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ζ potential measurement by means of the plane interface technique
~ Potential Measurement by Means of the Plane Interface Technique H I R O S H I SASAKI, A T S U S H I M U R A M A T S U , H I R O S H I A R A K A T S U , AND S H I N N O S U K E U S U I Research Institute of Mineral Dressing and Metallurgy, Tohoku University, Katahira, Sendai 980, Japan
Received June 18, 1990; accepted August 20, 1990 The ~"potential of quartz and sapphire plates in contact with aqueous solutions was measured by means of the plane interfacetechnique, which involvesestablishingthe liquid flowvelocity-depth profile using reference (polystyrene latex) particles. The electroosmotic velocity obtained by extrapolation of the velocityprofileto the cellwall permits calculation of the ~"potential of the cellwall-solution interface. The plane interface technique was also used to obtain the ~"potential at aqueous sodium dodecyl sulfate (SDS) solution surfaces with an open cell in which the upper boundary consists of an air-solution interface and the lower boundary, a quartz-solution interface. It was essentialto eliminate the meniscus in the open cell to obtain normal velocityprofiles. The ~ potential of the aqueous SDS solution surface paralleled the Stern potential, calculated from the surface tension-SDS concentration data by use of Gibbs adsorption equation and Gouy-Chapman theory, though the former was largerin magnitude than t h e latter.
© 199 i Academic Press, Inc.
INTRODUCTION The electrokinetic properties at the gasaqueous solution interface are of great significance in both theoretical and practical applications. However, quite few studies have been undertaken for determining the ~"potential of gas bubbles. Although electrophoresis, including the spinning cylinder method, has been used to obtain the ~"potential of bubbles ( 111 ), it requires a complicated procedure (6) to obtain the electrophoretic mobility at the stationary level from which the ~"potential can be calculated. The Dorn effect has proven to be useful in the study of electrokinetic phen o m e n a of gas-solution interfaces because of the simplicity in technique ( 12-16), compared with the electrophoretic method. However, it has been shown that the ~"potential of bubbles in aqueous solutions calculated by use of Dorn effect depends on the bubble size (13) and is abnormally large in magnitude in inorganic salt solutions (17) when the Smoluchowski equation is used. The plane interface technique for measuring the ~"potential at the air-aqueous solution in-
terface presented by Huddleston and Smith (9) is unique in its use of an open cell. Subtraction of the electrophoretic mobility of the reference particles, which can be determined by using a conventional cell, from the mobility profile experimentally obtained permits the liquid flow velocity profile in the open cell. Extrapolation of this velocity profile to the liquid surface provides the electroosmotic velocity of the liquid at the surface, from which the ~"potential at the air-solution interface can be calculated with the Smoluchowski equation. In our previous paper (18), the liquid flow velocity profile in the open cell was found to depend on the total thickness of the solution, which contradicts the theoretical requirement. In the present paper, the plane interface technique was applied to obtain the ~"potentials of quartz and sapphire plates in contact with aqueous solutions using a cell of different walls (asymmetric cell). This paper also focuses on the origin of the abnormal behavior of the liquid flow velocity profile with respect to solution thickness. For this paper, three open cells 266
0021-9797/91 $3.00 Copyright © 199I by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal of ColloM and Interface Science, Vol. 142, No. 1, March 1, 1991
267
~" POTENTIAL MEASUREMENT
were prepared, each of different depth. The test solution was placed in the cell in such a way that the solution thickness became equal to the cell depth to eliminate the meniscus effect.
1ram
2ram
,__,_ ] 3mm
EXPERIMENTAL
1. ~ Potential Measurement of Solid-Solution Interfaces
FIG. 2. Side view of open cells filled with latex suspensions differing in inside depth.
A cell used for measuring the electrophoretic mobility of reference (polystyrene latex) particles was made of quartz as shown in Fig. 1: outside dimensions--45 m m wide, 100 m m long, and 4 m m high; inside dimensions--15 m m wide, 60 m m long, and 3 m m deep. Two palladium plates (each 12 × 50 ram) were fixed to the cell in such a way that each end of the plate was dipped vertically into a test solution leaving a space of about 1 m m from each end wall of the cell (Fig. 1 ). The sapphire plate, the crystal phase of which was ( 1, 1, 0, 2), was then fixed with the quartz cell by paraffin wax leaving the electrodes. Thus, the lower and side boundaries of the cell consist of quartz-solution interface and the upper boundary, sapphire-solution interface. An appropriate a m o u n t of a dilute suspension of polystyrene latex was placed in the cell from an electrode clearance by a syringe and the electrophoretic velocity was measured under a microscope (magnification 150×) with a dark illumination as a function of the distance from the bottom of the cell. The electrophoretic mobility of the latex particles was also measured separately using a conventional quartz cell. The electric field was calculated as i~ ~S, where i is the electric current passed, is the specific conductance of the solution, and S is the cross-sectional area of the solution. The electric field was in the range 3 to 4 V 2 3 ..................... I~
-
60mm lOOmrn-
3
m
--~
FIG. 1. Schematic drawing of the side view of a cell. ( 1 ) Quartz plate, (2) palladium plates, (3) Pd-Pd electrodes.
cm -] in this study. The other experimental procedures are the same as those in conventional electrophoresis experiments. The pH of the solution was adjusted with HCI or NaOH. The concentration of NaC1, used as an indifferent electrolyte, was adjusted to 1 × 10 -3 mole dm -3. Inorganic reagents were of guaranteed reagent grade and were used without further purification.
