General Adsorption Model Research Articles

General Adsorption Model to Describe Sigmoidal Surface Tension Isotherms of Binary Liquid Mixtures

Surface tension (σ) isotherms of liquid mixtures can be divided into Langmuir-type (L-type, including LI- and LII-type) and sigmoid-type (S-type, including SI- and SII-type). Many models have been developed to describe the σ-isotherms. However, the existing models can well describe the L-type isotherms, but not the S-type ones. In the current work, a thermodynamic model, called the general adsorption model, was developed based on the assumption of surface aggregation occurring in the surface layers, to relate the surface composition with the bulk one. By coupling the general adsorption model with the modified Eberhart model, a two-parameter equation was developed to relate the σ with the bulk composition. Its rationality was examined using the σ data of 10 binary mixtures. The results indicate that the new model can accurately describe the S- and L-type isotherms of binary liquid mixtures, showing a good universality. One advantage of the model is that its two parameters, i.e., the adsorption equilibrium constant (K) and the average aggregation number (n), can be estimated by linear fitting experimental σ data, thereby obtaining unique values. This model suggests that the S- and LII-type isotherms arise from the surface aggregation (n ≠ 1). In addition, the standard molar Gibbs free energy of surface adsorption (ΔG̃ad0) and the apparent surface layer thickness (τ) were analyzed for 10 binary mixtures. The ΔG̃ad0 data suggest that the order of adsorption tendency is LI-type ≫ SI-type ≈ SII-type > LII-type, and the strong adsorption usually corresponds to large τ. This work provides a feasible model for describing the S-type isotherms and a better understanding of the surface properties of liquid mixtures.

Derivation and application of a generalised exchange-adsorption isotherm for the adsorption of hydrophobic compounds on soils

A general adsorption model able to provide a good description of the multilayer adsorption of ions and molecular compounds under any circumstances is proposed in this paper. In order to reach this goal, a general form of isotherm was deduced based on the Gapon equation and classical isotherm forms. The adsorption of molecular compounds with diverse hydrophobicity and acid-base characteristics were investigated and validated with a new model for the adsorption of four pesticides on different soils. The adsorption capacity and adsorption energy estimated by the new model were found to be related to the organic matter content of the soil. Great differences were found in the isotherm parameters (A<sub>i</sub>, K<sub>i</sub>, and n<sub>i</sub>) among both the soils and compounds investigated here.

General adsorption model for H2S, H2Se, H2Te, NH3, PH3, AsH3 and SbH3 on the V2O5(0 0 1) surface including the van der Waals interaction

Density functional theory, including the van der Waals interaction, has been used to study the interaction between some small molecules with lone pairs and the V2O5(001) surface. Results reveal that the naked vanadium atom is the most important centre of attraction to the hazardous molecules considered in the present work, regardless of the vdW functional employed. The contour plot of each charge density difference shows an increase of charge density in the lone pair close to the surface. The attractive interaction between each adsorbed molecule and the surface proves to be weak, with a strong role of the vdW interaction.

Design and analysis of siloxanes removal by adsorption from landfill gas for waste-to-energy processes

Separation of volatile methyl siloxanes from landfill gas using fixed adsorption beds was modeled with the objective of identifying appropriate technology and the economics associated with this purification step. A general adsorption model assuming plug flow and radial symmetry was developed and used to conduct a parametric sweep of 162 unique cases. The varied parameters were adsorbent type (activated carbon and silica gel), bed height (3.05–9.15 m/10–30 ft), inlet siloxane concentration (5–15 mg/m3), moisture content (0–100% relative humidity at STP or RH), and siloxane tolerance limit (0.094–9.4 mg/m3) that correlated to three distinct energy conversion technologies (electricity production using engines or fuels cells or catalytic conversion to liquid hydrocarbon fuels). Due to the detrimental effect of RH on siloxane absorption, the maximum allowable moisture content of LFG before purification is 50% RH and moisture removal processes are also required.The design calculations using a selected case study show that the adsorption bed height required needed for 6 months minimum breakthrough time for catalytic fuel production is twice that for engine applications. Fuel cell applications require 3 times the bed height compared to engine applications. However, the purification costs amounted to 94%, 16% and 52% of recovered product value for engine, liquefaction, and fuel cell applications, respectively indicating the need for a high value product to justify purification costs. The approaches and conclusions can be extended to specific process conditions for landfill gas purification and to other processes that use biogas produced from waste as a feedstock.

Hydrophilicity of Nonanoic Acid and Its Conjugate Base at the Air/Water Interface.

