Langmuir 1992,8, 1211-1217
1211
Electrophoretic Mobility Measurements in Low Conductivity Media R. E. Kornbrekke,*lt I. D. Morrison,$ and T. Ojag The Lubrizol Corporation, Wickliffe,Ohio 44092, Xerox Corporation, Webster, New York 14580, and Matec Applied Sciences, Hopkinton, Massachusetts 01 748 Received October 15, 1990. In Final Form: December 1 1 , 1991 Determining the sign and magnitude of the electric charge of colloidal particles suspended in low conductivity liquids (picosiemens/meterrange) by electrophoresiscontinues to be difficult and controversial. We have measured the electrophoretic mobility of suspensions of carbon black in dodecane under various conditions using two slightly different techniques. The first technique (Coulter DELSA 440) uses a cell consisting of a narrow rectangular flow channel placed between two electrodes and a dual laser beam with heterodyne optics to measure particle velocity. The second techniqueuses parallel plate electrodes immersed in the colloid system with a commercially available laser Doppler velocimeter from TSI with homodyne optics. We find that the uniform electric field, easily produced in the parallel plate cell, is satisfactorily reproduced in the rectangular cell as long as the cell is electrically isolated, Le., not in contact with a constant temperature water bath. Furthermore we find that a common technique of measuring electrophoretic mobilities a long time after the electric field has been appliedleads to errors caused by flocculation and/or sedimentation of the suspended particles. We have measured the effect of Chevron’s OLOA 1200 on the charging of carefully cleaned carbon black. OLOA 1200 causes carbon black to become negatively charged; the amount of charge increases with OLOA 1200 concentration, but the magnitude of charging is less than that previously reported.
Introduction Reliable techniques to measure electrophoretic mobilities of colloidal particles in aqueous suspensions are welland a variety of commercial instrumets are also available. We know that charges on suspended particles have an important influence on the stability of nonaqueous s u s p e n s i ~ n s , ~but - ~ ~measurements in nonaqueous suspensions, especially those of very low conductivity, have been difficult. One reason is experimental. When the dielectric constant of the liquid is less than 10, especially less than 5, and when one is working with the type of apparatus commonly used, irregular movements, rather than electrophoretic motion, are often ~ b s e r v e d . ~ - ~ J ~ A number of techniques to measure the electrical properties of colloids dispersed in nonconducting, nonpolar media have been proposed. These techniques were t T h e Lubrizol Corp. t Xerox Corp. 5 Matec Applied Sciences.
(1) Hunter, R. J. Zeta Potential in Colloid Science; Academic Press: New York, 1981. (2) Seaman, G. V. F. Electrokinetic Behavior of Red Cells. In The Red Blood Cell, 2nd ed.; Surgenor, D. MacN., Ed.; Academic Press: New York, 1975; Vol. 11, Chapter 27. (3) Kittaka, S.;Furusawa, K.;Ozaki, M.; Morimoto, T.; Kitahara, A. Electrokinetic Measurements. In Electrical Phenomena at Interfaces; Kitahara, A., Watanabe, A., Eds.; Marcel Dekker: New York, 1984; Chapter 7. (4) van der Minne, J. L.; Hermanie, P. H. J. J.Colloid Sci. 1952,7,600. (5) van der Minne, J. L.; Hermanie, P. H. J. J . Colloid Sci. 1953,8,38. (6) McGown, D. N. L.; Parfitt, G. D. Discuss. Faraday SOC.1966,42, 225. (7) McGown, D. N. L.; Parfitt, G. D.; Willis, E. J. Colloid Sci. 1965, 20, 650. (8)Kitahara, A.; Amano, M.; Kawasaki, S.; Kon-no, K. Colloid Polym. Sci. 1977,225, 1118. (9) Parreira, H. C. J. Electroanal. Chem. 1970, 25, 69. (10) Fowkes, F. M.; Jinnai, H.; Mostafa, A.; Anderson, F. W.; Moore, R. J. In Colloids and Surfaces in Reprographic Technology; Hair, M.,
Croucher, M. D., Eds.; American Chemical Society Symposium Series 200; American Chemical Society: Washington DC, 1982, pp 307-324. (11) Fowkes, F. M.; Pugh, R.J. Polymer Adsorption and Dispersion Stability; Goddard, E. D., Vincent, B., Eds.; American Chemical Society Symposium Series 240; American Chemical Society: Washington, DC, 1984; pp 331-354.
