Langmuir 1993,9, 2888-2894
2888
Background Electrolyte Correction for Electrokinetic Sonic Amplitude Measurements F. N. Desai,? H. R. Hammad, and K. F. Hayes* Department of Civil and Environmental Engineering, The University of Michigan, Ann Arbor, Michigan 48109-2125 Received April 21, 1993. I n Final Form: August 4,199P
Electroacoustics has recently been used to measure electrokineticproperties of colloidal systems. When an alternating electric field is applied to a colloidal suspension, charged particles in the liquid will move electrophoretically and create an alternating pressure wave. The electrokinetic sonic amplitude (ESA), which is the pressure amplitude per unit electric field, is related to the electrophoretic mobility and ( potential. For a solid suspension in an electrolyte solution, the measured ESA signal is a combination of two signals: one for the solid and the other for the background electrolyte. Under certain operating conditions, the contribution from the background electrolytesignalis not negligibleand must be subtracted from the measured value to arrive at the particle ESA value. Background electrolyte corrections were performed on a Geltech silica and a US Silica no. 40 quartz at two ionic strengths (0.01and 0.1 M NaC1) coveringthe pH range 2-8. These corrections are important at high ionic strengths because the ESA signal for the solid decreases and the background signal increases with increasing ionic strength. For 0.1 M ionic strength, the measured ESA changes sign around pH 4.7 for the Geltech silica and near pH 5.6 for no. 40 quartz. This suggests that silica particles were positively charged below pH 4.7and 5.6,respectively. However, the background-corrected ESA data correctly show that the solids do not change sign at least down to a pH of 2.
Introduction Electroacoustics has recently been used to obtain electrokinetic properties such as the electrophoretic mobility and the potential of colloidal systems.l" Some advantages of using electroacoustics instead of the more conventional electrokinetic techniques like microelectrophoresis are that (i) measurements can be made in concentrated suspensions up to 50vol 9% and with particles ranging in size from a few nanometers to 150 pm, (ii) measurements can be made on-line in a flowing stream, and (iii) the technique works for both transparent and opaque particles. The electroacoustic technique is based on the principle that when an alternating electric field is applied to a colloidal suspension, charged material in the liquid will move electrophoretically and create an alternating pressure wave. This effect is called the electrokinetic sonic amplitude (ESA). The magnitude of the ESA signal is related to the dynamic electrophoretic mobility by
r
ESA = PIE = cAp$'Gyd
(1) where P is the pressure amplitude of the sound wave, E is the amplitude of the applied electric field, c is the second velocity in suspension, Ap is the density difference between the particles and the solvent, 4' is the volume fraction of the particles, Gf is a geometric factor for the electrode geometry, and Nd is the dynamic electrophoretic mobility. The dynamic electrophoretic mobility is different from the static or dc electrophoretic mobility since it includes particle inertia. Equation 1 is valid in the linear regime
* To whom correspondence should be addressed.
t Current address: Winton Hill Technical Center, The Procter & Gamble Company, 6300 Center Hill Road, Cincinnati, Ohio 45224. Abstractpublishedin Advance ACSAbstracts, October 15,1993. (1) O'Brien, R. W. J. Fluid Mech. 1988, 190, 71. (2) Marlow, B. J.; Fairhurst, D.; Pendse, H. P. Langmuir 1988,4,611. (3) James, R. 0.;Texter, J.; Scales, P. J. Langmuir 1991, 7, 1993. (4) Scales, P. J.; Jones, E. Langmuir 1992,8, 385. (5) James, M.; Hunter, R. J.; O'Brien, R. W. Langmuir 1992, 8, 420.
