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The adsorption of sodium dodecyl sulphate on fluorite and its surface free energy
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surface science Applied Surface Science 81(1994) 95-102
ELSEVIER
The adsorption of sodium dodecyl sulphate on fluorite and its surface free energy B. Jaiiczuk ‘, M.L. GonzBlez-Martin, J.M. Bruque * Departamento de Fisica, Facultad de Ciencias, Universidad de Extremadura, Au. Elvas s/n, 06071 Badajoz, Spain
Received 8 November 1993; accepted for publication 6 June 1994
Abstract The contact angles of SDS solutions in the range of concentration from 0 to 5 x lo-’ M on fluorite and fluorite coated with SDS films of different thickness have been measured. The contact angles for these systems were also evaluated theoretically from the components of the surface free energy, resulting from Lifshitz-van der Waals and acid-base intermolecular interactions, of fluorite and solution. The interfacial free energies of interaction between DS ions and fluorite and fluorite/SDS film surface through water were determined for both the polar head of the DS- ion and its hydrocarbon chain. Using the contact angle values obtained, a relationship between the adhesion tension and the surface tension of the SDS solution has been established. There was found to be a linear dependence between the adhesion tension and the surface tension in the range of concentration of SDS from 0 up to the cmc. The slopes of the straight lines for fluorite/ SDS film formed from solutions in the range from 10e4 to lop3 M are almost equal to - 1, as for paraffin. It can also be stated that if the electrostatic interaction between the DSions and the Ca’+ ions is small, it is more probable that the DS- ions are oriented to the fluorite surface at the
fluorite/solution interface by their hydrocarbon chain than by their polar head.
1. Introduction
The adsorption of surfactants at the solid/ liquid interface plays a very important role in many branches of industry, among them in the recovering of minerals by flotation. It is known that the wettability of a solid is closely connected to the value of the components
* Corresponding author. ’ On sabbatical leave from the Department of Physical Chemistry, Faculty of Chemistry, Maria Curie-Sklodowska University, 20-031 Lublin, Poland..
of its surface free energy, which result from different intermolecular interactions [l]. The influence of surfactants on the wettability of solids has been studied from basic and technological points of view for decades. From a fundamental perspective there has been a great interest in quantifying the thermodynamic relationships between the adsorption of surfactants and the free energy of the interfaces involved. Many studies indicate that for nonpolar solids, such as paraffin and polyethylene, when the adsorption of surfactanti takes place via the hydrocarbon chain at the solid/liquid interface [2-51, the application of Gibbs’s and Young’s equations leads
0169-4332/94/$07.00 0.1994 Elsevier Science B.V. All rights reserved SSDZ 0169-4332(94)00154-S
to results
in very
good
agreement
with
96
B. Jariczuk et al. /Applied Surface Science 81 (1994) 95-102
experimental values. However, for highly polar solids, such as quartz and silica, for which the polar group of the surfactant interacts strongly with the OH groups present on the solid surface, the relationship between contact angle and adsorption is more complicated [6]. Despite the studies done for nonpolar and highly polar solids, there is a lack of information dealing with the relationship between the adsorption of an ionic surfactant with a long hydrocarbon chain on mineral surfaces and their wettability or surface free energy. Therefore, from a practical and a theoretical point of view, it could be interesting to use Young’s and Gibbs’s equations to explain the adsorption of the anionic surfactant sodium dodecyl sulphate on the surface of the semi-soluble fluorite in relation with the change of the wettability and surface free energy of the mineral. For this purpose the contact angles of SDS solutions on the fluorite surface coated with a SDS film (fluorite/ SDS film) have been measured.
mineral specimens of fluorite were cut into plates, polished by emery paper of various grades and then washed several times in doubly distilled and de-ionized water, cleaned in an ultrasonic bath for 15 min, dried at room temperature and kept in a desiccator. For the studies, sodium dodecyl sulphate (purity > 99% - from Merck) (SDS) was used. 2.2. Measurements SDS was dissolved in doubly distilled and deionized water, and then a series of solutions were prepared in the range of concentration from 5 x 10e6 to 2 X 1O-5 M. The pH was uncontrolled but in each case was about 5.85. The fluorite plates were equilibrated with a solution of SDS at a given concentration for 24 h, a time checked as long enough to ensure the adsorption equilibrium of SDS on the fluorite surface. After equilibration, the plates were dried at 50°C for 30 min and placed in the measuring chamber. The plates of “bare” fluorite (plates of fluorite without adsorbed SDS) were equilibrated with doubly distilled and de-ionized water at pH = 5.85 for 24 h before the contact angle measurements. The advancing contact angle was measured at 20 f 1°C by the sessile drop method [7] using a camera-computer system [8]. For a given system,
2. Experimental details 2.1. Materials Fluorite samples from Cordoba (Spain) were used for the contact angle measurements. The
Table 1 Contact angle 0, (deg) for SDS solutions on the fluorite and fluorite/SDS solutions taken from the literature 1151
film surfaces, and values of the surface tension of SDS
C CM) of SDS in drop
C (M) of SDS solution from which the film was constructed 0 5 x 10-6 10-s 5 x 10-5 10-4 5 x 10-4
10-s
5 x10-3
10-r
5 x 10-2
0 5 x 10-6 10-S 5 x 10-5 10-4 2 x 10-4 5 x 10-4 10-s 2 x 10-s 5 x 10-s 10-r 5 x 10-r
67.9 67.6 67.8 67.1 66.9 66.1 62.9 55.6 45.2 0.0 0.0 0.0
83.5 83.3 83.1 82.7 82.6 81.0 77.5 69.8 57.3 28.1 12.0 0.0
79.1 79.2 78.5 78.4 77.5 77.3 73.4 65.1 54.6 22.4 9.0 0.0
75.4 75.2 74.7 74.3 74.1 73.5 69.1 62.1 49.6 14.2 5.0 0.0
72.8 72.4 72.4 71.9 71.9 70.0 66.7 59.9 47.0 12.0 0.0 0.0
75.4 75.2 74.8 74.5 74.4 73.0 69.1 61.8 48.9 8.0 0.0 0.0
77.9 77.8 77.1 76.6 75.7 75.9 72.2 63.5 51.1 14.0 5.0 0.0
78.3 78.2 78.3 77.3 77.1 75.9 72.8 64.0 52.0 17.1 7.3 0.0
81.2 81.1 80.7 80.3 80.3 78.5 75.7 66.8 55.2 23.3 10.7 0.0
82.3 82.2 81.7 81.7 81.1 79.7 76.6 67.4 55.9 25.4 11.4 0.0
&J/m)
72.8 72.4 72.3 71.9 71.3 70.0 66.6 59.8 52.5 42.9 38.0 38.0
91
B. Jaticzuk et al. /Applied Surface Science 81 (1994) 95-102
at least 30 measurements were made and the accuracy was within 2”. For a given drop on the fluorite/SDS film surface, the contact angle was measured at intervals of 1 min from 1 until 30 min after it settled. The contact angle measurements were made for a series of SDS solutions in the range of concentration (C) from 0 to 5 X 10e2 M.
