Colloid characterization by sedimentation field-flow fractionation

Colloid Characterization by Sedimentation Field-Flow Fractionation V. Split Outlet System for Complex Colloids of Mixed Density H A R L A N K. JONES, K A T H L E E N PHELAN, M A R C U S N. MYERS, AND J. C A L V I N G I D D I N G S 1 Department of Chemistry, University of Utah, Salt Lake City, Utah 84112

Received November 3, 1986; accepted January 12, 1987 In this paper we report a new sedimentationfield-flowfractionation(sedimentationFFF) methodology which can be used to characterize complex colloidal populations whose particles vary in both diameter and density (or chemical composition). By this methodologythe outlet stream of the thin FFF channel is split along a specified flow plane to yield two distinguishable flow laminae whose contents enter two different outlet substreams.With a properlyadjusted carrier density, the population of colloidalparticles, driven by centrifugation, will divide into two subpopulations or classes, which move toward opposite channel walls and thus occupy different laminae. These subpopulations then undergo FFF migration and separation along their respectivewalls followed by elution into the two different substreams. This process yields the simultaneous fractionation and characterization of both subpopulationswith respect to density and particle diameter values. The theory of this new technique has been developed and applicability has been demonstrated by separating and characterizing a mixture of polystyrene and polymethyl methacrylate latex beads. © 1987AcademicPress,Inc. INTRODUCTION

Sedimentation field-flow fractionation (sedimentation FFF) has been shown in previous papers in this series to have unique capabilities for the fractionation and characterization of colloidal materials (1-4). It has been found to be possible to achieve high levels of resolution between unlike particles (5, 6) and to reduce run times to a few minutes (7). It has also been established that monodisperse colloidal populations can be accurately characterized with respect to particle diameter and density because of the accurate theoretical connection between physicochemical parameters and retention in the FFF system (1). The accurate characterization of the size distribution of m a n y polydisperse colloidal materials is also feasible (2-4, 8). This is made possible, foremost, because sedimentation FFF is a high-resolution fractionation technique which l To whom correspondence should be addressed.

gives cleanly isolated fractions for each small increment in size (9). These fractions are eluted from the system where their concentration can be monitored by sensitive detectors. The time of elution of each successive fraction is uniquely related by theory to particle size (or mass) and density (1). Thus for chemically homogeneous colloids, such as polystyrene or PVC latices, the particle size distribution can be accurately obtained (providing the detector response is calibrated) by taking advantage of the theoretical relationships (2). This capability extends to chemically homogeneous emulsions as well (3). While the above procedure is straightforward and highly effective for chemically homogeneous systems, m a n y colloidal materials, particularly of environmental or biological origin, lack the chemical uniformity needed for this simple approach. The characterization of such complex colloids is a major challenge in colloid science but suffers from a lack of

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0021-9797/87 $3.00 Copyright © 1987 by Academic Press, Inc. All rights of reproduction in any form reserved.

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applicable techniques. In the case of sedimen- elution time axis of the first run will then, in tation FFF, a problem arises in the fact that theory, provide rather complete information the retention time of a particle (the time re- on the size and density distributions of the quired to flush the particle completely through original sample. While reinjection FFF shows promise for the FFF flow channel) is a function of two parameters instead of just one: particle size the rather complete characterization of comand density. If both of these parameters vary plex colloids, its implementation is difficult. from particle to particle, as is typical for com- First of all, multiple runs are needed in order plex colloids of natural origin, then it is im- to obtain a thorough characterization. Second, possible within any collected FFF fraction to in order to collect enough material in the cut determine either size or density by the previ- to provide an adequate sample for detectability in the second run, the original sample injected ously mentioned method of calculation. The object of much of our recent work on for the first run must be considerably larger the characterization of complex colloids by than normal, threatening overloading. Consedimentation FFF has been to turn this ad- sequently, it is important to develop compleversity into advantage. While the concurrent mentary methods. The technique proposed here utilizes a sininfluence of two particle parameters (size and density) on retention is a source of compli- gle FFF channel with simple binary stream cation when both of these parameters vary splitting at its outlet (see Fig. 1). The flow is widely for a particle population, this com- divided into two substreams around a splitting plexity becomes an advantage provided means plane (Fig. l a). The position of the splitting are developed to isolate and identify the values plane is determined by the relative outflows of the two parameters. Where applicable, this of the two substreams. An outlet port at one approach yields a much more complete char- wall of the thin channel collects the substream acterization of colloidal species than those consisting of fluid material from the laminae based on a single parameter. In addition, since flowing between that wall and the splitting sedimentation FFF is a fractionation/elution plane while an outlet port in the opposite wall technique, fractions can be collected and sub- collects the fluid laminae from that side of the jected to additional characterization steps such channel. If appropriate conditions are estabas electron microscopy, elemental analysis, and the chromatographic determination of molecular constituents. One approach we have started to develop to penetrate this two-parameter complication is reinjection FFF (4). This technique requires F OW-_--7 . . . . that the operator collect one or more narrow cuts from the stream eluting from an FFF channel. These cuts then become samples to be reinjected into another FFF system or into the same system operating under different conditions (e.g., density of carrier). With an FLOW . ~ . ~ •..j appropriate second system, the measurement b of the elution time spectrum, when combined with elution time data from the first run, nO. 1. Edge view of two-outlet FFF systems showing should provide sufficient information to dethe splittingplane and, in (a), the divisionof stream planes termine both the size and the density distri- by the splitting plane into two distinct substreams. In (b) butions of the cut taken from the first run. the two particle subpopulations are undergoingFFF miThe reinjection of other cuts taken along the gration and separation along their respectivewalls.

