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water interface
Colloids and Surfaces, 42 (1989) 71-84 Elsevier Science Publishers B.V., Amsterdam
71 -
Printed in The Netherlands
Thermochemistry of Oleate Adsorption at the Fluorite/Water Interface J.D. MILLER,
J.S. HU and R. JIN
Department of Metallurgy and Metallurgical Engineering, University of Utah, Salt Lake City, UT 84112 (U.S.A.) (Received
4 October
1985; accepted 24 February 1989)
ABSTRACT A microcalorimetric technique has been used to measure heats of reaction of oleate in the fluorite system. These isoperibolic thermochemical measurements have been coupled with FTIR spectroscopic measurements to determine the corresponding adsorption densities. The results give further evidence for the initial hypothesis that the adsorption of oleate at the fluorite surface involves both chemisorption and surface-precipitation reactions. The chemisorption reaction is endothermic in nature and predominant at low levels of oleate adsorption. The surface-precipitation reaction is exothermic in nature and predominant at high levels of oleate adsorption.
INTRODUCTION
It is recognized in the fluorite/oleate system [ 1,2] as well as other semisoluble salt/collector systems [ 31 that important collector reactions include chemisorption, surface precipitation and aqueous-phase precipitation. In a recent study of oleate adsorption by fluorite, experimental techniques using radiotracer analysis have been developed to distinguish between adsorption (chemisorption and surface precipitation) and aqueous-phase precipitation [ 41. From the isotherms for oleate adsorption by fluorite at two different temperatures, shown in Fig. 1, at least two regions of adsorption can be identified: Region I. Chemisorption is predominant. Oleate is chemisorbed at the fluorite surface. The chemisorption reaction is endothermic with an increase in adsorption density at higher temperature. From the Clausius-Clapeyron equation, the isosteric enthalpy change associated with the adsorption process in this region (AH,) was estimated to be 2.77 kcal mol-’ of oleate [4]. The adsorbed oleate is tenacious and little is removed in this region by ultrasonic treatment. Region II. Surface precipitation is predominant. At higher oleate concentrations, surface-precipitated calcium oleate is formed
0166-6622/89/$03.50
0 1989 Elsevier Science Publishers B.V.
/
I
=lO
pli
With US Treatment
0
20°C
n
40°C
I
V -
monolayer
1
H - monolay~ 0
-0.5
1.0 EQUILIBRIUM
Fig. 1. Adsorption isotherms conditioning time, 2 h [ 41.
5.0 CONCENTRATION
.10 OF
50 OLEATE
J.-
100
, mg /I
of oleate on VOG fluorite at 20 and 40’ C with ultrasonic
treatment;
at the surface and the surface-precipitated calcium oleate, Ca(Ol)2, can be partially removed by ultrasonic treatment. In this region, the adsorption reaction appears to be exothermic with a decrease in adsorption density at higher temperature. The associated isosteric enthalpy change (AH,,) was estimated to be -6.7 kcal mol-1 of oleate using the Clausius-Clapeyron equation [ 41. In this current study, microcalorimetric techniques have been used to directly measure the heat of adsorption in Regions I and II. Also, FTIR transmittance techniques have been used to determine the corresponding adsorption densities of oleate at the fluorite surface after the microcalorimetric measurements. Based on the results of both microcalorimetric measurements and adsorption density measurements, a sequential adsorption model has been developed to describe oleate adsorption phenomena at the fluorite surface. EXPERIMENTAL
PROCEDURE
Materials Reagent-grade calcium fluoride obtained through the Ventron Division of Alfa Products, Danvers, MA, was used in this study. The specific surface area of the fluorite was found to be 14.89 m2 g-’ as determined by nitrogen adsorp-
73
tion using the BET method. Oleic acid of 99% purity was obtained from Alfa Products. The oleate used in microcalorimetric experiments was prepared by saponification of the oleic acid with a slight excess of NaOH (high purity). Calcium oleate was prepared by precipitation from 1O-3 M solutions of sodium oleate and calcium chloride (certified-grade reagent, Alfa Products) at 22 oC. Both solutions had their pH values adjusted to N 9.0 prior to precipitation. The precipitate was filtered, washed in distilled water at the same pH, washed in isopropanol and recrystallized from benzene. The calcium oleate was then dried overnight at 60°C and stored in a vacuum desiccator. Ultrapure NaOH and HCl (obtained from Alfa Products) were used to adjust the pH of the solution. Distilled water was used throughout the experiments. IR-grade KBr was obtained from Fisher Scientific Co., Pittsburgh, PA, and reagent-grade benzene was obtained from MC/B manufacturing Chemists, Inc. Los Angeles, CA. Thermochemical measurements The thermochemical measurements were accomplished with a microcalorimeter, Model 850, manufactured by Tronac Inc., Orem, UT. The apparatus consists of a water bath, reaction vessel, temperature controller and strip chart recorder. With the 16-gallon water bath, the temperature variations can be held within ? 5. 1O-4o C. Using suitable heating probes and coolant, the bath can be operated from - 10 to 80°C. The microcalorimeter was designed both for isothermal measurements in which the heat flux needed to maintain a constant temperature inside the reactor is measured and for isoperibolic measurements in which the temperature change inside the reactor is measured. Previous research had demonstrated that equivalent results were obtained using either experimental technique [ 5,6]. In this study, only the isoperibolic technique was used. The isoperibol calorimeter assembly is shown in Fig. 2. The reaction vessel is a wide-mouth aluminized Dewar flask with a 2-mm thin wall, a standard resistor heating coil (for heating and calibration) and a precision thermistor (2. 10e5”C sensitivity) connected to a Wheatstone bridge for temperature measurement. The thermistor had been calibrated with a Beckman 2°C differential thermometer. There are two techniques that can be used to measure the enthalpy change in this calorimeter, titration calorimetry and batch calorimetry [ 71. Titration calorimetry consists of introducing a titrant into the reaction vessel at a known constant rate (continuous titration) or in small equal volume amounts (incremental titration). Batch calorimetry refers to any calorimetric determination where no external mass is introduced across the vessel boundaries during the course of the determination. In this study, batch calorimetry was used. The batch calorimetric measurement consisted of putting 0.3 g of fluorite in a 2-cm3 thin wall ampoule which was then sealed with a microtorch. The am-
74
1
II II
_.__._._.. . PRECISION THERMISTER
‘AMPOULE BREAKING
ROD
I SYNCHRONOUS STIRRER DEWAR FLASK
Fig. 2. Schematic
representation
of the 25-ml isoperibol reaction vessel.
