Measurement of the Field Dependent Electrophoretic Mobility of

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Langmuir 2008, 24, 10698-10701

Measurement of the Field Dependent Electrophoretic Mobility of Surface Modified Silica/AOT Suspensions John C. Thomas,* Kathryn L. Hanton, and Bryan J. Crosby Laser Light Scattering & Materials Science Group, UniVersity of South Australia, Mawson Lakes, Adelaide, SA 5095, Australia ReceiVed March 16, 2008. ReVised Manuscript ReceiVed July 2, 2008 We have investigated the electrophoretic mobility of silica spheres in a silica/AOT/paraffin ternary system as a function of the applied electric field and observed a large discrepancy with data published on a similar system (Jin, F. H.; Davis, H. T.; Evans, D. F. Int. Conf. Digital Printing Technol. 1998, 206-209). We attribute the discrepancy to an artifact in the measurement technique used to obtain that published data. We believe the artifact is caused by high velocity particles being “swept” from the measurement volume, thereby biasing the result toward lower mobilities. Thus, the published measurements appear to indicate a high field plateau in mobility data around 500 kV/m. Our results indicate that the silica/AOT/paraffin solution is reaching dielectric breakdown prior to a conclusive high field plateau being unambiguously measured. At low field the mobility is in general agreement with the prior work (Jin, F. H.; Davis, H. T.; Evans, D. F. Int. Conf. Digital Printing Technol. 1998, 206-209). Any proposed models of apparent charging of particles which utilize the presence of a high field plateau are inappropriate unless the high field plateau is clearly established. Our work indicates that caution is required regarding the measurement of electrophoretic mobility at high electric fields.

Introduction Electrophoretic mobility is an important parameter for characterizing colloidal dispersions, as it is a key indicator and determinant of suspension stability. It also helps predict how colloidal particles will behave under an electric field. When colloidal particles are dispersed in an organic solvent, the electrophoretic mobilities become very small. In this case, large electric fields need to be applied to increase the velocities to levels that can be measured reliably. However, the increase in applied field also can affect the electrophoretic mobility. This may be due to dynamics of colloidal motion in a solvent, but the net effect is to increase the apparent surface charge density via an apparent charge stripping from the double layer surrounding the particles. The measurement of electrophoretic mobility is commonly done by laser Doppler electrophoresis (LDE). In one variant of LDE, crossed laser beams intersect and form a series of fringes between a set of parallel plate electrodes. When a bipolar symmetric square wave excites the electrodes, the charged colloidal particles will traverse the fringes. If the crossed beams have a small difference in frequency (ff), giving rise to moving fringes, the laser intensity is spatially and temporally sinusoidal over the interaction volume. If scattering centers are stationary in the crossed beams, then the time dependent scattered light signal varies in intensity at the same frequency as the shift frequency. If the particles are moving, however, then this frequency will be shifted away from ff (upshifted for velocities counter to fringe velocity). This shift in frequency of the intensity variation will be proportional to particle velocity, but not due to a Doppler effect per se. Thus, use of the word Doppler here is a misnomer, and we prefer to call this technique, more correctly, laser fringe velocimetry (LFV) or, when being applied to electrophoresis, laser fringe electrophoresis (LFE). * To whom correspondence should be addressed. E-mail: john.thomas@ unisa.edu.au. Web: www.unisa.edu.au/laser.

Phase analysis light scattering2–4 (PALS) is a more sensitive technique for determining electrophoretic mobility. It is similar to LFE except that a sinusoidal potential is applied to the electrodes and the phase shift of the scattered light with respect to the laser fringe motion is detected. We have developed an apparatus similar to that of Miller3 which can perform both PALS and LFE. During measurements of the electrophoretic mobility (µ) on modified silica particles with this apparatus, it was observed that results depended on the method of measurement, PALS or LFE, as well as the electric field parameters (square wave, sinusoidal wave, drive frequency). The key differences between the LFE and PALS techniques are the frequency and time dependent amplitude of the electric field. The experimental differences may be attributable to the analysis technique used in PALS. However, this has been addressed in a previous paper by the authors.2 For silica/AOT/ paraffin, even when measurements were only done using one of the techniques, a range of values for µ was possible by varying the electric field excitation frequency. This fact and the large discrepancy with other published data1 form the basis for this paper. Jin et al.1 measured electrophoretic mobility in a model system based on -CN modified silica in AOT and Isopar M (a commercial paraffin). They indicated that there is a low field regime (E < ∼100 V/m) where the base level of mobility is measured and a maximum mobility is reached for fields above 500 kV/m. “The mobility of these silica particles showed a general behaviour: constant when the field was lower than ∼100 V/cm, increases linearly with the external electric field, and levels off when the field is above 5000 V/cm.” In addition, they present a simple model of this behaviour based on a mechanism whereby (1) Jin, F. H.; Davis, H. T.; Evans, D. F. Int. Conf. Digital Printing Technol. 1998, 206–209. (2) Thomas, J. C.; Crosby, B. J.; Keir, R. I.; Hanton, K. L. Langmuir 2002, 18(11), 4243–4247. (3) Miller, J. F. The Determination of Very Small Electrophoretic Mobilities of Dispersions in Non-polar Media Using Phase Analysis Light Scattering. Ph.D. Thesis, University of Bristol, 1990. (4) Miller, J. F.; Scha¨tzel, K.; Vincent, B. J. Colloid Interface Sci. 1990, 143(2), 532–554.

