks (COFs) significant discrepancies between measured and simulated adsorption isotherms are often reported but rarely traced back to their origins. This is because little is known about the real structure of COFs and its effect on the sorption properties of these materials. In the present work molecular simulations are used to obtain adsorption isotherms of argon, nitrogen, and carbon dioxide in the COF-LZU1 at various temperatures. The (perfect) model COF has a BET surface that is higher than the experimental BET surface by a factor of approximately 1.33, suggesting defects or inclusions are present in the real structure. We find that the saturation adsorption loading of small gaseous species in COF-LZU1, as determined from grand canonical Monte Carlo simulations, is also higher by approximately the same factor compared to the experimental saturation loading. The influence of interlayer slipping on the shape of the adsorption isotherm and the adsorption capacity is studied. Comparison between simulation and experiment at lower loadings suggests the layers to be shifted instead of perfectly eclipsed. The sensitivity of the adsorption isotherms in this regime towards the underlying framework topology shows that real structure effects have significant influence on the gas uptake. Accounting for layer slipping is important to applications such as catalysis, gas storage and separation.

Nitrogen rejection from low quality natural gas by pressure swing adsorption experiments and simulation using dynamic adsorption isotherms

In order to remove N2 from low quality natural gas, a mathematical model has been established by Aspen adsorption, using the CH4-selective sorbent silicalite-1 pellets. The dynamic adsorption isotherm was first simulated by breakthrough simulation of a CH4/N2 mixture at different adsorption pressures and feed flow rates based on breakthrough experiments. The resulting simulated CH4 dynamic adsorption amounts were very close to the experimental data at three different adsorption pressures (100, 200, and 300 kPa). Moreover, a single-bed, three-step pressure swing adsorption (PSA) experiment was performed, and the results were in good agreement with the simulated data, further corroborating the accuracy of the gas dynamic adsorption isotherm obtained by the simulation method. Finally, based on the simulated dynamic adsorption isotherm of CH4 and N2, a four-bed, eight-step PSA process has been designed, which enriched 75% (vol) CH4 and 80% (vol) CH4 to 95% (vol) and 99% (vol), and provided 99% (vol) recovery.

Bacillus licheniformis a potential bio-collector for Barite-Quartz selective separation

Employing microorganisms and their metabolites as a potentially low-cost and environmentally friendly alternative for the synthetic compounds in many of the current mineral beneficiation techniques is receiving increasing attention. For the first time, the influence of the Bacillus licheniformis cells and its metabolites for selective flotation of barite from quartz was studied. The maximum adsorption density of 1.33 × 1010 cells/g was achieved at pH = 3 for barite, six times higher than quartz. Flotation experiments revealed that cell-assisted separation was more effective than metabolite-facilitated flotation, either for single mineral or the mixed sample (barite mixed with quartz). Barite was recovered up to 87% (at pH = 3) in sole-mineral flotation experiments, and flotation of the mixed sample, also, proved a successful selective separation of barite (76% recovery) from quartz at the bio-collector dosage of 6.55 × 103 cells/ml. Adsorption kinetics study showed that the pseudo second-order model could represent cell adsorption densities for both minerals, while the Langmuir model simulated adsorption isotherms. Finally, it was shown that B. licheniformis cells could selectively enhance particles hydrophobicity and successfully be utilized as a bio-collector.

Water Adsorption Control by Surface Nanostructures on Graphene-Related Materials by Grand Canonical Monte Carlo Simulations.