2. ~ Potential Measurement of Air-Solution Interface A cell without a sapphire plate as the upper wall served as the open cell, in which the upper boundary consists of the air-solution interface and the lower boundary, the quartz-solution interface. Three cells having different inside depths ( 1, 2, and 3 mm) were used (Fig. 2). After an appropriate amount of a dilute suspension of reference (polystyrene latex) particles was placed in the cell by pipet, the electrophoretic velocity was measured under a microscope as a function of the distance from the bottom of the cell. The volume of the suspension was equal to that of the cell so as to avoid the meniscus effect on the solution surface (Fig. 2). Precaution was taken to avoid the mechanical vibration of a solution surface during measurements under the microscope. A plastic (polymethacrylate) cover plate having a circular hole for microscopic observation was placed on the open cell through a silicon rubber spacer by which direct contact of the cover plate with sample solutions was prevented. The other experimental procedures are the same as those in the previous paper ( 18 ). Journal of Colloid and Interface Science. VoL 142, No. 1, March 1, 1991
268
SASAKI
The surface tension of SDS solution was measured by the Wilhelmy plate method using a surface tensiometer (Kyowa CBVP A-3 ). A commercial reagent of sodium dodecyl sulfate (SDS) was recrystallized twice from ethanol. Double-distilled water was used in all experiments. Measurements were made at ambient room temperature which varied from 23 to 25°C. RESULTS AND DISCUSSION
1. ~ Potentials of Quartz- and SapphireSolution Interfaces First, the electrophoretic velocity of reference particles was measured as a function of the cell level using the asymmetric cell. The liquid flow velocity profile, or the electroosmotic velocity profile, can be obtained by shifting the origin of the abscissa by a quantity of the electrophoretic velocity of the reference latex particles. Figure 3 shows some examples of the liquid flow velocity profile at various pH values, in which the lower boundary refers to the quartz-solution interface and the upper boundary, the sapphire-solution interface. The solid lines of the parabolas were drawn by computer curve fitting. A symmetric parabola was given at pH 9.3 where the surface charge of quartz is consistent with that of sapphire. The isoelectric point (iep) of sapphire was found to be pH 5.6 because the extrapolation of the velocity parabola to the upper boundary is estimated to be 0. It is interesting Sapphire
• 6.9 5.6 • 2,3
I
Quartz
-10
i
10 Liquid flow velocity(×10-6mse(~1)
20
lqG. 3. Liquid flow velocity-depthprofilein an asymmetric cell in solutions of various pH. Journal of Colloid and Interface Science, Vol. 142, No. 1, March 1, 1991
ET AL.
-150 Q u a r t ~ -1O0 •1 E] 0
~
.
"~ -50 o
N
50
S 3
4
•, &: conventionalcell 5 6
7 8
9 10
pH
FIG. 4. ~"potential of quartz and sapphire aqueous solution interfacesas a function ofpH togetherwith that of latex particles. to note that the velocity profile exhibits nearly a straight line at about pH 2.3, where the surface charges of sapphire and quartz are approximately equal in magnitude but different in sign. In Fig. 4, open squares and circles refer to ~ potentials of the quartz- and sapphire-solution interfaces which were obtained by extrapolation of the liquid flow velocity at the lower and upper boundaries, respectively. The negative ~"potential at the quartz-solution interface increased with increase in pH and reached a maximum at about pH 8. On the other hand, the positive ~"potential of sapphire decreased with increasing pH and the negative ~" potential increased with pH after passing through the iep at around pH 5.7. It is often the experience in electrophoresis experiments that when upper and lower walls are not identical in interfacial properties, the parabola of the electrophoretic velocity of particles becomes distorted. In such cases a true electrophoretic velocity can be obtained by averaging the values of velocity at the lower and upper stationary levels prescribed for a symmetric parabola of the same cell, i.e., ( 1/ 3 ) ] / 2 ( d / 2 ) apart from the center of the cell, where d is the inside height of the cell ( 1821 ). The effect of cell dimension on the stationary level has been discussed (20, 21 ). ~" potentials of the reference particles, obtained
~" POTENTIAL MEASUREMENT by averaging the electrophoretic mobilities at the two stationary levels (see above), are also presented in Fig. 4 as open triangles. They are seen to be approximately constant in the pH range tested. ~"potentials of polystyrene latex particles measured with a conventional electrophoresis cell are indicated by filled triangles in the same figure. Filled squares represent potentials of quartz measured separately with a conventional cell on particles that were obtained by grinding a quartz cell. In both cases, polystyrene latex and quartz, agreement in ~" potentials between both approaches is thought to be satisfactory. This offers justification of the plane interface technique in the case where the upper and lower walls are different in nature.
