Anal. Chem. 1986. 58,2052-2056
2052
doubtly more suitable for trapping very polar compounds from water than a chemically modified silica. The reusability of the GCB cartridge was evaluated by doing repeated extractions of phenols from water on the same cartridge. After each extraction the column was restored with 3 mL of methanol and 5 mL of water. After five such concentrations the recovery of the 11 phenols considered was unchanged within the precision of the method. The sole effect observed was that by sampling more than 1 L of water each time, the flow rate was progressively decreased from 32 to 14 mL/min. Registry No. HzO, 7732-18-5;p-nitrophenol, 100-02-7;2,4dinitrophenol,51-285; o-nitrophenol,8875-5; 2,4-dimethylphenol, 105-67-9;4-chloro-m-cresol,59-50-7;2,4-dichlorophenol,120-83-2; 4,6-dinitro-o-cresol, 534-52-1; 2,4,6-trichlorophenol, 88-06-2; pentachlorophenol, 87-86-5; phenol, 108-95-2;o-chlorophenol, 95-57-8. LITERATURE CITED (1) Saner, W. A.; Adamec, J. R.; Sager, R. W. Anal. Chem. 1979, 57, 2180-2 188. (2) Shoup. R. E.; Mayer, G. S. Anal. Chem. 1982, 5 4 . 1164-1169. (3) WerkhovenOoewle, C. E.; Brinkman. U. A. Th.; Frei, R. W. Anal. Chem. 1981, 53, 2072-2080.
(4) Rostad, C. E.; Pereira, W. E.; Ratcliff. S. M. Anal. Chem. 1984, 56, 2856-2860 -- - - - - - - .
(5) Bacaloni, A.; Ooretti. G.; Lagan& A.; Petronio, B.; Rotatori, M. Ana/. Chem. 1980, 52, 2033-2037. ( 6 ) Mangani, F.; Crescentini, G.; Bruner, F. Anal. Chem. 1981, 53, 1627-1631. (7) Andreolini, F.; Di Corcia. A.; Lagan& A.; Samperi, R. Clin. Chem. (Winston-Salem, N.C.)1983, 29, 2076-2078. (8) Andreollni, F.; Borra, C.; Di Corcia, A.; Samperi. R. J . Chromatogr. 1984, 370,208-212. (9) Andreolini, F.; Bora, C.; Caccamo, F.; Di Corcia, A,; Samperi, R. Clin. Chem. (Winston-Salem, N.C.)1985, 3 7 , 1698-1702. (IO) Di Corcia, A.; Samperi, R.: Sebastiani, E.; Severini, G. Anal. Chem. 1980, 52, 1345-1350. (11) Reallni, P. A. J. Chromatogr. Sci. 1981, 19, 124-129. (12) Campanella, L.; Di Corcia, A.; Samperi, R.; Gambacorta, A. Mater. Chem. 1982, 7 , 429-438. (13) Kornblum, N.; Berrigan, P. J.; Le Noble, W. J. J. Am. Chem. SOC. 1963, 85, 1141-1147. (14) Kiselev, A. V.; Yashin, Y. I. Gas-Adsorption Chromatography; Plenum Press: New York, 1969. (15) Ciccioli, P.; TaDDa, . . R.; Di Corcia, A.; Liberti. A. J. Chromatogr. 1981, 206, 35-42. (16) Ross, S.; Olivier, J. P. On Physical Adsorption; Wiiey: New York, 1964. (17) Snyder, L. R. Principles of Adsorption Chromatography;Marcel Dekker: New York, 1988.
RECEIVED for review December 9, 1985. Accepted April 7, 1986.
Cyclical-Field Field-Flow Fractionation: A New Method Based on Transport Rates J. Calvin Giddings Department of Chemistry, University of Utah, Salt Lake City, Utah 84112
A new form of field-flow fractionation (FFF) Is described In whkh the flew strength Is cycled up and down many times during a run. I t is shown that thk method, termed cyclical FFF (CFFF), leads to rnlgmtion rates depmwht on transport coe(fickrds. AHu devekpment of the general theory, resdts are obtained for coherent (no dmuslon) squarewave operation. For the latter, migration rates are shown to depend on the generalized mobility of the partldes and upon system parameters such as cycle time and fleM strength. Other varlants of CFFF are noted and several advantages are Indicated. A gravttathal CFFF system operating according to sedhrentatkm coemclents Is described and certain programming options are discussed.