The interfaces of carbon materials play an important role in various technological and scientific research fields. Graphene is the fundamental unit of sp2 carbon allotropes, and the evaluation of the interfacial properties of graphene-related materials is thus essential to clarify the molecular mechanisms occurring at the interfaces. Ideally, graphene is exclusively composed of sp2 carbon atoms; however, some parts of graphene normally contain sp3 carbon atoms with oxygen functional groups, vacancy, and grain boundary defects, and these structural characteristics need to be considered to reveal the interfacial properties. Herein, we demonstrate the interfacial properties of graphene-related materials by analyzing the water adsorption properties of graphene, hydrogenated graphene (graphane), and partially oxidized graphene (named as graphoxide) using grand canonical Monte Carlo simulations. The hydrophobicity evaluated from the simulated water adsorption isotherms followed the order: graphane > graphene > graphoxide with 1% oxygen atomic ratio > graphoxide with 3% oxygen atomic ratio > graphoxide with 5% oxygen atomic ratio. The potential calculations between a single water molecule and graphoxides revealed that the presence of oxygen functional groups enhanced the hydrophilicity of graphoxide. This study also disclosed some differences between the hydrophobic interfaces of graphene and graphane, which have been rarely evaluated. Surprisingly, the hydrophobicity of graphane was higher than that of graphene despite the similar potential well depths between a water molecule and graphene/graphane. This was caused by the restriction of water orientation on graphane; water was preferentially adsorbed on the honeycomb center or concave sites in the initial adsorption, and it was hard to interact with neighboring water molecules. The different structures revealed for the graphene-related materials with nanoscale roughness played important roles in controlling the water vapor adsorption mechanism.

Influence of force field used in carbon nanostructure reconstruction on simulated phenol adsorption isotherms in aqueous medium

Grand Canonical Monte Carlo (GCMC) simulations have been conducted to investigate the interaction between phenol and a commercial activated carbon cloth KIP1200 in aqueous solution. The nanostructure of KIP1200 has been extracted using Hybrid Reverse Monte Carlo (HRMC) simulations based on experimental measurements of XRD-based structure factor, and shows the presence of pore spaces inaccessible to both phenol and nitrogen. The impact of empirical force fields (EDIP and Erhart-Albe) on the structural parameters and adsorption capacity, as well as pore accessibility is investigated via molecular simulations and materials informatics employing lattice and Voronoi decomposition algorithms. While the Erhart-Albe force field leads to more amorphous structures and inaccessible pores, the EDIP force field creates more lamellar structures with sharp edges and narrow pore width. The molecular state of adsorbed phenol in these structures is markedly different, with the narrower pore spaces of the EDIP-based structure providing stronger interaction between phenol molecules and carbon structure than for water. The calculated X-ray intensities and adsorption isotherms for the simulation-based structure are in good agreement with corresponding experimental results. The simulated solvation state of phenol has been verified by experiments, and demonstrates the existence of inter-layer spaces inaccessible to phenol for both force fields.

Water adsorption isotherms on soil external particle surface by molecular simulation

Water adsorption isotherm describes soils’ ability in retaining water under given relative humidity and isothermal conditions, and is frequently utilized to characterize soils’ engineering properties. Fundamentally, the water adsorption isotherm on soil external particle surface is the macroscopic manifestation of atomistic scale soil–water interaction mechanisms, including van der Waals, surface hydration, cation hydration, and electrical double layer. Yet, the quantitative link between these mechanisms and water adsorption isotherms remains obscure, and it still lacks effective approaches to probe these mechanisms. Here, a general framework based on Grand Canonical Monte Carlo simulation was developed to directly obtain water adsorption isotherms on soil external particle surface from the interatomic potentials. The simulated adsorption isotherm agrees well with existing experimental and numerical results, confirming the validity of the proposed framework. The proposed framework facilitates a quantitative assessment of the impact of atomistic scale soil–water interaction mechanisms on the macroscale water adsorption isotherms. It reveals that the atomistic scale soil–water interaction mechanisms dictate the shape of adsorption isotherms, i.e., an ‘S’ shape by prevailing cation hydration and a concave shape by prevailing surface hydroxyl hydration; and divalent cations exhibit a much more intensive interaction with water molecules than univalent cations, increasing the adsorption capacity up to 9.5 times.