2. ~ Potential of Air-Solution Interface In our previous paper (18), it was demonstrated that the liquid flow velocity-depth profile depended on the solution thickness in the open cell. An example is shown in Fig. 5 which shows the liquid flow velocity in an 1 × 10 -3 mole dm -3 NaC1 aqueous solution. It is seen that with an increase in the solution thickness, the electrophoretic velocity at the air-solution interface, which is indicated by a broken line, gradually decreased and leveled off over 2.09 m m thickness. This result contradicts the theoretical prediction of the electrophoresis in a closed system, which indicates that the maximum velocity should be the same for all the profiles independent of the total
'
~o
,
5
,
'
0
5
10
Io ~-
Liquid flow velocity {*lO-6rn sec~/V cnl 1}
FIG. 5. Liquid flow velocity versus solution depth. Original data are taken from Ref. ( 18).
269
thickness of the solution. The anomalous behavior of the liquid flow velocity profile is clearly seen at small total solution thicknesses, where the requirement of no net flow in a closed cell is not fulfilled. On the other hand, for large total solution thicknesses, the requirement of no net flow is established as can be confirmed in the graph. In that case the solution thickness was changed by changing the amount of solution to be tested in the 3mm-deep open cell. In the present study three open cells were prepared, each of different depth ( 1, 2, and 3 mm). The test solution containing reference latex particles was placed in the cell in such a way that the solution thickness equaled the cell depth to eliminate the meniscus effect. The SDS concentration was adjusted to 1 × 10 -4 mole dm -3 in the presence of 1 × 10 3 mole dm -3 NaC1 at pH 5.5. The liquid flow velocity-depth profile obtained in this way is shown in Fig. 6, where solid lines were drawn by computer curve fitting. The lower boundary in the graph represents the quartz-solution interface and the upper boundary, the air-solution interface. Asymmetric parabolas were given in all cells, indicating that the electroosmotic velocity at the quartz-solution interface was different from that at the air-solution interface. It should be mentioned that the electroosmotic velocity extrapolated to the air-solution interface (upper boundary) does not depend on the thickness of the solution and shows a constant value. This satisfies the theoretical requirement. It may then be concluded that the contradiction to the theoretical requirements in the previous paper (18) was due to the effect evoked by the meniscus. One possible explanation for the meniscus effect is imperfect compensation of the return flow for the electroosmotic flow in the open cell. Details will be the subject of further study. ~ potentials of reference particles, obtained by averaging the electrophoretic mobilities of upper and lower stationary levels, were - 7 4 , - 8 1 , and - 7 4 mV for cell depths 1, 2, and 3 ram, respectively. These values are comparable to those obtained not only with the closed Journal of Colloid and Interface Science, Vol. 142, No. 1, March 1, 1991
270
SASAKI ET AL.
3 mm
~2 =¢ E 2
2mm 1
0
-5
0 5 10 15 Liquid flow velocity (Xl0-6rn sec-1/V c m -1)
20
FIG. 6. Liquid flow velocity-depth profile in the open cell. [SDS] = 1 × 10 -4 mole dm -3.
cell but also with a conventional electrophoresis cell, as shown in Fig. 4. The electroosmotic velocity (7.9 × 10 -6 m s e c - t / V c m -1 ) at the quartz-solution interface permits the potential of the quartz surface (-111 mV) which is also in good agreement with that at corresponding pH in Fig. 4. ~"potentials at the air-aqueous solution interface can also be calculated from the electroosmotic velocity, i.e., -223, -234, and -238 mV for total solution thicknesses 1, 2, and 3 mm, respectively. All of these values are higher than not only those reported in our previous paper (18) but also those reported by Huddleston and Smith (9) who used the plane interface technique. No clear understanding of the inconsistent results is available. In Fig. 7, the ~"potential at the air-aqueous solution interface is shown (solid line with triangles) as a function of SDS concentration in the presence of 1 × 10 -3 mole dm -3 NaCI, together with surface tension data (solid line with circles). The broken line represents the Stern potentials calculated from surface tension vs concentration data by using the Gibbs adsorption equation and Gouy-Chapman theory. Although there are some scattered results, it can be seen that with increasing SDS concentration up to 1 × 10 -5 mole dm -3, the negative ~"potential was kept almost constant because of the quite low concentration of SDS, causing no significant change in surface charge. As the concentration increased further, the negative ~-potential remarkably increased and leveled offat higher concentrations. ~'p0Journal of Colloid and Interface Science, Vol. 142, No. 1, M a r c h 1, 1991
tentials of reference particles and the quartz surface were found constant at all SDS concentrations tested, i.e., - 7 0 and -110 mV, respectively; these values were in good agreement with those measured by the conventional electrophoresis method. The Stern potential was calculated from the surface tension-concentration data by using the Gibbs adsorption equation and GouyChapman theory. The adsorption density of dodecyl sulfate (DS -~ ) ions, F (mole cm-2), is given by the Gibbs adsorption
1 P =
d7
nRTdln
[1]
Cs'
where 7 is the surface tension, Cs is the concentration of DS- ion, R is the gas constant, Tis the absolute temperature, and n is the salt constant, calculated by Eq. [2] (22):
c~
n = 1+
[2]
Cs -~- CNaC1
where CNaa is the concentration of NaC1. The saturated value of I" in the presence of 1 × 10-3 mole dm -3 NaC1 has been reported to be 3.31 X 10 -20 mole cm -2 (23); the corresponding SDS concentration was estimated to be 2.5 × 10 -3 mole dm -3. The Stern potential, ~ , is given by ad = - F F _ 1 ( 2 N A C s ~ k T ~ t/2
a ~ 10007r
zedps
sinh 2 ~
[3] - 300
A
8O
o
ze~-
70
./
-200
l
"~ 6 0
¢
-100
~ 5o
co N
4O 10-6
, 10-4
ii
SDS concentration 10-5
10-3
0 10-2
( m o l - d m -3)
FIG. 7. Comparison between ~ potential obtained by plane interface technique and the Stern potential calculated from surface tension-concentration data.
