Abstract:
Surface properties of pyrite (FeS2), chalcopyrite (CuFeS2), galena (PbS) and 
sphalerite (ZnS) most thermodynamically stable surfaces have been studied using first 
priniciples density functional theory. The most stable surfaces showed the highest 
surface exposure as it covered a higher percentage of the surface area on 
morphologies. The interaction of water with such sulphide surfaces was also 
investigated; the structures of sulphide minerals surfaces were changed in the 
presence H2O molecules. The surfaces of FeS2 and ZnS relax most while those of 
CuFeS2 and PbS surfaces change slightly in the presence of H2O molecules. 
The results on the effect of chain length of DTPs and DTCs on the enthalpies of 
adsorption on pyrite, galena, chalcopyrite and sphalerite have shown that an increase 
in chain length of the DTPs resulted in an increase in the enthalpies of adsorption 
trend for pyrite, galena and sphalerite. This is an important observation since the 
ligand is the same in all cases and therefore the effect is due to the role of the alkyl 
group Moreover, we noted a decrease of enthalpies of adsorption with an increase of 
DTCs chain lengths on pyrite, galena, chalcopyrite and sphalerite. 
The effect of the branching of the hydrocarbon chain length of the dithiocarbamates 
on the enthalpy of adsorption of pyrite was investigated. The results show that the 
configuration of the alkyl chain length of the same carbon number has an influence on 
the enthalpy of adsorption. Furthermore, the results indicate that there was minimal 
enthalpy of adsorption when DeDTP was dosed to galena, chalcopyrite and sphalerite 
minerals as compared to DeDTC and ethyl xanthate. On the other hand, the enthalpies 
of adsorption of DeDTP on pyrite were very high which represented a greater 
exothermic reaction than for any of the DeDTC and ethyl xanthate. The bond distance 
between thiol collector and the surface is consistent with the corresponding calculated 
adsorption energies. 
The Mulliken population of S-Fe/S-Pb/S-Zn bond for the adsorption of eX on 
CuFeS2 surface are high compared to PbS and ZnS surfaces, which indicated that 
there is a strong covalent bond between S and Fe atoms as compared to S-Pb and 
Pb-Zn bonds. Such observations are consistent with results of other thiol collectors. It 
was seen that the Mulliken atomic charges populations of CuFeS2, PbS and ZnS 
surface layers are different before and after DTPs adsorption. The charges of Fe atom 
reduce, which indicates that the Zn and Pb atoms become more positive and the Fe 
atom becomes more negative. In addition, there are changes in the charges of S atoms in ZnS and PbS surface layers before and after H2O absorption, suggesting that the 
presence of water would affect the adsorption of thiol collector. 
 The densities of states (DOS) of the thiol collectors on surfaces of sulphide 
minerals have shown a strong hybridisation between the S 3p-orbital HOMO, metals 
(Fe, Pb, Zn) 3d-orbital for pyrite and chalcopyrite, 6p-orbital for galena and (3d and
4s)-orbitals for sphalerite. The collector S 3p-orbital reduces to zero states on the 
surfaces of Fe, Pb and Zn atoms. The Fe-S bond population for DeDTP is lower than 
that of DispDTP and DbDTP in pyrite, respectively. For chalcopyrite the DeDTP Fe-S 
population is higher than both DispDTP and DbDTP: similar trends were observed for 
Pb-S and Zn-S, however, the Pb-S bonding was less covalent as compared to the Fe S in chalcopyrite. The DTPs Fe-S bond population is generally higher in chalcopyrite 
than in pyrite. Mulliken charges analysis indicated that the DTPs S atoms lost charges 
and the metals gained with a decreasing DTPs chain length for pyrite: a similar trend 
was observed for chalcopyrite. The DTPs gained electrons from galena and sphalerite 
surface. For DTCs pyrite and chalcopyrite surface Fe atoms gain more electrons in 
the presence of DeDTP than other DTPs, while galena and sphalerite lost most 
electrons in the presence of DbDTC than other DTCs. As for xanthate, the Mulliken 
bond charges indicated that the S atoms and the metals lost charges, suggesting that 
some charges reside at the internuclear region between the metals and sulphurs (M–
S). These show that electron charges are collector and mineral dependent; collector 
would be an electron acceptor or donor depending on the mineral makeup. 
A comparison of the computational results, isothermal titration calorimetry (ITC) and 
microfloatation experiments for the interaction of DeDTP, DeDTC and eX with pyrite 
and galena was made. The calculated adsorption energies between thiol collectors 
and mineral surfaces were always more exothermic than the experimentally 
determined ones. In computational calulations, water adsorption was found to reduce 
the reactivity of Fe and Pb atom for the interaction with thiol collectors and bring the 
adsorption energies closer to the magnitude of the experimental values. FeS2 (100) 
surface heat of adsorption depict similar trends to experimental recoveries from 
microfloation for DeDTP, DeDTC and eX, while FeS2 (111) heats of adsorptions for 
DeDTP and DeDTC are consistent with ITC experimental results. Lastly, calculated 
DeDTP and DeDTC adsorptions on the PbS (100) are also consistent with 
experimental recoveries.