developed to understand liquid toner materials12-21and the action of motor oil additives better.22-28 Electrophoretic mobilities in dilute aqueous suspensions are usually determined by applying an electric field and measuring the velocity of the moving particles. The simplest experimental procedure is to place two parallel electrodes a known distance apart in a suspension, apply a known voltage, and measure the velocity of the suspended particles (see Figure IC).The electrophoretic mobility is the ratio of the resultant velocity to the electric field. The electric field (at least initially) is the applied voltage divided by the electrode gap. In moderately conductive aqueous suspensions this simple procedure is not convenient because the electric current needed to obtain a sufficiently large electric field between the parallel plates is great enough to cause Joule heating. This heating results in liquid motion that obscures electrophoretic motion. One method to minimize (12) Novotny, V. J. Appl. Phys. 1979,50, 324. (13) Novotny, V. J. Appl. Phys. 1979, 50, 2787. (14) Novotny, V. Colloids Surf. 1989,2, 373. (15) Novotny, V. Colloids and Surfaces in Reprographic Technology;
Hair, M. L.,Croucher, M. D.,Eds.;AmericanChemicalSocietySympium Series 200; American Chemical Society: Washington, DC, 1982. (16) Vincett, P. S. J. Colloid Interface Sci. 1979,69, 354. (17) Vincett, P. S. J. Colloid Interface Sci. 1980, 76, 83. (18) Vincett, P. S. J. Colloid Interface Sci. 1980, 76, 95. (19) Croucher, M.; Drappel, S.;Duff, J.; Hamer, G.; Lok, K.; Wong, R. Photogr. SCL.Eng. 1984, 28, 119. (20) Croucher, M.; Lok, K.; Wong, R. W.; Drappel, S.;Duff, J. M.; Pundsack, A. L.; Hair, M. L. J. Appl. Polym. Sci. 1985, 30, 593. (21) Heebner, G. Ph.D. Thesis, Lehigh University, 1990. (22) Agaev, S. G.; Taranova, L. V. Khim. Tekhnol. Topl. Masel 1986, 10, 27. (23) Agaev, S. G.; Taranova, L. V. Khim. Tekhnol. Topl. Masel 1986, 3, 31. (24j Arndt, E. R.; Kreuz, K. L. J. Colloid Interface Sci. 1988,123 (l), 230. (25) Keller, M. A.; Saba, C. S.J. SOC.Tribologists Lubrication Eng. 1989, 45 (6), 347. (26) Smith, H. A. Report No. AFAPLTR-82-2109,DCNO AD B073132, 1983. (27) Forbes, E. S.; Neustadter, E. C. Tribology 1972, April, 72. (28) Northern Instruments Corp., 6680 N. Highway 49, Linolakes, MN 55014, reports by M. Ogawa, and I. H. Krause.
0743-7463/92/2408-1211$03.00/00 1992 American Chemical Society
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1212 Langmuir, Vol. 8, No. 4, 1992
controlled by a constant temperature heat sink,33 or sometimes the cell is immersed in a constant temperature water bath3* or encased in a water jacket.35 The reason for thermostated cells is that even small temperature changes can cause significant changes in the viscosity of the fluid. We believe that the presence of a water bath around some cells has led to a major misunderstanding in the use .......... of electrophoresis for nonaqueous suspensions. The ............ (c) ( + ) @::;::;:;;;;-(-) electric field lines in the cell follow the least resistive path. ............ ............ Well constructed cells are all made of highly insulating ............. materials, usually quartz, so that with aqueous suspensions all the electric field lines pass through the interior of the -) cell whether the cell is encased in a vacuum, is in the air, or is immersed in a water bath. But when the cell is filled with a low conductivity liquid and the cell is immersed in Figure 1. Schematic drawings of a capillary tube electrophoretic a water bath, the electric field lines go from the electrodes cell and a parallel plate electrophoretic cell. The electric field through the liquid, through the cell walls (which act as a lines are indicated by dotted lines. Electric field lines terminate dielectric of a capacitor) to the water bath which is at the cell walls when the cell is immersed in a water bath because essentially at ground potential (see Figure la). Ions and the water bath is a direct path to ground. In the parallel plate cell the diameter of the electrodes is substantially greater than particles will move along these field lines until they reach the gap. the cell walls where they accumulate until the effective cell wall capacitor is fully charged. As the cell walls acquire Joule heating is to reduce the cross-sectional area between charge, the electric field lines in the cell gradually bend the electrodes by connecting two larger volumes that to go through the connecting tube. Therefore, even with contain the electrodes with a small bore tube. Thermal highly insulating cell wallmaterials, the presence of a water instabilities due to Joule