Anal. Chem. 1980, 52, 201-203
“pockets” in the ash which were missed in taking aliquots for analysis. When the 14C-BaF’activity was redetermined on the sonicated (but unextracted) ash (samples d’-f’), 98% of the original tracer was recovered. This result suggests that evaporation of tracer solutions onto the ash is not an entirely satisfactory means of applying the tracer uniformly. I t is possible that the upper layers of ash sorb the tracer from the spiking solution as it is applied and that the sorbed tracer is not distributed evenly by shaking the ash slurry. However, the process of ultrasonicating the ash apparently does homogenize the distribution of the labeled ash particles.
CONCLUSIONS The ideal means of fly ash extraction for PAHs has yet to be devised. At the present, ultrasonication allows high recoveries of two- and three-ring PAHs, but recoveries of four-ring and larger PAHs may be incomplete, requiring careful recovery corrections. The careful use of 14C-labeled PAH tracers and/or the method of standard additions with cold, unlabeled PAHs seems highly advisable for obtaining the necessary recovery corrections. ACKNOWLEDGMENT G. M. Henderson provided valuable technical assistance in the fly ash combustion and liquid scintillation measurements for the tracer activity balance experiment. LITERATURE CITED (1) W. Cautreels and K. Van Cauwenberghe, Water, Air. Soilfollut., 6 , 103 (1976). (2) A. Bjorseth, Anal. Chlrn. Acta, 94, 21 (1977). (3) H. H. Hill, Jr., K. W. Chan, and F. W. Karasek, J. Chromtogr.. 131, 245 (1977). (4) G. Broddin, L. Van Vaeck, and K.Van Cauwenberghe, Atom. Environ., 11, 1060 (1977). (5) T. W. Stanley, J. E. Meker, and M. J. Morgan, Environ. Sci. Technol., 1, 927 (1967). (6) A. Albaglie, H. Oja, and L. Dubois, Environ. Left., 6 , 241 (1974).
20 1
(7) R. C. Pierce and M. Katz. Anal. Chem., 47, 1743 (1975). (8) E. Sawicki, R. C. Corey, A. E. Dooley, J. B. Gisclard, J. L. Monkman, R. E. Neligan, and L. A. Ripperton, Heahh Lab. Sci., Suppl.. 7 , 31 (1970). (9) J. L. Bove and V. P. Kukreja, Environ. Left., I O , 89 (1975). (10) M. Mulick, M. Cooke, F. Guyer, G. M. Semenink, and E. Sawicki. Anal. Left., 8 , 511 (1975). (11) E. Sawicki, T. Belsky, R. A. Friedman, D. L. Hyde, J. L. Monkman, R. A. Ramussen, L. A. Ripperton, and L. D. White, Health Lab. Sci., 12, 407 (1975). (12) C. Golden and E. Sawicki, Anal. Lett., A l l , 1051 (1978). (13) G. Chatot, M. Castegnaro, J. L. Roche, and R. Fontanges, Anal. Chirn. Acta, 53, 259 (1971). (14) V. P. Kukreja and J. L. Bove, J . Environ. Sci. Health, A l l , 517 (1976). (15) L. Kolar, Rostl. Vyroba, 15, 1103 (1969). (16) E. K. Diehl, F. duBraeuil, and R. A. Glann, J . Eng. Power, 276 (1967). (17) S.T. Cuffe, R. W. Gerstle, A. A. Orning, and C. H. Schwarts, J . Air follut. Control Assoc., 14, 353 (1964). (18) R. Guerrini and A. Pennacchi, Riv. Combust.. 29, 349 (1975). (19) D. F. S. Natusch and B. A. Tomkins, in “Carcinogenesis, Vol. 3: Polynuclear Aromatic Hydrocarbons”, P. W. Jones and R. I. Freudenthal, Eds., Raven Press, New York, 1978, pp 145-153. (20) J. Jaeger, Cesk. Hyg., 14, 135 (1969). (21) D. L. Coffin, M. R. Guerin, and W. H. Griest, “The Interagency Program in Health Effects of Synthetic Fuel Technologies: Operation of a Materials Repository”, Symposium on Potential Health and Environmental Effects of Synthetic Fossil Fuel Technologies, Gatlinburg, Tenn., September 25-28, 1978. (22) R. L. Davidson, D. F. S. Natusch, J. R. Wallace, and C. A. Evans, Jr., Environ. Sci. Technol., 13, 1107 (1974). (23) J. A. Campbell, J. C. Laul, K. K. Nielson, and R. D. Smith, Anal. Chem.. 5 0 , 1032 (1978).