10.1021/la800821e CCC: $40.75  2008 American Chemical Society Published on Web 08/30/2008

Electrophoretic Mobility of Silica/AOT Suspensions

Figure 1. Combined phase analysis light scattering (PALS) and laser fringe electrophoresis (LFE) system. AOM, acousto-optic modulator; AOD, acousto-optic driver; SELFOC, fiber optic probe detector; PMT, photomultiplier tube; FG, function generator; TC, temperature control unit; GPIB, general purpose interface bus controller; NIDAQ, data acquisition cards; PC, laboratory computer; PAMP, preamplifier. The broken lines indicate the signal path for the LFE configuration.

the particles’ apparent charging occurs via a dissociation of ions with a reaction constant. This may still be correct, because the basic mechanism appears to be intuitively sound. An inherent surface charge density (low field) is consistent with results from aqueous systems coupled with the effect of large fields effectively stripping charge from the double layer surrounding each independent particle. However, our attempts to duplicate the results have shown that the upper plateau is not achievable prior to dielectric breakdown of the suspension leading to arcing between the electrodes. The actual highest magnitude for µ is over 5 times higher than that reported by Jin et al.1 This means that any case for the charging mechanism is unproven using mobility measurements and the proposed model may need to be reconsidered.

Experimental Section Samples. Silica spheres with nominal diameter 7 µm with -CN surface terminations (Mac-Mod catalog no. 820962102) were used in this work. Aerosol OT (AOT; Fluka, ∼98% pure) was purified by dissolution in methanol (Univar, analytical grade) and tumbled with activated charcoal. This dispersion was filtered and centrifuged to obtain a clear supernatant. The methanol was extracted by rotary evaporation, and any remaining methanol was removed by heating in a vacuum oven at 120 °C for 24 h. The purified AOT was kept in a desiccator. An aliquot of -CN modified silica was placed into Isopar M (ExxonMobil), a light paraffin oil, containing Aerosol OT surfactant at 5 mM and 0.1 mM concentrations. Dispersions were made by adding 10 mg of silica particles to 10 mL of the AOT solution in a clean, dry glass vial so that the final silica concentration was 1 mg/mL. The resulting dispersions were tumbled on a mixer for 24 h prior to use. A sample of the dispersion was then put into a clean quartz cuvette for measurement in the PALS/LFE mobility apparatus. Experiments were carried out at 25 °C, and a value of 3.2 mPa s was used for the viscosity the suspensions. LFE Measurements. We have previously described our PALS apparatus.2 The same apparatus, shown in Figure 1, was used for the current measurements. The physical and electrical connections for LFE and PALS are identical. The difference is that, for LFE, the scattered intensity signal bypasses the lock-in amplifier necessary for PALS detection. Instead, a time dependent voltage is measured directly via an analog-to-digital converter card in the control computer (PC). The PC determines the power spectrum of the signal using a fast Fourier transform (FFT), and the frequency shift from the fringe frequency (ff) is calculated.

