Page 69 - Adsorbents fundamentals and applications

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PORE SIZE DISTRIBUTION

According to the IUPAC classification of pores, the size ranges are micropores
(<2 nm), mesopores (2–50 nm), and macropores (>50 nm) (IUPAC, 1972). All
useful sorbents have micropores. The quantitative estimation of pore size dis-
tribution (PSD), particularly for the micropores, is a crucial problem in the
characterization of sorbents. Numerous methods exist, of which three main meth-
ods will be described: Kelvin equation (and the BJH method), Horv´ ath–Kawazoe
approach, and the integral equation approach.

4.1. THE KELVIN EQUATION
The vapor pressure (P ) of a liquid over a meniscus that stretches across a cylindri-
cal pore is given by (Adamson and Gast, 1997; Gregg and Sing, 1982; Rouquerol
et al., 1999):
P 2γV
ln =− (4.1)
P 0 rRT
Here P 0 is the saturated vapor pressure at absolute temperature T , γ is the surface
tension, V is the molar volume of the liquid, r is the radius of the cylindrical
pore, and R is the gas constant.
The Kelvin equation is used to interpret type IV isotherms, which are the
general isotherms for adsorption on mesoporous materials (Gregg and Sing, 1982;
Yang, 1987). This equation applies to the range of the isotherm that corresponds to
capillary condensation, that is, the section of the isotherm above the first “knee.”
Using the Kelvin equation, one can calculate the value of the pore radius for
any point on the isotherm. That is, for any set of (q, P/P 0 ) along the isotherm,
there is a corresponding pore radius. According to the capillary condensation

Adsorbents: Fundamentals and Applications, Edited By Ralph T. Yang
ISBN 0-471-29741-0 Copyright  2003 John Wiley & Sons, Inc.

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