*4.3. Effect of the Concentration of Xanthate*

According to Equation (2), increasing the concentration of xanthate, i.e., the reactant, makes the reaction moves in the normal direction, resulting in more reaction product, i.e., CuX, produced on mineral surface. This concentration effect of xanthate is clearly shown in the AFM images obtained with the present work. For example, Figures 3, 4 and 6 clearly show that the amount of adsorbate increases greatly in surface coverage and the height of the adsorbate, when the concentration of KEX increases from 5 <sup>×</sup> <sup>10</sup>−<sup>5</sup> M to 5 <sup>×</sup> <sup>10</sup>−<sup>4</sup> M. The same conclusion can also be drawn for the case of PAX. By comparing Figures 8–10, one can see that when the concentration of PAX increases from 1 <sup>×</sup> <sup>10</sup>−<sup>5</sup> M to 1 <sup>×</sup> <sup>10</sup>−<sup>4</sup> M, the amount of adsorbate increases at a same contacting time.

## *4.4. Effect of Adsorption Time*

Figures 6, 7, 10 and 11 show that the height of the adsorbate and the surface coverage increased when the adsorption time increased from 10 min to 20 min in the xanthate solution at pH 6. In addition, as shown in Figure 12A–C and Figure 13A–C, the adsorption increased when the adsorption time increased from 5 min to 10 min and further to 20 min in the xanthate solution at pH 10. The trend was much more evident in the case of KEX. All these images clearly show that the adsorption of the xanthate on bornite increased with the adsorption time. The finding is in line with a common industrial practice of copper ore beneficiation, which involves adding collectors in a mill to increase the adsorption time, as well as the benefit from the adsorption of the collector on the freshly exposed mineral surface.

#### *4.5. Impact of Xanthate on Bornite Flotation*

In froth flotation, specific chemicals, i.e., collectors or promoters, are added to the pulp to increase the surface hydrophobicity of a target mineral. This results in the increase of both the attractive hydrophobic force and the adhesion force between the mineral particles and bubbles. The former can facilitate a particle/bubble attachment, and the latter can retard a particle/bubble detachment, which are both beneficial for froth flotation.

According to Cassie's equation [29]:

$$
\cos \theta \equiv f\_1 \cos \theta\_1 + f\_2 \cos \theta\_2 \tag{3}
$$

where *θ*<sup>1</sup> is the contact angle for component 1 with a surface area fraction *f* <sup>1</sup>, *θ*<sup>2</sup> is the contact angle for component 2 with surface area fraction *f* <sup>2</sup> and *θ* is the contact angle of the composite material. In addition, *f* <sup>1</sup> + *f* <sup>2</sup> = 1 for the case of the adsorption of the collector on the bornite surface, assuming that component 1 is the bare bornite and component 2 is the adsorbate, i.e., CuX, *θ*<sup>2</sup> should be larger than *θ*1. Therefore, increasing *f* <sup>2</sup> and/or *θ*<sup>2</sup> will increase *θ*, i.e., the hydrophobicity of bornite with adsorbate, resulting in a better flotation.

In the present study, as shown in the AFM images, it is clear that xanthate can effectively adsorb on a bornite surface, as xanthate showed an almost full coverage at a concentration above 1 <sup>×</sup> <sup>10</sup>−<sup>5</sup> M PAX. This suggests that the adsorption of cuprous xanthate resulted in a large *f* <sup>2</sup>, which is beneficial for a large *θ*. Increasing the dosage of xanthate and adsorption time will increase the cuprous xanthate's surface coverage, i.e., *f* <sup>2</sup>, and it is also beneficial for to increase the surface hydrophobicity.

The force measurement results show that the detach forces measured in the xanthate solutions were larger than the force measured with water. In general, a large detach force suggests a large adhesion between a probe and substrate through the media. Following the Derjaguin approximation [30], it is predicted that a larger adhesion force will be achieved when the probe/liquid/bornite interfacial tension increases. In the present investigation, the Si3N<sup>4</sup> AFM probe was inert in water, and it did not directly react with xanthate. Therefore, the surface energy of the Si3N<sup>4</sup> probe did not change. In addition, in the present study, the surface tension of water media remained the same because the short-chain xanthate surfactant was used at a very low concentration. Therefore, the increase in the detachment force, as shown by the AFM force measurement, was mainly due to the increase of the interfacial tension between bornite and water, suggesting an increase in the hydrophobicity of bornite because of the adsorption of the cuprous xanthate on the mineral surface. We also suggest carrying out an AFM "colloid force" measurement by directly measuring the interaction force between a hydrophobic "colloid probe" and the adsorbate on bornite surface. The results will help to better understand the interaction between a bubble and a bornite particle in xanthate solutions in froth flotation. Such an investigation of force measurement, which is beyond the scope of the present study, is recommended for a future work.

#### **5. Conclusions**

AFM surface image measurements were applied to study the adsorption of xanthate on bornite in an aqueous solution in situ. The AFM images showed that the xanthate adsorbed on the mineral surface strongly when bornite contacted the KEX and PAX solution. The ATR-FTIR result confirms that that the adsorbate was essentially cuprous xanthate. Increasing the hydrocarbon chain length of xanthate increased the collectivity of the collector by increasing the surface coverage of the cuprous xanthate on the mineral surface at a lower concentration. Both increasing the chemical dosage and increasing the adsorption time will increase the surface coverage of CuX on mineral surface, which contributes to a better flotation by increasing the surface hydrophobicity of bornite.

**Funding:** This research received no external funding.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available due to ethical.

**Acknowledgments:** J. Zhang is grateful to Freeport-McMoRan Copper & Gold, Inc. for sponsoring the Freeport McMoRan Copper and Gold Chair in Mineral Processing in the Department of Mining and Geological Engineering in the University of Arizona. Reviewers' insightful comments and valuable suggestions are greatly appreciated.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

1. Gaudin, A.M.; Schuhmann, R., Jr. The action of potassium n-amyl xanthate on chalcocite. *J. Phys. Chem.* **1936**, *40*, 257–275. [CrossRef]

