1509
Anal. Chem. 1986, 58, 1509-1516 PPBE plug with central bore f o r Ag/AgCl reference eleatrod;
m
n
x
d
e
Figure 5. Configuration of the cell used for the ac impedance measurement of PVC membranes.
of very high ac impedances can be built. The construction of the circuitry, including application of a guard technique, eliminates successfully the effect of stray capacitances in the complete system to less than 0.8 pF. Demonstration measurements indicate that this instrumental setup can be used for very high ac impedance measurements (up to 100 MQ) and still give highly accurate results. This instrument can be used for high-impedance membrane electrodes (PVC membrane, glass membrane) or in studies of the interface of two immiscible electrolyte solutions.
ACKNOWLEDGMENT We are grateful to J. Andersson for correcting the English. We also thank the Alexander von Humboldt Foundation and the German “Fond der chemischen Industrie” for financial support. Registry No. KTCPB, 14680-77-4; DBP, 84-74-2; PVC, 9002-86-2; KC1, 7447-40-7; valinomycin, 2001-95-8. LITERATURE CITED (1) MacDonald, D. D.; McKubre, M. C. H. Mod. Aspects Electrochem. 1982, 14, 61-150. (2) Buck, R. P. Ion-Sel. Electrode Rev. 1982, 4 , 3-74. (3) Armstrong, R. D.; Bell, M. F.; Metcalfe, A. A. Electrochemistry 1978, 6 , 98-121. (4) Archer, W. I.; Armstrong, R. D. Electrochemlstry 1978, 7, 157-201. (5) Armstrong, R. D.; Bell, M. F.; Metcalfe, A. A. J . Nectroanal. Chem. 1977, 77, 287. (6) Gabrlelll, C. Identlficatlon of Nectrochemlcal Processes by Frepency Response Analysis; Solartron: Paris, 1980. (7) Lang, J.; Schwitzgebel, G. GIT Fachz. Lab. 1984, 28(1 I), 997. (8) Bentz, A. J.; Sandifer, J. R.; Buck, R. P. Anal. Chem. 1874, 46(4), 543-547. (9) Cath, P. 0.; Peabody, A. M. Anal. Chem. 1971, 43(11), 91A. (10) Aitchlson, R. E.; Brown, T. J. Nectron. Eng. 1976, 48, 23. (11) Armstrong, R. D.; Covington, A. K.; Evans, G. P. J. Electroanal. Chem. 1883, 159, 33-40.
’*..f
0
IOOHz
,
RECEIVED for review September 3,1985. Accepted February 24, 1986.
Theory of Sedimentation Hyperlayer Field-Flow Fractionation Mark R. Schure,l Karin D. Caldwell, and J. Calvin Giddings* Department of Chemistry, University of Utah, Salt Lake City, Utah 84112
The theory of a new separation technique, sedimentation hyperlayer fleid-flow fractlonatlon, is presented. This technique differs from conventional field-flow fractlonatlon methods In that the solute zone is focused into a thin sheet by the opposing forces of centrifugal acceleration and buoyancy in a density gradient. Emphasls in this paper is glven to the nature and distrlbutlon of the density modlfler and its effect on the velocity profile, the zone concentration profile, zone spreadlng, selectivity of separation, and the conditions needed to achieve practical separations that approach the theoretical ilmlt. Both sample size and dllutlon are shown to be factors requiring conslderallon for achieving practical separations.
