properties, physical fundaments of the models, choice of the suitable isotherm
branch, and kernel availability, among others.
3.1 Specific Surface Area
The Brunauer-Emmett-Teller (BET) method is the most widely used procedure to
calculate the specific surface area of porous materials, despite its limitations
[7, 28]. The BET equation (Eq. 1) represents how is the increasing of the adsorbed
thickness in function of p/p
o where the mono-multilayer is formed. From the
adsorption isotherms data (amount adsorbed, n ads , versus p/p
o ), and using the
Eq. 1, obtaining a plot of points within a pressure region defined by the BET
model (BET-plot). By a linear fitting of these points, it is possible to obtain both
the monolayer capacity (n m ) and the C constant (exponentially related to the energy
of monolayer adsorption, then C > 0).
p = p
n ads  1 À p = p
À
Á¼
1
n m  C
þ
C À 1
n m  C
 p = p
À Á
ð1Þ
From the monolayer capacity per gram of adsorbent (n m ), the area occupied by
the adsorbate molecule in the complete monolayer, σ m (molecular cross-sectional
area), and the Avogadro constant (N ), the specific surface area (S BET ) is obtained
(Eq. 2).
S BET ¼ n m  N  σ m
ð2Þ
The linear behavior of this model corresponds to the region of relative pressures
that starts when the micropores filling is finishing, continues with the monomultilayer formation, and ending before the capillary condensation begins. In the
validity region of the BET equation, the adsorption isotherm presents a knee
followed by a linear increasing, where the called Point B, corresponding to the
completion of monolayer coverage, is within that zone (the location of Point B
depends on the isotherm Type). The C value gives a useful indication of the
isotherms shape in the BET range; if C ~ 80 the knee of the isotherm is sharp and
Point B is fairly well-defined, for C < 50, the Point B cannot be identified as a single
point and the estimation of the n m is not precise; a high C value (>150) is generally
associated with either adsorption on high energy surface sites or the filling of narrow
micropores [7], and when this value increases, the BET range moves to lower
relative pressures. Hudec et al. [40] studying the sensitivity of the C value for
micro- mesoporous materials concluded that extremely high values (C > 2,000)
have no physical meanings to associate it with the energy of adsorbate-adsorbent
interaction in the BET model. In the case of materials without or with a small amount
of micropores, where the “knee” of the isotherm is well defined (C ~ 80), the S BET
40
J. Villarroel-Rocha et al.
branch, and kernel availability, among others.
3.1 Specific Surface Area
The Brunauer-Emmett-Teller (BET) method is the most widely used procedure to
calculate the specific surface area of porous materials, despite its limitations
[7, 28]. The BET equation (Eq. 1) represents how is the increasing of the adsorbed
thickness in function of p/p
o where the mono-multilayer is formed. From the
adsorption isotherms data (amount adsorbed, n ads , versus p/p
o ), and using the
Eq. 1, obtaining a plot of points within a pressure region defined by the BET
model (BET-plot). By a linear fitting of these points, it is possible to obtain both
the monolayer capacity (n m ) and the C constant (exponentially related to the energy
of monolayer adsorption, then C > 0).
p = p
n ads  1 À p = p
À
Á¼
1
n m  C
þ
C À 1
n m  C
 p = p
À Á
ð1Þ
From the monolayer capacity per gram of adsorbent (n m ), the area occupied by
the adsorbate molecule in the complete monolayer, σ m (molecular cross-sectional
area), and the Avogadro constant (N ), the specific surface area (S BET ) is obtained
(Eq. 2).
S BET ¼ n m  N  σ m
ð2Þ
The linear behavior of this model corresponds to the region of relative pressures
that starts when the micropores filling is finishing, continues with the monomultilayer formation, and ending before the capillary condensation begins. In the
validity region of the BET equation, the adsorption isotherm presents a knee
followed by a linear increasing, where the called Point B, corresponding to the
completion of monolayer coverage, is within that zone (the location of Point B
depends on the isotherm Type). The C value gives a useful indication of the
isotherms shape in the BET range; if C ~ 80 the knee of the isotherm is sharp and
Point B is fairly well-defined, for C < 50, the Point B cannot be identified as a single
point and the estimation of the n m is not precise; a high C value (>150) is generally
associated with either adsorption on high energy surface sites or the filling of narrow
micropores [7], and when this value increases, the BET range moves to lower
relative pressures. Hudec et al. [40] studying the sensitivity of the C value for
micro- mesoporous materials concluded that extremely high values (C > 2,000)
have no physical meanings to associate it with the energy of adsorbate-adsorbent
interaction in the BET model. In the case of materials without or with a small amount
of micropores, where the “knee” of the isotherm is well defined (C ~ 80), the S BET
40
J. Villarroel-Rocha et al.