Langmuir 1991, 7, 2841-2852
2847
A Method To Measure the Average Charge to Mass Ratio of Particles in Low-Conductivity Media I. D. Morrison,* A. G. Thomas, and C. J. Tarnawskyj Webster Research Center, Xerox Corporation, Webster, New York 14580 Received December 7,1990. I n Final Form: June 12, 1991 The average charge to mass ratio of suspended particles is an electrical characteristic which can be related to surface charge density or f potential. A new method to measure the average charge per unit mass of particles dispersed in low-conductivity media is proposed. The method depends on the ability of a flow of an insulating liquid to separate the electric double layers from around charged particles held stationary on a porous support. The counterchargesare collected in a Faraday cup and the total is charge measured. The charge on the particles is equal to but opposite in sign to the collected charge. The average charge to mass ratio of the particles is the ratio of the total particle charge to the mass of particles. When a sample of dispersion with a known mass of particles is used, the only measured quantity is the charge collected in the Faraday cup. The reasonableness of the method is demonstrated with carbon black particles suspended in dodecane and charged with various concentrations of Chevron's OLOA 1200. Introduction The cause of a number of explosions and fires in the petroleum processing industry has been traced to static electric buildup.' This buildup of electric potential is not the usual one associated with the rubbing of two different materials (as in triboelectrification) but rather is due to the motion of nonconducting liquids through pipes and pumps. The source of the electric buildup has been traced to the separation of charges contained in the liquid from their countercharges on the metal walls of the pipes and pumps. The charge exchange between a metal wall and an insulating container depends on the presence of stabilizing structures (micelles) in the fluid. In most petroleum products, these abound. Emulsified water droplets also serve as structures in which charge can be stabilized. When the fluid is pumped rapidly from one container into another, the two sets of charges can be separated. This charge separation builds an electric field which can discharge with a spark. (Solutions to this problem have been threefold: first, to be careful about keeping all pipes, pumps, and containers grounded; second, to add more conducting species to the petroleum to bleed off the electric field; and third, to work in an oxygen-free environment and ignore the sparking.) Figure 1shows an. apparatus designed to measure the charging tendency of oil. The countercharges in the oil are separated from the charged metal surfaces by the flow of oil and collected in the Faraday cup. Xerographic developers are mixtures of pigmented plastic toner particles and large metallic carrier beads. The charge to mass ratio of the toner particles is important in imaging. A common method to measure the charge on the toner particles is to put the developer inside a porous Faraday cage and blow off the small toner particles with a stream of air.2 The charge remaining on the trapped carrier beads is measured. The ratio of the negative of the measured charge to the mass of toner blown off is the average charge per unit mass of the toner particles. These ideas suggest a method to measure the charge on particles dispersed in insulating fluids. If the particles (1) Klinkenberg, A.; van der Minne, J. L. Electrostatics in the Petroleum Industry. The Prevention of Explosion Hazards; Elsevier: New York, 1958. Apparatus to measure the charging tendency of oils is described on pp 49-51. (2) Schein, L. B. Electrophotography and Development Physics; Springer-Verlag: New York, 1988; pp 79-82.
0743-7463191/ 2407-2841$02.50/0
Faraday cup
1
i
t.....-,
X S Y
%--Electrometer
Figure 1. Apparatus to measure the charging tendency of oils.' The oil to be tested drains from a grounded metal container into a Faraday cup. The charges carried by the draining oil collect in the isolated Faraday cup. The electric potential produced on the Faraday cup as the oil drainsthrough the orifice is measured. The current or the charge transferred could also be meaeured. The greater the measured potential, the more dangerous the oil is to handle.
and the countercharges can be physically separated, then a measurement of the totalseparated charge and the mass of particles in the dispersion originally will give the charge per unit mass (or charge per particle if the particle size is known). The technique is to hold the particles on a porous support and wash them with a flow of liquid (See Figure 2). A sample of the dispersion is put on a filter with a pore size sufficient to hold the dispersed particles but not sufficient to inhibit a rapid flow of liquid. As an insulating liquid is forced through the dispersion, the charged particles remain on the filter while the countercharges are carried away, collected, and measured. Charged particles adhere to insulator surfaces quite readily so that the filter pore size can actually be greater than the diameter of the particles. The number of countercharges carried away is measured with an electrometer. Once all the countercharges are removed by the flow of solvent, the total charge on the particles is known; the two 0 1991 American Chemical Society
Morrison et al.