heating are minimized by the bath causes the electric field in the capillary tube to change small cross section, but the presence of the cell walls with time. The time to charge the cell walls is called a introduces another effect. The cell walls can become ‘relaxation time” and is inversely proportional to the charged for the same reasons that suspended particles conductivity of the suspension. During this time the become charged. When the electric field is applied, the electric field in the sensing volume will vary and the ions in the electric double layer near the walls move, particles will appear to be moving erratically. dragging with them a layer of liquid. This flow (elecThe best approach for nonaqueous measurements is to troosmosis) is counterbalanced by a return liquid flow down remove all conducting paths from cell walls to ground (see the center of the cell. The liquid flow is zero at only one Figure lb,c). In particular, water jacketsmust not be used distance between the center and the wall of the cell. This with low conductivity suspensions. With the removal of position is the “stationary layer”. At the stationary layer, the conducting path to ground, the time required to whose location depends on the geometry of the cell, the establish the electric field in the cell is determined by the motion of suspended particles is due solely to electrocapacitance of the cell and the output impedance of the phoresis. Electroosmosis can also be a factor in nonaquepower supply. Any reasonable power supply will establish ous dispersions when oil-soluble reagents adsorb and the electric field in a few microseconds. Measurements desorb from the cell walls. All the commercially available can be made immediately before any changes take place instruments are designed to take measurements at the in the composition of the suspension or before excessive stationary layer. space charge is built up around the electrodes. Another method to minimize Joule heating is to apply In nonaqueous (low conductivity) liquids the electric the electric field only for a short time. This requires a fast current between parallel plate electrodes is small and Joule method of measuring particle velocities. U z g i r i has ~ ~ ~ ~ ~heating ~ is not significant even when the electric field is on shown that laser Doppler velocimetry is capable of for a long time. While Joule heating is not important, the measuring the velocity of the particles during the few build up of a space charge near the electrodes can be. This seconds the field is on. He also finds that since both Joule space charge diminishes, the electric field in the liquid. heating and the onset of turbulence scale with applied The charged particles in the sensing zone far from the voltage (not field), the less the distance between the electrodes move more slowly because of the diminished electrodes, the greater the applied field can be. Ware et electric field and appear to have lower electrophoretic al.31,32have published a series of papers showing the use mobility than they actually do. of this technique with the capillary cell for biological In principle, polarization of the electrodes by the materials. accumulation of ions near the electrode is a problem in Most commercially manufactured devices for electroaqueous and nonaqueous suspensions alike. In practice phoretic mobility measurements use small diameter cirthe electrodes in aqueous suspensions can only polarize a cular or rectangular tubes with electrodes at both ends of volt or so before some species is oxidized or reduced, often the tube. These cells have been designed for aqueous water. Oxidation and reduction reactions are the mechmeasurements, and they have been optimized to obtain anisms by which the electrode injects charge into the a highly uniform electric field in the cell when it is filled suspension to neutralize the space charge. Nonaqueous with a high conductivity liquid. Temperature is sometimes media do not usually contain significant quantities of Parallel Plate Cell
Capillary Tube Cell
containing low conductivity llquid
1
1
(29) Uzgiris, E. E. Opt. Commun. 1972, 6, 55-57. (30) Uzgiris, E. E. Reu. Sci. Instrum. 1974, 45, 74. (31) Ware, B. R.; Flygare, W. H. Chem. Phys. Lett. 1971, 12, 81. (32) Ware, B. R.;Haas,D.D. InFast MethodsinPhysicalBiochemistry and Cell Biology; Sha’afi, R. I., Fernandez, S. M., Eds., Elsevier: New York, 1983; Chapter 8.
(33) Coulter Electronics, Inc., 590 West 20th St., Hialeah, FL 330120145. (34) Rank Brothers, 56 High Street, Bottisham, Cambridge CB59DA, England. (35) Pen K e m System 3000 Manual; Pen Kem, Inc.: 341 Adams St., Bedford Hills, NY 10507.