L%oo.o, '

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lished, the particle population, as well, divides into two well-defined subpopulations, one undergoing FFF migration down one wall and one down the other (Fig. lb). These are captured by the corresponding substreams and outlets. A detector downstream from each outlet port monitors and characterizes the two subpopulations individually. In this exploratory study, we have employed a mixed colloidal latex material having particles of two different densities. The density of the carrier liquid is increased in succeeding runs until it reaches a level intermediate between those of the two subpopulations. Under these conditions the two particle types rapidly accumulate at opposite walls because of different relative buoyancies. The mechanism of this initial fractionation belongs basically in the sink-float family, but its completion is rapid due to the short transport path (~0.25 mm) and the augmentation of transport speed by centrifugation. Following the initial separation step in which the particles accumulate at their respective walls, each subpopulation is then characterized individually by the two simultaneous FFF processes occurring along the two walls. While this method requires that samples must have particles of only two distinct densities for exact characterization, in practice useful information can be gained provided the sample is divisible into two broad classes. For example, we anticipate that this technique wiU be valuable in characterizing colloidal particles in natural water when a carrier density is chosen that will effectively divide the particle population into inorganic and organic classes. From a single sprit-outlet run at an appropriate carrier density, one would then be able to estimate the inorganic/organic ratio and establish approximate size distribution curves for both classes. We note that the errors introduced by the finite spread of densities in each class could be reduced by making additional runs at different carrier densities and using statistical techniques to mathematically isolate narrower density ranges. Journal of Colloid and Interface Science, Vol. 120, No. 1, November 1987

The concept of outlet splitting in FFF channels was first applied to steric FFF operating with the aid of the earth's gravitational field (10). Steric FFF is a technique applicable to larger particles, generally over 1 t~m in diameter. For the relatively simple 1-gravity channels used for steric FFF in the cited example, it was possible to use a thin membrane stretched across the outlet end of the channel part way between the walls in order to physically split the flow laminae into the required substreams. This system was used solely to obtain enrichment of the sample in the lower outlet substream in order to enhance the detector signal. A subsequent paper outlined the advantages of using a split inlet as well as a split outlet (11). A splitting system has also been developed for flow FFF (12), but none has so far been utilized in sedimentation FFF. The latter requires a significant modification of the rotating seal system in order to accommodate both outlet substreams. The new seal system is described later. Beyond the extension of the split-flow concept to sedimentation FFF, the present project differs from the previous work by being the first to couple a simple but important binary separation process in which particles accumulate at opposing channel walls with FFF separation (and characterization) along both of those walls. We note, however, that the enrichment process studied earlier is a bonus to the present technique because each component is detected within a substream that represents only a fraction of the dilution of the full stream. Consequently where detectability is a problem, we anticipate that the ratio of flow rates in the two outlet substreams could be adjusted to maximally enhance the detector signal for the component or fraction of interest. THEORY The basic mechanism of FFF has been described elsewhere in considerable detail (1, 6). Briefly, the application of the field causes sample particles to accumulate at one wall

