Anal. Chem. 1993, 65, 2928-2932
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Imaging of Hydrodynamic and Electrokinetic Flow Profiles in Capillaries John A. Taylor and Edward S. Yeung* Ames Laboratory-USDOE
and Department of Chemistry, Zowa State University, Ames, Zowa 50011
An imaging system based on microscope optics and a charge-coupled device camera is used to form high-resolution images of the liquid core inside narrow fused-silica capillaries. This technique allows direct examination of the fluid motion inside the capillary under electrokinetic and hydrodynamic (Poiseuille) conditions. Two experiments are described. The first involves monitoring the front of the fluorescence-labeled solvent as it travels through the capillary. The second is an examination of the local velocities using submicron-sized particles as probes. The results are discussed in context of band broadening in capillary electrophoresis. INTRODUCTION Electroosmotic flow is a phenomenon that arises from the formation of a double layer of complementary charges at a surface. One set of charges is fixed in place and the other is mobile, free to move with the attraction or repulsion of an applied electrical field. Early interest among analytical chemists was in harnessing electroosmosis to drive flow through chromatographicpackings.1J This approach offered greatly reduced band broadening without back pressure. The explosive development of capillary electrophoresis (CE) and electrokinetic chromatography has caused much discussion and theoretical speculation about electroosmosis. Most recently, several researchers have reported different approaches to controlling this flow. These methods range from the variation of electrolyticequilibria3to the direct application of an electric field to the capillary s ~ r f a c e . ~ . ~ One of the most heavily cited early references offering a theoretical perspective on these phenomena was published by Rice and Whitehead in 1965.6 The relation between linear velocity and radial position was derived as
where u(r) is the linear velocity a t radial position r,Q is the constant for a particular liquid and solidphase, E is the applied electrical field, I is the zero-order modified Bessel function of the first kind related to the potential a t a specified location along the capillary radius, k is the reciprocal of the doublelayer thickness, and a is the capillary radius. If ka is large, which is the case for a capillary with internal diameter of 75 Km and an electrical double-layer thickness (1) Pretorius, V.; Hopkins, B. J.; Schieke, J. D. J. Chromatogr. 1974,
99, 23-30.
(2) Stevens, T. S.; Cortes, H. J. Anal. Chem. 1983,55, 1365-1370. (3) Chang, H.-T.; Yeung, E. S. Anal. Chem. 1993,65, 660-652. (4) Wu, C.-T.;Huang, T.-L.;Lee, C. S.; Miller, C. J. Anal. Chem. 1993, 65,568-571. (5) Hayes, M. A.; Kheterpal, I.; Ewing, A. G. Anal. Chem. 1993, 65, 27-31. (6) Rice, C. L.; Whitehead, R. J. Phys. Chem. 1965, 69, 4017-4024. 0003-2700/93/0365-2928$04.00/0
of less than 10 11111,' the Z term becomes insignificant. This predicts a flat flow profile for fluid in the capillary in all but the small double-layer region. In contrast, for Poiseuille (hydrodynamic) flow,
where Q is the volume flow rate of the bulk. Equation 2 represents the classical parabolic profile for pressure-driven systems. Electrophoretic motion is expected to assume a flat flow profile in capillary tubes. This is because in moderately conducting electrolytes the electric field lines are uniformly oriented in the axial direction. The aspect ratio in CE is highly restrictive for the field direction, being 1:lOOO in the typical case. So, in the absence of a temperature gradient across the diameter of the capillary, the net electrokinetic motion (electrophoreticplus electroosmotic) can be described by a plug flow.' This has been used to explain the substantial increase in separation efficiency (theoretical plates) in CE and in electrochromatograph~~9 vs in pressure-driven capillary liquid chromatography. Further understanding of these electrokinetic flow profiles should prove valuable in the optimization of the separation conditions. Absorption measurements through a microscope by using a charge-coupled-device (CCD) camera have been used before to trace the concentration profile in the junction between two capillaries.10 Obtaining a radial profile of the concentrations inside the capillary, however, does not provide useful information about the flow patterns, vide infra. Besides, concentration profiles are not readily converted into velocity profiles. Here, we report the use of a fluorescent neutral marker and fluorescent submicron particles to characterize the flow patterns inside a 7 5 - ~ m capillary under hydrodynamic and electrokinetic regimes.