in 6'. where Darticle-Darticle interactions, volume conse&ation effeks, and iarticle effects on the speed of sound are negligible.4 O'Brien,' Babchin et al.? and Sawatsky and Babchin7 have derived theoretical equations relating the dynamic mobility to the {potential. O'Brien's formula, which is valid for thin double layers (Ka > 50,where K-' is the Debye length), is
with a defined by a = wa2/v (3) Equation 2 is the Helmholtz-Smoluchowski equation modified by the factor IG(a)-ll, a damping term which is a function of the frequency of the applied field (w), the average particle radius (a), and the kinematic viscosity (Y). Here, e is the dielectric permittivity of the suspension. For a solid suspension in an electrolyte solution, the measured ESA signal is a combination of two signals: one for the solid and the other for the background electrolyte. Under most operating conditions, the contribution from the background electrolyte is negligible compared to the ESA signal from the solid. However, the background signal can become significant when (i) the ionic strength is high, (ii) the pH is close to the isoelectric point (IEP),(iii) the solid has a low charge density, (iv) the density difference between the solid and the liquid is small, or (v) the solid concentration is relatively low. For example, our ESA measurements on silica reported here show that at low pH and high ionic strengths, the background signal can be as large or even larger than the solid signal. Scales and Jones4measured the background electrolyte signal and set their experimental conditions like volume (6) Babchin,A. J.; Chow, R. S.;Sawatzky, R. P. Adv. Colloid Interface Sci. 1989, 30, 111. (7) Sawatzky, R. P.; Babchin, A. J. J. Fluid Mech. 1993,246, 321.
0743-746319312409-2888$04.00/0 0 1993 American Chemical Society
Electrokinetic Sonic Amplitude Measurements
Langmuir, Vol. 9, No. 11, 1993 2889
fraction of solid and ionic strength such that the background contribution was less than 5% of the total ESA signal. James et also measured the ESA signal for the background electrolyte (electrolyte effect) with the software parameters set equal to those of the colloid. They found that the background signal for a 10-3 M KN03 solution was less than a few millivolts and could be neglected compared to the signal for the alumina particles and the 0.5 % particle volume fraction used in their study. For higher ionic strengths, the background electrolyte signal can be significant and therefore a relatively higher particle concentration has to be used in order to make the background contribution negligible small. Unfortunately, since the theory relating ESA to dynamic mobility is applicable only when the volume fraction of the solid is less than 5%, it is not always possible to reduce the background contribution by increasing the solid concentration while staying below 5% volume fraction. Background correction can also become important when only a limited amount of solid is available and experiments have to be done at relativelylow solid concentrations (below 0.5 % ' by volume). Even when background corrections are incorporated, the solid concentration should be limited to the point where the solid and background ESA signals are of the same order of magnitude in order to avoid excessive subtraction errors. Marlow et recognized that the background electrolyte signal would affect the magnitude and the phase angle of the colloid vibration potential, CVP, for particles. The CVP is related to the ESA by ESA = (CVP)K* (4) where K* is the high-frequency conductivity of the suspension. Normally, the CVPs are orders of magnitude greater than the ion vibration potentials (IVPs)for the electrolyte. However, the magnitude of the CVP approaches that of the IVP when (i) the potential is low, (ii) the solid concentartion is low, (iii) the density difference between the solid and liquid is small, or (iv) the ionic strength is relatively high. The resultant measured signal is a vector sum of the CVP and the IVP. The linear vector addition of the CVP and IVP is only valid for dilute colloidal systems. Marlow et aL2obtained the IVP by centrifuging the solid and making a measurement on the supernatant. The IVP was then vectorially subtracted from the measured CVP to give the solid CVP. have outlined the procedure Although Marlow et for subtracting the background electrolyte contribution to the CVP, such a procedure has not yet been applied to ESA measurements. The objective of this paper is to outline a general procedure to subtract the background electrolyte contribution from the measured ESA signal to give the ESA signal for the solid. This correction is important, as explained above, when the ionic strength is relatively high or the solid concentration is relatively low, and extends the range of experimental conditions (pH, ionic strength, and solid concentration) over which ESA data can be converted to electrophoretic mobility and potential. This method is applied to silica particles at different ionic strengths.
r
r
ESA-....
