Anal. Chem. 1002, 64, 3125-3132
ai25
Analytical SPLITT Fractionation: Rapid Particle Size Analysis and Measurement of Oversized Particles Chwan Bor Fuh, Marcus N. Myers, and J. Calvin Giddings’ Field-Flow Fractiomtion Research Center, Department of Chemistry, University of Utah, Salt Lake City, Utah 84112
I n SPLIR fractionation (SF), particles or molecules are separated rapidly by Ikkklrlven mlgratlon over a short (suknlllkneter) path lying across a ribbonlike flow cell having splitters at the ends. The outlet @mer separates components of high and low moMlitles, dlrectlng the fractlons to dtfferent outlet substreams for collection and measurement. The SF process, when run contlnuoudy, allows the scaleup of dtfflcuit separatlons. However, the rapid (often 1 pm in diameter to 10-30 min for high-resolution colloid or polymer fractionation. Analytical SPLITT fractionation (ASF), by contrast, can report continuously on an unbroken stream of suspended or dissolved sample, although it too can be fed discrete sample pulses if desired. However, rather than yielding a complete size or mass distribution (as does FFF) for each volume element of the entering sample stream, ASF divides the distribution into a small number of fiiite elements or %hannels”, each corresponding to a separate outlet substream. The cutoff between elements is controllable. The simplest and often most effective SPLITT cells are binary system that produce only two substreams, as shown in Figure 1. The suitability of ASF for analysis depends in part on whether the analytical problem can be adequately treated by the limited informational content of the two or more channels. In many cases such information is adequate. In these cases the high speed and the possibility for continuous SPLITT analysis would constitute significant gains in analytical capabilities. Even in those cases for which the limited informationof a single ASF run is inadequate, the high speed of ASF permits multiple runs in a short time period and thus the compounding of information as described below. One promising area where SF might be useful at both analytical and preparative levels is in the production, cleanup, and characterization of particulate materials from which
-
~
~
~~
(10) Giddings, J. C. Sep. Sci. Technol. 1992,27,148*1504.
0 1992 American Chemical Society
3120
ANALYTICAL CHEMISTRY. VOL. 64, NO. 24. DECEMBER 15. 1992
-L
.
i.,rncr rvblrcam
-;
b
frrriion b
Flgure 1. SchsmaHc dlagrarn of SpLITr call. Thickness 01 c s l l is exaggerated to illustratedifferenthltransport between wall A and wall E.
'oversized" particles (those exceeding a certain criterion diameter) must be rigorously excluded (or a t least reduced toverylowlevels) becauseoftheadverseeffectsthey produce. Examples include ahrasives," polishers,"J2 c o a t i n g ~ , ' ~ J ~ aerosols,'2 and injectable emulsion^.^' By setting the cutoff diameter d , of the SPLITT cell a t this criterion diameter, the oversize particles are isolated from their numerous small diameter counterparts, thus simplifying their detection and quantitation. The removal (and if desired the measurement) of oversize particles is highly efficient, and thus scaleup of the SPLITTcellis also promising for small- andintermediatescale preparative purposes. An analytical SPLITT cell could be used flexibly in several different ways for the determination of oversized particles. First of all, the ASF process could be readily automated using an autoinjector,giving in many cases thecapahility of making one or more determinations per minute on an ongoing basis. Alternately, ASF could be run continuously by tapping into a process feed stream. In this case, ASF would provide a continuous report on the oversized content of the stream. Undesirable shifts would be detected almost immediately because of the rapid response of the SPLITT cell. Another promising area where SF might be useful a t the analytical level is in the determination of particle size distributions. The mass of sample above a specified size can be obtained by measuring the relative content of the two outlet streams providing the cutoff diameter is adjusted to equal the specified diameter. This step is identical to that required to measure the relative amount of oversized particlea that exceed a specified criterion diameter. To obtain a full (cumulative) size distribution. this step must be repeated for a series of cutoff diameters. This multiple-step process is feasible because of the high speed of the individual steps. The throughput of a SPLITT cell is proportional to its length L and breadth b but independent of thickness w."' Thus the area bL of the cell can be increased (within limits) to accommodate throughput requirements. For analytical SPLITT fractionation, where information rather than fractionated material is the desired product, area bL and thus the overall size of the device can he reduced to levels dictated more by convenience than throughput. Accordingly, for this work we have constructed and utilized a miniature split cell many times smaller than any previously reported (see Figure 2).