Langmuir, Vol. 8, No. 4, 1992 1213
Electrophoretic Mobilities of Particles
oxidizable or reducible species (particularly water) to permit charge injection. Therefore, the electrodes can polarize to hundreds of volts if the electric field is on long enough.36 A technique to reduce electrode polarization is to reverse the direction of the electric field after a short time, typically every few seconds. The usual methods for measuring the velocity of particles are timing the particle motion when viewed through a micros~ope,3~ nulling the motion of particles by viewing them throughan adjustable rate r~tatingprism,~~detecting the time of flight of the particles viewed through a rotating grating,35or by laser ~ e l o c i m e t r y .The ~ ~ applicability of these techniques to measurements of mobilities in nonaqueous suspensions depends on the velocity of the particles. It is reasonable to expect that in nonaqueous media the number of charges per unit surface area on suspended particles is less than that in aqueous suspensions and, therefore, that electrophoretic velocities will be significantly lower. At the same time, however, the dielectric constants of nonaqueous liquids are also generally much less than water, so that equivalent applied voltages produce higher forces on the particles and, hence, higher velocities. Overall, the general observation is that the electrophoretic velocities in nonaqueous suspensions are an order of magnitude or so less than in water a t the same electric field. This means that electrophoretic measurements in nonaqueous media are often carried out at higher applied electric fields (about 10 times higher), often in the neighborhood of 100-300 Vlcm, to obtain the same accuracy in measuring particle velocities. Higher electric fields can cause several problems. They can induce charges on particles by causing some surface species to ionize or cause the electrical double layer surrounding the particle to become excessively distorted. High electric fields also polarize electrodes more rapidly. When the electric field is high, and there is a large difference in dielectric constant between the particle and medium, the particle will move in the direction of an electric field gradient. This is called dielectroph~resis~~ and is another phenomenon causing unwanted particle motion. It is therefore necessary to measure the electrophoretic mobility under various conditions. We have taken data in two completely different cells, one with a narrow rectangular cross section and the other with parallel plates to check for the effect of possible field nonuniformities.
Experimental Section We studied suspensions of carbon black in dodecane similar
to those previously studied" hoping that these systems can be considered as model nonaqueous suspensions. We hoped that these systems would be good model nonaqueous suspensions. However, they are not ideal. Carbon black is a complex material; it has a complicated morphology with high porosity making it difficult to clean, and its surface may become acidic or basic depending on the history and treatment of the material. Sterling NS carbon black obtained from Cabot Corp. was cleaned rigorously as previously described by Soxhlet extraction with acetone followed by hexane." We also cleaned the carbon by extractions with acetone and methylene chloride. The washed carbon was then baked at 120-168 "C in a vacuum (30 mmHg) oven overnight. Carbon, which had been cleaned and exposed to high humidity, was used in some measurements for mixtures without additives. No variation in the cleaning of carbon (Le., use of either hexane or methylene chloride as the second solvent or drying of carbon) showed any effect upon the electrophoretic mobility measurements. (36) Novotny, V. Colloids Surf. 1981, 2, 373. (37) Pohl, H. A. Dielectrophoresis; Cambridge University Press: Cambridge, 1978.
The purity of the carbon was checked by placing a portion in a thermal gravimetric analyzer (TGA) under a constant flow of nitrogen gas (20 cm3/min), while the temperature was ramped to lo00 OC a t 10 "C/min. The effluent from theTGA was monitored by Fourier transform infrared. About 0.1 wt 3' 6 water, 0.8 wt % organic, primarily hydrocarbon material, and 0.5 wt 76 carbon monoxide/carbon dioxide was evolved. The surface of the cleaned carbon was analyzed by X-ray photoelectron spectroscopy; the surface has 7 % oxygen and trace levels of sulfur and silicon. The surface area of the cleaned carbon, as determined from threepoint BET analysis of nitrogen adsorption, was 33 m*/g. High-purity (99% GC quality) dodecane from KodakChemical Co. and Aldrich Chemical Co. was used. The dodecane contained less than 5 ppm water as determined by Karl Fisher analysis. The interfacial tensions of various batches of dodecane against deionized/distilled water (with a surface tension of 72 dyn/cm a t 23 OC) were measured by the Wilhelmy plate technique a t 23 OC and averaged 50 1dyn/cm. Interfacial tensions are sensitive indicators of solvent purity. The literature value for the interfacial tension of water against dodecane is 52.9 dyn/cm at 20 0C.38 Values of interfacial tension for our liquids are close enough to indicate high purity. Repeated measurements of electrophoretic mobilities were made using different batches of dodecane with no noticeable effect. We believe that none of our results was affected by impurities in the solvent. Suspensions were prepared using ultrasound. Concentrated suspensions of 10-'weight fraction carbon in dodecane were made using a Braunsonic ultrasonic horn at 100 W of power for 10-12 min. Concentrated dispersions were also prepared by ball milling with glass beads as the milling media, following the procedure described by Heebner.