Mechanistic Study of Electrical Field Flow Fractionation. 1. Nature of

Anal. Chem. 1997, 69, 3223-3229

Mechanistic Study of Electrical Field Flow Fractionation. 1. Nature of the Internal Field Saurabh A. Palkar and Mark R. Schure*

Theoretical Separation Science Laboratory, Rohm and Haas Company, 727 Norristown Road, Spring House, Pennsylvania 19477

Experimental results indicate that the electric field governing retention in the electrical field-flow fractionation (FFF) experiment is very sensitive to experimental parameters such as the flow rate and carrier conductivity. In this paper, the first of a two-part study on the mechanics of electrical FFF, we present an electrical model of the channel and characterize the dependence of many of the system parameters. Understanding the nature of the electric field in the channel is essential for using electrical FFF as a separation tool as well as a physical characterization technique where electrophoretic mobility and particle size are estimated. The electrostatic charge on the surface of colloidal particles plays a key role in colloid stability, rheological behavior, filmforming properties of suspensions, etc.1 To understand these processes in depth it is of prime importance to characterize the size, shape, and surface charge density of the colloidal particles that are used in these processes. The surface charge density is routinely determined by measuring the electrophoretic mobility and the particle size by some variation of the electrophoretic light scattering technique.2 Unfortunately, this technique does not allow for the separation of particles and collection for further chemical analysis. Recently there has been a renewed interest in the utilization of electrical field-flow fractionation (FFF) methods3,4 to fractionate colloid particles by charge and size. The renewed interest lies in a redesigned channel3,4 that makes use of solid electrodes as channel walls instead of the previously utilized membrane system.5 The latter is difficult to use and problematic in operation. Lightfoot and co-workers6,7 developed “electropolarization chromatography” (EPC), where the separation chamber consisted of a hollow fiber positioned between two planar electrodes. The performance of EPC was found to be similar to the other membrane systems that were previously explored in parallel plate channels. Adsorption at varying degrees was found to be an additional problem with the hollow fiber technique. A different channel design based on (1) Hunter, R. J. Foundations of Colloid Science; Oxford: New York, 1986; Vol. 1. (2) Hunter, R. J. Zeta Potential in Colloid Science; Academic Press: London, 1991. (3) Caldwell, K. D.; Gao, Y. S. Anal. Chem. 1993, 65, 1764-1772. (4) Caldwell, K. D.; Schimpf, M. Am. Lab. 1995, 27, 64-68. (5) Kessner, L. F.; Caldwell, K. D.; Myers, M. N.; Giddings, J. C. Anal. Chem. 1976, 48, 1834-1839. (6) Reis, J. F. G.; Lightfoot, E. N. AIChE J. 1976, 22, 779-785. (7) Chiang, A. S.; Kmiotek, E. H.; Langan, S. M.; Noble, P. T.; Reis, J. F. G.; Lightfoot. E. N. Sep. Sci. Technol. 1979, 14, 453-474. S0003-2700(97)00013-9 CCC: $14.00

