Langmuir-type Equations Research Articles

Basics of the reaction kinetics on metallic alloys.

Kinetics of heterogeneous catalytic reactions are often complicated by various factors, and from the perspective of statistical physics the development of the corresponding models is frequently challenging especially in the case of practically important alloy catalysts. To extend the basics in this area, I use a generic kinetic model of N_{2} formation inthe NO reaction with such species as CO or H_{2}. The focus is onthe reaction on the surface of a bimetallic alloy with low integral fraction of one of the metals so that the alloy is formed only at the surface. The main goal is to illustrate the specifics of the reaction kinetics and to clarify the accuracy of various approximations which are often inevitable for the analysis of such systems. The key results are as follows. (i) In the baseline one-metal case with the Langmuir-type equations, the model predicts the existence of the optimal adsorbate binding energy corresponding to the maximal reaction rate. (ii) With suitable substitution of the symbols, the equations employed for a uniform surface [item (i)] can be used for the mean-field description of reaction on the surface of a random alloy. In particular, the maximum in the dependence of the reaction rate on the binding energy is converted to the maximum with respect to the alloy composition. (iii) The reaction kinetics on the random-alloy surface have been described exactly. The corresponding maximum in the reaction rate is lower and somewhat smeared compared to that predicted in the mean-field approximation for an alloy or for the optimal monometallic catalyst. (iv) The reaction kinetics have been scrutinized also in the case of two-dimensional (2D) segregation of metal atoms at the surface in the limits of slow and rapid adsorbate diffusion between the spots. The kinetics are shown to be qualitatively different in these limits and also compared to the random-alloy case. (v) The thermodynamic criteria for 2D segregation of metal atoms at the surface have been derived as well.

Effect of moisture content on methane adsorption- and desorption-induced deformation of tectonically deformed coal

Intermolecular forces that act between moisture and the atoms of the coal structure have a significant influence on methane adsorption- and desorption-induced deformation in coal. After analyzing the porous characteristics and existing forms of moisture in coal, both the adsorption-induced swelling and the desorption-induced shrinkage deformation experiments were carried out under the conditions of varying moisture content, constant temperature, and variable equilibrium pressure. Both the swelling and shrinkage volumetric strains with different coal moisture contents were fitted by Langmuir-type equations in which the fitting coefficients were functions of the moisture content. It was found that there is a lag between the swelling curve and the corresponding shrinkage curve, and a variable known as the hysteresis rate was defined to illustrate this characteristic. A mathematical model of swelling and shrinkage deformation that considers the effect of moisture content was established based on the experimental results and analysis.

A thermodynamic investigation of adsorbate‐adsorbate interactions of carbon dioxide on nanostructured carbons

A thermodynamic study of carbon dioxide adsorption on a zeolite‐templated carbon (ZTC), a superactivated carbon (MSC‐30), and an activated carbon (CNS‐201) was carried out at temperatures from 241 to 478 K and pressures up to 5.5•106 Pa. Excess adsorption isotherms were fitted with generalized Langmuir‐type equations, allowing the isosteric heats of adsorption and adsorbed‐phase heat capacities to be obtained as a function of absolute adsorption. On MSC‐30, a superactivated carbon, the isosteric heat of carbon dioxide adsorption increases with occupancy from 19 to 21 kJ•mol−1, before decreasing at high loading. This increase is attributed to attractive adsorbate–adsorbate intermolecular interactions as evidenced by the slope and magnitude of the increase in isosteric heat and the adsorbed‐phase heat capacities. An analysis of carbon dioxide adsorption on ZTC indicates a high degree of binding‐site homogeneity. A generalized Law of Corresponding States analysis indicates lower carbon dioxide adsorption than expected. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1026–1033, 2018

Soil-water repellency characteristic curves for soil profiles with organic carbon gradients

