Adsorption Kinetic Equations Research Articles

Mechanism of electrochemical interaction between sulfur-containing amino acids and anodically polarized platinum electrode

Electrooxidation of cysteine and methionine on a platinum electrode in solutions with various pH values is studied by the RDE and linear-sweep voltammetry methods. Based on this study and previous adsorption measurements, kinetic equations and mechanisms of main processes, which occur on the anodically polarized platinum electrode in the presence of the amino acids and lead to electrocatalytic dissolution of platinum, are proposed. Anodic dissolution of platinum in the presence of cysteine and methionine is accelerated due to immediate involvement of the sulfur atom in the adsorption and electrooxidation on the platinum electrode surface.

A Simultaneous Description of Equilibria and Kinetics of Adsorption on Flat Heterogeneous Solid Surfaces: Single Gas Adsorption at Low Surface Coverages

Based on the statistical theory of the rate of interfacial transport, a standard procedure is proposed for developing equations for adsorption kinetics and equilibria, corresponding to some model of a heterogeneous solid surface. By replacement of a certain function by another, in a kind of master equation, the isotherm equation is transformed into corresponding equation for adsorption kinetics, and vice versa. The detailed form of that master equation is related to the form of the adsorption energy distribution. The theoretical origin of the popular empirical equations for adsorption kinetics is reexamined and the range of their applicability is shown. The present theoretical treatment is limited to lower surface coverages where collective character of adsorption can be ignored, along with the readsorption kinetics.

Kinetic Equations for Transfer-Controlled Adsorption Kinetics

Kinetic equations are presented for the adsorption of a surfactant from a liquid bulk phase to a liquid/liquid or air/liquid interface, for a situation where diffusion equilibrium between bulk and subsurface is established, and consequently the transfer of surfactant from the subsurface to the surface is the rate-determining step in the adsorption process. These equations are obtained in a way very similar to that by which the Butler-Volmer equations are obtained in electrode kinetics, where also the reaction rate is the rate-determining step. Essential for both is that the standard free energy of the activated complex is split into a chemical part and a part which depends on the external force field (surface pressure for adsorption, electrical potential for transfer controlled electrochemical reactions). This part of the standard free energy of the activated complex is a fraction of the force-field-dependent part of the adsorption standard free energy. This reasoning leads f.i. to the Langmuir kinetic equation for the adsorption process. This Langmuir kinetic equation is extended for regular solution behavior and, for the case of an indifferent electrolyte, added to the surfactant system. These equations are in agreement with previous experimental observations, except for the regular system where experimental data are still lacking.

Kinetic equations for transfer-controlled adsorption kinetics

The dynamic surface tensions of five systems showing transfer-controlled adsorption kinetics at high concentrations have been measured. The experimental results are used to investigate the kinetic equations for the adsorption processes, with the surface behaviour being not ideal or with an indifferent electrolyte added to an ionic surfactant. For non-ideal surface behaviour, the Langmuir kinetic equation is modified with surface activity coefficients based on regular solution theory, and the dynamic surface tensions are then well described. For the adsorption of an ionic surfactant with an indifferent electrolyte, a kinetic equation including the effect of the non-surface-active electrolyte is proposed and a parameter is described for relating the rate constants to concentrations. For ideal ionic systems the Langmuir-von Szyszkowski constants obtained from the kinetic surface tensions agree with those from equilibrium data. Moreover it is observed that for micellar systems in the region above the CMC the rate constant still increases up to a high concentration.

The analysis of dynamic surface tension of sodium alkyl sulphate solutions, based on asymptotic equations of adsorption kinetic theory

We analysed existing and newly derived asymptotic solutions of the adsorption kinetic equations for the liquid phase interface in the regions of infinitely small and infinitely great surface lifetimes ( t) for the cases of one and of a few surfactants, on non-deforming and deforming surfaces, under non-stationary, stationary and quasi-stationary conditions, assuming either the diffusion adsorption mechanism or mixed adsorption mechanism. It was proved that in the region t → ∞, the adsorption barrier does not influence the dynamic surface tension σ, but the role of surface-active contaminants is significant. In contrast, in the region t → 0, the role of contaminants is small, but the adsorption barrier influences the dynamic surface tension substantially. The dynamic surface tension of sodium alkyl sulphate solutions was measured by the maximum bubble pressure method, in the t range 0.001–10 s. In the region t → ∞ we obtained good agreement of experimental results with asymptotic formulae. The diffusion adsorption mechanism of the surfactant solutions studied was confirmed and we also estimated the concentration values of the surfactant admixtures. Small additions of the more active surfactant sodium tetradecyl sulphate to sodium dodecyl sulphate substantially influences the shape of the σ— t curve in the region t → ∞, increasing (in full accordance with theoretical considerations) the tangent value of the curve inclination of the dependence of σ on t −1/2. In the regions t → 0, long-chained high molecular weight sodium alkyl sulphates adsorb according to the diffusion mechanism, whereas for sodium decyl and dodecyl sulphates the existence of the adsorption barrier was confirmed. We corroborated experimentally the absence of any influence of surfactant admixtures on the values of dynamic surface tension at t → 0.

