electrolyte interface

Electrical Double Layer at Alumina/Electrolyte Interface I. Surface Charge and Zeta Potential

RYSZARD SPRYCHA Department of Radiochemistry and Colloid Chemistry, Institute of Chemistry, Maria Curie-Sktodowska University, Lublin, Poland Received September 24, 1985; accepted December 11, 1987 Surface charge and zeta potential of T-ml203 in different 1: 1 electrolytes were determined. The solutions of NaC1, CsC1, and NaI of concentrations ranging from 0.0001 to 1.0 M were used. The potentiometric titration method was used to determine the surface charge of alumina. Zeta potential was calculated from electrophoretic mobilities of alumina particles. The data are described in terms of the site-binding model of the electrical double layer. Surface ionization constants, pKaa~t, a2, of-AIOH groups were determined by double extrapolation methods using zeta potential and surface charge data for the sample. Using electrokinetic data for the sample and knowing surface ionization constants, surface potential and -A1OH ~ and -A10- components, as a function of pH of the solution, were evaluated for different ionic strengths. © I989 Academic Press, Inc. INTRODUCTION

It is well known that the surface charge at the oxide/electrolyte interface, determined by the potentiometric titration method, is considerably higher than the diffuse charge, determined by use of, e.g., microelectrophoresis. This phenomenon can be explained by the site-binding model of the electrical double layer (1). The specific adsorption of supporting electrolyte ions is assumed to occur and form surface ion pairs with charged surface groups. It is believed that only four reactions take place at the interface (1, 2): -SOH~- ~ -SOH + H {

[1]

-SOH = -SO- + H +

[21

-SOHIX-

~- - S O H ~ + X -

-SO- + Y + ~ -SO-Y +

[31

of supporting electrolyte which bind pairwise with oppositely charged surface groups are located at the IHP (the same for cations and anions) and are separated from the surface by a region of constant capacity C1. These ions contribute to the charge aa and experience the potential ~k~. The IHP is separated from the OHP by a region of constant capacity C2. The potential at the OHP is ~ba and there is a corresponding diffuse layer charge ad. The knowledge of Ns, C, C1, C2, and corresponding constants of surface reactions [ 1][4] are indispensable for model calculations. All of them were used as parameters by Yates et al. (1). The set of these quantities is selected to fit the best experimental data for a given oxide. Davis et aL (3) have proposed that it is more instructive to write the reactions [ 3 ] and [41 as

[4] - S O H ~ X - ~ -SOH + H + + X -

According to the site-binding model, in the innermost layer only potential determining ions H + and O H - enter and contribute to the charge ao and experience the potential ~o. Ions

-SOH + Y + ~ - S O - Y + + H~+.

[5] [6]

This is only a formal change and it does not

0021-9797/89 $3.00 Journal of Colloid and Interface Science, Vol. 127, No. 1, January 1989

Copyright © 1989 by Academic Press, Inc. All rights of reproduction in any form reserved.

2

RYSZARD

change the basic idea of Yates et al. (1). The surface complexation constants can be expressed as , K ~ t = v,,,~,/,~xint/~'4nt [7] ,K~t+

=

/(int

re'int

[8 1

Davis et al. (3, 4) have also presented the method of determination of surface ionization and complexation constants from potentiometric titration data. However, Cj and C2 capacitances were adjustable parameters. In their first paper (3) they obtained "constants" dependent on electrolyte concentration. The intrinsic constants should be, by definition, independent on ionic strength. Thus the modified, so-called double extrapolation, method of determination of surface ionization and complexation constants has been proposed in the subsequent papers (4-7). The experimental data were extrapolated to a+_ = 0, i.e., to pHpzo as well as to C = 0 (to determine K~int "t or C = 1 (to determine --ai.a~s , T,l i n t •~x-,v+). The total number of surface sites, N~, can be estimated, for instance, from tritium exchange or crystallographic data (3, 79). Model calculations of Davis et al. (3) and James and Parks (7) agree well with a0-pH experimental relationships and rather feebly with ~'-pH ones. From Eqs. [ I ], [ 2 ], [ 5 ], and [ 6 ] we see that in order to determine the real surface ionization and complexation constants one has to know pure SO- and SOH ~- or SOH ~ X - and SO-Y + components, respectively. As far as the method of determination of surface ionization constants by double extrapolation ( 57) is correct, the method of determination of surface complexation constants from potentiometric titration data seems to be questionable because for higher electrolyte concentrations ~r0-pH relationships are completely different from the adsorption ones (10-13). Thus to determine the complexation constants properly the components of ~ charge have to be known vs pH. They can be determined experimentally. Journal of Colloid and Interface Science, Vol. 127, No. 1, January 1989