Wayne H. Griest* LeRoy B. Yeatts, Jr. lJohn E. Caton Analytical Chemistry Division Oak Ridge National Laboratory Oak Ridge, Tennessee 37830 RECEIVED for review May 18,1979. Accepted October 23,1979. Research sponsored jointly by the Electric Power Research Institute and the Department of‘ Energy under contract W-7405-eng-26 with the Union Carbide Corporation.
Sedimentation Field-Flow Fractionation in Macromolecule Characterization Sir: The concept of field-flow fractionation (FFF) as a tool for particle separation and mass characterization was introduced by Giddings more than a decade ago ( I ) . Since its introduction, this idea has been extensively tested, and the techniques have been steadily refined, by Giddings and coworkers ( 2 , 3 ) . The outstanding wide mass range covered and the remarkable resolution achieved in their recent experiments (2-5) are indeed noteworthy. Among the members of FFF, sedimentation field-flow fractionation (SFFF), in which a centrifugal field is utilized, is especially fascinating with its potential and theoretical simplicity. In SFFF, the retention parameter X defined as the ratio of the characteristic “thickness” 1 of the solute layer to the channel width w is given, under ideal conditions, by the simple equation ( 4 ) X = l / w = kT/(MGwAp/p)
(1)
where k is Boltzmann’s constant, T i s the temperature, M is the mass, G is the field strength, and Ap = p - po with p and po being the solute and solvent densities, respectively. The retention ratio R defined by
R =
L?/u0
(2)
0003-2700/80/0352-0201$01.OO/O
where D and Do are the mean velocities of the solute and solvent, respectively, is related to X generally by ( 4 )
R = GX[coth (1/2X)
- 2x1
(3)
Thus, given the single (and simple indeed) solute parameter p , one can, in principle, convert the elution curve to a mass distribution curve on an absolute scale without need of column calibration. This is considered to be the greatest advantage of SFFF. In addition, R may be given, for sufficiently high retention, by 6X, so that the sample elution volume eventually becomes proportional to the first power of hf. This feature specific to SFFF motivated us to develop EL powerful and convenient method for characterization of gigantic macromolecules which are difficult to characterize by the available methods, in particular, gel permeation chromatography, owing to problems on gel, solvent, and polymer chain degradation. To this end we are now constructing a ultracentrifuge specially designed for the SFFF in colaboration with Hitachi Kaki Co., Ltd. Below we will discuss some problems inherent in SFFF (or FFF in general) with its practical application to synthetic polymer systems in mind. @ 1979 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 52, NO. 1, JANUARY 1980
PROGRAMMING TECHNIQUES
(7)
Experiments of Giddings et al. on polystyrene beads (4)and T 2 virus (6) have already confirmed that the elution behavior of these particles almost strictly obeys Equation 3 in the ranges of M , G, and po examined. Despite such an excellent agreement between theory and experiment, one encounters a serious drawback when a sample of wide mass range is tested in a single run of any member of FFF, viz., either incomplete resolution of early peak components or excessive dilution, and retention time of late peak components is inevitable. The situation is especially serious in SFFF due to the inverse first-power dependence of X on M . T o cope with the above problem two programming techniques based on variations of field strength and solvent density have been developed by Giddings et al. (7), in which the retention parameter X is manipulated as a function of time (the A-programming techniques). Quite recently the above authors proved that another technique employing variations of solvent flow rate u, (the us-programming technique) is not only effective but also more advantageous than the former in view of the theory and data analysis (8). However, the problem of excessive dilution of late components remains unsettled in the us-programmed SFFF. This is, in practice, the problem of detector sensitivity, on the one hand, and the problem of solvent amount necessary for carrying out a run, on the other hand. As to the detection problem, use of a small-angle light scattering apparatus designed as a chromatographic detector will be promising because scattered light intensity is essentially proportional to the mass, and hence dilution of large mass components should be almost cancelled out.