© 1997 American Chemical Society

porous glass as wall material8 instead of membranes did not appear to yield improved results. Electrical FFF makes use of differences in the electrophoretic mobilities of particles to separate them. As a result, the retention of a particular particle depends on the particle size and surface charge density. If one of these two parameters is known independently, then previously derived theory3 suggests that the other parameter can be determined by measuring the retention time in the electrical FFF experiment. To operate electrical FFF in an analytical mode, where physical characteristics of the particles are to be estimated, we need to know an exact relation between various system parameters and retention times. In order to compare electrophoretic mobilities and particle sizes determined using electrical FFF with those obtained using other techniques such as electrophoretic light scattering, it is essential to understand the nature of the internal electric field and how it couples with various colloidal particles. In this paper we report our work on the characterization and mechanics of the electric field present in the electrical FFF channel. We dwell in this paper on effects that are internal to the channel and are dependent on the channel itself. In the companion paper,9 we continue to probe the retention mechanism in electrical FFF and explain the large experimentally observed dependence of retention on particle concentration. This paper is organized as follows. First, we present an electric circuit model of the channel. Then the sources of voltage drops in the channel are discussed. Next an explanation is offered as to why the electric field E is different in the channel compared with that calculated naively via ∆V/w, where ∆V is the applied potential difference across the fractionator walls and w is the channel width. The channel resistance and capacitance are characterized, and comments regarding field programming and stabilization time are given. Also discussed in this section is how current can be used to measure the field strength and why the effective field is such a strong function of carrier ionic strength. Finally, aspects of the current as a function of flow are presented from both theoretical and experimental perspectives, and regimes that dictate various limiting behaviors are presented. These results will be shown to be extremely important when considering the mechanics of stopped-flow relaxation in electrical FFF and in choosing carrier conditions where retention is predictable. EXPERIMENTAL METHODS Fractionator. The electrical FFF channel used here was obtained from Prof. Karin Caldwell at the University of Utah and (8) Davis, J. M.; Fan, F.-R.; Bard, A. J. Anal. Chem. 1987, 59, 1339-1348. (9) Palkar, S. A.; Schure, M. R. Anal. Chem. 1997, 69, 3230-3238 (following paper in this issue).

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Figure 1. Schematic of electrical FFF channel.

is described in detail in the publication by Caldwell and Gao.3 The channel consists of two graphite blocks separated by a thin Mylar spacer. The channel is 64 cm long and 2 cm wide, and the thickness of the spacer is 178 µm. These geometric dimensions are consistent with an experimentally measured void volume of 2.30 mL. The carrier solvent is deionized (DI) water without any buffer, and a peristaltic pump is used for flow. The colloidal particles exiting the channel are detected using a UV detector operating at 254 nm. Power Supply. The electric field is produced by applying a constant voltage (typically 1-2 V) across the two graphite blocks. The current is typically between 0.2 and 3.0 mA. The in-housebuilt power supply uses a BUF03 operational amplifier (Analog Devices, Norwood, MA) to provide a low-impedance voltage source for the channel. This particular amplifier can drive high capacitance loads under short circuit conditions. This is important here because high instantaneous currents can develop due to the large channel capacitance when the applied potential is changed. The use of a low-output impedance amplifier is necessary to maintain the source voltage (either dc through a voltage divider or a signal generator) independent of the channel resistance. The current drawn by the fractionator is converted to a voltage for the purpose of recording the time evolution of the current in the following way. The voltage drop across a 0.1Ω, 0.1% resistor is amplified by a differential instrumentation amplifier (Analog Devices AD625BN) with a gain of 2000. This allows a 1 mA current to drop 0.1 mV across the resistor; this voltage is then amplified to give a 0.2 V signal. The detector signal and the current signal (sampled as a voltage) are digitized at the rate of 1 data point/s with a Perkin-Elmer/Nelson 900 Series interface box (Perkin-Elmer, Norwalk, CT). The data acquisition software was written in-house and runs on a 386-based PC.

in this treatment because the breadth to width aspect ratio is large enough here to minimize edge effects.10 The electrophoretic mobility depends on the particle size, shape, and surface charge density and the ionic strength of the solution. The magnitude of µ is typically between 10-4 and 10-3 cm2 s-1 V-1 for particles in the colloidal size range.2 In electrical FFF experiments, we typically apply a potential difference of 1-2 V, and the channel width, w, is approximately 100-200 µm. Hence, a very high field strength of 50-100 V cm-1 is expected under these conditions if one naively assumes that the field is the quotient of the applied potential and the distance between electrode surfaces. The retention ratio, R, for FFF is related to the system properties by the following expression:11,12

R ) 6λ[coth(1/2λ) - 2 λ]

(2)

λ ) D/uxw

(3)

where

such that D is the particle diffusivity. The retention ratio, Rr, may be determined from measurements of the void volume, V0, and retention volume, Vr, so that

Rr ) V0/Vr

(4)

(1)