Soil water repellency (SWR) of soils is a property with significant consequences for agricultural water management, water infiltration, contaminant transport, and for soil erosion. It is caused by the presence of hydrophobic agents on mineral grain surfaces. Soils were samples in different depths at three forest sites in Japan and three pasture sites in New Zealand, covering soil organic carbon (SOC) contents between 1 and 26%. The SWR was measured over a range of water contents by three common methods; the water drop penetration time (WDPT) test, the molarity of an ethanol droplet (MED) method, and the sessile drop method (SDM). The aim to (i) compare the methods, (ii) characterize the soil-water repellency characteristic curves (SWRCC) being SWR as a function of the volumetric soil-water content (θ) or matric potential (ψ), and (iii) find relationships between SWRCC parameters and SOC content. The WDPT, MED, and SDM generally agreed well in predicting the θ range where SWR occurred, and there was close agreement between SWR results determined by average MED and SDM at similar θ. Generally, SWR was only found within the top 20cm of the soil profiles. Six SWR parameters were introduced: (i) the area under the curve (SWR(θ)); (ii) θ at the maximum SWR (θWR-max), (iii) θ where SWR ceased (θnon-WR), (iv) the maximum SWR (CAi-max), (v) pF at the maximum SWR (pFWR-max) and (vi) pF where SWR ceased (pFnon-WR). The relationship between the first three parameters and SOC content were best described with Langmuir type equations (r2 of 0.5–0.7), while the other three parameters changed linearly with SOC contents.

Effect of polyester blends in hydroentangled raw and bleached cotton nonwoven fabrics on the adsorption of alkyl-dimethyl-benzyl-ammonium chloride

The adsorption kinetics and isotherms of alkyl-dimethyl-benzyl-ammonium chloride (ADBAC), a cationic surfactant commonly employed as an antimicrobial agent, on hydroentangled nonwoven fabrics (applicable for wipes) including raw cotton, bleached cotton, and their blends with polyester (PES) were studied at room temperature. The adsorption kinetics of ADBAC on all nonwoven fabrics was best described by the pseudo-first-order kinetic model. Unlike bleached cotton/PES blends, the equilibrium adsorption capacities of ADBAC on raw cotton/PES blends were enhanced in comparison with predictions based on the binary mixing rule. The adsorption rates for raw cotton, determined by the KASRA (kinetics of adsorption study in the regions with constant adsorption acceleration) model and Elovich equation, were significantly greater than those for bleached cotton, resulting in a rapid decrease of adsorption rates when blending with PES, which has a negligible interaction with ADBAC. This distinctive adsorption property of raw cotton was attributed to its unique surface characteristics induced by the hydroentangling process: retained pectin, partial removal of waxes, and surface fibrillation, which enhance electrostatic interaction, hydrophobic interaction, and accessible surface area to ADBAC, respectively. In adsorption isotherms, raw cotton/PES blends exhibited a non-linear decrease in maximum adsorption capacity and monolayer adsorption capacity, calculated by the Langmuir and Langmuir-type equations, respectively, as a function of PES blend ratio.

Early construction and operation of highly contaminated water treatment system in Fukushima Daiichi Nuclear Power Station (I) – Ion exchange properties of KURION herschelite in simulating contaminated water

To support the design and operation of the decontamination system using KURION media for the treatment of highly contaminated water accumulated in Fukushima Daiichi Nuclear Power Station, Central Research Institute of Electric Power Industry has urgently carried out many kinds of research and development programs to support the operation of the decontamination system using columns filled with three kinds of KURION media (H, AGH and SMZ). Since the contaminated water at Fukushima Daiichi Nuclear Power Station contained seawater and oil, the effects of sea salt and dissolved oil on Cs adsorption behavior were examined closely by batch type. The concentration of sea salt in the solutions was varied between 0.0 and 3.4 wt%. The Cs adsorption capacity of KURION herschelite in seawater decreased to nearly 1/10th of that in pure water, but it was still concluded that herschelite has sufficient adsorption capacity to remove Cs from the contaminated water. The effect of dissolved oil could be ignored because of its low solubility in seawater. Langmuir-type adsorption isotherm equations, which can be applied for estimating Cs adsorption in sea salt containing water, were developed.