*l Aliquots of these mixtures were further diluted in dodecane and exposed to ultrasound for several minutes. Electrophoretic mobility measurements were made using 10-5to 1Wweight fraction carbon black. Our measurements did not show any difference caused by the variation in mixing. The particle size of the carbon black dispersed in dodecane was measured by quasielastic light scattering (QELS) with a Brookhaven BI2030AT QELS instrument. The data were analyzed by a nonnegatively constrained least-squares method.39 The dispersed carbon particles had a light scattering average diameter of 150-300 nm. OLOA 1200, obtained from Chevron as a 50% solution, was diluted in dodecane, and aliquots of concentrated carbon suspensions, 1g of lO-'weight fraction carbon, were added to 100 g of these solutions. OLOA 1200 has a molecular weight of about 1700 and a total base number (TBN) of 40-50 units (ASTM D2896-73). It is described by the manufacturer as a monosuccinimide. Mixtures of carbon in OLOA solution were made so that the concentration of OLOA would not be changed much by adsorption of OLOA onto the solid surface. The ratio of the total solid surface area to the amount of OLOA in solution was low enough that even saturated coverage, calculated from the adsorption isotherm,m would not change the solution concentration by more than a few percent of the initial value. The lowest concentration of OLOA 1200, wt fraction, would be reduced by only one hundredth, even if the surface became saturated, which is unlikely a t low concentrations. Measurements by FTIR of the supernatant for OLOA concentration before and after the addition of carbon confirmed the negligible change in concentration. Electrophoretic mobility measurements were made using these mixtures 24 h after they were prepared. No changes in mobility were detected after additional storage of the suspensions. Electrophoretic mobility measurements were made using a DELSA 440 manufactured by Coulter Electronics and a custombuilt system assembled a t Xerox. The two systems differ substantially in cell design and somewhat in optics. The Delsa 440 uses a rectangular cross-section capillary tube cell with hemispherical electrodes at the ends. The parallel plate cell is a large-volume cubic cell (50 cm3) with 2 cm diameter stainless steel parallel plate electrodes 4 mm apart and well separated
*
(38) Fowkes, F. J. Phys. Chem. 1980,84, 510. (39) Herb, C. A.; Berger, E. J.; Chang, K.; Morrison, I. D.;Grabowski, E. F. ACS Symp. Ser. 1987, N o . 332, 89. (40) Pugh, R. J.; Fowkes, F. M. Colloids Surf. 1984, 9, 33.
1214 Langmuir, Vol. 8, No. 4, 1992
Kornbrekke et al.
Coulter Delsa 440 Cell
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-4
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~-
measurement
I
I 050
100
150
200
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300
Time (Hrs )
I r
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Figure 2. Cross sections of the Coulter Delsa 440 cell and the parallel plate cell. The dotted lines show the depths a t which electrophoretic mobilities are measured. The laser beams pass through the cell at the depth of the doted lines at the midpoint between the electrodes. The Delsa 440 cell has hemispherical electrodes located outside the region in the diagram. from the walls. Quartz windows are provided for the laser beams to enter and exit the cell. Figure 2 shows the general configuration of the cells used. The Delsa 440 cell is thermostated with a Peltier surface so no water bath is present to provide an electric path to ground in nonaqueous measurements. The parallel plate cell is not thermostated. The Delsa 440 can make electrophoretic mobility measurements at either the upper or the lower stationary layers where fluid motion does not contribute to the electrophoretic motion of the particles (160" from the top or bottom). In the parallel plate cell the plates are electrically isolated from the cell walls and the measurements are made in the middle of the gap between the plates (2 cm from the liquid surface). The Delsa 440 cell is thermostated to 25.0 f 0.1 OC. At this temperature the viscosity of dodecane is 1.378 CP and the dielectric constant is 2.002. The parallel plate cell is not thermostated; therefore the temperature was measured to *0.1 "C and the viscosity corrected by -0.026 cP/"C. The dielectric constant was assumed to be temperature independent. To calculate sedimentation rates, the carbon black density was taken as 2.0 g/cm3 and the dodecane density as 0.745 g/cm3. The optics in the two devices are similar. Both use laser Doppler velocimetry (LDV) to determine the velocity of the particle^.^*^^ The DELSA 440 uses LDV in the heterodyne mode (strong local oscillator) as well as providing four different scattering angles permitting four simultaneous mobility measurements to be made. Multiple angle detection is an advantage in the analysis of the widths of the mobility distributions. The particle velocities in the parallel plate cell are measured with a standard optical train from TSI (Minneapolis, MN) where LDV is in the homodyne mode. The laser beam is split into two identical beams. The two beams are focused to intersect in the sampling volume. Each particle scatters light from both of the laser beams and the scattered light has a beat frequency proportional to velocity. The advantage of this mode is that the measurement is independent of detector position. In the DELSA 440the direction of the particle motion, hence the polarity of the particle charge, is determined by using a specially designed moving mirror system. In the TSI equipment the direction of particle motion is determined by Bragg shifting one of the laser beams. Field strengths from 100 to 1000 Vicm were tested and mobilities were generally independent of field strength. All the data reported were taken at 400 Vicm in both cells. The mobilities were lower than the critical values cited by Stotz" so no hydrodynamic alteration of the double layer is expected. All the data reported here were taken using a 0.5-Hz square wave with a 1 s delay between pulses. We checked for the influence of (41)Stotz, S. J. Colloid Interface Sci. 1978,6 5 , 118.
