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Anal. Chem. 1980, 52, 1944-1954
ratory is continuing with the goal of extending this approach in these directions. LITERATURE CITED Lane, R. F.; Hubbard, A. T. J . Phys. Chem. 1973, 7 7 , 1401-1410. Brown, A. P.; Koval. C.; Anson, F. C. J . Electroanal. Chem. 1976, 72, 379-387. Oyama, N.; Yap, K. B.; Anson, F. C. J . Electroanal. Chem. 1979, 100, 233-246. Merz, A.; Bard, A. J. J . Am. Chem. SOC. 1978, 100, 3222-3223. Sharp, M.; Petersson. M.: Edstrom, K. J. Electroanal. Chem. 1979, 95, 123-130. Lenhard, J. R.; Rocklin, R.; Abruno, H.; Willman, K.; Kuo, K.; Nowak, R.; Murray, R. W. J . Am. Chem. SOC.1978, 100. 5213-5215. Evans, J. F.; Kuwana, T. Anal. Chem. 1979, 51, 358-365. Watkins. B. F.: Behlina. J. R.: Kariv. E.: Miller. L. L. J , Am. Chem. SOC. 1975, 97, 3549-3555. Firth, 8. E.; Miller, L. L.; Mitani, M.; Rogers, T.; Lennox, J.; Murray, R. W.J . Am. Chem. SOC.1976, 98, 8271-6272. Kerr, J. B.; Miller, L. L. J . Electroanal. Chem. 1979, 107, 263-267. Evans, J. F.; Kuwana, T.; Henne, M. T.; Royer, G. R. J . Electroanal. Chem. 1977, 8 0 , 409-416. Stargardt, J. F.; Hawkridge, F. M.; Landrum, H. L. Anal. Chem. 1978, 5 0 , 930-932. Wrighton, M. S.;Austin, R. G.; Bocarsly, A. B.; Bolts, J. M.; Haas, 0.; Legg, K. D.; Nadjo, L.; Paiazodo, M. C . J . Am. Chem. Soc. 1978, 100, 1602-1 603.
(14) Miyasaka, T.; Watanabe, T.; Fujishima, A,; Honda, K. J . Am. Chem. SOC.1978, 100, 6657-6665. (15) Fujihara, M.; Osa, T. Nature (London) 1978, 264, 349-351. (16) Lane, R. F.; Hubbard, A. T. Anal. Chem. 1976, 4 8 , 1287-1293. (17) Lane, R. F.; Hubbard, A. T.; Fukunaga, K.; Bianchard, R. J. Brain Res. 1976, 174, 346-356. (18) Heineman, W. R.: Wmck, H. J.; Yacynych. A. M. Anal. Chem. 1980, 52, 345-346. (19) Cheek, G. T.; Nelson. R. F. Anal. Lett. 1978. 11, 393-402. (20) McLean, J. D.; Stenger, V. A.; Relm, R. E.; Long, M. W.; Huller, T. A. Anal. Chem. 1978, 50, 1309-1314. (21) "Ammonia", Application Brief A-3: Princeton Applied Research Corp.: Princeton, NJ, 1974. (22) "Model 364 Polarographic Analyzer Operating and Service Manual"; Princeton Applied Research Corp.: Princeton, NJ, 1977. (23) Bond. A. M.; Canterford, D. R. Anal. Chem. 1972, 44, 721-731.
RECEIVED for review February 27, 1980. Accepted July 25,
1980. This research was supported by the National Science Foundation RIAS Grant No. 77-06911, by the University of ~ ~ ~ i Graduate ~ v i School, u ~ and by the university of ~ ~ ~ i ~ v Chapter of the Sigma Xi Scientific Research Society. The work was presented in part a t the 31st Annual Southeastern Regional Meeting Of the Chemical Society? VA, Oct 1979.
Sedimentation Field Flow Fractionation of Macromolecules and Colloids J. J. Kirkland," W. W. Yau, and W. A. Doerner Central Research and Development Department, Experimental Station, E. I. du Pont de Nemours and Company, Wilmington, Delaware 79898
J. W. Grant Photo Products Department, Experimental Station, E. I. du Pont de Nemours and Company, Wilmington, Delaware
Sedimentation field flow fractionation (SFFF) is a promising technique for the high-resolution separation and analysis of a wide variety of colloids and macromolecules. High-resolution separations of inorganic particulates, polystyrene latices, viruses, and biopolymers have been carried out as rapidly as 10 min. Force fields of 15000 gravities (12000 rpm) are obtained with present SFFF equipment, although full capability of the method awaits exploration with even higher force fields. Experimental results show expected SFFF band retention, but band broadening is greater than predicted by simple theory. Unidentified flow rate independent band broadening was confirmed by reverse-flow and recycle experiments. The influence of various experimental operating parameters on SFFF separations and band broadening had been determined. Practical aspects and potential for SFFF as an analytical and preparative method are compared with other separation techniques.