poule was placed in the ampoule holder underneath the breaking rod shown in Fig. 2. The Dewar flask containing 25 cm3 of oleate solution was connected to the calorimeter assembly. After turning on the stirrer, the reaction vessel was positioned in the center of the bath. The temperature in the reaction vessel was allowed to rise to the exact bath temperature (25°C) by means of the heating coil and the heat effect from stirring during a conditioning period of 20 min. The heat of reaction was initiated by breaking the ampoule and the temperature was recorded as a function of time on the strip chart recorder. This order of addition (dry fluorite to oleate solution) is consistent with that used in the previous studies [4,8] and was favored over breaking oleate solution-filled ampoules into a fluorite suspension for the following reasons: (1) heat of dilution of oleate solution was eliminated, (2) heat of neutralization associated with pH differences was minimized, and (3 ) the aqueous-phase precipitation of calcium oleate was minimized. FTIR adsorption density measurements Immediately after the calorimetric measurements, the pH of the suspension was measured and was found to deviate from the initial pH value by not more than 50.1 pH units. The separation of fluorite from the suspension was achieved by two-stage filtration with a Nalgene vacuum membrane filter. In
75
the first stage, a 400-mesh gauze was used to remove the broken ampoule glass. In the second stage, a membrane of 0.2 pm pore size was used to retain the finest fluorite particles. The cake was dried at room temperature and atmospheric pressure. KBr discs for FTIR transmission measurements were prepared using the following sequence of steps: First, 300 milligrams of mixture (sample and KBr ) at a desired proportion, typically 10% sample, was mixed for 20 min in a stainless-steel vial on a Wig-L-Bug mixer. Second, a 150-milligram portion of the mixture was carefully weighed and transferred to a die. Finally, the die was evacuated for 10 min with no load, then a load of 20 000 pounds was imposed for 10 min. The pressure usually dropped to 18 000 pounds after 10 min, so the pressure was raised to 20 000 pounds for an additional minute. This pressing technique resulted in discs of approximately 1.2 cm in diameter and 0.12 cm in thickness. The pressed sample served as a window for the FTIR experiments. Infrared spectra were recorded by a Nicolet 7000 series Fourier Transform Infrared Spectrometer (6000 bench) at 1 cm-l resolution. A germanium-coated KBr beam-splitter and a liquid nitrogen-cooled Hg-Cd-Te detector were used and each sample was scanned 200 times. RESULTS
Microcalorimetric measurements A typical thermogram for isoperibol experiments, as shown in Fig. 3, is characterized by three periods, lead, run and trail. S, and S, are the initial and final rates of temperature rise due to heat contributions of stirring, radiation, conduction, etc. The pulse signals the breakage of the ampoule, i.e., the initiation of the adsorption reaction, which causes a temperature rise dp during time At. A response immediately observed after breakage of the ampoule indicates the rate of adsorption is rapid. The corrected temperature rise ( dpc,,,) is found from Eqn ( 1) :
and the heat of reaction in the reaction vessel (Q) is then given as
Q=&mr$Jb
(2)
where C, is the heat capacity of the reaction vessel plus its contents, and b is the thermistor constant which is obtained by parallel calibration using two liquids, distilled water and benzene. To determine the heat capacity, C,, two experiments were performed under the same conditions. After the regular microcalorimetric measurements, fluorite was immediately separated from the suspension for FTIR adsorption density measurement in the first experiment
Q = Aucor.Cp/ Cp
b
0
b
: Heat Capacity : Thermister Constant
LEAD-
’
I
I
I
8
6
4
2
TIME
Fig. 3. A typical thermogram
0
,min
from an isoperibol microcalorimetric
experiment.
and an electric calibration was performed to determine C, in the second experiment. The heats of reaction Q measured by the two experiments were found to be very close to each other and the average values are reported. The details of the calibration procedures are described in the instruction manual [9]. A series of blank experiments were performed in order to determine the effect of ampoule breakage. As shown in Fig. 4, when an empty ampoule and a distilled water-filled ampoule were broken in distilled water, no temperature rise was observed. This phenomenon indicates that the mechanical energy released from the breakage of the ampoule is negligible. When a fluorite-filled ampoule was broken in distilled water, the enthalpy change is defined as the heat of immersion (dHi,). When a fluorite-filled ampoule was broken in oleate solution, the enthalpy change is defined as the total heat involved in the oleate adsorption process (M&i). It has been found that, when LIH,, is being determined, the trailing slope, S,, is always greater than the lead slope, S,, and furthermore S, continually decreases with time, approaching S,. This phenomenon is not particularly significant but does show the presence of some slow equilibration processes, involving Ca(Ol), and other oleate species. For example, both calcium oleate Ca(Ol), and oleic acid (HOI) are present in very small quantities in the reaction vessel. Bulk Ca( 01)2 may be formed after fluorite is introduced into the reaction vessel due to the presence of a small amount of calcium ions from dissolved fluorite. It is expected that oleate spe-
CaF2 /Hz0
Fig. 4. Thermograms
for various microcalorimetric
exper
nents.
ties are in equilibrium after conditioning and prior to microcalometric measurements. At pH 9, the predominant species of oleate are Ol-, then [Ol]zand H [ 011 z [lo]. The activity of HO1 is about four orders of magnitude smaller than that of Ol-. On this basis, it is believed that the dI-&~ measured in this work can be attributed to oleate adsorption‘at the fluorite/water interface and not to the dissociation of oleic acid (HOl). The measured total heat (d&,) in kcal g-l of fluorite as a function of initial concentration of oleate is present in Table 1. Two features are obvious. First, in the entire oleate concentration range (5*10C5 to 3.75*10P3 M), the total heat (MI,,,) is negative (exothermic). Second, when the initial oleate concentration is lower than 1. 10V3 M, the absolute value of d&, decreases with an increase of oleate concentration, and when the initial concentration is higher than l- lop3 M, the absolute value of dH,,, increases with an increase of oleate concentration. These results, as discussed later, have particular significance
78 TABLE
1
Measured total heats for oleate adsorption Initial concentration
of
at the fluorite/water
interface
(pH 9 and 25 aC )
Measured total heats,
oleate, Ci (M)
AH,, (cal g-i of CaF,)
0 5.0.10-5 1.0*10P4 2.5.10-4 5.0.10-*
- 0.4490 - 0.4237 -0.4189 -0.3721
7.5*10P4 1.2.10-3
-0.3225 -0.2788
2.o*1o-3 2.5.10-”
-0.3400 - 0.3885
3.8.10-a
- 0.5053
- 0.4259
when correlated measurements.
with the results from the FTIR
adsorption
density
FTIR adsorption density measurements The band assignments for the infrared spectra of oleic acid, sodium oleate and calcium oleate have been well established [ 11-141. Based on the following 1.87
-
CALCIUM
OLEATE
STANDARD
1.61
-
1.35
-
P is 8 * s
1.09 3000
2920 WAVENUMBER
Fig. 5. Spectra of calcium concentrations.