143

FIELD-FLOW FRACTIONATION

where a thin atmosphere or layer results from the balance between the accumulation process and the diffusion. The concentration profile, expressing particle concentration c as a function of the distance x from the accumulation wall, is found to be exponential, c = coexp(-x/l),

[ 1]

where l is the mean particle elevation, a measure of the layer thickness. We have D

l =/I'U -='

[2]

where D is the particle diffusion coefficient and U is the induced particle velocity. The retention parameter )`, which is a dimensionless term given by )` = l / w , assumes the following form in the case of sedimentation FFF (1), 6 kT )` - 7rwGlAp[d3 ,

[3]

where w is the channel thickness, kT is the thermal energy, G is acceleration, Ap is the density difference between the particle and the carrier, and d is the particle diameter for spheres or the effective spherical diameter for nonspherical particles. Alternately, )` can be expressed by substituting Eq. [2], in which [U] is replaced by sG, into the equation defining )`, )` = l / w , yielding D )` - w s G '

[4]

Once the steady-state distribution has formed, flow is initiated through the channel and the particles are carried downstream. Larger particles, which hug the wall more closely in accordance with Eq. [3], travel downstream more slowly than smaller particles (of the same density) which protrude further into the channel where the flow velocity is higher. Consequently, particles of a given density fractionate according to size. Any given particle size will be observed to elute after a certain volume, equal to the retention volume V;, has swept through the channel. The retention volume is related to the retention ratio R and to )` by R = ~ = 6)` coth ~-~ - 2), ,

[5]

where V° is the channel void volume. We note that it is generally advisable to allow all particles to reach the wall before flow is initiated. This requires a stop-flow period of duration equal to or greater than r

W

W

U

sG

[61

where r is called the relaxation time. When FFF is carried out in a split-outlet system, it is important to identify the coordinate position xs of the splitting plane which divides the flow into the two substreams (see Fig. 1a). The value of xs is determined by the flow rates of the two substreams. For outlet b the volumetric flowrate l)b is given by

where s is the sedimentation coefficient of the I)b = b v(x)dx, [7] particle. Values of)` commonly fall in the range 0.10.01, which means that l values are a small where the multiplier b is the (usual) symbol fraction of w. Thus the particles are concen- for the channel breadth and v ( x ) is the velocity trated in very thin layers relative to the channel of the stream plane at any coordinate x. A thickness. When the sample is eluted, these similar expression applies to outlet a. Simiparticles are again diluted with the carrier and larly, the volumetric flowrate V for the entire are sometimes difficult to detect. Clearly, if channel stream is equal to the outlet stream is split into two outlet sub~= b v(x)dx, [81 streams, these thin sample layers will be collected in just one of the two and thus concentrated for detection. where w is the channel thickness.

fo

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ET AL.

v(x)

If for we use the parabolic flow equation for a stream confined between fiat plates

If the splitting plane is near the midpoint between channel walls and the particle atmospheres are thin (small l values), the efficiency v(x)= 6 ( v ) ( X - ~2) [9] o f collection is virtually 100%, but otherwise a finite fraction of the particle population may the above integrals are readily evaluated. We extend beyond the splitting plane. In this case some particles are captured by the opposing get substream and eluted into the "wrong" outlet. In reference to Fig. 1, the fraction of parl)b 3/Xs/2 2/Xs/3 -f= kw][lO] ticles of the type that accumulate at the lower wall which are collected at outlet port b is given which gives the relative flow from the desigby nated outlet (either outlet may be used with the proper choice of coordinates) in relationship to the position Xs of the splitting plane. fb- w [11] A plot of reduced splitting coordinate versus l?b/I) is shown in Fig. 2. We must now determine the fraction of particles associated with one wall that will elute which represents the particle flux below the in the "proper" substream, that is, with the splitting plane relative to that for the entire substream collecting fluid from near that wall. channel. Following integration and the substitution of X for Eq. [11] becomes

fff c(x)v(x)dx

xJw

fo c(x)v(x)dx

l/w,

(X-2X2)+[(-~)2+2X(~)+2X2-(~)-X]e-x~/wx A=

(X - 2X2) + (X + 2X2)e-l/x

For highly retained species (X --~ 0),fb -'~ 1 as expected. For nonretained species (X --~ ~ ) , fb --~ l?b/I?, Eq, [101. The enrichment E of solute, which is directly proportional to the enhancement of the detector signal, is expressed as