EXPERIMENTAL SECTION Optics. The microscope-based CCD imaging system with fiber-optic beam introduction (Figure 1) was similar to that reported previously.*lJ* In this case, however, a single capillary was placed between a microscope slide and a cover slipsupported by two other cover slipsso that the capillary could be surrounded with a fluid. The fluid was water for concentration imaging and glycerin for particle imaging. This roughly matches the refractive index, which is essential to obtaining high magnification in the images, providing an undistorted image with a narrow depth of field and reducing scatter from the capillary walls. The fluid around the capillary also allows efficient heat transfer (compared to operation in air) to eliminate radial temperature gradients. Another difference is the microscope (A0Spencer),which was (7) Ewing, A. G.; Wallingford, R. A,; Olefirowicz, T. M. Anal. Chem. 1989,61, 292A-303A. (8) Pfeffer, W. D.; Yeung, E. S. Anal. Chem. 1990, 62, 2178-2182. (9) Pfeffer, W. D.; Yeung, E. S. J. Chromatogr. 1991, 557, 125-136. (10) Kuhr, W. G.; Licklider, L.; Amankwa, L. Anal. Chem. 1993,65, 277-282. (11) Taylor, J. A.; Yeung, E. S. Anal. Chem. 1992,64, 1741-1744. (12) Taylor, J. A.; Yeung, E. S. Anal. Chem. 1993, 65,956-960. 0 1993 American Chemical Society
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Figure 1. Schematic for CCD imaging of fusedsiiica capillaries: CS, glass cover slip; CAP, fused-silica Capillary; OF, optical fiber; GS, glass microscope slide; SP, spacers made from glass cover slips; CCD, chargecoupleddevicecamera; 5X, magnifyingcamera adapter; 20X, microscope objective: MB, microscope body; GND, grounded buffer reservoir; HV, buffer reservoir held at high voltage or elevated for hydrodynamic flow. 15 >
used to obtain a higher magnification than the former model (Stereohm). A more powerfullaser (Uniphase)was also useful in increasingthe particle fluorescencesignal well over the darkcurrent limit. Flow Generation. The spatialdependenceof the eventsbeing recorded dictated largedifferencesin flow velocitiesbetween the two types of experiments. Band fronts ranged from 1to 3 mm in length for concentration imaging while the measurable movement of a single particle was limited to 200 pm for an observation time of 1.5 s (one frame). Hydrostatic flow was produced by elevating one end of the capillary 40 cm for the fluorescent band studies (64.5 cm long, 63 cm effective length) and 0.7 cm for the particle migration measurements(56cm long,54 cm effective length). Electrokinetic flow was driven with a high-voltagepower supply (Glassman)set at 10kV for band measurementsand +1650 V (minimumoutput) for the particle studies at pH = 7 and -1680 V at pH = 3. Image Acquisition and Analysis. A different strategy for data acquisition and analysis was applied to each type of experiment. For concentration imaging, 10 rows (5 pm) of the capillary image were binned along the capillary axis and 0.5-9 exposures were recorded every 1.2 s during the travel of the fluorescent band through the detection region. In the particle experiments,unbinned images of a 100pm X 200 pm region were collected at 5-s intervals with an exposure time of 1.5 s. The resulting particle fluorescencestreaks in a 15-20-pm focal plane can be easily differentiated from out-of-focusparticles or other anomalies. The lengths were measured from the CCD system by manually pointing to the ends of the streakson a high-resolution monitor. Data analysis and plotting were performed on an IBM PC/AT computer. Solutions and Buffers. All buffer solutions were 10 mM bicarbonate. The anion was selected because of its small size, so that adsorption on or complexation to the particles can be minimized. These solutions were adjusted to the indicated pH with HC1, degassed under vacuum in an ultrasonic bath, and filtered through 0.22-pm syringe filters. Carboxylate-modifiedfluorescing latex microspheres (282-nm diameter, CML polystyrene latex, L-5241) were obtained from Interfacial Dynamics (Portland, OR) and diluted 1000-5000-fold in the bicarbonate buffer.