In recent years, the family of separation techniques known as field-flow fractionation (FFF) has been found to be a ‘Present address: Digital Equipment Corp.,
1 Iron Way, M R 0 2 -
4/E33,Marlborough, M A 01752. 0003-2700/86/0358-1509$01.50/0
powerful and at the same time a very broad approach for resolving mixtures of macromolecules or particles into their components ( I ) . The wide applicability of the FFF technique stems from the numerous choices in field type, field strength, carrier type (aqueous, nonaqueous, etc.), flow conditions, programming options, and channel dimensions. In FFF, separations are carried out in a single phase in which an externally applied (and totally controllable) field transports components into regions of different flow velocities near the wall of a flow channel. Here they are displaced differentially by the nonuniform flow, and they thus emerge separately. The basic mechanism of transport is illustrated diagramatically in Figure 1A. Most applications of FFF have been carried out in ribbonlike channels whose geometry can be characterized as the space between infinite parallel plates; i.e., the flow chamber has a breadth far exceeding its thickness. The carrier fluid flows under laminar conditions, and the superimposed field acts uniformly in a direction perpendicular to the flow. In all the normal FFF methods, excluding steric FFF (2, 3),the sample particles form an exponential cloud against one 0 1986 American Chemical Society
1510
ANALYTICAL CHEMISTRY, VOL. 58, NO. 7, JUNE 1986
-
FIELD
Normal FFF x=w-
C C C
x=oZI,
A HvDerlaver . FFF Flgure 5. Flow-velocity profile in the channel at different volume fractions, a, of DM particles. All conditions are identical with those of Figure 2a, except in (a) a = 0 (ideal parabolic profile), (b) a = 0.025; (c) = 0.05, and (d) = 0.1.
i
O.lum
FFF, where a viscosity gradient exists and causes a distortion of the parabolic profile (16). In the case of SdHFFF it is expected that a viscosity gradient will exist due to the distribution of density modifying particles in the x direction. This phenomenon will now be investigated. We assume an empirical relationship (17) for the viscosity, 9,of the fluid as a function of the volume fraction, 4, of DM particles as follows:
~ ( 4=) o0(l + 2.54 + 10.0542 + al exp(a24)) ( 2 5 ) OV 0
I
I
0.2
I
I
0.4
1
I
0.6
CONCENTRATION Flgure 4. The effect of sample particle diameter on zone shape. Slzes used at xIw = 0.1 are 0.1, 0.5, and 1 pm. Sizes used at x / w = 0.6 are 0.3, 0.5, and 1 pm. Conditions are identical to those of Flgure 2a.
where al and u2 are adjustable coefficients and vo is the viscosity of the pure fluid without the particles. This equation, postulated to be applicable to many particle systems, was used to curve-fit viscosity data for Percoll (13) for which a, and u2 were found equal to 6.0 X and 22.2, respectively, in 0.15 M sodium chloride solution. Combining eq 3, 6, and 25, we get
1 + 2.5B exp(
in eq 22. In this case the concentration distribution around x is described by r
4x1
CO = exp[
-VGA exp(-xeq/Xw)(x - x e J P 2kT
-
1
2, XW + 10.05B2exp(
E)+
(23)
which is a Gaussian with a standard deviation of
This expression is equivalent to eq 5 in ref 8. The concentration profile for 1-pm-diameter sample particles of different densities, and thus different xeq positions, is shown in Figure 3. The results correspond to curve a of Figure 2. The truncation of the infinite series after one term has been examined under a number of conditions and found to cause negligible error for all zones except those where xq/w > 0.9. The higher order terms will become significant only for thicker zones (found with weaker fields and/or smaller sample particles), which, because of their decreased resolution, are of little practical importance. The effect of sample particle diameter, d,, on the zone thickness is shown in Figure 4. Since the theoretical treatment given here assumes particles to be point masses, the zone thickness for very large sample particles will not reflect the inherent size of the particle. Flow Profile. The flow profile in normal FFF is generally assumed to be parabolic in shape with the exception of thermal