2848 Langmuir, Vol. 7,No. 11, 1991
Filter Increarlng flow remow8 more charge. -4
c
I
Q
\
Electrometer
I
Figure 2. Apparatus for measuring the average charge to mass ratio of particles in nonaqueous dispersions. Solvent is pumped onto the top of a filter upon which has been placed a small sample of the dispersion. The charged particles from the dispersion are held on the filter. The flow of solvent carries the counterions into a Faraday cup, where the charge collected is measured by an electrometer.
1.5
t
i
i
Current Tnnrlent
All charge removed.
u -
-10
2
0
4
8
8
Flow Rate (gm/rec)
Figure 4. Charge separated from 10p L of carbon black dispersion dodecane flow rate. The dispersion is 2 vol % Sterling R in dodecane with 16 wt 7% OLOA 1200/carbonblack. Increasing the flow rate removes more charge until the flow rate is sufficient to remove all the charge (-3 g/s).
as a function of
0
Chargo nlnovrd (ooui x EO) I
Charge removed I6 proportlonal to rample rlze.
0.4
0.8
Time
(8.0)
2.4
2.8
Figure 3. Typical current transient from the apparatus shown in Figure2. The particles are negatively charged; hence the peak is negative. The scales are 5.0 X 10-8A/division and 0.4 s/division. The area under the curve is -3.20 X 10” C. quantities are equal but opposite in sign. The mass of the suspended particles is known or is easy to measure. All the excess ions in the dispersion come in electrically neutral pairs so they do not contribute to the net charge measured.
Theory The question is whether a reasonable liquid flow rate will be sufficient to separate all the counterions from charged particles held stationary on a porous support. We calculate the liquid velocity necessary to separate charges for two processes. The first is the fluid velocity necessary to remove a single countercharge from a position close to the particle surface. This velocity, eq 9, depends on the size, charge, and position of the counterion, the viscosity of the liquid, and the surface potential of the particle. The second calculation is the velocity necessary to remove all the counterions as a group from all of the particles as a group. This velocity, eq 14, depends on the amount of sample, the area over which it is spread on a porous support, and the electrophoretic mobility of the particles. The success of this technique will depend on attaining a sufficient liquid flow past a sufficiently small sample distributed over a sufficiently large area. The electric potential, 9,at a distance r from the center of a sphere with surface potential O,, of radius a is given
No more charge la removed.
~
I
-60 0
20
40
BO
80
100
120
Sample rim (mlcrollterr)
Figure 5. Charge separated with a constant flow rate of 5 g/s as a function of sample size. The dispersion is the same as in Figure 4. The charge removed is proportional to sample size (constant Q/M) until the sample size is too large for this flow rate to remove more charge.
approximately by3 O = u$,/r exp[-K(r
where the decay constant,
K,
- a)]
(1)
is4 .
e is the electronic charge, N A Avogadro’s number, I the ionic strength of the medium, D the dielectric constant, eo the permittivity of free space, k the Boltzmann constant, and T the absolute temperature. The hydrocarbon dispersions described below have conductivities on the order of 100 pS/cm (See Figure 6). Typical aqueous dispersions have conductivities 1Oe-1Oetimes greater. Even (3) Roee, S.;Morrieon, 1. D. Colloidal S y s t e m and Interfaces;WileyIntarscience: New York, 1988; p 234. (4) Hiemenz, P. C. Principles of Colloid and Surface Chemistry;Marcel Dekker: New York, 1977; p 369.
