- Email: [email protected]
Water film properties on mineral surfaces in flotation processes
Colloids and Surfaces A: Physicochemical and Engineering Aspects, 79 (1993) 97-104 Elsevier Science Publishers B.V.. Amsterdam
91
Water film properties on mineral surfaces in flotation processes P. Staszczuk”
and B. Bililiski
Department of Physical Chemistry, Faculty of Chemistry, M. Curie-Sklodovska Sq. 3,20031 Lublin, Poland (Received 28 September
1992; accepted
25 January
Maria Curie-Sklodovska
University,
1993)
Abstract This paper presents the properties of hydration layers on mineral surfaces and their importance in the enrichment by flotation processes. Water layers possessing different properties from those in bulk water may be spontaneously formed due to polar and dispersive interactions of the molecules on both hydrophobic and hydrophilic surfaces. The layers of the highest binding energy (per molecule) constitute an energy barrier against the approach of an air bubble, and hence they create a relatively low Rotability of even hydrophobic minerals. It is stated that for good flotability the specific properties of vicinal water should be changed to achieve the properties of bulk water. This may be done by the addition of suitable components (collectors) which eliminate polar interactions and reduce the dispersive interactions to 25-35 mJ m-‘. The structure and thermodynamic properties of hydration layers formed on hydrophobized mineral surfaces become similar to those in bulk water, and they may be spontaneously disrupted. The work of destruction of such layers becomes comparable to the work of water cohesion. This results in a significant flotability of minerals. Keywords: Flotation;
mineral
surfaces; thermodynamic
properties;
Introduction Water and hydration layers influence the properties of many systems. The surface water layers play a very important role in many processes of both practical and scientific importance such as wettability, adhesion, catalysis, adsorption, soil science, as well as in mineral enrichment (e.g. flotation). As a result of interaction between water molecules and a mineral surface a wetting process takes place which can be considered as the adsorption of water molecules on the surface. This process is considerably influenced by both the type and the magnitude of intermolecular interactions. Close to the solid surface, the interaction of active sites provides a certain change in the water structure, resulting from hydrogen bonding, which is depen*Corresponding
author.
water film
dent on the distribution of active sites and on the distance of the solid surface. Hence the properties of vicinal (bonded) water are different from those in the bulk phase [l-3]. The water molecules adsorbed on a mineral surface (ordered hydration layer) form an energetic barrier against adhesion of an air bubble. Therefore such a layer should be eliminated. Hydration layers may be made to disrupt spontaneously by coating the surface with some organic, surface-active compound (collector). The wettability of minerals is dependent on the nature of adsorbed collector molecules, as they participate in the creation of a force field above the surface. The adsorbed collector molecules depress the adsorption of water, remove adsorbed water molecules and occupy the active sites on the surface. The surface properties become similar to those of a hydrocarbon. The best flotability occurs when the formation of air
P. Staszczuk, B. Biliriski/Colloids Surfaces A: Physicochem. Eng. Aspects 79 (1993) 97-104
98
bubble-mineral
grain
aggregates
by low surface hydration, low
stability.
Under
layers
may
be disrupted
allows
the direct
According
conditions
spontaneously
contact
between and
0.1 urn, i.e. 1000 times
single
molecule.
This
this
layer
depends
on
dynamic properties. Their chemical potential (free energy) depends on the layer thickness h and differs
[1,9]
from that of bulk water. The differential free energy of a liquid layer in a
amounts
the diameter the
Thin water layers formed between a mineral surface and an air bubble possess specific thermo-
and
[448].
co-workers
of the hydration
about
such and
air bubble
with a collector)
to Derjaguin
the thickness
of hydration layers
i.e. a thin water layer of dynamic
grain surface (coated
Thermodynamics
is accompanied
to of a
structure
one-component dG=
formed. The most highly ordered structure is formed close to the surface; then the interactions between water and solid surface decrease, and at a certain distance from the surface the layer achieves
system may be described
-SdT-pdl’+ydA+pddn
as (1)
where y is the surface free energy, A is the surface area, and other symbols have their usual mean-
the same properties as in a bulk phase [ 1,6,10]. It was found [4,1 l-163 that unstable hydration layers are necessary for the formation of stable air
ings [6]. The condition allowing contact between air bubble and mineral grain in an aqueous environment may be written as
bubble-mineral
~G=~s,-YL,-YsL<~
grain
aggregates.
The formation
of such aggregates takes place immediately after disruption of a water layer of critical thickness h,,. Unstable
hydration
hydrophobization face by adsorption ness
of
amounts stability
the
layers
may
spontaneously
disrupting
these processes
result were
influenced
problems
in
Important nificant
by
layers
to 15-60 nm. An investigation of the of the hydration layers suggested that
actions, which static forces. hydration
be achieved
of the originally hydrophilic surof proper collectors. The thick-
layers energetic
from van der Waals
the
on mineral
also
investigation
surfaces
and geometric
inter-
by electroof
are the sig-
heterogeneity
of
such surfaces and the very small values of the specific surface area (0.04-0.05 m2 g ’ ). The interpretation because
of the properties of translational,
of water is very difficult orientational
and thermal
fluctuations of the molecules. Between the water molecules possessing a large dipole moment there are strong hydrogen bonding interactions with a lifetime of about lo- l2 s. Therefore special experimental techniques and highly sensitive detectors are required. Investigation of the thermodynamic properties
of water
(especially
systems) rarely appear
(2)
where AG is the free energy of replacement of a solid/liquid interface by a solid/gas interface and ~so, yLo and ysL are the values of surface free energy at solid/gas, liquid/gas and solid/liquid interfaces respectively [7]. It is assumed in this relationship that no water layer exists between the bubble and the grain after contact formation, which is not necessarily true in real conditions. In Refs [6,8] the modified form of the above-mentioned relationship was presented: G(h) = YLG(h)
-
(3)
YLG
where G(h) is the energy
barrier
which has to be
overcome when an air bubble approaches the mineral surface. The energy barrier G(h) corresponds to a certain change in chemical potential which depends on the film thickness h. This change may be expressed by an additional excess pressure ll appearing in the liquid layer besides the normal pressure existing inside liquid water. The change in chemical potential of a thin water layer may be written as follows
cG31:
in finely dispersed
in the literature.