Reference
Figure 1. Magnitude and phase angle for the ESA signals.
measured with respect to a phase reference solid of known polarity; the solid under investigation must be chosen as the phase reference solid. In addition, the solution conditions must be selected so that the background contribution to the measured ESA signalis negligibly small. With this reference system, the measured particle phase angle, referenced against itself, will be zero. This differs from past practices where care has not generallybeen taken to ensure that the electrolyte background contribution to the ESA of the phase reference solution was negligible. During the course of a potentiometric titration when the pH is varied or when a background electrolyteis added to the suspension, the phase angle may deviate from zero due to the following two reasons. First, the particle size may change because of aggregation. This, in most cases, ~ ~ as will result in a phase shift of about F J - ~ O O . ~ Second, the ionic strength increases, the relative magnitude of the background electrolyte ESA signal becomes larger and the ESA signal for the solid becomes smaller. In general, the background electrolyteESA signal is out of phase with respect to the solid ESA signal. Therefore, if the background contribution increases significantly, it is powible that the resultant measured phase angle may exceed 90°, causing the cosine of the phase angle to change sign and incorrectly suggesting that the polarity of the solid has changed. Figure 1 shows how the background electrolyte subtraction can be done. The magnitude and the phase angle of the uncorrected ESA signal (ESA,,, and 8) and the background electrolyte signal (ESAbkgd and 4) can be measured experimentally. The corrected ESA signal for the solid (ESqBOu)and its phase angle (8)can be calculated from the following two equations:
It should be noted that the absolute ESA values are used in eqs 5 and 6 above. The actual sign of ESLlid can be determined from the phase angle, 0. If 6 < 90°, the sign of ESLlid is the same as that of the phase reference, whereas if j3 > 90°, the sign of ESAsolidis opposite that of the phase reference. If the background electrolyte contribution is negligible, the measured phase angle, 8, would show a sudden jump 0 to 180' near the isoelectric point where the from about ' charge on the solid is reversed (Figure 2). On the other hand, if the background electrolyte contribution is significant, the measured phase angle, 8, would change ' to 180' over a range of pH values. The gradually from 0 smaller the background electrolyte contribution, the narrower is this range. Experimental Section
Background Electrolyte Correction
For the background correction procedure we propose, both the phase angle and the magnitude of the ESA signal are needed. The Matec 8000 ESA system described below is capable of measuring both. The phase angle should be
Materials. Potentiometric titrations were performed on two types of silica: Geltech silica and US Silica no. 40 quartz. The Geltech silica particles (Geltech, Alachua, FLJ are spherical, nonporous, and monodispersed with a median particle diameter of 1.5 pm and particle density of 2 g/cmg. The particle diameter was measured using the Capa-BOO centrifugal particle size
Desai et al.
2890 Langmuir, Vol. 9, No.11, 1993
bkgd
0 0.01MNaCl
Reierence
$
Q
p~ j u s t above t h e IEP
0
P ESA so1i d
Reference
.
2
pH Just below the IEP
,
*
(8) Cannon, D.; Mann, R. (Matec Applied Sciences, Hopkinton,MA). Personal communication. (9) Klingbiel et al. Colloids Surfaces 1992, 68, 103.
I
.
