Page 70 - Adsorbents fundamentals and applications

HORV ´ ATH–KAWAZOE APPROACH 55

hypothesis, all the pores with radii smaller than that size become filled at that
pressure. Consequently one can obtain the cumulative pore volume as a function
of pressure. The cumulative pore volume is obtained by assuming that the pores
are filled by liquid, or q/ρ,where ρ is the liquid density. The pore size distribution
is then obtained by taking the derivative of the cumulative pore volume as a
function of pore radius.
N 2 isotherms at 77 K are used for practical reasons (e.g., simultaneous deter-
mination of the BET surface area). The use of the Kelvin equation was a popular
approach for estimating the pore size distribution. Many procedures were pro-
posed for calculating the pore size distribution from the N 2 isotherms over the
period between 1945 and 1970 (Rouquerol et al., 1999). The method proposed
by Barrett, Joyner, and Halenda (1951), known as the BJH method, continues to
be used today. In the BJH method, the desorption branch of the isotherm is used,
which is the desorption branch of the usual hysteresis loop of the isotherm for
the mesoporous sorbent. The underlying assumptions for this method are

(a) All pores are non-intersecting, cylindrical pores.
(b) Hemispherical meniscus with zero contact angle, or complete wetting.
(c) The simple Kelvin equation is applied.
(d) Validity of the correction for multilayer adsorption.

Many questions have been raised concerning the validity of the Kelvin equa-
tion, in particular, the lower limit of the pore size that one could use with this
approach. Clearly, this method does not apply when the pore size approaches
molecular dimensions, or a few molecular sizes. Molecular simulations by Jes-
sop et al. (1991) showed that the Kelvin equation fails to account for the effects
of fluid-wall interactions. The density functional theory study of Lastoskie et al.
(1993), as well as other work, indicated that the Kelvin equation would underes-
timate the pore size and should not be extended below a pore size of ∼7.5nm.

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4.2. HORVATH–KAWAZOE APPROACH
A simple and popular method for evaluating PSD of microporous materials was
proposed by Horv´ ath and Kawazoe (1983). This technique has been success-
fully used for the determination of pore size distribution in microporous sorbents
such as activated carbons and zeolites (e.g., Seifert and Emig, 1987; Venero
and Chiou, 1988; Davis et al., 1988, 1989; Beck et al., 1992; Horv´ ath et al.,
1998, Kane et al., 1998). This technique utilizes adsorption isotherm data at a
temperature below or equal to the critical temperature of the adsorbate, which is
typically nitrogen (at 77 K), argon (at 87 K), or an organic vapor (e.g., CH 3 Cl) at
ambient temperature (Mariwala and Foley, 1994). By assuming micropore-filling
and equating the free-energy change upon adsorption to the average interaction
energy of the adsorbing molecules, the “step” in the isotherm data is translated
into a pore-size distribution. The model assumes that entropic effects are negligi-
ble for small adsorbate molecules and that networking effects are insignificant if