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n-heptane—water system
A Relationship between the Zeta Potential and Surface Free Energy Changes of the Sulfur/n-Heptane-Water System EM I L CHIBOWSKI AND ANDRZEJ W A K S M U N D Z K I Department o f Physical Chemistry, Institute o f Chemistt~y, Maria Curie-Sk4"odowska University, Lublin, Poland Received May 24, 1977; accepted February 17, 1978 Measurements of the zeta potential of sulfur in doubly distilled water were carried out by the streaming potential technique. The zeta potential of sulfur changes from -25.6 to -120 mV if the sulfur stirface is wetted with n-heptane. The relationship between the amount of heptane wetting the surface and the zeta potential has been determined. On this basis, the film pressure for heptane and then the dispersion part of surface flee energy of sulfur have been determined. For comparison, similar measurements have been made with a Teflon (PTFE)/n-hexane-water system. If the determined values of film pressure are treated as those resulting from immersional wetting, good values of dispersion energy are obtained, e.g., 97.6 and 19.7 ergs/cmz for sulfur and Teflon, respectively. It was assumed that n-heptane molecules are vertically oriented against the sulfur surface, at least in the first layer. This conclusion was verified theoretically by Fowkes' relation for calculation of the relative pressure, P/Po for first monolayer. It has been assumed here that relative zeta potential correlates to P/Po. The calculated relative zeta value is 0.28, and the experimental one is 0.26.
In an earlier paper (1) we described the zeta potential changes of the system: sulfur/ n-alkane-water. For this purpose, streaming potential measurements (2, 3) were carried out. It was also stated that in the pH 4-10 range, bare sulfur behaved as a nonionogenic substance having - 2 5 . 6 mV of zeta potential. If one wets the dry sulfur surface with n-alkane and then thoroughly washes it to remove the excess n-alkane (it is probable that no alkane molecules are transferred to the water phase), the zeta potential of sulfur in water changes from - 2 5.6 mV to an average of - 110 mV (1). This observation is based on experimental results; however, if the zeta potential of bare sulfur is measured in water charged with n-heptane, the streaming potential settles for as long as 2 hr, whereas in the case mentioned above it settles almost immediately. The zeta potential established from two measurements is - 32. 0 _+ 0.05 inV. The amount of heptane that is present in this water (200 ml of H 2 0 / - 3 g of S) is enough to obtain the maximum value of the
zeta potential of sulfur, if its dry surface is wetted. Thus, adsorption from the water phase seems to be very low, and equilibrium is not stable. The reason lies in the presence of the water film existing near the sulfur surface. The sulfur sample was stored for several months under water (1) and was not dried before use, so any cleaning effect (instead of adsorption) of the sulfur surface on zeta potential changes is hardly possible. Recently, much of the literature shows that structured water exists at many (or most) solid/water interfaces (4-8), and it may play a significant role in low-energy processes. Here, the essential contribution of the water dipole in the double layer structure may be expected, but more experimental work must be done. The variations in the surface free energy of sulfur, caused by the hydrocarbon film, should affect the water dipole structure (such as the orientation, arrangement, and charge density) near the sulfur surface, and in consequence, the measured zeta potential value. In view of the statements aboVe, it seems
213
Journal of Colloidand Interface Science, Vol. 66, No. 2, September1978
0021-9797/78/0662-0213502.00/0 Copyright© 1978by AcademicPress, Inc, All fightsof reproductionin any formreserved.