2800 ,
cm-’
oleate recorded from three KBr pellets with different
calcium oleate
19
w 0.30
Abs = 0.0063 CC.:
+ 2.9266Conc
0.9998
I 0.2 CONCENTRATION OF Ca012 IN KEr,% 0.1
Fig. 6. Linear plot of absorbance oleate in SO-mg KBr pellet.
at band 2927 cm-’
0.3
with respect to weight percentage of calcium
considerations, the band at 2927 cm-’ (assigned to asymmetric stretching vibration of -CH2) was chosen for the quantitative analysis used in this study: (1) this band is uniquely assigned and absent of interfering bands, (2 ) this band is identically observed in the spectra of oleic acid, sodium oleate, and calcium oleate; that is, the intensity of this band corresponds to the total amount of all oleate species and (3 ) the absorbance of this band obeys Beer’s Law very well. Figure 5 shows the spectra recorded from three KBr pellets with different calcium oleate concentrations. A linear regression between the absorbance of band 2927 cm-l (Abs) with respect to the weight percentage of calcium oleate in KBr (Cone) , as shown in Fig. 6, yields the following equation: Abs = 0.0063 + 2.9266 (Cone)
(3)
with a correlation coefficient of 0.9998. As described in a previous work [8], the absorbance (Abs) was obtained according to the following procedure: recording the original spectra of fluorite with adsorbed oleate, subtraction of the blank fluorite spectra from the original spectra using the water band as a reference and finally baseline correction to measure the absorbance difference between the peak and baseline. The adsorption density (r) was then calculated by Eqn (4): r=
KJ% 100 W, -Sa
(4)
where K is a constant to convert weight of calcium oleate to oleate, W, is the
80
TABLE 2 Adsorption density of oleate at fluorite/water interface as determined by FTIR Spectroscopy (pH 9 and 25°C) Initial concentration of oleate, Ci (M)
Adsorption density, r (mg of oleate/m’)
0 . 5.0*10-5 1.0.10-* 2.5*10-4
0 0.070 0.077 0.202
5.0*10-4 7.5.10-4 1.2*10-3 2.0*10-3
0.573 0.935 1.370 1.414
2.5.10-3
1.752
3.8*10-3
2.182
weight of the KBr pellet, W, is the weight of fluorite in the KBr pellet, and Sa the specific surface area of fluorite. The experimental results from FTIR adsorption density measurements are summarized in Table 2. Notice that the adsorption density included in Table 2 is always smaller than that presented in Fig. 1 for a given final oleate concentration. This difference between the two sets of adsorption density data is due to adsorption kinetics. As found by Hu et al. [4] oleate adsorption by fluorite can be a slow process. The adsorption density data included in Table 2 were obtained after only a 4 min conditioning time of oleate with fluorite during calorimetric measurements. These data in Table 2 are not equilibrium adsorption densities and should not correspond to isotherm data presented in Fig. 1, since a conditioning time of at least 2 h will be required for equilibration. Nevertheless, the adsorption densities included in Table 2 are still useful to describe the adsorption reaction and the state of the adsorbed species. DISCUSSION
Figure 1 and Tables 1 and 2 indicate that oleate species might adsorb at the fluorite/water interface with a horizontal orientation if the oleate adsorption density is not greater than 0.50 mg m2 (corresponding to monolayer coverage with horizontal orientation) [ 41. However, with an increase in adsorption density, the oleate species might tend to adsorb more with a vertical orientation. This transition between horizontal and vertical should eventually lead to a pseudo-vertical orientation when the adsorption density reaches 1.37 mg m’. The equilibrium concentration of the corresponding oleate adsorption density
81
0 ,
- 0.6 0.0
0.5
1 .s
1.0 SURFACE
COVERAGE,
Fig. 7. Measured total heats for oleate adsorption
2.0
8
at the fluorite/water
interface as a function of
surface coverage.
of 1.37 mg m2 distinguishes Region I from Region II. After reaching this adsorption density, the chemisorption reaction of Region I ceases, and the surface-precipitation reaction prevails. Since the enthalpy change associated with the oleate adsorption at the fluorite/water interface is positive in Region I and negative in Region II and chemisorption is expected to stop after 8 (e=r/T,, ratio of measured adsorption density over the adsorption density corresponding to monolayer coverage) reaches 1, a maximum heat of adsorption should be observed at this point, 8= 1. By combining the experimental results of microcalorimetric measurements and FTIR adsorption density measurements, a relationship between the measured total heat (D-J,,,) and surface coverage (0) was established as shown in Fig. 7. Here, a pseudo-vertical orientation of oleate at the fluorite/water interface was considered. The parking area of oleate was calculated to be 34.2 A”. The measured total heat (AH,,) reached a maximum when a complete oleate monolayer at this pseudo-vertical orientation was formed at the fluorite/water interface. This calculated parking area is greater than the cross-sectional area of oleate (20.5 A2) in a hydrated crystal state [ 151. However, it is smaller than the projected area of oleate (92.5 A”) in a horizontal orientation [ 41 and also smaller than the cross-sectional area of the oleate species (56.5 A”) as determined from Langmuir trough measurements with a monomolecular film of oleic acid on water [ 16,171. The oleate parking area (34.2 A”) at the fluorite/ water interface is consistent with the molecular area of oleate in the liquid crystal state (35 A”) [ 181. The microcalorimetric results (Fig. 7) show that, at lower oleate coverage, the absolute value of the heat decreases with an increase in adsorption density, whereas at higher oleate coverage, the absolute value of the heat increases with an increase in adsorption density. These results imply that, for lower coverage,
82
