Equilibrium mono- and multicomponent adsorption models: From homogeneous ideal to heterogeneous non-ideal binding

Electrokinetics at liquid-liquid interfaces: Physical models and transport mechanisms

The electrification effects and electrokinetic flow phenomena at immiscible liquid-liquid interfaces have been a subject of scientific inquiry for over a century. Unlike solid-liquid interfaces, liquid-liquid interfaces exhibit not only multiphysical and cross-scale characteristics but also diffuse soft properties, including finite thickness, fluidity, ion adsorbability, and permeability, which introduces diverse interfacial charging mechanisms and conductive dielectric properties, imparting unique characteristics to electrokinetic multiphase flow systems. Electrokinetic multiphase hydrodynamics (EKmHD), grounded in electrochemistry and colloid and interface science, has experienced renewed interest in recent years. This is particularly evident in systems such as the interface between two immiscible electrolyte solutions (ITIES) in electrochemistry, self-propelling droplets in physicochemical hydrodynamics, and digital microfluidics in electromechanics. The multiphase diffuse soft nature of charged liquid-liquid interfaces introduces novel physical scales and theoretical dimensions, positioning EKmHD as a potential foundation for a new interdisciplinary field rather than merely a cross-disciplinary area. This review highlights the need for an integrated research approach that combines interfacial charging mechanisms with electrokinetic flows, alongside a cross-scale modeling framework for interfacial multiphysical transport. It systematically organizes the characteristics of liquid-liquid interfaces from the perspectives of charging mechanisms and electrokinetic behaviors, with particular emphasis on spontaneous partition- and adsorption-induced charging at the interface, and the strong coupling between multiphase diffuse soft interface flow and ion transport. Furthermore, the paper comprehensively summarizes the transport mechanisms of electrokinetic multiphase flows concerning interfacial ion transport and fluid flow, while refining the corresponding dominant dimensionless parameters. Additionally, it systematically consolidates current understanding of typical electrokinetic multiphase flow scenarios, with special focus on potential future research directions. These include the electrokinetic double-sided coupling effects in ITIES systems, solidification and nonlinear effects in droplet/bubble electrophoresis, the validity of the leaky dielectric model, electrokinetic instabilities of jets and ion-selective soft interfaces, and the active and passive control of two-phase electrokinetic wetting dynamics and displacement.

Synergistic neurotoxicity of clothianidin and photoaged microplastics in zebrafish: Implications for neuroendocrine disruption

Microplastics (MPs), widely found in aquatic environments, pose a growing threat to environmental and biological health due to their complex interactions with pollutants and microorganisms. This study investigates the adsorption characteristics of clothianidin (CLO) on polystyrene (PS) and photoaged polystyrene (P-PS) and explores the neurotoxic effects of CLO combined with PS/P-PS in larval zebrafish (Danio rerio). Adsorption kinetics and isotherms showed that P-PS exhibited a higher adsorption capacity and faster equilibrium compared to PS, indicating the significant role of photoaging in enhancing CLO adsorption. Exposed to CLO combined with PS/P-PS resulted in reduced locomotor activity, particularly in the P-PS + CLO group, suggesting amplified neurotoxicity due to P-PS. Analysis of the hypothalamic-pituitary-interrenal (HPI) axis revealed elevated levels of adrenocorticotropic hormone (ACTH) and cortisol, along with downregulated expression of stress-related genes in co-exposed zebrafish, indicating disruption of neuroendocrine function. Neurotransmitter analysis showed significant changes in acetylcholine (ACh), dopamine (DA), serotonin (5-HT), and γ-aminobutyric acid (GABA) levels, further confirming the neurotoxic impact of co-exposure. The findings highlight the synergistic neurotoxicity of CLO and photoaged MPs, with potential implications for aquatic ecosystems. This study advances the field of environmental science by addressing critical knowledge gaps in pollutant-microplastic interactions, providing a foundation for developing targeted mitigation strategies and enhancing ecological risk management frameworks.

Nickel removal from synthetic wastewater by novel zeolite-doped magnesium- iron- and zinc-oxide nanocomposites by hydrothermal-calcination technique