(4)
P. Staszczuk, B. Bililiski/Colloids Surfaces A: Physicochem. Eng. Aspects 79 (1993) 97-104
where p,, is the chemical potential of the thin layer of thickness h, pc is the chemical potential of bulk water, V, is the molar volume, p is the vapour pressure in equilibrium with the thin layer and p,, is the saturated vapour pressure at temperature T. This excess pressure 17 in the thin water layer, called “disjoining pressure” by Derjaguin and coworkers [l,lS], is a measure of proper thermodynamic changes. The value of II tends towards zero when the layer thickness h tends to infinity, and then p,, tends to pL,.Finally, n corresponds to the change in free energy as a function of h, and it may be described as m
YLG(h)
=
YLG
Il
+
dh
(5)
s h
where yLGch)is the free energy of the thin layer and yLo is the surface tension of the pure liquid. The disjoining pressure may be considered as the sum of several components. Derjaguin and Churaev [9] considered the disjoining pressure H as the sum of components resulting from intermolecular dispersive interactions, nd, from interactions of double electric layers, ne, and from structural effects (orientation, solvation, specific interactions), P : n=nd+ne+ns
(6)
They determined the dependence of the structural component IIS of water on the distance h from a quartz surface, on the basis of experimentally measured total disjoining pressures and the values of IZd and ne theoretically calculated according to the DLVO theory [9]. The film thickness depends on the nature of the liquid for the same value of n. Depending on the nature of the solid and the liquid, the value of II may be positive or negative; moreover, the sign may change with varying values of h. If 1? > 0, the layer is stable, and n represents an attractive force between layers of the liquid. Under specific conditions, for certain values of contact angle and layer thickness,
99
II < 0, the layer becomes unstable and it may spontaneously disrupt. Then, 17 represents a repulsive force between layers of the liquid. The properties and the structure of bonded water result from physicochemical properties of the solid surface, especially surface free energy. The surface free energy is an excess energy per unit of surface area resulting from non-compensated forces within the surface interfacial layer. Therefore the solids, after grinding, possess very large surface free energy values (and a strong surface electric field) which result from broken bonds. The surface free energy of solids and liquids results from various types of interaction, and it may be expressed as a sum of several components [ll]: y = yd + yh + yd-d +
yd-di
+
ydpa
+
ye
+
yz-z
(7)
where yd is the dispersive (London) component, yh is the hydrogen bonding component, ydMdis the dipole-dipole component, yd-di is the dipoleinduced dipole component, ydPa is the donoracceptor component, y” is the electrical component and y”-” is the component of rc-electron interactions to the surface free energy, respectively. Depending on the specific properties of the system under consideration (the solid and the liquid), one, two or more types of interaction may occur. The surface free energy has also been considered as a sum of two components [17]:
y = yd + yp
(8)
and polar where yd and yp are the dispersive components respectively of the surface free energy. The dispersive component yd results from dispersive interactions (London effect) while the polar one yp results from interactions other than dispersive (see Eqn (7)). The surface free energy of a hydrophobic solid may be determined from contact angle measurements. However, this method possesses several limitations especially with respect to the determination of yp. The other method consists of the measurement of the adsorption of vapour by a liquid on the mineral surface. From the adsorption
100
P. Staszczuk,
film
pressure
of a liquid
B. Biliriski/Colloids
isotherm
the
calculated equation
according to the Bangham-Razouk (resulting from the Gibbs adsorption
may
be
equation)
[ 18,191:
(RT/A)
a
d(ln p) = y - ysL
(9)
s 0
where A is the specific surface area of the mineral, a is the adsorbed amount, ‘/ is the surface free energy of the solid and ysL is the surface free energy of the solid covered with a liquid layer. As a result of the adsorption process, the solid surface free energy decreases and becomes the value of the surface tension of the liquid (at a saturation state). The method for the determination of yp from adsorption data has been presented in Refs [ 19,201 (including the thermodynamic basis) and later in Refs [21,22]. It was demonstrated that the work of adsorption film formation W (equivalent to the maximal, extrapolated film pressure n,,,, and accessible by integration of Eqn (9) up to saturated vapour pressure) may be equal to the sum of the work of adhesion (W,) and the work of cohesion (Wc) [19,20]: w=n,,,=
w + w, = w, + wc
where w and W, are the values of the work immersion and condensation respectively.
A: Physicochem.
phase is usually
Eng. Aspects 79 ((993)
limited to submonolayer
97-104
coverage.
Recently, the authors performed measurements of adsorption close to the saturation state (p/p, = I), which allowed the investigation of multilayer adsorption. This investigation provided some inter-
P II=
Surfaces
(10) of
On the curve II = f(a) several inflection points may appear, which correspond to the work of spreading, the work of immersion or the work of adhesion [19]. By applying the methodology mentioned above, the surface free energy was determined for several minerals [23], including sulfur [24], graphite [25] and coal [26]. The results obtained usually agreed with those determined by other methods. Another problem dealing with hydration layers is surface heterogeneity. Some interesting conclusions may be drawn from thermodynamics as evaluated by Kiselev, Hill, Everett and Schay [6,7]. The investigation of adsorption from the gaseous
esting information changes, formation,
about structure
adsorption, and thickness
nal water layers. The experiments measurements of adsorption and
energy of vici-
consisted desorption
of of
water vapour using the so-called “combined method” [27], as well as thermodesorption of water under dynamic and quasi-isothermal conditions. In the “combined method”, nitrogen saturated with water vapour (adsorption) or pure nitrogen (desorption) was passed over the sample, and the changes in sample mass were recorded. From the measurements at two or three different temperatures molar functions such as enthalpy AH, entropy AS and activation energy E, may be calculated according to the equations [28-311 In AT=
C - (EJRT)
(11)
AH = R{d ln[T$(d~/dt)]/d(l/T~)}
(12)
AS = R{AH/RT,
+ ln(AH/R)
- ln(Q,lW where AT is the deviation
- ln[Ti/(dT,/dt)] (13) of the DTA curve from
the baseline, C is a constant, T, is the temperature of the extreme effect point on the DTA curve, Tp is the sample temperature, t is the time, k is the Boltzmann constant, h is the Planck constant and R is the gas constant. The investigation included both polar and nonpolar mineral (solid) surfaces. The results were usually presented as a function of the amount of water adsorbed. This allows an easy recalculation to the layer thickness, expressed as a number of statistical monolayers (calculated on the basis of the specific surface area). Lately, the results of thermodesorption of liquid under quasi-isothermal and dynamic conditions [32] were used for the investigation of surface heterogeneity. Most solid surfaces are energetically, geometrically and structurally heterogeneous and
