Kinetics of Isothermal Adsorption on Energetically Heterogeneous Solid Surfaces: A New Theoretical Description Based on the Statistical Rate Theory of Interfacial Transport

Fostering rehydration and facilitating bioactive release through cellulose-assisted leaf surface treatment

Glyphosate is a widely used herbicide in weed control and crop protection. However, its low bioavailability on leaf surfaces of weeds led to excessive use of glyphosate, inducing herbicide-resistant development and major sustainable agricultural and environmental concerns. This study addresses these challenges by developing cellulose-assisted glyphosate formulations using superior rehydration and sustainable release capability of nanocelluloses. We prepared glyphosate-loaded nanocellulose particles (CNP) and cellulose nanofibers (CNF) to enhance the rehydration and sustained release of glyphosate on leaf surfaces. Our results have demonstrated that nanocelluloses significantly improved water capture on the leaf surface and gradual release of glyphosate, with CNP and CNF formulations showing an 8.75-fold increase in water adsorption on cotton leaves compared to the control group over 12 h. Furthermore, incorporating an inorganic salt improved moisture adsorption efficiency. The formulations exhibited high compatibility with existing spray technologies, offering substantial economic and environmental benefits for agriculture practices. This approach highlights the potential application of polysaccharides in revolutionizing agrochemical applications and environmental sustainability, providing great potential in agricultural spraying practices.

Development of banana pseudo stem cellulose fiber based magnetic nanocomposite as an adsorbent for dye removal

A hybrid hydrogel nanocomposite derived from cellulose fiber extracted from Banana Pseudo Stem (BPS) was developed as an adsorbent material for wastewater treatment. The hydrogel was developed by graft copolymerization of N-hydroxyethylacrylamide on Cellulose Fiber (BPSCF-g-PHEAAm) with potassium peroxodisulphate (KPS) as an initiator and N, N'-methylene bisacrylamide (MBA) as a crosslinker using microwave irradiation. Magnetic nanoparticles generated by an in-situ method were incorporated into the network structure. Fourier Transform Infrared Spectroscopy (FTIR), Powder X-ray Diffraction (XRD), Thermogravimetric analysis (TGA), Vibrating Sample Magnetometer (VSM), Brunauer-Emmett-Teller analysis (BET), Field Emission Scanning Electron Microscopy (FESEM), and Energy Dispersive Spectrometer (EDS) were employed. The adsorption capacities of hydrogel and its nanocomposite were evaluated using Methylene Blue (MB) and Crystal Violet (CV) as model dyes. The parent gel exhibited the maximum absorption capacity of 235, and 219 mg g-1 towards MB and CV respectively which was enhanced to 320 and 303 mg g-1 for the nanocomposite. Adsorption data were best fitted with the pseudo-second-order kinetic model and the Freundlich isotherm model. Negative ΔG° and positive ΔH° indicated spontaneous and endothermic adsorption. Desorption was effective to an extent of 99 % in the HCl medium suggesting high reusability potential of the developed adsorbent material.

Adsorptive removal of antibiotic pollutants from wastewater using biomass/biochar-based adsorbents

This study explores adsorptive removal measures to shed light on current water treatment innovations for kinetic/isotherm models and their applications to antibiotic pollutants using a broad range of biomass-based adsorbents. The structure, classifications, sources, distribution, and different techniques for the remediation of antibiotics are discussed. Unlike previous studies, a wide range of adsorbents are covered and adsorption of comprehensive classes of antibiotics onto biomass/biochar-based adsorbents are categorized as β-lactam, fluoroquinolone, sulfonamide, tetracycline, macrolides, chloramphenicol, antiseptic additives, glycosamides, reductase inhibitors, and multiple antibiotic systems. This allows for an assessment of their performance and an understanding of current research breakthroughs in applying various adsorbent materials for antibiotic removal. Distinct from other studies in the field, the theoretical basis of different isotherm and kinetics models and the corresponding experimental insights into their applications to antibiotics are discussed extensively, thereby identifying the associated strengths, limitations, and efficacy of kinetics and isotherms for describing the performances of the adsorbents. In addition, we explore the regeneration of adsorbents and the potential applications of the adsorbents in engineering. Lastly, scholars will be able to grasp the present resources employed and the future necessities for antibiotic wastewater remediation.

Enhanced removal of mercury and lead by a novel and efficient surface-functionalized imogolite with nanoscale zero-valent iron material

A novel hybrid nanomaterial, nanoscale zero-valent iron (nZVI)-grafted imogolite nanotubes (Imo), was synthesized via a fast and straightforward chemical procedure. The as-obtained nanomaterial (Imo-nZVI) was characterized using transmission electron microscopy (TEM), electrophoretic mobility (EM), and vibrating sample magnetometry (VSM). The prepared Imo-nZVI was superparamagnetic at room temperature and could be easily separated by an external magnetic field. Sorption batch experiments were performed for single- and multicomponent systems and demonstrated that Hg²⁺ and Pb²⁺ could be quantitatively adsorbed at pH 3.0. For multicomponent systems, maximum adsorption capacities of 61.6 mg·g^-1 and 76.9 mg·g^-1 were obtained for Hg²⁺ and Pb²⁺ respectively. It was observed that the functional groups in Imo-nZVI interact preferentially with analytes according to the Misono softness parameter. The higher performance of Imo-nZVI compared with Imo and nZVI is related to the increased number of adsorption sites in the functionalized nanomaterial. The sorption equilibrium data obeyed the Langmuir model, while kinetic studies demonstrated that the sorption processes of Hg²⁺ and Pb²⁺ followed the pseudo-second-order model. This study suggests that the Imo-nZVI composite can be used as a promising sorbent to provide a simple and fast separation method to remove Hg and Pb ions from contaminated water.