~ POTENTIAL MEASUREMENT
271
where NA is Avogadro's number, e is the di2. Alty, T., Proc. R. Soc. London Ser. A 106, 315 (1924). 3. Komagata, S., Denki Kagaku 4, 380 (1936). [in Japelectric constant, k is the Boltzmann constant, anese ] z is the valence, e is the elementary charge, Ca 4. Bach, N., and Gilman, A., Acta Physicochim. URSS is the charge density in the diffuse layer, a is 9, 1 (1938). the conversion constant, 3 X 10 9, and F i s the 5. Cichos, C., NeueBergbautech 1, 941 (1971); 2, 928 Faraday constant and negative. The contri(1972). 6. Collins, G. L., Motarjemi, M., and Jameson, G. J., J. bution from anions ( O H - ions), initially Colloid Interface Sci. 63, 69 ( 1978 ). present at the solution surface, was ignored 7. Fukui, Y., and Yuu, S., Chem. Eng. Sci. 35, 1097 because their adsorption density at the solution (1980). surface was small, i.e., of the order of mag8. Kubota, K., Hayashi, S., and Inaoka, M., Z Colloid nitude of 10 -13 mole cm -2 (13). The Stern Interface Sci. 95, 362 (1983). 9. Huddleston, R. W., and Smith, A. L., in "Foams" potential calculated is shown by a broken line (R. J. Akers, Ed.), p. 163. Academic Press, New in Fig. 7. York, 1976. It is generally accepted that the ~- potential 10. McShea, J. A., and Callaghan, I. C., Colloid Polym. is smaller in magnitude than the Stern potenSci. 261, 757 (1983). tial, in contrast to the result in Fig. 7. No ex- 11. Yoon, R. H., and Yordan, J. L., J. Colloid Interface planation is available for the contradiction beSci. 113, 430 (1986). tween both results. However, attention should 12. Usui, S., and Sasaki, H., ,L Colloid Interface Sci. 65, 36 (1978). be given to parallelism between both poten13. Usui, S., Sasaki, H., and Matsukawa, H., J. Colloid tials. Interface Sci. 81, 80 ( 1981 ). The plane interface technique is based on 14. Kubota, K., Hayashi, S., and Yasue, A., Kagaku Kothe assumption that it is the counterions that gaku Ronbunshu 81, 311 (1982). [in Japanese] migrate under an applied electric field. The 15. Sotskova, T. Z., Bazhenov, Yu. F., and Kulskii, requirement is fulfilled for solid-solution inL. A., Kolloidn. Zh. 44, 989 (1982). terfaces. However, in the case of the air-so- 16. Sotokova, T. Z., Poberezhnyi, V. Ya., Bazhenov, lution interface there is no verification that Yu. F., and Kulgkii, L. A., Kolloidn. Zh. 45, 108 (1983). surface charges (adsorbed ions) do not move when an electric field is applied. When satu- 17. Sasaki, H., Dai Qi, and Usui, S., Kolloidn. Zh. 48, 1097 (1986). rated adsorption of surfactant ions is estab18. Usui, S., Imamura, Y., and Sasaki, H., J. Colloid Inlished, there is a reason to believe that surfacterface Sci. 118, 335 (1987). rant ions adsorbed at solution surfaces return 19. White, P., Philos. Mag. 23, 811,824 (1937). to their original position if they are distorted 20. Komagata, S., Res. Electrotech. Lab., No. 348, 1 by an external field (24). In view of this, it (1933). was hoped to study ~"potential measurements 21. Mori, S., Okamoto, H., Hara, T., and Aso, K., in "Fine in concentrated SDS solutions. However, inParticles Processing" (P. Somasundaran, Ed.), p. 632. Amer. Inst. Min. Metall. Petro. Eng. Inc., New consistent results made it difficult to check the York, 1980. problem in SDS concentrations higher than 1 22. Matijevilc, E., and Pethica, B. A., Trans. Faraday Soc. X 10 -3 mole dm -3. REFERENCES 1. McTaggart, H. A., Philos. Mag. 27, 297 ( 1914); 28, 367 (1914); 44, 386 (1922).
54, 1382 (1958). 23. Ikeda, S., Adv. Colloid Interface Sci. 18, 93 (1982). 24. Davis, J. T., and Rideal, E. K., "Interfacial Phenomena," p. 410. Academic Press, New York, 1963.