3. Results The average values of the contact angles obtained in the first three minutes after the drop of solution settled on the surface are shown in Table 1. From Table 1 it appears that for each fluorite sample the contact angle (0,) decreases as the concentration of SDS in the drop increases. The changes of 0, against C can be divided into two parts. The first corresponds to concentrations of SDS in the drop from 0 to 5 X 10m4 M, for which 0, decreases only a few degrees with C, and the second to the range of C from 5 X 10e4 to 5 x 10m2 M, for which there is an important fall of 0, with C. The contact angle also depends on the degree of coverage of the fluorite surface with ‘SDS molecules. For a given concentration in drop, 0, increases up to a maximum corresponding to the sample which was equilibrated, prior to the contact angle measurement, with a solution of SDS at concentration 10m3 M, except for C = 5 x 10e2 M which completely spreads on all the fluorite samples. It must also be noted that, for each C from 0 up to 5 x 10m3 M, 0, for “bare” fluorite is smaller than for any other fluorite sample, no matter the thickness of the SDS film. The measurements of the contact angle as a function of time for a given drop showed two different types of behaviour. The contact angle 8, changed considerably with time for “bare” fluorite and fluorite/SDS film formed from a solution at low and high concentration; therefore, for these cases the average contact angle values presented in Table 1 should be treated as dynamic contact angles. However, 0, was practically constant with time for fluorite/SDS film obtained from solutions at concentration from 5 X 10m5 up
to 10e3 M, and 0, can be taken as an advancing contact angle.
4. Discussion Fluorite is a semi-soluble mineral which can interact with the SDS molecules by Lifshitz-van der Waals, acid-base and electrostatic forces. The presence of calcium and dodecyl sulphate ions in solution leads to the precipitation of calcium dodecyl sulphate (CaDS) if the solubility product of the latter is exceeded. Then, chemisorption, precipitation and also physisorption of SDS from solution can occur on the fluorite surface [g-11], affecting the values of the contact angle in the fluorite-SDS solution drop-air system (Table 1). A relationship between the amount adsorbed at the surface under the drop and at the liquid/ vapour interface of the drop can be obtained via the changes of the adhesion tension with the surface tension. According to the Young equation, the adhesion tension, y,_ cos 8, [5] can be expressed [l] as: ysv - ysL = yL cos 0,
(1) where ysv and ysL are the interfacial free energy of the solid/vapour and solid/ liquid interfaces, respectively, yL is the surface tension of the liquid and 8 is the contact angle. Combining Young’s and Gibbs’ equations gives [41: eL
~0s0) 9L
=
rsv -
rs,
r LV
’
(2)
where rsv, rsL and rLv are the surface concentration of surfactant at the solid/vapour, solid/ liquid and liquid/vapour interfaces, respectively. According to Eq. (2), if the adsorption of surfactant from the drop onto the solid surface around it can be neglected Vsv = 01, the slope Xy, cos 8)/ay, coincides with the ratio -r,,/T,,. Figs. 1 and 2 show plots of the adhesion tension evaluated from the contact angles of SDS solutions measured on “bare” fluorite and on fluorite/SDS film versus the surface tension of the solution (it should be remembered that for
98
B. Jahczuk et al. /Applied
I
10
30
40
I
Surface Science 81 (1994) 95-102
I
50 yR CmN/m?O
70
80
Fig. 1. Adhesion tension evaluated from the contact angles measured on the surface of fluorite and fluorite/SDS film formed from solutions of different concentrations versus the surface tension of the SDS solution in the drop.
centrations higher than the cmc, it is impossible to state anything about the differences between rs, and r,,. The role played by the possible chemisorption of DS- ions during the time of measurement can be analyzed by comparing the measured contact angles with those evaluated with the aid of the van Oss et al. approach to the surface and the inter-facial free energy of systems including a solid phase [ 12-141. According to this approach, Eq. (1) can be written in the form: yr(cos 0 + 1) +ne, = 2( yiwy;w)i’* +
some systems the dynamic contact angle was used in Young’s equation). From these figures, there seems to be a linear relationship between the adhesion tension and the surface tension of the solution in the range of SDS concentration from 0 to 5 X 10e3 M, slightly lower than the cmc of SDS [l]. The slope of the straight lines depends on the degree of coverage of fluorite with the SDS film, decreasing to a minimum, close to - 1, for fluorite/SDS film systems formed from concentrations between 10e4 and 10m3 M for which, from Eq. (21, r,, = r,v. Of course, at SDS con-
8
00000 . . . . . 00000 . . . . . llanaa
I
1
I
I
40
50
60
70
80
YR (mN/m)
Fig. 2. Adhesion tension evaluated from the contact angles measured on the surface of fluorite/SDS film formed from solutions of different concentrations versus the surface tension of the SDS solution in the drop.
2(Ys+YLy* + 2(ysyty*,
(3)
where yLw is the Lifshitz-van der Waals component of the surface free energy of solid (S) and liquid CL), y+ is the electron-acceptor and ythe electron-donor part of the acid-base (yAB) component of the solid (S) and liquid (L) surface and ne, is the free energy (y AB= 2(y+y-)‘I*), spreading film pressure, which is commonly taken as zero for contact angles higher than zero [12141. If the yiw, Ys+, YSV YLLW 9 rt and y; values are known, it is possible to determine the contact angles, 8, from Eq. (3). The yr values for SDS solutions were taken from the literature [151. At the solution/vapour interface, the hydrocarbon chain of SDS is oriented towards the vapour phase with not-strongly-oriented water molecules around it. As the hydrocarbon chain of SDS possesses the properties of decane [161, ydecane= 23.9 mN/m [17], close to y$zer = 21.8 mN/m [12-14,181, then for the SDS solutions ykw could be taken as equal to y,$“,, and its yf” as the difference between yL and ykW. Also, as van Oss et al. assumed for water y+= y- 112-141, one can take y+= y- for SDS solutions below the cmc. Thus, assuming ykw = 21.8, yt= y;, IIe, = 0 [12-141 and the ykw, yS+ and the yS values for fluorite and fluorite/SDS film [19] (Table 2) and the values of yL taken from the literature (Table 1) [15], the contact angle can be calculated from Eq. (3) for each plate-drop system and is denoted as 0, in Table 3.
