g Liquid Air L V C o h e s i o n Q g g S V S L S o l i d A d h e s i o n The various symbols i refer to interfacial tensions between liquid (L), air saturated with vapour (V), and/or solid (S) Young equation (1805) Work of Adhesion, WA– work required to separate a unit area of a solid-gas interface. Dupréequation (1859) Work of Cohesion, WC - work required to break apart a column of a liquid having a unit cross-sectional area. LV, at 25 °C Water 72.8 mJ/m2 Propanol23.3 mJ/m2 Mercury485.5 mJ/m2
Work of Adhesion Work of Cohesion Adhesion between a solid and a liquid, or between two immiscible liquids. Cohesion within a liquid.
Combining the Young and Dupré equations, the following expression is obtained which describes the work required to remove the bubble from the solid in a liquid environment: • When Θ = 0, cosΘ = 1 – perfect "wetting" or total hydrophilicity. • When Θ = 180, cosΘ = -1 – perfect or total hydrophobicity.
Completely hydrophobic solid Completely hydrophilic solid When WA = WC , cosΘ = 1 (Θ = 0) – perfect wetting or complete hydrophilicity. When WA << WC , cosΘ → -1 (Θ = 180) – perfect “dewetting” or complete hydrophobicity. The higher the contact angle of water, the more hydrophobic the solid (easier to float).
Very few minerals show natural floatability (hydrophobicity) • Only ONE of those minerals is of any real value – molybdenite • Some types of coal are hydrophobic and easy to float • Coal is not a mineral…It is an organic rock (mixture of minerals) • Diamonds are also hydrophobic – too coarse to float • Vast majority of minerals are naturally hydrophilic (non-floating) • So, surface chemical modification is required to float
When a mineral particle is placed in water 1) It may dissolve in water – (e.g., sylvite– KClorapatite – Ca3(PO4)2 ) - releasing ions into solution 2) It may react with water (hydrolysis) forming functional groups on its surface (e.g., hematite Fe2O3 forms –OH groups) 3) It ALWAYS becomes electrostatically-charged - surfaces acquire positive or negative charges 4) It will adsorb almost anything- ions, dissolved organics, addedreagentspresent in solution
Compact (Stern) Layer of Ions Diffuse Layer of Ions The ion concentration profile that develops around a charged particle is known as the Electrical Double Layer (EDL)
Surface Potential Ψ0 is defined as Work required to bring a unit charge from to a charged solid surface
If x = 1/then /0 = 1/e = 0.3678 • is expressed in units of reciprocal distance (e.g., m-1) • So the parameter (1/ ) is referred to as the thickness of the EDL
A particle has a 0 = 40 mV Calculate the EDL thickness ofa particle in 10-3, 10-2&10-1M KCl solution 10-3 M KCl; = 0.10398 nm-1 1/ = 9.62 nm 10-2 M KCl; = 0.32881 nm-1 1/ = 3.04 nm 10-1M KCl; = 1.03979 nm-1 1/ = 0.96 nm As electrolyte concentration increases, the thickness of the EDL decreases. This phenomenon is known as the compression of the EDL.
Compact layer adsorbed Diffuse layer removed The shear plane These phenomena are the foundation of electrokinetic effects which are used inmeasuring the zeta potential (ζ) of mineral particles.
Zeta potential (ζ) is the electrical potential at the shear plane. It is not the Surface Potential (0) but rather, the potential at some distance from the surface. The shear plane
The zeta potential is always lower than the surface potential, but it always has the same sign (either positive or negative) Unlike Surface Potential, the Zeta Potential strongly depends on concentration of indifferent ions (such as K and Cl)
Some Practical Examples of Actual Zeta Potential Data Goethite (FeO(OH)) From Iwasaki et al. 1960. Zero Point of Charge 6.7 for FeO(OH) pH 2 4 6 8 10 12 Zero Point of Charge 5.7 for FeO(OH) Zirconia (ZrO2) From Cases (1967) Zero Point of Charge = ZPC or PZC Or the Iso-Electric Point (IEP)
Zero Point of Charge Mineral ZPC (pH units) Quartz/SiO2 ~ 2.0 Kaolinite ~ 2.5 Illite ~ 2.5 TiO2 3.5 Apatite 3.8 MnO2 4.0 -8.7