The solution of adsorption integral equations by means of the regularization method

Szombathely, M. v.; Bräuer, Peter; Jaroniec, Mietek

doi:10.1002/jcc.540130104

Cited by 230 publications

(176 citation statements)

References 32 publications

Supporting

Mentioning

173

Contrasting

Unclassified

Order By: Relevance

“…In contrast, for concentrations higher than 3C e , the process was limited by diffusion in the pores (McKay et al 1986;Qadeer and Hanif 1994). Over this time range, the kinetic curve displayed large deviations from a linear form.…”

Section: Resultsmentioning

confidence: 99%

“…With those experiments in which the largest amount of carbon was used, diffusion in the pores played only a minor role in the adsorption process. This may be linked to the larger contact area between the solution and the activated carbon grains (Qadeer and Hanif 1994). Such dependence was reversed for the adsorption of Cu 2+ ions, a tendency probably related to the high alkalinity of the carbon surface (Kapica et al 2002a).…”

Section: Resultsmentioning

confidence: 99%

“…Changes in the adsorption capacity with time can be expressed by the following equation (Bangham and Burt 1924;Qadeer and Hanif 1994):…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Kinetics of the Adsorption of Copper and Lead Ions from Aqueous Solution on to WD-ekstra Activated Carbon

Kapica

Pełech

Przepiórski

et al. 2002

Adsorption Science & Technology

View full text Add to dashboard Cite

ABSTRACT:The kinetics of the adsorption of Cu 2+ and Pb 2+ ions from aqueous solution on to WD-ekstra activated carbon was studied by batch methods. Such adsorption processes proceeded in two stages: an initial rapid stage followed by a slower one. The Bangham equation was used to describe the kinetics of both adsorption processes. Measurements were carried out for solutions containing only one type of metal ion and also for binary systems containing both Cu 2+ and Pb 2+ions. A considerable influence of Pb 2+ ions on the adsorption of Cu 2+ ions was observed in the binary system. It was found that the equilibrium isotherms could be analyzed using the Langmuir, Freundlich-Langmuir and Freundlich methods.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Kinetics of the Adsorption of Copper and Lead Ions from Aqueous Solution on to WD-ekstra Activated Carbon

Kapica

Pełech

Przepiórski

et al. 2002

Adsorption Science & Technology

View full text Add to dashboard Cite

show abstract

“…A solution of this system as presented on Eq (6) would actually result in a spiky PSD, regarded as a mathematical artefact [29]. These undesirable effects can be removed by applying an appropriate regularization method, such as that due to Tikhonov [30][31][32]. In the current work, regularization was incorporated in the PSD calculation by adding the smoothing term (αS) to the residual in Eq.…”

Section: Integral Inversion Proceduresmentioning

confidence: 99%

Uncertainty in pore size distribution derived from adsorption isotherms: II. Adsorption integral approach

Madani

Herrera

Biggs

et al. 2015

Microporous and Mesoporous Materials

View full text Add to dashboard Cite

Uncertainty in the amount adsorbed in manometric adsorption isotherm measurements is well established. Here, we extend uncertainty methodologies from adsorption isotherm data uncertainty and apply them to calculate pore size distributions based on adsorption integral methods. The analyses consider as variables: uncertainty in adsorption isotherm data, regularization parameter, molecular potential model, and the number of single pore isotherms calculated with an associated quadrature interval. We demonstrate how the calculated pore size distribution is quite insensitive to the uncertainty in experimental data, but in contrast, the uncertainty in the experimental data affects the calculated value of the optimized regularization parameter which, in turn, leads to considerable variation in the calculated pore size distribution. The calculated pore size distribution is also shown to be highly dependent on the potential model selected and on the number of single pore isotherms applied to the inversion process. We conclude and suggest a quantitative comparison between calculated pore size distributions should be discouraged unless the uncertainty in the experimental data is relatively small and, default values for regularization parameters, potential models, the number of single pore isotherms and their distribution are exactly the same for each pore size distribution evaluation.

show abstract

“…To find this function the Fredholm integral equation of the first kind must be solved. To avoid distorted results the regularization method is employed (von Szombathely et al 1992;Heuchel et al 1993). It should be emphasized that the regularization method makes no assumption about the shape of the energy distribution functions.…”

Section: Calculation Of Adsorption Energy Distribution (Aed) Functionsmentioning

confidence: 99%

Heterogeneity of multiwalled carbon nanotubes based on adsorption of simple aromatic compounds from aqueous solutions

et al. 2014

View full text Add to dashboard Cite

The surface heterogeneity of multiwalled carbon nanotubes (MWCNTs) is studied on the basis of adsorption isotherms from dilute aqueous phenol and dopamine solutions at various pH values. The generalized Langmuir-Freundlich (GLF) isotherm equation was applied to investigate the cooperative effect of the surface heterogeneity and the lateral interactions between the adsorbates. The theoretical isosteric heats of adsorption were obtained assuming that the heat of adsorption profile reveals both the energetic heterogeneity of the adsorption system and the strength of the interactions between the neighboring molecules. The adsorption energy distribution (AED) functions were calculated by using algorithm based on a regularization method. The great advantage of this method is that the regularization makes no assumption about the shape of the obtained energy distribution functions. Analysis of the isosteric heats of adsorption for MWCNTs showed that the influence of the surface heterogeneity is much stronger than the role of the lateral interactions. The most typical adsorption heat is 20-22 kJ/mol for both phenol and dopamine. After purification of nanotubes, heat value for phenol dropped to 16-17 kJ/mol. The range of the energy distribution is only slightly influenced by the surface chemistry of the nanotubes in the aqueous conditions.

show abstract

The solution of adsorption integral equations by means of the regularization method

Cited by 230 publications

References 32 publications

Kinetics of the Adsorption of Copper and Lead Ions from Aqueous Solution on to WD-ekstra Activated Carbon

Kinetics of the Adsorption of Copper and Lead Ions from Aqueous Solution on to WD-ekstra Activated Carbon

Uncertainty in pore size distribution derived from adsorption isotherms: II. Adsorption integral approach

Heterogeneity of multiwalled carbon nanotubes based on adsorption of simple aromatic compounds from aqueous solutions

Contact Info

Product

Resources

About