99
B. Jaficzuk et al. /Applied Surface Science 81 (1994) 95-102 Table 2 Values of the Lifsbitz-van der Waals (rkw), electron acceptor (yS+) and electron donor (y; 1 components of the surface free energy for fluorite covered with a SDS film, and the polar head and hydrocarbon chain of SDS and water taken from the literature [14,19] LW
Fluorite SDS film C(M)”
+
&/m21
10-s 5x 10-s 10-4 5x10-4 10-s 5x10-3 10-z 5x10-2
32.17 27.11 25.51 24.77 24.60 24.38 23.59 23.46 22.61 22.01
Head of SDS Chain of SDS Water
27.10 23.90 21.80
0.0
5x10-+-
a Concentration constructed.
Et/m’)
1.07 1.04 0.80 0.75 0.58 0.22 0.09 0.01
12.49 10.48 9.08 9.28 8.01 7.54 7.68 13.12 18.69 24.00
0.76 0.00 25.50
42.63 0.00 25.50
1.31 0.95
of SDS solution from which the film was
Results given in Table 3 show that 0, has the same behaviour as 0,. The differences between the two contact angles are less than 2” for drops of concentration less than 5 X low4 M, and less than 10” for concentrations between 10e3 and 2 X 10m3 M, but there is no correlation for higher concentrations.
Despite the rough nature of the assumptions, the small differences between 13, and 0, below the cmc suggest that the values of the contact angle measured during the first three minutes after the drop settles on the fluorite surface correspond to that condition of the three phase system in which the chemisorption at the fluorite/solution interface plays a minor role, while most of the SDS molecules at the solid/solution interface should be adsorbed with the hydrocarbon chain directed toward the fluorite or fluorite/SDS film. Also, as a consequence, Eq. (3) represents a possibility of predicting the wettability of the fluorite surface and the fluorite/SDS film surface by a SDS solution at least for concentrations of SDS lower than its cmc. This assumption of physical adsorption and the results shown in Figs. 1 and 2 are consistent with the structure of the adsorbed film of SDS. The study of the adsorption isotherm of SDS on fluorite 193has shown that, at an equilibrium SDS concentration of about 2 x 1O-4 M, the hydrocarbon chain of the DS ion is oriented parallel to the surface, and at a concentration of about 10m3 M a monolayer film is formed with a closest packing of molecules, in which the hydrocarbon chains are directed perpendicularly towards the solution phase [9]. Then the properties of the fluorite/SDS film formed from solutions of SDS at concentrations in the range 10m4 to lop3 M
Table 3 Contact angle gc (deg) for SDS solutions on the fluorite and fluorite/SDS
film surfaces calculated from Eq. (3)
C (MI of SDS solution from which the film was constructed
C (MI of SDS in drop
0
5 x 10-s
10-s
5 x 10-s
10-4
5 x 10-4
10-s
5 x 10-s
10-2
5 x 10-z
‘0 5 x 10-6 10-s 5 x 10-s 10-4 2 x 10-d 5 x 10-4 10-s 2 x 10-s 5 x 10-s 10-z 5x 10-s
67.9 67.6 67.5 67.2 66.7 65.6 62.6 55.4 45.0 19.4 0.0 0.0
75.4 75.1 75.1 74.8 74.3 73.4 70.8 64.7 56.3 39.5 24.4 24.4
77.9 77.7 77.6 77.3 76.9 76.0 73.5 67.7 59.9 44.6 32.1 32.1
78.3 78.1 78.0 77.7 77.3 76.5 74.0 68.3 60.5 45.6 33.7 33.7
81.2 81.0 80.9 80.6 80.2 79.4 77.0 71.5 64.0 49.9 39.0 39.0
82.3 82.0 82.0 81.7 81.3 80.5 78.1 72.7 65.3 51.6 41.0 41.0
83.5 83.3 83.2 83.0 82.6 81.8 79.4 74.1 67.0 53.7 43.7 43.7
79.1 78.9 78.8 78.5 78.1 77.3 74.9 69.3 61.8 47.6 36.6 36.6
75.4 75.2 75.1 74.9 74.5 73.6 71.1 65.4 57.6 42.7 30.6 30.6
72.8 72.6 72.5 72.2 71.8 70.9 68.4 62.5 54.5 38.9 25.6 25.6
100
B. Jariczuk et al. /Applied
are close to the properties of paraffin. Therefore, it can be expected that r,, = I’,, in the case of the drop settled onto fluorite/SDS film samples made from SDS solutions of concentration from 10M4 to 10m3. Of course, at DS- concentrations higher than the cmc, there is probably a reorientation of the aggregates of DS- at the fluorite/ SDS film/ solution interface. A notable fact in the 0, and 0, results is that both decrease with the increase of the concentration of SDS in the drop. This circumstance seems to contradict the behaviour expected for a hydrophobic surface such as “dry” fluorite has [20], because, for highly polar solids such as quartz and silica, the advancing contact angle increases with the increase of the surfactant concentration below the cmc [6]. However, it must be noted that the contact angles were determined after 3 min of contact, but the time needed to ensure the equilibrium of adsorption of SDS is 24 h [9]. At present, it is technically impossible to measure the contact angle of a given drop in the fluoritesolution drop-air system for 24 h. Nevertheless, one can make a theoretical evaluation from Eq. (1) of the contact angle for a drop of SDS solution on the surface of fluorite without an SDS film assuming that the SDS molecules from the drop attain equilibrium of adsorption with the surface of fluorite, that is, assuming for the sur-
Table 4 Values of contact angle 03:) calculated from Eq. (11, film pressure (ZIe) evaluated from Eqs. (4) and (51, respectively, and free energy of interfacial interactions (AC) calculated from Ea. (6)
c
0s
IZe(2) (mJ/m2)
AC,
(deg)
IJeW (mJ/m2)
AC,
&I)
(mJ/m2)
(mJ/m2)
0
67.9 69.4 70.4 69.9 71.5 68.1 61.2 9.5 0.0 0.0
0.00 0.00 0.05 0.70 1.47 2.61 5.53 8.60 10.60 22.00 32.60 -
0.00 0.20 - 0.07 0.59 0.58 0.97 2.95 6.40 9.60 15.51 -
-2.19 - 3.66 -5.55 -5.15 - 6.56 -7.16 - 6.55 1.44 7.70 13.36
-55.19 - 59.70 - 61.29 - 61.07 -64.51 - 65.64 - 66.40 - 60.76 - 55.35 -51.52
5~10-~ 10-s 5 x 1O-5 10-4 2x10-4 5 x 10-4 1O-3 2x10-3 5x10-s 10-r 5x10-2
Surface Science 81 (1994) 95-102 45
0
-40
-F
-
z 35 L +=30 -
0
0
2 6 25 -
8 Fig. 3. Adhesion tension evaluated from the contact angles calculated from Eq. (1) versus the surface tension of the SDS solution in the drop.
