Adsorption on a patchwise heterogeneous surface; mathematical analysis of the step-function approximation to the local isotherm

Harris, Lee B.

doi:10.1016/0039-6028(68)90015-0

Cited by 121 publications

(22 citation statements)

References 6 publications

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“…Small variation in experimental data caused by heterogeneity of the samples and detections capabilities of the balance leads to large variation in estimation of site fractions. Therefore, a condensation approximation CA was inserted (Harris, 1968). This method is based on the replacement of the local isotherm by a step-function.…”

Section: Surface Propertiesmentioning

confidence: 99%

Filter properties of seam material from paved urban soils

Nehls¹,

Józefaciuk

Sokołowska

et al. 2008

Hydrol. Earth Syst. Sci.

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Abstract.Depositions of all kinds of urban dirt and dust including anthropogenic organic substances like soot change the filter properties of the seam filling material of pervious pavements and lead to the formation of a new soil substrate called seam material.In this study, the impact of the particular urban form of organic matter (OM) on the seam materials CEC pot , the specific surface area (A s ), the surface charge density (SCD), the adsorption energies (E a ) and the adsorption of Cd and P b were assessed. The Cd and P b displacement through the pavement system has been simulated in order to assess the risk of soil and groundwater contamination from infiltration of rainwater in paved urban soils.A s , E a and SCD derived from water vapor adsorption isotherms, CEC pot , P b and Cd adsorption isotherms where analyzed from adsorption experiments. The seam material is characterized by a darker munsell-color and a higher C org (12 to 48 g kg −1 ) compared to the original seam filling. Although, the increased C org leads to higher A s (16 m 2 g −1 ) and higher CEC pot (0.7 to 4.8 cmol c kg −1 ), with 78 cmol c kg −1 C its specific CEC pot is low compared to OM of non-urban soils. This can be explained by a low SCD of 1.2×10 −6 mol c m −2 and a low fraction of high adsorption energy sites which is likely caused by the non-polar character of the accumulated urban OM in the seam material.The seam material shows stronger sorption of P b and Cd compared to the original construction sand. The retardation capacity of seam material for P b is similar, for Cd it is much smaller compared to natural sandy soils with similar C org concentrations. The simulated long term displacement scenarios for a street in Berlin do not indicate an acute contamination risk for P b. For Cd the infiltration from puddles can lead to a breakthrough of Cd through the pavement sysCorrespondence to: T. Nehls (thomas.nehls@tu-berlin.de) tem during only one decade. Although they contain contaminations itself, the accumulated forms of urban OM lead to improved filter properties of the seam material and may retard contaminations more effectively than the originally used construction sand.

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Section: Surface Propertiesmentioning

confidence: 99%

Filter properties of seam material from paved urban soils

Nehls¹,

Józefaciuk

Sokołowska

et al. 2008

Hydrol. Earth Syst. Sci.

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“…Thus, relating the computed values of e and" q, by means of a law of kind [9] by a least square procedure we can get an independent determination of 51 and 52.…”

Section: Cerofolini Et Al a Theoretical Isotherm For Adsorption On mentioning

confidence: 99%

“…Symbols in [1] and [2] have the following meaning: p, pressure; 0, overall coverage; kB, Boltzmann constant; T, absolute temperature; TF, a characteristic temperature (usually T¢ > T); pro, a pressure, characteristic of the surface-adsorbate pair; B, a suitable parameter. The adsorption-energy distributions, computed with the condensation approximation (9) and leading to [1] and [2] Colloid and Polymer Science, Vol. 256 • No.…”

Section: Odr(p) = {~Xp{ --B[kbtln(p/pm)] 2}mentioning

confidence: 99%

A theoretical isotherm for adsorption on heterogeneous surface

Cerofolini

Jaroniec²,

Sokołosvski³

1978

Colloid Polymer Sci

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“…The problem of finding the overall isotherm which in the condensation approximation originates the adsorption-energy distribution (17) is solved by recalling (5) and (6): Pm<P which obviously satisfies requirement (9) if B is identified with 1/kBTvx o = o~2/kBT f. Owing to the fact that the condensation approximation becomes effective at low temperature, expression (19) tends to become exact when the adsorption temperature tends to 0 K. We wish to stress that if we go away in the development (14) instead of stopping at the second power we obtain the adsorption-energy distribution (18) whose corresponding overall isotherm in the condensation approximation is the "exponential isotherm" proposed by Jaroniec et al 25 and for which a statistico-mechanical derivation has been found by Jaroniec z6 according to the ideas of Heer. 27 We remember, however, a fundamental difference between the approach by Jaroniec et al and the present one : there, the parameters ~-a, c~2 .... contained in the exponential isotherm are completely free and to be chosen with a best fit procedure ; here, the same parameters have a meaning specified by (14) and can be evaluated numerically with ab initio calculations.…”

Section: The Overall Isotherm In the Condensation Approximationmentioning

confidence: 99%

The theory of physisorption on real solid surfaces

Cerofolini¹

1976

J Low Temp Phys

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A theory is developed to explain the rather simple phenomenology of submonolayer adsorption on real solid surfaces in spite of the hazy situation characterizing the theoretical description of adsorption on ideal homogeneous surfaces. The situation is atypical : we cannot invoke the knowledge of the local behavior to explain the overall behavior. The new situation requires a quite new methodology. The main results of the present work consist in showing that the Freundlich and the Dubinin-Radushkevich adsorption isotherms are due to an equilibrium structure of adsorbing surfaces, this structure being that of equilibrium at their formation temperature.

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Adsorption on a patchwise heterogeneous surface; mathematical analysis of the step-function approximation to the local isotherm

Cited by 121 publications

References 6 publications

Filter properties of seam material from paved urban soils

Filter properties of seam material from paved urban soils

A theoretical isotherm for adsorption on heterogeneous surface

The theory of physisorption on real solid surfaces

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