Field-flow fractionation (FFF) is mainly an analytical separation tool, providing convenient operation and high selectivity for the separation of macromolecules, colloidal particles, and larger particles up to 100 hm diameter (1-6). A major advantage of FFF is that migration rates through the thin FFF flow channel can be rather exactly related to the various physicochemical parameters of the particles such as particle mass, charge, diffusion coefficient, etc. (7);thus, these latter parameters can be conveniently and accurately determined by observing the time at which the particles are eluted from the system. For polydisperse particle samples, one can measure the corresponding parameter distribution curves, e.g., the mass or molecular weight distribution curve (8).
With the exception of the subtechnique of flow FFF, most variants of FFF have migration rates that depend upon equilibrium or particle-specific parameters such as mass, density, thermal diffusion factor, charge, etc. With flow FFF, migration velocity depends on the fundamental transport parameter termed the friction coefficient, which can be expressed as a diffusion coefficient through the Plank-Einstein equation (2, 9). However, flow FFF is difficult to apply in a calculable way to particles much over 1Fm diameter because of steric effects (10,II). Often, it is useful to characterize the transport of larger particles. For example, sedimentation processes, involving mainly larger particles, have deposited much of our earth's surface and even now are responsible for the deposition of many toxic materials adsorbed on particles. To fully characterize such sedimentation processes, one needs access to the distribution of sedimentation coefficients within a particulate sample. The method detailed below should provide a convenient means for measuring distributions of such coefficients and, in principle, other transport coefficients as well. Normal FFF is based on the formation of a steady-state cloud (see Figure 1)whose effective thickness 1 is determined by the balance between the field-derived forces pushing the particles toward the accumulation wall of the channel at velocity U (absolute velocity IUl), and diffusion, measured by coefficient D, acting to disperse the particle cloud. It is found that 1 is the ratio of these two coefficients (12) 1 = D/lUl (1) Ordinarily, both D and IUl are inversely proportional to the
0003-2700/88/0358-2052$01.50/00 1986 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 58, NO. 9, AUGUST 1986
Flgure 1. Particle clouds in (a) normal FFF and (b) cycllcal-field FFF (CFFF). I n the former case, the mean or effective distance I of the cloud from the wall remains constant as mlgratlon proceeds. With CFFF, I undergoes cyclical changes caused by variations in field strength.
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of different stationary (equilibrium) or near stationary lateral distributions established for different particles. In CFFF, the lateral distributions are not stationary-in fact, they are frequently far from equilibrium-because of the varying S. However, if the time average of the distributions over one or several cycles remains constant throughout the run, the operation may be described as pseudostationary. The exception to the pseudostationary condition is programmed operation in which average conditions would vary gradually as the run progressed.
THEORY t
a
The theoretical description of migration rates in CFFF is a two-step process. First, one must find the lateral concentration distribution and its time dependence, c(x,t). This can be obtained as a solution to the lateral transport equation C
TIME
-
Flgure 2. Plot of various forms of periodic variation of field strength S with time.
particle friction coefficient f, thus canceling out the effect of this basic transport parameter. Only in flow FFF is I q determined independently (by the cross-flow rate), leaving l to depend solely on transport parameters D and thus f (13). Since cloud thickness 1 determines how far, on average, the particles protrude into the flow stream, and thus how fast they are carried down the channel by the parabolic flow profile, relative migration rates are controlled by 1 and are thus determined by the same factors governing l (2). In cyclical-field FFF (or simply CFFF), the field strength S is to be varied up and down many times in the course of a run, often in some periodic fashion with time. The cloud of sample particles will move up and down (see Figure 1)in response to the ebb and flow in S. With S variations of sufficiently high frequency, equilibrium, if reached at all, will be temporary. The average protrusion of particles into the flow stream will depend in part on the rate of relaxation between equilibrium distributions dictated by different S values. With a well-designed pattern of field variation and with appropriate frequency, migration rates will depend in a