face free energy of fluorite around the drop a constant value corresponding to fluorite without film [19]. The ysL values in E!q. (1) were calculated from the van Oss et al. approach 112-141 using the rkw, yS+ and y; values obtained for the fluorite/SDS film made from a solution at the same concentration as in the drop [19] (Table 2). The contact angles evaluated in this way, 0: (Table 4) increase with concentration in the drop up to C = 10m4 M, and then decrease, being in acceptable agreement with the behaviour displayed for polar solids [6]. For a. given concentration, f3: is a few degrees higher than the measured contact angle. Using the 0: values, the adhesion tension has been evaluated and plotted versus the surface tension in Fig. 3. This figure shows that there is not any linear relationship between y,_ cos 0: and yL, which implies that the ratio of r,, to r,v changes with the SDS concentration. However, if the equilibrium of adsorption is attained, there is chemisorption and precipitation of CaDS at the interface, and then Gibbs’ equation does not give real results about adsorption. This conclusion can be confirmed by comparison of the values of the surface pressure, IIe(SL), calculated from Gibbs’ and Young’s equations. Using the values of r,, determined earlier [9], ITe(SL) was evaluated from the following equation [4]:
(4)
B. Jahczuk et al. /Applied Surface Science 81 (1994) 95-102
denoted as ne(l> (Table 4). Also, from Young’s equation: ne(SL)
= yw cos ew - yL cos eL,
(5)
where W and L refer to water and SDS solution, respectively, denoted as ne(2) (Table 4). From Table 4 it seems that there is no correlation between ITe(1) and lie(2) at low concentration of SDS, while, at C higher than 10e4 M, ne(l> is considerably higher than fle(2), as should be expected. Thus, the agreement is not good between the values of the surface pressure as determined from Gibbs’ and from Young’s equations. It is possible to show that the orientation of the DS- ions in the fluorite/SDS film/solution drop interface with the hydrocarbon chain directed towards the fluorite/SDS film surface is thermodynamically favourable. The total free energy of interaction (AG) between the fluorite surface and the DS- moieties through water is equal to the sum of AGi, resulting from interfacial interactions, and AG,, from electrostatic interactions: AG, is the main contribution only if Ca2+ ions are present on the fluorite surface. The AG, values can be determined using the equation [16]: AGi
= [
(~;~)l” -
2
( Y)~)~“]
_[(yyy2_
(ygl’2]2
_ [(y;y_
(yy)1’2]2 (r;)“’ + (rwy2[(Y:y2
101
AG, were determined from Eq. (6) and are presented in Table 4. From Table 4 it can be seen that for all the systems AG, is negative and considerably lower than AG,, reaching a minimum value for the case when the film on the fluorite was made from concentrations of SDS of 5 X 10e4 M. This fact proves that the orientation of the DS- ions, when AG, = 0, with their hydrocarbon chains directed to the fluorite surface or fluorite/SDS film is more favourable than when directed by their polar heads. The best condition for such orientation of the DS- ions exists when a monolayer film of DS- ions is present on the fluorite surface, in agreement with the results presented in Figs. 1 and 2 showing straight lines with slopes close to - 1 for the case in which a monolayer film of SDS is present on the surface. At concentrations higher than the cmc, the only possible orientation of the DS- ions is towards the fluorite surface by their hydrocarbon chains, but in this case it is also possible for the structure of micelles to change and that there is a greater hydration of the fluorite surface.
Acknowledgements
One of the authors (B.J.) appreciates very much the support obtained from the Spanish MEC for his sabbatical stay at the Physics Department of the Extremadura University, Spain. Financial support for this work by DGICYT under project No. PB89-0519 is gratefully acknowledged.
+2((Y&p2[(Y;y2+
+y2] +(r:p2 - (rfY2] - (Y:Y;) 1’2- (r;r:)“2}9
where 1 refers to fluorite and 2 can be the DSpolar head (AGJ or the DS- hydrocarbon chain ($$,1. Using the values found in the literature of Y , y+ and y- for fluorite, for the polar head and the hydrocarbon moieties of the DS- ion [191, and for water [14], the values of AG, and
References 111W.A. Adamson, Physical Chemistry of Surfaces, 5th ed. (Wiley-Interscience, New York, 1990) pp. 82-84, 379411, 493-518. [2] R.E. Johnson and R.H. Detree, in: Surface and Colloid Science, Vol. 2, Ed. E. Matijevic (Wiley-Interscience, New York, 1969) p. 85. 131A.W. Zisman, in: Contact Angle, Wettability and Adhesion, Advances in Chemistry Series, Vol. 43 (American Chemical Society, Washington, DC, 1964) p. 1. 141 R.A. Pyter, G. Zografi and P. Mukerjee, J. Colloid Interf. Sci. 89 (1982) 144.
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B. Jahczuk et al. /Applied Surface Science 81 (1994) 95-102
[5] C.S. Gau and G. Zografi, J. Colloid Interf. Sci. 140 (1990) 1. [6] L. Ter Minassian Sorago, in: Contact Angle, Wettability and Adhesion, Advances in Chemistry Series, Vol. 43 (American Chemical Society, Washington, DC, 1964) p. 232. [7] A.W. Neumann and R.J. Good, in: Surface and Colloid Science, Vol. 11, Eds. R.J. Good and R.D. Stromberg (Plenum, New York, 1979) pp. 31-91. [8] B. Jadczuk, J.M. Bruque, M.L. Gonzalez-Martin and J. Moreno de1 Pozo, J. Colloid Interf. Sci. 161 (1993) 209. [9] M.L. Gonzalez-Martin and C.H. Rochester, J. Chem. Sot. Faraday Trans. 88 (1992) 873. [lo] J. Oberndorfer and B. Dobias, Progr. Colloid Polym. Sci. 76 (1988) 286. [ll] J. Oberndorfer and B. Dobias, Colloids Surf. 69 (1989) 91.
