Adsorption on a patchwise heterogeneous surface

Harris, Lee B.

doi:10.1016/0039-6028(69)90198-8

Cited by 61 publications

(7 citation statements)

References 11 publications

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“…To find f( E i ), a condensation approximation [34,35] was applied, replacing the true local isotherm by a step function, arriving at the final formula: f( E i ) = [(1- x i+1 )1/2 Θ( E i+1 ) - (1- x i )1/2 Θ( E i )]/( E i+1 - E i ), where E = -RTln( p 0 / p ).…”

Section: Methodsmentioning

confidence: 99%

Environmental-Friendly Modifications of Zeolite to Increase Its Sorption and Anion Exchange Properties, Physicochemical Studies of the Modified Materials

Cieśla

Franus

et al. 2019

Materials

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Zeolites, naturally possessing a high negative surface charge and large specific surface, are used in agriculture as cationic fertilizers, water holders, heavy metals, and organic pollutants sorbents. Since some nutrients occur in anionic forms, there is a need to modify the zeolite surface to hold anions. In this study, hydrogen (hydrochloric acid), iron (Fe2+ and Fe3+), and aluminum cations as well as the influence of sodium hydroxide modifiers on the specific surface area, water vapor, adsorption energy, fractal dimension, mesopore volumes and radii, electrokinetic (zeta) potential, and isoelectric point were investigated. The use of alkali solution did not affect the zeolite properties significantly, whereas hydrogen, iron, and treatments with aluminum cations resulted in an increase in the specific surface area, mesopore volumes, and radii, and a decrease in the water-binding forces. Aluminum cations were the most effective in recharging the zeolite surface from negative to positive, shifting the isoelectric point toward the highest values. Calcination enlarged the negative surface charge and mesopore radius, and diminished the surface area and mesopore volume. The modified zeolites are promising carriers of anionic nutrients, large surface area sorbents, and suppliers of water for plant roots in soil.

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Section: Methodsmentioning

confidence: 99%

Environmental-Friendly Modifications of Zeolite to Increase Its Sorption and Anion Exchange Properties, Physicochemical Studies of the Modified Materials

Cieśla

Franus

et al. 2019

Materials

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“…Cerofolini (6) however, obtained results by using the method based on "condensation approximation" (3)(4)(5). He showed that the iso-…”

mentioning

confidence: 96%

“…[4] and r5] the form of the distribution function X(s) depends on the parameter B, whereas the range of adsorption energy depends on the parameter p,,. Therefore, the method of determining the distribution function Z(e), proposed by Cerofolini (6) can be mostly limited by the fact that it can be only used to describe adsorbents with a distribution function X(e) showing one maximum.…”

mentioning

confidence: 99%

Determination of energy distribution function from observed adsorption isotherms

Jaroniec¹,

Rudziński²,

Sokołowski³

et al. 1975

Colloid Polymer Sci

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One of great unsolved problems of physical adsorption is the influence of heterogeneity on adsorptive properties of adsorption systems (1). Many theoretical procedures have been proposed in order to describe the heterogeneity effects (2-10). One of the most widely known and often used procedures is the integral representation for the overall adsorption isotherm Otwhere 01 is the local adsorption isotherm, )~(e) is the differential energy distribution, and Q is the range of possible variation of the adsorption energy e. The most interesting problem here is to solve the eq. [1] with respect to the function Z(e), when Ot and 01 are known as analytical expressions.Hobson and Armstron9 (11) were the first who investigated theoretically the Dubinin-Radushkievieh equation (D -R) as the overall adsorption isotherm. The D -R isotherm firstly proposed, and widely verified for porous adsorbents (12), has been found to hold for many non-porous adsorbents (metals, glasses) in the submonolayer range. The source of this success has been theoretically investigated by Hobson (13), Haul and Gottwald (14), Ricca, Medana and Bellardo (15), Sparnaay (8), and Marsh and Rand (16). Their results suggested that the D -R behaviour is due to a particular structure of the adsorbing surfaces.Most advanced theoretical results are due to Misra (9) and Cerofolini (6). Assuming that 01 corresponds to a Langmuir isotherm 0~(e,p)= 1 + --e x p ~-~[2] P they have pointed out though in different ways, that the D -R isotherm is related to special distribution Z (s), which is probably characteristic for the majority of heterogeneous adsorbents. Constant K is connected with the molecular partition function for molecules from the monolayer.These results has been obtained by Misra (9) by solving the Stieltjes transform, which is obtained from eq. [1], using the Langmuir isotherm for 01 (17) and by Heer (18) on the basic of statistical mechanics.Cerofolini ( Above B and Pm are two characteristic constants in the equation D-R. However, the energy s and the minimal adsorption energy s,. are given by the following relations P --.[5] e = -R T l n -~ and sm= RTIn K PmAs it appears from the eqs.[4] and r5] the form of the distribution function X(s) depends on the