As previously described by Giddings et al. (1-3), separation of sample components by field flow fractionation (FFF) is the result of the differential migration rate of components in the carrier liquid mobile phase in a manner similar to chromatography. However, in F F F there is no separate stationary phase. Sample retention is caused by the redistribution of sample components under the influence of the applied field from t h e fast to the slow moving streams within the mobile phase. In this "one-phase" chromatography, solutes elute slower than the solvent front. 0003-2700/80/0352-1944$01 .OO/O
19898
A FFF channel consists of two closely spaced parallel plates, typically 0.025 cm, with mobile phase flowing continuously through the narrow gap with a characteristic parabolic velocity profile. Flow velocity is the highest a t the middle of the channel and the lowest near the surface of the parallel plates or the two channel walls. An external force field applied perpendicular to the channel walls pushes sample components to the slower moving streams near the outer wall away from the applied field. However, the buildup of sample concentration near this wall as a result of the applied field is resisted by normal diffusion in the opposite direction, resulting in a layer of component particles with an exponential-concentration profile. T h e extent of F F F retention is determined by solute concentration buildup near the outer wall and, therefore, the balance between the applied field strength and the opposing tendency to diffuse. In principle, the applied field in F F F can be of any type t h a t can interact with sample components to cause a component to move across the channel. Gravitational, thermal, electrical, or hydraulic (as in a cross-flow arrangement) fields have all been used by Giddings et al. (1-3) to illustrate fractionation. T h e work reported in this paper specifically concerns sedimentation FFF (SFFF). The principle of using a centrifugal gravitational force field for S F F F separations is illustrated in Figure 1. A long, thin (-0.025 cm), beltlike SFFF channel is made to rotate within a centrifuge. The resultant centrifugal force causes components of higher density than the mobile phase to settle toward the outer wall of the channel. Because of higher diffusion rates, smaller particles of equal density will 8 1980 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 52, NO. 12, OCTOBER 1980
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Flgure 1. Schematic representation of sedimentation FFF in a centrifuge.
accumulate into a thicker, more diffuse layer near the outer wall, relative to larger particles; on the average, larger particles are forced closer to the outer wall. This effect is illustrated in Figure 1,where l Aand t Bare the average layer thicknesses for the larger and the smaller particles, respectively. These exponential-concentration solute-layer thicknesses (and resultant S F F F retention characteristics) can be quantitatively predicted on the basis of field-diffusion balance relationships. T h e liquid mobile phase is fed continuously to one end of the channel and carries the sample components through for detection at the outlet. As suggested in Figure l, because of the shape of the laminar velocity profile and the placement of particles in that profile, solvent flow causes smaller particles to elute first, followed by a continuous elution of components in the order of ascending solute mass. T h e resulting elution profile or fractogram contains information that can be related to sample molecular weight or particle size distribution. Among the various FFF subtechniques, SFFF was selected for our study for several important reasons. SFFF is versatile, with a potential t o separate soluble macromolecules and particulates in the lo5 to 10l2molecular weight (g/mol) range. T h e technique fits current needs for a better method to characterize materials such as pigments, polymer dispersions, very high molecular weight polymers, and a variety of biological macromolecules. (Besides being a high resolution analytical technique, we find that SFFF can be used for preparative isolations-milligram to gram quantities-of macromolecules and particulates.) Furthermore, SFFF retention is based on simple physical phenomena that can be accurately described mathematically. In contrast to size separation by packed-column liquid chromatography, the SFFF method is very gentle for large particles because of the low shear forces and the low working surface areas in a S F F F channel. These features are particularly desirable for separating fragile biopolymers. T h e approximate relative resolution of FFF over a wide molecular weight range vs. that for other separation techniques for high molecular weight (or particle size) analysis is qualitatively illustrated in Figure 2. In contrast to most of the other methods, FFF resolution continues to improve as molecular weight increases. This is an important advantage, in addition to the high peak capacity of the method. As illustrated in Figure 2, FFF shows much higher resolution than hydrodynamic chromatography, HDC, or separation-by-flow, SBF, techniques that have been proposed for separating and characterizing particulates ( 5 , 6). SFFF also has significant advantages over existing nonchromatographic methods for determining the particle size distribution of materials in the 0.001-1 km range. In effect, SFFF is a flow-modified equilibrium sedimentation separation method. Solute layers that are poorly resolved under static equilibrium sedimentation become well separated as they are eluted by the laminar-flow profile in the mobile phase. Resolved SFFF peaks resemble those obtained by sedimentation velocity techniques (e.g., disk centrifuge). However, SFFF is simpler to operate, is more definitive in terms of quantitative d a t a interpretation, and is capable of a much larger particle fractionation range.