Langmuir, Vol. 7, No. 11, 1991 2849
Particle Charge t o Mass Ratio in Low-Conductivity Media 0 S 7 1 l O6 1
condwtlvlty
V,
,* 0
6
10
Po
16
, PI
-ao SO
S6
wts OLOAl Cubon
M/om
*
nlomooullen
Figure 6. Average charge to mass ratio and conductivity of a series of 2 vol % SterlingR dispersionsin dodecane as a function of added OLOA 1200. The conductivity is in picosiemens per centimeter and the charge to mass in microcoulombs per gram.
with dielectric constants -40 times less and ionic mobilities l order of magnitude or so smaller than in water, the decay constants, K , in these hydrocarbon dispersions are nevertheless orders of magnitude smaller than in water. The Debye lengths, 1/K, are orders of magnitude larger. The force, F,, on a counterion of charge, Q, is the charge times the derivative of the potential (eq 1)
F, = (-aQ$o/r)(l/r
+ K ) exp[-r(r - a)]
(3) The viscous force, F,, due to a moving fluid on a counterion of radius 8 is given approximately by Stokes' law
F, = 6sSvq (4) where v is the fluid velocity and q the viscosity. Equating the two forces, eqs 3 and 4, and solvingfor the fluid velocity gives u = (-aQJ1,/6s@qr)(l/r + K ) exp[-n(r - a ) ] (5) as the velocity above which the counterion will be moved away from the charged surface. Note that Q and 9,are opposite in sign. The counterions nearest the particle surface will be most difficult to remove. Evaluating eq 5 at r s a and assuming the Debye length is much greater than the particle radius, 1/K >> r, gives v =-Q$o/64v (6) The velocity field around a sphere is a function of the polar angle (defined with respect to the direction of the incoming fluid) and radial distance. The fluid velocity away from the sphere along the axis of symmetry is given approximately by5 v = vO(l- a3/r3) (7) at low Reynolds numbers where uo is the incoming fluid velocity. For positions within 6a of the particle surface, eq 7 can be approximated by v 3v06a/a (8) Substituting eq 8 into eq 6 gives an expression for the fluid velocity needed to remove a counterion a distance 6a from the surface: ( 5 ) Prandtl, L.; Tietjene, 0. G. Fundamentals of Hydro- and Aeromechanics; Dover: New Yolk, 1957; pp 149-152.
= -Q$,/ 18~8qba
(9)
Interestingly, eq 9 shows that the necessary velocity to sweep countercharges from the surfaces of charged particles does not depend on the particle size or surface area, but only on the surface potential. Some approximate values can be substituted into eq 9 to obtain an estimate of the fluid velocity necessary to separate a counterion from near the surface of a charged particle. For example, if the countercharge is an inverse micelle with a radius (8) of 50 X 10-lo m, with a single charge (Q = 1.6 x 10-19 C), and is within one micelle diameter, 6a = 28, of a particle with a surface potential (q0)of 50 mV, a liquid with a viscosity ( q ) of 1 mPa.s and a velocity (v,) of 0.3 cm/s will remove the countercharge. This flow rate is obviously easy to attain experimentally with particles held on a filter surface and liquid pumped through the filter. Countercharges further from the surface are removed with even lower fluid velocities. Once the countercharges are removed from near the particle surfaces, the rest of the separation can be modeled as the separation of the plates of a charged capacitor. The force separating the charges is the viscous drag of the washing solvent. The force drawing the countercharges back to the particles is electrophoretic. The sample size, charge per unit mass, and the extent to which the sample is spread over the filter surface determines the electric field. What needs to be calculated is the fluid velocity away from the particles just sufficient to be greater than the electrophoretic motion of the counterions back toward the particles. Any fluid flow greater than this will separate the countercharges from the particles; any fluid flow less than this will not be sufficient to separate completely the two sets of charges. The field outside a surface containing q/A charges per unit area is
E = q/DtoA
(10)
where q is the total charge on the particles and A is the area the dispersion occupies on the filter surface. The amount of charge on the filter is the total charge on all the particles (since all the counterions are assumed to have been removed) q = VdF(Q/M) (11) where Vis the volume of the liquid sample, d is the density of the dispersion, F is the mass fraction of particles, and Q/M is the charge to mass ratio of the particles. Substituting eq 11 into eq 10 gives the electric field in terms of known quantities and the charge to mass ratio
E = VdF(Q/M/Dt,A
(12)
The velocity of the backflow of countercharges, vr, caused by the electric field, is the mobility of the countercharges times the electric field
v, = @E
(13)
Substituting eq 12 into eq 13 gives the minimum fluid velocity that will just balance the backflow due to electrophoresis: u, = VF(Q/M)d/DE,A
(14)
The equation shows that the necessary fluid velocity depends linearly on the sample size (V)and inversely on the area over which the dispersion is spread on the filter surface (A). Any flow greater than this will separate the countercharges from the particles.