an endothermic adsorption reaction occurs, causing the overall reaction to be less exothermic when the adsorption density increases, and in the higher surface coverage region, an exothermic adsorption reaction occurs, causing the overall reaction to be more exothermic when the adsorption density increases. As mentioned before, in a previous work [4] it was postulated that the adsorption of oleate at the fluorite surface involves two reactions, chemisorption and surface precipitation. The chemisorption reaction, dominating at low adsorption coverage, appeared to be endothermic in nature, and the surface precipitation, dominating at high adsorption coverage, appeared to be exothermic in nature. Obviously, this initial speculation is now supported by these experimental results from microcalorimetric measurements. Based on the above analysis, a sequential adsorption model was developed to describe the oleate adsorption phenomena at the fluorite/water interface. Adsorption is considered to occur in two stages. In the first stage, i.e., Region I (see Fig. l), chemisorption occurs with chemisorbed oleate at a fractional coverage of 19,.In the second stage, i.e., Region II (see Fig. l), surface precipitation with a fractional coverage of 19,takes place. It is assumed that oleate adsorption by fluorite starts after immersion of fluorite into water. Under these circumstances, the measured total heat (dH,,, in cal g-l) can be calculated according to the following equation: dHWi=dHim
+@I
dHacls,I
+fe2dHads,II
(5)
where dHi, (equal to - 0.4490 cal g-‘) is the heat of immersion of fluorite from ambient environment into water, in cal g-l of fluorite; dH,&,i and dHads,II are the integral heats of oleate adsorption at the fluorite/water interface in Region I and Region II (Fig. l), respectively, and their units are cal mole1 of oleate; f (equal to 7.22. 10-5) is a conversion factor by which dHadS,ianddHads,rI can be converted from cal mol-l of oleate to cal g-l of fluorite. Based on this model, integral heats of adsorption (dHadS,iand dHads,rI)were calculated from the measured total heats (d&i) as a function of 8 (equal to 19,+ 0,) as shown in Fig. 8. Notice that the integral heats of adsorption are positive at 8< 1 (below monolayer coverage) and negative at 8> 1 (above monolayer coverage). These microcalorimetric results indicate that the oleate chemisorption reaction (8~ 1) is endothermic, while the oleate surface-precipitation reaction (8~ 1) is exothermic. Obviously the microcalorimetric results give further evidence for the initial hypothesis made from the adsorption isotherm data [4]. It is interesting to note from Fig. 8 that the absolute value of the experimental heats of adsorption (M&i,) decrease with an increase of surface coverage (0, or 0,) in each surface layer. This discrepancy can be attributed to the surface heterogeneities and the activated site adsorption. Nevertheless, since the integral heats of adsorption at 13,(LP&~,~) and at 0, (dH,,,, II) are the average heats of adsorption at the surface coverage of 8, and &, respectively, they should be comparable to the isosteric heats of adsorption at a corresponding
83
FLUORITE/OLEATE 25’C.
0.0
1.0
pH 9
2.0
SURFACE
Fig. 8. The integral heats of adsorption
COVERAGE.
3.0
8
of oleate at the fluorite/water
interface at different levels
of surface coverage.
level of surface coverage. The comparison is made in Table 3. The small discrepancy between the heats of adsorption determined from these two different approaches may be attributed to the simplicity of the sequential adsorption model and the different surface properties of fluorite used in these two different experiments. An optical-grade fluorite (0.118 m2 g-l ) was used in the measurement of adsorption isotherm, whereas a reagent-grade fluorite (14.89 m2 g-l ) was used in the microcalorimetric measurements. Nevertheless, the analysis is satisfactory, and the consistent heats of adsorption obtained from two different experiments improve our understanding about the complex adsorption reactions involved in the fluorite/oleate flotation system. TABLE
3
Comparison of the measured heats of adsorption of oleate at the fluorite/water isosteric heats of adsorption for different levels of surface coverage Heats of adsorption Measured by microcalorimetry Chemisorption (monolayer coverage) Surface precipitation (above monolayer coverage ) “At oleate surface coverage 0,=0.59
2.36 - 5.31” (i.e., 0=1.59).
interface
with
of oleate (kcal mol-‘1 Calculated from adsorption isotherm data
2.71 -6.60
84 SUMMARY
Microcalorimetric experiments together with FTIR spectroscopy have been successfully used to determine the heat of oleate adsorption at the fluorite/ water interface. The experimental results of the current study support the initial hypothesis that the adsorption of oleate at the fluorite surface involves both chemisorption and surface-precipitation reactions. The chemisorption reaction is endothermic in nature and predominant at low levels,of collector adsorption. The surface-precipitation reaction is exothermic in nature and predominant at high levels of collector adsorption. ACKNOWLEDGEMENT
This research has been supported by Department of Energy Grant No DEFG-02-84ER13181.AO02.
REFERENCES 1 2 3 4 5
10 11 12 13 14 15 16 17 18
J.D. Miller and M. Misra, in L.F. Laughton (Ed.), Proc. Int. Conf. Miner. Sci. Technol., The Council for Mineral Technology, Johannesburg, South Africa, 1984, pp. 259-268. F.W. Giesekke and P.J. Harris, in L.F. Laughton (Ed.), Proc. Int. Conf. Miner. Sci. Technol. The Council for Mineral Technology, Johannesburg, South Africa, 1984, pp. 269-278. Pradip and D.W. Fuerstenau, Colloids Surfaces, 8 (1983) 10. J.S. Hu, M. Misra and J.D. Miller, Int. J. Miner. Process., 18 (1986) 57. H.H. Haung, J.V. Calara, D.L. Bauer and J.D. Miller, in N.N. Li, R.B. Long, S.A. Stern and P. Somasundaran (Eds), Development in Separation Sciences, IV, CRC Press, Boca Raton, FL, 1978, pp. 115-133. H.H. Haung and J.D. Miller, Int. J. Miner. Process., 5 (1978) 241. R.I. Izatt, E.H. Redd and J.J. Christensen, Thermochim. Acta, 64 (1983) 355. J.S. Hu, M. Misra and J.D. Miller, Int. J. Miner. Process., 18 (1986) 73. Calorimeter Instruction Manual, Model 450, Thermometric Titration and Solution Calorimeter, Tronac Inc., Orem, UT, 1976. P. Somasundaran and K.P. Ananthapadmanabhan, in P. Somasundaran (Ed.), Advances in Mineral Processing, AIME, 1986, pp. 137-153. J.S. Hu, Ph.D. Thesis, University of Utah, 1985. P.R.G. Brandao, Ph.D. Thesis, University of British Columbia, 1982. K. Nakanishi and P.H. Solomon, Infrared Absorption Spectroscopy, 2nd edn, Holden-Day, San Francisco, 1977. L.J. Bellamy, The Infrared Spectra of Complex Molecules, Chapman and Hall, London, 1975. V.L. Klassen and V.A. Mokrousov, An Introduction to the Theory of Flotation, Butterworths, London, 1963. V.L. Schneider, R.T. Holman and G.O. Burr, J. Colloid Chem., 53 (1949) 1016. M.H. Buckenham and J.M.W. Mackenzie, SME Trans. AIME, 220 (1961) 450. J.M. Cases, J.E. Poirier and D. Canet, in J.M. Cases (Ed.) Solid-Liquid Interactions in Porous Media, Technip, Paris, 1985, pp. 335-370.