[121

A modified rotating seal was necessary to keep the two flow streams separate. The flow from the outside wall was conducted through the seal assembly in the conventional way, while the flow from the inner wall entered the exit stationary shaft by a hole in the side of the A shaft and passed through a tube outside of and E = l?b/l?" [131 concentric with the normal exit tube. The When the solute is highly retained and flows were kept separate using another " O " J~ --~ 1, enrichment factor E assumes the sim- ring system at the downstream end of the staple form tionary shaft. E = V/l?b. [141 For the apparatus used in these experiments, the distance between the axis of rotation and the channel is 15.3 cm. The channel dimenEXPERIMENTAL sions are tip-to-tip length L = 90.5 cm, thickThe basic sedimentation FFF apparatus has ness w = 0.0254 cm, and breadth b = 2.0 cm. been described in detail elsewhere (6). For the The geometrical channel void volume was present system, the channel outlet flow was calculated to be 4.60 ml, the void volume split by providing an exit from the outside wall measured as the elution volume (less the exas well as the usual exit from the inside wall. trachannel volume) of a nonretained sodium Journal of Colloid and Interface Science, Vol. 120, No. 1, November 1987

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145

1.2

outlet flow rates in the experiments where carrier density was varied. The sample was injected onto the channel through a septum injector which was welded O.E .../ to the outside of the inner channel wall ring. IO.i ...'" Following injection, the flow was stopped for 20-30 min during which time the centrifugal >~ 0.4 .//i/"/ field was fully applied. This stop-flow procedure provides some margin for the relaxation // /of the sample, in which particles are trans0.2 / ported to the appropriate accumulation wall. (Calculations suggest that a time as short as 0.0 O. 0,2 0.4 0,6 0.8 0 10 min would normally suffice for the relaxation of the latex beads used here in dilute FIG. 2. Plots of the reduced splitting coordinate x~/w aqueous suspensions.) The flow was renewed and of the collectionefliciencyfcorrespondingto different X values as a function of the fractional flow rate term after the stop-flow period and the elution volume was monitored as the fluid filled a 50-ml Cb/~. burette calibrated to the nearest 0.1 ml. For the signal enhancement experiments, benzoate peak was 4.72 ml. The latter value the carrier liquid was distilled water which was was used for all calculations. deionized and purified further by a Barnstead The channel walls were made of a highly Nanopure filtration system. Following puripolished corrosion-resistant alloy, HasteUoy C. fication, 0.1% by volume FL-70 detergent from The channel spacer, sandwiched between the Fisher Scientific and 0.02% by weight sodium two metal rings constituting the walls, was azide were added to the water. The polystyrene made of Mylar and sealed with a 0.318-cm latex standard used in these experiments con(0.125-in.)-wide strip of Gortex gasket material sists of beads 0.364 # m in diameter acquired around its edge. from Dow Diagnostics (now Seragen DiagThe carrier liquid, held at 21 + 0.5°C nostics, Indianapolis, IN). Fluid from the outer throughout the run, was drawn through a 5- wall outlet passed through the seal assembly um stainless-steel frit MiUipore filter by a Gil- and directed into the sample cell of the detecson Miniplus 2 peristaltic pump. Following tor. This was immediately followed by either the pump, the carrier was driven through a the needle valve or the restrictive length of 0.22-#m cellulose acetate/nitrate filter, also narrow-bore tubing. The needle valve was opfrom Millipore, and then forced into the back erated manually to control and adjust the splitshaft of the sedimentation FFF system and outlet flow rates. The polystyrene latex susthrough the channel. After exiting the channel, pension, 10% by weight latex, was diluted 10effluent from each outlet was monitored by an fold and injected in 0.5-#1 volumes onto the Altex UV detector (Model No. 153) from channel. Beckman Instruments, operating with a merSucrose, used as the density modifier, was cury lamp filtered for 254 n m light. A dual added to the above carrier liquid for all expen strip chart recorder from Houston Instru- periments involving density variations. The ments (Model No. 5213-1) transcribed the re- carrier liquid density was measured by weighsponse from each detector. A needle valve was ing a filled calibrated 50-ml volumetric flask. installed on the outer outlet substream for the The volume of the flask was determined by signal enhancement experiments. A length of using purified laboratory water at a specified narrow-bore stainless-steel tubing was simi- temperature, and the mass of the modified sularly used as a constrictor to control the split- crose cartier was measured by difference. ~=0.01