SPRYCHA

Smit et al. (10, 11) have described the method of determination of ao components for SiO2 and a-Al:Oa monocrystals. The method demands a special procedure of crystal washing in order to minimize the time of solid-liquid separation. It seems that this technique cannot, however, be used in disperse systems. The prolongation of time of contact of the solid with washing solution, e.g., during centrifugation or filtration, will disturb the dynamic equilibrium at the interface. Therefore the mistaken adsorption results can be obtained. Thus, in our opinion, the method of determination of adsorption densities of cations and anions based on the measurement of their uptakes from solution by the oxide sample seems to be a more appropriate one (12, 14, 15). In the hitherto published papers (3-7, 1623) the model calculations were compared only with surface charge and zeta potential data for a given oxide and different concentrations of the background electrolyte. According to the site-binding model, however, the model calculations should be compared with complete experimental data, i.e., surface charge, zeta potential, and adsorption densities of anion and cation for the same sample of the oxide. Such complete data can be found in recently published papers ( 10-13, 24). In our previous papers (I 2, 25 ) the complete data for the TiO2 (anatase)/electrolyte interface were described in terms of the site-binding theory. It was found that this model has a limited applicability for this system. For low ionic strengths, C ~<0.001 M, the site-binding model can be easily employed, but for higher electrolyte concentrations the C~ capacity increases and ~ approaches the Ca potential, i.e., C2 capacity tends to infinity and the model becomes similar to the basic Stern model. However, these observations cannot be generalized and for the deeper understanding of oxide/electrolyte interface properties much more complete experimental data are needed for the same sample of the oxide. In this paper surface charge and zeta poten-

3

ELECTRICAL DOUBLE LAYER, 1

tial data for the '~'m1203/electrolyte system are presented. EXPERIMENTAL

Materials The aluminum oxide manufactured by POCh, Gliwice, Poland, was used. X-ray analysis showed that it was 3,-A1203. The sample was washed, prior to experiments, with triply distilled water to remove all soluble substances present in the oxide. A polyethylene vessel was used and the washing procedure was repeated many times so that the constant conductivity, about 3 uS cm -i, of the washing water has

been obtained. The sample was subsequently dried in the desiccator at room temperature. Specific surface area determined by the BET method was 154 m 2 g-1. The electrolyte solutions ofNaC1, CsC1, and NaI were prepared from high-purity reagents. The appropriate hydroxides and acids, in concentrations from 0.1 to 1.0 M, were used to regulate pH of the solution. HI solutions were prepared in darkness, just before the experiments, by use of an ion-exchange column. All the solutions were prepared on freshly redistilled water of conductivity ca. 1 #S cm -l. Nitrogen, free of carbon dioxide, was used in titration experiments.

(3

-I

-4 6

7

I0

©

pH

- O,OOIM - 0,01M

i2

[]

- O,IM

V

- 1,oM

FIG. 1. Variation of surface charge of "/-A1203 as a function of pH and concentration of NaC1 solution.

Journal of Colloid and Interface Science, Vol. 127, No. 1, January 1989

4

RYSZARD

Methods The potentiometric titration method was used to determine the net surface proton balance vs pH of the solution. This quantity was subsequently used to calculate the surface charge density using the site-binding model of the electrical double layer. The method and equipment used are described in detail elsewhere (12). The accuracy of the measurement was to 0.01 pH unit. The titration was performed for four different concentrations of the electrolyte--0.001, 0.01, 0.1, and 1.0 M. The classical method of electrophoresis was

SPRYCHA

used to determine zeta potential vs p H relationships. The procedure was the same as described previously for titanium dioxide (25). Because 3'-A1203 formed a polydisperse suspension, the particles of ca. 0.5 to 1.0 # m in diameter were separated from the suspension by sedimentation. These particles were subsequently used in microelectrophoretic measurements. From 5 to 10 particles were timed in each direction and average electrophoretic mobility was calculated. The electrophoretic mobilities were transferred into zeta potential using the method described in the literature (26).

-4 0 4

~ ^

'

'

~

'

pH

[] C[ C) Br

8

o

AI

oa

0

66

?