where
B = cP/h(l - e-ljA) (27) The velocity profile, v ( x ) ,can now be expressed as a function of the viscosity, ~ ( x ) A . general relationship was developed in conjunction with studies of thermal FFF (16,18) with the result
where A p / L is the pressure drop per unit length of channel and
The integrals in eq 28 and 29 have been evaluated by numerical methods using ~ ( xfrom ) eq 26. Figure 5 shows the substantial effect of nonuniform viscosity on the normalized velocity profile, u ( x ) / ( u ) , where ( u ) is the cross-sectional average velocity
ANALYTICAL CHEMISTRY, VOL. 58,NO. 7, JUNE 1986
1513
Table I. Values of R for 1-pm-DiameterSample Particles Located at Different Positions l7 = xeP/win a Hyperlayer FFF Channel Operated at G = 1635% xeB/w P(x), g/cm3 0.02 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1.106 1.073 1.047 1.030 1.019 1.012 1.008 1.004 1.003 1.002
R1
Rz
R3
R4
0.118 0.540 0.960 1.26 1.44 1.50 1.44 1.26 0.960 0.540
0.118 0.540 0.960 1.26 1.44 1.50 1.44 1.26 0.958 0.536
0.099 0.481 0.903 1.23 1.44 1.53 1.49 1.31 0.993 0.539
0.099 0.481 0.903 1.23 1.44 1.53 1.49 1.31 0.995 0.543
dXeq),
CP
1.401 1.317 1.238 1.181 1.139 1.107 1.083 1.065 1.051 1.042
nValues of R1 obtained for infinitely thin zones and parabolic flow (no viscosity variation). Corrections for finite zone thickness have been applied to R2 and R4,while viscosity corrections have been applied to R3 and R4 (see text). Conditions are T = 298 K, w = 0.0254 cm, 9 = 0.025, u = 0, X = 0.2205, d = 0.0205 hm, p 1 = 1.000 g/cm3, and pz = 2.016 g/cm3.
Table 11. Various R Values for G = 2226g x/w
px, g/cm3
R1
R2
R3
R4
dx,,), CP
0.02 0.1 0.2 0.3 0.4
1.138 1.084 1.045 1.024 1.013 1.007 1.004 1.002 1.001
0.118 0.540 0.960 1.26 1.44 1.50 1.44 1.26 0.960 0.540
0.118 0.540 0.960 1.26 1.44 1.50 1.44 1.26 0.956 0.532
0.0886 0.453 0.880 1.22 1.45 1.54 1.50 1.32
0.0886 0.453 0.880 1.22 1.45 1.54 1.50 1.32 1.01 0.553
1.591 1.421 1.282 1.193 1.134 1.095 1.068 1.049 1.035 1.026
0.5 0.6
0.7 0.8 0.9 (I
1.001
1.00 0.544
Other conditions same as Table I except X
= 0.162.
Figure 5 illustrates a potential disadvantage in separating species near the lower wall. When a high field pulls the density gradient particles into a highly concentrated exponential distribution, the increased viscosity will cause sluggish elution of any sample constituents that accumulate in this region. However, this may be offset by increased resolution. These performance parameters (time and resolution) can be optimized by adjusting the DM volume fraction and particle size along with the field strength. Retention. The retention ratio, R, equal to sample zone velocity divided by ( u ) , is described by (15)
where the brackets denote cross-sectional averages. If we assume that the zone of solute is infinitely thin in the x direction, a limiting form of the above equation gives (8)
R = u(x,,)/(u)
(32)
where u(x es) is the zone velocity at position xeq. For a parabolic flow profile the above equation gives (8)
R = 6(I' - r2)
(33)
where r is the dimensionless ratio xeq/w. The value of R may be calculated in a number of different ways that vary with respect to simplicity and accuracy. A comparison of the results in typical cases is shown in Tables I and 11. Here, the quantity labeled R1 stems from eq 33, which assumes an infinitely thin sample zone and parabolic flow (no viscosity gradient). The quantity R2 is also obtained by assuming parabolic flow, but in this case the concentration profile is described by eq 22 retaining seven terms of the Taylor series. The quantities R1 and R2are quite similar; it
1.00
1.05
11 .0
DENSITY
1.15
1.20
1.25
(g/cm3)
Figure 8. Selectivity, S,,plotted as a function of density. Conditions are those stated for Figure 2 with @ = 0.025 for curve a and @ = 0.05 for curve b.