major and generally calculable way on the relevant transport parameters. A nearly infiiite number of periodic field variations can be imagined. A few of these are shown in Figure 2. One could, in principle, use different intervals (chosen randomly or systematically) between successive field variations, and/or different step heights between successive maxima and minima, to extend the particle size range or otherwise manipulate the distribution of elution times. The mean value of S or the frequency of i h variation averaged over one (or several) cycles could be held constant, or it could be systematically varied according to a selected program, giving programmed CFFF. We should note that the most useful cycle times for field variations will be roughly the same order of magnitude as the relaxation times required for the particles to pass from one equilibrium state to another. This guideline is a very approximate one, however, first because one may have reason to choose cycle-times several times lower or higher than the relaxation times, and second because the relaxation times themselves may vary substantially for different kinds of particles in the sample. Also, the two steps of a field-variation cycle may have substantially different relaxation times. In general, the cycle time will be smaller, usually much smaller, than the run time of the experiment. The CFFF technique represents a significant departure from the other major FFF techniques, including normal FFF, steric FFF, and hyperlayer FFF (14). With the latter techniques, longitudinal (flow axis) separation takes place by virtue
using appropriate boundary conditions and accounting properly for the time variations in the field-induced particle velocity U . For normal FFF, which can be assumed to proceed under steady-state or stationary operation, which is defined by & / a t = 0, the solution c(x,t) depends only on the ratio D / U of the transport coefficients in eq 3. Thus, for the typical thin parallel-plate channel where U is negative, U = -I& the stationary solution is
(3) where c, is the concentration at the accumulation wall at x = 0 and where 1 = D / l Q as defined in eq 1. As pointed out in the introduction, dependence on the ratio D/lV of transport coefficients is tantamount to canceling out one transport effect against another. However, when & / a t remains finite as in CFFF, then c ( x , t ) retains a dependence on the individual coefficients D and U, giving a transport-based concentration profile. The field-induced transport velocity U is proportional to the force F exerted on the particle by the field, a fact expressed by U= F / f (4) c = c0e-x/~
where f is the friction coefficient; however, force F is proportional to the field strength S according to
F = 4s
(5)
U = # S / f = mS
(6)
yielding where 4 is the field-particle interaction parameter and m is a generalized mobility. This equation shows quantitatively how the variations in S give rise to the variations in U that in turn give a net transport dependence to eq 2 and its solution c(x,t).
We note that both eq 3 and solutions c ( x , t ) we seek for nonstationary operation do not account for the small disturbance in concentration caused by differential flow in the channel. The latter "nonequilibrium"effect is responsible for zone broadening (12),a subject beyond the scope of the present work. An important concept in the operation of CFFF is one we will describe as coherence. With coherent operation, a population of identical particles starting a cycle at a certain distance from the accumulation wall will travel together without significant diffusion, each remaining the same distance from the wall as the others. This coherence in lateral motion is analogous to a form of coherence found in field-based separations such as electrophoresis. The relative compactness
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ANALYTICAL CHEMISTRY, VOL. 58,NO. 9, AUGUST 1986
induced by unitlfield strength
m = U/S
TIME
+
Figure 3. Lateral particle coordinate x' as a function of time for coherent square wave particle displacement over one cycle.
of particle zones in the latter case is measured by the number of theoretical plates, expressed by the ratio of energies (15)
N = FX/kT
(7)
Thus, when the field-derived force F multiplied by the displacement distance X is large compared to thermal energy kT, N is large and identical particles remain relatively close to one another during displacement with little dispersion. For the succession of lateral displacement steps described here, coherence can also be described by the ratio in eq 7 , with X the appropriate displacement distance for any step being described. Once c(x,t) is obtained as a solution to eq 2, we proceed to the second step in which the average downstream particle velocity at time t is expressed as
Y, =
su x=o
(8)
u ( x ) c ( x , t ) dx