This study aims to modify raw zeolite with metal oxide nanocomposites to remove nickel (Ni) ions from synthetic wastewater. Novel zeolite-doped magnesium oxide (MgO), iron oxide (Fe3O4), and zinc oxide (ZnO) nanocomposites were synthesized by hydrothermal-calcination methods. The novel zeolite-doped metal oxide nanocomposites were used as adsorbents to remove Ni (II) ions from synthetic wastewater. Several advanced techniques, including X-ray diffraction (XRD), transmission electron microscopy (TEM), scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDS), X-ray photoelectron spectroscopy (XPS), and vibrating sample magnetometer (VSM) were applied to study the structural, morphological, chemical, and magnetic properties of the prepared materials. Doped zeolite with ZnO, MgO, and Fe3O4 significantly enhances the removal of Ni (II) ions from synthetic wastewater. The zeolite-doped MgO + Fe3O4 + ZnO sample achieved a Ni (II) ions removal efficiency of 99.6%, compared to 58.9% for raw zeolites. The removal efficiencies of Ni (II) ions (Ci = 30 mg/L) from highest to lowest were 99.56%, 99.53%, 91.4%, 67.8%, and 58.93% by zeolite-doped MgO + Fe3O4 + ZnO, zeolite-doped MgO, zeolite-doped ZnO, zeolite-doped Fe3O4, and raw zeolite sample, respectively. The highest adsorption capacity was 17.13 mg/g of zeolite-doped MgO + Fe3O4 + ZnO samples. The experimental adsorption data collected were fitted using five isotherm models, and four kinetic models. The Langmuir adsorption isotherm model and the pseudo-second-order kinetic model provided the best fit for the experimental adsorption data. This suggests that the adsorption process is complex, possibly involving electron interactions between the active sites of doped zeolite and Ni (II) species. The obtained data indicates that zeolite-doped with MgO, Fe3O4, and ZnO notably enhances the adsorptive properties of Ni (II) from synthetic wastewater. The obtained thermodynamic values confirmed that the adsorption process is spontaneous and endothermic, with increased randomness at the solid-solution interface during the adsorption process.

Generic phosphate affinity constants of the CD-MUSIC-eSGC model to predict phosphate adsorption and dominant speciation on iron (hydr)oxides

Estimating the availability of phosphorus in soils and sediments is complicated by the diverse mineralogical properties of iron (hydr)oxides that control the environmental fate of phosphorus. Despite various surface complexation models have been developed, lack of generic phosphate affinity constants (logKPO4s) for iron (hydr)oxides hinders the prediction of phosphate adsorption to iron (hydr)oxides in nature. The aim of this work is to derive generic logKPO4s for the Charge Distribution-Multisite Complexation extended-Stern-Gouy-Chapman (CD-MUSIC-eSGC) model using a large phosphate adsorption database and previously derived generic protonation parameters. The optimized logKPO4s of goethite, hematite and ferrihydrite are located in a much narrower range than those in the RES3T database. Specifically, the logKPO4 ranges of FeOPO3, FeOPO2OH, FeOPO(OH)2, (FeO)2PO2, and (FeO)2POOH complexes were 17.40-18.00, 24.20-27.40, 27.90-29.80, 26.50-29.60, and 30.70-33.40, respectively. A simplified CD-MUSIC-eSGC model with species FeOPO2OH and (FeO)2PO2 and generic logKPO4 values 26.0 ± 0.9 and 27.9 ± 0.8, respectively, provides an accurate prediction of phosphate adsorption and dominant speciation to the iron (hydr)oxides at environmental pH and phosphate levels. For ferrihydrite at low pH and high phosphate levels the species FeOPO(OH)2 and (FeO)2POOH cannot be neglected. The simplified model expands the application boundaries of CD-MUSIC-eSGC model in predicting the phosphate adsorption on natural iron (hydr)oxides without laborious characterization.

New Sorption Isotherms Derived from a Gamma Distribution of Binding Constants

New sorption isotherms for heterogeneous sorbents are derived by combining a Gamma distribution of binding constants with a local isotherm defined by a Langmuir or Hill equation. The new "Gamma isotherms" are expressed as Stieltjes transforms of the distribution and involve generalized exponential integrals. The related energy distributions are asymmetric and present a peak corresponding to the mean binding constant. The advantages of the new isotherms are (1) at low pressures or concentrations, with a Langmuir local isotherm, the global "Gamma-Langmuir" isotherm retrieves Henry's law; (2) contrary to the power Freundlich or hypergeometric Freundlich global isotherms, these Gamma isotherms do not need a redefinition of the standard state; (3) with a Hill local isotherm, the global "Gamma-Hill" isotherm allows a separate estimation of the cooperativity and heterogeneity parameters; and (4) the condensation approximation is a good approximation if the local isotherm is Hill and displays a high degree of cooperativity. The Gamma-Langmuir model is applied to three examples from the literature, with rather different Gamma distributions.

A new consistent modeling framework for the competitive adsorption of humic nanoparticles and oxyanions to metal (hydr)oxides: Multiple modes of heterogeneity, fractionation, and conformational change

HYPOTHESIS

The competitive interaction of oxyanions and humic nanoparticles (HNPs) with metal (hydr)oxide surfaces can be used to trace the ligand and charge distribution of adsorbed HNPs in relation to heterogeneity, fractionation, and conformational change.

EXPERIMENTS

Batch adsorption experiments of HNPs on goethite were performed in the absence and presence of phosphate. The size of HNPs was measured with size exclusion chromatography. The Ligand and Charge Distribution (LCD) model framework was further developed to describe the simultaneous interaction of HNPs and phosphate with goethite.

FINDINGS

Preferential adsorption decreases the mean molar mass of adsorbed HNPs, independent of the phosphate presence, showing a linear dependency on the adsorbed HNPs fraction. Phosphate ion can be used as a probe to trace the distribution of functional groups and the variation in affinity of HNPs. The spatial distribution of adsorbed HNPs is driven by the potential gradients in the electrical double layer, which changes the conformation of the adsorbed HNPs. At the particle level, the adsorption of heterogeneous HNPs has an affinity distribution, which can be explained by the variation in molar mass (kDa) and density of the functional groups (mol kg-1) of the HNPs. The presented model can simultaneously describe the competitive adsorption of HNPs and phosphate in a consistent manner.