~

9

10

pH

4

[ ] No OK

8

A Cs b FIG. 2. Variation of surface charge o£ 3'-A1203 as a function of pH in 0.1 M solutions of (a) NaCI, NaBr, and Na! and (b) NaC], KCI, and CsCI.

Journal of Colloid and Interface Science, Vol. 127, No. 1, January 1989

ELECTRICAL D O U B L E LAYER, I RESULTS

The example surface charge vs pH curves for different ionic strengths of NaCI solution are presented in Fig. 1. The surface charges for other electrolytes differ only imperceptibly. The pHpz¢ of'y-Al203 is at pH = 8.1 _+0.1 and is independent of the electrolyte concentration. Different values of the pzc are cited in the literature for A1203 dependent on the crystallographic form and the history of the sample. Most of them are contained in the pH range from 7.8 to 9.1 (27-31).

5

The cation and anion effect on surface charge value is depicted in Fig. 2 for 0.1 M solutions of three different electrolytes. As is seen, more emphatic differences are observed for cations. This observation agrees well with previous observations for TiO2 (12). The example g'-pH relationships for the AI203/NaC1 system are presented in Fig. 3. The isoelectric point is at pH = 8.1 _+0.1 and is in agreement with the pzc. The values of zeta potential ~" vs ApH are similar to those determined previously by Wiese and Healy (32).

00.O001M o.ooIM

t,O

[]

o,mM

30

20

10

0

-10

-20

-30

-40

-50

FIG. 3. Zeta potential vs pH relationships for the alumina/NaC1 system.

Journal of Colloid and Interface Science, Vol. 127,No. 1, January 1989

6

RYSZARD SPRYCHA DISCUSSION

The potentiometric titration and electrokinetic data presented in this paper were analyzed in terms of the site-binding model, taking into account its basic assumptions. Amphoteric dissociation reactions o f surface -A1OH groups can be written as -AlOHa- ~- -A1OH + H~+

[9]

-A1OH ~ - A 1 0 - + H +.

[10]

Assuming that the ratios of surface activity

d13.ff

coefficients of surface groups are constant (33), the effective equilibrium constants of reactions [ 9] and [ 10] can be defined as K i m = [A1OH] [ H+]

[AlOHa]

al

Kint= [ A 1 0 - ] [ H+ ] a2 [A1OH]

I ~

Ij 1!

0 0 , O001M

Z~ o,oolm [] O,mM i

0,1

0,15

0 01pH+[C~

N

+2

i i

0',05

o.,

i,

i

-

o,o,p.

FIG. 4. Determinatton • of p/%'"m ~.=~constants from electrokineticdata for the ~/-A12Oa/NaC1system by the double straight-line extrapolationmethod. The solid lines and open points refer to experimentaldata. The dashed lines and solid points are extrapolateddata. lournaI of Colloid and Interface Science, Vol. 127, No. 1, January 1989

[12]

Using the Boltzmann equation to describe the distribution of ions in the electrical double layer ( 3, 7, 11), Eqs. [ 11 ] and [ 12 ] can be written in the logarhythmic form as

5

0,05

[I l]

ELECTRICAL DOUBLE LAYER, I p/Ca]t = pH - log[AIOH] + log[AlOHa-] +

e¢o

2.3kT

[13]

7

be calculated vs pH for different ionic strengths. From the basic equations of the model, Eqs. [ 11 ] and [ 12 ], one obtains [AlOHa-] = [AlOH][H+]exp(-e~b°/kT)

p K ~ t = pH + log[A1OH]

~int

[16] - log[A10-]

+

e¢o

2.3kT "

[14]

The number of free -A1OH groups can be estimated from the site balance. If, e.g., the swamping electrolyte is NaC1, then [AIOH] = N, - [AlOHa-] - [AIO-] - [AlOHa-C1-] - [A10-Na+].

[15]

Adsorption densities of specifically adsorbed (as ion pairs) ions can be measured experimentally (10-12). The surface ionization constants can be determined from zeta potential data using the double straight-line extrapolation method (34) (see Fig. 4). The constants obtained are pgia]t = 5.0 and pKia~t = 11.25. A different model approach to determine acidity constants of surface hydroxyl groups from zeta potential data for oxides is presented by Johnson (35). The surface ionization constants can also be estimated using potentiometric titration data and the method described by James and Parks (6, 7). The results obtained are presented in Fig. 5. The constants are p K ~ t = 4.9 + 0.5 and pKi~t = 11.3 + 0.5. As is seen, both methods have given almost the same results. It must be taken into account, however, that the accuracy of determination of surface ionization constants using potentiometric titration data is rather poor because extrapolated smooth curves tend asymptotically to the vertical lines. Thus any inexactitude in tracing of the curves can give large differences in surface ionization constant values. Having determined the surface ionization constants and taking into account the electrokinetic data for the sample, the surface potential and AIO- and AlOHa- components can

and Kia~t[ AIOH ] [A10-] = [H+]exp(_e~o/kT).