[12] C.J. van Oss, R.J. Good and M.K. Chaudhuty, J. Chromatogr. 391 (1987) 53. [13] C.J. van Oss and R. Good, J. Dispersion Sci. Technol. 9 (1989) 355. [14] C.J. van Oss, R.J. Good and H. Busscher, J. Dispersion Sci. Technol. 11 (1990) 75. [15] R. Wfistneck and R. Miller, Colloids Surf. 47 (1990) 15. [16] C.J. van Oss and P.M. Constanzo, J. Adhes. Sci. Technol. 6 (1992) 477. [I71 B. Janczuk and E. Chibowski, J. Colloid Interf. Sci. 95 (1983) 268. [18] F.M. Fowkes, Ind. Eng. Chem. 56/12 (1964) 40. [19] B. Jabczuk, J.M. Bruque, M.L. Gonzalez-Martin and J. Moreno de1 Pozo, Powder Technol., in press. [20] B. Janczuk, J.M. Bruque, M.L. Gonzalez-Martin and J. Moreno de1 Pozo, Colloids Surf. 75 (1993) 163.
..,....-rr.v.:.:.:.> ......A
..n...... ..,,_........,..,,._, xx<.:.::<.:.:.:.:.:.::::::.:.:~:<~~;~ ,.:.::::::::~ .:.:: ::,:,:,, .,
r.:.:.~:~.~.~:~:~,:~:::~:~.:.:.:.:.::~;;.~:~: :::.:.~.~;,~,::~~,:: ,.,...
““““‘y.-..v $c.:.s:: :..,.,....
..A..
~ .,........
.,_.,
.,.,
,,,,,,.:,.
. . . .. . . . . .,:,:
~,....’
applied
surface science Applied Surface Science 81(1994) 95-102
ELSEVIER
The adsorption of sodium dodecyl sulphate on fluorite and its surface free energy B. Jaiiczuk ‘, M.L. GonzBlez-Martin, J.M. Bruque * Departamento de Fisica, Facultad de Ciencias, Universidad de Extremadura, Au. Elvas s/n, 06071 Badajoz, Spain
Received 8 November 1993; accepted for publication 6 June 1994
Abstract The contact angles of SDS solutions in the range of concentration from 0 to 5 x lo-’ M on fluorite and fluorite coated with SDS films of different thickness have been measured. The contact angles for these systems were also evaluated theoretically from the components of the surface free energy, resulting from Lifshitz-van der Waals and acid-base intermolecular interactions, of fluorite and solution. The interfacial free energies of interaction between DS ions and fluorite and fluorite/SDS film surface through water were determined for both the polar head of the DS- ion and its hydrocarbon chain. Using the contact angle values obtained, a relationship between the adhesion tension and the surface tension of the SDS solution has been established. There was found to be a linear dependence between the adhesion tension and the surface tension in the range of concentration of SDS from 0 up to the cmc. The slopes of the straight lines for fluorite/ SDS film formed from solutions in the range from 10e4 to lop3 M are almost equal to - 1, as for paraffin. It can also be stated that if the electrostatic interaction between the DSions and the Ca’+ ions is small, it is more probable that the DS- ions are oriented to the fluorite surface at the
fluorite/solution interface by their hydrocarbon chain than by their polar head.
1. Introduction
The adsorption of surfactants at the solid/ liquid interface plays a very important role in many branches of industry, among them in the recovering of minerals by flotation. It is known that the wettability of a solid is closely connected to the value of the components
* Corresponding author. ’ On sabbatical leave from the Department of Physical Chemistry, Faculty of Chemistry, Maria Curie-Sklodowska University, 20-031 Lublin, Poland..
of its surface free energy, which result from different intermolecular interactions [l]. The influence of surfactants on the wettability of solids has been studied from basic and technological points of view for decades. From a fundamental perspective there has been a great interest in quantifying the thermodynamic relationships between the adsorption of surfactants and the free energy of the interfaces involved. Many studies indicate that for nonpolar solids, such as paraffin and polyethylene, when the adsorption of surfactanti takes place via the hydrocarbon chain at the solid/liquid interface [2-51, the application of Gibbs’s and Young’s equations leads
0169-4332/94/$07.00 0.1994 Elsevier Science B.V. All rights reserved SSDZ 0169-4332(94)00154-S
to results
in very
good
agreement
with
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B. Jariczuk et al. /Applied Surface Science 81 (1994) 95-102
experimental values. However, for highly polar solids, such as quartz and silica, for which the polar group of the surfactant interacts strongly with the OH groups present on the solid surface, the relationship between contact angle and adsorption is more complicated [6]. Despite the studies done for nonpolar and highly polar solids, there is a lack of information dealing with the relationship between the adsorption of an ionic surfactant with a long hydrocarbon chain on mineral surfaces and their wettability or surface free energy. Therefore, from a practical and a theoretical point of view, it could be interesting to use Young’s and Gibbs’s equations to explain the adsorption of the anionic surfactant sodium dodecyl sulphate on the surface of the semi-soluble fluorite in relation with the change of the wettability and surface free energy of the mineral. For this purpose the contact angles of SDS solutions on the fluorite surface coated with a SDS film (fluorite/ SDS film) have been measured.
mineral specimens of fluorite were cut into plates, polished by emery paper of various grades and then washed several times in doubly distilled and de-ionized water, cleaned in an ultrasonic bath for 15 min, dried at room temperature and kept in a desiccator. For the studies, sodium dodecyl sulphate (purity > 99% - from Merck) (SDS) was used. 2.2. Measurements SDS was dissolved in doubly distilled and deionized water, and then a series of solutions were prepared in the range of concentration from 5 x 10e6 to 2 X 1O-5 M. The pH was uncontrolled but in each case was about 5.85. The fluorite plates were equilibrated with a solution of SDS at a given concentration for 24 h, a time checked as long enough to ensure the adsorption equilibrium of SDS on the fluorite surface. After equilibration, the plates were dried at 50°C for 30 min and placed in the measuring chamber. The plates of “bare” fluorite (plates of fluorite without adsorbed SDS) were equilibrated with doubly distilled and de-ionized water at pH = 5.85 for 24 h before the contact angle measurements. The advancing contact angle was measured at 20 f 1°C by the sessile drop method [7] using a camera-computer system [8]. For a given system,
2. Experimental details 2.1. Materials Fluorite samples from Cordoba (Spain) were used for the contact angle measurements. The
Table 1 Contact angle 0, (deg) for SDS solutions on the fluorite and fluorite/SDS solutions taken from the literature 1151
film surfaces, and values of the surface tension of SDS
C CM) of SDS in drop
C (M) of SDS solution from which the film was constructed 0 5 x 10-6 10-s 5 x 10-5 10-4 5 x 10-4
10-s
5 x10-3
10-r
5 x 10-2
0 5 x 10-6 10-S 5 x 10-5 10-4 2 x 10-4 5 x 10-4 10-s 2 x 10-s 5 x 10-s 10-r 5 x 10-r
67.9 67.6 67.8 67.1 66.9 66.1 62.9 55.6 45.2 0.0 0.0 0.0
83.5 83.3 83.1 82.7 82.6 81.0 77.5 69.8 57.3 28.1 12.0 0.0
79.1 79.2 78.5 78.4 77.5 77.3 73.4 65.1 54.6 22.4 9.0 0.0
75.4 75.2 74.7 74.3 74.1 73.5 69.1 62.1 49.6 14.2 5.0 0.0
72.8 72.4 72.4 71.9 71.9 70.0 66.7 59.9 47.0 12.0 0.0 0.0
75.4 75.2 74.8 74.5 74.4 73.0 69.1 61.8 48.9 8.0 0.0 0.0
77.9 77.8 77.1 76.6 75.7 75.9 72.2 63.5 51.1 14.0 5.0 0.0
78.3 78.2 78.3 77.3 77.1 75.9 72.8 64.0 52.0 17.1 7.3 0.0
81.2 81.1 80.7 80.3 80.3 78.5 75.7 66.8 55.2 23.3 10.7 0.0
82.3 82.2 81.7 81.7 81.1 79.7 76.6 67.4 55.9 25.4 11.4 0.0
&J/m)
72.8 72.4 72.3 71.9 71.3 70.0 66.6 59.8 52.5 42.9 38.0 38.0
91
B. Jaticzuk et al. /Applied Surface Science 81 (1994) 95-102
at least 30 measurements were made and the accuracy was within 2”. For a given drop on the fluorite/SDS film surface, the contact angle was measured at intervals of 1 min from 1 until 30 min after it settled. The contact angle measurements were made for a series of SDS solutions in the range of concentration (C) from 0 to 5 X 10e2 M.