214
CHIBOWSKI AND WAKSMUNDZKI
that the zeta potential in " p u r e " water could be a sensitive parameter for studying the properties of hydrocarbons film deposited on a dry sulfur surface. Thus, it should be possible to determine the correlation of the zeta potential and the surface free energy of sulfur, and this was the object of the study reported here. Previously published (1) resuits, as well as some recent ones obtained for Teflon (PTFE) powder, were used for the calculations. EXPERIMENTAL
Measurements similar to those for sulfur (1) have been made with Teflon powder. Teflon powder was obtained from grinding commercial Teflon chips in a coffee mill and sieving the grains of 0.25- to 0.385-mm size. It was then cleaned with a methanol, hydrochloric acid solution (1:10), washed with distilled and doubly distilled water (boiling), and dried at 150°C for 10 hr. This prepared sample was used for the measurements of the streaming potential in doubly distilled water. The specific surface area of the Teflon sample, determined by the same method as that for sulfur (1), was 0.03 m2/g. Next, measurements of zeta potential depending on the amount of n-hexane used for wetting the Teflon sample were made. The manner of wetting and the zeta potential measurements were the same as described earlier for sulfur (1), except for the use of liquid nitrogen instead of a dry ice-chloroform mixture for cooling the sample. In addition, platinium electrodes were employed in place of gilded platinium electrodes. The ampoules with Teflon samples after wetting were heated at 110°C for 2 hr, and cooled to 20°C. RESULTS AND DISCUSSION
Figure 1 presents the zeta potential changes of Teflon depending on the volume of n-hexane used for wetting its surface. In this case n-hexane was used for wetting the Teflon surface (instead of n-heptane, as for sulfur) because the literature (9-11) Journal of Colloid and Interface Science, Vol. 66, No. 2, September 1978
reports a higher vapor adsorption for hydrocarbons having a shorter chain. Bare Teflon in doubly distilled water has a zeta potential equal to -46.6 mV. When its surface is wetted with n-hexane, the value of zeta potential rises to - 7 0 mV. The complete change in zeta potential is about 20 mV, whereas that of sulfur (wetted with n-heptane) is almost 95 mV (1). This clearly shows the interdependence of the zeta potential and the surface free energy changes for a hydrophobic solid in water. In Fig. 1, vertical dashes denote the calculated statistical monolayers of the n-hexane film. An upright position for n-hexane molecules (as for sulfur, for comparison) and an 18-A2 crosssectional area for the hexane chain were assumed. As can be seen (Fig. 1), four statistical monolayers are formed on the Teflon surface. Because of the visible relationship between zeta potential and the volume of n-alkane wetting the surface (1), it seems reasonable to apply the Bangham and Razouk (10) relation for the film pressure 7r on the solid surface: vd In ~, ~'-
XV
[1]
~o
in which R and T have their usual meaning, V is the molar volume of the adsorbate, Y~ is the total surface area 9f the sample, v is the adsorbed volume, and ~0 is the zeta potential of the bare solid. Zeta potential assumes the place of pressure (10). Two assumptions are made here: first, that the whole volume of the hydrocarbon used for wetting the sample in the ampoules adsorbed on the material surface under heating and then cooling (to 293°K) processes, and second, that a parallel can be drawn between the pressure and the zeta potential. Then, it is possible to determine the 7r values by the graphic integration of Eq. [1]. Thus, values of ~ obtained as a function of calculated statistical monolayers are presented in Fig. 2, both for sulfur and for Teflon. The maximum value of ,r for sulfur
ZETA POTENTIAL AND SURFACE ENERGY
-70
215
4
I
....O
-65
> E -60 +.o o Cu
J
b~
-55
-50
-45 o
I
i
i
I
0.05
0.1
o.15
0.2
Volume of n-hexane,/zl/g of PTFE Fie. 1. Zeta potential changes of Teflon (PTFE) as a function of n-hexane volume used for wetting the Teflon surface. is 97.6 ergs/cm 2, and for Teflon it is 19.7 ergs/cm ~. F o r the first three m o n o l a y e r s on the sulfur surface, 7r reaches a b o u t 34% of its total magnitude and that for Teflon reaches a l m o s t 70% o f the total magnitude. The first statistical m o n o l a y e r has ~- values o f 9.4 and 0.41 ergs/cm 2 for sulfur and for Teflon, respectively. This evidence leads to the confirmation o f the a s s u m p t i o n of a vertical orientation o f n - h e p t a n e molecules on the sulfur surface. F o w k e s (12) has calculated that a b o u t 83% of the interaction energy is a c c o u n t e d
for b y the adjacent interfacial layers if the h y d r o c a r b o n phases (a solid and liquid one) have the chains parallel to the surface and not m u c h m o r e than half of the total interaction if their position is normal. So the upright position of the n-alkanes tested seems to be real. In the ranges of 3 - 9 and 9 - 1 4 statistical m o n o l a y e r s , the changes o f the determined ~- values (Fig. 2) are almost linear. This linear effect m a y be connected with a different structure of the film in the two regions o f thickness. N e x t , the m a x i m u m ~- values were used to Journal of Colloid and Interface Science, Vol. 66, NO. 2, September 1978
216
CHIBOWSKI
AND WAKSMUNDZKI
/
90
//
80
70
~
/o
60
¢D 5o .Of v
jo j
40
E 30
20
10
I'
2
3
h
i
i
5
6
I
7
i
I
I
I
l
I
I
8
9
10
11
12
13
14
15
Calculated statistical monolayers, n
FIG. 2. Film pressure, 7r, in relation to the calculated statistical monolayers; ©, for sulfur; O, for Teflon.
