2172 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
K =equilibrium constant
Once the equilibrium constant, K, is known, this can then
be used to calculate the change in Gibbs energy, enthalpy
and entropy by the well-known thermodynamic relation-
ships shown in Equations 2 and 3.
ln G RT K =-(2)
G H TS =-(3)
Table 1 shows the thermodynamic parameters generated as
a result of isothermal calorimetric titrations of 4 collectors
with PtCl42– salt. Also included in the data are subsequent
recoveries obtained in a microflotation cell for these collec-
tors with a synthetically produced PtAs2 mineral. All col-
lectors shown have the same alkyl chain but differ in the
nature of the polar head-group.
These parameters are now useful in assessing how
many collector molecules bind to the metal. This mostly
occurs by the displacement of chloride ions in the PtCl42–
complex. Where the model found that ‘n’ was not a whole
number, as in the case of the PnBX, this may mean that
three PnBX react with every two platinum molecules.
More importantly, this data gives an indication of the
strength of binding through the equilibrium constant, K,
and the change in Gibbs energy. Since the table is ordered
from highest K and ∆G, it is clear that the microflotation
recoveries of PtAs2 follow a similar trend to the strength
of the Pt-collector interaction. This positive relationship is
a somewhat unexpected result since it has previously been
shown that the flotation recovery does not always follow
the strength of the collector-mineral interaction. More so,
it would be expected that the recovery of a mineral would
be more complex than its relationship to the strength of
the collector-metal salt binding. Further test work is ongo-
ing in this regard and may provide further insights on this
question. However, the purpose of acquiring this data is
based on the fact that the procedure being relatively fast
and easy compared to flotation experiments and gives a
relatively rapid initial indication of collector interactions
when testing novel collectors. If the results indicate that the
collector does not bond to a metal salt, the possibility of it
being able to successfully recover the corresponding metal-
containing mineral is consequently very low.
Immersion Calorimetry
Immersion calorimetry is the measurement of the heat
evolved when a clean, dry powdered surface comes into
contact with a liquid, usually water. The relevance of this
interaction for flotation is that the extent of the reaction
has a direct relationship with the wettability of a mineral
surface and, therefore, the flotation recovery. In effect, it
removes the drawbacks of the isothermal titration method,
which only measures the collector-mineral interaction, and
replaces that with an actual measure of how the mineral
surface will respond to an air-water interface. The relation-
ship between heat of immersion and flotation performance
has been demonstrated in a previous study (Taguta et al.,
2018) where the microflotation rate constant of various
collector-coated and natural minerals was plotted against
the heat of immersion. As shown in Figure 3 a very strong
relationship was found particularly once the rate constant
was normalized with respect to the density of each mineral,
which impacts on the rate of flotation as accounted for in
many flotation models. Such a correction also validates the
results obtained in microflotation tests which were used
in this study since such recoveries would depend on den-
sity differences, all other factors being similar. This is not
surprising given that wettability, usually measured in the
form of a contact angle, is the fundamental driving force
for bubble-particle attachment and stability.
It was assumed that the heat of immersion measure-
ment would be useful in flotation modeling where a
measure of wettability is required to predict and model
flotation performance. Certainly, the heat of immersion is
relatively more accurate, precise and sensitive, and requires
less material than contact angle measurements. However,
it still requires the pure) mineral on which to perform the
tests. Tests have been conducted on mineral mixtures to
investigate its potential for predicting the flotation of real
ores. Figure 4 shows the exothermic heat of immersion of
a synthetic galena-albite mixture. This shows that there is
a linear relationship between the heat of immersion and
Figure 2. Cumulative heat of reaction versus the volume of
collector added. Model fit shown as a green line over the
experimental data points
K =equilibrium constant
Once the equilibrium constant, K, is known, this can then
be used to calculate the change in Gibbs energy, enthalpy
and entropy by the well-known thermodynamic relation-
ships shown in Equations 2 and 3.
ln G RT K =-(2)
G H TS =-(3)
Table 1 shows the thermodynamic parameters generated as
a result of isothermal calorimetric titrations of 4 collectors
with PtCl42– salt. Also included in the data are subsequent
recoveries obtained in a microflotation cell for these collec-
tors with a synthetically produced PtAs2 mineral. All col-
lectors shown have the same alkyl chain but differ in the
nature of the polar head-group.
These parameters are now useful in assessing how
many collector molecules bind to the metal. This mostly
occurs by the displacement of chloride ions in the PtCl42–
complex. Where the model found that ‘n’ was not a whole
number, as in the case of the PnBX, this may mean that
three PnBX react with every two platinum molecules.
More importantly, this data gives an indication of the
strength of binding through the equilibrium constant, K,
and the change in Gibbs energy. Since the table is ordered
from highest K and ∆G, it is clear that the microflotation
recoveries of PtAs2 follow a similar trend to the strength
of the Pt-collector interaction. This positive relationship is
a somewhat unexpected result since it has previously been
shown that the flotation recovery does not always follow
the strength of the collector-mineral interaction. More so,
it would be expected that the recovery of a mineral would
be more complex than its relationship to the strength of
the collector-metal salt binding. Further test work is ongo-
ing in this regard and may provide further insights on this
question. However, the purpose of acquiring this data is
based on the fact that the procedure being relatively fast
and easy compared to flotation experiments and gives a
relatively rapid initial indication of collector interactions
when testing novel collectors. If the results indicate that the
collector does not bond to a metal salt, the possibility of it
being able to successfully recover the corresponding metal-
containing mineral is consequently very low.
Immersion Calorimetry
Immersion calorimetry is the measurement of the heat
evolved when a clean, dry powdered surface comes into
contact with a liquid, usually water. The relevance of this
interaction for flotation is that the extent of the reaction
has a direct relationship with the wettability of a mineral
surface and, therefore, the flotation recovery. In effect, it
removes the drawbacks of the isothermal titration method,
which only measures the collector-mineral interaction, and
replaces that with an actual measure of how the mineral
surface will respond to an air-water interface. The relation-
ship between heat of immersion and flotation performance
has been demonstrated in a previous study (Taguta et al.,
2018) where the microflotation rate constant of various
collector-coated and natural minerals was plotted against
the heat of immersion. As shown in Figure 3 a very strong
relationship was found particularly once the rate constant
was normalized with respect to the density of each mineral,
which impacts on the rate of flotation as accounted for in
many flotation models. Such a correction also validates the
results obtained in microflotation tests which were used
in this study since such recoveries would depend on den-
sity differences, all other factors being similar. This is not
surprising given that wettability, usually measured in the
form of a contact angle, is the fundamental driving force
for bubble-particle attachment and stability.
It was assumed that the heat of immersion measure-
ment would be useful in flotation modeling where a
measure of wettability is required to predict and model
flotation performance. Certainly, the heat of immersion is
relatively more accurate, precise and sensitive, and requires
less material than contact angle measurements. However,
it still requires the pure) mineral on which to perform the
tests. Tests have been conducted on mineral mixtures to
investigate its potential for predicting the flotation of real
ores. Figure 4 shows the exothermic heat of immersion of
a synthetic galena-albite mixture. This shows that there is
a linear relationship between the heat of immersion and
Figure 2. Cumulative heat of reaction versus the volume of
collector added. Model fit shown as a green line over the
experimental data points