is unlikely that an experiment could discern a difference. Quantities R3and R4 are calculated with u(x,) and ( u ) given by eq 28 and 30, thus accounting for the effects of viscosity gradient on flow. The quantity R3 is calculated from eq 32, applicable if the zone is infinitely thin, while R4 is given by the most detailed calculation, allowing for both finite zone thickness (eq 22 with seven terms) and a viscosity gradient. The resulb presented in Tables I and I1 for a monodisperse DM material indicate that the infinitely thin zone assumption, under the limited conditions of the calculations, is a good approximation. (Larger errors would be expected for thicker zones.) However, the results show that the viscosity effect must be taken into account for a realistic assessment of the retention ratio. Selectivity. The density-based selectivity, defined here as
(34) is shown in Figure 6, under specified conditions at two different field strengths using R4as the retention ratio value. It is seen that selectivity is generally greatest in the upper (inner) regions of the channel, approaching 2000 at the wall where x,, = w. (The limiting values are very sensitive to crZ and approach infinity at both walls as a, 0.) Minimum (zero) selectivity is obtained, as expected, where the flow velocity is maximum in the channel. Most separations will take place with zones occupying positions outside that of the maximum fluid velocity because the density gradient is largest here and a greater density range is spanned. Experiments should be designed (by varying @ and G) in such a way that zone formation near the maximum velocity (and minimum selectivity) region is avoided. This point will be discussed further in the section on plate height. Relaxation. The process of relaxation in SdHFFF is complicated by the presence of two relaxation processes-one for the DM material and one for the sample particles-as described below. However, to provide context for a discussion of relaxation, we need a clearer idea of experimentaloperation. A reasonable experimental configuration for SdHFFF would be similar to that for normal sedimentation FFF, in which sedimentation forces are generated by spinning a ribbonlike flow channel with flow implemented through a two-way seal system. However, for the density gradient to be set up before the carrier reaches the sample zone, the sample would need to be injected into the channel some distance z'downstream from the head of the channel. This preseparation segment would provide time for the relaxation of the density gradient material into its steady-state exponential distribution, characterized by time constant #. An upper limit on the flow rate is thus found such that approximately . z'/u,,, > 7' (35) where u, is the maximum velocity. For an ideal parabolic flow profile, the above inequality can be written as z ' / 1 . 5 ( u ) > r' (36)
-
1514
ANALYTICAL CHEMISTRY, VOL. 58, NO. 7, JUNE 1986
Parameter T' is the same as the relaxation time applicable to normal sedimentation FFF (15) f = 18wq/d21ApJG (37) Obviously, the choice of field strength, G, influences the time required to fully develop the density gradient across the channel; for the experimental conditions of Table I, this relaxation process requires a T' of 660 s. Experimentally, a density gradient could be preformed by spinning the centrifuge for time #. The centrifuge would then be stopped and the sample injeded at the downstream sample inlet located a t or beyond z ! The centrifuge would then be brought up to the same speed as before so that the injected sample could relax into its Gaussian-shaped equilibrium distribution. After equilibration, the flow would be started and the sample eluted. (Other procedural options obviously exist; for example, both relaxations might be executed in a single stop-flow step, and the sample might be injected through an external valve without stopping the centrifuge.) The step where the sample aligns into the equilibrium position has been referred to as the "transient state" in theoretical studies involving density gradient sedimentation (19). Previous work by Meselson and Nazarian (19) has shown that the time needed to achieve alignment of the zone to within 1%of its equilibrium position for preformed gradients can be approximated by the equation
t* = D [In
(E)+ ,., I
Table 111. Values for Nonequilibrium Plate Height, H, Divided by Velocity, ( v ) H l ( v ) ,s
X IW 0.02 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
b
a
5.96 X 1.86 x 1.46x 1.22 x 6.63 X 0 4.07 x 4.61 x 3.37 x 0.264
1.02 x 4.13 X 4.49 x 5.23 X 3.93 x 0 4.64 x 7.30 x 7.41 X 0.805
lo4 10-4 10-4 10-4 10-4 10-3 10-2
Conditions found in Table I.
