XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 2327
Molecular modelling study was performed using the
density functional theory (DFT) (Hohenberg and Kohn,
1964 Kohn and Sham, 1965) using the Vienna Ab initio
Simulation Package (VASP) (Kresse and Hafner, 1993).
RESULTS &DISCUSSION
Experimental Investigations
The adsorption isotherms of the two collectors on kaolinite
at 25°C, 35°C and 45°C are shown in Figure 1 for DDA
and Figure 2 for EA. Isotherms display a L4-shape accord-
ing to the classification proposed by Giles et al. (Giles et
al., 1960 Hinz, 2001), which is similar to type IV or type
VI isotherms described by the IUPAC (Hinz, 2001 Sing,
1985). These isotherms present a first plateau, associated
to the formation of the monolayer then an increase of the
adsorption up to a second (or more) plateau which repre-
sented the bi-, tri-, … layers. In the case of DDA and EA,
only one plateau is well-observed. Above the tested concen-
trations, the CMC would be reached, and the conditions
would be too far from the conditions of flotation.
Using Eq. 1, it appears that the theoretical coverage
overestimates the adsorbed amount when compared to the
experimental values (see Table 2 and Table 3). At the three
temperatures, the adsorption characteristics (Table 2 and
Table 3) are similar showing no significant temperature
effect, as already observed by Giles et al. (Giles et al., 1960).
Table 4 gathers the packing area estimated from the
experimental data using Eq. 2. The values are greater
than the 25 Å2 usually described in the literature (Yoon
and Ravishankar, 1994). However, EA molecules are
more closely packed onto kaolinite surface than DDA
molecules. Two phenomena, probably occurring simulta-
neously, could explain this result: (i) EA is more soluble
thanks to the etheroxide group present in the chain (Araujo
et al., 2005), which should increase its availability for the
adsorption onto kaolinite and (ii) hydrogen bonds can
form between the oxygen of the chain of molecule and the
-C-H at the vicinity of the etheroxide group of another EA
molecule, which causes a faster attraction of the molecules
onto the surface and allows a stronger package than with
sole hydrophobic interactions between aliphatic chains of
DDA molecules and kaolinite. FTIR investigations also
confirmed the greater adsorption of EA than DDA at the
same concentrations.
Table 1. Adsorption models (Adsorbed amount vs Equilibrium concentration) used to fit the experimental data
Model Equation* Parameters
Langmuir kCe
S kCe
1
T +
ST is the saturation capacity (mol·m–2)
k is the affinity parameter depending on the interaction between the
adsorbent and the adsorbate (L·mol–1)
Dual-Site Langmuir
k C
S k C
k C
S k C
1 1
e
T e
e
T e
1
1 1
2
2 2 +++
ST1 and ST2 are the saturation capacities of the two sites (mol·m–2)
k1 and k2 are the affinity parameters of the two sites (L·mol–1)
Freundlich K C
f e
1/n
K
f is the Freundlich constant and depends on the adsorbate, the
adsorbent, and the temperature (mol1–1/n·L1/n·m–2)
1/n is the adsorption intensity, related to the surface heterogeneity
Langmuir-Freundlich ()
(
kC
S kCe)
1
e
T
1/n
1/n
+
S
T is the saturation capacity (mol·m–2)
k is the affinity parameter depending on the interaction between the
adsorbent and the adsorbate (L·mol–1)
1/n is the adsorption intensity, related to the surface heterogeneity
Dual-Site
Langmuir-Freundlich ()
(
()
(
k C
S k1Ce)
k C
S k2Ce)
1 1
e
n
T
n
e
n
T
n
1
1
1
1
2
1
2
1
1
1
2
2
+
+
+
ST1 and ST2 are the saturation capacities (mol·m–2)
k1 and k2 are the affinity parameter depending on the interaction
between the adsorbent and the adsorbate (mol1–1/n·L1/n)
1/n1 and 1/n2 are the adsorption intensities, related to the surface
heterogeneity of the two sites
Toth (kCe)
S kC
1
T e
+a a ^h1
ST is the saturation capacity (mol·m–2)
k is Toth parameter (L·mol–1)
α is Toth isotherm constant (L·mol–1)
Redlich-Peterson kC
S kC
1
e
T e
+^hb
S
T is the saturation capacity (mol·m–2)
k is the Redlich-Peterson parameter (L·mol–1)
β is a constant comprised between 0 and 1
*Ce is the equilibrium concentration
Molecular modelling study was performed using the
density functional theory (DFT) (Hohenberg and Kohn,
1964 Kohn and Sham, 1965) using the Vienna Ab initio
Simulation Package (VASP) (Kresse and Hafner, 1993).