U.-/'-

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JONES

A synthetic mixture of two narrowly distributed standard latices was used in all the density variation experiments. One is a 0.371#m polymethyl methacrylate (PMMA) latex bead with a reported density of 1.21 g/cm 3 provided by Dr. Theodore Provder of Glidden Coatings and Resins, a division of the SCM Corp. The second latex was a 0.620-#m polystyrene standard from Dow Diagnostics with a reported particle density of 1.05 g/cm 3. The PMMA suspension was reported to be 23% by weight solids, compared to 10% by weight for polystyrene. An initial mixture of the two latex suspensions was diluted 10-fold with cartier liquid and injected onto the channel in 10- to 20-pl volumes. RESULTS

AND

ET

AL.

100

b

a

%/~' = 0. 535 75

5D

r-

100 C

d

%/v = 0.253

Vb/V = 0.173

75

DISCUSSION 25

The 0.364-#m polystyrene latex bead was used to test splitting effectiveness and the postulated improvement of sample detectability due to stream splitting. Figure 3 contains a series of fractograms showing steadily increasing peak amplitudes with decreasing I?b]l/. (Since 17 is constant, the sequence is one of decreasing l)b). For these runs, the field was held at 46.3 gravities, the total volumetric flow rate I?was 1.05 ml/min, and the injection volume, 0.5 ~zl, contained approximately 5/~g of latex material. Figure 3a shows the "reference" fractogram obtained without splitting, with just the outer outlet (b) open. Figures 3a-3d illustrate the gain in signal as l?b/l)is decreased from unity to 0.173. A plot of enrichment factor E vs 12/12b is shown in Fig. 4. Also shown is the theoretical plot from Eq. [13]. The agreement is reasonably good for small values of 1)/Vb, but E fails to continue increasing as expected. Thus the signal enhancement due to splitting, although significant, does not match the theoretical gains. We now turn to the question of cross contamination, which is described by collection efficiencyf; q u a n t i t y f is related to enrichment factor E through Eq. [ 13]. Unexpectedly high levels of cross contamination not only reduce Journal of Colloid and Interface Science. Vol. 120, No. 1, November 1987

0

20

40

20 gO E]uLion Volume (ml)

4D

FIG. 3. Series of fractograms showing an increase in peak heightand area withdecreasingvaluesof l?b/12.Conditions: G = 46.3 gravities, 12= 1.05 ml/min. signal enhancement but also cloud data interpretation. Such cross contamination represents a failure to appropriately divide the particulate flux cleanly into two classes or subpopulations, each directed to its own outlet for collection and detection. In such circumstances the contamination of one subpopulation by particles from the other, normally negligible, will distort the detector signal and cause errors in the size distribution analysis. The level of cross contamination, which can be represented by the fractional loss 1 - f o f particles from their normal substream, can be estimated from the theoretical curves of Fig. 2. We have noted t h a t f r e m a i n s very close to unity for normal split ratios and for typical X values. Therefore the cross contamination term 1 - f should be near zero under most practical conditions. However, since we have found the enrichment E to be less than predicted, presumably representing an anomalous