71 -
Printed in The Netherlands
Thermochemistry of Oleate Adsorption at the Fluorite/Water Interface J.D. MILLER,
J.S. HU and R. JIN
Department of Metallurgy and Metallurgical Engineering, University of Utah, Salt Lake City, UT 84112 (U.S.A.) (Received
4 October
1985; accepted 24 February 1989)
ABSTRACT A microcalorimetric technique has been used to measure heats of reaction of oleate in the fluorite system. These isoperibolic thermochemical measurements have been coupled with FTIR spectroscopic measurements to determine the corresponding adsorption densities. The results give further evidence for the initial hypothesis that the adsorption of oleate at the fluorite surface involves both chemisorption and surface-precipitation reactions. The chemisorption reaction is endothermic in nature and predominant at low levels of oleate adsorption. The surface-precipitation reaction is exothermic in nature and predominant at high levels of oleate adsorption.
INTRODUCTION
It is recognized in the fluorite/oleate system [ 1,2] as well as other semisoluble salt/collector systems [ 31 that important collector reactions include chemisorption, surface precipitation and aqueous-phase precipitation. In a recent study of oleate adsorption by fluorite, experimental techniques using radiotracer analysis have been developed to distinguish between adsorption (chemisorption and surface precipitation) and aqueous-phase precipitation [ 41. From the isotherms for oleate adsorption by fluorite at two different temperatures, shown in Fig. 1, at least two regions of adsorption can be identified: Region I. Chemisorption is predominant. Oleate is chemisorbed at the fluorite surface. The chemisorption reaction is endothermic with an increase in adsorption density at higher temperature. From the Clausius-Clapeyron equation, the isosteric enthalpy change associated with the adsorption process in this region (AH,) was estimated to be 2.77 kcal mol-’ of oleate [4]. The adsorbed oleate is tenacious and little is removed in this region by ultrasonic treatment. Region II. Surface precipitation is predominant. At higher oleate concentrations, surface-precipitated calcium oleate is formed
0166-6622/89/$03.50
0 1989 Elsevier Science Publishers B.V.
/
I
=lO
pli
With US Treatment
0
20°C
n
40°C
I
V -
monolayer
1
H - monolay~ 0
-0.5
1.0 EQUILIBRIUM
Fig. 1. Adsorption isotherms conditioning time, 2 h [ 41.
5.0 CONCENTRATION
.10 OF
50 OLEATE
J.-
100
, mg /I
of oleate on VOG fluorite at 20 and 40’ C with ultrasonic
treatment;
at the surface and the surface-precipitated calcium oleate, Ca(Ol)2, can be partially removed by ultrasonic treatment. In this region, the adsorption reaction appears to be exothermic with a decrease in adsorption density at higher temperature. The associated isosteric enthalpy change (AH,,) was estimated to be -6.7 kcal mol-1 of oleate using the Clausius-Clapeyron equation [ 41. In this current study, microcalorimetric techniques have been used to directly measure the heat of adsorption in Regions I and II. Also, FTIR transmittance techniques have been used to determine the corresponding adsorption densities of oleate at the fluorite surface after the microcalorimetric measurements. Based on the results of both microcalorimetric measurements and adsorption density measurements, a sequential adsorption model has been developed to describe oleate adsorption phenomena at the fluorite surface. EXPERIMENTAL
PROCEDURE
Materials Reagent-grade calcium fluoride obtained through the Ventron Division of Alfa Products, Danvers, MA, was used in this study. The specific surface area of the fluorite was found to be 14.89 m2 g-’ as determined by nitrogen adsorp-
73
tion using the BET method. Oleic acid of 99% purity was obtained from Alfa Products. The oleate used in microcalorimetric experiments was prepared by saponification of the oleic acid with a slight excess of NaOH (high purity). Calcium oleate was prepared by precipitation from 1O-3 M solutions of sodium oleate and calcium chloride (certified-grade reagent, Alfa Products) at 22 oC. Both solutions had their pH values adjusted to N 9.0 prior to precipitation. The precipitate was filtered, washed in distilled water at the same pH, washed in isopropanol and recrystallized from benzene. The calcium oleate was then dried overnight at 60°C and stored in a vacuum desiccator. Ultrapure NaOH and HCl (obtained from Alfa Products) were used to adjust the pH of the solution. Distilled water was used throughout the experiments. IR-grade KBr was obtained from Fisher Scientific Co., Pittsburgh, PA, and reagent-grade benzene was obtained from MC/B manufacturing Chemists, Inc. Los Angeles, CA. Thermochemical measurements The thermochemical measurements were accomplished with a microcalorimeter, Model 850, manufactured by Tronac Inc., Orem, UT. The apparatus consists of a water bath, reaction vessel, temperature controller and strip chart recorder. With the 16-gallon water bath, the temperature variations can be held within ? 5. 1O-4o C. Using suitable heating probes and coolant, the bath can be operated from - 10 to 80°C. The microcalorimeter was designed both for isothermal measurements in which the heat flux needed to maintain a constant temperature inside the reactor is measured and for isoperibolic measurements in which the temperature change inside the reactor is measured. Previous research had demonstrated that equivalent results were obtained using either experimental technique [ 5,6]. In this study, only the isoperibolic technique was used. The isoperibol calorimeter assembly is shown in Fig. 2. The reaction vessel is a wide-mouth aluminized Dewar flask with a 2-mm thin wall, a standard resistor heating coil (for heating and calibration) and a precision thermistor (2. 10e5”C sensitivity) connected to a Wheatstone bridge for temperature measurement. The thermistor had been calibrated with a Beckman 2°C differential thermometer. There are two techniques that can be used to measure the enthalpy change in this calorimeter, titration calorimetry and batch calorimetry [ 71. Titration calorimetry consists of introducing a titrant into the reaction vessel at a known constant rate (continuous titration) or in small equal volume amounts (incremental titration). Batch calorimetry refers to any calorimetric determination where no external mass is introduced across the vessel boundaries during the course of the determination. In this study, batch calorimetry was used. The batch calorimetric measurement consisted of putting 0.3 g of fluorite in a 2-cm3 thin wall ampoule which was then sealed with a microtorch. The am-
74
1
II II
_.__._._.. . PRECISION THERMISTER
‘AMPOULE BREAKING
ROD
I SYNCHRONOUS STIRRER DEWAR FLASK
Fig. 2. Schematic
representation
of the 25-ml isoperibol reaction vessel.
