Theoretical basis for the DubininRadushkevitch (DR) adsorption isotherm equation
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DOI: 10.1007/BF01650130
 Cite this article as:
 Hutson, N.D. & Yang, R.T. Adsorption (1997) 3: 189. doi:10.1007/BF01650130
Abstract
The DubininRadushkevitch (DR) equation, which was originally proposed as an empirical adaptation The Polanyi adsorption potential theory, has been the fundamental equation to quantitatively describe the adsorption gases and vapors by microporous sorbents. The equation, based on the postulate that the mechanism for adsorption in micropores is that of porefilling rather than layerbylayer surface coverage, generally applies well to adsorption systems involving only van der Waals forces and is especially useful to describe adsorption on activated ???. The ability of the DR equation to describe gas adsorption on porous materials has inspired many to undertake studies, both experimental and theoretical, to explain the source of the success of the DR equation in ??? of molecular properties at the gassolid interface. In many cases, these studies have led to extensions or modifications of the original DR equation. Many of these attempts and the resulting extensions are reviewed and discussed here. Recently, an isotherm equation was derived for adsorption of gases and vapors on microporous ??? from statistical mechanical principles. It was shown that the DR equation is an approximated form of this potential theory isotherm. This development is also reviewed and discussed.
Keywords
DubininRadushkevitch equation DubininAstakhov equation adsorption micropore adsorptionNomenclature
 A

adsorption potential; differential molar work of adsorption; Helmholtz free energy
 B

parameter in DR. DA equations, related toE _{0}
 B _{0}

value of the parameterB for the minimum of the micropore distribution curve in the DRS equation
 E

characteristic energy of adsorption; energy
 E _{0}

characteristics energy of adsorption for standard vapor
 g(E)

energy distribution function
 G(x)

micropore size distribution
 h

Planck's constant
 k

Boltzmann's constant
 K

constant from approximation, Eq. (41)
 m

molecular weight
 n

parameter in DA equation
 N

number of molecules in the system
 N _{0}

Avogadro's number
 P

pressure
 P _{ m }

condensation pressure
 P ^{0}

saturated vapor pressure
 q

parameter of the Gamma micropore distribution
 q _{ c }

parameter of the Gamma micropore distribution for a reference vapor
 q _{ r }

rotational partition function
 q _{ v }

vibrational partition function
 R

gas constant
 r _{ k }

position coordinate of molecule “k”
 T

temperature
 U(r _{ u })

potential energy between moleculesi andj
 V ^{ s }

surface area
 W

volume of micropores filled at relative pressureP/P ^{0}
 W _{0}

total volume of micropore system
 x

halfwidth of slit pore
 X

empirical constant relating characteristic energy to pore size
 Z _{ N } ^{ s }

partition function of the canonical ensemble
Greek etc. Symbols
 α(T)

a function of temperature in Eq. (35)
 β

similarity coefficient
 Δ

dispersion (or variance)
 ΔG _{ads}

differential free energy of adsorption
 ε

energy
 ε_{0}

minimum adsorption energy
 η

packing fraction of the surface
 η _{0}

packing fraction of the surface atP =P ^{0}
 γ

l/kT
 Γ

gamma function
 λ

number of dimension
 Λ

de Broglie thermal wavelength
 ϕ

potential energy function
 ρ ^{ N }

number density of the solid phase
 ρ ^{ g }

number of density of the gas phase
 θ

fractional coverage (=W/W _{0})
 θ _{1}

overall isotherm for microporous system
 θ _{1}

local isotherm for microporous system
 χ(ε)

energy distribution