Bridging the Adsorption Data and Adsorption Process by Introducing a Polynomial Structure To Accurately Describe IUPAC Isotherms, Stepwise Isotherms, and Stepwise Breakthrough Curves

Porous heterogeneous adsorbents, those composed of multiple pore structures and surface chemical adsorption sites, can result in various gas or vapor adsorption isotherms, including five types of IUPAC adsorption isotherms and stepwise adsorption isotherms that have been difficult to model using a single adsorption equilibrium model. The limitation of the above equilibrium model further restricts the calculations of complex stepwise breakthrough curves. To bridge the adsorption data and adsorption process, it is important to first develop a simple model or method to describe these isotherms of various complex adsorption systems. In this work, assuming that the effect of the diffusion rate can be neglected under the static condition and the adsorption process is discontinuous, the number of adsorption isotherm inflection points can be used to represent the changed number of adsorption interactions. With the introduction of the polynomial structure, a series of empirical or semi-empirical polynomial adsorption models were developed. The N-site polynomial Langmuir-Freundlich equation could accurately fit common type I, II, III, IV, and V adsorption isotherms and complex stepwise adsorption isotherms covering various adsorbates, such as volatile organic compounds (VOCs), toxic industrial chemicals (TICs), water vapor, and carbon dioxide, as well as different adsorbents, such as metal/covalent organic frameworks (MOFs/COFs), zeolites, and porous carbons. Similarly, the introduction of a polynomial structure, such as the N-site polynomial Yoon-Nelson equation, was also successful in the description of interesting stepwise breakthrough curves. This work provides a more accurate adsorption equilibrium model to characterize all types of isotherms. As a foundation model, it is expected to be used to simulate the gas-solid adsorption process inside the fixed and fluidized beds packed with porous adsorbents.

On the nature of screening in charge-regulated macroion solutions

We present a derivation of the screening length for a solution containing a charge-regulated macroion, e.g. protein, with its counterions. We show that it can be obtained directly from the second derivatives of the total free energy by taking recourse to the "uncertainty relation" of the Legendre transform, which connects the Hessians or the local curvatures of the free energy as a function of density and its Legendre transform, i.e., osmotic pressure, as a function of chemical potentials. Based on the Fowler-Guggenheim-Frumkin model of charge regulation, we then analyze the "screening resonance" and the "overscreening" of the screening properties of the charge-regulated macroion solution.

Proton Binding Characteristics of Dissolved Organic Matter Extracted from the North Atlantic

Marine dissolved organic matter (DOM) presents key thermodynamic properties that are not yet fully constrained. Here, we report the distribution of binding sites occupied by protons (i.e., proton affinity spectra) and parametrize the median intrinsic proton binding affinities (log K̅H) and heterogeneities (m), for DOM samples extracted from the North Atlantic. We estimate that 11.4 ± 0.6% of C atoms in the extracted marine DOM have a functional group with a binding site for ionic species. The log K̅H of the most acidic groups was larger (4.01-4.02 ± 0.02) than that observed in DOM from coastal waters (3.82 ± 0.02), while the chemical binding heterogeneity parameter increased with depth to values (m1= 0.666 ± 0.009) ca. 10% higher than those observed in surface open ocean or coastal samples. On the contrary, the log K̅H for the less acidic groups shows a difference between the surface (10.01 ± 0.08) and deep (9.22 ± 0.35) samples. The latter chemical groups were more heterogeneous for marine than for terrestrial DOM, and m2 decreased with depth to values of 0.28 ± 0.03. Binding heterogeneity reflects aromatic carbon compounds' persistence and accumulation in diverse, low-abundance chemical forms, while easily degradable low-affinity groups accumulate more uniformly in the deep ocean.

Electrostatic interactions between charge regulated spherical macroions

We study the interaction between two charge regulating spherical macroions with dielectric interior and dissociable surface groups immersed in a monovalent electrolyte solution. The charge dissociation is modelled via the Frumkin-Fowler-Guggenheim isotherm, which allows for multiple adsorption equilibrium states. The interactions are derived from the solutions of the mean-field Poisson-Boltzmann type theory with charge regulation boundary conditions. For a range of conditions we find symmetry breaking transitions from symmetric to asymmetric charge distribution exhibiting annealed charge patchiness, which results in like-charge attraction even in a univalent electrolyte-thus fundamentally modifying the nature of electrostatic interactions in charge-stabilized colloidal suspensions.