A general adsorption model based on partial dissociation was developed for carboxylic acids. The model was applied to the adsorption of nonanoic acid at the air/water interface. Two cases were selected for experimental verification: acid-only and acid with a constant Na+OH– concentration. The model was applied simultaneously at both conditions, and the hydrophilicity of the ionic states was quantified by the adsorption constants, KA and KAH. It was found that the adsorption constant for the acidic group is significantly higher than that for the carboxylate group, KAH/KA ∼ 272. The model lays important groundwork for modeling and predicting carboxylic/carboxylate adsorption.

Fluid‐Solid Adsorption in Batch and Continuous Processing: A Review and Insights into Modeling

AbstractAdsorption is a highly versatile separation technique that can be used both for product separation and waste purification, involving selective interaction of one or more compounds from the liquid phase on a solid called adsorbent. In literature, several models have been proposed to describe both the kinetics and the equilibrium data of different systems. These models are relevant for fluid‐solid adsorption and fluid‐solid reactions. Kinetic models can be classified in either pseudo‐kinetic or diffusive models. Most of them cannot be applied directly in simulating the behavior of continuous columns, while others are applicable only in a narrow range of experimental conditions. The performances of a general continuous adsorption model have been tested by performing a dedicated parametric investigation with the aim to give an overview of how the parameters affect the continuous operation.

A new model for fluid velocity slip on a solid surface.

A general adsorption model is developed to describe the interactions between near-wall fluid molecules and solid surfaces. This model serves as a framework for the theoretical modelling of boundary slip phenomena. Based on this adsorption model, a new general model for the slip velocity of fluids on solid surfaces is introduced. The slip boundary condition at a fluid-solid interface has hitherto been considered separately for gases and liquids. In this paper, we show that the slip velocity in both gases and liquids may originate from dynamical adsorption processes at the interface. A unified analytical model that is valid for both gas-solid and liquid-solid slip boundary conditions is proposed based on surface science theory. The corroboration with the experimental data extracted from the literature shows that the proposed model provides an improved prediction compared to existing analytical models for gases at higher shear rates and close agreement for liquid-solid interfaces in general.

Surface geometry of tryptophan adsorbed on gold colloidal nanoparticles

Two distinct surface-enhanced Raman (SER) spectra of tryptophan depending on the surface adsorption geometry were obtained by using colloidal gold nanoparticles reduced by borohydride and citrate ions. According to the vibrational assignments based on DFT simulations, the SER spectra of tryptamine and 3-indolepropionic acid, and the pH dependence of tryptophan SER spectrum, we found that some indole ring vibrations are very sensitive to the surface adsorption geometry of the molecules. With citrate-reduced gold colloids, tryptophan and related molecules mainly adsorb via the protonated amine group while maintaining a perpendicular geometry of the indole ring to the surface. However, a flat geometry of the indole ring to the surface is preferred on the borohydride-reduced gold colloids where the surface adsorption occurs mainly through the indole ring π electrons. By comparing our results with previous reports on the SER spectra of tryptophan on various silver and gold surfaces, we propose a general adsorption model of tryptophan on metal nanosurfaces.

Interfacial Behavior of N-Nitrosodiethylamine/Bovine Serum Albumin Complexes at the Air−Water and the Chloroform−Water Interfaces by Axisymmetric Drop Tensiometry

Interfacial properties of N-nitrosodiethylamine/bovine serum albumin (NDA/BSA) complexes were investigated at the air-water interface. The interfacial behavior at the chloroform-water interface of the interaction product of phospholipid 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), dissolved in the chloroform phase, and NDA/BSA complex, in the aqueous phase, were also analyzed by using a drop tensiometer. The secondary structure changes of BSA with different NDA concentrations were monitored by circular dichroism spectroscopy at different pH and the NDA/BSA interaction was probed by fluorescence spectroscopy. Different NDA/BSA mixtures were prepared from 0, 7.5 x 10(-5), 2.2 x 10(-4), 3.7 x 10(-4), 5 x 10(-4), 1.6 x 10(-3), and 3.1 x 10(-3) M NDA solutions in order to afford 0, 300/1, 900/1, 1 500/1, 2 000/1, 6 000/1, and 12 500/1 NDA/BSA molar ratios, respectively, in the aqueous solutions. Increments of BSA alpha-helix contents were obtained up to the 2 000/1 NDA/BSA molar ratio, but at ratios beyond this value, the alpha-helix content practically disappeared. These BSA structure changes produced an increment of the surface pressure at the air-water interface, as the alpha-helix content increased with the concentration of NDA. On the contrary, when alpha-helix content decreased, the surface pressure also appeared lower than the one obtained with pure BSA solutions. The interaction of DPPC with NDA/BSA molecules at the chloroform-water interface produced also a small, but measurable, pressure increment with the addition of NDA molecules. Dynamic light scattering measurements of the molecular sizes of NDA/BSA complex at pH 4.6, 7.1, and 8.4 indicated that the size of extended BSA molecules at pH 4.6 increased in a greater proportion with the increment in NDA concentration than at the other studied pH values. Diffusion coefficients calculated from dynamic surface tension values, using a short-term solution of the general adsorption model of Ward and Tordai, also showed differences with pH and the NDA concentration. Both, the storage and loss dilatational elastic modulus were obtained at the air-water and at the chloroform-water interfaces. The interaction of NDA/BSA with DPPC at the chloroform-water produced a less rigid monolayer than the one obtained with pure DPPC (1 x 10(-5) M), indicating a significant penetration of NDA/BSA molecules at the interface. At short times and pH 4.6, the values of the storage elastic modulus were larger and more sensible to the NDA addition than the ones at pH 7.1 and 8.4, probably due to a gel-like network formation at the air-water interface.