calculate the dispersion part of the surface free energy for sulfur and Teflon. Two interpretations of these 7r values were tested: (i) one concerning spreading wetting (10, 13) when the adsorbed film reaches the liquid state at ~max.:
tic mean (AM) of the dispersion force attractions (10), it is possible to estimate the dispersion part of the surface free energy of the solid. The resulting equations for sulfur/n-heptane or Teflon/n-hexane are as follows:
'B'max. ""-> "riD =
(i) for spreading wetting:
Ws =
SLs = ")Is - - "YLs - - T L v ,
[2]
and (ii) one concerning immersional wetting (13): ~ m a x . ---> W w = ')is = "YsL,
[3]
where Ws is the work of spreading, SLs is the spreading coefficient of liquid over a solid, y~ is the surface free energy of a solid in vacuum, YL~ is the free energy of the solid-liquid interface, YLv is the surface tension of the liquid, and Ww is the work of immersional wetting. Applying Eqs. [2] or [3] and geometric mean (GM) or the arithmeJournal of Colloid and Interface Science, Vol. 66, No. 2, September 1978
"B'max. =
Ws =
--23tHe +
"n'max. =
Ws =
2 ( ' y s d ' Y H c d ) 1/~
--')/HC + ")/sd
(GM)
[4]
(AM);
[5]
(ii) for immersional wetting: "/Tmax. =
"/Tmax. =
Ww =
Ww =
--~nc
+ 2(ysdyHcd)~/2 (GM)
[6]
(AM)
[7]
ys d
It is assumed here that yHc = ~'HC° for n-alkanes. The values ofy~d obtained from Eqs. [4]-[7] are listed in Table I.
217
ZETA P O T E N T I A L AND S U R F A C E ENERGY TABLE I Calculated
yfl
Values for Sulfur and Teflon from the Determined Maximum ~" Values
Wetting (process tested)
Liquid
Surface tension yLa (dyn/cm)
Sulfur
Spreading Immersional
n -Heptane n-Heptane
20.3 20.3
235.3 171.3
117.9 97.6
Teflon (FI'FE)
Spreading Immersional
n-Hexane n-Hexane
18.5 18.5
43.5 19.7
38.2 19.7
Solid
F o r Teflon (14, 15), the literature values of ys° lie between 16 and 30 ergs/cm 2. Waksmundzki and Jaficzuk (16, 17) and W6jcik (17) have studied a sulfur/n-alkanew a t e r - a i r system, and they have obtained the contact angle values for n-alkane series (hexane to hexadecane) on sulfur in water (captive drop method) between 124° and 143 °. These values yielded the ysa for sulfur in the range of 119.9-127.6 ergs/cm 2. The plates of sulfur were obtained from molten sulfur by pouring it on a glass plate. Based on Fowkes' theory (18), the authors (16, 17) have also calculated the surface free energy of sulfur. Because of the great differences in the literature data for the dielectric constant of sulfur (2.3-4.05), the values calculated by these authors, yfl, varied from 59.5 to 165.3 ergs/cm ~. Considering the values presented in Table I, it can be seen that they are reasonable both for Teflon and sulfur if the 7r values are treated as those resulting from the immersional wetting process, especially calculated with (AM). In case of sulfur also the (AM) value for y a calculated from spreading wetting approaches the values determined from contact angles (16, 17). As Z e t t l e m o y e r (10) pointed out, the (AM) values for y a are more comparable with other measurements than the GM values are, though the first have a weaker scientific basis. The situation above also seems to o c c u r in the case discussed. Therefore, F o w k e s ' Eq. [33] from ref. (12) is applied to further verify the calculated y 0 of sulfur. Thus, the assumption of vertical
3~a (ergs/cm2) Geometric m e a n
Arithmetic mean
orientation for the n-heptane molecules in the first monolayer could be verified. In this equation, we have replaced the relative pressure P/Po by the relative zeta potential g - g0/gm - g0 (the same assumption is made as for Eq. [1]), so the following equation is tested: ~m - g0 -
k T In -
gl -- g0
2Ts[(ysOyc 0)1/2 - yc, o]
NsS%Ki
,
I-8]
where k is Boltzmann's constant; T is the absolute temperature, 293°K; gm= 120 mV; g0 = 25.6 mV; gi = 50 mV; ys° = 97.6 ergs/ cm2; yc7d = 20.3 dyn/cm; Ns is the n u m b e r of heptane molecules in the surface layer, 5.55 × 1014; f~ is a constant equal to 0.8; and Ki is the dielectric constant for the first monolayer, Ki = n 2 = 1.3882 (n is the refractive index). Ts = ~] a=0
d~ + a
~- 2.383,
[9]
dj
Sd= ~
a=0
)4
+a+b
4
aj/ = 2.632.