P. Staszczuk, B. Biliriski/Colloids Surfaces A: Physicochem. Eng. Aspects 79 (1993) 97-104
porous. These parameters determine the properties of liquid films (mainly their thickness and structure), and programmed thermodesorption reflects the state of the films on the surface studied. It appears from the data presented in Refs [33,34] that differential thermal analysis (DTA), differential thermogravimetry (DTG) and differential thermogravimetry in quasi- isothermal conditions (Q-TG) curves suggest heterogeneity of the investigated mineral surfaces. Some peaks and inflections on these curves correspond to desorption of water from active sites having different energies of interaction Based on the data from thermodesorption measurements, the adsorption potential distribution on the surface was calculated [32,35-371. For each solid a few characteristic peaks related to the solid physicochemical properties may be seen on the proper curves. These dependences allow the determination of some interesting parameters such as energy of adsorption and its distribution, and on the basis of this it is possible to determine the character of the studied surface by means of DTA and computer techniques. The influence of flotation collectors on surface water layers It is usually assumed that flotation collectors adsorb on adsorption sites of the highest energy, and this decreases the thickness and stability of the water layers and changes their structure. Some quantitative investigations of these parameters were performed, and then correlated with results of flotation tests [38-401. It was found that n-alkanes adsorbed on sulfur and quartz decrease the thickness of bonded water, the decrease depending on the length of the hydrocarbon chain; the thickness is smaller for even-numbered hydrocarbons. The flotability of sulfur coated with hydrocarbons was correlated with the adsorption of water and changes in zeta potential [41]. n-Alcohols also change the surface properties of quartz, the change depending on the length of the hydrocarbon chain. Compounds possessing 4-7 carbon atoms increase the hydration of the quartz
101
surface, while those possessing 8-10 carbon atoms result in its hydrophobation [42]. Diesel oil deposited on the surface of coal provides a significant depression of hydration of this surface. It was found that adsorption of water on coal conditioned with 400 g t-’ of diesel oil is smaller by about 60% when compared with that on a bare surface. The influence of flocculants is also dependent on the nature and concentration of a flocculant on the surface of coal and marble [38,39]. In Ref. [43] the investigation of froth flotation of model mixtures of coal and marble in the presence of some selected organic liquids was presented. Based on the values of the surface free energy determined, the work of wetting the coal and marble surfaces was calculated for those liquids, and some correlations were found between flotability and the work of spreading wetting. The measurements of water adsorption on copper ores demonstrated that coverage with ethyl xanthate results in an increase in the hydrophobicity of the surface. The adsorption of water is significantly influenced by the nature of waste minerals in copper ore [40]. Similar investigations were carried out for barite and a marble surface coated with tetradecylammonium chloride (TDACl) and galena coated with potassium ethyl xanthate (EtX) [28-311. DTA and gas chromatography were used in these investigations. The film thickness of water, the activation energy, enthalpy and entropy of adsorbed molecules were determined as a function of the amount of collector deposited on the mineral surface. Some examples of the relationships obtained are presented in Figs l-5. They show the important difference between the thickness and the properties of hydration layers on the recovery samples (curve 1) and the waste samples (curve 2) of marble after flotation. As can be seen from the figures, the properties of hydration layers on waste samples remain almost the same as those on bare (uncoated with collector) surfaces. This may result from surface heterogeneity and from differences in surface properties of particular mineral grains. The results from adsorption and thermodesorp-
P. Staszczuk. B. BiliriskilColloids Surfaces A: Physicochem. Eng. Aspects 79 (1993) 97-104
102
_-_-
-----
__--_------
.___--_------
Fig. 1. Amount of adsorbed water aA as a function of the TDACI statistical monolayer coverage of the marble surface, obtained using the combined method: curve 1, recovery samples; curve 2, waste samples.
1
I
I
0.5
1.0 N
*
Fig. 3. The relationship between the activation energy dE of the water molecules and the statistical monolayer coverage of TDACl deposited on the marble surface (dEa, activation energy of the bonded water on the bare marble surface; AE,, activation energy of bulk liquid water).
16 -
A
60 --13’ 0
I 0.5
I
I 1.0 N
)
Fig.2. Amount of adsorbed water aa as a function of the TDACl statistical monolayer coverage of the marble surface, obtained using the quasi-isothermal method: curve 1, recovery samples; curve 2, waste samples.
tion measurements in the galena/EtX system appear very similar to those obtained for marble and barite [31]. On the basis of these experimental data, as well as on data taken from the literature, the structure for the water layers was proposed. The presence of TDACl results in elimination of polar interactions from the surface (yp = 0) and in depression of dispersive interactions to 25-35 mJ me2; hence, the significant flotability of barite and marble. Similar changes in the structure of water layers were found for galena [31]. The results obtained for the galena/EtX system were analysed in a somewhat different way. Based on
~~,
----
.--
--_
___~Y5__
-
f
W
1.0
N Fig. 4. The enthalpy of water evaporation from the surface as a function of the TDACI statistical monolayer coverage deposited on the marble surface (AH,, enthalpy of evaporation of the bonded water from the bare marble surface; AHL, enthalpy of evaporation of bulk liquid water).
O0 ;2 r,
N 1.0
0.5 I
I As
1
I
m
bulk wotrr
Fig. 5. The relationship between the entropy of the water molecules and the statistical monolayer coverage of TDACl on the marble surface (dg,,,,,, ua,er, entropy of the water molecules on the bare marble surface).
P. Staszczuk. B. Bilitiski/Colfoids Surfaces A: Physicochem. Eng. Aspects 79 (1993) 97-104
the molar values of thermodynamic functions as well as on the thickness of the hydration layer (expressed as the number of statistical monolayers) the average values of these functions per unit surface were calculated (so called “surface functions”) [3 l] ES = aE”IA
Number of monolayers of adsorbed EtX 0
consumpfion.
kg/f
I
I
I
I
2
L
6
Initial
concentration,
mol/l
x 10L
Fig. 6. Flotability of galena (percentage recovery) as a function of EtX concentration in solution (lower scale) and collector consumption (upper scale).
phase contact line. Dixanthogen is an oily nonpolar compound which can additionally affect the durability of mineral grain-air bubble aggregates [45,46]; hence, the further increase in the flotability of galena. The calculations of the thermodynamic functions show significant changes in the structure of water layers, which becomes similar to that in bulk water. The activation energy and enthalpy of water molecules adsorbed onto the hydrophobized surface are lower compared with a bare mineral surface while the entropy of such molecules is higher. Under dynamic conditions such layers may be spontaneously disrupted, allowing an air bubble to approach the grain surface.