FIELD-FLOW FRACTIONATION

147

in this vicinity constitute reasonable operating values for most anticipated studies involving two particle subpopulations. Only in the case when we need high enrichment levels of one b or the other particle subpopulation would we seek ratios close to zero or unity as opposed ta_ to ½. While the nonideal splitting efficiency observed above should not hamper split-outlet w 2 operation if flow conditions are carefully chosen, it is important to understand the origin of this anomaly in order to better define the 0 2 4 6 8 acceptable range of experimental operation ~/% and to find ways to avoid such anomalies in FIG.4. Plot of experimentalenrichmentfactorE (for)~ future instrumentation. Insight is provided by = 0.0279) vs 1)/12b along with the theoretical plot from another study involving a 1-gravity instrument Eq. [13]. for continuous particle fractionation using both inlet and outlet splitting (13). In this leakage of particles into the opposite sub- study, very good agreement was found bestream, we can likewise expect higher levels of cross contamination than predicted by theory for the present split outlet channel. ~o~, To examine the cross contamination q u e s - i i I o tion, a series of fractograms was obtained for Vb/V = 0.535 - - o u t e r wall both the outer and the inner wall outlets for - - - inner wall the 0.364-#m polystyrene latex bead at different split ratios. The results are shown in Fig. 5. Since the carrier is a dilute aqueous suspenr sion, the particles (density 1.05 g/ml) should 3 I! accumulate at the outer wall. Under the ex- ~ ~s perimental conditions of 46.3 gravities, we ~ I I I calculate X = 0.0279 from Eq. [3], which in ~ I0[0I conjunction with Fig. 2 suggests t h a t f s h o u l d I c i d be near unity and cross contamination should l Vbl7 = 0.039 I '{b/~' = 0. 0 1 3 be negligible. However, consistent with our b 7 2 -I I - - o u t e r wall IL - outer wall - - -inn~wall - - - in~r ~all anomalous signal enhancement results, we observe cross contamination in the form of a ~c measurable particle peak emerging from the inner wall substream. Figure 5 shows that the cross contamination becomes greater a s Wb/W 25 decreases. In addition, there is considerable I t I peak distortion at very low values of this ratio. 0 I I I 25 50 75 lO0 25 50 75 100 These results suggest that the present system Elution Volume (ml) would operate most effectively at a l)b/I? ratio FIG. 5. Series of fractogramswith superimposedinner in the vicinity of ½. A value of ½ represents a and outer outlet traces showingthe effectof decreasing symmetrical split of the channel stream be- values of l/b/12.Conditions:G = 46.3 gravities, 12= 1.05 tween the two eluting substreams. Split ratios ml/min.

0

/

Journal of Colloid and Interface Science,

Vol.

120, No.

1, N o v e m b e r

1987

148

J O N E S ET AL.

tween experimental measurements and theo- both particles (densities 1.05 and 1.21 g/ml) retical predictions. However, in this case split- sediment to the outer wall and undergo normal ring was achieved with the aid of physical FFF migration at that wall. The two nearsplitters, thin membranes stretched across the monodisperse components emerge together channel to divide the flow. We suspect that and form a single peak as shown by the figure. the present anomalies are due to the absence We also observe a small cross contamination of such splitting elements. Without the re- peak from the inner wall substream but its area straint of physical splitters, the flow near the is not sufficient to disturb our observations. channel extremities would be highly suscepIn Fig. 6b the cartier density has been intible to distortions. A rotational motion of the creased to 1.018 g/ml by the addition of sufluid as it approaches outlet ports not perfectly crose. This has the effect of splitting the mixaligned with one another is likely. This motion ture into its two components, both emerging would lead to a disruption of planar flow and at the outer wall due to normal FFF separato cross contamination. Our tentative conclu- tion. (If the colloidal materials were more sion, therefore, is that physical splitters, which polydisperse, one would have a broader fused have not yet been developed for the centrifugal peak whose interpretation would remain difsedimentation FFF system, will represent a ficult.) The shift in the position of the two more effective splitting system once imple- peaks in going from Fig. 6a to Fig. 6b is, of mented. course, most pronounced for the polystyrene Having now established the necessary con- latex because of the greater particle size and ditions for split flow in the present system and larger relative buoyancy effects. having earlier established the conditions reThe above trend continues as we proceed quired for successful FFF runs, we are in a to Fig. 6c, in which the cartier density, 1.054 position to combine these two operations. For g/ml, is close to that of the polystyrene latex, this purpose the synthetic mixture of 0.620- 1.05 g/ml. At this density the polystyrene /zm polystyrene latex beads and 0.371-gm beads are almost neutrally buoyant and conPMMA latex beads was injected into the sequently this latex material appears as a void channel for a series of runs in which the carder peak distributed between the two outlets. density was varied from 0.997 to 1.108 g/ml. Meanwhile the denser PMMA has shifted A series of fractograms resulting from these slowly left in the series, much less dramatically experiments is shown in Fig. 6. For these runs than polystyrene because of its higher density, the field strength was held constant at 27.4 1.21 g/ml. In Fig. 6d the carrier density has increased gravities (400 rpm). The total volumetric flowrate l? remained constant throughout to such a level (1.073 g/ml) that the polystythese experiments at 0.558 ml/min with the rene latex is forced strongly to the inner wall inner split flow rate I?a set at 0.239 ml/min while the PMMA is still retained at the outer and the outer split flowrate ~f~b equal to the wall. The two detector traces from the two difference, 0.319 ml/min. Using the outer wall outlets clearly reveal the constituent peaks, outlet (b) as a reference, this corresponds to a which would strongly overlap in a normal sinratio I?b/l? = 0.572, which is in the vicinity of gle-outlet experiment. Figure 6e continues this the rough guideline value of 1 stated earlier. trend with the polystyrene particles now thrust For these flow conditions Eq. [10] and Fig. 2 out beyond the gradually receding PMMA show that the reduced coordinate of the split- peak. The above experimental series demonstrates ring plane xs/w is 0.548. Figure 6a shows the fractogram obtained conclusively that one can split apart two denusing the aqueous carrier without the addition sity-based classes of colloidal materials and of sucrose. At this cartier density, 0.997 g/ml, study them independently. Once the binary Journal of Colloid and Interface Science, Vol. 120, No. 1, November1987