RESULTS &DISCUSSION
Experimental Investigations
The adsorption isotherms of the two collectors on kaolinite
at 25°C, 35°C and 45°C are shown in Figure 1 for DDA
and Figure 2 for EA. Isotherms display a L4-shape accord-
ing to the classification proposed by Giles et al. (Giles et
al., 1960 Hinz, 2001), which is similar to type IV or type
VI isotherms described by the IUPAC (Hinz, 2001 Sing,
1985). These isotherms present a first plateau, associated
to the formation of the monolayer then an increase of the
adsorption up to a second (or more) plateau which repre-
sented the bi-, tri-, … layers. In the case of DDA and EA,
only one plateau is well-observed. Above the tested concen-
trations, the CMC would be reached, and the conditions
would be too far from the conditions of flotation.
Using Eq. 1, it appears that the theoretical coverage
overestimates the adsorbed amount when compared to the
experimental values (see Table 2 and Table 3). At the three
temperatures, the adsorption characteristics (Table 2 and
Table 3) are similar showing no significant temperature
effect, as already observed by Giles et al. (Giles et al., 1960).
Table 4 gathers the packing area estimated from the
experimental data using Eq. 2. The values are greater
than the 25 Å2 usually described in the literature (Yoon
and Ravishankar, 1994). However, EA molecules are
more closely packed onto kaolinite surface than DDA
molecules. Two phenomena, probably occurring simulta-
neously, could explain this result: (i) EA is more soluble
thanks to the etheroxide group present in the chain (Araujo
et al., 2005), which should increase its availability for the
adsorption onto kaolinite and (ii) hydrogen bonds can
form between the oxygen of the chain of molecule and the
-C-H at the vicinity of the etheroxide group of another EA
molecule, which causes a faster attraction of the molecules
onto the surface and allows a stronger package than with
sole hydrophobic interactions between aliphatic chains of
DDA molecules and kaolinite. FTIR investigations also
confirmed the greater adsorption of EA than DDA at the
same concentrations.
Table 1. Adsorption models (Adsorbed amount vs Equilibrium concentration) used to fit the experimental data
Model Equation* Parameters
Langmuir kCe
S kCe
1
T +
ST is the saturation capacity (mol·m–2)
k is the affinity parameter depending on the interaction between the
adsorbent and the adsorbate (L·mol–1)
Dual-Site Langmuir
k C
S k C
k C
S k C
1 1
e
T e
e
T e
1
1 1
2
2 2 +++
ST1 and ST2 are the saturation capacities of the two sites (mol·m–2)
k1 and k2 are the affinity parameters of the two sites (L·mol–1)
Freundlich K C
f e
1/n
K
f is the Freundlich constant and depends on the adsorbate, the
adsorbent, and the temperature (mol1–1/n·L1/n·m–2)
1/n is the adsorption intensity, related to the surface heterogeneity
Langmuir-Freundlich ()
(
kC
S kCe)
1
e
T
1/n
1/n
+
S
T is the saturation capacity (mol·m–2)
k is the affinity parameter depending on the interaction between the
adsorbent and the adsorbate (L·mol–1)
1/n is the adsorption intensity, related to the surface heterogeneity
Dual-Site
Langmuir-Freundlich ()
(
()
(
k C
S k1Ce)
k C
S k2Ce)
1 1
e
n
T
n
e
n
T
n
1
1
1
1
2
1
2
1
1
1
2
2
+
+
+
ST1 and ST2 are the saturation capacities (mol·m–2)
k1 and k2 are the affinity parameter depending on the interaction
between the adsorbent and the adsorbate (mol1–1/n·L1/n)
1/n1 and 1/n2 are the adsorption intensities, related to the surface
heterogeneity of the two sites
Toth (kCe)
S kC
1
T e
+a a ^h1
ST is the saturation capacity (mol·m–2)
k is Toth parameter (L·mol–1)
α is Toth isotherm constant (L·mol–1)
Redlich-Peterson kC
S kC
1
e
T e
+^hb
S
T is the saturation capacity (mol·m–2)
k is the Redlich-Peterson parameter (L·mol–1)
β is a constant comprised between 0 and 1
*Ce is the equilibrium concentration