Separation of the first adsorbed layer from others and calculation of the BET compatible surface area from type II isotherms

József Tóth, F. Berger, I. Dékány

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8 Citations (Scopus)

Abstract

In the previous paper it has been proven that a BET compatible specific surface area, a(c)/(s)(N2, 77), can be calculated from any Type I isotherm measured below the critical temperature. In this paper it is proven that the same calculation can be performed from any Type II isotherms if the isotherm has a pure monolayer domain. In order to distinguish the mono- and multilayer adsorption the relative free energy of the surface as a function of the adsorbed amount, π(r)(n(s)), and the functions ψ(p(r)) and ψ(n(s)) are applied, both defined by the differential expression (n(s)/p(r))(dp(r)/dn(s)). When the multilayer adsorption becomes the dominant process then the function π(r)(n(s)) has a point of inflexion and functions ψ(p(r)) and ψ(n(s)) have maximum values. It has been demonstrated that in most of the Type II isotherms the mono- and multilayer domains can be separated, so the monolayer component isotherm can be calculated by the T (Toth) equation. Therefore, it is possible to calculate the BET compatible specific surface area discussed in detail in the previous paper. It has also been proven that there are Type II isotherms which describe only multilayer adsorption; i.e., the functions ψ(p(r)) and ψ(n(s)) do not have maximum values. In these cases the Harkins-Jura equation should be applied.

Original languageEnglish
Pages (from-to)411-418
Number of pages8
JournalJournal of Colloid and Interface Science
Volume212
Issue number2
DOIs
Publication statusPublished - Apr 15 1999

Fingerprint

Isotherms
isotherms
Monolayers
Multilayers
Adsorption
Specific surface area
adsorption
Free energy
critical temperature
free energy
Temperature

Keywords

  • BET compatible surface area
  • Harkins-Jura equation
  • Mono- and multilayer domains
  • Separation of those
  • T equation
  • Type II isotherms

ASJC Scopus subject areas

  • Colloid and Surface Chemistry
  • Physical and Theoretical Chemistry
  • Surfaces and Interfaces

Cite this

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title = "Separation of the first adsorbed layer from others and calculation of the BET compatible surface area from type II isotherms",
abstract = "In the previous paper it has been proven that a BET compatible specific surface area, a(c)/(s)(N2, 77), can be calculated from any Type I isotherm measured below the critical temperature. In this paper it is proven that the same calculation can be performed from any Type II isotherms if the isotherm has a pure monolayer domain. In order to distinguish the mono- and multilayer adsorption the relative free energy of the surface as a function of the adsorbed amount, π(r)(n(s)), and the functions ψ(p(r)) and ψ(n(s)) are applied, both defined by the differential expression (n(s)/p(r))(dp(r)/dn(s)). When the multilayer adsorption becomes the dominant process then the function π(r)(n(s)) has a point of inflexion and functions ψ(p(r)) and ψ(n(s)) have maximum values. It has been demonstrated that in most of the Type II isotherms the mono- and multilayer domains can be separated, so the monolayer component isotherm can be calculated by the T (Toth) equation. Therefore, it is possible to calculate the BET compatible specific surface area discussed in detail in the previous paper. It has also been proven that there are Type II isotherms which describe only multilayer adsorption; i.e., the functions ψ(p(r)) and ψ(n(s)) do not have maximum values. In these cases the Harkins-Jura equation should be applied.",
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T1 - Separation of the first adsorbed layer from others and calculation of the BET compatible surface area from type II isotherms

AU - Tóth, József

AU - Berger, F.

AU - Dékány, I.

PY - 1999/4/15

Y1 - 1999/4/15

N2 - In the previous paper it has been proven that a BET compatible specific surface area, a(c)/(s)(N2, 77), can be calculated from any Type I isotherm measured below the critical temperature. In this paper it is proven that the same calculation can be performed from any Type II isotherms if the isotherm has a pure monolayer domain. In order to distinguish the mono- and multilayer adsorption the relative free energy of the surface as a function of the adsorbed amount, π(r)(n(s)), and the functions ψ(p(r)) and ψ(n(s)) are applied, both defined by the differential expression (n(s)/p(r))(dp(r)/dn(s)). When the multilayer adsorption becomes the dominant process then the function π(r)(n(s)) has a point of inflexion and functions ψ(p(r)) and ψ(n(s)) have maximum values. It has been demonstrated that in most of the Type II isotherms the mono- and multilayer domains can be separated, so the monolayer component isotherm can be calculated by the T (Toth) equation. Therefore, it is possible to calculate the BET compatible specific surface area discussed in detail in the previous paper. It has also been proven that there are Type II isotherms which describe only multilayer adsorption; i.e., the functions ψ(p(r)) and ψ(n(s)) do not have maximum values. In these cases the Harkins-Jura equation should be applied.

AB - In the previous paper it has been proven that a BET compatible specific surface area, a(c)/(s)(N2, 77), can be calculated from any Type I isotherm measured below the critical temperature. In this paper it is proven that the same calculation can be performed from any Type II isotherms if the isotherm has a pure monolayer domain. In order to distinguish the mono- and multilayer adsorption the relative free energy of the surface as a function of the adsorbed amount, π(r)(n(s)), and the functions ψ(p(r)) and ψ(n(s)) are applied, both defined by the differential expression (n(s)/p(r))(dp(r)/dn(s)). When the multilayer adsorption becomes the dominant process then the function π(r)(n(s)) has a point of inflexion and functions ψ(p(r)) and ψ(n(s)) have maximum values. It has been demonstrated that in most of the Type II isotherms the mono- and multilayer domains can be separated, so the monolayer component isotherm can be calculated by the T (Toth) equation. Therefore, it is possible to calculate the BET compatible specific surface area discussed in detail in the previous paper. It has also been proven that there are Type II isotherms which describe only multilayer adsorption; i.e., the functions ψ(p(r)) and ψ(n(s)) do not have maximum values. In these cases the Harkins-Jura equation should be applied.

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