where u ( x ) is the carrier velocity at lateral position x and w is the channel thickness; the concentration distribution c ( x , t ) is assumed to be normalized, Le., S O W c ( x , t )dx = 1. The distance the particle cloud is carried in the course of one cycle of duration 7, is then
2, =
1"2', dt t=O
=
srcju' t=o
x=o
u ( x ) c ( x , t ) dx
dt
(9)
The average velocity Y is then obtained as the ratio
in accordance with eq 6. For electrical fields, S is the electrical field strength E and m becomes the electrophoretic mobility H. With a centrifuge or gravity producing an acceleration G in place of S, m becomes the sedimentation coefficient s. Other specific mobilities are similarly incorporated within this general treatment. With a lateral velocity of U = mS,the lateral position of the particle as a function of time (as shown in Figure 3) is given by x ' = Ut = mSt ~ , / 22 t 2 0 (12) x ' = U(T,- t ) = mS(r, - t )
EXAMPLE: COHERENT SQUARE-WAVE OPERATION We will illustrate CFFF operation with S taking the form of a square wave alternating between the fixed levels +So and -So. This square wave function is illustrated by line b in Figure 2. We will assume that particles of any given type start a t the wall (x = 0) at the beginning of a cycle, penetrate into the channel a distance lo during application of the +So field, and then fall back after S is switched to -So, returning to x = 0 as the cycle ends after time 7,. We further assume that 7, is sufficiently short that lo < w for the most mobile particles; i.e., particles do not come to rest at the opposite wall. The lateral particle coordinate for these conditions is shown as a function of time in Figure 3. Because the particle displacement is assumed to be coherent, the coordinate-time plot of Figure 3 consists of straight line segments, with no irregularities due to Brownian motion. Different particles will penetrate to different distances lo because of unequal transport rates. We will express this in terms of the generalized mobility m, defined as the velocity
T
2 t 2 r c / 2 (13)
The simplicity of these expressions is due to the assumed coherence;with coherence, the concentration distribution c(x,t) of the last section, obtained with D = 0, becomes a d function d(x1 in which all like particles are shown to travel together with lateral coordinates as described by eq 12 and 13. For the motion described above, the maximum lateral extension lo, reached a t time r c / 2 , equals
lo = U r c / 2 = mSr,/2
(14)
Thus, the dimensionless retention parameter Xo = lo/w, analogous to the retention parameter X = l / w in normal FFF, becomes Xo = UrC/2w= mSrJ2w
(15)
Equation 14 shows that the particles that have the greatest mobility m penetrate into the channel the greatest distance 1,; these are carried down the channel most rapidly by the carrier stream. The higher average velocity of more mobile particles is due to the fact that the carrier flow velocity u normally increases with increasing distance x from the wall according to the parabolic expression U(X)
Different values of velocity Y for different particles stem from differences in c(x,t); these lead to differential elution and thus particle separation. The above general formulation should be applicable to all cyclical forms of S and to all kinds of macromolecules and particles; however, the application is most simply illustrated by a case involving the coherent displacement of particles subject to a simple square-wave variation in S.
(11)
(; ;:>
= 6 ( ~ )- - -
where ( u ) is the average velocity in the channel and w is the distance between channel walls. The longitudinal particle displacement 2,in one cycle can be expressed as the following simplification of eq 9:
2, = &"u(x')
dt
(17)
obtained by writing c(x,t) in eq 9 as 6(x'). The step length 2, consists of two equal parts, corresponding to the two segments shown in Figure 3. Thus, we can write 2, = 2 & T c ' 2 ~ ( dt ~)
(18)
Changing the variable of integration from t to x'using eq 12, we obtain
The substitution of eq 16 into this expression followed by integration and the use of eq 14 and 15 gives
The average downstream displacement velocity ?I can be written in the form of eq 10
ANALYTICAL CHEMISTRY, VOL. 58, NO. 9, AUGUST 1986
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the retention ratio R, defined as Y/(u) becomes
-
R = 3,,(,
$)
For small Xo values, R approaches the limit 3X0, in contrast to the 6X limit for normal FFF, when Xo increases to 0.75, R reaches its maximum level of 1.125. Then, as expected, R falls back to unity for X, = 1; this X, represents the maximum allowed excursion of the particle involving a path over the full channel thickness in which the particle samples all streamline equally. A direct relationship between R and generalized mobility m results when eq 15 is substituted into eq 22
v ,
\ I 0 0
I.o
I
I
2.0
3.0
4.0
TFigure 4. Plot of retention ratio R and mobility-based selectivity S , vs. dimensionless cycle time T for coherent square wave operation.