Langmuir, Vol. 24, No. 19, 2008 10699 The opto-electronic system produces a moving fringe pattern in the sample cell. Light from a 5 mW HeNe laser is passed through a long focal length lens (f ) 850 mm) and into a 50% beam splitter. The two resulting beams are passed through acousto-optic modulators, or Bragg cells (Isomet model 1205C-2). One Bragg cell is driven by one channel of an acousto-optic driver (Brimrose model FFA-80) at 80 MHz. The other Bragg cell is driven by the other, single sideband, channel of the acousto-optic driver at a frequency of 80 MHz plus a modulation frequency provided by the lock-in amplifier (Stanford Research Systems model SR830). For the current experiments, the modulation frequency was set in the range 2-40 kHz depending on the sample mobility. Thus, one laser beam is frequency shifted by 80 MHz and the other by 80 MHz + modulation frequency, and the difference (modulation) frequency gives rise to the moving fringe pattern. Mirrors are then used to direct the two beams so that they intersect in the center of the sample cell. The beams cross at an angle in the cell of 10.6°, giving rise to a set of moving fringes spaced 3.4 µm apart. The scattering cell contains a pair of parallel plate palladium electrodes with a separation of 2.1 mm and a width of 6 mm. The electrodes are driven by a high voltage amplifier (Trek model 610D) which in turn is driven by a programmable function generator (Stanford Research Systems model DS335). For the current experiments the electrode drive was a bipolar square wave. The forward scattered light from the particles is collected by a fiber optic probe consisting of a SELFOC lens and a single mode fiber5 and detected by a photomultiplier tube (Hammamatsu model R649). The photomultiplier output is fed to either the lock-in amplifier which performs lock-in detection for PALS or to a preamplifier (Stanford Research Systems model SR560) for LFE measurements. The x and y output of the lock-in amplifier or the preamplifier output is acquired by the control computer via a high speed data acquisition card (National Instruments model PCI-6035E). A GPIB controller card (National Instruments model AT-GPIB/TNT) is used for computer control of both the lock-in amplifier and the function generator. LFE is able to measure mobility if the electric fields are high enough for the charged particles to produce frequency shifts of ∼10 Hz. In our system, this corresponds to a minimum velocity of ∼25 µm/s. PALS on the other hand is able to more sensitively detect particle velocities. The practical limit (∼20% statistical error in reproducibility) for the same particles is achieved with velocities of about 3 µm/s. For smaller particles, a higher precision is possible due to longer measurement times. The 7 µm silica particles tend to sediment out. Therefore, significant systematic errors occur for experiments of duration longer than ∼300 s. Data analysis in our LFE experiment requires that the operator fit a Gaussian profile to the power spectrum. In displaying a power spectrum, the shift frequency fs is displayed as the difference between the calculated peak frequency (f ) and the fringe frequency (ff):

fs ) f - ff

(1)

The frequency shift is given by

fs ) µE

2n sin(θ ⁄ 2) λ0

(2)

Here, µ is the electrophoretic mobility of the particles, E is the electric field amplitude, n is the refractive index of the liquid, θ is the angle between the crossed laser beams, and λ0 is the laser wavelength in vacuo. In addition to the position of the shifted peak, we are interested in its relative width. This is conveniently monitored via the quality factor or Q of the peak, defined as (5) Suparno; Duerloo, K.; Stamatelopolous, P.; Srivastva, R.; Thomas, J. C. Appl. Opt. 1994, 33, 7200.

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Q)

central shifted frequency of peak fs (Hz) full width at half maximum of peak FWHM (Hz) (3)

The Q of the peak is normally deemed acceptable if it is higher than ∼1.3. As shown below, the Q depends on the electrode frequency used to accelerate the colloid particles. The electrode frequency is generally chosen so that the Q is at a maximum (peak width is at a minimum). This is the crux of the measurement protocol and is justified later. The PALS data are measured at lower fields for samples where the greater sensitivity of the PALS technique is most useful. As indicated in a previous paper,2 the original PALS analysis is valid only at lower magnitude electric fields where the mobility is independent of the applied electric field.

Results and Discussion Figure 2a shows raw power spectra for LFE data collected at different electrode drive frequencies in the range 8-26 Hz. The sample was -CN modified silica spheres suspended in IsoPar M containing 5 mM AOT. The amplitude of the applied field

Thomas et al.

was 800 kV/m. It can be seen that, as the electrode drive frequency is increased, the spectra become narrower and the peak shift is smaller. The Brownian motion dependent peak broadening is only ∼2 Hz in this system. Thus, the width of the power spectrum is probably a result of electric field gradients broadening the particle velocity distribution. However, given that the electrode geometry is constant for these different experiments, the change in broadening may be due to temporal field gradients during the experiment (charging time for a capacitor). In any event, it is clear from these data that different results are obtainable at different electrode drive frequencies. The effect of electrode frequency is more clearly seen in Figure 2b where we show the peak shifts and the Q for the measured power spectra as a function of electrode drive frequency for an applied field of 800 kV/m. In order to minimize noise in the evaluation of Q, a Gaussian curve is fitted to the highest twothirds of the central peak, and the Q is derived from the parameters of the fitted curve. In the figure, we also show the percentage of the gap between the electrodes traversed by the electrophoresing particles during a half-period of the electrode drive frequency. This is done by taking the measured particle velocity and calculating the average distance traveled by particles during a half-period. The % gap traversed (GT) is calculated thus

%GT )

100 × µ × E G × 2 × FE

µ ) calculated electrophoretic mobility (m2 V-1 s-1) E ) applied electric field (V/m) G ) electrode spacing (or gap) ) 2.18 × 10-3 m FE ) electrode field excitation frequency (Hz) (4)

Figure 2. (a) Raw shifted-frequency power spectra for LFE measurements on a 5 mM sample. Data for three frequencies are shown to indicate the effect of altering electrode frequency. Values of 12, 16, and 22 Hz are shown here for electrode field magnitude E ) 8 × 105 V/m. (b) Frequency shift, peak Q, and the calculated gap traversal against electrode frequency. The fringe frequency was 30 kHz for E ) 8 × 105 V/m and 40 kHz for E ) 106 V/m. The number of averages was 150 for each sample, and the run time was 70 s.

