XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 2329
Langmuir and Langmuir-Freundlich models have
been considered as the best fit with the experimental data
(R2 0.93). The parameters of the fitting of the Langmuir
equation with the Arrhenius equation and the calculated
enthalpies of adsorption are gathered in Table 5. The ΔH of
approximatively –20 kJ·mol–1 is an expected value for phy-
sisorption of amines (considering the desorption of water
molecules).
DFT investigations
Amine molecules (neutral RNH2) with a chain counting
from 6 to 12 (DDA) carbon atoms were placed manually at
approximatively the same location onto the kaolinite octa-
hedral basal surface. Then the structures were relaxed at the
PBE+D2 level of theory. The adsorption is only due to the
formation of hydrogen bonds and dispersion forces (van der
Waals interactions) which represented around a third of the
total interaction (see Table 6). The adsorption energies are
not influenced by the chain length when the molecules are
adsorbed alone in vacuo conditions on kaolinite (Table 6).
However, when a second molecule is adsorbed near the
first, the isosteric heat of adsorption of the second molecule
increases with the chain length (Figure 3). Therefore, due
to the increase of the lateral interaction, the adsorption of
several molecules, and the formation of monolayers, will
be influenced by the chain length. Besides, intermolecular
interactions have already been proven to stabilize certain
adsorption configurations, as shown for the adsorption of
fatty acids onto fluorite (Foucaud et al., 2021b).
Four molecules, one fatty amine and three etheramine
(1 etheroxide group located within the chain) were vertically
adsorbed alone onto the same site in vacuum (static DFT)
on both basal surfaces of kaolinite, all with chain long of 8
atoms: one fatty amines with 8 atoms of carbon (FA), one
etheramine with 1 carbon atoms separating the nitrogen
from the oxygen (ETA1), one etheramine with 3 carbon
atoms separating the nitrogen from the oxygen (ETA3), and
one etheramine with 4 carbon atoms separating the nitro-
gen from the oxygen (ETA4). All molecules were adsorbed
under their neutral form (RNH2) (Figure 4). Table 7 dis-
plays the results of DFT calculations. The presence of the
etheroxide group and its position within the chain length
influenced the adsorption. The more the oxygen was close
to the amine group, the lower was the adsorption energy
Table 2. Parameters of DDA monolayer onto kaolinite, estimated from theoretical coverage or from experimental data
Temperature
Theoretical Monolayer*,** Experimental Monolayer*
Adsorbed Amount,
µmol·m–2
Equilibrium
Concentration,
mol·L–1
Adsorbed Amount,
µmol·m–2
Equilibrium
Concentration,
mol·L–1
25°C 6.4 2.0×10–3 4.0 6.0×10–4
35°C 6.6 2.9×10–3 4.5 1.0×10–3
45°C 6.6 2.7×10–3 4.9 9.2×10–4
*Values approximated from the visual aid curve
**For a packing area fixed at 25 Å2
Table 3. Parameters of EA monolayer onto kaolinite estimated from the theoretical coverage and from the experimental curve
Temperature
Theoretical Monolayer*,** Experimental monolayer*
Adsorbed Amount,
µmol·m–2
Equilibrium
Concentration, mol·L–1
Adsorbed Amount,
µmol·m–2
Equilibrium
Concentration, mol·L–1
25°C 6.8 1.2×10–3 5.4 6.0×10–4
35°C 6.6 6.0×10–4 6.6 6.0×10–4
45°C 6.8 7.0×10–4 5.8 3.2×10–4
*Values approximated from the visual aid curve
**For a packing area fixed at 25 Å2
Table 4. Calculation of corrected packing areas of DDA and
EA molecules in the monolayer adsorbed on Sigma-Aldrich
kaolinite
Temperature Γm, µmol·m–2 Packing area, Å2
DDA
25°C 4 42
35°C 4.5 37
45°C 4.9 34
EA
25°C 5.4 31
35°C 6.6 25
45°C 5.8 29
Langmuir and Langmuir-Freundlich models have
been considered as the best fit with the experimental data
(R2 0.93). The parameters of the fitting of the Langmuir
equation with the Arrhenius equation and the calculated
enthalpies of adsorption are gathered in Table 5. The ΔH of
approximatively –20 kJ·mol–1 is an expected value for phy-
sisorption of amines (considering the desorption of water
molecules).