[10]
The summation procedure (12) has been applied, which allowed the molecules' orientation to be accounted for. F o r details see Fowkes' paper (12). In calculations of the S O value the summation is bounded to a = 5. The subscripts i and j denote n-heptane and sulfur, respectively; and di = 1.26 Journal o f CoUoid and Interface Science,
Vol. 66, No. 2, September 1978
218
CHIBOWSKI AND WAKSMUNDZKI
4.0
3.6 t., ~.~ 3.2 0 ~m 2.8
/
~ 2.4
~:~2.0
0
:/
~*0 1,6 ©
g
20
0.8
0.4
I
0 0
0.1
I
0.2
I
I
I
I
J
J
0.3
o.a
0.5
0.6
0.7
0.8
Relative zeta potential,
I 0.9
! 1.0
~ -}'o
FI~. 3. The relationship between the volume of n-heptane wetting the sulfur surface (adsorbed) and relative zeta potential, an "adsorption isotherm."
A ( C - C distance), dj = 2.07 A, and du = 1.66/~. The calculated value of relative zeta potential for the first monolayer from Eq. [8] equals 0.28, which is in good agreement with that from the experiments, 0.26, as shown in Fig. 3. CONCLUSIONS
At present, abstracting from the double layer structure and the mechanism of its formation, the relationship between the zeta potential and surface free energy of a hydrophobic solid is rather obvious. The calculated theoretical value of relative zeta potential confirms the vertical orientation of Journal of Colloid and Interface Science, Vol. 66, No. 2, September 1978
the n-heptane molecules on the sulfur surface, at least in the first monolayer. It also shows that the determined 7rmax. value corresponds to the immersional wetting process. Because of some doubts which arise, further experiments hopefully for verification with other hydrophobic materials will be carried out. REFERENCES 1. Chibowski, E., and Waksmundzki, A., J. Colloid Interface Sci. 64, 380 (1978). 2. Fuerstenau, D. W., Trans. A I M E 206, 834 (1956). 3. Parreira, H. C., and Schulman, J. H., in "Solid Surfaces and The Gas-Solid Interface" (R. F. Gould, Ed.), Advances in Chemistry Set., No.
ZETA POTENTIAL AND SURFACE ENERGY
4. 5. 6. 7. 8. 9. 10.
11.
33, p. 160, American Chemical Society, Washington, 1969. Drost-Hansen, W., J. Colloid Interface Sci. 58, 251 (1977). Kelier, K., and Zettlemoyer, A. C., J. Colloid Interface Sci. 58, 216 (1977). Bell, G. M., and Levine, P. L., J. Colloid Interface Sci. 60, 177 (1977). Zettlemoyer, A. C., and Hising, H. H., J. Colloid Interface Sci. 58, 263 (1977). Eagland, D., and Allen, A. P., J. Colloid Interface Sci. 58, 230 (1977). Hu, P., and Adamson, A. W., J. Colloid Interface Sci. 59, 605 (1977). Zettlemoyer, A. C., in "Hydrophobic Surfaces" (F. M. Fowkes, Ed.), p. 1, Academic Press, New York and London, 1969. Whalen, J. W., in "Hydrophobic Surfaces" (F. M.
