CONTACT ANGLE AND ABSOLUTE SURFACE COVERAGE
1219
CONTACT ANGLE AND SURFACE COVERAGE FOR POTASSIUM ETHYL XANTHATE ON GALENA ACCORDING TO FREE ACID COLLECTOR THEORY MILTON E. WADSWORTH, ROBERT G. CONRADY, AND MELVIN A. COOK Department of Metallurgy and Utah Engineering Ezperiment Station, University of Utah, Salt Lake City, Utah Received August 10, 1960
The purpose of this paper is to investigate the relationship between contact angle and absolute surface coverage from the viewpoint of the free acid collector theory of Cook ( 2 , 3 , 4 ) .Such a relationship will have obvious value in facilitating the application of contact-angle measurements in studies of collector-mineral and collector-depressant-mineral adsorption equilibria. Captive-bubble data have been very useful in flotation studies. These data have been used to establish relationships between m (concentration of collector ealt added) and pH. Captive-bubble curves ordinarily represent the threshold of bubble contact which has previously been thought to represent the zero contact angle. It is possible to establish a series of parallel captive-bubble curves, each corresponding to a particular contact angle, since the contact angle is also a function of reagent concentration (m)and pH. This paper considers the adsorption of potassium ethyl xanthate on galena, the maximum contact angle (+,,,) being 60" (12). Previous work by Wark and Cox (13) showed the relationship of + to reagent concentration for potassium ethyl xanthate on galena at, it is assumed, constant pH, but no correlation of contact angle with coverage has yet been. demonstrated. EXPEFUMENTAL PROCEDURE
Polished galena specimens were used, prepared according to the method of Wark and Cox (13, 14). A series of tests were made in which contact angles as a function of pH were measured, each test being carried out a t a constant concentration of collector salt. Potassium ethyl xanthate was used in all tests. An interval of 20 min. was allowed before the bubble was brought into contact with the mineral surface, and it was assumed that equilibrium was established in this time. This length of time is sufficient, according to the observations of Siedler (8, 11). Absolute values of contact angles less than 20" are difficult to determine by this method. However, since this region is along the linear portion of the q+pH curves, little error should be introduced by extrapolating linearly to zero contact angle with the help of whatever data may be obtained below + = 20". It is interesting to note that the contact angle increased sharply with a very small decrease in pH. As is shown later, this increase in apparently represents a relatively large increase in surface coverage. A constant ionic strength of 0.1 m was maintained in all tests, since ionic strength has been shown to be of great importance when considering the adsorption of capillary-active substances (4). Table 1 presents the experimental (contact angle) and pH values for constant
+
1220
M. E. WADSWORTH, R. 0 . CONRADP, AND M. A. COOK
TABLE I Ezperimental data: contact angle us. p H at a aeries of constant concentrations of collector salt fc potassium ethyl xanthate on galena (K. = S X l G - 8 ) ~~
CAU'OL*~D (FIXE ACID CONCENTRATION)
CONTACI ANOLE
U
[=I In#./!.