Figure 2. Relative resolution of analytical separation techniques. A qualitative comparison of the separating abilities of various methods as a function of sample molecular weight.
SFFF exhibits significant advantages over conventional nonseparation approaches for particle size distribution analysis. For example, light-scattering particle size methods are used for determining only the average particle size of a sample, not the detailed sample particle size distribution ( 7 ) . While microscopy and electrozone-sensing techniques are used to determine particle size distributions (7), these techniques are more tedious, require highly skilled operators, and usually involve more elaborate sample handling techniques than that required in SFFF. None of the existing particle size methods covers as wide a particle size range in a single analysis as SFFF. T h e intent of this study was to broaden the scope and improve the precision of existing S F F F technology. Faster, high-resolution SFFF separations were sought by constructing equipment with much higher fields than used by Giddings ( I , 4 , 12); practical analytical separations of less than 1 h were desired. Various operational pararneters were also studied to determine the manner in which convenient separations could best be performed; for example, procedures for sample injection were investigated and experiments for elucidating the basic band broadening mechanism and for exploring parameters important to preparative S F F F were developed. In addition, several applications of SFFF are described. Simple Retention Theory. For reader convenience we now give a brief review of S F F F retention theory so that a n adequate background is established for discussing the experimental results presented in the remainder of this paper. In the same manner as chromatography, SFFF retention can be expressed by the retention rat io, R, defined as the ratio of solute migration velocity to carrier solvent velocity. In terms of retention volume, R is expressed as ( I )
where Vo = the void volume (cm3)(i.e., the total liquid volume in the S F F F channel, including the volume of the sample injector a n d detector connecting tubes) and VR = the component retention volume (cm3). Experimentally, V , is the retention volume of an unretained peak (e.g., solvent impurity peak or peak resulting from a small amount of a low molecular weight solute that is purposely added for internal Vo calibration). Each retention volume is specified by a unique R value, which for retained peaks is always less than unity. Assuming that the particle distribution is near field-diffusion equilibrium, the concentration distribution near the wall is expected to follow an exponential profile ( I ) with a characteristic layer thickness 1, as shown in Figure 1. The mean or center of gravity for the entire exponential concentration profile is located a t this 1 distance away from the wall, and
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ANALYTICAL CHEMISTRY, VOL. 52, NO. 12, OCTOBER 1980
A=
A . O R P/W(RATIO OFSOLUTE LAYER THICKNESS TO FFF CHANNEL WIDTH1
Figure 3. Theoretical R vs. X plot for field flow fractionation
this characteristic thickness 1 directly influences component retention. By combination of the parabolic velocity profile and the exponential concentration profile, the following retention equation has been derived ( I ) :
R = 6X[c0th (1/2h) - 2A] X = 1/w
(2) (24
where, X = a dimensionless retention parameter, W = channel thickness, a n d coth ( x ) = ex + e-x)/(ex - e-x), with x in this case representing the quantity 1/2X. Figure 3 is a convenient plot for interconverting experimental X or R values. For retained peaks with R < 0.3 (components eluting a t least two channel volumes beyond the void peak V,,),retention can be adequately described by
R
E
6X
-
12A2
(3)
and
R
E
6X
(3a)
for highly retained peaks, indicating a simple linear relationship between R and X at small R values. Equation 2 is general for all F F F subtechniques with different kinds of force fields. More specific retention equations for each FFF subtechnique can be derived by expressing the characteristic thickness e in terms of relevant experimental parameters (1). By considering the steady-stage mass-transfer balance between the applied gravitational field and the opposing natural diffusion forces, Giddings has shown that in SFFF ( 1 )
A = - =e
w
ROT
Mw2rW(Ap/p,)