1
The “surface”
4.08 8.21 12.33 24.70
Collector
(14)
where ES is the surface function and Em is the molar function. These correspond to thermodynamic effects resulting from formation of the hydration layer possessing a certain structure and a certain thickness at the unit interfacial area. The results of these calculations are presented in Table 1. The flotability of galena with EtX is presented in Fig. 6 as a function of concentration and collector consumption. It may be seen that flotability increases in two steps: below and above the collector consumption of 2.0 kg t- ’ (corresponding to about eight monolayers of adsorbed xanthate). It was found that at this collector consumption the polar interactions of the galena surface were eliminated (yp = 0.15 mJ m-‘) [44]. At higher collector coating the total value of the free energy of the whole hydration layer (the work of destruction of this layer) appeared very close to the work of water cohesion (145.6 mJ mP2). The interactions between water molecules within the surface layer become comparable to those in bulk water, and therefore the layer may be easily disrupted. This may also result from the presence of dixanthogen in the surface collector layer and its activity at the threeTABLE
103
thermodynamic
functions
for hydration
layers on a galena
surface coated
with potassium
ethyl xanthate
(EtX)
AS’ (mJ m-‘)
Collector consumption (kg t-l) 0
1.0 2.0 3.0 6.0
4.780 5.861 4.249 -0.229 0.077
19.00 8.91 3.52 1.37 0.18
10.385 8.489 5.287 0.175 0.130
7.912 7.502 4.469 1.397 0.692
P. Staszczuk. B. Bililiski/Colloids Surfaces A: Physicochem. Eng. Aspects 79 (1993) 97-104
104
References 1 2 3 4
5 6 7
8 9 10
11 12 13 14 15 16 17 18 19 20
B.V. Derjaguin, N.V. Churaev and Z.M. Zorin, Izv. Akad. Nauk SSSR, Ser. Khim., 8 (1982) 1698. F.M. Etzler and W. Drost-Hansen, Croat. Chim. Acta, 56 (1983) 563. P.A. Rebinder, General Course in Colloid Chemistry, Moscow University Press, 1949. H.J. Schulze, Colloid Science Aspects of Mechanical Process Engineering, IXth European Chemistry of Interfaces Conference, Zakopane, Poland, 1986, Academy of Mining and Metallurgy, Krakow. H.J. Schulze, E. Topfer and G. Gottschalk, Aufbereit.Tech., 22 (1981) 465. J. Leja, Surface Chemistry of Froth Flotation, Plenum, New York, 1982, p. 107. D.W. Fuerstenau and S. Raghavan, in M.C. Fuerstenau (Ed.), Flotation, American Institute of Mining Engineers, New York, 1976, p. 21. J. Laskowski, Mater. Sci. Eng., 6 (1974) 4, 233. B.V. Derjaguin and N.V. Churaev, J. Colloid Interface Sci., 66 (1978) 389. P. Staszczuk and B. Bilinski, 10th Int. Conf. on Surface Forces, Moscow, 1992, Russian Academy of Sciences, Moscow. S. Wu, in D.R. Paul and S. Newman (Eds), Polymer Blends, Vol. 1, Academic Press, New York, 1978, p, 243. R.M. Pashley and J.A. Kitchener, J. Colloid Interface Sci., 71 (1979) 1545. H.J. Schulze, Colloid Polym. Sci., 254 (1976) 438; 256 (1978) 1037. J.N. Israelachvili, Faraday Discuss. Chem. Sot., 65 (1978) 20. B.V. Derjaguin, J.I. Rabinovich and N.V. Churaev, Izv. Akad. Nauk SSSR, Ser. Chim., 8 (1982) 1743. G. Peschel and P. Belouschek, Z. Phys. Chem., 108 (1977) 145. F.M. Fowkes, J. Adhes., 4 (1972) 155. A.C. Zettlemoyer, in F.M. Fowkes (Ed.), Hydrophobic Surface, Academic Press, New York, 1969, p. 1. P. Staszczuk, Chromatographia, 12 (1985) 724. P. Staszczuk, B. Janczuk and E. Chibowski, Mater. Chem. Phys., 12 (1985) 1 Il.
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
36
37 38 39 40 41 42 43 44 45 46
B. Bilinski and W. Wojcik, Colloids Surfaces, 25 (1987) 183. W. Wojcik and B. Bilinski, Colloids Surfaces, 30 (1988) 275. P. Staszczuk, Thesis, Maria Curie-Sklodovska University, Lublin, 1987. P. Staszczuk, J. Mater. Sci., 22 (1987) 4011. P. Staszczuk, Mater. Chem. Phys., 14 (1986) 279. P. Staszczuk, Fuel Sci. Technol. Int., 7 (1989) 89. P. Staszczuk, J. Therm. Anal., 30 (1985) I1 15. P. Staszczuk and B. Bilinski, Thermochim. Acta, 122 (1987) 363. P. Staszczuk and B. Bihnski, J. Therm. Anal., 32 (1987) 1457. P. Staszczuk and B. Bilinski, J. Therm. Anal., 36 (1990) 267. B. Bilinski, Powder Technol., 68 (1991) 125. P. Staszczuk, J. Therm. Anal., 38 (1992) 12. P. Staszczuk, R. Dobrowolski and M. Jaroniec, Langmuir, 8 (1992) 229. P. Staszczuk, M. Jaroniec and R.K. Gilpin, Anal. Chim. Acta, 269 (1992) 157. P. Staszczuk, Int. Symp. on Effects of Surface Heterogeneity in Adsorption and Catalysis on Solids, Kazimierz Dolny, Poland, 1992, Lublin Division of the Polish Chemical Society, Lublin, Abstract of Papers, p. 127. M. Jaroniec, R.K. Gilpin and P. Staszczuk, Int. Symp. on Effects of Surface Heterogeneity in Adsorption and Catalysis on Solids, Kazimierz Dolny, Poland, 1992, Lublin Division of the Polish Chemical Society, Lublin, Abstract of Papers, p. 145. P. Staszczuk, M. Cabrerizo-Vilchez and R. HidalgoAlvarez, Colloid Polym. Sci., in press. P. Staszczuk, Powder Technol., 34 (1983) 161. P. Staszczuk, Powder Technol., 34 (1983) 167. P. Staszczuk, Powder Technol., 35 (1983) 97. E. Chibowski, L. Hoiysz and P. Staszczuk, Pol. J. Chem., IO-12 (1986) 1167. P. Staszczuk, Mater. Chem. Phys., 10 (1984) 473. P. Staszczuk, L. Holysz, T. Biatopiotrowicz and B. Bilinski, Przem. Chem., 65 (1986) 158. B. Bihnski and W. Wojcik, J. Adhes. Sci. Technol., submitted for publication. R. Woods, J. Phys. Chem., 75 (1971) 354. D. Toperi and R. Tolun, Trans. Inst. Miner. Met., Section C, 78 (1969) 191.