RESULTS AND DISCUSSION The most important factor in planning these experiments was the necessity of depth resolution perpendicular to the capillary axis. In studying the flow inside a cylindrical capillary, only a thin, two-dimensional plane including the capillary axis will yield accurate information about the radial dependence of flow velocities. In the present case, a common light microscope was used with loOX magnification to obtain a depth of field of around 20 pm. Intensity information from
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Figure2. Three-dimensional plots of normalizedfluorescenceintensity from riboflavin (8 X M) injected at t = 0: (A) hydrodynamic flow, pH = 7; (B) electrokinetic flow, pH = 7.
outside this thin focal plane was either lost into the background or easily discriminated from in-focus information by appearance. Immersion of the capillary in a fluid provides an undistorted image despite the cylindrical capillary walls. Concentration Imaging. Fluorescence imaging of the liquid inside a capillary tube under electrophoretic conditions has been reported before.12J3 The applications so far have been for detection of analytes rather than for following the flow patterns. By appropriate synchronization of the CCD framing rate to the motion of the analyte band, signal integration over long times can be implemented to enhance the signal level and to discriminate against the (stationary) stray light from the capillary walls.13 Fluorescence imaging alsoallowsthe simultaneousmonitoring of multiple capillaries under electrophoresis in a multiplex scheme.12 Three-dimensional plots can be drawn (Figure 2) which show the normalized fluorescence intensities in the image as a function of radial position and time during the emergence of a fluorescent front. The front is generated by injecting a plug of buffer containing riboflavin, which is assumed to be neutral under these conditions, into the capillary. In order to compensate for variations in pixel response and illumination, the intensity of each pixel (radial position) of each frame was normalized to that at the last frame of the sequence, i.e., the maximum in fluorescence intensity. The capillary walls appear in the plot as a series of mountains and valleys because the peak intensities in these regions remained close to the dark current of the sensor and noise is magnified during normalization. A few important observations are apparent in these plots. First, even though the rates of travel for the two band fronts are roughly the same, as judged by their appearance time at the observation region after injection, the rise time for the (13) Sweedler,J. V.; Shear, J. B.;Fishman, H. A.; Zare,R. N.; Scheller,
R. H.Anal. Chem. 1991,63,496-502.
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hydrodynamic front is almost a factor of 4 longer than that for the electrokinetic front. This is consistent with observations in CE of increased band broadening caused by axial dispersion when pressure-driven flow is operative. Second, the normalized intensity as the front emerges is constant across the capillary radius for both flow regimes, as opposed to a bullet-shapedconcentration front due to varyingvelocities under Poiseuille flow. This supports the idea that radial diffusion is fast enough to "average" the riboflavin concentration across the capillary over the migration time from injection to observation. For a material with a diffusion coefficient of 10-5 cm2/s, one can estimate that the diffusion distance is 1.3 mm over a time of 830 s. This is substantially larger than the 38-pm internal radius of the capillary. Complete radial mixing is therefore expected. So, even though in Poiseuille flow the velocity at the center is higher than those at the walls, we do not expect to find the front to arrive earlier along the axis compared to the walls in Figure 2A. Furthermore, the diffusion distance is 38 pm (capillary radius) in a time of 0.7 s, or roughly the exposure time. This is to be compared to the flow velocity of approximately 1mm s-l. A much shorter exposuretime (e.g., 1ms) would be needed to freeze the front in the field of view to record any differences in appearance time as a function of radial position. The implication is that concentration profiles as a function of time and as a function of radial position are not very useful for revealing flow dynamics in these capillary tubes, unless short excitation pulses (e.g., pulsed lasers) are used for excitation. Finally, we note that the rise time of the fluorescent front under electrokinetic flow is about 3.5 s, or roughly 0.28 cm in length alongthe capillary. This is consistent with typical peak widths for small molecules in CE. There has been an earlier report14 of fluorescence flow imaging in zone electrophoresis. A distinct curvature was observed in the front of the migrating fluorophore. However, the experiments were performed in a lo00 X 50 pm channel and curvature was observed along the long axis. It is not clear why any wall-related effect can extend hundreds of microns into the channel. The larger channel is also more susceptibleto temperature gradients created by Joule heating. Particle Imaging. The seeding of particles in a fluid stream to track local velocities is a known method. In one approach, a double exposure of short duration is recorded for the region of interest by a ~amera.159~6 Typically, a laser is used to provide sufficient scattering intensity for the photographic image. The interval between exposures is chosen to record correlated spots for each particle, the spacing between which corresponds to the distance traveled during that interval. Data analysis can be based on the interference pattern generated by each set of correlated spots, very much like a diffraction grating. For more sensitive measurements or for use with low-power lasers, fluorescent particles can be used." In another approach, a single exposure of moderate exposuretime is used to record streaks resulting from motion of the particles during the exposure.'* In unknown systems, a special coding technique was employed18to uniquely define the direction of motion. The advantage of the second approach is that changes in the velocity direction during the exposurecan be recorded. In this work, we followedthe second approach. However, instead of first capturing the images on film and then digitizing these with a CCD camera, we used (14)Tsuda, T. XVI International Symposium on Column Liquid Chromatography, Baltimore, MD, May 1992;Abstract 409. (15) Dudderar, T. D.; Simpkins, P. G. Nature 1977,270,4547. (16) Grousson, R.; Mallick, S. Appl. Opt. 1977,16, 2334-2336. (17) Northrup, M. A.; Kulp, T. J.; Angel, S. M. Appl. Opt. 1991,30, 3034-3040. (18)Khalighi, B.; Lee, Y. H. Appl. Opt. 1989,28,4328-4332.