DFT investigations
Amine molecules (neutral RNH2) with a chain counting
from 6 to 12 (DDA) carbon atoms were placed manually at
approximatively the same location onto the kaolinite octa-
hedral basal surface. Then the structures were relaxed at the
PBE+D2 level of theory. The adsorption is only due to the
formation of hydrogen bonds and dispersion forces (van der
Waals interactions) which represented around a third of the
total interaction (see Table 6). The adsorption energies are
not influenced by the chain length when the molecules are
adsorbed alone in vacuo conditions on kaolinite (Table 6).
However, when a second molecule is adsorbed near the
first, the isosteric heat of adsorption of the second molecule
increases with the chain length (Figure 3). Therefore, due
to the increase of the lateral interaction, the adsorption of
several molecules, and the formation of monolayers, will
be influenced by the chain length. Besides, intermolecular
interactions have already been proven to stabilize certain
adsorption configurations, as shown for the adsorption of
fatty acids onto fluorite (Foucaud et al., 2021b).
Four molecules, one fatty amine and three etheramine
(1 etheroxide group located within the chain) were vertically
adsorbed alone onto the same site in vacuum (static DFT)
on both basal surfaces of kaolinite, all with chain long of 8
atoms: one fatty amines with 8 atoms of carbon (FA), one
etheramine with 1 carbon atoms separating the nitrogen
from the oxygen (ETA1), one etheramine with 3 carbon
atoms separating the nitrogen from the oxygen (ETA3), and
one etheramine with 4 carbon atoms separating the nitro-
gen from the oxygen (ETA4). All molecules were adsorbed
under their neutral form (RNH2) (Figure 4). Table 7 dis-
plays the results of DFT calculations. The presence of the
etheroxide group and its position within the chain length
influenced the adsorption. The more the oxygen was close
to the amine group, the lower was the adsorption energy
Table 2. Parameters of DDA monolayer onto kaolinite, estimated from theoretical coverage or from experimental data
Temperature
Theoretical Monolayer*,** Experimental Monolayer*
Adsorbed Amount,
µmol·m–2
Equilibrium
Concentration,
mol·L–1
Adsorbed Amount,
µmol·m–2
Equilibrium
Concentration,
mol·L–1
25°C 6.4 2.0×10–3 4.0 6.0×10–4
35°C 6.6 2.9×10–3 4.5 1.0×10–3
45°C 6.6 2.7×10–3 4.9 9.2×10–4
*Values approximated from the visual aid curve
**For a packing area fixed at 25 Å2
Table 3. Parameters of EA monolayer onto kaolinite estimated from the theoretical coverage and from the experimental curve
Temperature
Theoretical Monolayer*,** Experimental monolayer*
Adsorbed Amount,
µmol·m–2
Equilibrium
Concentration, mol·L–1
Adsorbed Amount,
µmol·m–2
Equilibrium
Concentration, mol·L–1
25°C 6.8 1.2×10–3 5.4 6.0×10–4
35°C 6.6 6.0×10–4 6.6 6.0×10–4
45°C 6.8 7.0×10–4 5.8 3.2×10–4
*Values approximated from the visual aid curve
**For a packing area fixed at 25 Å2
Table 4. Calculation of corrected packing areas of DDA and
EA molecules in the monolayer adsorbed on Sigma-Aldrich
kaolinite
Temperature Γm, µmol·m–2 Packing area, Å2
DDA
25°C 4 42
35°C 4.5 37
45°C 4.9 34
EA
25°C 5.4 31
35°C 6.6 25
45°C 5.8 29