where k = Boltzmann constant (1.38 x g-cm'/(s2.deg)). (Note that k = RO/No.)As indicated below, these retention relationships appear to be valid for a wide range of particle types. R e t e n t i o n w i t h E x p o n e n t i a l F i e l d P r o g r a m m i n g . As suggested by eq 4 and 6, SFFF retention is linearly dependent on particle molecular weight and has a cubic power dependence on particle size. T h u s for a particular constant field force which adequately retains and resolves small components, elution times for large components often are excessive. As a result, when samples with a broad particle size or molecular weight range are analyzed, it is convenient (and often a practical necessity) to program a decrease of the force field during the SFFF separation. This approach causes earlier elution of the larger components, which saves analysis time and also improves detection sensitivity. Because of band broadening which leads to relatively low concentrations in the eluting peak, a highly retained component often is not easily detected when a constant force field is used during the separation. T h e same peak eluted under a decreasing field will be sharper and more concentrated for easier detection. Force field programming needs to be precise and accurate for predictable SFFF retention and quantitative interpretation of t h e fractogram. Previous SFFF force-field programming has been a step function or linear decrease in rotor speed ( I , 15). We find that field programming with a simple exponential decay is more appropriate for S F F F separations. With exponential decay, S F F F retention becomes nearly linear to the logarithm of molecular weight. This near log-linear molecular weight (or particle size) vs. retention time relationship can be conveniently used for accurate interpretation of SFFF fractograms in terms of sample molecular weight or particle size distribution, in much the same way as linear calibration curves are used in size-exclusion chromatography (8). With exponential programming, decrease in the gravitational force (rotor speed) can be controlled by a decay time constant T according to
where Go and G ( t )are the gravitational force fields at the start of programming and after time t , respectively. T h e time constant 7 is the elapsed time in the field programming for the field to decay to l / e times (or about 37%) of its original value. During field programming, the retention ratio R also becomes a function of time and varies according to the particular field strength a t the time, as
L = J t R R ( t ) ( u )dt 0
(4)
where Ro = gas constant (8.31 X lo7 g.cm2/(s2.deg.mol));T = absolute temperature (Kelvin), M = molecular weight of solvated macromolecules or particle mass of colloid dispersions (g/mol), w = centrifuge speed (rad/s), r = the radial distance from the centrifuge rotating axis to the SFFF channel (cm), Ap = density difference between sample component and mobile phase (g/cm3),and p s = density of the sample component (g/cm3). Field strength is measured by the centrifugal gravity which equals w2r. S F F F retention can also be related to the size of particles. For spherical particles
M = No(xdp3/6)p,
6k T 7rdp3uZr WAp
(5)
where N O= Avogadro's number (6.022 X mol-') and d, = particle diameter (cm). Using eq 4 and 5 , one can write
where t R = solute peak retention time (min), L = channel length (cm), R ( t ) = the time-dependent retention ratio, and ( u ) = average mobile phase velocity (cm/s). For well-retained SFFF peaks of relatively large t R , eq 2, 3, 7 , and 8 lead to the log-linear approximation of SFFF calibration (13)
In M = In A
+~R/T
(9) (10)
B a n d B r o a d e n i n g . Current quantitative theoretical predictions of SFFF band broadening are less supported by experiments t h a n those concerning SFFF retention. In the development of the S F F F band broadening theory, considerations have been given to the usual chromatographic band broadening processes ( 1 , 4 ) . Conclusions were quite
ANALYTICAL CHEMISTRY, VOL. 52, NO. 12, OCTOBER 1980
straightforward, indicating that there should be minimal effect of the eddy ( A term) and the longitudinal (23 term) diffusion contributions to SFFF band broadening. T h e theory of Giddings e t al. ( 4 ) suggests t h a t the only significant band broadening effect should result from the lateral nonequilibrium mass transfer of components between different velocity flow streams (similar t o the C term in the usual chromatographic equations for plate height H ) . In chromatography (and also in FFF), plate height H is proportional to the square of the peak width. Also, just as in chromatography, large H values in SFFF mean large undesirable band broadening and, therefore, poor separating efficiency. In SFFF the expected mass-transfer plate height has been expressed as (9-11)
1947
SOLVENT RESERMIR
Y
DETECTOR
ROTOR
-___-_-____---
, 1
Figure 4. Schematic of sedimentation fiekl flow fractionation equipment.
(11) where xi is the nonequilibrium mass-transfer coefficient, which is a complex function of X (and R ) , and D is the particle or solutesolvent binary diffusion coefficient. For highly retained sample component peaks (A and R