Assuming a constant fluid flow with time, the volume ratio may be replaced with elution times so that V0/Vr ) t0/tr, where t0 and tr are the void time and the retention time, respectively. For a 100 nm particle with diffusion coefficient of 4 × 10-8 2 cm s-1 and void time of 2 min, eqs 1-4 predict a retention time of ≈2 days. This, when contrasted with experimental retention times of the order of 10-30 min, suggests that the actual field inside the channel is very different from its apparent value. An explanation of this behavior can be found in electrochemistry text books where electrode processes are discussed in detail.13,14 We present one such explanation now. Circuit Model. First consider a simple case where we have two parallel plates separated by air. If we apply a potential difference across these plates, then this system acts as a parallel plate capacitor. Now we replace air by a salt solution having a certain finite ionic strength. The ions present in the solution are mobile and they move in response to the external applied field; i.e., cations migrate toward the cathode while the anions migrate toward the anode. This separation of charges results in an internal field that is equal in magnitude but opposite in direction to the external applied field. As a result, the vector sum of the electric fields is zero and particles placed in the medium will not experience a net electric field. At low potentials where Faradaic (redox) processes at the electrodes are negligible, this zero field condition appears in the

where ux is the transverse particle velocity due to the field and µ is the electrophoretic mobility of the particles.2 The coordinate system used in this and many other papers on FFF is shown in Figure 1. This figure illustrates the transverse (width) coordinate x and the axial coordinate z. The breadth coordinate y is not used

(10) Giddings, J. C.; Schure M. R. Chem. Eng. Sci. 1987, 42, 1471-1479. (11) Giddings, J. C. J. Chem. Phys. 1968, 49, 81-85. (12) Hovingh, M. E.; Thompson, E. H.; Giddings, J. C. Anal. Chem. 1970, 42, 195-203. (13) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications; Wiley: New York, 1980. (14) Bockris, J. O.; Reddy, A. K. N. Modern Electrochemistry; Plenum: New York, 1970; Vol. 1.

RESULTS AND DISCUSSION The Electric Field. It is of crucial importance to understand from a quantitative standpoint what the strength of the electric field is at all locations inside the channel and how this field couples with the particles. Because of the presence of surface charge on the colloidal particles, they attain a steady-state velocity when placed in an electric field. For dilute systems this electrophoresis of particles can be described as

ux ) µE

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Figure 3. Electric potential profile across the channel.

Figure 2. Electrical circuit representation of the electrical FFF channel without (a) and with (b) electron transfer. Note that the capacitive contributions of the electrical double layers are lumped into one circuit element.

electrical FFF channel. For this particular case, the electrode system can be represented by two capacitors, corresponding to two double layers at the plates, and a pure resistance, due to the conductivity of the carrier solution, in series. This is shown in Figure 2a. Thus, if the fluid medium contains mobile ions, there is a balance between the external applied field and the internal ion distribution resulting in a zero net electric field internal to the channel. There are, however, local electric fields near the double layers at the wall surface due to concentration gradients. This is similar to what happens in a metallic conductor where the free charges move to the surface in response to an external static field and the net electric field inside the conductor is always zero. The electric field that is required in bulk solution for the migration and subsequent retention of particles is produced as follows. The rate of electron transport across the electrodesolution interface increases as the external applied potential difference increases, and this electron transport gives rise to a steady current through the fractionator and hence through the external circuit. Thus, the electrical FFF channel can be expressed in terms of an electrical circuit as shown in Figure 2b when electron transport takes place between the electrodes and solution. Re represents the resistance for electron transport across the interface and includes contributions due to the reaction and mass transport of reduced and oxidized electrode material into and out of solution.13,14 This resistance is a function of the external applied voltage, carrier flow rate, and ionic strength. In general, it is a characteristic of the electrode-electrolyte interface. From this circuit diagram, it is apparent that the actual field inside the channel is proportional to the voltage drop across the solution, and it is given as

E(x) )