3. Results The average values of the contact angles obtained in the first three minutes after the drop of solution settled on the surface are shown in Table 1. From Table 1 it appears that for each fluorite sample the contact angle (0,) decreases as the concentration of SDS in the drop increases. The changes of 0, against C can be divided into two parts. The first corresponds to concentrations of SDS in the drop from 0 to 5 X 10m4 M, for which 0, decreases only a few degrees with C, and the second to the range of C from 5 X 10e4 to 5 x 10m2 M, for which there is an important fall of 0, with C. The contact angle also depends on the degree of coverage of the fluorite surface with ‘SDS molecules. For a given concentration in drop, 0, increases up to a maximum corresponding to the sample which was equilibrated, prior to the contact angle measurement, with a solution of SDS at concentration 10m3 M, except for C = 5 x 10e2 M which completely spreads on all the fluorite samples. It must also be noted that, for each C from 0 up to 5 x 10m3 M, 0, for “bare” fluorite is smaller than for any other fluorite sample, no matter the thickness of the SDS film. The measurements of the contact angle as a function of time for a given drop showed two different types of behaviour. The contact angle 8, changed considerably with time for “bare” fluorite and fluorite/SDS film formed from a solution at low and high concentration; therefore, for these cases the average contact angle values presented in Table 1 should be treated as dynamic contact angles. However, 0, was practically constant with time for fluorite/SDS film obtained from solutions at concentration from 5 X 10m5 up
to 10e3 M, and 0, can be taken as an advancing contact angle.
4. Discussion Fluorite is a semi-soluble mineral which can interact with the SDS molecules by Lifshitz-van der Waals, acid-base and electrostatic forces. The presence of calcium and dodecyl sulphate ions in solution leads to the precipitation of calcium dodecyl sulphate (CaDS) if the solubility product of the latter is exceeded. Then, chemisorption, precipitation and also physisorption of SDS from solution can occur on the fluorite surface [g-11], affecting the values of the contact angle in the fluorite-SDS solution drop-air system (Table 1). A relationship between the amount adsorbed at the surface under the drop and at the liquid/ vapour interface of the drop can be obtained via the changes of the adhesion tension with the surface tension. According to the Young equation, the adhesion tension, y,_ cos 8, [5] can be expressed [l] as: ysv - ysL = yL cos 0,
(1) where ysv and ysL are the interfacial free energy of the solid/vapour and solid/ liquid interfaces, respectively, yL is the surface tension of the liquid and 8 is the contact angle. Combining Young’s and Gibbs’ equations gives [41: eL
~0s0) 9L
=
rsv -
rs,
r LV
’
(2)
where rsv, rsL and rLv are the surface concentration of surfactant at the solid/vapour, solid/ liquid and liquid/vapour interfaces, respectively. According to Eq. (2), if the adsorption of surfactant from the drop onto the solid surface around it can be neglected Vsv = 01, the slope Xy, cos 8)/ay, coincides with the ratio -r,,/T,,. Figs. 1 and 2 show plots of the adhesion tension evaluated from the contact angles of SDS solutions measured on “bare” fluorite and on fluorite/SDS film versus the surface tension of the solution (it should be remembered that for
98
B. Jahczuk et al. /Applied
I
10
30
40
I
Surface Science 81 (1994) 95-102
I
50 yR CmN/m?O
70
80
Fig. 1. Adhesion tension evaluated from the contact angles measured on the surface of fluorite and fluorite/SDS film formed from solutions of different concentrations versus the surface tension of the SDS solution in the drop.
centrations higher than the cmc, it is impossible to state anything about the differences between rs, and r,,. The role played by the possible chemisorption of DS- ions during the time of measurement can be analyzed by comparing the measured contact angles with those evaluated with the aid of the van Oss et al. approach to the surface and the inter-facial free energy of systems including a solid phase [ 12-141. According to this approach, Eq. (1) can be written in the form: yr(cos 0 + 1) +ne, = 2( yiwy;w)i’* +
some systems the dynamic contact angle was used in Young’s equation). From these figures, there seems to be a linear relationship between the adhesion tension and the surface tension of the solution in the range of SDS concentration from 0 to 5 X 10e3 M, slightly lower than the cmc of SDS [l]. The slope of the straight lines depends on the degree of coverage of fluorite with the SDS film, decreasing to a minimum, close to - 1, for fluorite/SDS film systems formed from concentrations between 10e4 and 10m3 M for which, from Eq. (21, r,, = r,v. Of course, at SDS con-
8
00000 . . . . . 00000 . . . . . llanaa
I
1
I
I
40
50
60
70
80
YR (mN/m)
Fig. 2. Adhesion tension evaluated from the contact angles measured on the surface of fluorite/SDS film formed from solutions of different concentrations versus the surface tension of the SDS solution in the drop.