10-4 10-5
10-5 10-4 10-3
Conditions found in Table 11.
Inserting the expression for u, given by eq 24 into eq 41 gives
where the symbol'I replaces xeq/w, as defined above. For the case of a nonuniform viscosity along the channel coordinate x
(38)
where t* is the time in seconds, uz is given by eq 24, and D is the diffusion coefficient. For simplicity we obtain D from the Stokes-Einstein relationship
D =kT/3~qd,
(39) where k is the Boltzmann constant, q the fluid viscosity, and d, the diameter of the sample particle. Values calculated for the conditions given in Table I indicate the attainment of a near (1%)equilibrium zone in less than 1min. Most typical zones will form in less than 20 s. This rapid zone formation is in distinct contrast to that for normal isopycnic sedimentation where times on the order of 15 h (20) are not uncommon to establish the zone near its equilibrium position. The difference is due to the much shorter migration distances and the much higher density gradients formed in the hyperlayer experiment; these conditions lead to small values for u, and thus t* in the hyperlayer case. Plate Height. The treatment described here begins with a theory presented earlier for zone broadening in hyperlayer FFF (8). The latter theory is based on a simple random-walk model (21,22). The random-walk model accounts for the fact that irregular Brownian excursions over the distance *mu, will cause a dispersion of arrival times at the end of the channel due to fluctuations in the residence time of sample particles in different flow regimes. (The zone dispersion can also be described as a nonequilibrium effect.) Parameter m has been assumed (8) to be approximately equal to 2. The plate height, H,due to nonequilibrium in a uniform channel, given by u;/L (22), was found to be
With diffusion coefficient D expressed in terms of particle diameter as specified by eq 39, in which q is assigned the value of the viscosity at x,,, eq 40 become6
When the flow profile possesses a uniform viscosity, eq 42 is reduced to
H=
1296rn4kTq(u)X4(1- e-1/X)2 (1 - 219~ (@(p2- pl)G)2ad,5e-2r/x
(r - r2)
(44)
This expression is equivalent to eq 17 of ref 8, but here the factors controlling the density gradient are given in explicit form. Evaluation of eq 44 is given in Table I11 for some of the conditions used in Tables I and 11. Particular notice should be given to the erroneous plate height value (equal to zero) calculated for the middle of the channel. The true value is low but obviously not zero; the discrepancy is due to the simplifyingassumption used in deriving eq 41 of ref 8, where the flow velocity was assumed to be linear in a small region adjacent to xeq. Also note that for low r values, where the density gradient is high, the plate height is very low, showing that this method has outstanding potential for density-based separations. Unlike sedimentation FFF, where plate height decreases with increasing selectivity, SdHFFF exhibits a region above urn, in the channel where plate height increases with increasing selectivity. Although selectivity is highest in the region of the channel above the position where the maximum fluid velocity exists (as noted above), particles focused in this region will exhibit relatively large dispersion upon elution as indicated by the plate height values given in Table 111. However, the region above urn, will generally have a very limited density range as shown by Tables I and 11. Consequently, most components will accumulate in the lower part of the channel under typical conditions. This would indicate that steps to linearize the
ANALYTICAL CHEMISTRY, VOL. 58, NO. 7, JUNE 1986
flow profile (10)are unnecessary. For completeness we will briefly consider other factors involved in zone broadening. For hyperlayer FFF, like normal FFF, the plate height can be approximated (15) by the sum of terms (45)
where B is the longitudinal diffusion term (generally equal to 20),C is the nonequilibriumterm (treated above), and CH, is the sum of instrumental and nonideal contributions such as those from detector and tubing dead volume, channel imperfections, and the finite dimensions of the injected zone. The B term is generally negligible, while the C term, based on the preceding equations, can generally be reduced to reasonably low levels. Most terms in CHi can presumably be reduced to low levels, with one possible exception. In hyperlayer techniques, the injection of the zone may lead to significant disturbances. To preserve the integrity of the density gradient, the sample must be injected in such a way that the gradient is neither disturbed (although i t will eventually re-form) nor diluted by the injection. By injecting into a small dead volume region above the channel inlet and spinning (possibly at low speed), the sample will sediment gently into the gradient. For this type of injection, the sample will enter the gradient as a thick disk with subsequent compression into a thin disk by the focusing forces. If the disk has inadequate volume to contain the sample, nonideal effects will ensue, probably with considerable zone broadening. A related problem that has been identified in preliminary experiments is that of dilution of the density gradient by the volume of the injected sample and its solvent. If the sample is injected after the density gradient has formed, the gradient will be breached by the exclusion of densifier material by the sample/solvent. In this case, the sample should be premixed with adequate DM material to fill the void. After injection, a longer stop-flow time may be needed to allow not only for sample relaxation but also for adequate DM relaxation to “heal” the breach in the gradient caused by the injection.