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“…Using the patchwise model, the adsorption of monomers, dimers and linear k-mers on a square lattice with ''square-patches'' and ''strip'' topographies has been studied. [28][29][30][31][32][33][34][35][36][37][38][39][40][41] It is shown that the surface topography and the characteristic size of patches significantly affect the phase behavior of the adsorption layers. In particular, it is established that the presence or absence of long-range order and the type of phase transition are determined by the ratio between the absorption energy and size of the patches and strips.…”

Section: Introductionmentioning

confidence: 99%

“…[27][28][29][30] In this model, the surface is assumed to be composed of isotropic domains consisting of the same adsorption sites. Using the patchwise model, the adsorption of monomers, dimers and linear k-mers on a square lattice with ''square-patches'' and ''strip'' topographies has been studied.…”

Section: Introductionmentioning

confidence: 99%

Cross-impact of surface and interaction anisotropy in the self-assembly of organic adsorption monolayers: a Monte Carlo and transfer-matrix study

Горбунов

Akimenko

Myshlyavtsev

2017

Phys. Chem. Chem. Phys.

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abUsing a simple lattice gas model we study the features of self-assembly in adsorption layers where both ''molecule-surface'' and ''molecule-molecule'' interactions are anisotropic. Based on the example of adsorption layers of mono-functional organic molecules on the heterogeneous surface with strip-like topography, we have revealed plenty of possible self-assembled structures in this simple system, such as discrete, linear, zigzag, chess board-like, two-dimensional porous and close-packed patterns. However, the phase behavior of the adsorption layer is much richer, if the interactions between functional and non-functional parts of adjacent adsorbed molecules have comparable strength and opposite signs. It is demonstrated that filling of the strips composed of relatively ''strong'' adsorption sites with the increase of chemical potential can be non-monotonic. This effect is associated with surface anisotropy and results from the changing of the driving force of the self-assembly process -interactions between the adsorbed molecule and the surface dominate at low surface coverages, but intermolecular forces prevail at higher ones. Additionally, when the width of the strip composed of ''strong'' adsorption sites is two or more times greater than that of the adsorbed molecule, a local assembly of the ordered phases on the ''strong'' adsorption sites is observed. Our results suggest strategies for controlling the self-assembly in experiments involving mono-functional organic molecules on a strip-like heterogeneous surface.

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Adsorption on a patchwise heterogeneous surface

Cited by 61 publications

References 11 publications

Environmental-Friendly Modifications of Zeolite to Increase Its Sorption and Anion Exchange Properties, Physicochemical Studies of the Modified Materials

Environmental-Friendly Modifications of Zeolite to Increase Its Sorption and Anion Exchange Properties, Physicochemical Studies of the Modified Materials

Determination of energy distribution function from observed adsorption isotherms

Cross-impact of surface and interaction anisotropy in the self-assembly of organic adsorption monolayers: a Monte Carlo and transfer-matrix study

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