∆V(x) IR(x) ) ∆x w

(5)

where I is the current that is related to voltage and resistance through Ohm’s law, I ) ∆V/R, and R is the resistance. Note that we treat the voltage, field, and resistance as a function of x for the reasons discussed below. It is important to note that the actual

internal field is independent of the channel thickness since the solution resistance is directly proportional to the thickness for a carrier fluid with a particular ionic strength. The potential profile across the channel is given schematically in Figure 3. The extremes on the abscissa represent the electrodes, and the region in between is filled by the carrier fluid. There is a large potential drop very close to the electrodes due to the Faradaic reaction and the presence of an electric double layer. The potential drop in the middle, ∆Vs, is due to the ohmic solution resistance, Rs, and it is this potential drop that is important for particle migration. As seen from this figure, the effective field responsible for particle migration is very small compared to the one based on the external applied voltage. This is the reason we get retention times on the order of 10-30 min. Channel Resistance and Capacitance. The channel resistance and capacitance can be characterized by a potential step experiment13 where a finite potential difference, ∆V, is applied at time zero and the resulting decay of current is observed as a function of time. For small values of ∆V, the Faradaic reaction is negligible, and the decay of current can be expressed as13

I)

∆V -(t/RsCD) e Rs

(6)

where t is time and CD is the combined capacitance of the two double layers. The potential difference is applied for t > 0 and the capacitor is getting charged during this time. When the voltage drop across the capacitor equals ∆V, no more current flows through the circuit. Figure 4 shows a typical current vs time plot recorded for our channel. Also shown in Figure 4 is the data fit with eq 6 using a nonlinear least-squares technique. The parameter estimates for this curve are Rs ) 551 Ω and CD ) 0.087 F (87 000 µF). However, we note that Rs varies from 200 to 600 Ω and CD varies from 70 000 to 90 000 µF, depending on the extent to which the water has equilibrated with air. These resistances correspond to a specific conductivity of 0.7-0.2 µS cm-1, which compare well with those expected for DI water.15 The channel walls comprise a large geometric surface area, and as a result the capacitance for the system is large. This is important when the field is changed; with an RC time constant of the order of 40 s, relaxation takes place on a scale of minutes. This value is inherent in the data shown in Figure 4. This suggests that it will be very difficult to use alternating fields, field programming, or pulses because the response time of the (15) CRC Handbook of Chemistry and Physics, Chemical Rubber Co.: Boca Raton, FL, 1971.

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Figure 4. Decay of current as a function of time in a potential step experiment. The solid line is the least-squares fit to the data calculated using eq 6. The parameters used are given in the text.

fractionator will be extremely slow in changing the electric field. Also note that the current requires about 5-10 min to attain a steady value after the power supply is turned on. Hence, sufficient time must be allowed to establish the electric field before retention will be assured. Effect of Carrier Ionic Strength. Caldwell and Gao3 observed that the retention in electrical FFF decreases dramatically with increasing ionic strength of the carrier fluid. To explain this behavior, we first need to consider what happens in the solution. As mentioned above, there is a Faradaic process occurring at the electrodes that allows electron transport across the interface, or in other words, some species undergoes oxidation or reduction at the electrode surface. This species is transported to (from) the electrode from (to) the bulk solution by diffusion and electromigration. If an electrolyte is present in the system, then the transport process just mentioned is important in a very small region next to the electrodes, and most of the charge transport in the bulk is due to the electrolyte, which we assume does not get reduced or oxidized in the process. It is the bulk solution where the colloidal particles are predominately present, and any changes in electric field here result in changes in retention behavior. As mentioned before, the field in this region is proportional to the potential drop in the bulk solution and, hence, to the electrical resistance of this solution. In order to figure out the effective field, we must first determine this solution resistance, Rs, and how the potential drop in the solution, ∆Vs, will change with it. The solution resistance is governed by the charge-carrying species present in the bulk. If there are different types of charge carriers, then the amount of current carried by each of these depends on the mobility, charge, and concentration of these species, or their conductivity. As a result the total conductivity of the solution is just the sum of the conductivities of the individual species. In the case of electrical FFF, the solution between the plates contains the particles that we want to separate as well as some kind of indifferent electrolyte, and both of these are responsible for charge transport in this region. In the dilute limit, we assume that the movements of electrolyte ions and particles in the solution are not coupled, and the conductivity of the solution between the plates is just the sum of contributions due to the particles and the indifferent electrolyte. In terms of circuit elements this can be represented by resistances connected in 3226

