Kinetics of adsorption and desorption of Pb(II) in aqueous solution on activated carbon by two-site adsorption model

The adsorption and desorption equilibrium and kinetics of lead ions from aqueous solutions on a granular activated carbon (GAC) were examined. Rapid increase followed by slow increase in Pb(II) amount on the GAC was observed as a function of time for the adsorption, while rapid decrease and consecutive very slow decrease was observed in desorption. Based on the experimental results, a two-site adsorption model was proposed for the adsorption and the desorption of Pb(II) under the study conditions. The Pb(II) adsorption on the GAC was estimated to have simultaneously occurred on the strong and the weak adsorption sites. Conventional Langmuir-type kinetic equations were introduced to quantitatively predict the adsorption and desorption with the two-site model by optimizing the parameters to fit the equilibrium and the kinetic experimental results. The equilibrium and kinetic experimental results could be represented by the equations by using one set of the common Langmuir parameters. Resultant kinetic parameters revealed that the adsorption equilibrium constant was two orders of magnitude greater for strong adsorption site than for weak adsorption site, though the maximum number of weak adsorption site was 1.5 times as great as that of strong adsorption site. The strong adsorption equilibrium constant resulted from a small desorption rate constant for the site. The equations were demonstrated to be applicable for predicting other desorption performances as well.     

From Langmuir kinetics to first- and second-order rate equations for adsorption

So far, the first- and second-order kinetic equations have been most frequently employed to interpret adsorption data obtained under various conditions, whereas the theoretical origins of these two equations still remain unknown. Using the Langmuir kinetics as a theoretical basis, this study showed that the Langmuir kinetics can be transformed to a polynomial expression of dtheta t /d t = k 1(theta e - theta t ) + k 2(theta e - theta t ) (2), a varying-order rate equation. The sufficient and necessary conditions for simplification of the Langmuir kinetics to the first- and second-order rate equations were put forward, which suggested that the relative magnitude of theta e over k 1/ k 2 governs the simplification of the Langmuir kinetics. In cases where k 1/ k 2 is greater than theta e or k 1/ k 2 is very close to theta e, adsorption kinetics would be reasonably described by the first-order rate equation, whereas the Langmuir kinetics would be reduced to the second-order equation only at k 1/ k 2 < theta e. It was further demonstrated that both theta e and k 1/ k 2 are the function of initial adsorbate concentration ( C 0) at a given dosage of adsorbent, indicating that simplification of the Langmuir kinetics indeed is determined by C 0. Detailed C 0-depedent boundary conditions for simplifying the Langmuir kinetics were also established and were verified by experimental data.     

Modeling of adsorption dynamics at air-liquid interfaces using statistical rate theory (SRT)

A large number of natural and technological processes involve mass transfer at interfaces. Interfacial properties, e.g., adsorption, play a key role in such applications as wetting, foaming, coating, and stabilizing of liquid films. The mechanistic understanding of surface adsorption often assumes molecular diffusion in the bulk liquid and subsequent adsorption at the interface. Diffusion is well described by Fick's law, while adsorption kinetics is less understood and is commonly described using Langmuir-type empirical equations. In this study, a general theoretical model for adsorption kinetics/dynamics at the air-liquid interface is developed; in particular, a new kinetic equation based on the statistical rate theory (SRT) is derived. Similar to many reported kinetic equations, the new kinetic equation also involves a number of parameters, but all these parameters are theoretically obtainable. In the present model, the adsorption dynamics is governed by three dimensionless numbers: psi (ratio of adsorption thickness to diffusion length), lambda (ratio of square of the adsorption thickness to the ratio of adsorption to desorption rate constant), and Nk (ratio of the adsorption rate constant to the product of diffusion coefficient and bulk concentration). Numerical simulations for surface adsorption using the proposed model are carried out and verified. The difference in surface adsorption between the general and the diffusion controlled model is estimated and presented graphically as contours of deviation. Three different regions of adsorption dynamics are identified: diffusion controlled (deviation less than 10%), mixed diffusion and transfer controlled (deviation in the range of 10-90%), and transfer controlled (deviation more than 90%). These three different modes predominantly depend on the value of Nk. The corresponding ranges of Nk for the studied values of psi (10(-2)相似文献   

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.     

Heterogeneous photocatalytic kinetics: beyond the adsorption/desorption equilibrium concept

Summary Rigorous kinetic analysis is presented for a range of photocatalytic mechanisms based on the steady-state approximation, while typically photochemical kinetics is discussed within the framework of Langmuir-Hinshelwood rate equations, assuming a slow rate-determining step and adsorption/desorption equilibrium. Performed comparison with experimental data reveals additional features inconsistent with adsorption/desorption equilibrium concept.     