Journal of Colloid and Interface Science, Vol. 142, No. I, March 1, 1991
Received June 18, 1990; accepted August 20, 1990 The ~"potential of quartz and sapphire plates in contact with aqueous solutions was measured by means of the plane interfacetechnique, which involvesestablishingthe liquid flowvelocity-depth profile using reference (polystyrene latex) particles. The electroosmotic velocity obtained by extrapolation of the velocityprofileto the cellwall permits calculation of the ~"potential of the cellwall-solution interface. The plane interface technique was also used to obtain the ~"potential at aqueous sodium dodecyl sulfate (SDS) solution surfaces with an open cell in which the upper boundary consists of an air-solution interface and the lower boundary, a quartz-solution interface. It was essentialto eliminate the meniscus in the open cell to obtain normal velocityprofiles. The ~ potential of the aqueous SDS solution surface paralleled the Stern potential, calculated from the surface tension-SDS concentration data by use of Gibbs adsorption equation and Gouy-Chapman theory, though the former was largerin magnitude than t h e latter.
© 199 i Academic Press, Inc.
INTRODUCTION The electrokinetic properties at the gasaqueous solution interface are of great significance in both theoretical and practical applications. However, quite few studies have been undertaken for determining the ~"potential of gas bubbles. Although electrophoresis, including the spinning cylinder method, has been used to obtain the ~"potential of bubbles ( 111 ), it requires a complicated procedure (6) to obtain the electrophoretic mobility at the stationary level from which the ~"potential can be calculated. The Dorn effect has proven to be useful in the study of electrokinetic phen o m e n a of gas-solution interfaces because of the simplicity in technique ( 12-16), compared with the electrophoretic method. However, it has been shown that the ~"potential of bubbles in aqueous solutions calculated by use of Dorn effect depends on the bubble size (13) and is abnormally large in magnitude in inorganic salt solutions (17) when the Smoluchowski equation is used. The plane interface technique for measuring the ~"potential at the air-aqueous solution in-
terface presented by Huddleston and Smith (9) is unique in its use of an open cell. Subtraction of the electrophoretic mobility of the reference particles, which can be determined by using a conventional cell, from the mobility profile experimentally obtained permits the liquid flow velocity profile in the open cell. Extrapolation of this velocity profile to the liquid surface provides the electroosmotic velocity of the liquid at the surface, from which the ~"potential at the air-solution interface can be calculated with the Smoluchowski equation. In our previous paper (18), the liquid flow velocity profile in the open cell was found to depend on the total thickness of the solution, which contradicts the theoretical requirement. In the present paper, the plane interface technique was applied to obtain the ~"potentials of quartz and sapphire plates in contact with aqueous solutions using a cell of different walls (asymmetric cell). This paper also focuses on the origin of the abnormal behavior of the liquid flow velocity profile with respect to solution thickness. For this paper, three open cells 266
0021-9797/91 $3.00 Copyright © 199I by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal of ColloM and Interface Science, Vol. 142, No. 1, March 1, 1991
267
~" POTENTIAL MEASUREMENT
were prepared, each of different depth. The test solution was placed in the cell in such a way that the solution thickness became equal to the cell depth to eliminate the meniscus effect.
1ram
2ram
,__,_ ] 3mm
EXPERIMENTAL
1. ~ Potential Measurement of Solid-Solution Interfaces
FIG. 2. Side view of open cells filled with latex suspensions differing in inside depth.
A cell used for measuring the electrophoretic mobility of reference (polystyrene latex) particles was made of quartz as shown in Fig. 1: outside dimensions--45 m m wide, 100 m m long, and 4 m m high; inside dimensions--15 m m wide, 60 m m long, and 3 m m deep. Two palladium plates (each 12 × 50 ram) were fixed to the cell in such a way that each end of the plate was dipped vertically into a test solution leaving a space of about 1 m m from each end wall of the cell (Fig. 1 ). The sapphire plate, the crystal phase of which was ( 1, 1, 0, 2), was then fixed with the quartz cell by paraffin wax leaving the electrodes. Thus, the lower and side boundaries of the cell consist of quartz-solution interface and the upper boundary, sapphire-solution interface. An appropriate a m o u n t of a dilute suspension of polystyrene latex was placed in the cell from an electrode clearance by a syringe and the electrophoretic velocity was measured under a microscope (magnification 150×) with a dark illumination as a function of the distance from the bottom of the cell. The electrophoretic mobility of the latex particles was also measured separately using a conventional quartz cell. The electric field was calculated as i~ ~S, where i is the electric current passed, is the specific conductance of the solution, and S is the cross-sectional area of the solution. The electric field was in the range 3 to 4 V 2 3 ..................... I~
-
60mm lOOmrn-
3
m
--~
FIG. 1. Schematic drawing of the side view of a cell. ( 1 ) Quartz plate, (2) palladium plates, (3) Pd-Pd electrodes.
cm -] in this study. The other experimental procedures are the same as those in conventional electrophoresis experiments. The pH of the solution was adjusted with HCI or NaOH. The concentration of NaC1, used as an indifferent electrolyte, was adjusted to 1 × 10 -3 mole dm -3. Inorganic reagents were of guaranteed reagent grade and were used without further purification.