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Figure 5. Current as a function of applied voltage and carrier flow rate. The carrier fluid is DI water.

parallel. Hence the solution resistance, Rs, is given by

1 1 1 ) + Rs Rc Rp

(7)

where Rc is resistance due to the carrier fluid and Rp is the resistance due to the particles. If we use DI water as the carrier phase, and a moderate particle concentration (≈1 wt % or less), then the magnitudes of Rc and Rp are comparable, and the solution resistance, Rs, is half of these individual resistances. Now assume that the electrode resistance, Re, is constant, and we apply a constant potential difference, ∆V, across the channel. Using Figure 2b we find that the voltage drop across the solution is given by

∆Vs ) IRs

(8)

and the current in the circuit is

I ) ∆V/(Re + Rs)

(9)

If we now increase the ionic strength of the carrier fluid by adding more salt, its conductivity goes up and the resistance Rc drops. As the ionic strength of the carrier is increased, the salt ions carry most of the current in the solution, Rc , Rp and Rs ≈ Rc. Although the solution resistance, Rs, decreases, the current given by eq 9 does not increase by the same amount. As a result, the potential drop, ∆Vs, in the solution starts decreasing with increasing carrier ionic strength. At the high ionic strength limit, ∆Vs is almost negligible, and so is the effective electric field responsible for particle migration. Current as a Function of Flow Rate. The current that passes through the channel is a function of the lumped resistances and the effective potential drops which occur throughout the electrode processes. Hence, this current is a function of conditions that exist at the electrode-solution interface. As mentioned previously, the resistance at this interface is determined by processes at the interface and mass transport of the reacting species. Hence, the interfacial process can be characterized by measuring current as a function of the applied voltage. These data are presented in Figure 5 where current vs

voltage curves are presented for four different flow rates. There are three distinct regions in Figure 5. At low applied voltages, below ≈1 V, the current is reaction limited; i.e., there is a very high barrier for transport of electrons across the electrodesolution interface. The current is almost negligible here, and since the effective field is proportional to the current, this region is useless for colloid retention. At higher voltages, the current increases exponentially according to the Butler-Volmer rate law.14 As the voltage is increased further, the current reaches a plateau value where the mass transport processes are limiting. In this plateau region, the rate at which the reactant species gets oxidized or reduced at the electrode is much faster than its transport between the solution and the electrode. Hence, the currentvoltage curve for a particular system depends on the characteristics of the carrier fluid, electrode material, and flow rate. As seen from Figure 5, there is a significant effect of carrier flow rate on the observed current. As expected, when the current is reaction limited, it is independent of the flow rate. At higher voltages, where the mass transport of the reacting species to and from the electrode is the slower process, the current starts increasing with increasing flow rate. Thus the effective field inside the channel is a strong function of the carrier flow rate, something unusual compared to other forms of FFF. For the fractionator used in this study, the measured currentvoltage curves depend on the state of the graphite blocks; i.e., there is a change in the current-voltage curves after the treatment of the graphite walls with solvents or abrasives. The observed current is also a good indicator of any contamination or trapped graphite particles. The current-voltage curves also show hysteresis if the voltage is first increased and then decreased to a lower value; this may be due to the present redox state of the graphite electrodes. It is quite likely that the nature of the graphite surface of these plates changes over a period of time. Hence, it is important to run the electrical FFF experiment at the same current value (since the operating field is proportional to the current) if reproducible retention data are desired. This aspect has been repeatedly demonstrated in our laboratory. The hysteresis phenomenon discussed above is also noticed in Figure 5. When the applied potential difference is between 1 and 1.6 V, both reaction and mass transfer are important. It is expected that the current will increase with increasing carrier flow rate. We observe from Figure 5 that the current actually decreases as the flow rate is increased from 1 to 2 mL min-1. This happens because of the way these measurements were made. We first select a flow rate and then measure the current as a function of applied potential difference (from 0 to 2 V) and then move to a higher flow rate. Since the reaction at the electrode is important in this region, the hysteresis effect is observed and the current for the 2 mL min-1 flow rate experiment is lower. In the purely mass transfer-limited region, above 1.7 V, we do see a higher current corresponding to a higher flow rate. We further investigate the dependence of the current on the carrier flow rate. Under the condition of stopped-flow, the voltage was increased in steps of 0.1 V until ≈2.1 V, maintained at this voltage, and then the flow rate was increased slowly. At each flow rate the current was allowed to reach the steady state by holding the flow rate constant for ≈10 min. The results of this experiment are presented in Figure 6. If the current is purely mass transport-limited then the consumption of reacting species can be given as