EFFECTS OF SOLUTE INTERACTIONS Usually, macromolecule solutions are highly nonideal. In the FFF process, molecules are necessarily compressed into a small volume, so that the effects of nonideality should appear the more strongly, rendering the ideal retention (Equation 3) and plate height expressions (3,4 ) invalid. Rigorous description of the SFFF process with a nonideal solution is not easily given. In what follows, we will try to give one criterion for judging a t which levels of solute concentration and interactions the effects become significant. The concentration c has dependences along both field coordinate x and flow coordinate t . The x-dependence in a thin zone d t may be approximately described by the following equation based on an equilibrium argument dx/dc, = (l/c,)(l
+ BMc,)
(4)
where B is the second coefficient of the virial expansion for the sedimentation equilibrium formula (9) ( R corresponds to twice the osmotic second virial coefficient), and 1 is as given by Equation 1. The higher terms in c, have been neglected, and the channel width w has been assumed to be small enough that the field may be regarded as uniform along x. The retention ratio of this solute zone is
For the present purpose, it will suffice to assume that E , has a Gaussian dependence along z . Then the retention ratio of the entire sample is
R = S c c , R , d t / S x-uc , d t m
= R,,j[l
R, = R,,j[l + B M c , ( ~- X)/h]
(6)
where Rd = 6X(1 2X) is the ideal retention ratio (cf. Equation 3), and c, is the average zone-concentration given by ~
-
X)/X]
(8)
where Eo is the concentration at the Gaussian center. As one would have expected ( 4 ) , positive solute interactions ( R > 0) make the sample migrate faster than in the absence of the interactions. In the limit of high retention, the second term in Equation 8 becomes independent of X:
R = 6X
+ (6/21'2)BMC,
(9)
Because BM increases with increasing molecular weight, the SFFF principle that larger particles migrate more slowly can, in certain cases, be fatally counteracted by solute interactions. Equation 8 expresses the instantaneous migration rate in terms of the Gaussian-center concentration. As the sample migrates down the column, the Gaussian breadth and hence co would continuously vary owing mainly to two effects. One is the nonequilibrium effect as discussed by Giddings et al. ( 4 ) . The other is that of solute interactions themselves. Essentially, these two may be envisioned as stemming from the x- and t-dependences, respectively, of migration rate. The 2-dependence results from the Gaussian or quasi-Gaussian profile of concentration. Whether interactions are significant on the overall retention behavior must be judged from a certain representative value of co. Giddings et al. ( 4 ) have suggested the use of the Co at the column exit, for the ideal solution. This is ( 4 )
where hid is the theoretical number of plates, m'is the amount of sample injected, and V,,is the column void volume. In the limit of high retention, Nid has been given by (10)
where L is the column length, and D is the diffusion coefficient. This value of Eo should be near the high end of the concentration scale ( 4 ) . The low end would be the experimental value, COobs, a t the column exit (this is observable), which would reflect a situation in which interactions have already done their damage and spread the zone breadth. The actual retention would be characterized by an intermediate value between Eo and tg,obs. Incidentally, it is noted that a chain molecule occupies a large volume in space for its mass. There is a critical distance from the wall beyond which the molecular center cannot approach the wall. For a Gaussian chain, the distance d averaged over all possible conformations is ( 2 1 )
d = where uo is the solvent velocity, which is assumed to be given by uo = constant X x ( w - x ) with x = 0 at the bottom wall of the channel. The integrals in Equation 5 have been evaluated by using Equation 4. For small values of R M E , and A, the resultant expression converges to
+ 2 "2BMCo(l
(2/K1'2)(,52)1 2
(12)
where ( S 2 ) is the mean-square radius of gyration. This relation should approximately hold also for a perturbed chain. Putting Equation 12 into the retention expression given earlier (3) we have for X 0
-
R = 6[X
+ (2/7r1 ')((S2)'' / w ) ]
(13)
This equation shows another limit of the SFFF feasibility. Very roughly, chain molecules larger than about l o l o in mas? would be difficult to separate.
Anal. Chem. 1980, 52,203-205
LITERATURE CITED Giddings, J. C. Sep. Sci. 1966, 1 , 123. Giddings, J. C. J. Chromatogr. 1976, 125,3. Giddings, J. C.;Myers, M. N.; Moellmer, J. F. J. Chromafogr. 1978, 149, 501. Giddings, J. C.;Yang, F. J. F.; Myers, M. N. Anal. Chem. 1974, 46, 1917. Giddings, J . C.; Smith, L. K.; Myers, M. N. Anal. Chem. 1976, 48, 1587. Giddings, J . C.; Yang. F. J. F.; Myers, M. N. Sep. Sci. 1975, IO, 133. Yang, F. J. F.; Myers, M. N.; Giddings, J. C. Anal. Chem. 1974, 46, 1924. Giddings, J . C.;Caldwell, K. D.; Moellmer, J. F.; Dickinson, T. H.; Myers, M. N.; Martin, M. Anal. Chem. 1979, 51,30. See, e.g., Fujita, H. "Foundation of Ultracentrifugal Analysis"; Wiley Interscience: New York, 1975.
