A Freundlich-type multicomponent isotherm

Sheindorf, C.; Rebhun, M.; Sheintuch, Moshe

doi:10.1016/0021-9797(81)90056-4

Cited by 335 publications

(165 citation statements)

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“…Multi-component Langmuir [29] and Freundlich [30] isotherms were applied to elaborate dual metal tests results.…”

Section: Equilibrium Isothermsmentioning

confidence: 99%

“…The theoretical maximum sorption capacity for sorbate "i", q max,i (mmol g −1 ), and the Langmuir equilibrium constants for sorbates "i" and "j", K L,i and K L,j (L mmol −1 ), were taken from previous work performed on single-component systems, carried out under the same conditions as this one [13]. The multi-component Freundlich model proposed by Sheindorf et al [30], assuming that each component individually obeys the Freundlich isotherm, is given as:…”

Section: Equilibrium Isothermsmentioning

confidence: 99%

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Metal biosorption onto dry biomass of Arthrospira (Spirulina) platensis and Chlorella vulgaris: Multi-metal systems

Rodrigues

Ferreira

Carvalho

et al. 2012

Journal of Hazardous Materials

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“…Multi-component Langmuir [29] and Freundlich [30] isotherms were applied to elaborate dual metal tests results.…”

Section: Equilibrium Isothermsmentioning

confidence: 99%

Section: Equilibrium Isothermsmentioning

confidence: 99%

Metal biosorption onto dry biomass of Arthrospira (Spirulina) platensis and Chlorella vulgaris: Multi-metal systems

Rodrigues

Ferreira

Carvalho

et al. 2012

Journal of Hazardous Materials

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“…11) Note that contrary to the equation of Sheindorf et al (year), Fritz-Schundler equations predict the possibility of the competition even when single-species isotherms are linear. Roy et al (1986) applied a multicomponent Freundlichtype equation, the Sheindorf-Rebhun-Sheintuch (SRS) equation (Sheindorf et al, 1981), to the adsorption of binary-solute mixtures containing arsenate-phosphate, and arsenate-molybdate. The associated competitive coefficient for each solute-soil system was viewed as a measurement of the relative affinity each soil has for a particular anion from an anionic mixture.…”

Section: Introductionmentioning

confidence: 99%

“…The associated competitive coefficient for each solute-soil system was viewed as a measurement of the relative affinity each soil has for a particular anion from an anionic mixture. Their expression of a competitive adsorption coefficient can be written for the adsorption of solute 1 from a binary mixture as and the a ij term is defined as a competitive coefficient by Sheindorf et al (1981). where aij = (Bi/Cj)-Ci/Cj , (Eq.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Models of Competitive Adsorption of Inorganic Anions in Soils

Lee¹,

Lee²,

Lee³

et al. 2015

Korean Journal of Soil Science and Fertilizer

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Competition among anion species in solution for same sorption sites and soil surface can be of major significance in determining the effective mobility of any potentially adsorbing species. HAsO 4 2-. Pesticides such as 2,4,5-T and 2,4-D also exist as anions. Many anion species are retained by more complex mechanisms than the simple electrostatic attractions involved in most cation adsorption reactions. In binary system composed of two anions, the adsorption of one anion is influenced by the other anion due to the competition for the available and limited binding sites in soil constituents. The specifically adsorbed anions may compete more effectively for sorption sites than that of nonspecifically adsorbed anion. In this study, we aim to evaluate the mathematical models to determine the magnitude of concentration variations in adsorption due to competitive interactions between anions introduced to a system in binary mixtures.