poule was placed in the ampoule holder underneath the breaking rod shown in Fig. 2. The Dewar flask containing 25 cm3 of oleate solution was connected to the calorimeter assembly. After turning on the stirrer, the reaction vessel was positioned in the center of the bath. The temperature in the reaction vessel was allowed to rise to the exact bath temperature (25°C) by means of the heating coil and the heat effect from stirring during a conditioning period of 20 min. The heat of reaction was initiated by breaking the ampoule and the temperature was recorded as a function of time on the strip chart recorder. This order of addition (dry fluorite to oleate solution) is consistent with that used in the previous studies [4,8] and was favored over breaking oleate solution-filled ampoules into a fluorite suspension for the following reasons: (1) heat of dilution of oleate solution was eliminated, (2) heat of neutralization associated with pH differences was minimized, and (3 ) the aqueous-phase precipitation of calcium oleate was minimized. FTIR adsorption density measurements Immediately after the calorimetric measurements, the pH of the suspension was measured and was found to deviate from the initial pH value by not more than 50.1 pH units. The separation of fluorite from the suspension was achieved by two-stage filtration with a Nalgene vacuum membrane filter. In
75
the first stage, a 400-mesh gauze was used to remove the broken ampoule glass. In the second stage, a membrane of 0.2 pm pore size was used to retain the finest fluorite particles. The cake was dried at room temperature and atmospheric pressure. KBr discs for FTIR transmission measurements were prepared using the following sequence of steps: First, 300 milligrams of mixture (sample and KBr ) at a desired proportion, typically 10% sample, was mixed for 20 min in a stainless-steel vial on a Wig-L-Bug mixer. Second, a 150-milligram portion of the mixture was carefully weighed and transferred to a die. Finally, the die was evacuated for 10 min with no load, then a load of 20 000 pounds was imposed for 10 min. The pressure usually dropped to 18 000 pounds after 10 min, so the pressure was raised to 20 000 pounds for an additional minute. This pressing technique resulted in discs of approximately 1.2 cm in diameter and 0.12 cm in thickness. The pressed sample served as a window for the FTIR experiments. Infrared spectra were recorded by a Nicolet 7000 series Fourier Transform Infrared Spectrometer (6000 bench) at 1 cm-l resolution. A germanium-coated KBr beam-splitter and a liquid nitrogen-cooled Hg-Cd-Te detector were used and each sample was scanned 200 times. RESULTS
Microcalorimetric measurements A typical thermogram for isoperibol experiments, as shown in Fig. 3, is characterized by three periods, lead, run and trail. S, and S, are the initial and final rates of temperature rise due to heat contributions of stirring, radiation, conduction, etc. The pulse signals the breakage of the ampoule, i.e., the initiation of the adsorption reaction, which causes a temperature rise dp during time At. A response immediately observed after breakage of the ampoule indicates the rate of adsorption is rapid. The corrected temperature rise ( dpc,,,) is found from Eqn ( 1) :
and the heat of reaction in the reaction vessel (Q) is then given as
Q=&mr$Jb
(2)
where C, is the heat capacity of the reaction vessel plus its contents, and b is the thermistor constant which is obtained by parallel calibration using two liquids, distilled water and benzene. To determine the heat capacity, C,, two experiments were performed under the same conditions. After the regular microcalorimetric measurements, fluorite was immediately separated from the suspension for FTIR adsorption density measurement in the first experiment
Q = Aucor.Cp/ Cp
b
0
b
: Heat Capacity : Thermister Constant
LEAD-
’
I
I
I
8
6
4
2
TIME
Fig. 3. A typical thermogram
0
,min
from an isoperibol microcalorimetric
experiment.
and an electric calibration was performed to determine C, in the second experiment. The heats of reaction Q measured by the two experiments were found to be very close to each other and the average values are reported. The details of the calibration procedures are described in the instruction manual [9]. A series of blank experiments were performed in order to determine the effect of ampoule breakage. As shown in Fig. 4, when an empty ampoule and a distilled water-filled ampoule were broken in distilled water, no temperature rise was observed. This phenomenon indicates that the mechanical energy released from the breakage of the ampoule is negligible. When a fluorite-filled ampoule was broken in distilled water, the enthalpy change is defined as the heat of immersion (dHi,). When a fluorite-filled ampoule was broken in oleate solution, the enthalpy change is defined as the total heat involved in the oleate adsorption process (M&i). It has been found that, when LIH,, is being determined, the trailing slope, S,, is always greater than the lead slope, S,, and furthermore S, continually decreases with time, approaching S,. This phenomenon is not particularly significant but does show the presence of some slow equilibration processes, involving Ca(Ol), and other oleate species. For example, both calcium oleate Ca(Ol), and oleic acid (HOI) are present in very small quantities in the reaction vessel. Bulk Ca( 01)2 may be formed after fluorite is introduced into the reaction vessel due to the presence of a small amount of calcium ions from dissolved fluorite. It is expected that oleate spe-
CaF2 /Hz0
Fig. 4. Thermograms
for various microcalorimetric
exper
nents.
ties are in equilibrium after conditioning and prior to microcalometric measurements. At pH 9, the predominant species of oleate are Ol-, then [Ol]zand H [ 011 z [lo]. The activity of HO1 is about four orders of magnitude smaller than that of Ol-. On this basis, it is believed that the dI-&~ measured in this work can be attributed to oleate adsorption‘at the fluorite/water interface and not to the dissociation of oleic acid (HOl). The measured total heat (d&,) in kcal g-l of fluorite as a function of initial concentration of oleate is present in Table 1. Two features are obvious. First, in the entire oleate concentration range (5*10C5 to 3.75*10P3 M), the total heat (MI,,,) is negative (exothermic). Second, when the initial oleate concentration is lower than 1. 10V3 M, the absolute value of d&, decreases with an increase of oleate concentration, and when the initial concentration is higher than l- lop3 M, the absolute value of dH,,, increases with an increase of oleate concentration. These results, as discussed later, have particular significance
78 TABLE
1
Measured total heats for oleate adsorption Initial concentration
of
at the fluorite/water
interface
(pH 9 and 25 aC )
Measured total heats,
oleate, Ci (M)
AH,, (cal g-i of CaF,)
0 5.0.10-5 1.0*10P4 2.5.10-4 5.0.10-*
- 0.4490 - 0.4237 -0.4189 -0.3721
7.5*10P4 1.2.10-3
-0.3225 -0.2788
2.o*1o-3 2.5.10-”
-0.3400 - 0.3885
3.8.10-a
- 0.5053
- 0.4259
when correlated measurements.
with the results from the FTIR
adsorption
density
FTIR adsorption density measurements The band assignments for the infrared spectra of oleic acid, sodium oleate and calcium oleate have been well established [ 11-141. Based on the following 1.87
-
CALCIUM
OLEATE
STANDARD
1.61
-
1.35
-
P is 8 * s
1.09 3000
2920 WAVENUMBER
Fig. 5. Spectra of calcium concentrations.