[17]

Substituting Eqs. [ 16 ] and [ 17 ] into the equation for #d (34), one obtains K~a~t[ AIOH ] O"d =

[H +]exp(_e~o/ kT) -

[AlOH] [H+ ]exp(-e~Po/ kT)

[18]

The if0 vs pH relationships can be obtained from Eq. [ 18 ] taking into account the adsorption and electrokinetic data and using Eq. [ 15 ] and Gouy-Chapman theory (to determine ad charge from zeta potential). Moreover, Eq. [ 15 ] can be simplified. From Eqs. [ 13 ]- [ 15 ] one can write [AIOH] + [AIO-] + [AlOHa-] = N~ - [AIOH~-CI-] - [AIO-Na + ]

[191

and ApKa = 2 log[A1OH] - log [ A1OH ~-] - log [ A 1 0 - ].

[20]

At the pzc, [AIO-]p~c = [A1OH~-]ozc, and Eq. [ 19 ] can be written as [A1OH]pzc + 2[A10-]pzc = Ns - [AIOH~C1]pz¢- [AlO-Na+]pz¢.

[21]

The second and third terms of the RHS of Eq. [ 21 ] can be determined experimentally. It arises from Eq. [20] that at the pzc, [ AIOH ]pzc _ [ AIOH ]pzc [AIO-]pzc [A1OH~-]pz~ =

10~PKa/2"

[22]

Now from Eqs. [ 21 ] and [ 22 ] one can write Journal of Colloid and lnteOrace Science, Vol. 127, No. 1, January 1989

8

RYSZARD

SPRYCHA

/-.------ C=O

"tt

j

ll~

C:z,.//'' \

\

1

oo.oo, a O,O~M

/

[]

O.~M

-,r

10

j

i

i

i

o.z

0,4

0,6

//

--

/

,

0,8

i

i

1,0

lOOZ.+l/~

\ \

0

o,oo~,,4

I
~

c=o 0,2

0,4

0,6

0.8

1,0

10~ - + ~

FIG. 5. D e t e r m i n a t i o n o f pKa,,a2 i.t constants from potentiometric titration data for the ~,-AI203/NaC1 system by the double smooth line extrapolation method (7). The solid fines and open symbols are experimental data. The dashed lines and solid points are extrapolated data.

[AlOH~lpz~= [AlO-]pz~ Ns- [AlOH~Cl-]pzc- [AlO-Na+]pzc 2 + 10 apKa/2 [23] and [AlOH]pz¢

{ us - [ AIOHIC1- ]p~ - [AIO-Na+]pz¢ } l 0 ApKJ2 2 + 10 ApKa/2

[24]

Journal of Colloid and Interface Science, Vol. 127, No. 1, January 1989

F r o m electrokinetic data for oxides the ad charge does not exceed, as a rule, ca. 2 ~tC c m -2 (3, 10, 19, 24, 3 4 - 3 8 ) . Therefore the changes o f [ A 1 0 - ] and [ AlOHa-] vs p H in relation to [ A I O H ] are rather small and it can be assumed (to estimate [A1OH] concentration) that [ A I O - ] = [ A l O H a ] ~ [A10-]pzc =~ [ A1OH ~ ] pzc in the whole p H range studied. Moreover, f r o m Eq. [ 24 ], [ A1OH ] pzc depends on ApKa considerably only when ApKa ~< 2. For ApKa > 2 the t e r m (lOaPKa/2)/(2

9

ELECTRICAL DOUBLE LAYER, I

d- 10 ApKa/2) --~ 1 and Eq. [24] can be rewritten as

[A1OH] - Ns - [A1OH~CI-] - [A10-Na +]

[25]

and used, with quite good accuracy, in the whole pH range studied. Because ApKa determined for A1203 is greater than 2, Eq. [25] can be used and substituted for Eq. [18 ] to estimate the ff0-pH relationships for different electrolyte concentrations. The results of such calculations for

ApKa = 6.2 are depicted, for the A1203/NaC1 system, in Fig. 6. The results for 0.1 M solutions were obtained from extrapolated electrokinetic data, as ~"vs log C curves are almost straight lines (39). As is seen for the 0.0001 M solution, the derivative d$o/dpH is almost constant at ca. - 5 5 mV. When electrolyte concentration increases the d6o/dpH, in the vicinity of the pzc, decreases, but far enough from the pzc it is nearly the same as for the 0.0001 Msolution. The data obtained are qualitatively consistent with model calculations by Wiese et aL and the modified Nernst equation (40).