Unravelling the metal uptake process in mosses: Comparison of aquatic and terrestrial species as air pollution biomonitors

Transplanted mosses have been widely shown to be excellent tools for biomonitoring air pollution; however, it is not clear how the functional groups present on their surfaces affect the uptake of metal cations. In the present study, we examined differences in trace metal accumulation in two terrestrial and one aquatic moss species, and investigated whether the differences depended on their physico-chemical characteristics. In the laboratory, we determined C, N and H contents in their tissues and obtained the ATR-FTIR spectra (to identify the presence of functional groups). We also conducted surface acid-base titrations and metal adsorption assays with Cd, Cu and Pb. In the field, we exposed transplants of each species near different air-polluting industries, and determined the mosses enrichment of Al, Cd, Co, Cr, Cu, Fe, Ni, Pb and V. Laboratory results demonstrated higher metal uptake capacity in the terrestrial mosses Sphagnum palustre and Pseudoscleropodium purum, compared to that in the aquatic moss Fontinalis antipyretica, which can be attributed to a greater abundance of acidic functional groups (i.e. negatively charged binding sites) on the surface of the terrestrial mosses. The affinity of moss for certain elements depends on the abundance and nature of surface functional groups. Accordingly, the metal concentrations generally reached higher levels in S. palustre transplants compared to the other species, except for the uptake of Hg, which was higher in F. antipyretica. However, the findings also suggest an interaction between the type of environment (terrestrial or aquatic) and the moss characteristics that may influence the abovementioned trend. Thus, irrespective of the physico-chemical characteristics, metal uptake varied depending on the environment of origin of the mosses "i.e. atmospheric or aquatic". In other words, the findings suggest that species that accumulate more metals in terrestrial environments will accumulate lower amounts of metals in aquatic environments and vice versa.

Curvature effects in interfacial acidity of amphiphilic vesicles

We analyze the changes in the vicinal acidity (pH) at a spherical amphiphilic membrane. The membrane is assumed to contain solvent accessible, embedded, dissociable, charge-regulated moieties. Basing our approach on the linear Debye-Hückel approximation, as well as on the nonlinear Poisson-Boltzmann theory, together with the general Frumkin-Fowler-Guggenheim adsorption isotherm model of the charge-regulation process, we analyze and review the dependence of the local pH on the position, as well as bulk electrolyte concentration, bulk pH, and curvature of the amphiphilic single membrane vesicle. With appropriately chosen adsorption parameters of the charge-regulation model, we find a good agreement with the available experimental data.

Size selectivity in adsorption of polydisperse starches on activated carbon

The influence of molecular weight, polydispersity, and degree of branching of four potato starches (Paselli MD10, Eliane MD6, Eliane MD2, and highly branched starch) on the adsorption rates on activated carbon (Norit CA1) was investigated. Changes in starch concentration and size distribution over time were analysed by Total Starch Assay and Size Exclusion Chromatography. Average molecular weight and degree of branching of a starch scaled negatively with average adsorption rate. Within a size-distribution, adsorption rates scaled negatively with increasing molecule size, resulting in an increased average molecular weight in solution of between 25 % and 213 % and a decreased polydispersity of between 13 % and 38 %. Simulation with dummy distributions estimated the ratio of adsorption rates for 20th percentile and 80th percentile molecules within a distribution to range between a factor 4 and 8 for the different starches. Competitive adsorption decreased the adsorption rate of molecules above the average size within a sample distribution.

Generic CD-MUSIC-eSGC model parameters to predict the surface reactivity of iron (hydr)oxides

The surface reactivity of iron (hydr)oxides plays a crucial role in controlling their interfacial reactions, for which various surface complexation models have been developed. The diversity of mineralogical properties of iron (hydr)oxides has resulted in a redundancy of model parameters, which hampers the modeling of iron (hydr)oxides in soils and sediments, where goethite, hematite and ferrihydrite dominate the iron (hydr)oxide mass fraction. To capture their combined surface reactivity, optimized generic protonation parameters of the Charge Distribution-Multisite Complexation (CD-MUSIC) extended-Stern-Gouy-Chapman (eSGC) model were derived by reanalyzing literature datasets and tested with some newly synthesized iron (hydr)oxides. It was observed that the proton and monovalent ion affinity constants of the different iron (hydr)oxides were located in a narrow range. For the singly- and triply-coordinated hydroxyl sites the obtained generic log(affinity constants) were 8.3 and 11.7 for the protonation reaction and -0.5 for the reaction with the monovalent background ions. Their combination with fixed site densities of singly-/triply-coordinated hydroxyl sites of 3.45/2.70, 5.00/2.50, and 5.80/1.40 sites/nm² for goethite, hematite, and ferrihydrite, respectively, provided good results. The Stern layer capacitances of the inner and outer Stern layers were set equal and could be acquired by an empirical correlation with the sample specific surface area (SSA). The CD-MUSIC-eSGC model with the generic model parameters enables good quality predictions of the proton reactivity of iron (hydr)oxides in 1:1 electrolyte solutions regardless of the sample heterogeneity. The advantages of the generic CD-MUSIC-eSGC model are twofold: (1) protonation of iron (hydr)oxides can be described without making use of spectroscopic measurements and proton titrations, and (2) the model calculations are greatly simplified.