219
Fowkes, Ed.), p. 101. Academic Press, New York and London, 1969. 12. Fowkes, F. M., J. Colloid Interface Sci. 28, 493 (1968). 13. Off. J. Int. Union Pure Appl. Chem. 31(4), 597 (1972). 14. Dann, J. R., J. Colloid lnterface Sci. 32, 302 (1970). 15. Tamai, Y., Progr. Colloid Polymer Sci. 61, 93 (1976). 16. Waksmundzki, A., and Jaficzuk, B., "Energy Changes of Sulfur-Water-Air System Under the Influence of Nonpolar Collectors. A Comparison to Sulfur Ore Flotation." Paper accepted for "XII International Mineral Processing Congress," Brasil, 1977. 17. Jaficzuk, B., Waksmundzki, A., and W6jcik, W., Rocz. Chem. 51, 985 (1977). 18. Fowkes, F. M., Ind. Eng. Chem. 40, 54 (1964).
Journal of Colloid and Interface Science, Vol. 66, No. 2, September 1978
In an earlier paper (1) we described the zeta potential changes of the system: sulfur/ n-alkane-water. For this purpose, streaming potential measurements (2, 3) were carried out. It was also stated that in the pH 4-10 range, bare sulfur behaved as a nonionogenic substance having - 2 5 . 6 mV of zeta potential. If one wets the dry sulfur surface with n-alkane and then thoroughly washes it to remove the excess n-alkane (it is probable that no alkane molecules are transferred to the water phase), the zeta potential of sulfur in water changes from - 2 5.6 mV to an average of - 110 mV (1). This observation is based on experimental results; however, if the zeta potential of bare sulfur is measured in water charged with n-heptane, the streaming potential settles for as long as 2 hr, whereas in the case mentioned above it settles almost immediately. The zeta potential established from two measurements is - 32. 0 _+ 0.05 inV. The amount of heptane that is present in this water (200 ml of H 2 0 / - 3 g of S) is enough to obtain the maximum value of the
zeta potential of sulfur, if its dry surface is wetted. Thus, adsorption from the water phase seems to be very low, and equilibrium is not stable. The reason lies in the presence of the water film existing near the sulfur surface. The sulfur sample was stored for several months under water (1) and was not dried before use, so any cleaning effect (instead of adsorption) of the sulfur surface on zeta potential changes is hardly possible. Recently, much of the literature shows that structured water exists at many (or most) solid/water interfaces (4-8), and it may play a significant role in low-energy processes. Here, the essential contribution of the water dipole in the double layer structure may be expected, but more experimental work must be done. The variations in the surface free energy of sulfur, caused by the hydrocarbon film, should affect the water dipole structure (such as the orientation, arrangement, and charge density) near the sulfur surface, and in consequence, the measured zeta potential value. In view of the statements aboVe, it seems
213
Journal of Colloidand Interface Science, Vol. 66, No. 2, September1978
0021-9797/78/0662-0213502.00/0 Copyright© 1978by AcademicPress, Inc, All fightsof reproductionin any formreserved.
214
CHIBOWSKI AND WAKSMUNDZKI
that the zeta potential in " p u r e " water could be a sensitive parameter for studying the properties of hydrocarbons film deposited on a dry sulfur surface. Thus, it should be possible to determine the correlation of the zeta potential and the surface free energy of sulfur, and this was the object of the study reported here. Previously published (1) resuits, as well as some recent ones obtained for Teflon (PTFE) powder, were used for the calculations. EXPERIMENTAL
Measurements similar to those for sulfur (1) have been made with Teflon powder. Teflon powder was obtained from grinding commercial Teflon chips in a coffee mill and sieving the grains of 0.25- to 0.385-mm size. It was then cleaned with a methanol, hydrochloric acid solution (1:10), washed with distilled and doubly distilled water (boiling), and dried at 150°C for 10 hr. This prepared sample was used for the measurements of the streaming potential in doubly distilled water. The specific surface area of the Teflon sample, determined by the same method as that for sulfur (1), was 0.03 m2/g. Next, measurements of zeta potential depending on the amount of n-hexane used for wetting the Teflon sample were made. The manner of wetting and the zeta potential measurements were the same as described earlier for sulfur (1), except for the use of liquid nitrogen instead of a dry ice-chloroform mixture for cooling the sample. In addition, platinium electrodes were employed in place of gilded platinium electrodes. The ampoules with Teflon samples after wetting were heated at 110°C for 2 hr, and cooled to 20°C. RESULTS AND DISCUSSION