rate of reaction )

dCR ) k∆CR dt

(10)

where ∆CR is the difference between the concentrations of the reacting species in the bulk and at the electrode surface and k is the mass transport coefficient. The current is directly proportional to the rate of the reaction. When there is a laminar flow parallel to the plates, the mass transport coefficient is given by the Leveque solution:16

( )( )

Dr L〈v〉F k ) 0.626 L η

1/2

η FDr

1/3

(11)

where L is the length of the channel, Dr is the diffusivity of the reactant species, 〈v〉 is the average velocity, F is the density, and η is the viscosity of the carrier fluid. Thus the mass transport coefficient is proportional to the square root of the flow rate. A monotonic increase of current with flow rate is indeed observed experimentally, as shown in Figure 6; however, the experimentally observed current is almost proportional to the flow rate. The reason for this discrepancy with eq 11 might be due to the presence of multiple reactions, or that the experiment is not purely mass transport limited. We have observed that if the voltage is increased beyond 2.5 V under no flow conditions the current increases suddenly. This is probably due to the electrolysis of water. The rate of bubble formation appears to be suppressed in the presence of flow since we can operate the channel at voltages higher than 2.5 V without generating a substantial amount of bubbles, which interfere with the the simple detection scheme used here. Figure 7 shows how the current-voltage curve changes when 10-3 M KCl is present in the bulk fluid. Since KCl is an indifferent electrolyte here, it does not take part in the electrode reaction and only affects the charge transport processes in the bulk. As a result, the current-voltage curve is not greatly affected in the reaction-limited region. However, the mass transport-limited current at higher voltages is higher for DI water than that for 10-3 M KCl. The reason for this behavior can be explained as follows. The reacting species is transported to (from) the electrode from (to) the bulk solution by two mechanisms, diffusion and electromigration. When a supporting electrolyte is present in the bulk, it reduces the electric field near the interface, and this decreases the transport of the reacting species due to electromigration. This effect is discussed in detail by Bard and Faulkner.13 The fact that the internal field is a function of the carrier flow rate has serious implications. In FFF experiments, a stoppedflow period is typically used to obtain a steady-state concentration profile. As can be seen from Figure 5, under stopped-flow conditions the current is very low. To further illustrate this point, we switched off the flow after the current had reached a steady value and monitored the current. The results of this experiment are shown in Figure 8. The current dropped from its initial value of 1 mA to ≈0.1 mA in 10 min. After 16 min, the flow was turned on again and the current increased back to its original value in ≈2 min. This effect will be significant for higher voltages where mass transport is important. (16) Cussler, E. L. Diffusion: Mass Transfer in Fluid Systems; Cambridge University Press: Cambridge, U.K., 1984.

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Figure 6. Current as a function of flow rate for DI water and applied voltage of 2.1 V.

Figure 7. Current as a function of applied voltage and carrier ionic strength. The flow rate is 1 mL min-1.

Figure 8. Current as a function of time. Flow stopped at t ) 0 min and then restarted at t ) 16 min. The DI water flow rate is 1 mL min-1, and the applied voltage is 2.1 V.