Adsorption and desorption kinetics of benzene derivatives on mesoporous carbons

Adsorption and desorption of benzoic and salicylic acids and phenol from a series of synthesized mesoporous carbons is measured and analyzed. Equilibrium adsorption isotherms are best described by the Langmuir–Freundlich isotherm. Intraparticle diffusion and McKay’s pore diffusion models, as well as mixed 1,2-order (MOE), integrated Langmuir kinetic equation (IKL), Langmuir–Freundlich kinetic equation and recently derived fractal-like MOE (f-MOE) and IKL models were compared and used to analyze adsorption kinetic data. New generalization of Langmuir kinetics (gIKL), MOE and f-MOE were used to describe desorption kinetics. Analysis of adsorption and desorption half-times shows simple relation to the size of carbon pores.     

Kinetic derivation of common isotherm equations for surface and micropore adsorption

The Langmuir equation is one of the most successful adsorption isotherm equations, being widely used to fit Type I adsorption isotherms. In this article we show that the kinetic approach originally used by Langmuir for 2D monolayer surface adsorption can also be used to derive a 1D analogue of the equation, applicable in ultramicropores with single-file diffusion. It is hoped that such a demonstration helps dispel the idea that the Langmuir isotherm equation cannot apply to some micropores as more than a mathematical correlation. We furthermore seek to extend the insight provided by the simple kinetic derivation of the Langmuir equation to other isotherm equations capable of modelling Type I isotherms. The same kinetic approach is thus also used to derive the Volmer, Fowler–Guggenheim and Hill–de Boer equations, both for surface (2D adsorbed phase) and micropore adsorption (1D and 3D adsorbed phases). It is hoped that this will help make more intuitively clear that these equations can be used as phenomenological models in some instances of adsorption in micropores.     

Product desorption rate influence on catalytic reactivity of spatially inhomogeneous surfaces

We investigate numerically a phenomenological mathematical model of unimolecular reactions proceeding on inhomogeneous planar surfaces in the two-dimensional space case taking into account: the bulk diffusion of the reactant from the bounded vessel toward the adsorbent and the product bulk one from the adsorbent into the same vessel, the adsorption and desorption of reactant particles, long-range surface diffusion of the adsorbate, and a slow product desorption from the adsorbent. Simulations were performed using the finite difference technique. The influence of the long-range surface diffusion and product desorption rate on the kinetics of processes catalysed by inhomogeneous surfaces with different arrangements of reactive and nonreactive adsorption sites are studied.     

A site-selective in situ study of CO adsorption and desorption on Pt(355)

Using time-dependent high-resolution x-ray photoelectron spectroscopy at BESSY II, the adsorption and desorption processes of CO on stepped Pt(355) = Pt[5(111) x (111)] were investigated. From a quantitative analysis of C 1s data, the distribution of CO on the various adsorption sites can be determined continuously during adsorption and desorption. These unique data show that the terrace sites are only occupied when the step sites are almost saturated, even at temperatures as low as 130 K. The coverage-dependent occupation of on-top and bridge adsorption sites on the (111) terraces of Pt(355) is found to differ from that on Pt(111), which is attributed to the finite width of the terraces and changes in adsorbate-adsorbate interactions. In particular, no long-range order of the adsorbate layer could be observed by low-energy electron diffraction. Further details are derived from sticking coefficient measurements using the method devised by King and Wells [Proc. R. Soc. London, Ser. A 339, 245 (1974)] and temperature-programmed desorption. The CO saturation coverage is found to be slightly smaller on the stepped surface as compared to that on Pt(111). The initial sticking coefficient has the same high value of 0.91 for both surfaces.     

The kinetic study of specific adsorption of phosphate species on Pt(111) in acidic solutions

The study of the adsorption/desorption mechanism of phosphate anions at Pt(111) in acidic solution of pH 4.3 and 0.8 was performed by the potential step method in order to reveal the kinetics of anion adsorption. The current-time curve due to phosphate adsorption/desorption showed various decay features, being dependent on the potential region. The rate of current decay depended on pH, being faster in a lower pH solution. Specific adsorption processes were analyzed by the Langmuir and Elovich adsorption equations and also in terms of a two-dimensional nucleation-growth mechanism in different adsorption/desorption regions. In the case of adsorption in 0.3M phosphate buffer solution of pH 4.3, random adsorption without interaction following the Langmuir adsorption, takes place at low coverage, while random adsorption with repulsive force was observed at high coverage. In the desorption process, random desorption with repulsive force takes place at high coverage, and the repulsive force disappears where random adsorption without interaction takes place at medium coverage. When the surface coverage becomes further lower, the desorption mechanism changes dramatically into a two-dimensional nucleation-growth type, suggesting that an ordered adsorbate structure is formed after a rapid discharge process of anion adsorption.     