Complete Analytical Solution of the Statistical Rate Theory: Desorption from Solid/Solution Interfaces

One of the essential steps in the design and regeneration of catalysts is desorption. Kinetics modeling of the desorption process is essential for a better understanding of this process. The statistical rate theory (SRT) method is one of the essential theoretical methods that can be used to study the rate of desorption. For the first time, a complete solution of the SRT equation for desorption from the solid surface to the solution phase (SRT-D) is reported. The new integrated equations are provided as the linear forms, which have been denoted as the SRT-LFD equations. The first complete analytical solution of the SRT-D equation is confirmed using the created data by numerical solution of the SRT-D equation and the experimental data. The perfect agreement between the obtained results of the SRT-LFD equations and the results of the created and experimental data confirms the accuracy of the obtained equations.

Study of Sorption Kinetics and Sorption-Desorption Models to Assess the Transport Mechanisms of 2,4-Dichlorophenoxyacetic Acid on Volcanic Soils

The sorption behavior of 2,4-dichlorophenoxyacetic acid (2,4-D) in the abundant agricultural volcanic ash-derived soils (VADS) is not well understood despite being widely used throughout the world, causing effects to the environment and human health. The environmental behavior and risk assessment of groundwater pollution by pesticides can be evaluated through kinetic models. This study evaluated the sorption kinetics and 2,4-D sorption-desorption in ten VADS through batch sorption experiments. Differences in the sorption extent for the fast and slow phases was observed through the IPD model where 2,4-D sorption kinetics was controlled by external mass transfer and intra organic matter diffusion in Andisols (C1 ≠ 0). We confirmed from the spectroscopic analysis that the carboxylate group directly drives the interaction of 2,4-D on Andisol soil. The MLR model showed that IEP, FeDCB, and pH×Silt are important soil descriptors in the 2,4-D sorption in VADS. The Freundlich model accurately represented sorption equilibrium data in all cases (Kf values between 1.1 and 24.1 µg1-1/n mL1/ng-1) with comparatively higher sorption capacity on Andisols, where the highest hysteresis was observed in soils that presented the highest and lowest OC content (H close to 0).

Fiber-Based Gas Filter Assembled via In Situ Synthesis of ZIF-8 Metal Organic Frameworks for an Optimal Adsorption of SO2: Experimental and Theoretical Approaches

For environmental protection from exposure to airborne toxic gases, metal organic frameworks (MOFs) have drawn great attention as gas adsorbent options, with their advantages in chemical tailorability and large porosity. To develop a fiber-based gas filter that is effective against SO₂ gas, zeolite imidazole framework-8 (ZIF-8) was applied to polypropylene nonwoven by various methods. Among the tested methods, the sol-gel impregnation method showed the highest ZIF-8 loading efficiency. There existed an optimal loading of ZIF-8 for the maximum adsorption efficiency, and it was associated with the accessibility of gas molecules to the ZIF-8 pores and active sites. Dominant adsorption processes and mechanisms were investigated by fitting the theoretical sorption models to experimental data. The results demonstrate that the increased ZIF-8 loading to fibers, beyond a certain level, may hinder the diffusivity and increase the barrier effect, eventually decreasing the adsorption efficiency. This study is novel and significant in that a multifaceted approach, including experimental analysis, theoretical investigation, and computational modeling, was made for scrutinizing the intricate phenomena occurring in the gas sorption process. The results of this study provide the fundamental yet practical information on the manufacturing considerations for the optimal design of MOF-loaded fibrous adsorbents.

New Adsorption Models for Entirely Describing the Adsorption Isotherm and Heat of Methane in Heterogeneous Nanopore Structures of Coal

To understand the adsorption mechanism of methane in heterogeneous nanopore structures of coal, integral adsorption models based on linear, exponential, hyperbolic and quadratic energy distribution functions are established. The adsorption energy domain of the new models is assumed to be a finite interval. These new adsorption models can describe both the adsorption isotherm and the adsorption heat. A volumetric method of adsorption with a microcalorimetry system is used to measure the adsorption isotherms and integral heat, and then the parameters of the new models are obtained by fitting the experimental data. Since the adsorption heat can be different for different adsorption models, it is necessary to fit the adsorption isotherms and heat simultaneously. The fitting results of the adsorption isotherms and heat show that the new models are able to describe the experimental data better than the Langmuir model. By comparing the fitting results and the effective range of adsorption energy of the different adsorption models, it is shown that the exponential energy distribution function is the most reasonable model for methane adsorption in coals, which can be used to evaluate the energetic heterogeneity of nanopores in coal samples. The decreasing exponential energy distributions of three coal samples indicate that a larger adsorption energy corresponds to fewer adsorption sites in the coal samples. The proportion of high adsorption energy is related to the micro-nanopore volume in the coal samples.