Morrison et al.
2850 Langmuir, Vol. 7, No. 11, 1991
The flow necessary to separate the countercharges from the particles depends on the total number of charges on the particles but not on the total number of ions in solution. The ions in solution above and beyond those that correspond to the charges on the particles come in electrically neutral sets. No work is required to separate them from the particles. Since the separation is independent of the total number of ions in solution, it is also independent of the ionic strength and hence the doublelayer thickness as long as the ionic strength is low. Some approximate values can be substituted into eq 14 to obtain an estimate of the fluid velocity necessary to separate countercharges from the particles as a function of sample size. For example, consider a hydrocarbon of 2, a density ( d ) dispersion with a dielectric constant (D) of 1 g/cm3, with a particle weight fraction (F)of 0.01, counterion mobility (p) of 10" cm2V-ls-l, and a particle charge to mass ratio (Q/Wof 100 pC/g, covering an area ( A ) of 0.5 cm2 (10% of a typical filter surface area). Substituting these values into eq 14 gives the minimum necessary fluid velocity (in cm/s) as u, = O.l(cm/s.pL)V (15) where Vis the sample volume in microliters. Equation 15 shows that for a sample volume of a few microliters, the fluid velocity only has to be greater than a few centimeters per second for the countercharges to be carried free of the particles. This condition is easy to meet experimentally. The fluid flow necessary to separate counterions from the surface of a particle, eq 9, and to separate all the counterions in a few microliters of dispersion spread on a filter surface, eq 14,is about the same, a few centimeters per second. An assumption in this method is that a flow of liquid can be made sufficiently fast around a particle to remove the countercharges but not so fast so as to remove adsorbed charged surface-active solutes. It is possible that examples can be found where the method fails because the double layer is too compressed to be removed (particularly at higher ionic strengths) or the surface charges are too labile and are removed by the flowing liquid. The test will be whether the results are consistent with other measurements. However, even inconsistencies may provide information about the nature of the adsorbed charges.6
Experimental Section Figure 2 shows a schematic of the apparatus set up in our laboratory to test this new method. Reagent grade solvent is pumped from its bottle through S/le-in.-i.d. Teflon tubing by a FMI Lab pump, Model RP-D, with a Type RP-11 head. This pump was selected becausethe solvent does not contact any metal parts and the solvent is always kept insulated from ground. The sample is pipeted onto the filter surface with an Eppendorf, disposable tip, microliter pipet, being careful not to place any of the sample on the filter walls. The filter tip is rinsed several times with the dispersion to be tested before the actual sample is pipeted. A Teflon tube from the pump carries solvent to the top of the filter housing through a Kel-F Luer-lockadapter from Anspec. This connection is adequate for preliminary work but a high-pressure connector will be necessary for flows at higher pump speeds. We have also set up the experiment using a tank of compressed nitrogen to force solvent flow. This has the advantage of a smoother flow of liquid (The data taken with the pump show the pulsing of the pump.), but using compressed gas makes it more difficult to repeat experiments at the same flow rate. The simple connections described here will withstand up to about 20-30 lbs/in.2 (0.14-0.2 MPa). (6) Morrison, I. D.;Tarnawskyj,C. J. Presented at the 6th International Congress on Advances in Non-impact Printing, SPSE, Orlando, FL, October 23, 1990, submitted for publication in Langmuir.