Figure 1 presents the zeta potential changes of Teflon depending on the volume of n-hexane used for wetting its surface. In this case n-hexane was used for wetting the Teflon surface (instead of n-heptane, as for sulfur) because the literature (9-11) Journal of Colloid and Interface Science, Vol. 66, No. 2, September 1978
reports a higher vapor adsorption for hydrocarbons having a shorter chain. Bare Teflon in doubly distilled water has a zeta potential equal to -46.6 mV. When its surface is wetted with n-hexane, the value of zeta potential rises to - 7 0 mV. The complete change in zeta potential is about 20 mV, whereas that of sulfur (wetted with n-heptane) is almost 95 mV (1). This clearly shows the interdependence of the zeta potential and the surface free energy changes for a hydrophobic solid in water. In Fig. 1, vertical dashes denote the calculated statistical monolayers of the n-hexane film. An upright position for n-hexane molecules (as for sulfur, for comparison) and an 18-A2 crosssectional area for the hexane chain were assumed. As can be seen (Fig. 1), four statistical monolayers are formed on the Teflon surface. Because of the visible relationship between zeta potential and the volume of n-alkane wetting the surface (1), it seems reasonable to apply the Bangham and Razouk (10) relation for the film pressure 7r on the solid surface: vd In ~, ~'-
XV
[1]
~o
in which R and T have their usual meaning, V is the molar volume of the adsorbate, Y~ is the total surface area 9f the sample, v is the adsorbed volume, and ~0 is the zeta potential of the bare solid. Zeta potential assumes the place of pressure (10). Two assumptions are made here: first, that the whole volume of the hydrocarbon used for wetting the sample in the ampoules adsorbed on the material surface under heating and then cooling (to 293°K) processes, and second, that a parallel can be drawn between the pressure and the zeta potential. Then, it is possible to determine the 7r values by the graphic integration of Eq. [1]. Thus, values of ~ obtained as a function of calculated statistical monolayers are presented in Fig. 2, both for sulfur and for Teflon. The maximum value of ,r for sulfur
ZETA POTENTIAL AND SURFACE ENERGY
-70
215
4
I
....O
-65
> E -60 +.o o Cu
J
b~
-55
-50
-45 o
I
i
i
I
0.05
0.1
o.15
0.2
Volume of n-hexane,/zl/g of PTFE Fie. 1. Zeta potential changes of Teflon (PTFE) as a function of n-hexane volume used for wetting the Teflon surface. is 97.6 ergs/cm 2, and for Teflon it is 19.7 ergs/cm ~. F o r the first three m o n o l a y e r s on the sulfur surface, 7r reaches a b o u t 34% of its total magnitude and that for Teflon reaches a l m o s t 70% o f the total magnitude. The first statistical m o n o l a y e r has ~- values o f 9.4 and 0.41 ergs/cm 2 for sulfur and for Teflon, respectively. This evidence leads to the confirmation o f the a s s u m p t i o n of a vertical orientation o f n - h e p t a n e molecules on the sulfur surface. F o w k e s (12) has calculated that a b o u t 83% of the interaction energy is a c c o u n t e d
for b y the adjacent interfacial layers if the h y d r o c a r b o n phases (a solid and liquid one) have the chains parallel to the surface and not m u c h m o r e than half of the total interaction if their position is normal. So the upright position of the n-alkanes tested seems to be real. In the ranges of 3 - 9 and 9 - 1 4 statistical m o n o l a y e r s , the changes o f the determined ~- values (Fig. 2) are almost linear. This linear effect m a y be connected with a different structure of the film in the two regions o f thickness. N e x t , the m a x i m u m ~- values were used to Journal of Colloid and Interface Science, Vol. 66, NO. 2, September 1978
216
CHIBOWSKI
AND WAKSMUNDZKI
/
90
//
80
70
~
/o
60
¢D 5o .Of v
jo j
40
E 30
20
10
I'
2
3
h
i
i
5
6
I
7
i
I
I
I
l
I
I
8
9
10
11
12
13
14
15
Calculated statistical monolayers, n
FIG. 2. Film pressure, 7r, in relation to the calculated statistical monolayers; ©, for sulfur; O, for Teflon.