Preparation and performance of arsenate (V) adsorbents derived from concrete wastes

Solid adsorbent materials, prepared from waste cement powder and concrete sludge were assessed for removal of arsenic in the form of arsenic (As(V)) from water. All the materials exhibited arsenic removal capacity when added to distilled water containing 10–700mg/L arsenic. The arsenic removal isotherms were expressed by the Langmuir type equations, and the highest removal capacity was observed for the adsorbent prepared from concrete sludge with heat treatment at 105°C, the maximum removal capacity being 175mg-As(V)/g. Based on changes in arsenic and calcium ion concentrations, and solution pH, the removal mechanism for arsenic was considered to involve the precipitation of calcium arsenate, Ca3(AsO4)2. The enhanced removal of arsenic for the adsorbent prepared from concrete sludge with heat treatment was thought to reflect ion exchange by ettringite. The prepared adsorbents, derived from waste cement and concrete using simple procedures, may offer a cost effective approach for arsenic removal and clean-up of contaminated waters, especially in developing countries.

Use of Two-Surface Langmuir-Type Equations for Assessment of Phosphorus Requirements of Lentil on Differently Textured Alluvial Soils

If soil solution phosphorus (P) optimum levels for plant growth (external P) are known, P adsorption isotherms or their equations could further be used to assess how much fertilizer P may be needed for optimum plants yield (QFPN) by adjusting this known external solution P requirement in the soil (ESPR). Surface soil samples were collected from a farmer's field area and research area. An adsorption study was conducted on Ustic Endoaquerts (S1 soil), Typic Calciargids (S2 soil), and Typic Torripsamments (S3 soil) to develop the two-surface Langmuir-type equations. Phosphorus adsorption data were obtained by equilibrating 10-g soil samples in 100 mL of 0.01 M calcium chloride (CaCl2) containing various amounts of monopotassium phosphate (KH2PO4). Thereafter, 11 P fertilizer rates were calculated by two-surface Langmuir-type equations to adjust different estimated soil solution P levels (EPAS) that were designated as treatments (0.05 to 0.90 mg L−1). Then field experiments on lentil (cv. Niab Masoor 2002) were conducted according to a randomized complete block design (RCBD) on these soils to determine internal (plant tissue), external (soil solution), and fertilizer P requirements. Maximum lentil seed yield (Mg ha−1) was 0.87 with T4 (0.17 mg P L−1) in S1 soil, 1.8 with T3 (0.20 mg P L−1) in S2 soil, and 0.73 with T7 (0.28 mg P L−1) in S3 soil, obtained by applying 170 kg P2O5 ha−1 in S1 soil, 110 kg P2O5 ha−1 in S2 soil, and 78 kg P2O5 ha−1 in S3 soil. Internal P concentrations (%) of the whole plant associated with 95% of maximum lentil seed yield at flowering stage were 0.245, 0.210, and 0.315 in S1, S2, and S3 soils, respectively. Internal P requirements of lentil seed were 0.290 in S1, 0.245% in S2, and 0.380% in S3 soil. The ESPRs for 95% of maximum yield of lentil were 0.16 mg L−1, in S1 soil, 0.23 mg L−1 in S2 soil, and 0.27 mg L−1 in S3 soil. The QFPN estimated from graphs corresponding to these ESPR values were 160 kg P2O5 ha−1 in S1 soil, 125 kg P2O5 ha−1 in S2 soil, and 74 kg P2O5 ha−1 in S3 soil. The QFPNs estimated from corresponding two-surface Langmuir-type equation by using respective ESPR values were 164, 127, and 75 kg P2O5 ha−1 in S1, S2, and S3 soil, respectively. Field-applied P2O5 amounts to adjust soil solution P levels (mg L−1) at 0.166 (T4), 0.229 (T4), and 0.281 (T7) were 170, 126, and 78 kg ha−1 in S1, S2, and S3 soil, respectively. Based on the results of these studies, we propose that QFPNs estimated by graphs against identified ESPR values or calculated by the use of corresponding two-surface Langmuir-type equations are in close proximity to the field-applied P to adjust desired EPAS value. Therefore, either of the two techniques may be used to estimate QFPN for optimum lentil yield. Close

Biosorption of Zn and Co ions by Evernia prunastri from single and binary metal solutions