We measure the mass of solvent collected per unit time. The flow of liquid past the particles and through the filter could be turbulent so we do not know the actual magnitude of liquid velocity sweeping counterchargesfrom the vicinity of the particles. To a first approximation,the velocity is the mass flow rate divided by fluid density and the cross-sectionalarea of the filter. When dodecane is pumped across a 25-mm-diameter filter surface at 1.0 g/s, the approximate linear velocity is 0.3 cm/s. Equation 15 can be rewritten in turns of a mass flow rate, m, (in g/s), as m, = 0.3(g/s.pL)'b
(16)
where the sample volume is still in microliters. We report the experimentally measured quantity, mass per unit time, as the measure of the fluid velocity. The data shown in Figures 4-6 were taken with 25-mmdiameter, 5-pm pore size, disposable filters (AcrodiscNo. 4199 from Gelman Sciences). This filter is described as a supported acrylic copolymer in a modified acrylic housing. A more complete description of filter selection will be given in the next section. Whenever we use filters held in a housing, we use either the polypropylene Swinnex holders from Millipore or the polycarbonate Swin-Lok holders from Nuclepore. We avoided the use of metal components in the apparatus other than the brass collection cup. Any shielded, conducting, isolated container can be used to collect the effluent. We use a brass beaker, 7.2 cm in diameter and 5.0 cm in depth covered with aluminum foil through which is punched a 1-cm hole. The brass beaker sits on a l/d-in. Teflon plate to isolate it from the top-loading balance used to measure the mass of solvent being pumped. The charge collected in the brass cup is drained to ground through a Keithley 617 programmable electrometer running in either the charge mode (low charges)or the current mode (highercharges). The analog output from the electrometer is sent to a Nicolet 4094A digital oscilloscope sampling at 200 ps/point. The Nicolet Math Pak is used to take averagesfor background readings and to integrate current transients to get totalcharge. Data are stored on disc and output to an IBM 7372 color plotter. The mass is known from the sample size and the percent solids. Occasionally the filter itself can be charged with surface-active solutes from the dispersion and so an erroneously large charge could be ascribed to the particles in the dispersion. To check for this, a portion of the dispersion is centrifuged to obtain a clear supernatant. The sample of the supernatant is put on the filter and washed with solvent. If the number of charges generated by surface-active solutes on the filter is significant, then the charge on the sample is taken to be the differencebetween that measured for the same quantity of dispersion and serum. Different sample sizes and flow rates are checked to make sure that the sample size is sufficiently small and the flow rate sufficiently high that the number of countercharges per unit mass swept away is constant. No good model system has been suggested in the literature for which the charge per particle is well established. Fowkes et al. have reported in a series of papers the charging of Sterling NS carbon black by solutions of Chevron Chemicals' OLOA 1200 (a poly(isobuty1enesuccinimide))in saturated hydrocarbons.7.8They cleaned their carbon black by Sohxlet extraction. We have examined both cleaned and as-receivedcarbon blackseand have not seen a large difference. Therefore, to demonstrate the use of this new method we use carbon black, Sterling R from Cabot Corp., without cleaning. We also used the OLOA 1200asreceived. The concentrations reported here are for the commercialproduct and are not corrected for percent actives. The dodecane was reagent grade from both Fisher and Aldrich. All the dispersions were 2 vol % carbon/dodecane and were made by shaking the (7) Fowkes, F. M.; Jinnai, H.; Mostafa, M. A.; Anderson, F. W.; Moore, R. J. In Colloids and Surfaces in Reprographic Technology; Hair, M., Croucher, M. C., Eds.; ACS Symposium Series 200, American Chemical Society: Washington, DC, 1982; pp 307-324. (8)Fowkes, F. M.; Pugh, R. J. In Polymer Adsorption and Dispersion Stabrlrty; Goddard,E. D., Vincent, B., Eds.; ACS Symposium Series 240; American Chemical Society: Washington, DC, 1984; pp 331-354. (9) Kombrekke,R. E.;Morrison,I.D.;Oja,T.,submittedforpublication in Langmuir.
Particle Charge to Mass Ratio in Low-Conductivity Media
Table I. Snurious Charge Washed from Filters pore charge size, removed, filter material pm C/(g X 10") Metrice' cellulose triacetate 1.2 1.0 (in a Swinnex holder) Acrodisc" acrylic copolymer 1.2 1.1 Fisher Teflon PTFE 1.0 -1.7 AcroDisc CRa PTFE 1.0 2.5 Nuclepore polycarbonate 1.0 -2.8 _
a
_
_
_
_
_
~
~
~
~
~
Manufactured by Gelman Sciences.
carbon black in solutions of OLOA 1200 in dodecane overnight. Each data point reported is an average of five measurements. The only troublesome observation was that the pipet tips often were coated with a noticeable amount of carbon black. We have assumed that by rinsing the tip several times with the dispersion this effect is negligible.