:>

E

O,01M

80

O.O01M 60

O,O001M

\ \

40

\ \ \

k

20

0

-20

6

\

7

10

9

4.,

pH

~X \ \

-40

\ \ \ \

- 60

\

-80 \ \

-100

-120

FIG. 6. Surface potential vs pH relationships obtained from electrokinetic data (ApKa = 6.2) for different concentrations of NaC1 solution. Journal of Colloid and Interface Science, Vol. 127, No. 1, January 1989

10

RYSZARD SPRYCHA

,

'oE

0,01M

E,

1o,,

<_.

~

O.O01M 0.4 10f0001M

O~ '

0,2 o,ooolM

6

70

O

8

pH opH -0,2

~

~

O,O01M~

/

/ O,OiM~

0,2

00,O001M

A

O,O01M

[] O,01M

-0/. -0,6

FIG.7. [AIOH~] and [A10-] componentsvspH ofNaC1solutionobtainedby use ofthe ~bo-pHrelationships from Fig. 6. The diffuselayerchargesare presented for comparison(open symbols). The presented method of surface potential estimation is of course model dependent. However, using always the same site-binding model, preestimation of Xb0allows one to evaluate all the values characterizing the electrical double layer at the alumina/electrolyte interface without using adjustable parameters. Attempts to estimate ff0-pH relationships for oxides were made by others, e.g., (41) involving potentiometric titration data. We have showed (25, 34) that using the surface charge seems to be a rather inaccurate method. Having known ~b0-pH relationships for different ionic strengths it is possible to calculate [A10- ] and [ A1OH ~ ] components from Eqs. [16] and [17]. The results obtained for the alumina/NaC1 system are depicted in Fig. 7. The run of the curves is similar to that obtained previously for anatase (25). The diffuse layer charges are also presented for comparison. As is seen, the diffuse charge curves almost coincide with the [AIO-] and [AlOHa] curves for pH > PHpzc and pH < pHpzc, respectively, for C < 0.001 M. The divergence Journal of Colloid and Interface Science, Vol. 127,No. 1, January 1989

between curves is observed in the vicinity of the pzc because then the assumptions that ad ~B[A10-] for pH > pHpze and ad -B[A1OH~] for pH < PHpzc are invalid (25). Other features of the curves can be explained by taking into account the analysis given previously (25). Comparing the potentiometric titration data with the electrokinetic data it is dearly seen that surface ionization processes play a minor role in surface charge creation. Most of the surface -A10- and -AlOHa- groups are complexed with swamping electrolyte ions. It is assumed that these groups lose their activity and behave as the individual species - A 1 0 - N a + and-A1OH ~-C1-. The experimental data referring to the extent of adsorption of swamping electrolyte ions at the A1203/ electrolyte interface are published in Part II of this paper (42). ACKNOWLEDGMENTS The author thanksthe PolishAcademyof Sciences,Institute of Catalysis and Surface Chemistry,Cracow, for their financialsupport under Grant CPBR 3.20.