149

FIELD-FLOW F R A C T I O N A T I O N

l°°[ o 7s +a ~

r

p=o.+~;~,~, --~,+-.oH ---

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t

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-ii

25

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15

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45

100

60

75

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90 O

20 413 60 Elutlon Volume (ml)

~ 0=1"0739/®1 -

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I I l I I I I ~ 10 20 30 40 50 60 70 0 25 Elution Volume (ml)

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t 100

FIG. 6. A series of five fractograms shows the separation of a mixture of 0.620-ttm polystyrene and 0.371/zm P M M A latices achieved by an incremental increase in the density of the cartier. Superimposed inner and outer outlet traces show that separation first occurs by FFF along a single wall (b) and then, when the carrier density significantly exceeds the density (1.05 g/m1) of polystyrene latex (d and e), the two latex populations separate by going to opposite walls. Conditions: G = 27.4 gravities, l)" = 0.558 ml/min, 12b = 0.319 ml/min.

division has taken place the two subpopulafions can be characterized by FFF as elucidated earlier in this series of papers. The latter characterization will be demonstrated next. The retention volume V, was measured for each of the constituent peaks in the above series and the resultant values were converted into X values by means of Eq. [5]. These X's are predicted to be inversely proportional to the density difference dip (relative to the car-

rier) as shown by Eq. [3]. Thus X --~ ~ or X-1 __~ 0 as the carrier density p approaches the sample density Ps, at which point the condition is one of neutral buoyancy. Thus ps could be identified as the carrier density under neutrally buoyant conditions, which would be the carrier density yielding R = 1. Unfortunately, the precise density at which R = 1 is difficult to identify experimentally. Consequently, we use a plotting procedure similar Journal of Colloid and Interface Science, Vol. 120,No. 1, November1987

150

JONES ET AL. I. 25

\

\ \

.I S , s "~:3

X \

m

Polystyrene ]ate\ • OutQr outlet o inner outtQt ~s, /

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~ 2

I 50

t 75

X-~

I 10D

125

FIG. 7. Plots of carrier densityp against X-1 for PMMA and polystyrenelaticesproduce fineswhich yield the density and particle diameter values reported in Table II.

to that developed earlier to determine the size and density of single-component monodisperse populations. Our plotting procedure is based on a rearrangement of Eq. [3] to the form +{ 6kT /1 P = P s - k~rd3wG] X"

[ 15]

This equation suggests that a plot of carrier density P vs X-I would yield two straight lines with a c o m m o n intercept at particle density as and with a slope related to the particle diameter d. The line with the negative slope would correspond to particles undergoing FFF along the outside wall, while the positive slope would be associated with particles forced by buoyancy effects to the inside wall. In Fig. 7 we show the plots of this kind arising from the data accumulated in the runs shown in Fig. 6. Figure 7a shows a plot of the single line resulting from the data for the PMMA latex. Figure 7b shows the two lines obtained for polystyrene, which at different times accumulated at different channel walls. The data obtained from the slopes and intercepts of these plots are shown in Table I. We see that the agreement with reported values is quite good. However, uncertainties in the Journal of Colloid and Interface Science, Vol. 120, No. 1, November 1987