,
6
8
6
8
PH
Figure 2. Background correction for small background electrolyte signals. distribution analyzer (Horiba Instruments, Irvine, CA) and was identical to the particle diameter specified by the manufacturer. This silica has a purity of 99.9% and was used without any purification. The US Silica no. 40 quartz (US Silica, Berkeley Springs, WV) has particles varying in diameter from 1 to 15 pm with a median particle diameter of 5.1 pm and particle density of 2.65 g/cm3. This solid is nonporous with a wide range of particle shapes. The no. 40 quartz was washed with 0.1 M HCl and 15% hydrogen peroxide (pH 2-3) to remove any metal ions and to oxidizethe organicmatter. This solid was then thoroughly rinsed with MU-Q water to remove the residual acid and peroxide, and dried in an oven at 105 "C. The sodium chloride (purity of 99.999% ) was purchased from JohnsonMatthey (Seabrook,NH) and was used without further purification. Methods. Potentiometric titrations for each solid were performed at two ionic strengths ([NaCl] = 0.01 and 0.1 M) using the Matec ESA-8OOO instrument. The solids were sonicated for 5 h before use. Before s t a r t i n g the titration, the SP-80 ESA probe was calibrated using 10 vol % Ludox TM (Du Pont, Wilmington, DE). The ESA value for the Ludox was taken to be -5.32 mPa-(m/V) at 25 0C.8 This value, within the experimental error of 2 % ,8 is equivalent to the value of -5.21 mPa.(m/ V) determined for 10 vol % Ludox TM by Klingbeil et al? The apparatus was calibrated to the Ludox standard value prior to each titration and was checked again following the completion of the titration. In all cases reported, the value for the Ludox calibration solution measured after each titration was within *5% of the original value of -5.32 mPa-(m/V) at 25 "C. Since the magnitude and phase angle of the ESA signal change with temperature, all experiments were performed at 25.0 0.2 "C. A nitrogen blanket was maintained above the solution to prevent carbon dioxide contamination. For each solid at a particular ionic strength, two titrations were performed, one with the solid at the given ionic strength and the other an electrolyte background in the absence of the solid. The volume fraction of the Geltech silica was 0.050, and that for the no. 40quartz was 0.056. In a typical experiment, the solid was suspended in pure water without any added background electrolyte and used as the phase reference. The solid's polarity was known to be negative under these conditions. The phase angle for each solid, referenced against itself, was zero. An appropriate amount of NaCl was added to adjust the ionic strength, and then the potentiometric titrations were performed. During the course of the titration, the magnitude and phase angle of the ESA signal, the temperature, the electrical conductivity, and the amount of acid or base added as a function of pH were recorded a u t o m a t i d y by the computer-controlled Matec 8OOO system. An electrolyte blank titration was performed in exactly the same manner, but in the absence of the solid. The same phase reference was used in the blank titrations. The precisions of the phase angle and ESA measurements were h5O and *0.01 mPa.(m/V), respectively. Electrokinetic Sonic Amplitude System. Electrokinetic sonic amplitude measurements were performed using a Matec Model 8OOO system (Matec Applied Sciences, Hopkinton, MA),
.
4
W
2
t P
d -20
+2
I 4
PH Figure 3. ESA,,
and phase angle, 8, for no. 40 quartz.
s i m i i to the one described by Texter.Io The measurement system consista of a Matec SSP-1sample cell assembly which includes a titrating cell, a combination glass electrode for pH measurement, a conductivity probe, a temperature probe, a highviscosity stirrer, provisions for an inert gas atmosphere, a temperature control jacket, and a digital buret. The primary electronic components of the instrumentation include a Matec MBS-8OOO ampWier rack, a Wavetek Model 23 frequency synthesizer (Wavetek San Diego, Inc., San Diego, CA), a Hameg 60-MHz oecilloscope (Hameg, Inc., Port Washington, NY),a Northgab 386 computer (Northgate Computer Systems, Inc., Plymouth, MN), and a Matec SP-80 ESA measuring probe. The Matec supplied software package was used to perform the potentiometric titrations and data collection.
Results and Discussion Figures 3 and 4 show the measured ESA and phase angle for the no. 40 quartz and Geltech silica. At 0.1 M ionic strength, the phase angle shows a gradual change from 20° to M O O , indicating that the background electrolyte contribution is important. The more gradual change in the measured phase angle for the no. 40 quartz compared to the Geltech silica indicates a more significant background contributionas discussedabove. The ESA changes sign when the phase angle, 0, crosses 90". For the Geltech silica, 0 equals SOo when the pH is near 4.7 and the ESA changes from -0.01mPa.(m/V) just before the sign change to a value of 0.01 mPa*(m/V)just after the sign change. On the other hand, for the no. 40 quartz, the sign change occurs at a pH value near 5.6 where the ESA goes from a value of -0.05 to +0.05 mPa.(m/V). Hence, a more dramatic discontinuity is seen is the case of the no. 40 quartz compared to the Geltech silica. Figure 5 gives the magnitude and phase angle of the ESA signal for the background electrolytewith respect to the Geltach silica and no. 40quartz as the phase references. (10) Texter, J. Langmuir 1992,8, 291.