As can be seen from the figure, when the distance traveled by the particles reaches the order of 30% of the electrode separation, the peak width broadens (Q decreases) and the peak frequency shift increases in magnitude. A rationalization for this is that, when the field is in the one direction for a time comparable with the time it takes particles to traverse the electrode gap, most of the particles are swept out of the region containing the fringes during the measurement. The means that significant portions of the data are not due to scattering from the silica particles and do not relate to their electrophoresis. As more of the particles are removed from the temporal average, the average number of particles in the beam will also reduce, thus reducing the signalto-noise (S/N) ratio of the experiment. This will also add to the broadening of the shifted peak. Consequently, low frequency electrode excitations will not only give erroneous values for the high field mobility, but will also degrade the Q of the central shifted peak. In light of the above analysis, it would be expected that high frequency electrode excitations would be preferable for determining the correct values for mobility. We have observed that, in fact, a peak in measured mobility for the LFE experiment occurs at an optimal excitation frequency. Above this frequency, the mobility actually decreases with increasing excitation frequency. This may be due to the acceleration of the particles to the terminal velocity taking finite time and hence systematically underestimating the steady state mobility. Consequently, the lowest reasonable estimate for the mobility of a sample at high electric fields is assumed to be the highest value measured using different electrode excitation frequencies. The electrophoretic mobility of the silica dispersions is negative. Figure 3 shows the mobility magnitude measured for the 5 mM AOT sample as a function of applied electric field for

Electrophoretic Mobility of Silica/AOT Suspensions

Langmuir, Vol. 24, No. 19, 2008 10701

Figure 4. Upper envelope LFE mobility magnitude results for 0.1 mM AOT colloids. Also included are the relevant Jin et al.1 data. Figure 3. LFE results at one electric field amplitude for a range of electrode field frequencies for the 5 mM AOT colloids sample. The electrode frequencies shown are 0.75 and 2 Hz. Also displayed are the values derived from Jin et al.1(electrode frequency unknown).

electrode excitation frequencies of 0.75 and 2 Hz. These frequencies were chosen, as they are comparable with the 0.5-1.0 Hz frequencies commonly used in LFE experiments. The fringe frequency was altered to separate the central peak from the “pedestal” frequencies. The amount of averaging was reduced at higher electrode fields, because the successive “sweeping out” of particles reduced the Q to such an extent that determination of the central peak shift was subjective. For very low Q peaks, the Gaussian fitting produces a central frequency shift that is very dependent on the actual boundaries chosen for the analysis. Thus, the data are somewhat noisy. We have drawn smooth lines through the data to enable the trends to be readily discerned. The data clearly show that the sample has a field dependent mobility and, further, that the observed nature of this depends on the electrode drive frequency at higher field strengths. For fields up to ∼200 kV/m, similar behavior is observed for both the 0.75 and 2 Hz electrode drive frequency data. However, at higher field, the 0.75 Hz data clearly plateau out whereas the 2 Hz data continue to increase with applied field until they too plateau at around 500 kV/m. For purposes of comparison, we have reproduced the data of Jin et al.1 in Figure 3, and it can be seen that these data give a similar field dependence to our data recorded at 0.75 Hz electrode drive frequency. Figures 4 and 5 show the best results for 0.1 mM AOT and 5 mM AOT samples along with the Jin et al.1 data. Also shown in Figure 4 is the electrode frequency at which the optimized data were taken. It became necessary to use electrode frequencies as high as 40 Hz in order realize the best results at the highest fields. The main difference to note is the distinct lack of a high plateau in the mobility data. For the highest electric fields, the data appear to be turning over. However, these data were collected near the upper limits of the experimental apparatus. It may simply have been that significant current was causing a potential drop which reduced the actual electric fields below those calculated

Figure 5. Upper envelope LFE mobility magnitude results for 5 mM AOT colloids. Also included are the relevant Jin et al.1 data.

from geometry and applied voltage. In which case, the apparent reduction in curvature may also be an artifact. Nonetheless, no plateau was measured before dielectric breakdown of the solvent precluded experiments at higher applied voltages.

Conclusion From the foregoing, it is clear that, for reliable electrophoretic mobility measurements using laser fringe velocimetry, consideration must be given to the interplay of the electrode drive frequency, the magnitude of the applied field, and the mobility of the particles. This is especially important in the case of high electric fields. In that case, it may be that the particles are being swept out of the measuring volume so quickly that they are not being reliably measured. If measurements are performed under appropriate experimental conditions, there is little evidence of a high field plateau in the electrophoretic mobility which has been reported by others.1 LA800821E