Dried biomass of lichen Evernia prunastri was studied as biosorbent for zinc and cobalt removal from single and binary ZnCl2 and CoCl2 solutions. The solution pH significantly influenced both cobalt and zinc biosorption. Maximum uptake was reached at pH 4–6 and negligible biosorption was observed at pH 2. The experimental data were fitted to the adsorption isotherms. The Langmuir, Redlich-Peterson and Langmuir-Freundlich isotherms were found to represent the measured sorption data well. The maximum sorption capacities onto lichen biomass from single metal solutions calculated by Langmuir equation were 112 μmol g−1 for Zn and 97 μmol g−1 for Co. To evaluate the Zn-Co sorption system, simple curves were replaced by three-dimensional sorption isotherm surfaces. Binary Langmuir type equations were used to fit the experimental data. Results revealed that E. prunastri exhibited preferential uptake of zinc from equimolar binary Zn 2+−Co 2+ mixtures.

Absorption Characteristics of Fission Product Elements on Zeolite

In pyrometallugical reprocessing, the spent electrorefiner salt containing fission product (FP) elements may be purified by zeolite and reused. Batch-type absorption tests were conducted using one or two FP chlorides in a LiCl-KCl eutectic electrolyte in order to obtain absorption isotherms to fit to a Langmuir equation model. For the trivalent FP elements in the one-component or two-component systems, the FP-element uptake in the zeolite can be related to its concentration in the salt using a single Langmuir-type equation. In contrast, for monovalent and divalent FP elements, it was necessary to use three different Langmuir-type equations. Using these derived absorption equations and a stage concentration diagram, it was found that only a three-stage process is required to attain a decontamination factor of 50 for trivalent FP elements via a countercurrent multistage process.

Effect of Dissolved Organic Matter on Copper - Zinc Competitive Adsorption by a Sandy Soil at Different pH Values

The effect of dissolved organic carbon from sewage sludge on copper and zinc adsorption and interaction on samples from the surface layer (0 - 10 cm) of a sandy soil (Gleyic Podzol) were studied at two pH levels (4 and 7). This soil presented acidification hazards and sewage sludge with a high content of Cu and Zn was used as a fertilizer. Soil samples were treated by solutions of Cu and Zn as nitrate salts with concentration levels up to 30 mg l−1 in a Ca(NO3)2 background at a constant level (180 mg l−1) of dissolved organic carbon (DOC). Copper and zinc sorption capacity decreased in the presence of DOC. As the pH increased, the decrease in Cu adsorption due to interaction with DOC was more obvious. Conversely, without addition of DOC, Cu and Zn adsorption increased with pH. More Cu than Zn was adsorbed. Soil sorption of these cations was described by equilibrium isotherms that fitted both Langmuir and Freundlich type equations, presenting however a better fit to the Freundlich equation (R2>98%). Adsorption dependence on DOC was more noticeable at pH 7.

Prediction of simultaneous adsorption of Cu(II) and Pb(II) onto activated carbon by conventional Langmuir type equations

Removal of Cu(II) and Pb(II) by adsorption onto activated carbon was examined in single- and binary-component aqueous solutions representative of contaminated solutions containing heavy metals. Reversibility of adsorption of the heavy metals on the activated carbon was evaluated by desorption experiments. The number of the maximum adsorption sites and adsorption equilibrium constants of Cu(II) and Pb(II) were estimated by the results of single-component systems assuming the Langmuir adsorption model. The adsorption sites per gram of activated carbon resulted in similar values for Cu(II) and Pb(II) from the isotherms. The adsorption constant for Pb(II) was nearly 1.8 times greater than that of Cu(II). Rate constants of adsorption and desorption were also estimated from the kinetic analysis. Using the single set of common parameters obtained from the single-component systems, the experimental results for a binary-component system were quantitatively predicted. Competitive adsorption of Cu(II) and Pb(II) on the same adsorption sites was confirmed by both experimental and predicted results of adsorption in the binary mixture.