Figure 3. Change in electrophoretic mobility as measured in the Delsa 440 as a function of time for a clean carbon in dodecane suspension. space charge a t the electrodes by measuring the mobilities for the most charged suspensions a t higher applied frequencies where space charge has less time to form. We saw no affect on the mobilities and concluded that space charge does not build up at the electrodes a t 0.5 Hz. The zeta potential was calculated from measured electrophoretic mobilities by using the Huckel equati01-1.~~ This equation should give a good calculation of zeta potential since the ionic strength is low and the double layers must be large compared to particle radii.
Results Our goal is to understand the mechanisms by which soluble compounds charge particles in nonaqueous media. To do so we need a solid that is initially uncharged when dispersed in the neat medium. Our expectation was that if carbon was carefully washed so that it contained no soluble components, then it would have no charge when dispersed in an alkane. However, when we dispersed the cleaned carbon in dodecane, we discovered an unexpected phenomenon. We discovered that after filling either cell with a carbon in dodecane suspension, the electrophoretic mobility changed steadily with time, usually starting near zero and going to a larger negative value (see Figure 3). The steady change in electrophoretic mobility was reproducible for each cell (especially in the Delsa 440) although the time scale was different between the two cells. We examined and discounted numerous possible explanations: contaminated cells, charging of the particles by the electrodes, sorption of water or other species from the ambient (by the addition of water to freshly prepared samples), temperature changes, effects of sonification, fluid flow in the cells, photoinduced charging of the particles, impure dodecane, and impurities on carbon. (Neither surface oxides nor trace levels of sulfur or silicon alone would be expected to cause carbon to become charged in dodecane.) Since we used two different experimental setups, systematic electrical or optical errors seemed unlikely. One clue to the final explanation was that while the results were similar in the two cells, the Delsa 440 cell showed the changes more rapidly. Another clue was that the lowest particle charge (near zero) came immediately after filling the cell, and again after any refilling of the cell, even with the same suspension. The time at which the particles had the lowest charge did not depend on when we made the suspension or when the suspension was sonicated, only on how long it had been since the cell was filled. We propose that the underlying cause of the phenomenon is the flocculation of unstabilized carbon particles in the cell. Flocculation and sedimentation eliminate uncharged particles quickly. Particles with a small electric (42)Ross, S.;Morrison, 1. D. Colloidal Systems and Interfaces;John Wiley & Sons: New York, 1988;p 347.
Electrophoretic Mobilities of Particles r
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Langmuir, Vol. 8, No. 4, 1992 1215
+ Parallel Plate Cell A Capillary Tube Cell
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z.:;F, --
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Figure 4. Electrophoretic mobility versus time for unstable carbon black suspensions in dodecane: a, (A)suspension 1in the Coulter Delsa 440 cell and (+) suspension 1 in the parallel plate cell; b, ( 0 )suspension 2 measured in the parallel plate cell and (0) suspension 3 measured in the Coulter Delsa 440 cell.
charge can also flocculate, but as they do, the charge per floc builds. In aqueous systems the charge equilibrates with the medium to maintain a constant zeta potential (i-e., zeta potential is approximately independent of particle size). In low conductivity media the accumulated charge does not re-equilibrate quickly. The charge per floc will grow linearly (tofiist order) with the accumulation of particles. The Stokes drag will increase depending on the floc structure, but nevertheless a t a rate less than linear. Therefore flocculation leads to an increase in electrophoretic mobility with time. The net result is that with time the only particles remaining in the sensing zone are those particles with high electric charge or those flocs that have accumulated high electric charge. This is exactly what was observed (see Figure 3). We do not know why the charge for this carbon black always appears to grow more negative with flocculation. In the Delsa 440, the top stationary layer is 160 pm from the top edge of the cell. In the parallel plate cell, the sensing zone is 2 cm from the top of the liquid. Figure 4a shows the variation in electrophoretic mobility with time after filling the two cells with the same carbon in dodecane suspension a t the same time; Figure 4b shows a similar comparison for other carbon suspensions. These data are typical. We have seen similar behavior in 20 other experiments. The magnitude of changes in mobility are different between the two pieces of equipment, but the trends are the same. In the Delsa 440, the charge on the particles appears to build up faster (we were sensing only the better stabilized particles with time) than the parallel plate cell where sedimentation takes longer to eliminate less charged particles. The rate of change in mobility diminishes with time. This happens more quickly in the Delsa cell, than in the larger Xerox cell. The two instruments show the particle mobility approaching the same limit a t long times. Ultimately we see a stable suspension consisting of small particles or flocs which will not settle and which are charged enough to prevent further growth in size.