Differences in the sorption kinetics of various non-ionisable pesticides in a limited number of agricultural soils from the Mediterranean basin

Adsorption in soil of organic contaminants, such as pesticides, is a time-dependent process, which can be relevant for understanding and predicting the potential pollution risk of different water sources. The adsorption behavior of six different pesticides with a wide range of physicochemical properties (log K_OW 1.26-5.8) was evaluated in up to three different soils with low organic carbon (OC) content (≤1.2%). Pesticide sorbed amounts were fitted to several mathematical models to unravel the mechanisms involved in the adsorption process. The linear distribution constants revealed that pendimethalin and the pyrethroid insecticides were strongly retained in soil, whereas the other three compounds were moderately or weakly adsorbed. In the three soils, the pseudo second order model described more accurately the sorption kinetics of all the contaminants. The more hydrophobic pesticides (log K_OW ≥ 4.6) presented lower kinetic rates as compared with the other compounds under study. Both Elovich and intraparticle diffusion models reflected a strong contribution of a rapid initial adsorption on soil surface for thiacloprid, dimethenamid and fenarimol. For the hydrophobic pesticides this contribution was moderate according to the intraparticle diffusion model. Therefore, slower diffusion into the soil micropores was more relevant for the more hydrophobic compounds and for the bigger molecules, and less significant for the more polar pesticides because almost 90% of the total amount adsorbed was achieved in the rapid initial stage.

Isotherms, Kinetics, and Thermodynamics of NH4+ Adsorption in Raw Liquid Manure by Using Natural Chabazite Zeolite-Rich Tuff

The search for safer and sustainable management of animal manure is a global and topical challenge, in particular for the reduction of nitrogen (N) content. The use of natural adsorbents as zeolite-rich tuffs is recognized as a valid method to recover N, in the form of ammonium (NH4+), from animal manure. While the scientific literature is rich in studies performed on synthetic solutions and using clinoptilolite zeolites as adsorbent, it lacks information concerning adsorption in real liquid manure and using other types of zeolite-rich tuffs (e.g., chabazite). This work aims at exploring the NH4+ adsorption process from raw liquid swine manure, using a chabazite-rich zeolite tuff as adsorbent. The effects of temperature, contact time, and grain size have been assessed. Isotherms, kinetic models, and thermodynamic parameters have been investigated. Harkins-Jura isotherm correlates well with the observed data, in accordance with the formation of an adsorption multilayer. Kinetic data have been explained by intraparticle diffusion and pseudo-second-order models. In conclusion, the natural chabazite tuff has proven to be a valid material for NH4+ adsorption from raw liquid swine manure. In particular, to reach the highest adsorption capacities and adsorption rates, it is recommended to use it at a fine particle size and with dosages < 6 %.

Nicosulfuron sorption kinetics and sorption/desorption on volcanic ash-derived soils: Proposal of sorption and transport mechanisms

Nicosulfuron sorption/desorption kinetics were studied through batch sorption studies in ten volcanic ash-derived Andisol and Ultisol soils with acidic pH and variable surface charge. Two different kinetic models were used to fit the experimental data: i) Models to establish kinetic parameters (Pseudo-First and Pseudo-Second-Order), and ii) Models to describe solute transport mechanisms of organic compounds on sorbents (Intraparticle Diffusion, Dimensionless Intraparticle, Boyd, and Two-Site Nonequilibrium). Sorption kinetic data best fit the pseudo-second-order model. Application of these models to describe solute transport suggests that underlying mechanisms are complex in all soils due to: i) surface sorption, with mass transfers controlling sorption kinetics across the boundary layer; and ii) pore diffusion (i.e. intraparticle diffusion into macropores and micropores). The Freundlich model explained equilibrium sorption data in all cases (R² > 0.9979) with K_f values higher than those reported for different class of soils (6.85-16.08 μg^1-1/n mL^1/n  g^-1). The hysteresis was significant in all studied soils. The lower sorption rate on Ultisols must be considered in regards to Nicosulfuron leaching potential.

Electrochemical method to study the environmental behavior of Glyphosate on volcanic soils: Proposal of adsorption-desorption and transport mechanisms

Glyphosate is used extensively worldwide, but current evidence suggests detrimental effects on the environment, pollinators, and human health. Glyphosate adsorption kinetics and adsorption/desorption were studied through batch sorption experiments in ten typical volcanic ash-derived soils from Andisol and Ultisol orders. Two kinetic models were used to fit the experimental data: i. Models that allowed establishment of principally kinetic parameters and modeling of the adsorption process, and ii. Models described solute transport mechanisms commonly used for remediation purposes. Adsorption kinetic data were best fitted by the pseudo-second-order kinetic model and Two-Site Nonequilibrium model. These models suggest that mechanisms are complex due to rapid surface adsorption in ultisols with mass transfer controlling adsorption kinetics across the boundary layer, as indicated by the highhand lowt_1/2values. High intraparticle diffusion into macropores and micropores was observed for Andisols. The Freundlich model accurately represented adsorption equilibrium data in all cases (R² > 0.9580) with comparatively higher adsorption capacity on Andisols. K_f values (2.50-52.28 μg^1-1/n mL^1/n g^-1) and hysteresis were significant in all studied soils. Taken together, these data suggest that Glyphosate may be adsorbed more on Andisol soils in comparison to Ultisols.