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“…4,5 For systems that exhibit nonlinear increases in adsorption with solute concentration, several mathematical formulas can describe the adsorption process. Examples of nonlinear isotherms include Freundlich, 6 Dubinin-Ashtakov, 7,8,9 Tempkin, 10 Volmer, 11 Sips, 12 Fowler-Guggenheim, 13,14 Frumkin-Damskin, 15 RedlichPeterson, 16 Toth, 17 Levan-Vermeulen, 18 Vacancy Solute Theory, 19 Radke-Prausnitz, 20 Sigmoidal, 21 General Adsorption Theory, 22 Langmuir-Freundlich, 23 Margules, FowlerGuggenheim/Langmuir-Freundlich, 24 Fowler-Guggenheim/Jovanovic-Freundlich, 25 Jaroniec, 26,24 Ideal Adsorbed Solute Theory, 27,28,29 and Sheindorf-Rebuhn-Sheintuch 30 (see Appendix A). It is important to note that successfully fitting isotherms to adsorption data does not, in general, provide information about the mechanism of sorption.…”

Section: Introductionmentioning

confidence: 99%

Sorption Modeling of Strontium, Plutonium, Uranium, and Neptunium Adsorption on Monosodium Titanate

Fondeur

Hobbs

Fink

et al. 2005

Separation Science and Technology

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We examined the ability of various equilibrium isotherms to replicate the available data for the adsorption of strontium (Sr), plutonium (Pu), uranium (U) and neptunium (Np) on monosodium titanate (MST) during the treatment of simulated and actual Savannah River Site high-level waste. The data comes from numerous experimental studies conducted between 1999 and 2002. The analysis considered 29 isotherm models from the literature. As part of this study, we developed a general method for selecting the best isotherm models. The selection criteria for rating the isotherms considered the relative error in predicting the experimental data, the complexity of the mathematical expressions, the thermodynamic validity of the expressions, and statistical significance for the expressions.The Fowler Guggenheim-Jovanovic Freundlich (FG-JF), the Fowler GuggenheimLangmuir Freundlich (FG-LF) and the Dubinin-Astashov (DA) models each reliably predicted the actinide and strontium adsorption on MST. The first two models describe the adsorption process by single layer formation and lateral interactions between adsorbed sorbates while the Dubinin-Astashov model assumes volume filling of micropores (by osmotic pressure difference). These two mechanisms include mutually exclusive assumptions. However, we can not determine which model best represents the various adsorption mechanisms on MST. Based on our analysis, the DA model predicted the data well. The DA model assumes that an initial sorption layer forms after which networking begins in the pore spaces, filling the volume by a second mechanism. If this mechanism occurs in MST, as the experimental data suggests, then we expect all the empty and closed spaces of MST to contain actinides and strontium when saturated. Prior microstructure analyses determined that the MST surface is best described as heterogeneous (i.e., a semi-crystalline outer layer on an amorphous core) or composite material for adsorption. Therefore, we expect the empty spaces (of nanometer size) between the crystalline units in the fibrous material to provide sorption area for the actinides and strontium. Additional conclusions from this study follow.Since each of the three models work reliably, we recommend use of the computationally simplest model as the primary tool until future work can differentiate between the two mechanisms. The Dubinin-Astashov model possesses a simpler mathematical form with fewer parameters and operations. WSRC-TR-2003-00180Page 5 of 66The experimental data for actual and simulated wastes generally showed consistent agreement. However, the data sets do include considerable variance from a number of causes including the following.• The plutonium sorption data appears most consistent (e.g., between actual and simulated waste) and most easily predicted. Since plutonium removal efficiency proves most important for the process design efforts, this consistency of the data proves especially beneficial.• Extremely high mass loadings of uranium on MST result in multilayer sorption behavior an...

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A Freundlich-type multicomponent isotherm

Cited by 335 publications

References 2 publications

Metal biosorption onto dry biomass of Arthrospira (Spirulina) platensis and Chlorella vulgaris: Multi-metal systems

Metal biosorption onto dry biomass of Arthrospira (Spirulina) platensis and Chlorella vulgaris: Multi-metal systems

Mathematical Models of Competitive Adsorption of Inorganic Anions in Soils

Sorption Modeling of Strontium, Plutonium, Uranium, and Neptunium Adsorption on Monosodium Titanate

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