values reported for size and density parameters for most latices are sufficiently uncertain that it is difficult to tell whether the results from these plots are more or less accurate than the values with which they are compared (1). In particular, we note good agreement of the density of polystyrene beads from this study (1.046 and 1.047 g/ml) and values (1.050) from a previous study using a single outlet (14). The value 1.05 g/ml was provided by the supplier. The 0.557-#m particle diameter is approximately 10% below the supplier's value of 0.620 ~m. An earlier sedimentation FFF run on this same sample yielded d = 0.556 ~m, whereas quasi-elastic light scattering (QELS) gave us d = 0.605 ~m. There is some evidence that the QELS values may also be high, judging by the results obtained for the PMMA latex. TABLE I Particle Diameter d and DensityPs Obtained from a Mixture of Polystyreneand PMMA LaticesUsing a Split-Outlet Systemand the Plots of Fig. 7 Latex

Outlet

d (#m)

p, (g/ml)

Polystyrene Polystyrene PMMA

Outer Inner Outer

0.564 0.551 0.353

1.047 1.046 1.200

FIELD-FLOW FRACTIONATION TABLE II Diameter in Micrometers of PMMA Latex Beads Determined by Various Particle-Sizing Techniques This study 0.353

SdFFFa 0.371

Turbidity QELSb 0.357

0.413

TEMc

VSDCP a

0.292

0.351

"SdFFF, sedimentation FFF based on o = 1.21 g/ml. b QELS, quasi-electric light scattering. c TEM, transmission electron microscopy. d VSDCP, variable-speed disk centrifuge photosedimentometer.

151

been developed (2); for complex colloids we would simply have two fractograms as illustrated by Fig. 6, one for each of the two subpopulations. The acquisition of density data would then require some different strategy, such as taking a narrow cut from the elution stream and reinjecting this for another FFF run at a different carrier density. Such procedures are just now being developed but are beyond the scope of the present paper. CONCLUSIONS

For PMMA we obtained a density of 1.200 g/ml, which is reasonably close to the reported value of 1.21 g/ml. We found (Table I) a mean particle diameter 0.353 ~m for which, fortunately, there are a number of comparative values provided by other techniques. Table II summarizes the mean particle diameter for this sample obtained by six different methods. The sedimentation FFF results shown in the second column were obtained with several independent single-outlet measurements in which the value 0 = 1.21 g/ml was assumed. These values are compared with the results of four other measurement techniques applied to this sample by Dr. Provder and his colleagues at Glidden. We see from this table that transmission electron microscopy yields a distinctly lower d than sedimentation FFF, while disk centrifugation and turbidity yield comparable particle diameters. QELS, by contrast, gives the value 0.413 #m, which is over 10% higher than the values obtained from sedimentation FFF and higher also than values from the other three techniques. While it is difficult to resolve these anomalies at this time, we feel, based on past consistency, that the sedimentation FFF values are at least as reliable as those obtained from the other methods (1). The plotting procedure used in Fig. 7 is appropriate for relatively monodisperse populations but would be more difficult to apply for polydisperse distributions. The procedures for handling polydisperse distributions have

The particle diameters and densities obtained from the mixture of polystyrene and PMMA components are in reasonable agreement with those obtained from other sources. A further evaluation of errors will require, first, a closer look at the alternate particle sizing methods in that these methods fail to agree among themselves. We note that while our results are consistent with those obtained from other techniques, these alternate techniques are capable only of characterizing the isolated subpopulations, in some cases requiring near monodispersity, whereas in the split-outlet sedimentation FFF technique, values are derived directly from the colloid mixture. This fact illustrates the promise of split-outlet systems in dealing with complex colloidal materials. While the above results demonstrate the potential utility of split-outlet sedimentation FFF systems for the characterization of complex colloids, the present system did not yield the clean separation predicted for the two latex subpopulations. We believe that the low level or cross contamination observed would be largely eliminated by constructing a channel with a physical splitter at the outlet end. Such channels have not yet been developed for centrifugal FFF systems although we have made some advances toward this goal. ACKNOWLEDGMENT This work was supported by Grant D E - F ~ 2 86ER60431 from the Department of Energy.

Journal of Colloid and Interface Science, Vol. 120,No. 1, November1987

152

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