Calcium alginate entrapped Eupatorium adenophorum Sprengel stems powder for chromium(VI) biosorption in aqueous mediums

A novel biosorbent, Eupatorium adenophorum Sprengel-alginate beads was used for chromium(VI) biosorption from aqueous solutions. Biosorption process was optimized at pH 2.0, biomass concentration 1.0 g/L, contact time 60 min, and temperature 30 oC respectively. Maximum uptake capacity of Cr(VI) was calculated at 28.011 mg/g. It was found that the overall biosorption process was best described by pseudo second-order kinetics with high correlation coefficient values. Intraparticle diffusion model suggested that Cr(VI) biosorption may proceed within multiple steps. Data obtained from the batch studies confirmed well to the Langmuir, Temkin, and Hill-der Boer isotherm models. Scatchard plot analysis further supported the mono-layer biosorption of Cr(VI) ions on Eupatorium adenophorum Sprengel-alginate beads as described by Langmuir isotherm model. Numerical values of E obtained from Dubinin-Radushkevich isotherm model identified the physisorption as predominant mechanism for Cr(VI) biosorption. The negative values of ΔGo confirmed the spontaneous and feasibility nature, whereas positive value of ΔHo showed the endothermic nature of biosorption process. Positive value of ΔSo indicated an increase in the randomness at the solid/solution interface during the biosorption process. The endothermic nature of Cr(VI) biosorption was also described by Temkin isotherm model. The results indicated that Cr(VI) biosorption was not significantly affected by the presence of co-ions at lower concentrations. Desorption of Cr(VI) ions from metal-loaded Eupatorium adenophorum-alginate beads was observed at 92.091% with 0.5 M HNO3 solution in solid to liquid ratio of 1.0 g/L.

Carbon Nanofibers: A New Adsorbent for Copper Removal from Wastewater

This research describes the adsorption of Cu2+ onto a helical ribbon carbon nanofiber. The characterization of carbon nanofiber by zeta potential showed an isoelectronic pH of 1.9. The influence of different adsorption factors, such as stirring speed, temperature, pH, adsorbent concentration, etc., on the Cu2+ adsorption capacity have been evaluated. The pH has a great influence on Cu2+ adsorption, with the maximum adsorption capacity reached at a pH of 10. The experimental data fit well to pseudo-second order kinetic and Langmuir isotherm models (qm = 8.80 mg·g−1) at T = 298 K and pH = 4. The Cu2+ adsorption could be explained by the particle diffusion model. Results showed that carbon nanofiber could be successfully used for the elimination of Cu2+ from wastewater.

Efficient removal of anti-inflammatory phenylbutazone from an aqueous solution employing a composite material based on poly(aniline-co-pyrrole)/multi-walled carbon nanotubes

Poly(Ani-co-Py)/MWCNT was synthesized by chemical oxidation in a triple-phase interface system and presented a high capacity for the removal of PBZ from wastewater.

Selective Adsorption and Steric Recognition by Molecularly Imprinted Polymers: a Study on Molecular Self-Assembly and its Effect on Selectivity

This article presents an interesting study on molecular self-assembly and its effect on steric recognition by molecularly imprinted polymers. With S-naproxen as the template and acrylamide as the functional monomer, the self-assembly appears to play important roles in the selective adsorption, affecting not only the adsorption amount but also the enantioselective recognition. Both of them become evident by the change of monomer–template ratio. An increase in the monomer–template ratio will result in a higher level of adsorption. The best selectivity for steric recognition is, however, shown at an optimal composition (corresponding to the saturation interaction of monomer and template). A higher or lower monomer–template ratio leads to a dramatic decrease in this selectivity. Related information indicates that this may be a result from the matched arrangement between the binding sites and the template, which makes the binding sites capable of selectively recognizing the imprint species.

Time Evolution of the Wettability of Supported Graphene under Ambient Air Exposure

The wettability of graphene is both fundamental and crucial for interfacing in most applications, but a detailed understanding of its time evolution remains elusive. Here we systematically investigate the wettability of metal-supported, chemical vapor deposited graphene films as a function of ambient air exposure time using water and various other test liquids with widely different surface tensions. The wettability of graphene is not constant, but varies with substrate interactions and air exposure time. The substrate interactions affect the initial graphene wettability, where, for instance, water contact angles of ∼85 and ∼61° were measured for Ni and Cu supported graphene, respectively, after just minutes of air exposure. Analysis of the surface free energy components indicates that the substrate interactions strongly influence the Lewis acid-base component of supported graphene, which is considerably weaker for Ni supported graphene than for Cu supported graphene, suggesting that the classical van der Waals interaction theory alone is insufficient to describe the wettability of graphene. For prolonged air exposure, the effect of physisorption of airborne contaminants becomes increasingly dominant, resulting in an increase of water contact angle that follows a universal linear-logarithmic relationship with exposure time, until saturating at a maximum value of 92-98°. The adsorbed contaminants render all supported graphene samples increasingly nonpolar, although their total surface free energy decreases only by 10-16% to about 37-41 mJ/m2. Our finding shows that failure to account for the air exposure time may lead to widely different wettability values and contradicting arguments about the wetting transparency of graphene.

Preparation and characterization of a composite based on polyaniline, polypyrrole and cigarette filters: adsorption studies and kinetics of phenylbutazone in aqueous media

PAni–PPy–CFs composite was prepared by a static one-step triple-phase interfacial reaction, in which the PAni and PPy particles were formed and aggregated on CFs resulting in a composite with fibrous domains and good adsorption proprieties.