2. ~ Potential Measurement of Air-Solution Interface A cell without a sapphire plate as the upper wall served as the open cell, in which the upper boundary consists of the air-solution interface and the lower boundary, the quartz-solution interface. Three cells having different inside depths ( 1, 2, and 3 mm) were used (Fig. 2). After an appropriate amount of a dilute suspension of reference (polystyrene latex) particles was placed in the cell by pipet, the electrophoretic velocity was measured under a microscope as a function of the distance from the bottom of the cell. The volume of the suspension was equal to that of the cell so as to avoid the meniscus effect on the solution surface (Fig. 2). Precaution was taken to avoid the mechanical vibration of a solution surface during measurements under the microscope. A plastic (polymethacrylate) cover plate having a circular hole for microscopic observation was placed on the open cell through a silicon rubber spacer by which direct contact of the cover plate with sample solutions was prevented. The other experimental procedures are the same as those in the previous paper ( 18 ). Journal of Colloid and Interface Science. VoL 142, No. 1, March 1, 1991
268
SASAKI
The surface tension of SDS solution was measured by the Wilhelmy plate method using a surface tensiometer (Kyowa CBVP A-3 ). A commercial reagent of sodium dodecyl sulfate (SDS) was recrystallized twice from ethanol. Double-distilled water was used in all experiments. Measurements were made at ambient room temperature which varied from 23 to 25°C. RESULTS AND DISCUSSION
1. ~ Potentials of Quartz- and SapphireSolution Interfaces First, the electrophoretic velocity of reference particles was measured as a function of the cell level using the asymmetric cell. The liquid flow velocity profile, or the electroosmotic velocity profile, can be obtained by shifting the origin of the abscissa by a quantity of the electrophoretic velocity of the reference latex particles. Figure 3 shows some examples of the liquid flow velocity profile at various pH values, in which the lower boundary refers to the quartz-solution interface and the upper boundary, the sapphire-solution interface. The solid lines of the parabolas were drawn by computer curve fitting. A symmetric parabola was given at pH 9.3 where the surface charge of quartz is consistent with that of sapphire. The isoelectric point (iep) of sapphire was found to be pH 5.6 because the extrapolation of the velocity parabola to the upper boundary is estimated to be 0. It is interesting Sapphire
• 6.9 5.6 • 2,3
I
Quartz
-10
i
10 Liquid flow velocity(×10-6mse(~1)
20
lqG. 3. Liquid flow velocity-depthprofilein an asymmetric cell in solutions of various pH. Journal of Colloid and Interface Science, Vol. 142, No. 1, March 1, 1991
ET AL.
-150 Q u a r t ~ -1O0 •1 E] 0
~
.
"~ -50 o
N
50
S 3
4
•, &: conventionalcell 5 6
7 8
9 10
pH
FIG. 4. ~"potential of quartz and sapphire aqueous solution interfacesas a function ofpH togetherwith that of latex particles. to note that the velocity profile exhibits nearly a straight line at about pH 2.3, where the surface charges of sapphire and quartz are approximately equal in magnitude but different in sign. In Fig. 4, open squares and circles refer to ~ potentials of the quartz- and sapphire-solution interfaces which were obtained by extrapolation of the liquid flow velocity at the lower and upper boundaries, respectively. The negative ~"potential at the quartz-solution interface increased with increase in pH and reached a maximum at about pH 8. On the other hand, the positive ~"potential of sapphire decreased with increasing pH and the negative ~" potential increased with pH after passing through the iep at around pH 5.7. It is often the experience in electrophoresis experiments that when upper and lower walls are not identical in interfacial properties, the parabola of the electrophoretic velocity of particles becomes distorted. In such cases a true electrophoretic velocity can be obtained by averaging the values of velocity at the lower and upper stationary levels prescribed for a symmetric parabola of the same cell, i.e., ( 1/ 3 ) ] / 2 ( d / 2 ) apart from the center of the cell, where d is the inside height of the cell ( 1821 ). The effect of cell dimension on the stationary level has been discussed (20, 21 ). ~" potentials of the reference particles, obtained
~" POTENTIAL MEASUREMENT by averaging the electrophoretic mobilities at the two stationary levels (see above), are also presented in Fig. 4 as open triangles. They are seen to be approximately constant in the pH range tested. ~"potentials of polystyrene latex particles measured with a conventional electrophoresis cell are indicated by filled triangles in the same figure. Filled squares represent potentials of quartz measured separately with a conventional cell on particles that were obtained by grinding a quartz cell. In both cases, polystyrene latex and quartz, agreement in ~" potentials between both approaches is thought to be satisfactory. This offers justification of the plane interface technique in the case where the upper and lower walls are different in nature.