2(Ys+YLy* + 2(ysyty*,
(3)
where yLw is the Lifshitz-van der Waals component of the surface free energy of solid (S) and liquid CL), y+ is the electron-acceptor and ythe electron-donor part of the acid-base (yAB) component of the solid (S) and liquid (L) surface and ne, is the free energy (y AB= 2(y+y-)‘I*), spreading film pressure, which is commonly taken as zero for contact angles higher than zero [12141. If the yiw, Ys+, YSV YLLW 9 rt and y; values are known, it is possible to determine the contact angles, 8, from Eq. (3). The yr values for SDS solutions were taken from the literature [151. At the solution/vapour interface, the hydrocarbon chain of SDS is oriented towards the vapour phase with not-strongly-oriented water molecules around it. As the hydrocarbon chain of SDS possesses the properties of decane [161, ydecane= 23.9 mN/m [17], close to y$zer = 21.8 mN/m [12-14,181, then for the SDS solutions ykw could be taken as equal to y,$“,, and its yf” as the difference between yL and ykW. Also, as van Oss et al. assumed for water y+= y- 112-141, one can take y+= y- for SDS solutions below the cmc. Thus, assuming ykw = 21.8, yt= y;, IIe, = 0 [12-141 and the ykw, yS+ and the yS values for fluorite and fluorite/SDS film [19] (Table 2) and the values of yL taken from the literature (Table 1) [15], the contact angle can be calculated from Eq. (3) for each plate-drop system and is denoted as 0, in Table 3.
99
B. Jaficzuk et al. /Applied Surface Science 81 (1994) 95-102 Table 2 Values of the Lifsbitz-van der Waals (rkw), electron acceptor (yS+) and electron donor (y; 1 components of the surface free energy for fluorite covered with a SDS film, and the polar head and hydrocarbon chain of SDS and water taken from the literature [14,19] LW
Fluorite SDS film C(M)”
+
&/m21
10-s 5x 10-s 10-4 5x10-4 10-s 5x10-3 10-z 5x10-2
32.17 27.11 25.51 24.77 24.60 24.38 23.59 23.46 22.61 22.01
Head of SDS Chain of SDS Water
27.10 23.90 21.80
0.0
5x10-+-
a Concentration constructed.
Et/m’)
1.07 1.04 0.80 0.75 0.58 0.22 0.09 0.01
12.49 10.48 9.08 9.28 8.01 7.54 7.68 13.12 18.69 24.00
0.76 0.00 25.50
42.63 0.00 25.50
1.31 0.95
of SDS solution from which the film was
Results given in Table 3 show that 0, has the same behaviour as 0,. The differences between the two contact angles are less than 2” for drops of concentration less than 5 X low4 M, and less than 10” for concentrations between 10e3 and 2 X 10m3 M, but there is no correlation for higher concentrations.
Despite the rough nature of the assumptions, the small differences between 13, and 0, below the cmc suggest that the values of the contact angle measured during the first three minutes after the drop settles on the fluorite surface correspond to that condition of the three phase system in which the chemisorption at the fluorite/solution interface plays a minor role, while most of the SDS molecules at the solid/solution interface should be adsorbed with the hydrocarbon chain directed toward the fluorite or fluorite/SDS film. Also, as a consequence, Eq. (3) represents a possibility of predicting the wettability of the fluorite surface and the fluorite/SDS film surface by a SDS solution at least for concentrations of SDS lower than its cmc. This assumption of physical adsorption and the results shown in Figs. 1 and 2 are consistent with the structure of the adsorbed film of SDS. The study of the adsorption isotherm of SDS on fluorite 193has shown that, at an equilibrium SDS concentration of about 2 x 1O-4 M, the hydrocarbon chain of the DS ion is oriented parallel to the surface, and at a concentration of about 10m3 M a monolayer film is formed with a closest packing of molecules, in which the hydrocarbon chains are directed perpendicularly towards the solution phase [9]. Then the properties of the fluorite/SDS film formed from solutions of SDS at concentrations in the range 10m4 to lop3 M
Table 3 Contact angle gc (deg) for SDS solutions on the fluorite and fluorite/SDS
film surfaces calculated from Eq. (3)
C (MI of SDS solution from which the film was constructed
C (MI of SDS in drop
0
5 x 10-s
10-s
5 x 10-s
10-4
5 x 10-4
10-s
5 x 10-s
10-2
5 x 10-z
‘0 5 x 10-6 10-s 5 x 10-s 10-4 2 x 10-d 5 x 10-4 10-s 2 x 10-s 5 x 10-s 10-z 5x 10-s
67.9 67.6 67.5 67.2 66.7 65.6 62.6 55.4 45.0 19.4 0.0 0.0
75.4 75.1 75.1 74.8 74.3 73.4 70.8 64.7 56.3 39.5 24.4 24.4
77.9 77.7 77.6 77.3 76.9 76.0 73.5 67.7 59.9 44.6 32.1 32.1
78.3 78.1 78.0 77.7 77.3 76.5 74.0 68.3 60.5 45.6 33.7 33.7
81.2 81.0 80.9 80.6 80.2 79.4 77.0 71.5 64.0 49.9 39.0 39.0
82.3 82.0 82.0 81.7 81.3 80.5 78.1 72.7 65.3 51.6 41.0 41.0
83.5 83.3 83.2 83.0 82.6 81.8 79.4 74.1 67.0 53.7 43.7 43.7
79.1 78.9 78.8 78.5 78.1 77.3 74.9 69.3 61.8 47.6 36.6 36.6
75.4 75.2 75.1 74.9 74.5 73.6 71.1 65.4 57.6 42.7 30.6 30.6
72.8 72.6 72.5 72.2 71.8 70.9 68.4 62.5 54.5 38.9 25.6 25.6
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B. Jariczuk et al. /Applied
are close to the properties of paraffin. Therefore, it can be expected that r,, = I’,, in the case of the drop settled onto fluorite/SDS film samples made from SDS solutions of concentration from 10M4 to 10m3. Of course, at DS- concentrations higher than the cmc, there is probably a reorientation of the aggregates of DS- at the fluorite/ SDS film/ solution interface. A notable fact in the 0, and 0, results is that both decrease with the increase of the concentration of SDS in the drop. This circumstance seems to contradict the behaviour expected for a hydrophobic surface such as “dry” fluorite has [20], because, for highly polar solids such as quartz and silica, the advancing contact angle increases with the increase of the surfactant concentration below the cmc [6]. However, it must be noted that the contact angles were determined after 3 min of contact, but the time needed to ensure the equilibrium of adsorption of SDS is 24 h [9]. At present, it is technically impossible to measure the contact angle of a given drop in the fluoritesolution drop-air system for 24 h. Nevertheless, one can make a theoretical evaluation from Eq. (1) of the contact angle for a drop of SDS solution on the surface of fluorite without an SDS film assuming that the SDS molecules from the drop attain equilibrium of adsorption with the surface of fluorite, that is, assuming for the sur-
Table 4 Values of contact angle 03:) calculated from Eq. (11, film pressure (ZIe) evaluated from Eqs. (4) and (51, respectively, and free energy of interfacial interactions (AC) calculated from Ea. (6)
c
0s
IZe(2) (mJ/m2)
AC,
(deg)
IJeW (mJ/m2)
AC,
&I)
(mJ/m2)
(mJ/m2)
0
67.9 69.4 70.4 69.9 71.5 68.1 61.2 9.5 0.0 0.0
0.00 0.00 0.05 0.70 1.47 2.61 5.53 8.60 10.60 22.00 32.60 -
0.00 0.20 - 0.07 0.59 0.58 0.97 2.95 6.40 9.60 15.51 -
-2.19 - 3.66 -5.55 -5.15 - 6.56 -7.16 - 6.55 1.44 7.70 13.36
-55.19 - 59.70 - 61.29 - 61.07 -64.51 - 65.64 - 66.40 - 60.76 - 55.35 -51.52
5~10-~ 10-s 5 x 1O-5 10-4 2x10-4 5 x 10-4 1O-3 2x10-3 5x10-s 10-r 5x10-2
Surface Science 81 (1994) 95-102 45
0
-40
-F
-
z 35 L +=30 -
0
0
2 6 25 -
8 Fig. 3. Adhesion tension evaluated from the contact angles calculated from Eq. (1) versus the surface tension of the SDS solution in the drop.