Langmuir, Vol. 9,No. 11,1993 2891
Electrokinetic Sonic Amplitude Measurements
II
I 2
4
8
6
-6."
PH
2
ESA(meas), 0.01M ESA(solid),O.OlM
1 6
4
I 8
PH Figure 6. Comparison of the ESA,,
0 0.1MNaCl 0 0.01MNaCl
i
0
0
l3O/
0
I "1
I
0 0
I 2
6
4
8
PH and phase angle, 0, for Geltech silica.
Figure 4. ESA,,
0.00 2
4
6
8
6
8
PH
m h
k 180
9 d
8
140 2
4
and ES&,Kd for no. 40
quartz.
FH
Figure 5. ESAbw and phase angle, 6, as a function of pH and ionic strength. For both the silica references, the ESA was measured at the same frequency (0.928 MHz). Therefore, the magnitude of the ESA signal for the background electrolyte was the same (within the precision of the measurement) when measured using either the Geltech silica or the no. 40 quartz as the phase reference. The phase angle for the
background electrolytecan depend on the phase reference solid chosen, particularly as the ionic strength increases. However, as seen in Figure 5, the background electrolyte phase contributions are very similar for the two solids. The measured (ESAme,) and background-corrected (ES&,fid) ESA for the no. 40 quartz for two ionic strengths (0.01and 0.1 M) are compared in Figure 6. For 0.01 M ionic strength, the background electrolyte contribution results in an overestimation of the value of the solid's ESA of 3% at pH 8 and 37% at pH 2; for 0.1 M ionic strength, the overestimation of the solid's ESA value is 24% at pH 8 and 365% at pH 2. At the higher ionic strength, the measured ESA changes sign at a pH of 5.6 (the break in the curve in Figure 6). An inexperienced experimenter might have taken this as the isoelectricpoint (IEP) for the quartz. However, the background correction shows that the ESAeofidvalue does not change sign at least down to a pH of 2. This result is consistent with the electrophoreticmobility and (potential data of Allen and Matijevic'l and Li and de Bruijn12which show that quartz is negatively charged above pH 2. The ESA data for no. 40 quartz can be converted to dynamic electrophoretic mobility [m2/(V s)] by multiplying the ESA values by 7.13 X W; a multiplication factor of 47.10 is needed to convert the ESA values to ( potential (mV). It should be noted that the disappearance of the discontinuity in ES&,,lid following the background correction is expected. When ESAm,, (a scalar quantity) is multiplied by the cosine of the phase angle, 8, the resulting vector quantity is a smooth function of pH. When this vector quantity is then subtracted from the background vector quantity, ESAbkgdcos 4, which was the cause of the discontinuity in the first place, the resulting backgroundcorrected ESAsofidcurve is smooth and continuous. In fact, the extent of the discontinuity observed in ESAm,, is related to how gradually the measured phase angle, 8, varieswith pH (compare Figures 3 and 4). A more gradual change in the measured phase angle, 8, indicates a greater relative background contribution and results in a greater discontinuity. In the limit of no background electrolyte effect, the phase angle would show a step function shift from Oo to l8Ooat the solid IEP. In this case, the ESAm, and ES&lid curves would be identical. In general, the ES&,nd data would always be expected to be a smooth function of pH unless the particle size or surface charge changed discontinously instead of gradually with pH. Figure 7 gives the phase angle, 8, calculated from eq 5 for the no. 40 quartz. For the low ionic strength, 8 is (11)Allen, L. H.;Matijevic, E. J. Colloid Interface Sci. 1969,31 (3), 287. (12)Li,H.C.;de Bruijn, P. L. Surf. Sci. 1966,5, 203.
Desai et al.
2892 Langmuir, Vol. 9, No. 11,1993
201 I
10 0.1MNaCl
h
v1
3
0.01M NaCl
1
I
I
h
20
3.E
10-
;I
e
v
u
.
0
0
-10 2
6
4
8
PH
ESA(solid),O.OlM
I
-4
2
6
4
2
6
4
8
PH
Figure 7. Calculated phase angle, j3, for no. 40 quartz.