2. ~ Potential of Air-Solution Interface In our previous paper (18), it was demonstrated that the liquid flow velocity-depth profile depended on the solution thickness in the open cell. An example is shown in Fig. 5 which shows the liquid flow velocity in an 1 × 10 -3 mole dm -3 NaC1 aqueous solution. It is seen that with an increase in the solution thickness, the electrophoretic velocity at the air-solution interface, which is indicated by a broken line, gradually decreased and leveled off over 2.09 m m thickness. This result contradicts the theoretical prediction of the electrophoresis in a closed system, which indicates that the maximum velocity should be the same for all the profiles independent of the total
'
~o
,
5
,
'
0
5
10
Io ~-
Liquid flow velocity {*lO-6rn sec~/V cnl 1}
FIG. 5. Liquid flow velocity versus solution depth. Original data are taken from Ref. ( 18).
269
thickness of the solution. The anomalous behavior of the liquid flow velocity profile is clearly seen at small total solution thicknesses, where the requirement of no net flow in a closed cell is not fulfilled. On the other hand, for large total solution thicknesses, the requirement of no net flow is established as can be confirmed in the graph. In that case the solution thickness was changed by changing the amount of solution to be tested in the 3mm-deep open cell. In the present study three open cells were prepared, each of different depth ( 1, 2, and 3 mm). The test solution containing reference latex particles was placed in the cell in such a way that the solution thickness equaled the cell depth to eliminate the meniscus effect. The SDS concentration was adjusted to 1 × 10 -4 mole dm -3 in the presence of 1 × 10 3 mole dm -3 NaC1 at pH 5.5. The liquid flow velocity-depth profile obtained in this way is shown in Fig. 6, where solid lines were drawn by computer curve fitting. The lower boundary in the graph represents the quartz-solution interface and the upper boundary, the air-solution interface. Asymmetric parabolas were given in all cells, indicating that the electroosmotic velocity at the quartz-solution interface was different from that at the air-solution interface. It should be mentioned that the electroosmotic velocity extrapolated to the air-solution interface (upper boundary) does not depend on the thickness of the solution and shows a constant value. This satisfies the theoretical requirement. It may then be concluded that the contradiction to the theoretical requirements in the previous paper (18) was due to the effect evoked by the meniscus. One possible explanation for the meniscus effect is imperfect compensation of the return flow for the electroosmotic flow in the open cell. Details will be the subject of further study. ~ potentials of reference particles, obtained by averaging the electrophoretic mobilities of upper and lower stationary levels, were - 7 4 , - 8 1 , and - 7 4 mV for cell depths 1, 2, and 3 ram, respectively. These values are comparable to those obtained not only with the closed Journal of Colloid and Interface Science, Vol. 142, No. 1, March 1, 1991
270
SASAKI ET AL.
3 mm
~2 =¢ E 2
2mm 1
0
-5
0 5 10 15 Liquid flow velocity (Xl0-6rn sec-1/V c m -1)
20
FIG. 6. Liquid flow velocity-depth profile in the open cell. [SDS] = 1 × 10 -4 mole dm -3.
cell but also with a conventional electrophoresis cell, as shown in Fig. 4. The electroosmotic velocity (7.9 × 10 -6 m s e c - t / V c m -1 ) at the quartz-solution interface permits the potential of the quartz surface (-111 mV) which is also in good agreement with that at corresponding pH in Fig. 4. ~"potentials at the air-aqueous solution interface can also be calculated from the electroosmotic velocity, i.e., -223, -234, and -238 mV for total solution thicknesses 1, 2, and 3 mm, respectively. All of these values are higher than not only those reported in our previous paper (18) but also those reported by Huddleston and Smith (9) who used the plane interface technique. No clear understanding of the inconsistent results is available. In Fig. 7, the ~"potential at the air-aqueous solution interface is shown (solid line with triangles) as a function of SDS concentration in the presence of 1 × 10 -3 mole dm -3 NaCI, together with surface tension data (solid line with circles). The broken line represents the Stern potentials calculated from surface tension vs concentration data by using the Gibbs adsorption equation and Gouy-Chapman theory. Although there are some scattered results, it can be seen that with increasing SDS concentration up to 1 × 10 -5 mole dm -3, the negative ~"potential was kept almost constant because of the quite low concentration of SDS, causing no significant change in surface charge. As the concentration increased further, the negative ~-potential remarkably increased and leveled offat higher concentrations. ~'p0Journal of Colloid and Interface Science, Vol. 142, No. 1, M a r c h 1, 1991
tentials of reference particles and the quartz surface were found constant at all SDS concentrations tested, i.e., - 7 0 and -110 mV, respectively; these values were in good agreement with those measured by the conventional electrophoresis method. The Stern potential was calculated from the surface tension-concentration data by using the Gibbs adsorption equation and GouyChapman theory. The adsorption density of dodecyl sulfate (DS -~ ) ions, F (mole cm-2), is given by the Gibbs adsorption
1 P =
d7
nRTdln
[1]
Cs'
where 7 is the surface tension, Cs is the concentration of DS- ion, R is the gas constant, Tis the absolute temperature, and n is the salt constant, calculated by Eq. [2] (22):
c~
n = 1+
[2]
Cs -~- CNaC1
where CNaa is the concentration of NaC1. The saturated value of I" in the presence of 1 × 10-3 mole dm -3 NaC1 has been reported to be 3.31 X 10 -20 mole cm -2 (23); the corresponding SDS concentration was estimated to be 2.5 × 10 -3 mole dm -3. The Stern potential, ~ , is given by ad = - F F _ 1 ( 2 N A C s ~ k T ~ t/2
a ~ 10007r
zedps
sinh 2 ~
[3] - 300
A
8O
o
ze~-
70
./
-200
l
"~ 6 0
¢
-100
~ 5o
co N
4O 10-6
, 10-4
ii
SDS concentration 10-5
10-3
0 10-2
( m o l - d m -3)
FIG. 7. Comparison between ~ potential obtained by plane interface technique and the Stern potential calculated from surface tension-concentration data.