2800 ,
cm-’
oleate recorded from three KBr pellets with different
calcium oleate
19
w 0.30
Abs = 0.0063 CC.:
+ 2.9266Conc
0.9998
I 0.2 CONCENTRATION OF Ca012 IN KEr,% 0.1
Fig. 6. Linear plot of absorbance oleate in SO-mg KBr pellet.
at band 2927 cm-’
0.3
with respect to weight percentage of calcium
considerations, the band at 2927 cm-’ (assigned to asymmetric stretching vibration of -CH2) was chosen for the quantitative analysis used in this study: (1) this band is uniquely assigned and absent of interfering bands, (2 ) this band is identically observed in the spectra of oleic acid, sodium oleate, and calcium oleate; that is, the intensity of this band corresponds to the total amount of all oleate species and (3 ) the absorbance of this band obeys Beer’s Law very well. Figure 5 shows the spectra recorded from three KBr pellets with different calcium oleate concentrations. A linear regression between the absorbance of band 2927 cm-l (Abs) with respect to the weight percentage of calcium oleate in KBr (Cone) , as shown in Fig. 6, yields the following equation: Abs = 0.0063 + 2.9266 (Cone)
(3)
with a correlation coefficient of 0.9998. As described in a previous work [8], the absorbance (Abs) was obtained according to the following procedure: recording the original spectra of fluorite with adsorbed oleate, subtraction of the blank fluorite spectra from the original spectra using the water band as a reference and finally baseline correction to measure the absorbance difference between the peak and baseline. The adsorption density (r) was then calculated by Eqn (4): r=
KJ% 100 W, -Sa
(4)
where K is a constant to convert weight of calcium oleate to oleate, W, is the
80
TABLE 2 Adsorption density of oleate at fluorite/water interface as determined by FTIR Spectroscopy (pH 9 and 25°C) Initial concentration of oleate, Ci (M)
Adsorption density, r (mg of oleate/m’)
0 . 5.0*10-5 1.0.10-* 2.5*10-4
0 0.070 0.077 0.202
5.0*10-4 7.5.10-4 1.2*10-3 2.0*10-3
0.573 0.935 1.370 1.414
2.5.10-3
1.752
3.8*10-3
2.182
weight of the KBr pellet, W, is the weight of fluorite in the KBr pellet, and Sa the specific surface area of fluorite. The experimental results from FTIR adsorption density measurements are summarized in Table 2. Notice that the adsorption density included in Table 2 is always smaller than that presented in Fig. 1 for a given final oleate concentration. This difference between the two sets of adsorption density data is due to adsorption kinetics. As found by Hu et al. [4] oleate adsorption by fluorite can be a slow process. The adsorption density data included in Table 2 were obtained after only a 4 min conditioning time of oleate with fluorite during calorimetric measurements. These data in Table 2 are not equilibrium adsorption densities and should not correspond to isotherm data presented in Fig. 1, since a conditioning time of at least 2 h will be required for equilibration. Nevertheless, the adsorption densities included in Table 2 are still useful to describe the adsorption reaction and the state of the adsorbed species. DISCUSSION
Figure 1 and Tables 1 and 2 indicate that oleate species might adsorb at the fluorite/water interface with a horizontal orientation if the oleate adsorption density is not greater than 0.50 mg m2 (corresponding to monolayer coverage with horizontal orientation) [ 41. However, with an increase in adsorption density, the oleate species might tend to adsorb more with a vertical orientation. This transition between horizontal and vertical should eventually lead to a pseudo-vertical orientation when the adsorption density reaches 1.37 mg m’. The equilibrium concentration of the corresponding oleate adsorption density
81
0 ,
- 0.6 0.0
0.5
1 .s
1.0 SURFACE
COVERAGE,
Fig. 7. Measured total heats for oleate adsorption
2.0
8
at the fluorite/water
interface as a function of
surface coverage.
of 1.37 mg m2 distinguishes Region I from Region II. After reaching this adsorption density, the chemisorption reaction of Region I ceases, and the surface-precipitation reaction prevails. Since the enthalpy change associated with the oleate adsorption at the fluorite/water interface is positive in Region I and negative in Region II and chemisorption is expected to stop after 8 (e=r/T,, ratio of measured adsorption density over the adsorption density corresponding to monolayer coverage) reaches 1, a maximum heat of adsorption should be observed at this point, 8= 1. By combining the experimental results of microcalorimetric measurements and FTIR adsorption density measurements, a relationship between the measured total heat (D-J,,,) and surface coverage (0) was established as shown in Fig. 7. Here, a pseudo-vertical orientation of oleate at the fluorite/water interface was considered. The parking area of oleate was calculated to be 34.2 A”. The measured total heat (AH,,) reached a maximum when a complete oleate monolayer at this pseudo-vertical orientation was formed at the fluorite/water interface. This calculated parking area is greater than the cross-sectional area of oleate (20.5 A2) in a hydrated crystal state [ 151. However, it is smaller than the projected area of oleate (92.5 A”) in a horizontal orientation [ 41 and also smaller than the cross-sectional area of the oleate species (56.5 A”) as determined from Langmuir trough measurements with a monomolecular film of oleic acid on water [ 16,171. The oleate parking area (34.2 A”) at the fluorite/ water interface is consistent with the molecular area of oleate in the liquid crystal state (35 A”) [ 181. The microcalorimetric results (Fig. 7) show that, at lower oleate coverage, the absolute value of the heat decreases with an increase in adsorption density, whereas at higher oleate coverage, the absolute value of the heat increases with an increase in adsorption density. These results imply that, for lower coverage,
82