Kinetics of salicylic acid adsorption on activated carbon

The adsorption and desorption of salicylic acid from water solutions was investigated in HPLC microcolumns packed with activated carbon. The adsorption isotherm was obtained by the step-up frontal analysis method in a concentration range of 0-400 mg/L and was well fitted with the Langmuir equation. The investigation of rate aspects of salicylic acid adsorption was based on adsorption/desorption column experiments where different inlet concentrations of salicylic acid were applied in the adsorption phase and desorption was conducted with pure water. The concentration profiles of individual adsorption/desorption cycles data were fitted using several single-parameter models of the fixed-bed adsorption to assess the influence of different phenomena on the column behavior. It was found that the effects of axial dispersion and extraparticle mass transfer were negligible. A rate-determining factor of fixed-bed column dynamics was the kinetics of pore surface adsorption. A bimodal kinetic model reflecting the heterogeneous character of adsorbent pores was verified by a simultaneous fit of the column outlet concentration in four adsorption/desorption cycles. The fitted parameters were the fraction of mesopores and the adsorption rate constants in micropores and mesopores, respectively. It was shown that the former rate constant was an intrinsic one whereas the latter one was an apparent value due to the effects of pore blocking and diffusional hindrances in the micropores.     

Free energy of adsorption of water and metal ions on the [1014] calcite surface

We calculated the free energy profiles of water and three metal ions (magnesium, calcium, and strontium) adsorbing on the [1014] calcite surface in aqueous solution. The approach uses molecular dynamics with parametrized equations to describe the interatomic forces. The potential model is able to reproduce the interactions between water and the metal ions regardless of whether they are at the mineral surface or in bulk water. The simulations predict that the free energy of adsorption of water is relatively small compared to the enthalpy of adsorption calculated in previous papers. This suggests a large change in entropy associated with the water adsorption on the surface. We also demonstrate that the free energy profile of a metal ion adsorbing on the surface correlates with the solvent density and that the rate of formation of an innersphere complex depends on overcoming a large free energy barrier, which is mainly electrostatic in nature. Furthermore, comparison among the rates of desorption of magnesium, calcium, and strontium from the calcite surface suggests that magnesium has a much lower rate of desorption due to its strong interactions with both water and the surface.     

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.     

Modeling of temperature-programmed desorption thermograms for the determination of adsorption heat considering pore and surface diffusion

In this work, two partial differential equation-based models have been proposed for the quantitative analysis of temperature-programmed desorption (TPD) thermograms when the adsorption cell can be modeled as a well-mixed reactor, using the Langmuir equation as the adsorption isotherm and including the effect of diffusional resistance. One model considers pore diffusion, and the other considers surface diffusion. For both models, the rate of adsorption is proportional to the gas pressure. By nondimensionalizing these models, the range of design parameters for which the accumulation in the gas cell, diffusional resistance, and readsorption have an important effect on the TPD signal is proposed. An important conclusion is that the dimensionless numbers accounting for the diffusional resistance and the corresponding range of parameters are quite different for both mechanisms. The models have been validated with two systems where surface and pore diffusion are the relevant mechanisms: (i) CO2-Na-mordenite and (ii) CO2-Na-mordenite pellets.     

Impact of carbon dioxide on the surface tension of 1-hexanol aqueous solutions

Effects of carbon dioxide presence on the surface tension and adsorption kinetics of 1-hexanol solutions were investigated. Experiments were performed at a range of carbon dioxide vapor pressures and varying concentrations of 1-hexanol aqueous solution. Both dynamic and steady-state surface tensions of 1-hexanol aqueous solution were found to decrease with carbon dioxide pressure, and a linear relationship was observed between the steady-state surface tension and carbon dioxide pressure. To explain the experiments, adsorption and desorption of the two species (1-hexanol and carbon dioxide) from two sides of the vapor-liquid interface were considered. A modified Langmuir isotherm, the modified Langmuir equation of state and the modified kinetic transfer equation were developed. The resulting steady-state and dynamic surface tension data were modeled using the modified Langmuir equation of state and the modified kinetic transfer equation, respectively. Equilibrium constants and adsorption rate constants of 1-hexanol and carbon dioxide were evaluated through a minimization procedure for CO₂ pressures ranging from 0 to 690 kPa. From the steady-state modeling, the equilibrium parameters for 1-hexanol and carbon dioxide adsorption from vapor phase and liquid phase were found unchanged at different pressures of carbon dioxide. From the dynamic modeling, the adsorption rate constants for 1-hexanol and carbon dioxide from vapor phase and liquid phase were found to decrease with carbon dioxide pressure. Some fluctuations in the fitting parameters of the dynamic modeling (adsorption rate constants) were observed. These fluctuations may be due to experimental errors, or more likely the limitations of the model used. A major limitation of the model is related to large differences in adsorption/desorption between initial and final stages of the process, and a single set of property parameters cannot describe both initial and final states of the system. Variations may occur depending on which set of data, of initial or final states, is used in the model predictions over the entire time range.