~ POTENTIAL MEASUREMENT
271
where NA is Avogadro's number, e is the di2. Alty, T., Proc. R. Soc. London Ser. A 106, 315 (1924). 3. Komagata, S., Denki Kagaku 4, 380 (1936). [in Japelectric constant, k is the Boltzmann constant, anese ] z is the valence, e is the elementary charge, Ca 4. Bach, N., and Gilman, A., Acta Physicochim. URSS is the charge density in the diffuse layer, a is 9, 1 (1938). the conversion constant, 3 X 10 9, and F i s the 5. Cichos, C., NeueBergbautech 1, 941 (1971); 2, 928 Faraday constant and negative. The contri(1972). 6. Collins, G. L., Motarjemi, M., and Jameson, G. J., J. bution from anions ( O H - ions), initially Colloid Interface Sci. 63, 69 ( 1978 ). present at the solution surface, was ignored 7. Fukui, Y., and Yuu, S., Chem. Eng. Sci. 35, 1097 because their adsorption density at the solution (1980). surface was small, i.e., of the order of mag8. Kubota, K., Hayashi, S., and Inaoka, M., Z Colloid nitude of 10 -13 mole cm -2 (13). The Stern Interface Sci. 95, 362 (1983). 9. Huddleston, R. W., and Smith, A. L., in "Foams" potential calculated is shown by a broken line (R. J. Akers, Ed.), p. 163. Academic Press, New in Fig. 7. York, 1976. It is generally accepted that the ~- potential 10. McShea, J. A., and Callaghan, I. C., Colloid Polym. is smaller in magnitude than the Stern potenSci. 261, 757 (1983). tial, in contrast to the result in Fig. 7. No ex- 11. Yoon, R. H., and Yordan, J. L., J. Colloid Interface planation is available for the contradiction beSci. 113, 430 (1986). tween both results. However, attention should 12. Usui, S., and Sasaki, H., ,L Colloid Interface Sci. 65, 36 (1978). be given to parallelism between both poten13. Usui, S., Sasaki, H., and Matsukawa, H., J. Colloid tials. Interface Sci. 81, 80 ( 1981 ). The plane interface technique is based on 14. Kubota, K., Hayashi, S., and Yasue, A., Kagaku Kothe assumption that it is the counterions that gaku Ronbunshu 81, 311 (1982). [in Japanese] migrate under an applied electric field. The 15. Sotskova, T. Z., Bazhenov, Yu. F., and Kulskii, requirement is fulfilled for solid-solution inL. A., Kolloidn. Zh. 44, 989 (1982). terfaces. However, in the case of the air-so- 16. Sotokova, T. Z., Poberezhnyi, V. Ya., Bazhenov, lution interface there is no verification that Yu. F., and Kulgkii, L. A., Kolloidn. Zh. 45, 108 (1983). surface charges (adsorbed ions) do not move when an electric field is applied. When satu- 17. Sasaki, H., Dai Qi, and Usui, S., Kolloidn. Zh. 48, 1097 (1986). rated adsorption of surfactant ions is estab18. Usui, S., Imamura, Y., and Sasaki, H., J. Colloid Inlished, there is a reason to believe that surfacterface Sci. 118, 335 (1987). rant ions adsorbed at solution surfaces return 19. White, P., Philos. Mag. 23, 811,824 (1937). to their original position if they are distorted 20. Komagata, S., Res. Electrotech. Lab., No. 348, 1 by an external field (24). In view of this, it (1933). was hoped to study ~"potential measurements 21. Mori, S., Okamoto, H., Hara, T., and Aso, K., in "Fine in concentrated SDS solutions. However, inParticles Processing" (P. Somasundaran, Ed.), p. 632. Amer. Inst. Min. Metall. Petro. Eng. Inc., New consistent results made it difficult to check the York, 1980. problem in SDS concentrations higher than 1 22. Matijevilc, E., and Pethica, B. A., Trans. Faraday Soc. X 10 -3 mole dm -3. REFERENCES 1. McTaggart, H. A., Philos. Mag. 27, 297 ( 1914); 28, 367 (1914); 44, 386 (1922).
54, 1382 (1958). 23. Ikeda, S., Adv. Colloid Interface Sci. 18, 93 (1982). 24. Davis, J. T., and Rideal, E. K., "Interfacial Phenomena," p. 410. Academic Press, New York, 1963.
Journal of Colloid and Interface Science, Vol. 142, No. I, March 1, 1991