Ionizable lipids in bio-inspired nanocarriers

In applications of bio-inspired nanoparticles (NPs), their composition is often optimised by including ionizable lipids. I use a generic statistical model to describe the charge and potential distributions in lipid nanoparticles (LNPs) containing such lipids. The LNP structure is considered to contain the biophase regions separated by narrow interphase boundaries with water. Ionizable lipids are uniformly distributed at the biophase-water boundaries. The potential is there described at the mean-filed level combining the Langmuir-Stern equation for ionizable lipids and the Poisson-Boltzmann equation for other charges in water. The latter equation is used outside a LNP as well. With physiologically reasonable parameters, the model predicts the scale of the potential in a LNP to be rather low, smaller or about [Formula: see text], and to change primarily near the LNP-solution interface or, more precisely, inside an NP near this interface because the charge of ionizable lipids becomes rapidly neutralized along the coordinate towards the center of a LNP. The extent of dissociation-mediated neutralization of ionizable lipids along this coordinate increases but only slightly. Thus, the neutralization is primarily due to the negative and positive ions related to the ionic strength in solution and located inside a LNP.

Tetracycline adsorption trajectories on aged polystyrene in a simulated aquatic environment: A mechanistic investigation

Microplastics (MPs) have attracted widespread attention as an organic class of pollutants as well as pollutant carriers in recipient aquatic ecosystems. In this study, tetracycline (TC) adsorption by polystyrene (PS), with multiple aging-based temporal changes in the adsorption mechanism, was observed. The results revealed that the pseudo-second-order model accurately predicted the TC adsorption kinetics for different types of PS. In addition, the isothermal adsorption processes fit the Freundlich model; however, their interactions were drastically weakened at lower temperatures or increasing salinities. Corresponding to the electrostatic interactions, adsorption TC was largely pH-dependent, with the maximum adsorbed TC content on the PS surface at a pH of 5 in an aqueous environment. More importantly, mechanistic studies have revealed that, compared to virgin PS, TC complexes with aged PS are principally controlled by hydrogen bonding and ionic interactions, followed by π-π, polar-polar, and van der Waals interactions. These findings will aid in understanding the insights of TC and aged PS interactions and the underlying interactive molecular forces, which will be advantageous for comprehending the real case scenario of inter-pollutant interactions and related environmental pollution.

Competition adsorption of malachite green and rhodamine B on polyethylene and polyvinyl chloride microplastics in aqueous environment

Microplastics (MPs) will cause compound pollution by combining with organic pollutants in the aqueous environment. It is important for environmental protection to study the adsorption mechanism of different MPs for pollutants. In this study, the adsorption behaviors of malachite green (MG) and rhodamine B (RhB) on polyethylene (PE) and polyvinyl chloride (PVC) were studied in single systems and binary systems, separately. The results show that in single system, the adsorptions of between MPs for pollutants (MG and RhB) are more consistent with the pseudo-second-order kinetics and Freundlich isotherm model, the adsorption capacity of both MPs for MG is greater than that of RhB. The adsorption capacities of MG and RhB were 7.68 mg/g and 2.83 mg/g for PVC, 4.52 mg/g and 1.27 mg/g for PE. In the binary system, there exist competitive adsorption between MG and RhB on MPs. And the adsorption capacities of PVC for the two dyes are stronger than those of PE. This is attributed to the strong halogen-hydrogen bond between the two dyes and PVC, and the larger specific surface area of PVC. This study revealed the interaction and competitive adsorption mechanism between binary dyes and MPs, which is of great significance for understanding the interactions between dyes and MPs in the multi-component systems.

Lipid nanoparticles with ionizable lipids: Statistical aspects

Lipid nanoparticles (LNPs) with size ∼100 nm are now used for fabrication of a new generation of drugs and antiviral vaccines. To optimize their function or, more specifically, interaction with cell membranes, their composition often includes ionizable lipids which are neutral or cationic (after association with H^{+}). Physically, such LNPs represent an interesting example of mesoscopic nanosystems with complex and far from understood properties. Experimentally, they can be studied at cell-membrane mimics. Herein, I analyze theoretically three related aspects. (i) I describe how the extent of protonation of ionizable lipids located at the surface of LNPs depends on the H^{+} concentration by using the phenomenological Langmuir-Stern and Poisson-Boltzmann models with continuum distribution of charges and the dipole model with discrete charges. In these frameworks, the H^{+} adsorption isotherms are predicted to be close to Langmuirian provided the fraction of ionizable lipids is smaller than 0.5. (ii) I scrutinize the interaction between charged LNPs and their interaction with a supported lipid bilayer (SLB) by using the phenomenological theory and lattice-gas model. The long-term association or attachment is predicted provided the charges are opposite. The models make it possible to estimate the size of the contact region (provided a LNP is not deformed) and the number of lipid-lipid bonds in this region. (iii) I briefly discuss denaturation of a LNP during interaction with the SLB and argue that it may occur via a few stepwise transitions.