Determining competitive nitrate and chloride adsorption in an andisol by the unsaturated transient flow method

Adsorption of monovalent electrolyte anions during transport process in Andisols is largely due to the increase in the total anion adsorption rather than through anion exchange with strongly adsorbed native S04 2−. The unsaturated transient flow method has been developed for determining adsorption isotherms for weakly reactive ions without causing excessive desorption of strongly adsorbed native ions. The objective of this study was to extend the method to determine NO3 − adsorption isotherms in an Andisol in the absence or presence of Cl competing for the adsorption sites Kannondai subsoil (Hydric Hapludand), premixed with a Ca(NO3)2 or CaCl2-Ca(NO3)2 solution at different concentrations, was packed into sectionable columns, and one-dimensional water absorption experiments were conducted. Anion adsorption by soil, Q n, and the liquid-phase concentration, C n, prior to the water imbibition were obtained from the plots of the anion content vs. water content in the region beyond the ‘plane of separation,’ where the antecedent solution was accumulated. The values of Qn and C n found in a series of column experiments were then used to construct the isotherms describing the solution composition-dependent adsorption of NO3 − and Cl−. e fitted to Langmuir-type equations, the maximum adsorption for NO3 − (Qmax= 27,1-29.0 mmolc kg−1) was consistently smaller than that for Cl− (Qmax = 455 46.1 mmolc kg−1), while the empirical constant K (= 0.0238 - 0.0274 m3 molc −1) was insensitive to the anion species. The anion content profiles predicted by the inferred adsorption isotherms closely agreed with the measured content profiles.

Kinetics of catalytic oxidation of carbon monoxide and methane combustion over alumina supported Ga2O3, SnO2 or V2O5

Carbon monoxide oxidation and methane combustion were studied on Ga2O3, SnO2 or V2O5 supported on γ-Al2O3 catalysts under the stoichiometric conditions. It was found that the catalytic activity depends on the pretreatment conditions (oxygen or hydrogen atmosphere) of the catalyst. Detailed kinetic investigations allowed determination the reaction rates and adsorption coefficients of Langmuir-type equations in the case of catalysts pretreated under oxygen atmosphere and reaction conducted with oxygen excess.

Influence of pH on Copper - Zinc Competitive Adsorption by a Sandy Soil

Copper and zinc adsorption and interaction were studied at different pH levels in a sandy soil (Gleyic Podzol) to understand heavy metal behaviour in soils with acidification hazards, polluted by the use of sewage sludge with high content of Cu and Zn. Soil samples were treated by solutions of Cu and Zn as nitrate salts with concentration levels up to 30 mg l−1 in a Ca(NO3)2 background. More Cu than Zn was adsorbed, mainly specifically adsorbed. Copper and Zn in the exchange complex varied with soil solution pH. Adsorbed Cu and Zn increased with pH and as pH increased, more Cu than Zn was specifically adsorbed. Soil sorption of these cations was described by equilibrium isotherms that fitted either Freundlich or Langmuir type equations. The competitive Langmuir and extended Freundlich equations predicted for Cu and Zn values are in good agreement with the experimental data. Adsorption dependence on pH was more marked above pH 5 with a sharp increase of the distribution ratio D. Values for pH50, offering a relative measure of the selectivity of the adsorbent for the metal cations, were higher for Zn than for Cu increasing with the amount of heavy metal added to the soil sample.

Preliminary study of pH effect in the application of Langmuir and Freundlich isotherms to Cu–Zn competitive adsorption

Assessing the behaviour of Cu and Zn in adsorption reactions in soils and the associated risks to soil and water pollution requires the use of sorption equations. Therefore, Langmuir and Freundlich isotherms were derived for Cu and Zn applied to soil samples of the surface layer (0–20 cm) of two Dystryc Fluvisols, a Gleyic Podzol and a Haplic Luvisol. The adsorption data obtained fitted both Langmuir and Freundlich isotherms. The goodness of fit was evaluated by the determination coefficient R 2. The effect of pH on Cu–Zn competitive adsorption was quantified using competitive Langmuir-type equations as well as the extended Freundlich equations. The results obtained for Cu–Zn adsorption with the monocomponent Langmuir equation or with the competitive Langmuir-type equation were not significantly different according to the Student's t-test. Conversely, when Cu and Zn were added to the soil samples by the binary solution, the results from the Freundlich monocomponent equation were significantly different (Student's t-test) from those obtained with the extended Freundlich equation. The competitive Langmuir-type and extended Freundlich equations predicted for Cu and Zn both in single and binary solutions values in good agreement with the experimental data, confirming the interest of the introduction of a pH term.

