Adsorption

, Volume 3, Issue 3, pp 189–195 | Cite as

Theoretical basis for the Dubinin-Radushkevitch (D-R) adsorption isotherm equation

  • Nick D. Hutson
  • Ralph T. Yang
Article

Abstract

The Dubinin-Radushkevitch (D-R) 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 pore-filling rather than layer-by-layer 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 D-R 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 D-R equation in ??? of molecular properties at the gas-solid interface. In many cases, these studies have led to extensions or modifications of the original D-R 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 D-R equation is an approximated form of this potential theory isotherm. This development is also reviewed and discussed.

Keywords

Dubinin-Radushkevitch equation Dubinin-Astakhov equation adsorption micropore adsorption 

Nomenclature

A

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

B

parameter in D-R. D-A equations, related toE0

B0

value of the parameterB for the minimum of the micropore distribution curve in the D-R-S equation

E

characteristic energy of adsorption; energy

E0

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 D-A equation

N

number of molecules in the system

N0

Avogadro's number

P

pressure

Pm

condensation pressure

P0

saturated vapor pressure

q

parameter of the Gamma micropore distribution

qc

parameter of the Gamma micropore distribution for a reference vapor

qr

rotational partition function

qv

vibrational partition function

R

gas constant

rk

position coordinate of molecule “k

T

temperature

U(ru)

potential energy between moleculesi andj

Vs

surface area

W

volume of micropores filled at relative pressureP/P0

W0

total volume of micropore system

x

half-width of slit pore

X

empirical constant relating characteristic energy to pore size

ZNs

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)

ΔGads

differential free energy of adsorption

ε

energy

ε0

minimum adsorption energy

η

packing fraction of the surface

η0

packing fraction of the surface atP =P0

γ

l/kT

Γ

gamma function

λ

number of dimension

Λ

de Broglie thermal wavelength

ϕ

potential energy function

ρN

number density of the solid phase

ρg

number of density of the gas phase

θ

fractional coverage (=W/W0)

θ1

overall isotherm for microporous system

θ1

local isotherm for microporous system

χ(ε)

energy distribution

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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Nick D. Hutson
    • 1
  • Ralph T. Yang
    • 1
  1. 1.Department of Chemical EngineeringUniversity of MichiganAnn Arbor

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