For the work reported here, fractionation is achieved through differential transport in a gravitational field. However, a number of other transport mechanisms that have been proposed and in some cases utilized for preparative SPLITT operation could also be harnessed for analytical purposes. (11) Miller, B.V.; Lines. R. W. CRC &it. Reo. Anal. Chem. 1988.20, 75115. (12) Cadle, R. D.Porticle Sire; Reinhold Publishing: New York. 1965; Chapter 6. (13) Rump, H.Particle Technology; Chapman and Hall:New York, 1591; pp 1-15. (14) HerseyJ. A. InPortieleChometerirotionin Teehnology;Beddow. J. K.,Ed.; CRC Baea Raton, FL, 1984, Vol. 1, pp 69-79.
---
-/
b
S
'>
,.m
.~
Flgum 2. photograph of analytical SpLlTr cell used In ttmse sMles.
Alternate driving forces for transport include centrifugation, electrical force^,'^ hydrodynamic lift forces,%nd concentration gradient^.^ Using the appropriate force it should be possible to achieve rapid analytical fractionation based on differencesin sedimentation coefficient and size (aswereport here), density, electrical mobility, isoelectric point, and diffusion coefficient.
THEORY Figure 1shows the principles underlying the operation of asimple binary SPLITTcell. Due to theactionof theexternal field or driving force, particles or molecules are transported differentially across the thickness w of the cell, which in the experimental system reported here is only 0.38mm. Rapidly migrating particles are separated from those undergoing slower transport by means of an outlet splitter that divides the channel laminae into two outlet substreams, a and b. The effectiveness of the SPLITT process is enhanced by the active control of the positions of the inlet splitting plane (ISP) and the outlet splitting plane (OSP), a control gained hy varying the flow rates of inlet and outlet substreams. As shown in Figure 1, the ISP divides the sample-containing lamina originating a t inlet a' from the sample-free lamina whose source is inlet b'. When the volumetric flow rate of the suhstream entering b', V(b'), exceeds that of the substream entering a', V(a'), then the ISP swervea upward from the inlet splitter, compressing the sample feed lamina into a thin band ideal for initiating separation. The degree of compression is arbitrary as dictated by the flow rate ratio. The only negative effect of increasing the compression is its association with a low rate of feed input, which is proportional to V(a'), but this is of little concern for analytical SF. The OSP, dividing the thin ribbon of flow in the cell into the two laminae that eventually emerge as substreams a and b, is likewise controlled by the ratio of the outlet volumetric flow rates V(a) and V(b). It is, of course, necessary that the s u m of inlet flow rates equal the sum of outlet flow rates as (15) Giddings. J. C. J. Chmmotogr. 1989.480.21-33.