'
deg?M
sb
59
50 50 50 50 50 50
60
6
0 50
51 39 32 30 10-20 10-20 0
4.2 5.5 9.7 10.7 10.7 11.0 11.2 10.9 11.0
6.55 X 3.33 x 2.08 x 2.08 x 2.08 x 1.04 x 6.86 X 1.35 X 1.04 x 2.18 x 1.31 X 8.32 X 2.08 x 8.32 X 2.62 X
10-6 lo-'
lo-" 10-1' lo-" lo-" 10-1a 10-1: lo-" 10-6
100
60 51
100 100 100 100
36 10-20 0
3.95 10.2 10.4 11.0 11.4 11.9
60 52 45 39 10-20 0
6.35 11.00 11.40 11.70 12.00 12.10
1.88 x 4.17 X 1.67 X 8.33 X 4.17 X 3.3 x
300 300
60 48 37 10-20
7.75 11 .OO 11.40 11.70
1.12 x lo-' 6.23 X 10-12 2.49 X lo-'' 1.25 x 10-12
400
60
400 400
51
1.84 x 8.34 X 3.34 x 1.67 X 1.09 x
lo-" lo-*
36 10-20
7.65 11.0 11.4 11.7 11.9
60 50 32 10-20
6.6 11.0 11.4 11.7
2.92 x 1.04 x 4.16 X 2.08 x
10-11
60 55
6.6 11.4 11.7 11.9 12.0 12.1 12.2
3.12 X 5.0 X 2.5 X 1.6 X 1.25 x 9.9 x 7.88 x
lo-' lW1: lo-" lo-" lo-" lo-" 10-1'
100
200 200 200 200 200 200
300 300
400
400 500 500
500 500
600 800 800
800 800 800 800
50
40
48 29 29
iwm 0
lOW* 10-12
1W1* 1Wla 10-7
10-12 10-1; 10-la lO-" 10-1'
10-8
lo-" 10-1' 10-7
1W1: lo-"
CONTACT ANQLE AND ABSOLUTE SURFACE COVERAGE
1221
values of m. The maximum value of $I depends upon the collector in question. Many such values have been established by investigators in the past (10, 12). THEORETICAL CONSIDERATIONS
The sensitivity of the contact angle to changes in pH suggests the contributing importance of hydrolysis, although this has previously been explained by assuming a competition between collector anion and hydroxide ion for the surface of the mineral. According to the free acid hypothesis of Cook, however, the effective collector is obtained by the hydrolysis of the collector salt according to the equilibrium: HXSHffX-
(1)
In any event it may be shown that the absolute value of $I is a function either of [HX], the free acid concentration, the product [H+] [X-1, or the ratio [x-]/[OH-]. This leads us to explore the hitherto disregarded alternative that the true collector is either the free collector acid or these ions adsorbed in pairs. Previously the only theoretical method of differentiation between the two mechanisms was by comparison of the corresponding adsorption potentials. The product [H+][X-] is a measure of the free acid concentration, since [H+][X-] = K.[HX] where K, is the dissociation constant of the free acid. From theoretical considerations the value of K, is taken as 3 X which is the corrected constant suggested by Cook and Nixon (3). Figure 1 presents the experimental data on contact angle in terms of the concentration of free collector acid. For purposes of evaluation, two types of adsorption will be considered: (1) double-site adsovtion and (2)single-site adsorption. The free collector acid will be used in these calculations as the true collector. Similar results are obtained, however, if ions in pairs are considered; also, the possibility of the ion-exchange mechanism of Gaudin and Wark will be considered. For double-site adsorption
HX
+ S’ + S”
$ S’H
+ S”X
(3)
where S’ and S” represent the sulfur and lead sites, respectively. From equation 3. therefore (S’H)(S”X) K = (Si - S’H)(Sf - S”X)(HX) Under conditions of constant ionic strength the activity coefficients are assumed constant..For galena, (S’H) = (S”X) and Si = Sf are the concentrations of the sulfur and lead sites before adsorption. Also where e written:
S”X = esf (5) is the fraction of the surface covered. Therefore equation 4 may be
1,222
M. E. WADSWOBTH, R. G . CONRADY, AND M. A. COOK
In the case of single-site adsorption, considering
Pb-
I
S-
aa a single site
= + I
S‘ S”
-
S‘H
S’X
7
(7)
Collector Concentration I W m p /I I
0
50
8
400
e 500 0 -
600
---
Eipcr~mantol
Theoreticol
T‘ese win15 ?‘e :Is:ritJ:ea sn
LOG tHX3 WO.1. Experimental contact angle (9) u8. log [Hx] (concentration of collector free. acid)
from which one obtains
where 9 again represents the fraction of the surface covered. From the curves of best fit drawn through the experimental contact angle u6. pH data of table 1, interpolated pH values were read for certain predetermined values of the contact angle. These interpolated quantities are shown in figure 2 (solid curvea) as contact angle (9)us. pH. Contact angle (when finite) is related to the surface free eqergy of the solidliquid interface by the equation
1223
CONTACT ANGLE AND ABSOLUTE SURFACE COVERAGE
where ySA,ySL,and represent the surface tension values (surface free energy) at the solid-air, solid-liquid, and liquid-air interfaces, respectively. DeWitt, Roper, and Makens (5,lO) have shown that yLAchanges only slightly at ordinary collector concentrations for the collectors considered here. The contact angle
-
3
2
t I
600
v
0
E
Y
I
I
~
I-
a
a
40
i
I-
z 300-
2
0
50’
o a
I
I I