91
Water film properties on mineral surfaces in flotation processes P. Staszczuk”
and B. Bililiski
Department of Physical Chemistry, Faculty of Chemistry, M. Curie-Sklodovska Sq. 3,20031 Lublin, Poland (Received 28 September
1992; accepted
25 January
Maria Curie-Sklodovska
University,
1993)
Abstract This paper presents the properties of hydration layers on mineral surfaces and their importance in the enrichment by flotation processes. Water layers possessing different properties from those in bulk water may be spontaneously formed due to polar and dispersive interactions of the molecules on both hydrophobic and hydrophilic surfaces. The layers of the highest binding energy (per molecule) constitute an energy barrier against the approach of an air bubble, and hence they create a relatively low Rotability of even hydrophobic minerals. It is stated that for good flotability the specific properties of vicinal water should be changed to achieve the properties of bulk water. This may be done by the addition of suitable components (collectors) which eliminate polar interactions and reduce the dispersive interactions to 25-35 mJ m-‘. The structure and thermodynamic properties of hydration layers formed on hydrophobized mineral surfaces become similar to those in bulk water, and they may be spontaneously disrupted. The work of destruction of such layers becomes comparable to the work of water cohesion. This results in a significant flotability of minerals. Keywords: Flotation;
mineral
surfaces; thermodynamic
properties;
Introduction Water and hydration layers influence the properties of many systems. The surface water layers play a very important role in many processes of both practical and scientific importance such as wettability, adhesion, catalysis, adsorption, soil science, as well as in mineral enrichment (e.g. flotation). As a result of interaction between water molecules and a mineral surface a wetting process takes place which can be considered as the adsorption of water molecules on the surface. This process is considerably influenced by both the type and the magnitude of intermolecular interactions. Close to the solid surface, the interaction of active sites provides a certain change in the water structure, resulting from hydrogen bonding, which is depen*Corresponding
author.
water film
dent on the distribution of active sites and on the distance of the solid surface. Hence the properties of vicinal (bonded) water are different from those in the bulk phase [l-3]. The water molecules adsorbed on a mineral surface (ordered hydration layer) form an energetic barrier against adhesion of an air bubble. Therefore such a layer should be eliminated. Hydration layers may be made to disrupt spontaneously by coating the surface with some organic, surface-active compound (collector). The wettability of minerals is dependent on the nature of adsorbed collector molecules, as they participate in the creation of a force field above the surface. The adsorbed collector molecules depress the adsorption of water, remove adsorbed water molecules and occupy the active sites on the surface. The surface properties become similar to those of a hydrocarbon. The best flotability occurs when the formation of air
P. Staszczuk, B. Biliriski/Colloids Surfaces A: Physicochem. Eng. Aspects 79 (1993) 97-104
98
bubble-mineral
grain
aggregates
by low surface hydration, low
stability.
Under
layers
may
be disrupted
allows
the direct
According
conditions
spontaneously
contact
between and
0.1 urn, i.e. 1000 times
single
molecule.
This
this
layer
depends
on
dynamic properties. Their chemical potential (free energy) depends on the layer thickness h and differs
[1,9]
from that of bulk water. The differential free energy of a liquid layer in a
amounts
the diameter the
Thin water layers formed between a mineral surface and an air bubble possess specific thermo-
and
[448].
co-workers
of the hydration
about
such and
air bubble
with a collector)
to Derjaguin
the thickness
of hydration layers
i.e. a thin water layer of dynamic
grain surface (coated
Thermodynamics
is accompanied
to of a
structure
one-component dG=
formed. The most highly ordered structure is formed close to the surface; then the interactions between water and solid surface decrease, and at a certain distance from the surface the layer achieves
system may be described
-SdT-pdl’+ydA+pddn
as (1)
where y is the surface free energy, A is the surface area, and other symbols have their usual mean-
the same properties as in a bulk phase [ 1,6,10]. It was found [4,1 l-163 that unstable hydration layers are necessary for the formation of stable air
ings [6]. The condition allowing contact between air bubble and mineral grain in an aqueous environment may be written as
bubble-mineral
~G=~s,-YL,-YsL<~
grain
aggregates.
The formation
of such aggregates takes place immediately after disruption of a water layer of critical thickness h,,. Unstable
hydration
hydrophobization face by adsorption ness
of
amounts stability
the
layers
may
spontaneously
disrupting
these processes
result were
influenced
problems
in
Important nificant
by
layers
to 15-60 nm. An investigation of the of the hydration layers suggested that
actions, which static forces. hydration
be achieved
of the originally hydrophilic surof proper collectors. The thick-
layers energetic
from van der Waals
the
on mineral
also
investigation
surfaces
and geometric
inter-
by electroof
are the sig-
heterogeneity
of
such surfaces and the very small values of the specific surface area (0.04-0.05 m2 g ’ ). The interpretation because
of the properties of translational,
of water is very difficult orientational
and thermal
fluctuations of the molecules. Between the water molecules possessing a large dipole moment there are strong hydrogen bonding interactions with a lifetime of about lo- l2 s. Therefore special experimental techniques and highly sensitive detectors are required. Investigation of the thermodynamic properties
of water
(especially
systems) rarely appear
(2)
where AG is the free energy of replacement of a solid/liquid interface by a solid/gas interface and ~so, yLo and ysL are the values of surface free energy at solid/gas, liquid/gas and solid/liquid interfaces respectively [7]. It is assumed in this relationship that no water layer exists between the bubble and the grain after contact formation, which is not necessarily true in real conditions. In Refs [6,8] the modified form of the above-mentioned relationship was presented: G(h) = YLG(h)
-
(3)
YLG
where G(h) is the energy
barrier
which has to be
overcome when an air bubble approaches the mineral surface. The energy barrier G(h) corresponds to a certain change in chemical potential which depends on the film thickness h. This change may be expressed by an additional excess pressure ll appearing in the liquid layer besides the normal pressure existing inside liquid water. The change in chemical potential of a thin water layer may be written as follows
cG31:
in finely dispersed
in the literature.
