BASIC CONCEPTS AND AN OVERVIEW - Foundations of Nanotechnology: Pore Size in Carbon-Based Nano-Adsorbents - page 89

properties that such equations is commonly used for description of gas and vapor
adsorption on microporous active carbons.
A more general expression is that proposed by Dubinin and Astakhov, which
is known as the DA equation: a mi :

n

� A �

0

-

aa = exp − €

‚

mi mi

(57)

b

ƒ E „

-

0

In Eqs. (55), (56) and (57) a mi represents the amount adsorbed in micropores at
relative pressure p/p o and temperature T, is the limiting volume of adsorption
or the volume of micropores and Vm is the molar volume of the adsorbate. The
specific parameters of Eqs. (55) and (56) are and n, respectively, where E o is the
characteristic energy of adsorption for the reference vapor, usually benzene. Du-
binin proposed to extract the amount ami adsorbed in micropores from the total
adsorbed amount a(p/p o ) as follows:

=− g

(58)

a aS

mi me s

The amount adsorbed per unit surface area was evaluated from the adsorption
isotherm measured on a reference adsorbent, whereas the specific surface area
Sine of mesopores was estimated from the adsorption isotherm. To analyze ni-
trogen adsorption isotherms by means of the DR and DA equations, we extracted
according to Eq. (58) the adsorption isotherm a mi (p/p o ) for micropores from the
total adsorption isotherm a(p/p o ). To calculate a mi according to Eq. (58), we evalu-
atedfrom the standard nitrogen isotherm at 77°Kshown by the -plot method. The
extracted adsorption isotherm was described by DR equation (the Eq. (55)) and
also by DAequation (the Eq. 56)[1, 19, 126].

1.2.2.10 DFT-NLDFT MODELS BASE ON KERNELS OF
EXPERIMENTAL ADSORPTION ISOTHERM DATA
The PSD is calculated from the experimental adsorption isotherm with (P/P 0 ) by
solving the integral adsorption equation:

D

max

( ) ( )

( )

= ∫ N PP / N PPDfDdD /,

(59) exp 0 QSDFT 0

D

min

The experimental isotherm is represented as the convolution of the DFT kernel
(set of the theoretical isotherms NQSDFT(P/P 0 ,D)in a series of pores within a
given range of pore sizes D) and the unknown PSD function f (D), where D min
and D max are the minimum and maximum pore sizes in the kernel, respectively.
Two kernels of the selected DFT adsorption isotherms for the slit geometry are
reviewed, include NLDFT and QSDFT. In contrast to the NLDFT kernels, the
QSDFT isotherms are smooth prior to the capillary condensation step, which is
characteristic of mesopores (D > 2 nm), and thus do not exhibit stepwise inflections