Effectiveness and mechanism for the simultaneous adsorption of Pb(II), Cd(II) and As(III) by animal-derived biochar/ferrihydrite composite

The emerging animal-derived biochar (AB) has shown potential for mitigating the contamination of cationic heavy metals, but has no affinity to oxyanionic metals. In this study, we developed an AB/ferrihydrite composite with a AB/Fe mass ratio of 4.0 (ABF-4) for the simultaneous adsorption of cationic Pb(II)/Cd(II) and anionic As(III). ABF-4 is a type of hydroxyapatite-rich biochar coated with nanoscale iron hydroxide aggregates. The adsorption of Pb(II), Cd(II), and As(III) on ABF-4 were 2.64, 1.55, and 0.48 mmol/g, and were 135%, 150%, and 4500% higher than those of pure AB, respectively. The enhanced adsorption of Pb(II) and Cd(II) by ABF-4 is partially due to the increase in surface area and micropores. The nano-sized ferrihydrite on ABF might help form surface complexation with As(III) and oxidize As(III) to As(V). In multimetal systems, Pb(II) and Cd(II) can promote As(III) adsorption due to the formation of NaPb₄(AsO₄)₃ precipitate and the ternary complex of arsenite and cadmium with ABF-4, whereas Cd(II) adsorption might be inhibited because of the surface coverage of Pb₅(PO₄)₃Cl precipitate on ABF-4. However, the coexistence of Pb in soils does not influence the immobilization of Cd. The amendment of ABF-4 can considerably decrease the availability of Pb, Cd, and As in soils from Pb-Zn smelting sites. Hence, ABF-4 is a promising multifunctional material for the potential immobilization of multicomponent heavy metals.

Curvature effects in charge-regulated lipid bilayers

We formulate a theory of electrostatic interactions in lipid bilayer membranes where both monolayer leaflets contain dissociable moieties that are subject to charge regulation. We specifically investigate the coupling between membrane curvature and charge regulation of a lipid bilayer vesicle using both the linear Debye-Hückel (DH) and the non-linear Poisson-Boltzmann (PB) theory. We find that charge regulation of an otherwise symmetric bilayer membrane can induce charge symmetry breaking, non-linear flexoelectricity and anomalous curvature dependence of free energy. The pH effects investigated go beyond the paradigm of electrostatic renormalization of the mechano-elastic properties of membranes.

A Review of the Modeling of Adsorption of Organic and Inorganic Pollutants from Water Using Artificial Neural Networks

The application of artificial neural networks on adsorption modeling has significantly increased during the last decades. These artificial intelligence models have been utilized to correlate and predict kinetics, isotherms, and breakthrough curves of a wide spectrum of adsorbents and adsorbates in the context of water purification. Artificial neural networks allow to overcome some drawbacks of traditional adsorption models especially in terms of providing better predictions at different operating conditions. However, these surrogate models have been applied mainly in adsorption systems with only one pollutant thus indicating the importance of extending their application for the prediction and simulation of adsorption systems with several adsorbates (i.e., multicomponent adsorption). This review analyzes and describes the data modeling of adsorption of organic and inorganic pollutants from water with artificial neural networks. The main developments and contributions on this topic have been discussed considering the results of a detailed search and interpretation of more than 250 papers published on Web of Science ® database. Therefore, a general overview of the training methods, input and output data, and numerical performance of artificial neural networks and related models utilized for adsorption data simulation is provided in this document. Some remarks for the reliable application and implementation of artificial neural networks on the adsorption modeling are also discussed. Overall, the studies on adsorption modeling with artificial neural networks have focused mainly on the analysis of batch processes (87%) in comparison to dynamic systems (13%) like packed bed columns. Multicomponent adsorption has not been extensively analyzed with artificial neural network models where this literature review indicated that 87% of references published on this topic covered adsorption systems with only one adsorbate. Results reported in several studies indicated that this artificial intelligence tool has a significant potential to develop reliable models for multicomponent adsorption systems where antagonistic, synergistic, and noninteraction adsorption behaviors can occur simultaneously. The development of reliable artificial neural networks for the modeling of multicomponent adsorption in batch and dynamic systems is fundamental to improve the process engineering in water treatment and purification.

Identification of naturally weathering microplastics and their interactions with ion dyes in aquatic environments

Here, naturally weathering plastics were collected and identified to understand the effect of the weathering conditions on their properties. The adsorption and desorption of crystal Violet (CV), a candidate of cationic organic pollutant, on microplastics (MPs) under various environmental conditions were simultaneously explored. The first type was the aged polyethylene (PE-MPs), which exhibited a fibrous structure with a smoother and uniform surface attached some flaps, while the second type was recognized as the aged polypropylene (PP-MPs), which showed a lamellar structure with less smooth and distorted texture surface attached with fragments and small grains. The experiment data fitted well with the pseudo-second-order kinetic and Freundlich isotherm models. The possible interactions between CV and MPs included electrostatic attraction, hydrogen bonding and hydrophobic interactions. This study demonstrates that the high possibility of transport ionic pollutants from fresh water to ocean by the naturally weathering microplastics, highlighting their potential risk in various environments.