DISCUSSION Optimization in SdHFFF requires a consideration of the role of assorted parameters described by theory. The nonequilibrium plate height detailed above shows that this key plate height term is proportional to the average flow velocity ( u ) . This leads to the usual trade-off between resolution, highest at low { IJ),and speed, greatest a t high ( u ) . Plate height is also proportional to X4, which suggests that a compressed layer of density modifier is desirable. Also, plate height is proportional to d ~ showing ~ , that large sample particles will yield much narrower zones than small particles and will thus be subject to less stringent operating requirements. Some aspects of the sample particle size dependency do not appear in the theory because of the assumption that particles are point masses. For large particle size, the particle may be sterically excluded from the zone or it may be subject to hydrodynamic forces. In addition, rotational effects must be considered for large nonspherical particles. Rotational effects have been dealt with in the case of normal FFF (23). This correction is, however, rather complex. Other complications beseige the low end of the sample particle size spectrum. Most importantly, zone broadening is severe for small particles, which includes those less than 0.1 pm for the conditions assumed here (see Figure 4). Below this size, specific buoyancy disturbances may occur as the sample particle diameter approaches the diameter of the density gradient former, under which circumstances the density of the fluid no longer acts as a continuous property.
1515
An experimental complication, not previously addressed, is the detection problem. Most FFF detectors, including the common UV “absorption” detectors, depend largely on the measurement of scattered light. With the required concentrations of small density gradient particles such as Ludox or Percoll, the background scattering is expected to be quite high. Although most detectors have provision for background bucking in either a single beam (electronic) or double beam (optical) mode, the amount of bucking necessary may overwhelm some detectors. This problem will be amplified by the fact that any fluctuations in the centrifuge speed will lead to variations in background particulate levels. Since scattering by small particles in the Rayleigh regime is governed by a (~avelength)-~ dependence, longer wavelengths may provide more effective detection. The applicability of SdHFFF to the fractionation of biological particles could be extremely broad, as is the application of equilibriumdensity gradient sedimentation (EDGS). Many specific applications of the latter have been reviewed at length for Percoll (11). With the introduction of denser particles, the effective density range of SdHFFF could be extended into the range where silica could be density fractionated, thus making the technique applicable to environmental particles. The main advantages of SdHFFF compared to equilibrium density gradient sedimentation are those of speed, possibly resolution, and convenience. The speed advantage is dictated by the channel thickness, where a typical w of 0.0254 cm (SdHFFF) should be compared to a cell length of about 5 cm (EDGS), indicating that the sample zone is formed in a much smaller distance and thus in a greatly reduced time for SdHFFF. There is also, in theory, a resolution advantage for SdHFFF stemming from the fact that an additional separation axis, namely that of flow, compounds the separation effect. As noted in ow initial publication (8), a large degree of overlap between equilibrium hyperlayers can be tolerated because the zones displace differentially and thus separate along the flow axis. The operation of SdHFFF should be more convenient and streamlined than that of EDGS. Since SdHFFF is an elution technique, the necessity of careful sample removal from the experimental device, as required for EDGS, is eliminated. A comparison between sedimentation hyperlayer FFF and normal sedimental FFF (SdFFF) is more difficult to make, since the two techniques are selective toward different sample characteristics, Le., density in the case of SdHFFF and effective mass in the case of SdFFF (15). In general, the SdHFFF method is applicable to larger particles than SdFFF, where (wall-induced) steric effects become prominent for particle sizes around 1 pm (8). The focusing of zones at locations removed from the wall in SdHFFF has the additional advantage of eliminating interface-related nonidealities, such as sample adsorption and zone broadening caused by surface roughness. Thus, it appears that SdHFFF offers a valuable complement to the versatile SdFFF technique.
