2.1. Pure Minerals and Reagents
Pure fluorite, barite and calcite were from Chongqing, China. Their chemical compositions were determined using an X-ray fluorescence spectrometer (XRF) (Axios advanced, PANalytical B.V., Almelo, The Netherlands) and are summarized in
Table 1.
As shown in
Table 1, the CaF
2 content of fluorite was 97.25%; the BaSO
4 content of barite was 97.02%; and the CaCO
3 content of calcite was 97.50%. The −150 μm +74 μm fraction was used in the flotation tests. The −74 μm fraction was removed in the case of fine particle entrainment. Some samples were further ground to −10 μm in an agate mortar and were used for zeta potential measurements. The mixed minerals were obtained by blending the pure fluorite, barite and calcite with a mass ratio of 45:45:10.
The chemical reagents used in this study included: analytical-grade sodium carbonate (Na
2CO
3, Hongguang Chemical Factory, Shanghai, China) and analytical-grade sulfuric acid (H
2SO
4, Dongda Chemical Co., Ltd., Kaifeng, China) for pH adjustment; analytical-grade hydrochloric acid (HCl, Xinyang, China) for the analysis of calcite content; analytical-grade sodium oleate as the collector and boric acid (H
3BO
3, Chinese medicine group chemical reagent Co., Ltd., Shanghai, China) for the analysis of barite content; analytical-grade sodium fluosilicate (Zonghengxing Gongmao Co., Ltd., Tianjin, China); and technical-grade valonea extract from a valonea extract factory for depressants. Valonea extract was a polyphenol mixture that mainly consisted of different types of tannins [
14]. The typical molecule structure of tannin in the valonea extract is shown in
Figure 1.
2.2. Flotation Experiment
Single mineral flotation tests were carried out in an RK/FGC flotation machine (Wuhan rock grinding equipment manufacture Co., Ltd., Wuhan, China) with a 30-mL cell at an impeller speed of 1960 rpm. The mineral suspension was prepared by adding 2.0 g of minerals to 30 mL of solution with a certain pH value, which was first adjusted by adding Na2CO3 or H2SO4. After the flotation reagent was added, the suspension was agitated for 2 min. The flotation lasted for 4 min before the products were collected, dried and weighed. The recovery was calculated based on the weight of the dried floating products divided by the feed solids.
The mixed mineral flotation tests were carried out in the same flotation machine with a 70-mL cell. The mineral suspension was prepared by adding 5.0 g of minerals to 70 mL of solution with a certain pH value. The agitation and flotation time were also 2 min and 4 min, respectively. The calcite content of the flotation material was calculated after dissolving the material with concentrated hydrochloric acid. The barite content was obtained by dissolving fluorite with concentrated hydrochloric acid and 40 g/L boric acid.
2.4. Molecular Dynamics Simulations
The calculations were performed in the framework of the MD, using the Material Studio 6.0 (MS) package. First, the Cambridge Sequential Total Energy Package (CASTEP) module included in the MS software was adopted to optimize the crystal structures of fluorite, barite and calcite. By comparing different parameters to be optimized, the best optimization parameters were as follows: a function was modified with Perdew–Burke–Ernzerhof generalized gradient approximation (PBEsol GGA); the
k-point set was 3 × 3 × 4; the self-consistent-field (SCF) tolerance was 1.0 × 10
−6 eV/atom; and the custom energy cut-off was 300 eV. The lattice optimization results are shown in
Table 2. It is encouraging to note that the simulation agreed well with the experimental results analysed from X-ray experiments. Then, 2D periodic surface cells were created from the unit cells of fluorite, barite and calcite at the cleavage plane (111), (001) and (104), respectively. The optimized surface slab was extended to a periodic super lattice of approximately 20 Å × 20 Å with a certain vacuum thickness of 30 Å [
15].
Second, the tannin, sodium fluosilicate and water molecule were optimized using the DMol3 module. The optimization parameters are as follows: the quality was medium, and the functional was a local spin density approximation with the Perdew–Wang correlation (LDA/PWC). A symmetry calculation was performed.
Finally, the DISCOVER module was employed to calculate adsorption energies. Tannin, the main component of valonea extract, and sodium fluosilicate were used as adsorbates. The optimized adsorbate molecules were placed on the top mineral surface, while the bottom-most layers were kept frozen. The initial geometry of the mineral surface-adsorbate molecule complex was created with the help of molecular graphics tools. First, the geometry optimization of the system of reagent-mineral was conducted using a Smart Minimizer with the COMPASS force field [
16], and the atom-based cut-off method was employed for calculating both the van der Waals and electrostatic interactions (Coulombic) [
15]. The atom-based cut-offs were used with a 9.5 Å cut-off distance, which was less than half of the length of the simulation cell [
15,
17] with a spline width of 1.0 Å and a buffer width of 0.5 Å. Because the configuration obtained with this method was only one of the possible adsorption modes, approximately 20 starting conformations were assessed in order to locate the minimum energy conformation of the molecule on the mineral surface. The most stable configuration of mineral surface-surfactant complex with the highest negative total energy was chosen for further MD simulations, and the coordinates of surface atoms were constrained during the MD simulations with the adsorbates being free [
15].
In the current formulation, it was difficult to account for the effect of aqueous environments on mineral-reagent interactions [
18]. Solvent (water) molecules were not included in the simulations, but the interaction energy of water molecules for each mineral surface was computed and compared with the corresponding adsorbate-mineral interaction energy [
15].
MD simulations were conducted with the COMPASS force field. The settings were the same as the geometry optimization procedure. All simulations were performed at constant volume and temperature (NVT). The time step was 1.0 fs, and the total run length was 300 ps. Finally, the interaction energy was calculated using the following equation [
18,
19]:
where
Et,
Em and
Er are the total energy of the optimized reagent-mineral complex, surface cluster and reagent molecule, respectively [
17]. More negative magnitudes of interaction energy (
Ei) correspond to more favourable interactions between the mineral surface and the depressants. The magnitude of
Ei is thus an excellent measure of the relative efficiency of interaction of different collectors with minerals [
20].