(4)
P. Staszczuk, B. Bililiski/Colloids Surfaces A: Physicochem. Eng. Aspects 79 (1993) 97-104
where p,, is the chemical potential of the thin layer of thickness h, pc is the chemical potential of bulk water, V, is the molar volume, p is the vapour pressure in equilibrium with the thin layer and p,, is the saturated vapour pressure at temperature T. This excess pressure 17 in the thin water layer, called “disjoining pressure” by Derjaguin and coworkers [l,lS], is a measure of proper thermodynamic changes. The value of II tends towards zero when the layer thickness h tends to infinity, and then p,, tends to pL,.Finally, n corresponds to the change in free energy as a function of h, and it may be described as m
YLG(h)
=
YLG
Il
+
dh
(5)
s h
where yLGch)is the free energy of the thin layer and yLo is the surface tension of the pure liquid. The disjoining pressure may be considered as the sum of several components. Derjaguin and Churaev [9] considered the disjoining pressure H as the sum of components resulting from intermolecular dispersive interactions, nd, from interactions of double electric layers, ne, and from structural effects (orientation, solvation, specific interactions), P : n=nd+ne+ns
(6)
They determined the dependence of the structural component IIS of water on the distance h from a quartz surface, on the basis of experimentally measured total disjoining pressures and the values of IZd and ne theoretically calculated according to the DLVO theory [9]. The film thickness depends on the nature of the liquid for the same value of n. Depending on the nature of the solid and the liquid, the value of II may be positive or negative; moreover, the sign may change with varying values of h. If 1? > 0, the layer is stable, and n represents an attractive force between layers of the liquid. Under specific conditions, for certain values of contact angle and layer thickness,
99
II < 0, the layer becomes unstable and it may spontaneously disrupt. Then, 17 represents a repulsive force between layers of the liquid. The properties and the structure of bonded water result from physicochemical properties of the solid surface, especially surface free energy. The surface free energy is an excess energy per unit of surface area resulting from non-compensated forces within the surface interfacial layer. Therefore the solids, after grinding, possess very large surface free energy values (and a strong surface electric field) which result from broken bonds. The surface free energy of solids and liquids results from various types of interaction, and it may be expressed as a sum of several components [ll]: y = yd + yh + yd-d +
yd-di
+
ydpa
+
ye
+
yz-z
(7)
where yd is the dispersive (London) component, yh is the hydrogen bonding component, ydMdis the dipole-dipole component, yd-di is the dipoleinduced dipole component, ydPa is the donoracceptor component, y” is the electrical component and y”-” is the component of rc-electron interactions to the surface free energy, respectively. Depending on the specific properties of the system under consideration (the solid and the liquid), one, two or more types of interaction may occur. The surface free energy has also been considered as a sum of two components [17]:
y = yd + yp
(8)
and polar where yd and yp are the dispersive components respectively of the surface free energy. The dispersive component yd results from dispersive interactions (London effect) while the polar one yp results from interactions other than dispersive (see Eqn (7)). The surface free energy of a hydrophobic solid may be determined from contact angle measurements. However, this method possesses several limitations especially with respect to the determination of yp. The other method consists of the measurement of the adsorption of vapour by a liquid on the mineral surface. From the adsorption
100
P. Staszczuk,
film
pressure
of a liquid
B. Biliriski/Colloids
isotherm
the
calculated equation
according to the Bangham-Razouk (resulting from the Gibbs adsorption
may
be
equation)
[ 18,191:
(RT/A)
a
d(ln p) = y - ysL
(9)
s 0
where A is the specific surface area of the mineral, a is the adsorbed amount, ‘/ is the surface free energy of the solid and ysL is the surface free energy of the solid covered with a liquid layer. As a result of the adsorption process, the solid surface free energy decreases and becomes the value of the surface tension of the liquid (at a saturation state). The method for the determination of yp from adsorption data has been presented in Refs [ 19,201 (including the thermodynamic basis) and later in Refs [21,22]. It was demonstrated that the work of adsorption film formation W (equivalent to the maximal, extrapolated film pressure n,,,, and accessible by integration of Eqn (9) up to saturated vapour pressure) may be equal to the sum of the work of adhesion (W,) and the work of cohesion (Wc) [19,20]: w=n,,,=
w + w, = w, + wc
where w and W, are the values of the work immersion and condensation respectively.
A: Physicochem.
phase is usually
Eng. Aspects 79 ((993)
limited to submonolayer
97-104
coverage.
Recently, the authors performed measurements of adsorption close to the saturation state (p/p, = I), which allowed the investigation of multilayer adsorption. This investigation provided some inter-
P II=
Surfaces
(10) of
On the curve II = f(a) several inflection points may appear, which correspond to the work of spreading, the work of immersion or the work of adhesion [19]. By applying the methodology mentioned above, the surface free energy was determined for several minerals [23], including sulfur [24], graphite [25] and coal [26]. The results obtained usually agreed with those determined by other methods. Another problem dealing with hydration layers is surface heterogeneity. Some interesting conclusions may be drawn from thermodynamics as evaluated by Kiselev, Hill, Everett and Schay [6,7]. The investigation of adsorption from the gaseous
esting information changes, formation,
about structure
adsorption, and thickness
nal water layers. The experiments measurements of adsorption and
energy of vici-
consisted desorption
of of
water vapour using the so-called “combined method” [27], as well as thermodesorption of water under dynamic and quasi-isothermal conditions. In the “combined method”, nitrogen saturated with water vapour (adsorption) or pure nitrogen (desorption) was passed over the sample, and the changes in sample mass were recorded. From the measurements at two or three different temperatures molar functions such as enthalpy AH, entropy AS and activation energy E, may be calculated according to the equations [28-311 In AT=
C - (EJRT)
(11)
AH = R{d ln[T$(d~/dt)]/d(l/T~)}
(12)
AS = R{AH/RT,
+ ln(AH/R)
- ln(Q,lW where AT is the deviation
- ln[Ti/(dT,/dt)] (13) of the DTA curve from
the baseline, C is a constant, T, is the temperature of the extreme effect point on the DTA curve, Tp is the sample temperature, t is the time, k is the Boltzmann constant, h is the Planck constant and R is the gas constant. The investigation included both polar and nonpolar mineral (solid) surfaces. The results were usually presented as a function of the amount of water adsorbed. This allows an easy recalculation to the layer thickness, expressed as a number of statistical monolayers (calculated on the basis of the specific surface area). Lately, the results of thermodesorption of liquid under quasi-isothermal and dynamic conditions [32] were used for the investigation of surface heterogeneity. Most solid surfaces are energetically, geometrically and structurally heterogeneous and