NOMENCLATURE
A , B , C: constants in eq 19, 27, and 29 a ] , az: constants in eq 25 4x1: concentration of sample particles as function of x CO: concentration of sample particles at xeq (c): average concentration D: diffusion coefficient d, d: particle diameter of densifier particles, average diameter d,: particle diameter of solute particles F(x): force on solute particle as a function of x G: field strength H: plate height k : Boltzmann’s constant L:channel length 1: mean layer thickness of DM material
1516
Anal. Chem. lQ88, 58,1516-1520
m: Brownian excursion distance constant m: cumulative mass distribution of densifier particles no:total mass of densifier particles per cubic centimeter fluid No: total number of densifier particles per cubic centimeter fluid n: number of random steps taken by solute Ap: pressure drop across channel 8: d(mlmdldd R, R1,R2,R3, R4: retention ratio S : density-based selectivity 7! absolute temperature t*: equilibration time telution:elution time of solute particle U(x):potential energy of sample particles V: volume of a densifier particle u(x): velocity of carrier fluid as a function of x ( u ) : average flow velocity urn=: maximum flow velocity w: channel width x : distance from lower wall x,q: position where p ( x ) = pa z: distance from fluid inlet to outlet z’: distance from fluid inlet to sample inlet p(x),p’(x, d), p’(x): enrichment-depletion factors
r: X , J W
t,~($1,d x ) , to: viscosity X: dimensionless layer thickness of DM A‘: daA p ( x ) : density as a function of x pl: density p2: density pa: density AP: P2 - P1
of carrier fluid of densifier particles of sample particles
4, d x ) , 40: volume fraction of densifier particles 2:downstream displacement due to a random step LITERATURE CITED (1) (2) (3) (4) (5) (6) (7)
(6) (9) (10) (11) (12)
Giddings, J. C. Anal. Chem. 1981, 5 3 , 1171A. Giddings, J. C.; Myers, M. N. Sep. Scl. Technol. 1978, 13, 637. Myers, M. N.; Giddings, J. C. Anal. Chem. 1982, 54, 2284. Bier, M.; Palusinski, 0. A.; Masher, R. A.; Saville, D. A. Science (Washington, D.C.) 1983, 219, 1281. Morris, C. J. 0. R.; Morris, P. Separation Methods in Biochemistry; Wiley: New York, 1976; p 609. Giddings, J. C.; Dahlgren, K. Sep. Sci. 1971, 6, 345. Giddings, J. C. I n Treatise on Analytical Chemistry; Eking, P. J., Ed.; John Wlley: New York, 1982; Part 1, Vol. 5, Chapter 3. Giddings, J. C. Sep. Scl. Technol. 1983, 18, 765. Janca, J. Makromol. Chem. RapM Commun. 1982, 3 , 867. Janca, J.; Chmelik, J. Anal. Chem. 1984, 56, 2481. Percoll: Methodology and Appllcations ; Pharmacia Flne Chemlcals, Divlsion of Pharmacia, Inc.: Piscataway, NJ. Pertoft, H.; Laurent, T. C.; h a s , T.; Kagedal, L. Anal. Biochem. 1978,
8 8 , 271. (13) Laurent, T. C.; Pertoft, H.; Nordli, 0. J . Colloid Interface Sci. 1980, 76, 124. (14) Laurent, T. C.; Ogston, A. G.; Pertoft, H.; Carlsson, B. J . Colloid Interface Sci. 1980, 76, 133. (15) Giddlngs, J. C.; Yang, F. J. F.; Myers, M. N. Anal. Chem. 1974, 46, 1979. (16) Myers, M. N.; Caldwell, K. D.; Giddings, J. C. Sep. Sci. 1974, 9 , 47. (17) Thomas, D. G. J. Colloid Interface Sci. 1965, 20, 267. (18) Gunderson, J. J.; Caldwell, K. D.; Giddings, J. C. Sep. Sci. Technol. 1984, 19, 667. (19) Meselson, M.; Nazarian, G. M. I n Ultracentrifugal Analysls In Theory