Effect of cations in the background electrolyte on the adsorption kinetics of copper and cadmium and the isoelectric point of imogolite

Modification of surface charge and changes in the isoelectric point (IEP) of synthetic imogolite were studied for various cations in the background electrolyte (K(+), NH4(+), Mg(2+), and Ca(2+)). From the electrophoretic mobility data, it was established that the K(+) (KCl) concentration does not affect the IEP of imogolite; therefore, KCl is a suitable background electrolyte. In terms of the magnitude of changes in the IEP and surface charge, the cations may be ranked in the following order: Mg(2+)≈Ca(2+)>>NH4(+)>>K(+). Four different kinetic models were used to evaluate the influence of Mg(2+), Ca(2+), NH4(+), and K(+) on the adsorption of Cd and Cu on synthetic imogolite. When adsorption occurs in the presence of cations with the exception of K(+), the kinetics of the process is well described by the pseudo-first order model. On the other hand, when adsorption is conducted in the presence of K(+), the adsorption kinetics is well described by the pseudo-second order, Elovich, and Weber-Morris models. From the surface charge measurements, the affinity between imogolite and the cations and their effect on the adsorption of trace elements, namely Cu and Cd, were established.

Rhodamine B doped silica encapsulation matrices for the protection of photosynthetic organisms

An advanced encapsulation matrix that efficiently protects microalgae from harmful UV light without causing toxicity to the entrapped culture is developed based on the electrostatic adsorption of the dye Rhodamine B on silica preformed particles during sol-gel synthesis. The three microalgae (Chlorella vulgaris, Pseudokirchneriella subcapitata and Chlamydomonas reinhardtii) were previously immobilized in alginate following the Two-step procedure. Once entrapped in the silica gel, Rhodamine B act as an inner cut-off filter, protecting the encapsulated organisms from UV radiation. This matrix allows the sterilization of encapsulation devices without affecting the viability of the entrapped microalgae cells. The condensation of Si(IV) in the presence of silica particles with adsorbed dye generates silica matrices with good mechanical stability. Furthermore; no appreciable differences in microstructure, as assessed by SAXS (Small Angle X-ray Scattering), are caused by the addition of the dye.

Modelling the biphasic sorption of simazine, imidacloprid, and boscalid in water/soil systems

The sorption kinetics of simazine (6-chloro-N,N'-diethyl-1,3,5-triazine-2,4-diamine), imidacloprid (1-(6-chloro-3-pyridylmethyl)-N-nitroimidazolidin-2-ylideneamine), and boscalid (2-chloro-N-(4'-chlorobiphenyl-2-yl)nicotinamide), three pesticides of wide use in agriculture, was determined in five different water/soil systems over a time interval from the initial few seconds to about 1 month. In all the experiments, sorption kinetics showed a biphasic pattern characterized by an initial, relatively short phase with a high sorption rate and a later phase with much a lower sorption rate. Initial sorption capacity increased with soil organic carbon content and with sorbate hydrophobicity. We postulate that the first phase of the process involves a fast second-order sorption reaction on superficial sites of soil particles, whereas the second phase depends on diffusion-controlled migration to internal binding sites. A kinetic equation based on this hybrid model accurately fitted all data sets. Less satisfactory results were obtained employing the pseudo-first order, pseudo-second order, Elovich, two site non-equilibrium, or Weber-Morris equation. The superior performance of the hybrid model for describing boscalid sorption probably reflects the high hydrophobic character and consequent low diffusion rates of this compound. The accuracy of modelling was in any case strongly dependent on the time interval considered.

On the thermodynamics of refrigerant + heterogeneous solid surfaces adsorption

This Article presents a theoretical framework for the understanding of pressurized adsorption systems using the statistical rate methodology. Utilizing results from the statistical rate theory, basic thermodynamic variables including enthalpy (h(a)), entropy (s(a)), and the specific heat capacity (c(p,a)) of the adsorbed phase are derived using the thermodynamic requirements of chemical equilibrium, Gibbs law, as well as Maxwell relations. A built-in constant (K) describes the adsorbed molecular partition function (q(s)), and it captures the heterogeneous properties of the adsorbent + adsorbate pair at equilibrium states. Improved adsorbed-phase volume considerations were incorporated in the formulations of these variables where they could be utilized with relative ease for analyzing the energetic performances of any practical adsorption system. In this Article, we have demonstrated how derived thermodynamic quantities can bridge the information gap with respect to the states of adsorbed phase, as well as resolved some theoretical inconsistencies that were found in previously derived quantities. Experimentally, the adsorption isotherms of propane (refrigerant) on activated carbon powder (Maxsorb III) for temperatures from 5 to 75 °C and pressures up to 8 bar are presented, and they are used to illustrate the behaviors of the adsorbed-phase during uptakes, temperatures, and pressure excursions or changes.

Sorption kinetics of diuron on volcanic ash derived soils

Diuron sorption kinetic was studied in Andisols, Inceptisol and Ultisols soils in view of their distinctive physical and chemical properties: acidic pH and variable surface charge. Two types of kinetic models were used to fit the experimental dates: those that allow to establish principal kinetic parameters and modeling of sorption process (pseudo-first-order, pseudo-second-order), and some ones frequently used to describe solute transport mechanisms of organic compounds on different sorbents intended for remediation purposes (Elovich equation, intraparticle diffusion, Boyd, and two-site nonequilibrium models). The best fit was obtained with the pseudo-second-order model. The rate constant and the initial rate constant values obtained through this model demonstrated the behavior of Diuron in each soil, in Andisols were observed the highest values for both parameters. The application of the models to describe solute transport mechanisms allowed establishing that in all soils the mass transfer controls the sorption kinetic across the boundary layer and intraparticle diffusion into macropores and micropores. The slowest sorption rate was observed on Ultisols, behavior which must be taken into account when the leaching potential of Diuron is considered.