P. Staszczuk, B. Biliriski/Colloids Surfaces A: Physicochem. Eng. Aspects 79 (1993) 97-104
porous. These parameters determine the properties of liquid films (mainly their thickness and structure), and programmed thermodesorption reflects the state of the films on the surface studied. It appears from the data presented in Refs [33,34] that differential thermal analysis (DTA), differential thermogravimetry (DTG) and differential thermogravimetry in quasi- isothermal conditions (Q-TG) curves suggest heterogeneity of the investigated mineral surfaces. Some peaks and inflections on these curves correspond to desorption of water from active sites having different energies of interaction Based on the data from thermodesorption measurements, the adsorption potential distribution on the surface was calculated [32,35-371. For each solid a few characteristic peaks related to the solid physicochemical properties may be seen on the proper curves. These dependences allow the determination of some interesting parameters such as energy of adsorption and its distribution, and on the basis of this it is possible to determine the character of the studied surface by means of DTA and computer techniques. The influence of flotation collectors on surface water layers It is usually assumed that flotation collectors adsorb on adsorption sites of the highest energy, and this decreases the thickness and stability of the water layers and changes their structure. Some quantitative investigations of these parameters were performed, and then correlated with results of flotation tests [38-401. It was found that n-alkanes adsorbed on sulfur and quartz decrease the thickness of bonded water, the decrease depending on the length of the hydrocarbon chain; the thickness is smaller for even-numbered hydrocarbons. The flotability of sulfur coated with hydrocarbons was correlated with the adsorption of water and changes in zeta potential [41]. n-Alcohols also change the surface properties of quartz, the change depending on the length of the hydrocarbon chain. Compounds possessing 4-7 carbon atoms increase the hydration of the quartz
101
surface, while those possessing 8-10 carbon atoms result in its hydrophobation [42]. Diesel oil deposited on the surface of coal provides a significant depression of hydration of this surface. It was found that adsorption of water on coal conditioned with 400 g t-’ of diesel oil is smaller by about 60% when compared with that on a bare surface. The influence of flocculants is also dependent on the nature and concentration of a flocculant on the surface of coal and marble [38,39]. In Ref. [43] the investigation of froth flotation of model mixtures of coal and marble in the presence of some selected organic liquids was presented. Based on the values of the surface free energy determined, the work of wetting the coal and marble surfaces was calculated for those liquids, and some correlations were found between flotability and the work of spreading wetting. The measurements of water adsorption on copper ores demonstrated that coverage with ethyl xanthate results in an increase in the hydrophobicity of the surface. The adsorption of water is significantly influenced by the nature of waste minerals in copper ore [40]. Similar investigations were carried out for barite and a marble surface coated with tetradecylammonium chloride (TDACl) and galena coated with potassium ethyl xanthate (EtX) [28-311. DTA and gas chromatography were used in these investigations. The film thickness of water, the activation energy, enthalpy and entropy of adsorbed molecules were determined as a function of the amount of collector deposited on the mineral surface. Some examples of the relationships obtained are presented in Figs l-5. They show the important difference between the thickness and the properties of hydration layers on the recovery samples (curve 1) and the waste samples (curve 2) of marble after flotation. As can be seen from the figures, the properties of hydration layers on waste samples remain almost the same as those on bare (uncoated with collector) surfaces. This may result from surface heterogeneity and from differences in surface properties of particular mineral grains. The results from adsorption and thermodesorp-
P. Staszczuk. B. BiliriskilColloids Surfaces A: Physicochem. Eng. Aspects 79 (1993) 97-104
102
_-_-
-----
__--_------
.___--_------
Fig. 1. Amount of adsorbed water aA as a function of the TDACI statistical monolayer coverage of the marble surface, obtained using the combined method: curve 1, recovery samples; curve 2, waste samples.
1
I
I
0.5
1.0 N
*
Fig. 3. The relationship between the activation energy dE of the water molecules and the statistical monolayer coverage of TDACl deposited on the marble surface (dEa, activation energy of the bonded water on the bare marble surface; AE,, activation energy of bulk liquid water).
16 -
A
60 --13’ 0
I 0.5
I
I 1.0 N
)
Fig.2. Amount of adsorbed water aa as a function of the TDACl statistical monolayer coverage of the marble surface, obtained using the quasi-isothermal method: curve 1, recovery samples; curve 2, waste samples.
tion measurements in the galena/EtX system appear very similar to those obtained for marble and barite [31]. On the basis of these experimental data, as well as on data taken from the literature, the structure for the water layers was proposed. The presence of TDACl results in elimination of polar interactions from the surface (yp = 0) and in depression of dispersive interactions to 25-35 mJ me2; hence, the significant flotability of barite and marble. Similar changes in the structure of water layers were found for galena [31]. The results obtained for the galena/EtX system were analysed in a somewhat different way. Based on
~~,
----
.--
--_
___~Y5__
-
f
W
1.0
N Fig. 4. The enthalpy of water evaporation from the surface as a function of the TDACI statistical monolayer coverage deposited on the marble surface (AH,, enthalpy of evaporation of the bonded water from the bare marble surface; AHL, enthalpy of evaporation of bulk liquid water).
O0 ;2 r,
N 1.0
0.5 I
I As
1
I
m
bulk wotrr
Fig. 5. The relationship between the entropy of the water molecules and the statistical monolayer coverage of TDACl on the marble surface (dg,,,,,, ua,er, entropy of the water molecules on the bare marble surface).
P. Staszczuk. B. Bilitiski/Colfoids Surfaces A: Physicochem. Eng. Aspects 79 (1993) 97-104
the molar values of thermodynamic functions as well as on the thickness of the hydration layer (expressed as the number of statistical monolayers) the average values of these functions per unit surface were calculated (so called “surface functions”) [3 l] ES = aE”IA
Number of monolayers of adsorbed EtX 0
consumpfion.
kg/f
I
I
I
I
2
L
6
Initial
concentration,
mol/l
x 10L
Fig. 6. Flotability of galena (percentage recovery) as a function of EtX concentration in solution (lower scale) and collector consumption (upper scale).
phase contact line. Dixanthogen is an oily nonpolar compound which can additionally affect the durability of mineral grain-air bubble aggregates [45,46]; hence, the further increase in the flotability of galena. The calculations of the thermodynamic functions show significant changes in the structure of water layers, which becomes similar to that in bulk water. The activation energy and enthalpy of water molecules adsorbed onto the hydrophobized surface are lower compared with a bare mineral surface while the entropy of such molecules is higher. Under dynamic conditions such layers may be spontaneously disrupted, allowing an air bubble to approach the grain surface.