and Experiment; Wllliams, J. W., Ed.; Academic Press: New York,
1963. (20) Hearst, J. E.; Ifft, J. B.; Vinograd, J. Proc. Natl. Acad. Scl. USA 1981, 47, 1015. (21) Glddings, J. C. J. Chem. Ed. 1973, 50, 667. (22) Giddings, J. C. Dynamics of Chromatography: Marcel Dekker: New York, 1965. (23) Gajdos, L. J.; Brenner, H. Sep. Scl. Technol. 1978, 13, 215.
ux,a,:
u: standard deviation of densifier particle sizes standard deviation of sample zone along x and z axes
RECEIVED for review November 18,1985. AcceDted Februarv
r’: densifier relaxation time 9: average volume fraction of densifier particles
3,1986. This work was funded by’Grant CHEk218503 from the National Science Foundation.
On-Line Liquid-Liquid Extraction in a Segmented Flow Directly Coupled to On-Column Injection into a Gas Chromatograph Elisabet Fogelqvist* and Mikael Krysell Department of Analytical and Marine Chemistry, University of Goteborg, S-412 96 Goteborg, Sweden Lars-Goran Danielsson Department of Analytical Chemistry, The Royal Institute of Technology, S-100 44 Stockholm, Sweden
A mechanized system for extractive sample workup for gas chromatography coupled on-llne to an on-column Injector Is described. Extraction Is performed In a Ilquld-llquld segmented flow In a glass coil Internally coated with a hydrophobic layer. Atter extraction the phases are separated with the ald of a hydrophobic membrane supported by a screen coated with Teflon. The organic phase is fed to a loop injector. The system is closed from the atmosphere and was proven to provlde rapld and preclse workup of seawater samples for the determlnatlon of the halocarbons chloroform, bromodlchloromethane, dlbromochloromethane, bromoform, trlchloroethyiene, tetrachioroethyiene,carbon tetrachloride, and l,l,l-trlchioroethane. Compared to manual extractlon, smaller volumes of sample and organlc phase are needed. Reliability was tested during a 3-week crulse when 350 seawater samples were processed without system fallure. Concentratlons down to the picogram-per-liter level In water can be determlned, uslng Injectlon volumes up to 130 ILL, 0003-2700/86/0356- 15 16$01.50/0
Sample workup is often the most time-consuming and labor-demanding step of a chemical analysis. This has been even more accentuated during later years with the increased mechanization and computerization of analytical instrumentation. The introduction of autosamplers and built-in evaluation procedures has increased the capacity of the instruments, but the nominal capacity can often not be fully utilized due to the large amount of manual work needed for sample preparation. Looking specifically at gas chromatography (GC), sample workup often involves an extraction as a first separation and enrichment step and a way to transfer the substances of interest into a suitable solvent. As GC is often used for the determination of very low concentrations, contamination is a common nuisance, as is the volatility of the substances to be determined, as well as their liability to adsorption onto surfaces. Thus, both the laboratory atmosphere and the various utensils used can be sources of disturbance during the 0 1986 American Chemical Society