Non-linear adsorption modeling of fatty esters and oleic estolide esters via boundary lubrication coefficient of friction measurements

The frictional behaviors of a variety of fatty esters (methyl oleate (MO), methyl palmitate (MP), methyl laurate (ML), and 2-ethylhexyl oleate (EHO)) and oleic estolide esters (methyl oleic estolide ester (ME) and 2-ethylhexyl oleic estolide ester (EHE)) as additives in hexadecane have been examined in a boundary lubrication test regime using steel contacts. Critical additive concentrations were defined and used to perform novel and simple Langmuir analyses that provide an order of adsorption energies: EHE ≥ ME > EHO > MP > MO ≥ ML. Application of Langmuir, Temkin, and Frumkin–Fowler–Guggenheim (FFG) adsorption models via non-linear fitting demonstrates the necessary inclusion of cooperative effects in the applied model. Fits of the steady-state coefficient of friction (COF)-concentration data for EHE, ME, and EHO indicate slight cooperative adsorption. MO, MP, and ML data require larger attractive interaction terms ( α ≤ −2.3) to be adequately fit. Primary adsorption energies calculated via a general adsorption model are necessarily decreased while total adsorption energies correlate well with values obtained via critical concentration analyses. To account for multiple surface-site coverage a multiple-site model was defined. The intuitive assumption of multiple-site coverage of more massive components suggests deceptively increased calculated adsorption energies for typically applied models (e.g. FFG, Langmuir).

Interfacial properties and structural conformation of thermosonicated bovine serum albumin

Aqueous Bovine Serum Albumin (BSA) solutions were treated with high-intensity ultrasound (20 W cm−2) for 15, 30 and 45 min at temperatures of up to 85 °C. The equilibrium and dynamic surface tension of native and ultrasonicated BSA at the air-solution interface was measured using drop shape analysis. The effect of ultrasound on the secondary structure of BSA was monitored by circular dichroism spectroscopy. Surface pressure of BSA at the air-solvent interface increased as a consequence of sonication treatment at 20 °C. Both the rate of surface pressure increase and the equilibrium surface pressure of sonicated BSA were significantly different than that of native BSA. Diffusion coefficients calculated from dynamic surface tension values using long-term and short-term solutions of the general adsorption model of Ward and Tordai increased upon application of ultrasound, e.g. Deff,shortterm≈5.2×10−9 m2/s for native BSA and Deff,shortterm≈2×10−8 m2/s for BSA solutions sonicated for 45 min. Deconvolution of circular dichroism spectra indicated a small but reproducible increase in helical content and a 22% decrease in unordered structure elements after 45 min of sonication. The increase in the rate of protein adsorption with ultrasonication was more pronounced at elevated temperatures. Above the denaturation temperature of the protein, both heat treatment and thermosonication were found to reduce helical content of BSA, e.g. from 61% for native protein to 31 and 40% for heat-treated and thermosonicated proteins at 85 °C, respectively. Results were attributed to an ultrasonically-induced modification of the molecular structure of BSA with increased intramolecular mobility and surface activity.

Overloaded gradient elution chromatography on heterogeneous adsorbents in reversed-phase liquid chromatography

Overloaded band profiles of phenol were measured on a C 18-Kromasil column in gradient elution conditions. The mobile phase used was a mixture of methanol and water. The volume fraction of methanol was allowed to vary between 0 and 0.5. A general adsorption model, which expresses the amount of phenol adsorbed q ∗ as a function of both its concentration C and the composition ϕ of the organic modifier (methanol) in the mobile phase, was empirically derived from previous independent adsorption experiments based on frontal analysis (FA) and frontal analysis by the characteristic point (FACP). Accordingly, the general model was an extension of the simplest heterogeneous model, the Bilangmuir model, to non-isocratic conditions. The low-energy sites followed the classical linear solvent strength model (LSSM), but not the high-energy sites whose saturation capacity linearly decreased with ϕ. The general model was validated by comparing the experimental and simulated band profiles in gradient elution conditions, in linear and non-linear conditions, as well. The band profiles were calculated by means of the equilibrium-dispersive model of chromatography with a finite difference algorithm. A very good agreement was observed using steps gradient (Δ ϕ) from 0 to 50% methanol and gradient times t g of 20, 25, 30, 40, 60, 80 and 100 min. The agreement was still excellent for steps gradient from 5 to 45% ( t g=25 min), 5 to 35% ( t g=50 min), 5 to 25% ( t g=50 min) and 5 to 15% ( t g=50 min). Significative differences appeared between experience and simulation when the slope of the gradient (Δ ϕ/ t g) became too strong beyond 3.3% methanol per minute. This threshold value probably mirrored the kinetic of arrangement of the G 18-bonded chains when the methanol content increased in the mobile phase. It suggested that the chromatographic system was not in a full thermodynamic equilibrium state when very steep mobile phase gradients were applied.