Composition of Filter The purpose of the filter is to retain the particles as the counterions are swept away by the flow of solvent. Physically the filter must have small enough pores (or effective pore diameters) to retain the particles. Chemically the filter must neither adsorb charges from the flowing liquid nor desorb charges into the flowing liquid. The requirement of small pores is easy to meet practically. The pore size can be larger than the particle size since charged particles adsorb onto insulator surfaces readily. The dispersions we test most frequently have particle diameters on the order of 1pm and we use filters with pore diameters up to 5 pm. Essentially all the particles are retained even with the pore 5 times larger in diameter than the particles. Smaller pore sizes reduce the risk of having particles swept away, but the smaller the pore size, the higher the solvent pressure need be to attain adequate flow rates. The filter material must not produce charge when washed by the solvent. Table I gives the average charge removed per gram of dodecane washed through the filter for several types of filters. Some filters charge positive, some negative. The sign convention is that the sign of the charge reported is the same as the sign of the charge of the filter itself. The data presented in Figures 3-6 were obtained with 15 g of solvent wash across the Acrodisc filter. The spurious charge generated by this solvent flow amounts to 1.5 X 10-loC. For samples larger than 1pL, this is negligible. We eliminate this error for the smaller sample sizes by using the current after the transient as a base line. The filter material must not adsorb species from the dispersion and acquire a surface charge itself. This is checked by rinsing the filter with both solvent and supernatant and seeing if there is any difference. The filters did not charge with solutions of OLOA 1200 used here.
-
-
Composition of Carrier Fluid The measurement of charge by this method requires separating charged particles from their countercharges without changing the nature of the charges or particles. Ideally the particles could be washed with a solution of the same composition as the supernatant. As the volume of fluid used (usually 10-25 mL) is fairly large, at least compared to the sample sizes of a few microliters, this is inconvenient; rather, the sample is washed with solvent. This switch raises the possibility of changing the nature of adsorption on the particle surfaces. All of the data presented here have been taken using pure solvent as the
Langmuir, Vol. 7, No. 11, 1991 2851
washing fluid and hence the assumption is that the solvent does not wash off charges. This assumption seems to be acceptable. Three reasons may be suggested: First, charged particles are held strongly to the surfaces and are difficult to remove. Ions, being much smaller, are even more tightly bound to surfaces and would not be expected to be removed by viscous flow. Furthermore, the velocity of the liquid flow decreases to zero near the particle surfaces. Second, the time scale of the washing is short (on the order of a few seconds) and desorption processes are slow. We have some evidence from measurements of electrophoretic mobilities that the charges can be eliminated from the surface of the particles by sufficient solvent, but the time scale seems to be several hours or longer. Third, Figure 1shows the apparatus to measure the charging tendency of oils. If adsorbed charge were washed off, no net charge would be measured in this standard test. Effect of Liquid Flow Rate The model behind this method is one of establishing a sufficient liquid flow rate past stationary particles that the countercharges are swept away like the separation of the plates of a capacitor. The liquid flow rate has to be greater than the backward electrophoretic drift of the countercharges. If the flow rate is too low, then the countercharges cannot be completely separated. What this model predicts, then, is that the amount of charge separated should be small at low flow rate and increase as the flow rate is increased. At fast flow rates the charge separated should be a constant. Figure 4 shows the charge separated from constant-size samples (10 pL) as a function of the liquid flow rate. As the flow rate is increased from zero, the amount of charge separated increases. After the flow rate exceeds some criticalvalue (here, -3g/s), theamountof chargeremoved remains constant with increasing flow rate. This is consistent with the scaling law (eq 14). The average charge of 10 p L of this dispersion, 16 wt 5% OLOA 1200/carbon black, is taken from the asymptote and is --8 X lo4 C. Effect of Sample Size The scaling law (eq 14) also shows that the minimum fluid velocity to separate the countercharges from the particles scales with the sample size. If the fluid flow is fixed, then for all samples below a critical size a given fluid velocity is capable of removing all the countercharges. Above a critical size, this fluid flow is insufficient to remove all of the countercharges. Figure 5 shows the charge removed as a function of sample size at constant fluid flow (-5g/s). In the initial linear region, the amount of charge removed is proportional to sample size; hence the average charge to mass ratio is constant. This dispersion is the same as the one used for Figure 4 and these data also show C for a 10-pL sample the dispersion to have --8 X size. Above the critical sample size (here, -60 pL) no more charge is removed even as the sample size is increased. This is exactly what the simple scaling theory predicts. Results Particles in hydrocarbon dispersions are usually charged by the addition of a surface-active solute. At low concentrations most of the agent is adsorbed and the particles have no charge.' A t low volume loadings, the dispersion is not conductive. Beyond some critical quantity of added solute, the particles acquire a charge and the conductivity of the dispersion increases. The acquired charge can be measured both by electrophoresis and by this new method.