face free energy of fluorite around the drop a constant value corresponding to fluorite without film [19]. The ysL values in E!q. (1) were calculated from the van Oss et al. approach 112-141 using the rkw, yS+ and y; values obtained for the fluorite/SDS film made from a solution at the same concentration as in the drop [19] (Table 2). The contact angles evaluated in this way, 0: (Table 4) increase with concentration in the drop up to C = 10m4 M, and then decrease, being in acceptable agreement with the behaviour displayed for polar solids [6]. For a. given concentration, f3: is a few degrees higher than the measured contact angle. Using the 0: values, the adhesion tension has been evaluated and plotted versus the surface tension in Fig. 3. This figure shows that there is not any linear relationship between y,_ cos 0: and yL, which implies that the ratio of r,, to r,v changes with the SDS concentration. However, if the equilibrium of adsorption is attained, there is chemisorption and precipitation of CaDS at the interface, and then Gibbs’ equation does not give real results about adsorption. This conclusion can be confirmed by comparison of the values of the surface pressure, IIe(SL), calculated from Gibbs’ and Young’s equations. Using the values of r,, determined earlier [9], ITe(SL) was evaluated from the following equation [4]:
(4)
B. Jahczuk et al. /Applied Surface Science 81 (1994) 95-102
denoted as ne(l> (Table 4). Also, from Young’s equation: ne(SL)
= yw cos ew - yL cos eL,
(5)
where W and L refer to water and SDS solution, respectively, denoted as ne(2) (Table 4). From Table 4 it seems that there is no correlation between ITe(1) and lie(2) at low concentration of SDS, while, at C higher than 10e4 M, ne(l> is considerably higher than fle(2), as should be expected. Thus, the agreement is not good between the values of the surface pressure as determined from Gibbs’ and from Young’s equations. It is possible to show that the orientation of the DS- ions in the fluorite/SDS film/solution drop interface with the hydrocarbon chain directed towards the fluorite/SDS film surface is thermodynamically favourable. The total free energy of interaction (AG) between the fluorite surface and the DS- moieties through water is equal to the sum of AGi, resulting from interfacial interactions, and AG,, from electrostatic interactions: AG, is the main contribution only if Ca2+ ions are present on the fluorite surface. The AG, values can be determined using the equation [16]: AGi
= [
(~;~)l” -
2
( Y)~)~“]
_[(yyy2_
(ygl’2]2
_ [(y;y_
(yy)1’2]2 (r;)“’ + (rwy2[(Y:y2
101
AG, were determined from Eq. (6) and are presented in Table 4. From Table 4 it can be seen that for all the systems AG, is negative and considerably lower than AG,, reaching a minimum value for the case when the film on the fluorite was made from concentrations of SDS of 5 X 10e4 M. This fact proves that the orientation of the DS- ions, when AG, = 0, with their hydrocarbon chains directed to the fluorite surface or fluorite/SDS film is more favourable than when directed by their polar heads. The best condition for such orientation of the DS- ions exists when a monolayer film of DS- ions is present on the fluorite surface, in agreement with the results presented in Figs. 1 and 2 showing straight lines with slopes close to - 1 for the case in which a monolayer film of SDS is present on the surface. At concentrations higher than the cmc, the only possible orientation of the DS- ions is towards the fluorite surface by their hydrocarbon chains, but in this case it is also possible for the structure of micelles to change and that there is a greater hydration of the fluorite surface.
Acknowledgements
One of the authors (B.J.) appreciates very much the support obtained from the Spanish MEC for his sabbatical stay at the Physics Department of the Extremadura University, Spain. Financial support for this work by DGICYT under project No. PB89-0519 is gratefully acknowledged.
+2((Y&p2[(Y;y2+
+y2] +(r:p2 - (rfY2] - (Y:Y;) 1’2- (r;r:)“2}9
where 1 refers to fluorite and 2 can be the DSpolar head (AGJ or the DS- hydrocarbon chain ($$,1. Using the values found in the literature of Y , y+ and y- for fluorite, for the polar head and the hydrocarbon moieties of the DS- ion [191, and for water [14], the values of AG, and
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[5] C.S. Gau and G. Zografi, J. Colloid Interf. Sci. 140 (1990) 1. [6] L. Ter Minassian Sorago, in: Contact Angle, Wettability and Adhesion, Advances in Chemistry Series, Vol. 43 (American Chemical Society, Washington, DC, 1964) p. 232. [7] A.W. Neumann and R.J. Good, in: Surface and Colloid Science, Vol. 11, Eds. R.J. Good and R.D. Stromberg (Plenum, New York, 1979) pp. 31-91. [8] B. Jadczuk, J.M. Bruque, M.L. Gonzalez-Martin and J. Moreno de1 Pozo, J. Colloid Interf. Sci. 161 (1993) 209. [9] M.L. Gonzalez-Martin and C.H. Rochester, J. Chem. Sot. Faraday Trans. 88 (1992) 873. [lo] J. Oberndorfer and B. Dobias, Progr. Colloid Polym. Sci. 76 (1988) 286. [ll] J. Oberndorfer and B. Dobias, Colloids Surf. 69 (1989) 91.
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