I
-10
8
PH Figure 8. Comparison of the ESA,,, and ESAmIidfor Geltech silica.
essentiallyzero, whereas for the high ionic strength, j3varies from 20' to 25'. At high ionic strengths, the phase angle increase may be due to particle aggregation. In simulated plots of phase angle versus particle radius, Scales and Jones4 have shown that the phase angle can change as much as 35' when the particle radius varies from 0.1 to 3 pm. To test whether a particle size change might explain the calculated phase change in these systems, the particle size distribution was measured as a function of pH during the course of a potentiometric titration. As the pH was lowered from 8 to 2, samples of the suspension were removed a t unit pH intervals and diluted by a factor of 100 in a solution having the same pH and ionic strength. The median particle diameter was then measured within an hour using the Capa-500 centrifugal particle size distribution analyzer. Within experimental error (f0.3 pm), the particle diameter was independent of pH when the pH was lowered from 8 to 2. The particle diameter in the presence of 0.1 M NaCl(5.5 pm) was slightly higher than the particle diameter in the absence of the salt (5.1 pm). While this increase in particle diameter might, at least partially, account for the increase of j3 with ionic strength, it was not sufficient to make a convincing case for this hypothesis. The same analysis was repeated for the Geltech silica (Figures 8 and 9). As before, the background correction has a small effect at low ionic strength and a more significant effect a t high ionic strength. The measured ESA suggests that silica is positively charged below pH 4.7. However, the background correction correctly shows that this silica is negatively charged at least down to pH 2. For Geltech silica, the ESA values can be converted to dynamic electrophoretic mobility [m2/(V s)] by multiplying by 1.33 X 10-8; a multiplication factor of 25.97 is needed to convert the ESA values to { potential (mV).
Figure 9. Calculated phase angle, j3, for Geltech silica.
As expected, the background-corrected phase angle, j3, is close to zero at the low ionic strength. Assuming this phase angle gives an indication of particle aggregation, a t high ionic strengths, decreases in j3 with decreasing pH suggest a decrease in particle size with pH. As before, the particle size distribution was measured as a function of pH. The median particle diameter in the absence of salt was 1.5pm (i0.3pm). At 0.1 M ionic strength, the particle size did not change significantly during the course of the 5-h experiment when the pH was lowered from 8 to 2 (median particle diameter was 2.2 i 0.3 pm). Thus, the apparent change in j3 with pH could not be explained on the basis of particle size distribution changes. On the other hand, the calculated increase in Bwithionic strength might be explained, at least qualitatively, on the basis of particle aggregation. As with the no. 40 quartz, on the basis of the effects of particle size on the phase angle reported by Scales and Jones? the particle size change for the Geltech silica would not appear to be great enough to account for the change in phase angle, j3, that was calculated. Because the reproducibility of the phase angle measurement for d or B was only i 5 ' , a sensitivity analysis was performed to look at the effect of measured errors in 6 and B on the value of ES%ofid and the phase angle, j3, calculated by eqs 5 and 6. Figures 10 and 11show that a f5' error in 4 or 8 would have a negligible effect on the ES&a,d value, but a substantial effect on the calculated value of j3. On the basis of this analysis, the data in Figures 10 and 11suggest that an error in or 8 of f5' can lead to an uncertainty in the calculated value of j3 between -20' and +20°. This implies that, within experimental error, the values of j3 shown in Figures 10 and 11may not be different from zero. If the values of j3 are actually closer to zero and less variable, this would be more consistent with the lack of particle size change observed with ionic strength and pH. It would also suggest that the greater influence of the background electrolyte on no. 40 quartz compared to the Geltech silica was more a result of the smaller magnitude of ESAsoadfor no. 40 quartz than due to differences in the phase properties of the solids. In the near future, it may be possible to make a more definitive assessment of the relative importance of the ES&n,d versus phase angle, 8, in the overall background electrolyte effect. For example, the newest Matec instrument, the AcoustoSizer, has been reported by the companyto be capableof measuring the phase angle correct to better than With this improved accurticy, it will be possible to more accurately determine the value of 8. This, in turn, will make it possible to separate the relative importance of ESAsolid and j3 using eqs 5 and 6. With a more accurate determination of j3, it will also be possible
Langmuir, Vol. 9,No.11,1993 2893
Electrokinetic Sonic Amplitude Measurements
to check the measured ESA value for theoretical consistency in eqs 5 and 6 to within an error in /3 of 120'. Hence, in this study it was not possible to determine the relative importance of the ESA magnitude versus phase contributions to the electrolyte effect or to correlate particle size with j3.