Protein adsorption on ion exchange adsorbers: A comparison of a stoichiometric and non-stoichiometric modeling approach

For mechanistic modeling of ion exchange (IEX) processes, a profound understanding of the adsorption mechanism is important. While the description of protein adsorption in IEX processes has been dominated by stoichiometric models like the steric mass action (SMA) model, discrepancies between experimental data and model results suggest that the conceptually simple stoichiometric description of protein adsorption provides not always an accurate representation of nonlinear adsorption behavior.In this work an alternative colloidal particle adsorption (CPA) model is introduced. Based on the colloidal nature of proteins, the CPA model provides a non-stoichiometric description of electrostatic interactions within IEX columns. Steric hindrance at the adsorber surface is considered by hard-body interactions between proteins using the scaled-particle theory. The model’s capability of describing nonlinear protein adsorption is demonstrated by simulating adsorption isotherms of a monoclonal antibody (mAb) over a wide range of ionic strength and pH. A comparison of the CPA model with the SMA model shows comparable model results in the linear adsorption range, but significant differences in the nonlinear adsorption range due to the different mechanistic interpretation of steric hindrance in both models. The results suggest that nonlinear adsorption effects can be overestimated by the stoichiometric formalism of the SMA model and are generally better reproduced by the CPA model.

Porous Covalent Organic Polymers for Efficient Fluorocarbon‐Based Adsorption Cooling

AbstractAdsorption‐based cooling is an energy‐efficient renewable‐energy technology that can be driven using low‐grade industrial waste heat and/or solar heat. Here, we report the first exploration of fluorocarbon adsorption using porous covalent organic polymers (COPs) for this cooling application. High fluorocarbon R134a equilibrium capacities and unique overall linear‐shaped isotherms are revealed for the materials, namely COP‐2 and COP‐3. The key role of mesoporous defects on this unusual adsorption behavior was demonstrated by molecular simulations based on atomistic defect‐containing models built for both porous COPs. Analysis of simulated R134a adsorption isotherms for various defect‐containing atomistic models of the COPs shows a direct correlation between higher fluorocarbon adsorption capacities and increasing pore volumes induced by defects. Combined with their high porosities, excellent reversibility, fast kinetics, and large operating window, these defect‐containing porous COPs are promising for adsorption‐based cooling applications.

Pore-Scale Simulation of Confined Phase Behavior with Pore Size Distribution and Its Effects on Shale Oil Production

Confined phase behavior plays a critical role in predicting production from shale reservoirs. In this work, a pseudo-potential lattice Boltzmann method is applied to directly model the phase equilibrium of fluids in nanopores. First, vapor-liquid equilibrium is simulated by capturing the sudden jump on simulated adsorption isotherms in a capillary tube. In addition, effect of pore size distribution on phase equilibrium is evaluated by using a bundle of capillary tubes of various sizes. Simulated coexistence curves indicate that an effective pore size can be used to account for the effects of pore size distribution on confined phase behavior. With simulated coexistence curves from pore-scale simulation, a modified equation of state is built and applied to model the thermodynamic phase diagram of shale oil. Shifted critical properties and suppressed bubble points are observed when effects of confinement is considered. The compositional simulation shows that both predicted oil and gas production will be higher if the modified equation of state is implemented. Results are compared with those using methods of capillary pressure and critical shift.

Adsorption of Pb Ions from Oily Wastewater by Anthraquinone Modified Carbon Nanotube

The aim of this research was to investigate the adsorption properties of anthraquinone modified carbon nanotube (ACNT) in oily wastewaters containing Pb ions. The modified adsorbents were characterized using Fourier transform infra-red spectroscopy and SEM analysis. The adsorption and regeneration studies were conducted in batch mode using a Taguchi (L16) orthogonal array to optimize experimental runs. The controllable factors used in this study consisted of: pH of the solution (A); adsorbent dosage (B); adsorbent type (C); contact time (D); temperature (F). The effects of each factor were studied at four levels on the removal efficiency of metals from aqueous solution. Concentrations of metal ions were assessed by atomic absorption spectrometer. The total optimum adsorptive removal of lead ions was obtained with C0 = 10 mg•l-1, T = 338 K, pH = 6, m = 0.020 mg and t = 60 min. The Langmuir model was representative to simulate adsorption isotherms. The adsorption kinetics of Pb adsorption by ACNT was modeled using the pseudo-first order, the pseudo-second order, and intraparticle diffusion kinetics equations. The results indicate that the pseudo-second order kinetic equation and intraparticle diffusion model were adequate to describe the adsorption kinetics.