Adsorption of cadmium ion and gallium ion to immobilized metallothionein fusion protein.

A fusion protein made from maltose binding protein (pmal) and human metallothionein (MT) was expressed using E. coli. The purified recombinant protein (pmal-MT) was immobilized on Chitopearl resin, and characteristics of pmal-MT for metal binding were evaluated. As expected from the tertiary structure of metallothionein, the pmal-MT ligand adsorbed 12.1 cadmium molecules per one molecule of the ligand at pH 5.2. The pmal-MT ligand also bound 26.6 gallium molecules per one molecule of the ligand at pH 6.5. Neither cadmium ion nor gallium ion bound to a control protein bovine serum albumin (BSA). Adsorption isotherms for both ions were correlated by Langmuir-type equations. Two types of binding sites have been elucidated on the basis of HSAB (hard and soft acid and base) theory. It was suggested that gallium ion specifically binds to amino acid residues containing oxygen and nitrogen atoms, while cadmium ion binds to specific binding sites formed by multiple cysteine residues. The pmal-MT ligand bound these metals in the concentration range of 0.2-1.0 mM, and the bound metal ions could be eluted under relatively mild conditions (pH 2.0). The pmal-MT Chitopearl resin was stable and could be used repeatedly without loss of binding activity. Thus, this new ligand would be useful for recovery of toxic heavy metals and/or valuable metal ions from various aqueous solutions.

Copper and Zinc Competitive Adsorption: Desorption in Calcareous Soils

The behavior in competitive adsorption-desorption reactions of Cu and Zn was studied in four calcareous soils. Cu and Zn were added to the soil by Cu, Zn, and Cu+Zn sulfate solutions in a CaSO4 background. Soil sorption of these cations was described by equilibrium isotherms that fitted either Freundlich- or Langmuir type equations, although Cu desorption data fitted only Freundlich isotherms. Cu and Zn competition was quantified by distribution coefficients, Kd, relating cation distribution between soil and solute and by the competitive Langmuir equation. The competitive Langmuir equation was the better suited to describe the Cu-Zn competitive adsorption in these soils. Distribution coefficients presented lower values when both cations were present, decreasing when the Cu and Zn concentration in solution increased (decreasing soil affinity for these cations), thereby increasing their mobility through the soil. However, the distribution coefficient of specifically adsorbed Cu in equilibrium with cations extracted by a Mg (NO) solution increased with Cu concentration. Cu adsorption was more depres 3 se 2 d by Zn than Zn adsorption by Cu. The different behavior of Cu and Zn seems dependent on the percentage Ca (CO) and, to a lesser degree, on Cu and Zn organic matter complexes, free iro 3 n 2 content, and surface precipitation on oxides and carbonates.

Selection of adsorbents to be used in an ethanol fermentation process. Adsorption isotherms and kinetics

Adsorption equilibrium assays were carried out in order to find adsorbents selective for ethanol to use in a fermentation process. Three hydrophobic adsorbents — silicalite, ZSM-5 and CMS-5A — were tested. Results of adsorption equilibrium at 298 K of ethanol, glucose, fructose and glycerol from aqueous solutions of each single solute are given. Ethanol adsorption isotherms were described by Langmuir-type equations. Some kinetic assays of ethanol adsorption are also presented. The results obtained appear to be useful for practicioners on the fermentation-processes field.

Neodymium sorption by clay minerals and zeoliferous rocks

The sorption of neodymium from its aqueous solutions (concentration range approx. 10–450 mg l−1) by montmorillonite, kaolinite and a clinoptilolite-containing rock has been investigated, using147Nd as radioactive tracer and γ-ray spectrometry. The neodymium uptake by montmorillonite was found to be much higher than of the other two materials in the whole investigated concentration range. However, in the case of montmorillonite and zeoliferous rock, the uptake ability is lower than that allowed by the measured CEC values and can be described by Langmuir-type equations. In the case of kaolinite, the observed higher than CEC-allowed uptake values could be attributed to sorption by mechanisms other than ion-exchange. The corresponding data obey a Freundlich-type sorption equation. Among the three geological materials investigated, montmorillonite exhibits the highest perspectives of application for the treatment and disposal of neodymium and trivalent actinides in nuclear industry.