10
20 30 Time (minutes)
40
50
60
Figure 5. Particle size versus time for an unstable suspension of carbon black in dodecane as measured by a Brookhaven BI2030AT QELS instrument. The particle diameter of a stable suspension is 150-300 nm.
The magnitudes of the two phenomena, flocculation and sedimentation, and their relative effects in the two cells can be estimated. We can calculate two characteristic functions, the time it takes for each particle to collide with one other particle, to flocculate, and hence increase their rate of sedimentation, and the time it takes for particles or flocs to settle out of the sensing zone. The simple theory of F u ~ h can s ~ be ~ used to calculate the rate of particle flocculation assuming only binary collisions occur, the particles are uniform in size, and they diffuse through the liquid as individual particles with a laminar flow of liquid around them. The time for half of the particles to collide with the other half is t1,2 = 3qW/(4kTIV) = *d3p,qW/(8kTp,9)
(1)
where 7 is the viscosity of the liquid, k is Boltzmann’s constant, Tis the temperature, Nis the number of particles per unit volume, d is diameter, PI is the liquid density, ps is the particle density, 9 is the weight fraction, and W is the stability coefficient (which depends on the interparticle forces). Equation 1was used to calculate tip, the half-life, for wt fraction carbon in dodecane) used suspensions (3 X in these electrophoretic mobility measurements. In this calculation, the stability constant is taken to be unity. It is assumed that all collisions result in flocculation. For these systems the half-life (in minutes) can be expressed as a function of particle diameter, d (in micrometers) t1,2 = 200d3
Figure 5 shows the growth in particle size with time for this cledhed carbon black suspended in dodecane while in a QELS cell. The particle size doubles in volume in about 25 min which is about 30 times slower than predicted by eq 2 for the rate of flocculation of unstable particles. This is consistent with the hypothesis that even these particles are slightly charged initially slowing their rate of flocculation. If the particles are initially slightly charged, the electrophoretic mobility should increase with time as charged particles flocculate. The two types of experimental data, electrophoretic mobilities and particle sizes, (43) Reference 41, p 257.
Kornbrekke et al.
1216 Langmuir, Vol. 8, No. 4, 1992
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Figure 6. Calculated curves depicting flocculation half-life (--) and settling of an unstable suspension of carbon black in the Coulter and the parallel plate (- - -) cells. The vertically shaded region corresponds to a time and particle size range during which measurements could be made in the parallel plate cell. The hatched region corresponds to the useful range of the Delsa 440 cell. (-a)
are consistent with the model of slightly charged particles flocculating to larger, more charged flocs. If the fluid maintains a laminar flow around the particles as they settle, and the particles can be approximated as isolated spheres, the Stokes equation can be used to calculate the settling rate V
Figure 7. Change in electrophoretic mobility as measured in the Delsa 440 as a function of time from the filling of the cell for clean carbon in a 1 wt % OLOA 1200 solution (A)and a 0.001 wt. % OLOA 1200 solution (+). The suspension had equilibrated 24 h before the measurements.
7n C
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I
00001
where g is the acceleration due to gravity and the other terms are the same as in eq 1. By use of constants appropriate for our system the time, t (minutes),for carbon particles (diameter in micrometers) to cross the position where particle velocities are measured in the two cells (Figure 2) can be calculated t = 5.4/d2 (Delsa 440 cell, upper stationary plane)
t = 676/d2 (parallel plate cell)
(4) (5)
Brownian diffusion can retard the settling rate for small particles. The mean distance traveled varies as the square root of time and inversely with size. For small particles and short times this distance is much greater than the movement due to sedimentation. However, for the time scales over which we take data, sedimentation is more significant than Brownian diffusion. Figure 6 is a plot of the characteristic sedimentation and flocculation times as a function of particle size for carbon black in dodecane suspensions for the concentration of suspensions we tested for both the DELSA 440 and the parallel plate cells. The area under the intersection of the flocculation curve with the sedimentation curve represents the time/particle size regime in which a measurement can be made in each cell for unstabilized suspensions* Times outside this regime correspond either to significant sedimentation or significant flocculation. A notable observation is that after just a few minutes no uncharged particles can remain in the sensing zone of the Delsa 440 cell (or any other cell with a short distance from the top of the cell to the sensing zone). The sensing zone in the parallel plate cell is farther from the liquid surface; hence even slightly charged floccs are present for longer times. The important conclusion is as follows: after a short time the only particles in the sensing volume are the charged particles, all others are lost to flocculation and sedimen-
0 001
0 01
01
1
Concentration (wt YO)
Figure 8. Zeta potential versus concentration of OLOA 1200 for suspensions of carbon black in dodecane measured in the (+) parallel plate cell and the (A)Coulter Delsa 440 cell.