I
-1.04 2
8
6
4
PH
"t
Geltech silica 0.1M NaCl
-30 4 2
I 6
4
8
PH Figure 10. Dependence of the E S & i dand j3 on values of the electrolyte phase angle, 4. u.u
Geltech silica 0.1M NaCl
I
-1.04 2
8
6
4
PH 30
Acknowledgment. We gratefully acknowledge the support of the U.S. Department of Energy, Office of Health and Environmental Research, Subsurface ScienceProgram (Grant DOE-FG02-89-ER60820; Dr. Frank J. Wobber, Program Manager) for funding this research.
I
-201
-,us
2
Geltech silica 0.1MNaCl .
I
4
.
, 6
.
, 8
PH Dependence of the E S L Mand B on values of the combined phase angle, 0. Figure
Conclusions The background electrolyte correction method outlined above extends the range of experimental conditions (e.g., pH, ionic strength, and solid concentration) over which ESA data can be measured and, hence, accurately converted to electrophoretic mobility and f potential. With this technique, it is now possible to measure the electrophoretic mobility and { potentials for systems where (i) the ionic strength is high, (ii) the pH is close to the IEP, (iii) the solid has a low charge density, (iv) the density difference between the solid and the liquid is small, or (v) the solid concentration is relatively low. Ionic strength has a significant effect on the ESA signal for the background electrolyte, whereas pH has negligible effect provided the pH is far from its extremes (pH 4-10). Under these conditions, a blank electrolyte titration is not necessary and a single ESA measurement for the background correction at a particular ionic strength would suffice. ESA measurements on the silica solids over a range of pH and ionic strengths have shown that the background electrolyte has a negligible effect a t 0.01 M ionic strength and a significant effect at 0.1 M ionic strength. For 0.1 M ionic strength, the measured ESA changes sign around pH 4.7 for the Geltech silica and near pH 5.6 for the US Silica no. 40 quartz. This suggests that silica particles are positively charged below pH 4.7 and 5.6, respectively. However, the background-corrected ESA data correctly show that the solids do not change sign at least down to a pH of 2. On the basis of a sensitivity analysis of the effects of 5' on the calculated errors in the measurement of 9 or 0 of h solid phase angle, 8, it was not possible to definitively assess the relative importance of changes in the solid phase angle versus the magnitude of the E S & , E d signal to the overall background effect observed. The rather large uncertainty in estimating /3 also precluded using its value for making meaningful assessments of particle size changes or lack thereof.
11.
to determine if j3 correlates with particle size changes. With the current Matec 8000 system, it is only possible
Nomenclature average particle radius sound velocity in suspension colloid vibration potential amplitude of the applied electric field magnitude of the measured ESA signal for the background electrolyte magnitude of the measured ESA signalfor the solid magnitude of the background-correded ESA signal for the solid geometric factor for the ESA electrode geometry a damping term which is a function of cy ion vibration potential high-frequency conductivity of the suspension
2894 Langmuir, Vol. 9, No. 11, 1993
P
pressure amplitude of the sound wave
Greek Symbokr a
B AP € K
Wa2/Y phase angle of the background-corrected ESA signal for the solid density difference between the particles and the solvent dielectric permittivity of the suspension inverseof the Debye length (‘electrical double layer thickness”)
Desai et al. Ka:
4 4’ 9 Pd V
e W
relative thickness of the electrical double layer to the particle radius phase angle of the measured ESA signal for the background electrolyte volume fraction of the particles viscosity dynamic electrophoretic mobility kinematic viscosity phase angle of the measured ESA signal for the solid frequency of the applied field