Phenomenological equations for adsorption kinetics.

Phenomenological equations for adsorption kinetics.

New Equations for Multicomponent Adsorption Kinetics

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTNew Equations for Multicomponent Adsorption KineticsJ. Talbot, X. Jin, and N.-H. L. WangCite this: Langmuir 1994, 10, 6, 1663–1666Publication Date (Print):June 1, 1994Publication History Published online1 May 2002Published inissue 1 June 1994https://doi.org/10.1021/la00018a009RIGHTS & PERMISSIONSArticle Views396Altmetric-Citations56LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (472 KB) Get e-Alerts Get e-Alerts

Monte Carlo simulations and kinetic theory of homogeneous and heterogeneous adsorption with lateral interactions

Using the kinetic form of the Monte Carlo (MC) simulation method, a comparison has been made between the results that predict the phenomenological equations for adsorption kinetics and MC experiments in systems with and without lateral interactions on homogeneous and heterogeneous surfaces with random topography and varying degrees of surface heterogeneity. A very good correspondence exists between the theoretical results and those obtained from the MC experiments.

On the theory of adsorption kinetics of ionic sufactants at fluid interfaces 4. Deceleration of the adsorption rate due to non-equilibrium distribution of adsorbed ions in the diffuse layer

An approximate analytical solution is obtained for the adsorption kinetics equation derived earlier. On the basis of these relations the importance of the consideration of a non-equilibrium diffuse layer has been shown. To describe the retarded adsorption kinetics the distribution of adsorbed ions in the diffuse layer section of multivalent surfactant ions has been taken into account. The rate of adsorption calculated for a non-ionic surfactant is compared with the adsorption rate for monovalent and bivalent ionic surfactants, respectively.

Prediction of activated carbon adsorption performance under high relative humidity conditions

AbstractHumidity effects on carbon adsorption were investigated using five volatile organic compounds (VOCs). Relative humidities ranged from 54% to 92%. Under these high relative humidity conditions, the Dubinin–Polanyi equation was used to analyze the results of activated carbon adsorption capacity. Based on the Dubinin–Polanyi equation and the concept of a mass transfer zone, an adsorption kinetic equation was derived to predict the carbon adsorption (MTZ) velocity and the adsorbate concentration profile in the bed.

The influence of the solution composition on the O-electroadsorption and O-electrodesorption on gold in acid electrolytes

The O-electroadsorption E/I profile obtained on polycrystalline gold after controlled-potential adsorption conditions is remarkably dependent on the electrolyte composition. The electrochemical results are interpreted in terms of the specific adsorption of the anions. According to the anion influence on the E/I profile, two groups of anions are distinguished. Group I contains those anions contributing to the electrolyte solution structure through hydrogen bonds, while group II comprises those anions where such bonds are in principle less relevant. A general electrochemical adsorption isotherm and an adsorption kinetic equation for the anions on polycrystalline gold are discussed.

The influence of the solution composition on the o-electroadsorption and o-electrodesorption on gold in acid electrolytes

The O-electroadsorption E/I profile obtained on polycrystalline gold after controlled-potential adsorption conditions is remarkably dependent on the electrolyte composition. The electrochemical results are interpreted in terms of the specific adsorption of the anions. According to the anion influence on the E/I profile, two groups of anions are distinguished. Group I contains those anions contributing to the electrolyte solution structure through hydrogen bonds, while group II comprises those anions where such bonds are in principle less relevant. A general electrochemical adsorption isotherm and an adsorption kinetic equation for the anions on polycrystalline gold are discussed.

Prediction of activated carbon performance for carcinogenic vapors

After an activated carbon was characterized with a reference vapor (CCl4), gas adsorption kinetic equations were used to predict carbon performance for 31 carcinogenic vapors. Previous work has shown that predicted and experimental values will correspond within a range of about ±15%.

On Ritchie's equation for adsorption kinetics of gases on solids

Ritchie's equation for the kinetic adsorption isotherm has been derived on the basis of the theory describing the kinetics of adsorption of gases on energetically heterogeneous solid surfaces. This eqation has also been generalized to the kinetics of adsorption of multicomponent gas mixtures.

Dependence of gas adsorption rates on carbon granule size and linear flow velocity

A study was made of the dependence of the adsorption rate constant of an activated carbon for dimethyl methylphosphonate vapor on carbon granule size and superficial linear velocity using the adsorption kinetics equation to calculate the rate constant from critical bed weight values. Over a 30-fold range of velocities and a 7-fold range of granule diameters it was found, in accord with adsorption kinetics theory, that although the adsorption capacity for the vapor was invariant, the time for vapor breakthrough of the bed varied because of the effects of linear flow velocity and carbon granule size on the adsorption rate constant. In general, the rate constant increased nonlinearly with increase in velocity and decrease in carbon granule size. The slowest adsorption kinetics existed for the largest granule size at the lowest linear flow velocity, becoming increasingly faster as the velocity was increased and/or the granule size was decreased. For the smallest granule size the rate constant reached a limiting value of 2600 sec −1 becoming essentially independent of linear velocity due to a change in the rate controlling step.

