AN INVESTIGATION INTO THE RELATIONSHIP BETWEEN EXCESS GIBBS ENERGY AND
CONTACT ANGLE, SURFACE TENSION, CCC95 AND FROTH/FOAM BEHAVIOR USING
REAGENTS WITH CONSTANT FUNCTIONAL GROUPS BUT VARYING ALKYL CHAIN
LENGTHS.
C T O’Connor1 and M C Harris2
1&2
. Centre for Minerals Research, Department of Chemical Engineering, University of Cape Town,
Rondebosch, 7700, South Africa (cyril.oconnor@uct.ac.za; martin.harris@uct.ac.za)
1
Corresponding author
ABSTRACT
Excess Gibbs energy is a thermodynamic parameter which quantifies the difference between the Gibbs
energy of a component in a real mixture compared to an ideal mixture. It is obtained from the activity
coefficient which is determined using a variety of models. The most widely used approach is to use the
UNIFAC model. Flotation requires the use of reagents such as frothers and collectors whose structures
consist of a functional group (e.g. –OH in alcohols or a ligand such as –CS2 in the case of xanthates) and
linear or branched alkyl groups of varying chain lengths. These alkyl groups result in mixtures of these
reagents and water being typical of non-ideal mixtures. Since the role of the collectors or frothers in
changing contact angles, bubble size, surface tension or froth behavior is closely associated with the
properties arising from their molecular structure it is reasonable to assume that excess Gibbs energy would
be a useful parameter to quantify the changes which occur when using reagents of different alkyl chain
lengths. In this paper it is shown that there is a strong linear relationship between the excess Gibbs energy
of collectors with a constant functional group and varying alkyl chain lengths and the measured contact
angles on a mineral (e.g. Fig.1) and the critical micelle concentration. Similarly strong linear relationships
exists between excess Gibbs energy of frothers with different alkyl chain lengths and parameters such as
froth volume (e.g.Fig.2), foam height, surface tension, CCC95 and bubble size. It is proposed that these
relationships provide strong quantitative thermodynamic confirmation of the role of the alkyl group in
determining flotation behavior. Since it is known that there is a strong correlation between alkyl chain
length and hemi-micelle formation it is further proposed that the excess Gibbs energy may quantify, using
robust thermodynamic calculations, the relationship between alkyl chain length and hemi-micelle
formation.
Contact angle
80
60
40
20
0
10
30
50
70
Thousands
Excess Gibbs Energy (J/mol)
Figure 1: Relationship between the excess Gibbs energy and the measured contact angle of a series of
primary amines with hydrocarbon chains ranging from C8 to C18 on sylvite (from Fuerstenau et al , 1956).
Figure 2: Relationship between froth volume and Excess Gibbs Energy using alcohols of different chain
lengths (C2-C8) (Leja and Schulman, 1954).
KEYWORDS
Excess Gibbs energy, reagents, contact angle, froth, surface tension, bubble size, hemi-micelles