tation. Even a suspension with an average electrophoretic mobility (or zeta potential) nearly zero will appear to be charged after a short time simply because all the uncharged particles are gone. Therefore a claim that the particles in a nonaqueous suspension are highly charged based on mobility measurements taken after a long time after the field was applied is suspect.ll A minimum requirement to make such a claim appears to be that the mobility remain constant with time or that the data can be extrapolated to zero time. Changes in electrophoretic mobility with time depend upon the characteristics of the suspension, the shape and position of the electrophoretic mobility distribution, the particle size distribution, and the particle concentration. The details are quite complex but the general conclusion is the same: when suspensions are measured in nonaqueous media, just because the measured electrophoretic mobility is large after some time does not mean necessarily that the individual particles are significantly charged. Our goal is to understand the mechanisms by which soluble compounds charge particles in nonaqueous media. We need a particle suspension where the particles have no net charge before any agents are added, and we need a procedure to measure the charge on particles even when the particles have very little charge. We propose to use electrophoresis with the proper cell design as described above as well as the procedure of measuring zeta potential versus time and extrapolating to zero time to be the measure of the charge on individual particles. Figure 7 shows this extrapolation procedure for two typical suspensions. OLOA 1200 from Chevron is a typical lubricating oil dispersant. It is a poly(isobuty1enesuccinimide) with a
Electrophoretic Mobilities of Particles number average molecular weight of about 1700. With such a large molecular weight it is reasonable to assume that it stabilizessoot in oil Suspensionssterically. However, Fowkes et al.1OJ1,4'Jla have reported that this basic solute charges carbon black particles sufficiently negative to account for ita dispersing ability by electrostatic forces alone or a t least that electrostatics play a significant role. Our results on the effect of the addition of OLOA 1200 to the cleaned carbon black in dodecane are shown in Figure 8. The agreement between data taken in the two devices is not as good as we would like. Nevertheless these results confirm the conclusion of the earlier work that the basic OLOA 1200 charges carbon black negatively. However, we find the magnitude of the charge to be substantially less. The previous work was done in a manner which we now find suspect. Long time intervals were used before data were taken." During this time any particles with low charge would have flocculated and formed more highly charged flocs. It is also possible, however, that the carbon previously used had stronger acid sites or more of them than the carbon we used. The carbon we used had relatively weak acid sites.21 The acid/base characteristics of the carbon used in previous studies were not described. In that earlier work the authors cleaned the OLOA 1200 by adsorption on silica. We used it as received. ~~
(44) Pugh, R. J.; Matsunaga, T.;Fowkes,F. M. Colloids Surf. 1983,7,
183.
Langmuir, Vol. 8, No. 4, 1992 1217
Conclusions Electrophoretic measurements in low conductivity media require particular attention to how the electric field is created. Simple parallel plate electrodes can be used because the field is uniform and none of the problems for high conductivity liquids, such as joule heating, will occur. If the more standard microelectrophoresis cells are used, they cannot be surrounded by water jackets as the water jacket provides a direct path to ground, distorting the electric field in the cell for some time. The practice of waiting long times before taking data in nonaqueous leads to serious errors as any particles with little or no charge flocculate and settle out of the sensing zone. The time scale over which data can be taken is a function of the cell dimensions and can be estimated from sedimentation velocities and rates of rapid flocculation. The preferred procedure is to take data as quickly as possible after filling the cell and to measure mobility as a function of time in the cell. When the sensing depth is short, the determination of the initial value of the electrophoretic mobility (by extrapolation) may be very difficult for unstable suspensions, so cells with great sensing depths are preferable. Solvent-washed carbon blacks are uncharged (or very slightly negatively charged) in dodecane. The basic additive OLOA 1200 charges the cleaned carbon in dodecane negatively, although not so much as previously reported. Registry No. OLOA 1200,51004-97-8; dodecane, 112-40-3.