Consideration of diffusion resistance of entrance into microporous formations in adsorption kinetics equations for adsorbents with a bidisperse structure

A method was discussed for taking into account the diffusion resistance of entrance of an adsorptive molecule into the individual zeolite crystallite in a granule in the macroequations for the adsorption kinetics in biporous adsorbents (granulated zeolites). The indicated resistance is associated with the molecule overcoming the potential barrier at the boundary of the crystallite and can, according to the experimental data, limit the diffusion process in the crystallite in certain cases.

The rate of gas adsorption by activated carbon

A study was made of the rate of gas adsorption by activated carbon in terms of the functional dependence of the pseudo first order adsorption rate constant. Benzene was used as the adsorbate vapor and a packed bed column of a Pittsburgh activated carbon as the adsorbent. Benzene at a concentration of 2 × 10 −6 g/cm 3, equivalent to a relative pressure of 0·005 at 25°C, was flowed into the carbon bed at superficial linear velocities ranging from 2 to 50 cm/sec. The time at which 1% of the inlet concentration appeared in the exit stream of the bed was the breakpoint time. By applying the Wheeler adsorption kinetic equation to the experimental plot of breakpoint time vs bed weight pseudo first order adsorption rate constants at various linear velocities were determined. Using a presumed mathematical model and an overdetermined set of six equations the Univac 1108 computer provided the coefficients for an expression showing the dependence of the adsorption rate constant on the linear flow velocity.

The kinetics of adsorption of organo-phosphorus vapors from air mixtures by activated carbons

The adsorption characteristics of activated carbons for the vapors of dimethyl methylphosphonate (DMMP) and of isopropyl methylphosphonofluoridate (IMPF) were studied under kinetic flow conditions. The carbon granules were packed to a reproducible bulk density in beds of uniform cross-sectional area and subjected to constant inlet vapor concentration, volume flow rate, and temperature but varying bed weights. The breakthrough time of the vapor through the bed, at an exit concentration equal to 1 per cent of the inlet concentration, was determined for each bed weight, and plotted as a straight line in accordance with the equation for adsorption kinetics. The kinetic saturation capacity of the carbon for each vapor was determined from the slope and the pseudo first order adsorption rate constant from the intercept. Kinetic equations were constructed for each vapor and, when solved simultaneously, showed that the breakthrough time for IMPF could be correlated with that of DMMP in accord with the equation t b (IMPF) = 0.911 t b (DMMP)−8.86 for activated carbon and t b (IMPF) = 1.084 t b (DMMP)−4.32 for the same carbon after impregnation with copper, silver, and chromium salts. The close agreement between the relationships of these organophosphorus vapors on the two carbons suggests that the prediction of adsorption of one vapor based upon prior characterization with a reference vapor, originally applicable only under equilibrium, can be extended for use under kinetic conditions. A method is presented for calculating the kinetic adsorption capacity of an activated carbon for IMPF from the experimental DMMP value using equilibrium relationships, and shown capable of predicting the capacity within 4.1 per cent.

ELECTRODE PROCESSES WITH SPECIFIC OR NON-SPECIFIC ADSORPTION: FARADAIC IMPEDANCE AND RECTIFICATION

Abstract : Faradaic impedance and faradaic rectification are discussed for processes with specific or non-specific adsorption of reactants and/or reaction products. No explicit form of the rate equation for adsorption kinetics is postulated. Analysis of the faradaic impedance for processes with specific adsorption includes: derivation of a general current - potential characteristic for small amplitudes without the postulating of an explicit form for the rate equation for charge transfer kinetics; an equivalent circuit for electrode processes in which adsorption processes are independent of one another (e.g., as for metal deposition with amalgam formation); variations of the phase angle with frequency and analysis of some existing data in the literature; and correction for the double layer capacity. Equivalent circuits for processes with non-specific adsorption of reactants, i.e., with repulsion or attraction of the discharged species, are also derived for the faradaic impedance. Faradaic rectification is treated for the above cases, and the frequency dependence of the rectification voltage is analyzed in detail. Implications in the determination of kinetic parameters are pointed out. (Author)

Rectification by the Electrical Double Layer and Adsorption Kinetics

Abstract : Qualitative and quantitative treatments are given of non-faradaic rectification by the electrical double layer for specific adsorption of a neutral substance or an ionic species in presence of a large excess of supporting electrolyte. Control of the mean charge (q) and/or mean potential (E) is considered. Rectification at constant q results in a shift of E for an ideal polarized electrode and vice-versa. It is best to maintain E constant and to supply the rectification charge by means of a double pulse method. A theory of this method is developed without assumption about the explicit form of the rate equation for adsorption kinetics. The charge variation due to rectification is expressed in terms of the elements of the equivalent circuit for the non-faradaic impedance and the latter are given as functions of thermodynamic and kinetic parameters for adsorption. The influence of frequency is analyzed; the general equation can be applied directly to the analysis of experimental results. Particular types of adsorption kinetics are also discussed. The method is applicable to frequencies greater than 1 mc at which non-faradaic impedance measurements with a bridge are hardly feasible. (Author)