Mixed Potential Theory

The interaction between collector reagent and mineral takes place at the mineral-solution interface. For ease of reference, and in view of the vast body of investigative work done on it, our discussion will focus on the use of xanthates as collector agents. In the case of sulfide minerals, which are generally semiconductors, the interactions with xanthate collectors involve charge transfer across the electrical double layer at the solid-liquid interfaces. Woods et al. suggested three ways by which the xanthate ion could confer hydrophobicity to a mineral surface. Firstly the anodic reaction leads to dixanthogen formation (see eqn [1]). Secondly they distinguish between dixanthogen produced by the anodic reaction of the xanthate ion and the xanthate ion adsorption at a lower potential which is held by electrostatic attraction:

Finally there is chemisorption for which the anodic oxidation of the xanthate ion on lead sulfide is:

The corresponding cathodic reaction typically requires the reduction of oxygen in industrial flotation systems. If it assumed that the process is Faradaic in nature, i.e. no charge accumulation can occur, the oxidation and reduction reactions will be coupled by the flow of charge. The rate of the electrochemical reactions can now be determined by considering the driving force available for the process and the kinetics of the individual processes. If the respective electrical and ionic resistance of the mineral and solution is low, the system will with time reach a common potential called the 'mixed potential' at which the individual reactions will take place at steady state. This will typically be the case for solutions with a high salt loading and with anodic and cathodic areas in close proximity. The situation may be further complicated by the involvement of more than two half cell reactions and also by cathodic and anodic areas of varying sizes as is typically the case in galvanic interactions.

The mixed potential theory has been used to account for the collectorless flotation of sulfide minerals such as chalcopyrite, by considering the contributions of both surface oxidation and oxygen reduction reactions to the common potential. For example, Trahar has shown that surface oxidation of sulfide minerals results in the formation of hydrophobic sulfur layers and thus enhances flotation. It has been suggested that for sulfide minerals, surface oxidation involves the progressive removal of metal atoms, leaving a hydrophobic, metal-deficient sulfide layer with a crystal lattice only marginally altered from the original structure. More recent studies by Buckley and Woods, using X-ray photoelectron spectroscopy, have confirmed that sulfur species are indeed formed on the mineral surfaces. The concepts are summarized in Figure 1.

In the presence of xanthate collector conditions for the formation of dixanthogen have been shown by Allison et al. to occur when the rest potential of the mineral is greater than the reversible potential of the xanthate/dixanthogen couple ER(0.13V at pH 7.0), which for these minerals is the active collector species in xanthate-based flotation, except for galena, where the metal xanthate was indicated, as discussed by Cheng and lwasaki (see Further Reading). The rest

Table 1 Rest potentials at various dissolved oxygen contents (Reproduced from Cheng and Iwasaki (1992) with permission Copyright Gordan and Breach Publishers.)

Table 1 Rest potentials at various dissolved oxygen contents (Reproduced from Cheng and Iwasaki (1992) with permission Copyright Gordan and Breach Publishers.)

Mineral

Rest potential (V i/s SHE) Range reported in 6.25 x 10~4M KEX at 0-7ppm O2 solution

Mild steel

-0.515 to -0.255

Sphalerite

-0.15

Stibnite

-0.125

Realgar

-0.12

Orpiment

-0.10

Antimonite

-0.09

Covellite

+ 0.05

Bornite

+ 0.06

Chalcocite

+ 0.06

Chalcopyrite

+ 0.14

0.115-0.355

Galena

+ 0.14

0.142-0.172

Molybdenite

+ 0.16

Pyrrhotite

+ 0.21

0.055-0.290

Pyrite

+ 0.22

0.389-0.445

Arsenopyrite

+ 0.22

0.277-0.303

potential of a mineral surface, is the potential associated with a finite reaction rate in a specific solution environment (see Table 1). This is illustrated by Figure 2 from the work of Gardner and Woods, which

Figure 2 Pyrite electrode at 25°C in 0.05 M Na2B4O7 solution (pH 9.2) containing 1000 ppm of three potassium alkylxanthates. (A) Cyclic voltammograms at 4 mV s~1; (B) Contact angles measured after holding the electrode at each potential for 30s. The vertical lines are the Er values for the xanthates. (Reproduced with permission from Gardner and Woods (1977) Copyright CSIRO Publishing.)

Figure 1 Generalized depiction of galvanic interaction between electrically connected particles.

Figure 2 Pyrite electrode at 25°C in 0.05 M Na2B4O7 solution (pH 9.2) containing 1000 ppm of three potassium alkylxanthates. (A) Cyclic voltammograms at 4 mV s~1; (B) Contact angles measured after holding the electrode at each potential for 30s. The vertical lines are the Er values for the xanthates. (Reproduced with permission from Gardner and Woods (1977) Copyright CSIRO Publishing.)

Figure 3 Galena electrode at 25°C in 0.05 M Na2B4O7 solution (pH 9.2) containing 1000 ppm of three potassium alkylxanthates. (A) Cyclic voltammograms at 4 mV s"1; (B) contact angles measured after holding the electrode at each potential for 30 s. The vertical lines are the Er values for the xanthates. (Reproduced with permission from Gardner and Woods (1977) Copyright CSIRO Publishing.)

Figure 3 Galena electrode at 25°C in 0.05 M Na2B4O7 solution (pH 9.2) containing 1000 ppm of three potassium alkylxanthates. (A) Cyclic voltammograms at 4 mV s"1; (B) contact angles measured after holding the electrode at each potential for 30 s. The vertical lines are the Er values for the xanthates. (Reproduced with permission from Gardner and Woods (1977) Copyright CSIRO Publishing.)

clearly indicates that of pyrite hydrophobicity only develops at potentials more noble than the reversible potential for xanthate/dixanthogen reaction. For galena the response shown in Figure 3 is somewhat different, with a significant current flow occurring below Er due to the contribution of the chemisorbed reaction. It is also interesting to observe a zero contact angle at — 0.2V.

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