Characterization of the atrazine sorption process on Andisol and Ultisol volcanic ash-derived soils: kinetic parameters and the contribution of humic fractions

Atrazine sorption was studied in six Andisol and Ultisol soils. Humic and fulvic acids and humin contributions were established. Sorption on soils was well described by the Freundlich model. Kf values ranged from 2.2-15.6 μg(1-1/n)mL(1/n)g⁻¹. The relevance of humic acid and humin was deduced from isotherm and kinetics experiments. KOC values varied between 221 and 679 mLg⁻¹ for these fractions. Fulvic acid presented low binding capacity. Sorption was controlled by instantaneous equilibrium followed by a time-dependent phase. The Elovich equation, intraparticle diffusion model, and a two-site nonequilibrium model allowed us to conclude that (i) there are two rate-limited phases in Andisols related to intrasorbent diffusion in organic matter and retarded intraparticle diffusion in the organo-mineral complex and that (ii) there is one rate-limited phase in Ultisols attributed to the mineral composition. The lower organic matter content of Ultisols and the slower sorption rate and mechanisms involved must be considered to assess the leaching behavior of atrazine.

Development of microbial-enzyme-mediated decomposition model parameters through steady-state and dynamic analyses

We developed a microbial-enzyme-mediated decomposition (MEND) model, based on the Michaelis-Menten kinetics, that describes the dynamics of physically defined pools of soil organic matter (SOC). These include particulate, mineral-associated, dissolved organic matter (POC, MOC, and DOC, respectively), microbial biomass, and associated exoenzymes. The ranges and/or distributions of parameters were determined by both analytical steady-state and dynamic analyses with SOC data from the literature. We used an improved multi-objective parameter sensitivity analysis (MOPSA) to identify the most important parameters for the full model: maintenance of microbial biomass, turnover and synthesis of enzymes, and carbon use efficiency (CUE). The model predicted that an increase of 2 degrees C (baseline temperature 12 degrees C) caused the pools of POC-cellulose, MOC, and total SOC to increase with dynamic CUE and decrease with constant CUE, as indicated by the 50% confidence intervals. Regardless of dynamic or constant CUE, the changes in pool size of POC, MOC, and total SOC varied from -8% to 8% under +2 degrees C. The scenario analysis using a single parameter set indicates that higher temperature with dynamic CUE might result in greater net increases in both POC-cellulose and MOC pools. Different dynamics of various SOC pools reflected the catalytic functions of specific enzymes targeting specific substrates and the interactions between microbes, enzymes, and SOC. With the feasible parameter values estimated in this study, models incorporating fundamental principles of microbial-enzyme dynamics can lead to simulation results qualitatively different from traditional models with fast/slow/passive pools.

Statistical rate theory insight into evaporation and condensation in multicomponent systems

Current approaches to mathematically modeling liquid-vapor mass transport (e.g., film theory, penetration theory, boundary layer theory) treat bulk phase transport accurately with diffusion models, but leave the transport across the interface to be described by empirically determined mass transfer coefficients. In multicomponent systems, this requires empirical mixing rules for the single-component mass transfer coefficients. Such approaches can only give estimates of net rates at the interface but cannot examine the movement of individual components. Here we use statistical rate theory to provide new physical insight into evaporation and condensation at interfaces in systems containing multiple volatile components. In contrast to the traditional multicomponent mass transfer approach, we show ranges where one component evaporates while the other condenses even when the net transport is unidirectional.

Modeling the sorption kinetic of metsulfuron-methyl on Andisols and Ultisols volcanic ash-derived soils: kinetics parameters and solute transport mechanisms

Metsulfuron-methyl sorption kinetic was studied in Andisol and Ultisol soils in view of their distinctive physical and chemical properties: acidic pH and variable surface charge. Different kinetic models were applied to the experimental results. The pseudo-second-order model fitted sorption kinetics data better than the pseudo-first-order model. The rate constant and the initial rate constant values obtained through this model demonstrated the different behavior of metsulfuron-methyl in both kinds of soils, both parameters being the highest for Andisol. The application of Elovich equation, intraparticle diffusion model and a two-site nonequilibrium model (TSNE) allowed to conclude that: (i) the high organic matter content is the governing factor for Andisols where mass transfer across the boundary layer, and in a lesser degree, intraparticle diffusion were the two processes controlling sorption kinetic and (ii) the mineral composition was more relevant in Ultisols where rate was controlled almost exclusively by intraparticle diffusion into macropores and micropores. The slower sorption rate on Ultisols, the mechanism involved and the lower sorption capacity of this kind of soils must be taken into account to assess leaching behavior of this herbicide.

Theoretical models of sorption kinetics including a surface reaction mechanism: a review

A review of a certain class of theoretical models describing the kinetics of pollutants sorption onto various sorbents is presented. These assuming the rate of surface reaction as the rate-limiting step are considered. A special attention is paid to possible theoretical grounds of the most commonly applied mathematical expressions, such as the pseudo-second and the pseudo-first order equations. Simple theoretical considerations based on some fundamental theories suggest that these two formulae do not correspond to any specific physical model. They simply approximate well the behaviours predicted by many different theoretical approaches.

A new isotherm for multisite occupancy adsorption of binary gaseous mixtures

Adsorption is one of the most popular methods for reducing pollutants or separation of gases. Therefore it is important to introduce new and extended isotherm equations for binary systems. In the previous adsorption isotherms for binary systems, it is assumed that an adsorbate occupies one site in lattice sites. However, the adspecies may occupy more than one site in the lattice. Here we propose an adsorption isotherm for binary systems where the adsorbates occupy more than one site. The new isotherm equation for multisite occupancy of binary mixtures was derived based on statistical thermodynamics. The present new adsorption isotherm provides information about the structure of molecules in adsorbed form. Finally, the results of the present theoretical study were confirmed by analysis of two experimental systems.