For sufficiently small 7 , values, this approaches the limiting form 3mSrc 2w
R=-
R=3T(l-Y)
Thus, the particle velocity, in this limit, is proportional to mobility m. The mobility-based selectivity (11) becomes
s,=
:1 I:
-
=
This selectivity, representing the ratio of the relative change in displacement (proportional to R) to a given relative change in m, is the same as that for direct field-displacementmethods such as centrifugation and electrophoresis but has the advantage of being incorporated in an elution system. Along with simplified detection and sample collection, elution systems provide more flexibility in manipulating separation speed as a trade-off with resolution. The thin-channel FFF configuration is also highly favorable for reduced convection. For larger T,, eq 23 must be used in place of the linearized form eq 24. Equation 23, of course, is a form of eq 22 and, like the latter, yields a maximum R of 1.125, this occurring for T~ = 3w/2mS. At the maximum, selectivity vanishes. If rc is restrained so that particles are never allowed to come to rest at the opposite wall, as postulated at the beginning of this section, then it must be limited by the maximum value rc* = 2w/mS
(26)
which corresponds to Xo = 1 in eq 15. It is interesting to extend the above treatment to include the case where particles arrive at the opposite wall before the field is reversed. In this case, the more mobile particles cross the channel in the shortest time, equal to rC*/2. Compared to more sluggish particles, they spend more time at the walls and less in the channel between where the downstream displacement takes place; thus, they migrate more slowly down the channel. The resultant R value is the time-weighted average of the value R = 1 experienced while in transit (time T,*) across the channel and R = 0 (ignoring steric migration) during the remainder of the cycle time rc - T,* spent at the wall. Thus
R = i C * / r c= 2w/mSr,
With this, the R value in the two ranges is obtained in simple form from eq 23 and 27
r C2
rc*
(27)
Here, with m in the denominator, R takes an opposite dependence on m compared to the case described by eq 24. In either limiting case, the selectivity is unity. The two distinct cases, T , Q T,* and T , T,*, can be best summarized by defining the dimensionless cycle time T = T,/T,* = mSrC/2w (28)
R = 1/T
TG1
T >1
(30)
These functions, which dovetail together at T = 1, are plotted in Figure 4. Also plotted is the selectivity S,, which, using eq 25,28, 29, and 30, can be shown to equal
S,=1
T a l
(32)
DISCUSSION There are many possible experimental arrangements and applications of CFFF. While our treatment, for theoretical simplicity, has focused on methods having coherent displacements, many possibilities exist without significant coherence. For example, the application of the square wave shown as a in Figure 2 (varyingbetween +So and zero) would' leave the particles without any field-induced displacement (and thus, no coherence) during half the cycle. This process could be arranged with a sufficiently large Soto quickly force all particles very close to the wall while the field is on; when it is off, particles would diffuse out into the flow stream where they would undergo downstream migration. The extent of migration would increase with D112in the limit of high cycle frequencies and correspondingly small (compared to w ) diffusive displacements. Thus, the method would achieve separation on the basis of differences in D, although the D-based selectivity would be only 1/2. This compares to unit selectivity in flow FFF. The CFFF approach has the advantage,however, that any field having a strong interaction with the sample particles could be used. The square-wave operation (+So, -So) that we discussed in detail earlier could be implemented in either coherent or noncoherent form. The coherent form on which we have mainly focused attention is itself subject to numerous variations. It will work with any field/particle combination for which the force F i n eq 7 is large enough to give high coherence (a large effective N ) . Electrical forces, for example, are very powerful and should work for charged particles of any size, giving separation according to differences in electrical mobility p. Fewer nonidealities should be encountered than in electrophoresis, which also separates on the basis of p. For example, lateral temperature gradients established by Joule heating (16) should not cause zone smearing because each identical particle would be cycled over the same lateral range and therefore over the same temperature range. Consequently,
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ANALYTICAL CHEMISTRY, VOL. 58, NO. 9, AUGUST 1986