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a high-sensitivity CCD camera directly to obtain the digitized images. The movement of particles inside a capillary has been reported by us previously11 in conjunction with an investigation of noise sources in fluorescence detection in CE. Even for filtered buffer solutions, submicron particles create noise spikes when they pass through the laser beam and scatter light. Here we attempt to correlate particle velocities with the radial positions to determine the flow profiles inside the capillary. While the relativelyfast diffusion of molecular fluorophores prevents the measurement of linear velocity as a function of radial position, submicron-sizedparticles,which do not diffuse quickly,can be used to trace the flow. The time-lapsed images collected (Figure 3) show streaks which define the travel of the particles through the capillaryduring the time of exposure. The streak length in the x-direction is thus proportional to the particle velocity along the capillary axis. Actual measurements were performed with a mouse-driven pointer on the video display unit. The x- and y-coordinates of the beginning and of the end of each streak were recorded. The streak length is simply the difference in x-coordinates and the radial position is simply the average of the y-coordinates. The actual distances can be derived from calibration based on the locations of the capillary walls (75-pm i.d.) that are recorded in the same image. The direction of motion cannot be determined from the images alone. However, visual observation through the microscope reveals the direction of the motion immediately. Since the electric field is welldefined and is unmistakably in the x-direction only, interpretation of the measured streak lengths is straightforward. In Figure 3, pointers a-e and o indicate examples of streaks that were observed in cases of electrokinetic and hydrodynamic flow. The streaks in each figure have different widths (0 > c > a > b = d > e). These are due to particles present at varying distances from the shallow focal plane in the acquired image. The various intensities are probably due to uneven tagging of the latex spheres and nonuniform illumi-
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Flguro 4. Scatterplotof streak lengthvs radial dlstance from caplllary center: exposure time, 1.5 8; hydrodynamic flow at pH = 7. SolM line represents theoretical predictions from eq 2.
Flgurs 5. Scatterplotof streak lengthvs radlal distance from capillary center: exposure t h e , 1.5 s; eiectroklnetlc flow at pH = 7. Flow is from posltive to negatlve polarity.