Description of desorption kinetics at the solid/solution interface based on the statistical rate theory

Desorption is one of the popular methods for the design and regeneration of catalysts. For better understanding and modeling of this process, it is important to have models with theoretical basis. In the present work, the statistical rate theory (SRT) approach was used for the description of desorption kinetics at the solid/solution interface. Based on the SRT approach, two rate equations at initial times of desorption have been derived. A comparison between these two rate equations was done based on numerically generated kinetic data points ( t, q) by the SRT equation. On the basis of experimental data, it has been shown that the kinetics of desorption can be analyzed by the SRT rate equation. Also, the experimental data approve the accuracy of derived rate equations at initial times of desorption.

Adsorption kinetics at the solid/solution interface: statistical rate theory at initial times of adsorption and close to equilibrium

The kinetics of solute adsorption at the solid/solution interface has been studied by statistical rate theory (SRT) at two limiting conditions, one at initial times of adsorption and the other close to equilibrium. A new kinetic equation has been derived for initial times of adsorption on the basis of SRT. For the first time a theoretical interpretation based on SRT has been provided for the modified pseudo-first-order (MPFO) kinetic equation which was proposed empirically by Yang and Al-Duri. It has been shown that the MPFO kinetic equation can be derived from the SRT equation when the system is close to equilibrium. On the basis of numerically generated points ( t, q) by the SRT equation, it has been shown that we can apply the new equation for initial times of adsorption in a larger time range in comparison to the previous q vs radical t linear equation. Also by numerical analysis of the generated kinetic data points, it is shown that application of the MPFO equation for modeling of whole kinetic data causes a large error for the data at initial times of adsorption. The results of numerical analysis are in perfect agreement with our theoretical derivation of the MPFO kinetic equation from the SRT equation. Finally, the results of the present theoretical study were confirmed by analysis of an experimental system.

Thermodynamics of carbon monoxide adsorption on polycrystalline titania studied by static adsorption microcalorimetry

The adsorption of CO on polycrystalline TiO2 was investigated by static adsorption microcalorimetry. The initial differential heat of adsorption (qdiff,0) of CO on polycrystalline titania is 40 kJ/mol, and the standard adsorption entropy (Deltas0) is -104 J mol(-1) K(-1). These results are consistent with those derived from temperature-programmed desorption and FTIR results in the literature. The good reproducibility of the isotherms and the stable qdiff indicate that the lattice oxygen and hydroxyl groups on titania surface are basically not reactive to adsorbed CO.

Kinetics of solute adsorption at solid/solution interfaces: a theoretical development of the empirical pseudo-first and pseudo-second order kinetic rate equations, based on applying the statistical rate theory of interfacial transport

For practical applications of solid/solution adsorption processes, the kinetics of these processes is at least as much essential as their features at equilibrium. Meanwhile, the general understanding of this kinetics and its corresponding theoretical description are far behind the understanding and the level of theoretical interpretation of adsorption equilibria in these systems. The Lagergren empirical equation proposed at the end of 19th century to describe the kinetics of solute sorption at the solid/solution interfaces has been the most widely used kinetic equation until now. This equation has also been called the pseudo-first order kinetic equation because it was intuitively associated with the model of one-site occupancy adsorption kinetics governed by the rate of surface reaction. More recently, its generalization for the two-sites-occupancy adsorption was proposed and called the pseudo-second-order kinetic equation. However, the general use and the wide applicability of these empirical equations during more than one century have not resulted in a corresponding fundamental search for their theoretical origin. Here the first theoretical development of these equations is proposed, based on applying the new fundamental approach to kinetics of interfacial transport called the Statistical Rate Theory. It is shown that these empirical equations are simplified forms of a more general equation developed here, for the case when the adsorption kinetics is governed by the rate of surface reactions. The features of that general equation are shown by presenting exhaustive model investigations, and the applicability of that equation is tested by presenting a quantitative analysis of some experimental data reported in the literature.

Consistent approach to adsorption thermodynamics on heterogeneous surfaces using different empirical energy distribution models

Adsorption on heterogeneous surfaces with three basic energy distribution models (uniform model, exponential model, and normal-like model) is studied. Exact analytical solutions of the adsorption isotherms and the heats of adsorption are derived for the uniform and exponential models, and, with these solutions including a numerical solution for the normal-like model, the behavior of the differential heat of adsorption and the "apparent" standard adsorption entropy concerning the overall surface is described as a function of coverage and temperature. The approximations underlying the isotherms and heats of adsorption in the Temkin, Freundlich, and Langmuir-Freundlich types of adsorption are rationalized. By comparing these empirical formulas to the exact solutions, the level of these approximations is found to be identical, which is similar to the "condensation approximation". Their preconditions are that either the temperature is low enough, or the surface is strongly heterogeneous. Generally, they are suitable for the middle coverage range. The exact solutions provide a method to obtain more information on the heats, entropy, and heterogeneity of the catalyst surface from the calorimetric measurement of the heat of adsorption.

Application of the Statistical Rate Theory of Interfacial Transport to Interpret the Relaxation Time of Proton Adsorption from Solution onto Oxides

A new way to analyze the rate of hydrogen ion adsorption from solution onto oxides was described. The statistical rate theory of interfacial transport (SRT) was applied to interpret relaxation time of ion adsorption. The new procedure for determination of rate constants of surface reaction was compared with the classical theory of activated adsorption and desorption (TAAD). It was found that for adsorption of uncharged species, both models give the same result, but for ion adsorption, their predictions differ considerably. Influence of surface potential and total concentration of adsorption sites on calculated rate constants was also discussed.