all identical particles would experience identical (though perhaps "disturbed") conditions and would emerge in a very narrow zone. Also, any electroosmotic flow would occur in the lateral (field) direction and would likewise affect all identical particles identically. In addition, CFFF has the advantage of being an elution system with the attendant properties of convenient detection and controllable separation speed. It should be noted that any operation at cycle times T~ less than rC* (7' < 1)requires assurance that all like particles are migrating over the same portion of channel thickness, e.g., x ' should either have the range 0 to lo or w - lo to w ,or some other definite range of extent lo. In other words, particles having displacements of lo must not have different end points (unless they occur at symmetricalpositions around the channel center). Therefore, a small biasing force of some kind may be needed to keep all 1,'s in the same range, usually with an end at one wall. Sedimentation is another potentially valuable displacement for utilization in CFFF. Again, for a high level of coherence, the force F in eq 7 must be large, due to either rapid centrifugation or massive particles. Gravitational sedimentation will normally require particles 31 gm diameter for satisfactory coherence. However, this larger size dominates most natural sedimentation processes and is, therefore, highly important. Gravity could be applied to a flat FFF channel by rotating the channel 180' around its long axis after the passage of each Tc/2 units of time. The channel could also be continuously rotated, which would give a sinusoidal (curve c of Figure 2) variation in S. This would lead to departures from the details (but not the trends) of the square-wave model described in the last section. Perhaps the most practical system for gravitational sedimentation would be a continuously rotating annular channel. The S curve for such continuous rotation would be sinusoidal, as noted above. The axis of the annulus would be basically horizontal, although a downward or upward tilt might enhance selectivity for operation at small or large T values (see eq 28), respectively. (With increasing tilt, but not to the vertical, the latter operation might acquire characteristics of a very effective elutriation separator.) It is possible that the rotation of the device would be rapid enough at T < 1to provide a centrifugal biasing force to keep the particles in the vicinity of the outer wall. It is suggested that an effective gravitational sedimentation CFFF system of the type described above might also incorporate programming to best separate samples of broad size distribution. However, field strength S in this case is simply gravitational acceleration and cannot be directly controlled, although some degree of effective control and programming could be gained by varying the tilt angle. It might be more satisfactory to program the cycle time r,; eq 23 shows that 7, has as much influence on R as S and, thus, should be equally effective and more convenient for programmed operation. For programming on the T < 1 branch of Figure 4, one would start with a T~ value small enough to keep the larger (higher rn) particles in a selective mode below about X,= 112 (where for the square-wave case the selectivity has dropped from unity to one-half). After the largest particles were eluted, 7, would be gradually increased to speed the elution of the smaller particles. However, the rate of increase in T , would
be controlled 80 that the smaller particles would also undergo most of their migration in a selective condition with a limited Xo value. Programming for the T > 1condition would require starting with a very large T , for the elution of small particles, followed by a gradual reduction in T , to speed the migration of larger particles. The above proposals are intended to illustrate some useful directions for CFFF; there has been no intention to treat the scope of CFFF comprehensively. Considerable experimental and theoretical work will be necessary to more fully evaluate this new approach. GLOSSARY C concentration k Boltzmann's constant 1 effective cloud thickness maximum penetration distance into channel 10 m generalize mobility, U / S U flow velocity mean cross-sectional flow velocity (U) W channel thickness X distance from wall X' particle position along x D diffusion coefficient F force exerted on particle by field N number of theoretical plates R retention ratio, V / ( u ) S field strength T dimensionless cycle time, r , / T C * T temperature U field-induced velocity cv average particle migration velocity average migration velocity at time t 'v* migration distance in time rc 2, dimensionless retention parameter, lo/w x, electrical mobility w field-particle interaction parameter 9 cycle time TC T , for particle traversing full channel thickness TC* LITERATURE CITED (1) Wings, J. C. Sep. Sci. 1988, I, 123. (2) Giddbrgs, J. C.; Myers, M. N.; Caldwell, K. D.; Fisher, S. R. Methods of BIochemlcal Analysis; Why: New York. 1978; p 79. (3) W i n g s , J. C.; Myers, M. N. Sep. Sci. 1978, 73. 637. (4) W i n g s , J. C. AMI. Chem. 1981, 53, 1170A. (5) Wings, J. C.; Myers, M. N.; Caldwell, K. D. Sep. Sci. 1981. 76(6), 549. (6) Yau, W. W.; Kirkland, J. J. J . Chromatogr. 1981, 278, 217. (7) Wings, J. C.; Karalskakls,G.; Caldwell, K. 0.; Myers, M. N. J . C o l M Intefface Sci. 1983, 92, 66. (8) Yang, F. S.; Caldwell, K. D.; W i n g s , J. C. J . C o l M Interface Sci. 1983, 92, 6 1 ~ (9) Tanford. C. physical Chemistry of Macromolecules;WUey: New York, 1961; Chapter 6. 101 CaMweil. K. D.: Nawen. T. T.: Mvers, M. N.; Gddinas. J. C. SeD. Sci. 1979, 74, 935. 11) Myers, M. N.; W i n g s , J. C. AMI. Chem. 1981, 54, 2264. 12) Giddings. J. C. J . C b m . Wys. 1988, 49, 81. 13) W i n g s , J. C.; Yang, F. J.; Myers, M. N. Anal. Biocbm. 1977, 87,
__
395
14) G i n g s , J. C. Sep. Sci. 1983, 78. 765. 15) W i n g s , J. C. Treat& of A ~ l y t l c a lChemistry, Pat? I , Section 0 ; Wlley: New York, lg81; p 63. (16) Morris. C. J. 0. R.;Mor&, P. Separatbn Methods In Blodremstry; 2nd Ed.; Pitman: London, 1976; Chapter 12.
RECEIVED for review February 10, 1986. Accepted April 7, 1986. This research was supported by Department of Energy Grant No. De-AC02-79EV10244.