Adsorption of a Diverse Set of Organic Vapors on the Bulk Water Surface

The bulk water surface is of fundamental interest to physical as well as environmental chemistry. As there is a lack of wide-ranging adsorption data from the air to the bulk water surface, a large and diverse data set of adsorption coefficients of nonionic, organic compounds has been produced with inverse gas chromatography. The 61 compounds were chosen to cover a large range of properties, considering the intermolecular interactions between the compounds and the bulk water surface, i.e., van der Waals and electron-donor/acceptor interactions. The data set gained in this work was interpreted with a linear free energy relationship (LFER) based on these intermolecular interactions. From this LFER, a general adsorption model is derived, including compound ( i) and surface (surf) properties: log K i surf/air (m 3/m 2)=0.135(±0.003) log K i hexadecane/air (γ surf vdW) 0.5+5.11(±0.15)Σβ i2 H EA surf+3.60(±0.28)Σα i2 H ED surf−8.47. This adsorption model can be used for the characterization of adsorption to any other surface. The adsorption model for bulk water surface adsorption as well as the general adsorption model can be used as prediction tools in natural or technical systems.

New approximate model for nonlinear adsorption and diffusion in a single particle

A new approximate model of the general adsorption and diffusion model is derived that describes gas and adsorbed phase dependent diffusion in a single spherical sorbent particle governed by a nonlinear adsorption isotherm. This new approximate model compares very well with the exact (numerical) solution of the general adsorption and diffusion model over a wide range of (Langmuir) isotherm nonlinearity, and pore and surface diffusivities. Thus, it provides a significant advantage in terms of computation compared to the exact (numerical) model. This new model is simple to use and far superior to the popular linear driving force model, which severely underpredicts the uptake curve (compared to the new model) unless the adsorption isotherm is very favorable and the bulk concentration is low, approaching the Henry's law region of the isotherm.

Multisite Adsorption of Cadmium on Goethite

Recently a new general ion adsorption model has been developed for ion binding to mineral surfaces (Hiemstra and van Riemsdijk, 1996). The model uses the Pauling concept of charge distribution (CD) and is an extension of the multi-site complexation (MUSIC) approach. In the CD–MUSIC model the charge of an adsorbing ion that forms an inner sphere complex is distributed over its ligands, which are present in two different electrostatic planes. In this paper we have applied the CD–MUSIC model to the adsorption of metal cations, using an extended data set for cadmium adsorbing on goethite. The adsorption of cadmium and the cadmium–proton exchange ratio were measured as function of metal ion concentration, pH, and ionic strength. The data could be described well, taking into account the surface heterogeneity resulting from the presence of two different crystal planes (the dominant 110 face and the minor 021 face). The surface species used in the model are consistent with recent EXAFS data. In accordance with the EXAFS results, high-affinity complexes at the 021 face were used in the model.

Statistical thermodynamics of multilayer adsorption from binary mixtures onto homogeneous solid surfaces

The statistical thermodynamics of the multilayer adsorption of binary gas and liquid mixtures on energetically homogeneous solid surfaces is formulated. The theoretical considerations are presented for mixtures containing components of identical molecular sizes. For bilayer adsorption the isotherm equations are derived and are compared with those known from the literature. For a general adsorption model assuming multilayer formation, however, only the canonical partition functions and the equations defining the equilibrium state are discussed.

Low cycle fatigue properties of type 316 stainless steel in vacuum

Low cycle fatigue tests in vacuum were carried out on Type 316 stainless steel under the push-pull type, strain-controlled, continuous cycling mode in the temperature range from room temperature to 1073 K and strain rate from 5 × 10 −3 to 5 × 10 −5/s . Little temperature dependence of the fatigue life at a given plastic strain range is observed. The fatigue life decreases with decreasing strain rate at room temperature and 823 K, but shows little change at 973 and 1073 K. The fracture mode is transgranular in most cases, but an indication of intergranular cracking is observed in the specimens tested at 1073 K and at the lowest strain rate. The results are treated by the general adsorption model.