AG0 AAs[ysl y0v Ylv cos6 A6 [9

where ySL, yLV and y°V are the interfacial energies for solid-liquid, liquid-vapour and solid-saturated vapour. At equilibrium this leads to the Young

The work of adhesion for the three-phase contact is then obtained from the Young equation after substituting for ySL from eqn [12] into eqn [13]:

Equation [14] is a form of the Dupre equation that relates an increasing contact angle to a reduction in the adhesion energy between the solid surface and water, or alternatively to an increase in the hydropho-bicity of the solid surface.

Fowkes modified the Girifalco-Good equation for the work of adhesion and suggested that it was due to the London-van der Waals dispersive forces in each phase rather than the total intermolecular energies. Equation [15] describes the resulting expression for the interface energy between a solid and liquid:

surface activities:

dy= -TRTdln p from which:

($ is commonly taken as unity).

Fowkes applied eqn [15] to eqn [12], to express a relationship between the contact angle and the dispersive energy of the solid surface, yf, this being considered to be a parameter most characteristic of the influence of the nature of the surface on the interface phenomena important in flotation:

By substituting for ySL from eqn [15], Fowkes obtained an expression which links yf with n as determined from adsorption studies:

The derivation assumes that the adsorption of vapour is determined solely by dispersion forces (physical adsorption):

The dispersion forces in a particular solid, yf, can therefore be estimated by using contact angle measurements with different liquids obviously of known surface dispersion yL. Linear plots of cos 6 against the ratio of dispersive energies of the liquids confirm the validity of eqn [16] and the slope of the line gives Jyj.

Experimental characterization of interfacial energies - adsorption studies Adsorption data may be used to estimate n which reflects changes in interfacial energies. These require knowledge of the adsorption isotherm, relating r, the mols of vapour adsorbed per square centimetre of solid surface with p, the partial pressure of the solute in the gas.

Bangham and Razouk derived an expression for n by integrating the Gibbs equation. This states that:

It is clearly of interest to compare the surface free energies yf determined from gaseous adsorption studies with those obtained from contact angle measurements. Fowkes quotes an average value of 122 ergs cm-2 for the dispersive energy of a graphite surface, yf, from the adsorption of N2 and n-heptane, which compares well with the value of 109 ergs cm-2 from contact angle measurements of a water droplet on a graphite surface (6 = 85.7° and n0 = 19 ergs cm-2).

The surface free energies can also be experimentally determined from heats of immersion AH,-since:

dyi dT

- 2jilv djTS-2Jyd Hf dT

n = - Jdy = RTjrdln p n = ys-ysv = RTjPpTdln p [17]

Harkins by defining ysv as being equal to ySL + yLV related the energy n of the adsorbed liquid film to the

Experimental characterization of interfacial energies - heat of immersion Equation [21] can be used with heats of immersion measured calorimetrically to determine the contribution of polar interactions between the solid and the liquid into which it has been immersed. If dispersion forces only were significant at the interface, then the equality of eqn [19] should hold. Deviations from the equality of eqn [19] referred to as the excess by Fowkes are a measure of the strength of the polar interaction:

Table 2 Polar interfacial interactions at solid-liquid interfaces

Solid

Liquid

(ergs cm ~2)

Excess (ergs cm ~2)

Graphite

n-Heptane

96

96

0

Benzene

114

134

20

Silica

n-Heptane

100

100

0

Benzene

118

138

20

Acetone

98

156

58

n-Propanol

98

182

84

Water

94

462

368

Reproduced with permission from Fowkes FM (1964) The Interface Symposium. Industrial and Engineering Chemistry 56(12), 40-52, Table IX.

Reproduced with permission from Fowkes FM (1964) The Interface Symposium. Industrial and Engineering Chemistry 56(12), 40-52, Table IX.

Table 2 shows polar interactions at some solid-liquid interfaces in terms of the excess.

From the limited data reproduced in table it can be seen that the adsorption of hydrocarbons both on graphite and silica is principally through dispersion forces while that of n-propanol and water on silica show significant polar interactive forces. Clearly, the presence of these strong attractive forces will result in very stable films.

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