Morrison et al.
2852 Langmuir, Vol. 7, No. 11,1991
As the level of charging agent is raised, the particle charge approaches a limit. These phenomena are demonstrated with a series of Sterling R carbon black dispersion in dodecane with OLOA 1200 as the charging agent. Figure 6 shows the conductivity and charge to mass ratio of these dispersions as a function of OLOA 1200/ carbon black ratios. The average charge to mass ratios were measured with this new method. The conductivities were measured with a Model 627 conductivity meter from Scientifica. The data show what is expected. Below -12% by weight OLOA 1200/carbon black, the particles have no (or little) charge; the dispersion has no (or little) con' carbon/dodecane dispersions ductivity. These 2 vol % are too dilute to show the high conductivity at low charging levels due to particle bridging as reported by Fowkes et al. Above this critical concentration of charging agent, the average charge to mass ratio increases (particles have a negative charge) and the conductivity of the dispersion increases. A more detailed comparison of the results of this method and those obtained by electrokinetics is being prepared. Limitations of t h e Method A limitation of the method as now practiced is that the particles are washed with pure solvent and not with supernatant. This change in environment around the particle might lead to some change in chemistry. So far we have seen no indication of this (e.g., by measuring no charge for a dispersion that behaves in other experiments as if it were charged), but we have no proof. This limitation can certainly be eliminated by separating particle-free serum from a quantity of the dispersion and using it as the wash fluid. A second limitation of the technique is that it gives only one data point, the average charge per unit mass. If the dispersion contains particles with a distribution of charges, this cannot be determined. If the dispersion contains particles of different sign, the measured charge will be the algebraic sum. The measurement is essentially a zero-
field measurement. In a subsequent publication we compare the results of this method with other methods of measuring the charge on particles which do use electric
field^.^^^ A third limitation is in the method of measuring sample size. We work with samples of a few microliters. this is the lower limit at which liquids can conveniently be measured. This is a source of experimental error. An apparatus constructed for higher pressures would allow the use of higher flow rates and hence larger samples. Summary Charged particles are surrounded by counterions in a diffuse electrical double layer. When the ionic strength is low, this electrical layer is highly extended and the countercharges can be separated from the particles easily. If the particles are held stationary on a filter, the countercharges can be separated with a flow of solvent. If the solvent flow is sufficiently fast, then all of the countercharges can be separated from the particles, collected, and measured. The total charge on the particles is the negative of the total charge of the collected counterions. Knowing the mass of particles left on the filter gives the charge per unit mass of the particles. The details of a simple apparatus and the experimental procedure to make the measurement have been given. The method does not suffer from electrode polarization problems or space charge effects, which are common to the usual methods for measuring charge in low-conductivity media. The method is less influenced by excess charges in the fluid, since they must be present in electrostatically equivalent pairs and do not contribute to the total charge collected. The method is limited by charging of the filter surface by soluble components in the dispersion or by dissolution of components from the filter and by the need to have pores small enough to trap dispersed particles but large enough to permit a significant flow of liquid. The method has been shown to scale with sample size and flow rate as predicted by a simple theory.