ELECTRICAL DOUBLE LAYER, I REFERENCES 1. Yates, D. E., Levine, S., and Healy, T. W., J. Chem. Soc., Faraday Trans. 1 70, 1807 (1974). 2. Wiese, G. R., James, R. O., Yates, D. E., and Healy, T. W., in "International Review of Science" (J. O. M. Bockris, Ed.), Phys. Chem. Series 2, Vol. 6. Butterworths, London, 1976. 3. Davis, J. A., James, R. O., and Leckie, J. O., J. Colloid Interface Sci. 63, 480 (1978). 4. Davis, J. A., and Leckie, J. O., J. Colloid Interface Sci. 67, 90 (1978). 5. James, R. O., Davis, J. A., and Leckie, J. 0., J. Colloid Interface Sci. 65, 331 (1978). 6. James, R. O., in "Adsorption of Inorganics at Solid/ Liquid Interfaces" (M. A. Anderson and A. J. Rubin, Eds.), p. 219. Ann Arbor Science Pub., Ann Arbor, MI, 1981. 7. James, R. O., and Parks, G. A., in "Surface and Colloid Science" (E. Matijevir, Ed.), Vol. 12, p. 110. Wiley-Interscience, New York, 1982. 8. Yates, D. E., and Healy, T. W., J. Chem. Soc., Faraday Trans. 1 76, 9 (1980). 9. Peri, J. B., J. Phys. Chem. 69, 211 (1965). 10. Smit, W., and Holten, C. L. M., J. Colloid Interface Sci. 78, 1 (1980). 11. Smit, W., Holten, C. L. M., Stein, H. N., de Goeij, J. J. M., and Theelen, H. M. J., J. Colloid lnterface Sci. 63, 120 (1978). 12. Sprycha, R., ,/. ColloidlnterfaceSci. 102, 173 (1984). 13. Jafferzic-Renault, N., Pichat, P., Foissy, A., and Mercier, R., J. Phys. Chem. 90, 2733 (1986). 14. Shiao, S. Y., and Meyer, R. E., J. Inorg. Nucl. Chem. 43, 3301 (1981). 15. Shiao, S. Y., Egozy, Y., and Meyer, R. E., J. lnorg. Nucl. Chem. 43, 3309 (1981). l& Regazzoni, A. E., Blesa, M. A., and Maroto, M. J. G., J. Colloid Interface Sci. 91, 560 (1983 ). 17. Milonijr, S. K., Ili6, Z. E., and Kopecni, M. M., Colloids and Surfaces 6, 167 (1983). 18. Sposito, G., J. Colloid Interface Sci. 91, 329 (1983). 19. James, R. O., Colloids and Surfaces 2, 201 (1981). 20. Janusz, W., in "5th International Conference on Surface Colloid Science, Potsdam, NY, 1985," Paper No. 69.

11

21. Houchin, M. R., and Warren, L. J., J. Colloidlnterface Sci. 100, 278 (1984). 22. Blesa, M. A., Figliolia, N. M., Maroto, A. J. G., and Regazzoni, A. E., J. Colloidlnterface Sci. 101, 410 (1984). 23. Barringer, E. A., and Bowen, H. K., Langmuir 1,420 (1985). 24. Foissy, A. M., Pandou, A., Lamarche, J. M., and Jafferzic-Renault, N., Colloids and Surfaces 5, 363 (1982). 25. Sprycha, R., J. Colloid Interface Sci. 110 (1986). 26: Wiersema, P. H., Loeb, A. L., and Overbeek, J. Th. G., J. Colloid Interface Sci. 78, 22 (1966). 27. Huang; C. P., and Stumm, W., J. Colloid Interface Sci. 43, 409 (1973). 28. Stumm, W., Huang, C. P., and Jenkins, D., Croatica Chem. Acta 42, 223 (1970). 29. Hohl, W., and Stumm, W., J. Colloid Interface Sci. 55, 281 (1976). 30. Kummert, R., and Stumm, W., J. Colloid Interface Sci. 75, 373 (1980). 31. Modi, H. J., and Fuerstenau, D. W., J. Phys. Chem. 61,640 (1957). 32. Wiese, G. R., and Healy, T. W., J. Colloid Interface Sci. 51, 427 (1975). 33. Chan, D., Pertain, J. W., White, L. P., and Healy, T. W., J. Chem. Soc., Faraday Trans. 1 71, 1046 (1975). 34. Sprycha, R., and Szczypa, J., J. Colloid Interface Sci. 102, 288 (1984). 35. Johnson, R. E., J. Colloid Interface Sci. 100, 540 (1984). 36. Hunter, R. J., in "Zeta Potential in Colloid Science." Academic Press, New York, 1981. 37. Ney, P., "Zeta Potentiale und Flotirberkeit von Mineralen." Springer-Verlag, Vienna/New York, 1973. 38. Michael, H. L., and Williams, D. J. A., J. Electroanal. Chem. 179, 131 (1984). 39. Hunter, R. J., and Wright, H, J. L., J. Colloidlnterface Sci. 37, 564 (1971). 40. Levine, S., Discuss. Faraday Soc. 52, 320 (1971). 41. Sidorova, M. P., Dmitrieva, J. P., and Golub, T. P., Kolloidn. Zh. 41,488 (1979). 42. Sprycha, R., J. Colloid Interface Sci. 115, 590 (1987 ).

Journal of Colloid and Interface Science, Vol. 127, No. 1, January 1989