an endothermic adsorption reaction occurs, causing the overall reaction to be less exothermic when the adsorption density increases, and in the higher surface coverage region, an exothermic adsorption reaction occurs, causing the overall reaction to be more exothermic when the adsorption density increases. As mentioned before, in a previous work [4] it was postulated that the adsorption of oleate at the fluorite surface involves two reactions, chemisorption and surface precipitation. The chemisorption reaction, dominating at low adsorption coverage, appeared to be endothermic in nature, and the surface precipitation, dominating at high adsorption coverage, appeared to be exothermic in nature. Obviously, this initial speculation is now supported by these experimental results from microcalorimetric measurements. Based on the above analysis, a sequential adsorption model was developed to describe the oleate adsorption phenomena at the fluorite/water interface. Adsorption is considered to occur in two stages. In the first stage, i.e., Region I (see Fig. l), chemisorption occurs with chemisorbed oleate at a fractional coverage of 19,.In the second stage, i.e., Region II (see Fig. l), surface precipitation with a fractional coverage of 19,takes place. It is assumed that oleate adsorption by fluorite starts after immersion of fluorite into water. Under these circumstances, the measured total heat (dH,,, in cal g-l) can be calculated according to the following equation: dHWi=dHim
+@I
dHacls,I
+fe2dHads,II
(5)
where dHi, (equal to - 0.4490 cal g-‘) is the heat of immersion of fluorite from ambient environment into water, in cal g-l of fluorite; dH,&,i and dHads,II are the integral heats of oleate adsorption at the fluorite/water interface in Region I and Region II (Fig. l), respectively, and their units are cal mole1 of oleate; f (equal to 7.22. 10-5) is a conversion factor by which dHadS,ianddHads,rI can be converted from cal mol-l of oleate to cal g-l of fluorite. Based on this model, integral heats of adsorption (dHadS,iand dHads,rI)were calculated from the measured total heats (d&i) as a function of 8 (equal to 19,+ 0,) as shown in Fig. 8. Notice that the integral heats of adsorption are positive at 8< 1 (below monolayer coverage) and negative at 8> 1 (above monolayer coverage). These microcalorimetric results indicate that the oleate chemisorption reaction (8~ 1) is endothermic, while the oleate surface-precipitation reaction (8~ 1) is exothermic. Obviously the microcalorimetric results give further evidence for the initial hypothesis made from the adsorption isotherm data [4]. It is interesting to note from Fig. 8 that the absolute value of the experimental heats of adsorption (M&i,) decrease with an increase of surface coverage (0, or 0,) in each surface layer. This discrepancy can be attributed to the surface heterogeneities and the activated site adsorption. Nevertheless, since the integral heats of adsorption at 13,(LP&~,~) and at 0, (dH,,,, II) are the average heats of adsorption at the surface coverage of 8, and &, respectively, they should be comparable to the isosteric heats of adsorption at a corresponding
83
FLUORITE/OLEATE 25’C.
0.0
1.0
pH 9
2.0
SURFACE
Fig. 8. The integral heats of adsorption
COVERAGE.
3.0
8
of oleate at the fluorite/water
interface at different levels
of surface coverage.
level of surface coverage. The comparison is made in Table 3. The small discrepancy between the heats of adsorption determined from these two different approaches may be attributed to the simplicity of the sequential adsorption model and the different surface properties of fluorite used in these two different experiments. An optical-grade fluorite (0.118 m2 g-l ) was used in the measurement of adsorption isotherm, whereas a reagent-grade fluorite (14.89 m2 g-l ) was used in the microcalorimetric measurements. Nevertheless, the analysis is satisfactory, and the consistent heats of adsorption obtained from two different experiments improve our understanding about the complex adsorption reactions involved in the fluorite/oleate flotation system. TABLE
3
Comparison of the measured heats of adsorption of oleate at the fluorite/water isosteric heats of adsorption for different levels of surface coverage Heats of adsorption Measured by microcalorimetry Chemisorption (monolayer coverage) Surface precipitation (above monolayer coverage ) “At oleate surface coverage 0,=0.59
2.36 - 5.31” (i.e., 0=1.59).
interface
with
of oleate (kcal mol-‘1 Calculated from adsorption isotherm data
2.71 -6.60
84 SUMMARY
Microcalorimetric experiments together with FTIR spectroscopy have been successfully used to determine the heat of oleate adsorption at the fluorite/ water interface. The experimental results of the current study support the initial hypothesis that the adsorption of oleate at the fluorite surface involves both chemisorption and surface-precipitation reactions. The chemisorption reaction is endothermic in nature and predominant at low levels,of collector adsorption. The surface-precipitation reaction is exothermic in nature and predominant at high levels of collector adsorption. ACKNOWLEDGEMENT
This research has been supported by Department of Energy Grant No DEFG-02-84ER13181.AO02.
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10 11 12 13 14 15 16 17 18
J.D. Miller and M. Misra, in L.F. Laughton (Ed.), Proc. Int. Conf. Miner. Sci. Technol., The Council for Mineral Technology, Johannesburg, South Africa, 1984, pp. 259-268. F.W. Giesekke and P.J. Harris, in L.F. Laughton (Ed.), Proc. Int. Conf. Miner. Sci. Technol. The Council for Mineral Technology, Johannesburg, South Africa, 1984, pp. 269-278. Pradip and D.W. Fuerstenau, Colloids Surfaces, 8 (1983) 10. J.S. Hu, M. Misra and J.D. Miller, Int. J. Miner. Process., 18 (1986) 57. H.H. Haung, J.V. Calara, D.L. Bauer and J.D. Miller, in N.N. Li, R.B. Long, S.A. Stern and P. Somasundaran (Eds), Development in Separation Sciences, IV, CRC Press, Boca Raton, FL, 1978, pp. 115-133. H.H. Haung and J.D. Miller, Int. J. Miner. Process., 5 (1978) 241. R.I. Izatt, E.H. Redd and J.J. Christensen, Thermochim. Acta, 64 (1983) 355. J.S. Hu, M. Misra and J.D. Miller, Int. J. Miner. Process., 18 (1986) 73. Calorimeter Instruction Manual, Model 450, Thermometric Titration and Solution Calorimeter, Tronac Inc., Orem, UT, 1976. P. Somasundaran and K.P. Ananthapadmanabhan, in P. Somasundaran (Ed.), Advances in Mineral Processing, AIME, 1986, pp. 137-153. J.S. Hu, Ph.D. Thesis, University of Utah, 1985. P.R.G. Brandao, Ph.D. Thesis, University of British Columbia, 1982. K. Nakanishi and P.H. Solomon, Infrared Absorption Spectroscopy, 2nd edn, Holden-Day, San Francisco, 1977. L.J. Bellamy, The Infrared Spectra of Complex Molecules, Chapman and Hall, London, 1975. V.L. Klassen and V.A. Mokrousov, An Introduction to the Theory of Flotation, Butterworths, London, 1963. V.L. Schneider, R.T. Holman and G.O. Burr, J. Colloid Chem., 53 (1949) 1016. M.H. Buckenham and J.M.W. Mackenzie, SME Trans. AIME, 220 (1961) 450. J.M. Cases, J.E. Poirier and D. Canet, in J.M. Cases (Ed.) Solid-Liquid Interactions in Porous Media, Technip, Paris, 1985, pp. 335-370.