nation. The reproductions of the video images shown in Figure 3 do not provide a large dynamic range. However, by using the built-in software of the CCD camera system, different contrast levels can be obtained on the video monitor for inspecting each streak. We find that the widths of streaks a and c are reduced somewhat when the contrast was lowered, but never approached the widths of streak b, d, or e. This implies that there is very little contribution from blooming to these widths. Also, these exposures correspond to charge accumulation well below saturation of the pixel capacities in the CCD, making the presence of blooming unlikely. For velocity measurements, only particle streaks with widths of the order of streaks b, d, and e are included. This guarantees that the radial distances can be determined by the y-axis positions, without the need for three-dimensional deconvolution. When particle tracks with intermediate widths (e.g., streaks a and c in Figure 3) are included, the trends discussed below are identical, but the standard deviations become larger. It is interesting to note that the particle streaks in Figure 3show very little motion in the radial (y) direction. Although there is some wandering from straight lines, the deviations are less than a few micrometers. This is expected from the much smaller diffusion coefficients of the particles (282-nm diameter) compared to small molecules. One can estimate from the Stokes-Einstein relationship that the diffusion coefficient of 282-nm particles in water at room temperature is around 108 cm2/s. This translates to a diffusion distance of 2 pm during the exposure time. The streaks also show small variations in thickness along their length. The effect is most pronounced for (e). This is consistent with motion in the out-of-plane ( 2 ) direction, replicating motion in the y-direction. These radial components of the velocity can be decoupled from the axial component (x-direction), which reflects hydrodynamic and electrokinetic flow. Figure 4 shows the velocity of particles measured for different radial positions under hydrodynamic flow. The uncertainty in reading the axial coordinates and from Brownian motion in the x-direction is around f 2 pm, as discussedabove. The parabolic velocity distribution is clearly evident. The average standard deviation from the theoretical line (eq 2) is 13 pm. These deviations cannot be attributed to inhomogeneities in the particles, since they should all be carried along equally by bulk flow. Rather, the observed deviations are related to the finite depth of field of the imaging system. By observing the internal capillary walls, which are evident in Figure 3.2, while translating the microscope objective via the fine-focusing knob, we estimate the depth of field to be f10 pm. With these error-bars superimposed, the fit in Figure 4 is quite good. It is interesting to note that
the deviations are smaller near the capillary walls (at f38 pm). The cylindrical tube actually confines the particles to a narrower range of depths around the focal plane there. While Figure 4 confirmsthe expected Poiseuille flow profiie and that our velocity measurements are valid, the determination of electrokinetic flow profilesis more of direct relevance to CE. Several subtle considerations are necessary. Hydrodynamic contributions must be completely decoupled from the electrokinetic velocities. In our experiments, even an extremely small pressure differential between the buffer vials at the ends of the capillary can cause motion in the micrometer per second range, as Figure 4 shows. We therefore balanced the hydrostatic heights of the buffer vials by adding buffer to one or the other vials dropwise while visually monitoring the particles. When balanced, no motion is evident on the several-second time scale. Only then are the electrokinetic images recorded. Another consideration is the distinction between electroosmotic and electrophoretic components acting on the particles. For neutral particles, electroosmoticflow generated by the capillary walls will carry them with the bulk liquid, identical to the case of neutral molecules. In the hypothetical case of particles made of the same material, i.e., having the same {potential, as the capillarywalls, they will not experience any net motion because electroosmotic flow generated by the walls is exactly compensated by the electrophoretic motion due to the net charge on the particles. So, it is the difference in {potentials on the surface of the particle and on the capillary walls that is relevant. Figures 5 and 6 show the velocity profiles of electrokinetic flow at pH = 7 and 3, respectively. At pH = 7, the carboxylate groups are expected to be completely ionized. At pH = 3, the carboxylate groups are expected to be mostly un-ionized. We can see from both figures that the electrokinetic flow profiles are essentially flat, confirming eq 1. The actual velocities can be calculated as 62 f 7 and -47 f 8 pm/s at pH = 7 and 3, respectively, and are independent of radial position. There is however a noticeable increase in velocity in Figure 5 near the capillary walls. For comparison, if only the middle 60 pm of the capillary is considered, the velocity in Figure 5 becomes 59 f 6 pm/s. Clearly, the curvature extends well beyond the electrical double-layer thickness, l / k . Our spatial resolution is insufficient to image the double layer region. Besides, the particles are too large to feel the double-layer directly. The edge effect here is not due to temperature gradients, since immersion of the capillary in a fluid should allow adequate heat dissipation. In addition, the amount of Joule heating here is 10-100 times lower than typical CE experiments because of the use of low ionic strength buffers and low