Proton binding to humic nano particles: electrostatic interaction and the condensation approximation

Proton binding to "carboxylic" and "phenolic" sites of humic nano particles (HNPs) is determined by the total proton affinity that is due to a specific and an electrostatic affinity. Both affinities are accounted for in the bi-modal Langmuir-Freundlich (bi-LF)-equation extended with a Boltzmann factor that includes the electrostatic site potential(s), y. For y → 0 the equation reduces to the bi-LF Master Curve (MC). Commonly, an electrical double layer model is used to obtain y, e.g., the bi-LF-Donnan-V_app (monocomponent NICA-Donnan) model and bi-LF-soft-particle-Poison-Boltzmann-Theory (SPBT). A new method is presented that combines the "condensation approximation" (CA) with the MC concept (CA-MC). With the CA, the proton binding curve and MC can be transformed in, respectively, the total and specific affinity distribution. The difference at a given charge density provides the electrostatic affinity and CA-potentials vs. charge density. The MC can be obtained theoretically or by using the convention that the electrostatic interaction is negligible at 1 M salt concentration. For five HNPs CA-potentials corresponding with the bi-LF-SPBT are compared with results of the bi-LF-Donnan-V_app model using the MC(SPBT). The bi-LF-Donnan-V_app model fails when the Debye length > hydrated particle radius. The CA-MC(1M) method does not require characteristics of the HNPs. Combination of the bi-LF-eq. with the CA-MC(1 M) method gives the bi-LF-CA-MC(1 M) model. The CA-MC(1 M) differs from the MC(SPBT); therefore, resulting parameters can only be compared when the same method is used.

Seasonal Variations in Proton Binding Characteristics of Dissolved Organic Matter Isolated from the Southwest Baltic Sea

The physicochemical characteristics of dissolved organic matter (DOM) strongly influence its interactions with inorganic species such as protons and trace elements in natural waters. We collected water samples at Boknis Eck, a time series station in the Baltic Sea with a low exposure to freshwater inputs, to investigate how seasonal fluctuations impact the proton binding properties of the isolated DOM. We used potentiometric titrations to assess the binding properties of solid-phase extracted DOM (SPE-DOM) over a seasonal cycle. We report and critically analyze the first NICA parameters estimates of carboxylic-like and phenolic-like sites for brackish water SPE-DOM. The total amount of functional groups (Q_maxH,tot) showed no seasonal fluctuations and an average value of 136 ± 5.2 mmol·mol C^-1. The average proton affinity (logK_H) and binding site heterogeneity (m) showed a relatively minor variability for samples obtained between April and September, when the water remained stratified. These results contribute to a better understanding of the ion binding characteristics of DOM in natural brackish waters.

A critical overview of adsorption kinetics for cooling and refrigeration systems

The dynamic uptake of adsorbate onto the porous adsorbent plays a crucial role in determining the performance of the adsorption-based cooling system. Therefore, it is imperative to know the kinetics parameters of an adsorbate - adsorbent pair to design a system to be operated at variable working conditions. The kinetics models of adsorption, used to simulate the adsorption rate of different pairs, are derived and presented in this paper. Besides, the limitations and advantages of the models are also mentioned. Moreover, the dynamic performance of different adsorption pairs is analyzed, and the values of kinetics parameters, determined through experimental procedures and fitting of kinetics models, are also summarized. It is opined that during the initial unsaturated condition of adsorption, the semi-infinite model can be preferred to determine the diffusion time constant. The modification of different models, e.g., Langmuir and linear driving force models, can significantly overcome the drawbacks of the models, as shown by several researchers. However, research may be carried out to investigate different models' fitting errors from a statistical perspective. Furthermore, to evaluate the dynamic performance of different adsorbates, a lot of research needs to be done, specifically, on the adsorption of the newly developed environment-friendly refrigerants, onto the promising composite adsorbents possessing high thermal conductivity and significantly improved adsorption uptakes.

Phase Separation of Polyelectrolytes: The Effect of Charge Regulation

Complex coacervation, known as the liquid–liquid phase separation of solutions with oppositely charged polyelectrolytes, has attracted substantial interest in recent years. We study the effect of the charge regulation (CR) mechanism on the complex coacervation by including short-range interactions between the charged sites on the polymer chains as well as an association–dissociation energy parameter in the CR mechanism. We investigate the phase diagrams of two CR models: (i) the hopping CR model (HCR) and (ii) the asymmetric CR model (ACR). It is shown that during the phase separation that the polymers in the condensed phase are more charged than those in the dilute phase, in accordance with Le Chatelier’s principle. In addition, secondary CR effects also influence the change in the volume fraction of the two phases. The latter can cause the charge difference between the two phases to change nonmonotonically as a function of the CR parameters.

Adsorption behaviors of the pristine and aged thermoplastic polyurethane microplastics in Cu(II)-OTC coexisting system

In this work, the hypothesis that thermoplastic polyurethane (TPU) microplastics (MPs) could form complex toxic pollution by absorbing both antibiotics and heavy metals simultaneously was proposed. The unique features of the adsorption of Cu(II) and oxytetracycline (OTC) on the pristine TPU and photo-aged (aged) TPU MPs in single and coexisting system were investigated, which included the kinetics, isothermal equilibrium and thermodynamics. The possibly synergistic or competitive effects between Cu(II) and OTC were also evaluated. The results showed that the adsorption process of Cu(II) and OTC could be described well by pseudo-second-order kinetic equation. The entire process could be divided into two stages: internal diffusion and external diffusion. The Sips model could give good fitting for the isothermal adsorption equilibrium. The thermodynamic parameters depicted the endothermic nature of adsorptions and the process was spontaneous. In the coexisting system, synergistic or competitive effects depended critically on the ratio of concentrations (Cu(II) vs OTC). When the ratio was 1:1, Cu(II) significantly enhanced the adsorption of OTC, while OTC showed a weak effect on Cu(II) adsorption. The synergies could be attributed to the formation of Cu(II)-OTC complex and the bridging effect of Cu(II). Overall, the adsorption capacity of aged TPU was higher than that of pristine TPU, which was due to the differences in morphological characteristics and functional groups. FTIR studies revealed that ester carbonyl and acylamino groups in the TPU may be involved in the adsorption of Cu(II) and OTC.