calculate the dispersion part of the surface free energy for sulfur and Teflon. Two interpretations of these 7r values were tested: (i) one concerning spreading wetting (10, 13) when the adsorbed film reaches the liquid state at ~max.:
tic mean (AM) of the dispersion force attractions (10), it is possible to estimate the dispersion part of the surface free energy of the solid. The resulting equations for sulfur/n-heptane or Teflon/n-hexane are as follows:
'B'max. ""-> "riD =
(i) for spreading wetting:
Ws =
SLs = ")Is - - "YLs - - T L v ,
[2]
and (ii) one concerning immersional wetting (13): ~ m a x . ---> W w = ')is = "YsL,
[3]
where Ws is the work of spreading, SLs is the spreading coefficient of liquid over a solid, y~ is the surface free energy of a solid in vacuum, YL~ is the free energy of the solid-liquid interface, YLv is the surface tension of the liquid, and Ww is the work of immersional wetting. Applying Eqs. [2] or [3] and geometric mean (GM) or the arithmeJournal of Colloid and Interface Science, Vol. 66, No. 2, September 1978
"B'max. =
Ws =
--23tHe +
"n'max. =
Ws =
2 ( ' y s d ' Y H c d ) 1/~
--')/HC + ")/sd
(GM)
[4]
(AM);
[5]
(ii) for immersional wetting: "/Tmax. =
"/Tmax. =
Ww =
Ww =
--~nc
+ 2(ysdyHcd)~/2 (GM)
[6]
(AM)
[7]
ys d
It is assumed here that yHc = ~'HC° for n-alkanes. The values ofy~d obtained from Eqs. [4]-[7] are listed in Table I.
217
ZETA P O T E N T I A L AND S U R F A C E ENERGY TABLE I Calculated
yfl
Values for Sulfur and Teflon from the Determined Maximum ~" Values
Wetting (process tested)
Liquid
Surface tension yLa (dyn/cm)
Sulfur
Spreading Immersional
n -Heptane n-Heptane
20.3 20.3
235.3 171.3
117.9 97.6
Teflon (FI'FE)
Spreading Immersional
n-Hexane n-Hexane
18.5 18.5
43.5 19.7
38.2 19.7
Solid
F o r Teflon (14, 15), the literature values of ys° lie between 16 and 30 ergs/cm 2. Waksmundzki and Jaficzuk (16, 17) and W6jcik (17) have studied a sulfur/n-alkanew a t e r - a i r system, and they have obtained the contact angle values for n-alkane series (hexane to hexadecane) on sulfur in water (captive drop method) between 124° and 143 °. These values yielded the ysa for sulfur in the range of 119.9-127.6 ergs/cm 2. The plates of sulfur were obtained from molten sulfur by pouring it on a glass plate. Based on Fowkes' theory (18), the authors (16, 17) have also calculated the surface free energy of sulfur. Because of the great differences in the literature data for the dielectric constant of sulfur (2.3-4.05), the values calculated by these authors, yfl, varied from 59.5 to 165.3 ergs/cm ~. Considering the values presented in Table I, it can be seen that they are reasonable both for Teflon and sulfur if the 7r values are treated as those resulting from the immersional wetting process, especially calculated with (AM). In case of sulfur also the (AM) value for y a calculated from spreading wetting approaches the values determined from contact angles (16, 17). As Z e t t l e m o y e r (10) pointed out, the (AM) values for y a are more comparable with other measurements than the GM values are, though the first have a weaker scientific basis. The situation above also seems to o c c u r in the case discussed. Therefore, F o w k e s ' Eq. [33] from ref. (12) is applied to further verify the calculated y 0 of sulfur. Thus, the assumption of vertical
3~a (ergs/cm2) Geometric m e a n
Arithmetic mean
orientation for the n-heptane molecules in the first monolayer could be verified. In this equation, we have replaced the relative pressure P/Po by the relative zeta potential g - g0/gm - g0 (the same assumption is made as for Eq. [1]), so the following equation is tested: ~m - g0 -
k T In -
gl -- g0
2Ts[(ysOyc 0)1/2 - yc, o]
NsS%Ki
,
I-8]
where k is Boltzmann's constant; T is the absolute temperature, 293°K; gm= 120 mV; g0 = 25.6 mV; gi = 50 mV; ys° = 97.6 ergs/ cm2; yc7d = 20.3 dyn/cm; Ns is the n u m b e r of heptane molecules in the surface layer, 5.55 × 1014; f~ is a constant equal to 0.8; and Ki is the dielectric constant for the first monolayer, Ki = n 2 = 1.3882 (n is the refractive index). Ts = ~] a=0
d~ + a
~- 2.383,
[9]
dj
Sd= ~
a=0
)4
+a+b
4
aj/ = 2.632.