Coverage-Dependent Kinetics and Thermodynamics of Carbon Monoxide Adsorption on a Ternary Copper Catalyst Derived from Static Adsorption Microcalorimetry

A reliable method for adsorption systems in equilibrium is established to derive coverage-dependent kinetics and thermodynamics from the volumetric data obtained during the static microcalorimetric measurement of heats of adsorption. The Wigner-Polanyi equation is applied to analyze the pressure change as a function of time during stepwise dosing of the adsorptive until thermodynamic adsorption-desorption equilibrium is established. For carbon monoxide adsorption on a hydrogen-reduced Cu/ZnO/Al2O3 catalyst, the adsorption rate constant (ka) is found to be in the range from 10(-6) to 10(-4) Pa(-1) s(-1), and the desorption rate constant (kd) from 10(-4) to 10(-2) s(-1), both increasing with fractional coverage theta. The kinetically derived equilibrium constant Ktheta is in good agreement with Ktheta obtained from the adsorption isotherm. RT ln(Kp0) and the differential heat of adsorption (qdiff) were found to decrease in parallel, reflecting a normal Temkin-type heterogeneity.

Sticking coefficient and pressure dependence of desorption rate in the statistical rate theory approach to the kinetics of gas adsorption. Carbon monoxide adsorption/desorption rates on the polycrystalline rhodium surface

The statistical rate theory (SRT) fundamental kinetic equation for the Langmuir model of adsorption reveals some features which are difficult to understand. These are the infinitely high adsorption rate for zero coverage limit, infinitely high desorption rate at full saturation of the surface and dependence of the desorption rate on the adsorbate pressure. These features do not allow for a correct formulation of such important physical parameters as sticking and initial sticking probabilities. In this work these peculiar features of the fundamental SRT kinetic equation are discussed and explained. It is shown that the non-physical behavior of the SRT kinetic equation follows from neglecting possible changes of adsorbate concentration near the adsorbing surface. A simple model accounting for the changes of adsorbate concentration close to the adsorbing surface is discussed. As a result, it was shown that application of even such a simple model leads to fully physical behavior of the SRT kinetic equation for the Langmuir model of adsorption. The model is used to build up equations describing the kinetics of adsorption/desorption of carbon monoxide on the energetically heterogeneous rhodium surface. The values of the parameters in these equations were determined from the analysis of equilibrium adsorption isotherms and from the description of experimental conditions. One additional parameter (having well defined limiting values) had to be adjusted in order to satisfactorily reproduce kinetic data. The experimental data used in this work were taken from the article by Yamada and Tamaru (T. Yamada and K. Tamaru, Surf. Sci., 1984, 138, L155).

Collisions of ideal gas molecules with a rough/fractal surface. A computational study

The frequency of collisions of ideal gas molecules (argon) with a rough surface has been studied. The rough/fractal surface was created using random deposition technique. By applying various depositions, the roughness of the surface was controlled and, as a measure of the irregularity, the fractal dimensions of the surfaces were determined. The surfaces were next immersed in argon (under pressures 2 x 10(3) to 2 x 10(5) Pa) and the numbers of collisions with these surfaces were counted. The calculations were carried out using a simplified molecular dynamics simulation technique (only hard core repulsions were assumed). As a result, it was stated that the frequency of collisions is a linear function of pressure for all fractal dimensions studied (D = 2, ..., 2.5). The frequency per unit pressure is quite complex function of the fractal dimension; however, the changes of that frequency with the fractal dimension are not strong. It was found that the frequency of collisions is controlled by the number of weakly folded sites on the surfaces and there is some mapping between the shape of adsorption energy distribution functions and this number of weakly folded sites. The results for the rough/fractal surfaces were compared with the prediction given by the Langmuir-Hertz equation (valid for smooth surface), generally the departure from the Langmuir-Hertz equation is not higher than 48% for the studied systems (i.e. for the surfaces created using the random deposition technique).

New approach to determination of surface heterogeneity of adsorbents and catalysts from the temperature programmed desorption (TPD) technique: One step beyond the condensation approximation (CA) method

Recovery of the desorption activation energy distribution from the experimental temperature programmed desorption (TPD) spectra is among the most difficult problems of adsorption science. Since the heterogeneity effects strongly influence on transport, diffusion, and catalytic reaction time, the estimation of their magnitude is very important for practical purposes. Up to the present, several theories have been used for the interpretation of the TPD results. Almost all advanced theoretical approaches take into account the effect of surface disorder (heterogeneity in desorption activation energy); however, they ignore the numerical difficulties coming from the "ill-posed" character of the linear Fredholm integral equations appearing in the theoretical description of the TPD results. Thus, there is a growing interest in developing novel methods supported by powerful numerical algorithms taking this into account. In the current study we propose a new approach and consider the theoretical aspect as well as numerical problems appearing in the TPD analysis. Our modeling is based on the well-known and generally accepted "absolute rate theory," which has been used extensively for the interpretation of TPD results. We propose and verify (applying computer simulations) the new advanced numerical hybrid type algorithms taking into account the heterogeneity effects. They seem to be very promising in TPD spectra analysis. The stability of the proposed advanced numerical methods is confirmed by the computer simulation experiments, and the results are compared with those obtained from the condensation approximation (CA) method.