Lattice-gas model of a charge regulated planar surface

In this work, we consider a lattice-gas model of charge regulation with electrostatic interactions within the Debye-Hückel level of approximation. In addition to long-range electrostatic interactions, the model incorporates the nearest-neighbor interactions for representing non-electrostatic forces between adsorbed ions. The Frumkin-Fowler-Guggenheim isotherm obtained from the mean-field analysis accurately reproduces the simulation data points.

The Role of Chemical Heterogeneity in Surfactant Adsorption at Solid-Liquid Interfaces

Chemical heterogeneity of solid surfaces disrupts the adsorption of surfactants from the bulk liquid. While its presence can hinder the performance of some formulations, bespoke chemical patterning could potentially facilitate controlled adsorption for nanolithography applications. Although some computational studies have investigated the impact of regularly patterned surfaces on surfactant adsorption, in reality, many interesting surfaces are expected to be stochastically disordered and this is an area unexplored via simulations. In this paper, we describe a new algorithm for the generation of randomly disordered chemically heterogeneous surfaces and use it to explore the adsorption behavior of four model nonionic surfactants. Using novel analysis methods, we interrogate both the global surface coverage (adsorption isotherm) and behavior in localized regions. We observe that trends in adsorption characteristics as surfactant size, head/tail ratio, and surface topology are varied and connect these to underlying physical mechanisms. We believe that our methods and approach will prove useful to researchers seeking to tailor surface patterns to calibrate nonionic surfactant adsorption.

Assessing the Reactive Surface Area of Soils and the Association of Soil Organic Carbon with Natural Oxide Nanoparticles Using Ferrihydrite as Proxy

Assessment of the surface reactivity of natural metal-(hydr)oxide nanoparticles is necessary for predicting ion adsorption phenomena in soils using surface complexation modeling. Here, we describe how the equilibrium concentrations of PO₄, obtained with 0.5 M NaHCO₃ extractions at different solution-to-soil ratios, can be interpreted with a state-of-the-art ion adsorption model for ferrihydrite to assess the reactive surface area (RSA) of agricultural top soils. Simultaneously, the method reveals the fraction of reversibly adsorbed soil PO₄ (R-PO₄). The applied ion-probing methodology shows that ferrihydrite is a better proxy than goethite for consistently assessing RSA and R-PO₄. The R-PO₄ pool agrees well with ammonium oxalate (AO)-extractable phosphorus, but only if measured as orthophosphate. The RSA varied between ∼2 and 20 m²/g soil. The corresponding specific surface area (SSA) of the natural metal-(hydr)oxide fraction is ∼350-1400 m²/g, illustrating that this property is highly variable and cannot be represented by a single value based on the AO-extractable oxide content. The soil organic carbon (SOC) content of our top soils increases linearly not only with the increase in RSA but remarkably also with the increase in mean particle size (1.5-5 nm). To explain these observations, we present a structural model for organo-mineral associations based on the coordination of SOC particles to metal-(hydr)oxide cores.

Addressing the electrostatic component of protons binding to aquatic nanoparticles beyond the Non-Ideal Competitive Adsorption (NICA)-Donnan level: Theory and application to analysis of proton titration data for humic matter

HYPOTHESIS

Charge descriptors of aquatic nanoparticles (NPs) are evaluated from proton titration curves measured at different salt concentrations and routinely analysed by the Non-Ideal Competitive Adsorption-Donnan (NICAD) model. This model, however, suffers from approximations regarding particle electrostatics, which may bias particle charge estimation. Implementation of Poisson-Boltzmann (PB) theory within consistent treatment of NPs protolytic data is expected to address NICAD shortcomings.

EXPERIMENTS

An alternative to NICAD is elaborated on the basis of nonlinearized PB equation for soft particle electrostatics to properly unravel the electrostatic and chemical components of proton binding to NPs. A numerical package is developed for automated analysis of proton titration curves and proton affinity spectra at different salt concentrations. The performance of the method is illustrated for humic matter nanoparticles with different charge and size, and compared to that of NICAD.

FINDINGS

Unlike NICAD, PB-based treatment successfully reproduces particle charge dependence on pH for practical salt concentrations from the thin to thick electric double layer limit. Donnan representation in NICAD leads to moderate to dramatic misestimations of proton affinity and binding heterogeneity depending on particle size to Debye layer thickness ratio. Interpretation of NPs protolytic properties with PB theory further avoids adjustment of the 'particle Donnan volume' empirically introduced in NICAD.