If a stopped-flow relaxation is used in this region, then the current (and as a result the effective field) will drop as the flow is stopped, and it will appear as if the channel is operating at a very low applied field. Thus, stopped-flow relaxation may be ineffective. We also notice an overshoot of current in this figure when the flow is turned on or off. As explained before, the flow of carrier modifies the transport of charged species toward and away from the electrodes. It is possible that this flow also modifies the profile 3228

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of electric double layers near the electrode surface. This may then be the reason for observed overshoots in the current since the double layer will relax to a different extent as the flow is turned on or off. We have made an attempt to solve many questions regarding the operation of electrical FFF in this paper. Characterization of the channel in terms of electric circuit elements allows us to figure out operating potential drops in this system, and this information can then be used to estimate the magnitude of the internal field that drives the colloidal particles to the channel walls. As mentioned before, Lightfoot and co-workers6,7 developed an analogous separation scheme, EPC, using a cylindrical channel geometry where the electrodes are external to the channel. Although the mathematical relations developed in this paper are for a rectangular channel geometry, the underlying physics remains the same even for other geometries. Thus, the concepts developed here can be used to estimate the effects of various system parameters on retention for a hollow fiber system. Electrical FFF is unique compared to other forms of FFF in that the characteristics of channel material and carrier type dictate the nature of the effective electric field. Thus the type of electrode used and the presence of the corresponding reactant species in the solution determine the current-voltage relationship and, hence, the operating field. At high voltages where mass transport is important, even the carrier flow rate plays a key role in determining the current and the potential drop in solution. Thus a stopped-flow relaxation appears to be useless in this region. Fortunately the field strength is high and the zones relax in a couple minutes; hence it is not necessary to use stopped-flow relaxation. This point will be further explored using retained colloidal particles in part 2 of this series.9 It is impossible to use carriers that have ionic strengths higher than 10-4 M. This fact has many implications. First, it appears to be impossible to determine electrophoretic mobilities by electrical FFF at the higher ionic strength conditions that are typically used in many industrial colloidal formulations. Second, although the use of fresh DI water can provide a higher effective field inside the channel, the conductivity of this water changes with time as it equilibrates with air. This can lead to reproducibility problems for retention times. One remedy for this problem is to use ammonium carbonate buffer that has a low ionic strength.17 Finally, the concentration of injected sample can also have an influence on the retention behavior for low ionic strength carrier fluids. This is discussed in part 2 of this series of papers.9 CONCLUSIONS The internal field in electrical FFF is a function of electrode material and geometry, carrier composition, and flow rate. The strength of this field can be estimated by monitoring the current and the conductivity of the carrier. Use of a carrier with a high ionic strength severely reduces the potential drop in the solution, and thus, little retention is observed under these conditions. This limits the range of carrier ionic strength that can be used in electrical FFF experiments. Since the current depends also on the mass transport of the reacting species, it is affected by the carrier flow rate. Thus, the effective field that is responsible for particle migration changes (17) Caldwell, K. D.; Gao, Y. S.; Shi, L. Presented in the Polymeric Materials Science and Engineering division of the ACS, Orlando, FL, August 1996; paper 5.

with changing flow. This makes it difficult to use stopped-flow relaxation at the beginning of the experiment to get a relaxed zone because of the low field. ACKNOWLEDGMENT We thank Nancy Cohlberg, of Cohlberg Analytical, Blue Bell, PA, for editorial assistance. We also thank Dave Strumfels for developing the data acquisition software for our system. SYMBOLS

t0

void time

tr

retention time

ux

solute transverse velocity

V

electrical potential

V0

void volume

Vr

retention volume

∆Vs

potential drop in the solution

∆V

external applied potential difference

〈v〉

fluid average velocity

w

channel width

x

transverse coordinate of the channel

CD

lumped capacitance of the two double layers

CR

concentration of material reacting at the electrode surface

D

diffusion coefficient of particles

y

breadth coordinate of the channel

Dr

diffusion coefficient of the electrode reactant species

z

axial coordinate of the channel

E

electric field

η

solution viscosity

I

current

λ

nondimensional mean layer thickness

k

mass transport coefficient

µ

electrophoretic mobility

L

channel length

F

fluid density

Rr

retention ratio equal to V0/Vr

R

resistance

Rc

resistance due purely to the carrier fluid

Re

solution-electrode interfacial resistance

Received for review January 2, 1997. 1997.X

Rp

resistance due purely to the solute particles

AC9700134

Rs

total solution resistance

t

time

X

Accepted May 21,

Abstract published in Advance ACS Abstracts, July 1, 1997.

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