[10]
The summation procedure (12) has been applied, which allowed the molecules' orientation to be accounted for. F o r details see Fowkes' paper (12). In calculations of the S O value the summation is bounded to a = 5. The subscripts i and j denote n-heptane and sulfur, respectively; and di = 1.26 Journal o f CoUoid and Interface Science,
Vol. 66, No. 2, September 1978
218
CHIBOWSKI AND WAKSMUNDZKI
4.0
3.6 t., ~.~ 3.2 0 ~m 2.8
/
~ 2.4
~:~2.0
0
:/
~*0 1,6 ©
g
20
0.8
0.4
I
0 0
0.1
I
0.2
I
I
I
I
J
J
0.3
o.a
0.5
0.6
0.7
0.8
Relative zeta potential,
I 0.9
! 1.0
~ -}'o
FI~. 3. The relationship between the volume of n-heptane wetting the sulfur surface (adsorbed) and relative zeta potential, an "adsorption isotherm."
A ( C - C distance), dj = 2.07 A, and du = 1.66/~. The calculated value of relative zeta potential for the first monolayer from Eq. [8] equals 0.28, which is in good agreement with that from the experiments, 0.26, as shown in Fig. 3. CONCLUSIONS
At present, abstracting from the double layer structure and the mechanism of its formation, the relationship between the zeta potential and surface free energy of a hydrophobic solid is rather obvious. The calculated theoretical value of relative zeta potential confirms the vertical orientation of Journal of Colloid and Interface Science, Vol. 66, No. 2, September 1978
the n-heptane molecules on the sulfur surface, at least in the first monolayer. It also shows that the determined 7rmax. value corresponds to the immersional wetting process. Because of some doubts which arise, further experiments hopefully for verification with other hydrophobic materials will be carried out. REFERENCES 1. Chibowski, E., and Waksmundzki, A., J. Colloid Interface Sci. 64, 380 (1978). 2. Fuerstenau, D. W., Trans. A I M E 206, 834 (1956). 3. Parreira, H. C., and Schulman, J. H., in "Solid Surfaces and The Gas-Solid Interface" (R. F. Gould, Ed.), Advances in Chemistry Set., No.
ZETA POTENTIAL AND SURFACE ENERGY
4. 5. 6. 7. 8. 9. 10.
11.
33, p. 160, American Chemical Society, Washington, 1969. Drost-Hansen, W., J. Colloid Interface Sci. 58, 251 (1977). Kelier, K., and Zettlemoyer, A. C., J. Colloid Interface Sci. 58, 216 (1977). Bell, G. M., and Levine, P. L., J. Colloid Interface Sci. 60, 177 (1977). Zettlemoyer, A. C., and Hising, H. H., J. Colloid Interface Sci. 58, 263 (1977). Eagland, D., and Allen, A. P., J. Colloid Interface Sci. 58, 230 (1977). Hu, P., and Adamson, A. W., J. Colloid Interface Sci. 59, 605 (1977). Zettlemoyer, A. C., in "Hydrophobic Surfaces" (F. M. Fowkes, Ed.), p. 1, Academic Press, New York and London, 1969. Whalen, J. W., in "Hydrophobic Surfaces" (F. M.
219
Fowkes, Ed.), p. 101. Academic Press, New York and London, 1969. 12. Fowkes, F. M., J. Colloid Interface Sci. 28, 493 (1968). 13. Off. J. Int. Union Pure Appl. Chem. 31(4), 597 (1972). 14. Dann, J. R., J. Colloid lnterface Sci. 32, 302 (1970). 15. Tamai, Y., Progr. Colloid Polymer Sci. 61, 93 (1976). 16. Waksmundzki, A., and Jaficzuk, B., "Energy Changes of Sulfur-Water-Air System Under the Influence of Nonpolar Collectors. A Comparison to Sulfur Ore Flotation." Paper accepted for "XII International Mineral Processing Congress," Brasil, 1977. 17. Jaficzuk, B., Waksmundzki, A., and W6jcik, W., Rocz. Chem. 51, 985 (1977). 18. Fowkes, F. M., Ind. Eng. Chem. 40, 54 (1964).
Journal of Colloid and Interface Science, Vol. 66, No. 2, September 1978