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ANALYTICAL CHEMISTRY, VOL. 65, NO. 20, OCTOBER 15, 1993 110
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From Figure 2A, we can determine that the electroosmotic flow rate (as generated by the capillary walls) is 182 pm/s in Figure 5, after correction for applied field and capillary length. This is assuming the f potential of the wall did not change between experiments. Thus, the net electrophoretic velocity of the particles must be (182 59) = 123 pm/s, from negative to positive polarity. Since the electroosmotic flow rate generated by the walls is negligible at pH = 3, the net electrophoretic velocity of the particles must be 47 pm/s, also from negative to positive polarity. These values reflect the differences in charge on the particles at the two pH's. These net charges provide some insight as to why Figure 6 shows a larger relative standard deviation than Figure 5. Inhomogeneities in the population of particles in terms of number of functional groups or size should lead to similar relative deviations. The particles in Figure 5 have more charged groups per unit area compared to those in Figure 6. So, the particles in Figure 6 have a reasonable chance of forming dimers and trimers, affecting the effective electrophoretic mobility and leading to a larger standard deviation. This is consistent with the observation that we were not able to go to even lower pH because the particles tend to precipitate out (i.e., form much larger aggregates) when they are totally devoid of charge. It is interestingto note that Figure 5 actually shows a smaller standard deviation than Figure 4. Since the flow profile is relatively flat in the former case, uncertainties in the radial position of each event (finite depth of field) cause smaller deviations from the general trend in the plot. In summary, we have been able to confirm the parabolic flow profiles in hydrodynamic flow and the flat (plug) flow profile in electrokinetic flow in CE. A slight edge effect is observed at pH = 7 due to slippage in the electroosmotic driving force a t the walla vs viscous drag of the particles in the opposite direction at the capillary axis. This may be an important consideration in optimizing CE separations of particles because the cumulative effect of the edge behavior is band broadening. One may therefore want to eliminate electroosmoticflow entirely if possible. Finally, since in these experiments one can confirm the absence of particle-wall interactions during observation, the results should allow the direct determination of f potentials of particles by electrophoresis.'B@
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RADIAL POSITION (MICRONS) Flguro 8. Scatterplot of streak length vs radial distance from capillary center: exposure time, 1.5 s;electroklnetlc flow at pH = 3. Flow is
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applied potentials. In fact, any temperature gradient would create higher temperatures along the axis and lower temperatures at the walls. This is contrary to the observation here that the velocities are actually higher at the walls. We can also discount particle-wall interactions19 as a possible explanation of this edge effect. Adsorptive interaction will retard rather than increase the velocity of the particles at the wall. There is also no evidence that any of the observed streaks (e.g., e) touched the walls inside the observation region. One explanation of the edge effect is the localization of the two electrokinetic driving forces. Electroosmoticflow, which is expected to be substantial at pH = 7 (and is confirmed in Figure 2), is generated at the capillary walls where the net excess charge is the highest. For our conditions,the particles, being negatively charged, are actually trying to move against the electroosmoticflow. Unlike small molecules, the particles and their counterions are so different in size that bulk flow is created in the direction of the electrokinetic motion of the particles due to viscous drag. The opposing forces will cause the bulk fluid in the center of the capillary to move somewhat slower than electroosmoticflow. The electroosmoticflow thus shows hysteresis from the wall toward the center of the capillary that extends well beyond the double-layer region. In Figure 6 (pH = 31, there is no clear edge effect present. Under this condition, the wall-generated electroosmotic flow is expected to be minimal, and so the bulk fluid behaves uniformly across the radius of the capillary. We note that this particle-specificedge effect is minor and the fraction of particles at the edge is low. This is probably why bandbroadening due to this edge effect has not been reported before.10-21 (19)Vanorman, B.B.;McIntire, G. L. J. Microcolumn Sep. 1989,1, 289-293. (20) Jones, H. K.; Ballou,N. E.Anal. Chem. 1990,62,2484-2490. (21) Peterson, S. L.; Ballou, N. E.Anal. Chem. 1992,64, 1676-1681. (22) VanOrman, B. B.; McIntire, G. L. Am. Lab. 1990, (Nov), 66-67.
ACKNOWLEDGMENT The Ames Laboratory is operated for the U.S.Department of Energy by Iowa State University under Contract No. W-7405-Eng-82. This work was supported by the Director of Energy Research, Office of Basic Energy Sciences,Division of Chemical Sciences, and the Office of Health and Environmental Research. Prints of video images were produced at the Image Analysis Facility, which is supported by the Iowa State University Biotechnology Council. RECEIVEDfor review May 12, 1993. Accepted July 16, 1993.'
* Abstract published in Advance ACS Abatracta, September 1,1993.