1
The “surface”
4.08 8.21 12.33 24.70
Collector
(14)
where ES is the surface function and Em is the molar function. These correspond to thermodynamic effects resulting from formation of the hydration layer possessing a certain structure and a certain thickness at the unit interfacial area. The results of these calculations are presented in Table 1. The flotability of galena with EtX is presented in Fig. 6 as a function of concentration and collector consumption. It may be seen that flotability increases in two steps: below and above the collector consumption of 2.0 kg t- ’ (corresponding to about eight monolayers of adsorbed xanthate). It was found that at this collector consumption the polar interactions of the galena surface were eliminated (yp = 0.15 mJ m-‘) [44]. At higher collector coating the total value of the free energy of the whole hydration layer (the work of destruction of this layer) appeared very close to the work of water cohesion (145.6 mJ mP2). The interactions between water molecules within the surface layer become comparable to those in bulk water, and therefore the layer may be easily disrupted. This may also result from the presence of dixanthogen in the surface collector layer and its activity at the threeTABLE
103
thermodynamic
functions
for hydration
layers on a galena
surface coated
with potassium
ethyl xanthate
(EtX)
AS’ (mJ m-‘)
Collector consumption (kg t-l) 0
1.0 2.0 3.0 6.0
4.780 5.861 4.249 -0.229 0.077
19.00 8.91 3.52 1.37 0.18
10.385 8.489 5.287 0.175 0.130
7.912 7.502 4.469 1.397 0.692
P. Staszczuk. B. Bililiski/Colloids Surfaces A: Physicochem. Eng. Aspects 79 (1993) 97-104
104
References 1 2 3 4
5 6 7
8 9 10
11 12 13 14 15 16 17 18 19 20
B.V. Derjaguin, N.V. Churaev and Z.M. Zorin, Izv. Akad. Nauk SSSR, Ser. Khim., 8 (1982) 1698. F.M. Etzler and W. Drost-Hansen, Croat. Chim. Acta, 56 (1983) 563. P.A. Rebinder, General Course in Colloid Chemistry, Moscow University Press, 1949. H.J. Schulze, Colloid Science Aspects of Mechanical Process Engineering, IXth European Chemistry of Interfaces Conference, Zakopane, Poland, 1986, Academy of Mining and Metallurgy, Krakow. H.J. Schulze, E. Topfer and G. Gottschalk, Aufbereit.Tech., 22 (1981) 465. J. Leja, Surface Chemistry of Froth Flotation, Plenum, New York, 1982, p. 107. D.W. Fuerstenau and S. Raghavan, in M.C. Fuerstenau (Ed.), Flotation, American Institute of Mining Engineers, New York, 1976, p. 21. J. Laskowski, Mater. Sci. Eng., 6 (1974) 4, 233. B.V. Derjaguin and N.V. Churaev, J. Colloid Interface Sci., 66 (1978) 389. P. Staszczuk and B. Bilinski, 10th Int. Conf. on Surface Forces, Moscow, 1992, Russian Academy of Sciences, Moscow. S. Wu, in D.R. Paul and S. Newman (Eds), Polymer Blends, Vol. 1, Academic Press, New York, 1978, p, 243. R.M. Pashley and J.A. Kitchener, J. Colloid Interface Sci., 71 (1979) 1545. H.J. Schulze, Colloid Polym. Sci., 254 (1976) 438; 256 (1978) 1037. J.N. Israelachvili, Faraday Discuss. Chem. Sot., 65 (1978) 20. B.V. Derjaguin, J.I. Rabinovich and N.V. Churaev, Izv. Akad. Nauk SSSR, Ser. Chim., 8 (1982) 1743. G. Peschel and P. Belouschek, Z. Phys. Chem., 108 (1977) 145. F.M. Fowkes, J. Adhes., 4 (1972) 155. A.C. Zettlemoyer, in F.M. Fowkes (Ed.), Hydrophobic Surface, Academic Press, New York, 1969, p. 1. P. Staszczuk, Chromatographia, 12 (1985) 724. P. Staszczuk, B. Janczuk and E. Chibowski, Mater. Chem. Phys., 12 (1985) 1 Il.
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
36
37 38 39 40 41 42 43 44 45 46
B. Bilinski and W. Wojcik, Colloids Surfaces, 25 (1987) 183. W. Wojcik and B. Bilinski, Colloids Surfaces, 30 (1988) 275. P. Staszczuk, Thesis, Maria Curie-Sklodovska University, Lublin, 1987. P. Staszczuk, J. Mater. Sci., 22 (1987) 4011. P. Staszczuk, Mater. Chem. Phys., 14 (1986) 279. P. Staszczuk, Fuel Sci. Technol. Int., 7 (1989) 89. P. Staszczuk, J. Therm. Anal., 30 (1985) I1 15. P. Staszczuk and B. Bilinski, Thermochim. Acta, 122 (1987) 363. P. Staszczuk and B. Bihnski, J. Therm. Anal., 32 (1987) 1457. P. Staszczuk and B. Bilinski, J. Therm. Anal., 36 (1990) 267. B. Bilinski, Powder Technol., 68 (1991) 125. P. Staszczuk, J. Therm. Anal., 38 (1992) 12. P. Staszczuk, R. Dobrowolski and M. Jaroniec, Langmuir, 8 (1992) 229. P. Staszczuk, M. Jaroniec and R.K. Gilpin, Anal. Chim. Acta, 269 (1992) 157. P. Staszczuk, Int. Symp. on Effects of Surface Heterogeneity in Adsorption and Catalysis on Solids, Kazimierz Dolny, Poland, 1992, Lublin Division of the Polish Chemical Society, Lublin, Abstract of Papers, p. 127. M. Jaroniec, R.K. Gilpin and P. Staszczuk, Int. Symp. on Effects of Surface Heterogeneity in Adsorption and Catalysis on Solids, Kazimierz Dolny, Poland, 1992, Lublin Division of the Polish Chemical Society, Lublin, Abstract of Papers, p. 145. P. Staszczuk, M. Cabrerizo-Vilchez and R. HidalgoAlvarez, Colloid Polym. Sci., in press. P. Staszczuk, Powder Technol., 34 (1983) 161. P. Staszczuk, Powder Technol., 34 (1983) 167. P. Staszczuk, Powder Technol., 35 (1983) 97. E. Chibowski, L. Hoiysz and P. Staszczuk, Pol. J. Chem., IO-12 (1986) 1167. P. Staszczuk, Mater. Chem. Phys., 10 (1984) 473. P. Staszczuk, L. Holysz, T. Biatopiotrowicz and B. Bilinski, Przem. Chem., 65 (1986) 158. B. Bihnski and W. Wojcik, J. Adhes. Sci. Technol., submitted for publication. R. Woods, J. Phys. Chem., 75 (1971) 354. D. Toperi and R. Tolun, Trans. Inst. Miner. Met., Section C, 78 (1969) 191.