(16) Ciddinps, J. C. Sep. Sei. Teehnol. 1988,23. 119-131
ANALYTICAL CHEMISTRY, VOL. 64, NO. 24, DECEMBER 15, lQQ2 8127
expressed by
The use of eq 1gives the alternate expression
+
V(a’) V(b3 = V(a) + V(b) (1) Sandwiched between the ISP and the OSP is a thin film of liquid termed the transport lamina. As the particles enter the cell and pase beyond the inlet splitter, they are gradually driven into this transport lamina by the applied field. However, as made clear by Figure 1,particles must be driven across the entire thickness of the transport lamina in order to emerge from outlet b. Particles whose field-driven migration is too slow to allow passage through the transport lamina in the c o m e of their residence in the cell fail to penetrate through the OSP and thus emerge from outlet a. Because of the thinness of the compressed feed lamina and the uniformity of the transport lamina, a fairly sharp cutoff in migration velocity distinguishesthe particles emergingfrom outlets a and b. If the field-induced velocity depends upon particle size, as is the case for sedimentation, this cutoff velocity can be translated into a unique value of the cutoff diameter d,. The theory definingthe cutoff diameter has been described in previous publications.2J0 It is assumed that particles are driven a t constant velocity U from wall A to wall B during their residence in the SPLITT cell. Aa a consequence of this uniform transport, the particles are driven across a thin filament of the flowing liquid. The volumetric flowrate of the filament traversed by the particles is given simply by2
AV = bLU
(2)
where b is the breadth of the cell and L is its length as measured between the inlet and outlet splitting edges. When transport is driven by gravity or a centrifuge, U is given by
U=sG (3) where s is the sedimentation coefficient and G is the field strength measured as acceleration. For spherical particles of diameter d , s is given by (4)
where p p is the particle density, p is the carrier density, Ap is the density difference, and 11 is the carrier viscosity. The substitution of eqs 3 and 4 into 2 shows that for sedimenting particles AV = bLsG = M A p d 2 (5) 181 Of critical importance is the relative magnitude of AVand V(t),the latter being the volumetric flow rate of the transport lamina. For present purposes, we assume that all particles for which A V > V(t) will emerge from outlet b. Particles of lesser AV, such that A V < V(t), will emerge from outlet a. Therefore the cutoff value of A V is given by AV, = V(t)
(6)
The cutoff value AVCspecifies the cutoff particle diameter d,. Thus from eqs 5 and 6 (7)
and d, is therefore expressed by (8)
The volumetric flowrate of the transport lamina given by (see Figure 1)
V(t) = V(a) - V(a’)
V(t) is (9)
V(t) = V(b’) - V(b)
(10)
The substitution of eq 9 (or one can use eq 10 ifprefered) into eq 8 yields
(11) In principle, all particles smaller than d, exit outlet a while larger particlee exit b. Clearly, d, depends upon particle density p p because of the influence of p p on sedimentation velocities. Thus a unique value of d, can only be established for particles of uniform density. As shown by eq 11, the cutoff diameter can be readily adjusted or altered by changing the volumetric flow rates of substreams a and a’. Somewhat less flexible means for controlling d, include altering the SPLI’M’ cell dimensions b and L, changing the field strength G (through tilting the cell on end or applying a centrifugal force), using an additive to change p , or varying the temperature to change viscosity. In addition, we note that the same basic methodology can be used both for floating particles as for sinking particles except in the former case the feed substream a’ would be introduced adjacent to the wall of lowest gravitational potential. While eq 11gives a unique value for the cutoff diameter, there w i l l actually be a small range in diameters that divide between outlets a and b.l0 This range is introduced by imperfections in the system, particularly in the splitters, and sometimes in the measurable displacement caused by Brownian motion. In addition, we note that eq 11slightly underestimates the true cutoff diameter because in reality particles must migrate somewhat further than the distance between the ISP and the OSP to gain outlet b. The additional distance depends upon the initial position of a given particle within the compressedfeed lamina. Sinceparticles sediment toward the inlet splitter between the time of their entrance a t inlet a’ and the time that they reach the splitter edge, conditions can be adjusted such that particles in the critical diameter range sediment to the surface of the splitter before the two inlet substreams are merged. (Such conditions apply in the present experiments.) In this case the incremental migration distance is only slightly larger than a single particle radius, leading generally to only a small perturbation in the cutoff diameter relative to the value given by eq 11. Although eq 11fixes the flow rate difference V(t) = V(a) - V(a’) once d, is chosen, the four constituent flow rates (two in and two out) are not rigidly fixed by the above equations, leading to additional flexibility in operation. Some criteria for choosing these flow rates has been discussed in a recent paper on the optimization of SPLI’M’ operation.1° Briefly, we require V(a’)