203
(IO) Giddings, J. C.; Yoon. Y. H.; Caldwell, K. D.; Myers, M. N.; Hovingh, M. E. Sep. Sci. 1975, IO, 447. (11) Casassa, E. F.; Tagami, Y. Macromolecules 1969, 2 , 14.
Hiroshi Inagaki* Takeshi Tanaka Institute for Chemical Research Kyoto University Uji, Kyoto-Fu 611, Japan RECEIVED August 13, 1979. Accepted October 1, 1979.
AIDS FOR ANALYTICAL CHEMISTS Electrochemical Detector Flow Cell Based on a Rotating Disk Electrode for Continuous Flow Analysis and High Performance Liquid Chromatography of Catecholamines B. Oosterhuis, K. Brunt,' B. H. C. Westerink, and D. A. Doornbos Laboratory for Pharmaceutical and Analytical Chemistry, Research Groups Medicinal Chemistry and Optimization, State University of Groningen, Antonius Deusinglaan 2, 9713 A W Groningen, The Netherlands
Several different instrumental techniques of electrochemical origin have been applied in detectors for high performance liquid chromatography (HPLC). Recently a review paper with more than 70 references concerning electrochemical detection in liquid chromatography has been published ( 1 ) . Amperometric detectors have been especially successful and some designs are already commercially available. Flow cells for amperometric detectors based on different principles have been designed: the thin-layer cell (2),the wall jet cell ( 3 ) ,and the partial electrolysis cell ( 4 ) . Not only the construction of flow cells but also the electronics in the POtentiostat have been subject to the process of development. Blank constructed the dual amperometric detector ( 5 ) while Brunt introduced the differential amperometric detector (6, 7). In this paper we introduce a new type of flow cell based on a rotating disk electrode (RDE) for amperometric detection, which can be used in combination with continuous flow analysis as well as with HPLC. Wang and Ariel (8) have adapted the RDE for a flow-through cell for anodic stripping voltammetry. But to the best of our knowledge the application of a RDE as detector principle for HPLC and continuous flow analysis has not been described yet.
THEORY The response of an amperometric detector is dependent on the mass transport of the electroactive component from the bulk solution in the flow cell to the electrode, assuming that the reaction rate a t the electrode surface is infinitely fast compared with the rate of mass transfer. According to Fick's law, the rate of mass transfer depends on the concentration gradient of the electroactive components from the bulk solution in the flow cell to the electrode surface. This means that the thickness of the diffusion layer at the electrode surface is a very important parameter concerning the detector response. A decrease in the thickness of the diffusion layer results in an increase in the concentration gradient and subsequently in an increase in the detector response. The thickness of the diffusion layer depends mainly on the flow cell geometry and on the flow rate in the detector flow cell. The influence of the flow rate on the thickness of the 0003-2700/80/0352-0203$01 .OO/O
diffusion layer in a thin-layer cell is subject t o some controversy in the literature. Some authors find a square root dependence ( 7 ) ,and others find a cubic root dependence (9). In the wall jet cell, a more complex relationship exists (10). However, the response of both types of flow cells depends on the flow rate. This indicates that fluctuations in the flow rate (due to the pump) cause fluctuations in the detector response and sensitivity. In the design of the presently described flow cell, the first goal was to minimize the thickness of the diffusion layer and the second was to make the thickness of the diffusion layer independent of the flow rate. In order to fulfill these goals, a rotating disk electrode (RDE) has been used as a working electrode. Using a RDE, the thickness of the diffusion layer is mainly determined by the rotation speed of the electrode.
EXPERIMENTAL Flow Cell Design. The working electrode compartment of the flow cell is in principle a wall jet construction with a rotating electrode (Figure 1). Via the inlet the eluent enters the flow cell and impinges normally on the RDE. The solution leaves the working electrode compartment by streaming upward between the RDE and the wall of the vessel, through channel (a),diameter 2 mm, to compartment (A) in which the reference and auxiliary electrode are located. The working electrode is constructed from a Kel-F tube (b), diameter 6 mm, and a brass rod (c). The outer diameter of the lower part of the RDE (d) is 8.5 mm and fits in the working electrode compartment of the flow cell, diameter 9.0 mm, leaving enough space between the RDE and the wall of the vessel for the eluent to stream upward. The hole (e), diameter 6 mm, in the electrode is filled with carbon paste. The carbon paste surface acts as the working electrode. A t the top of the electrode, a mercury contact (0 has been constructed to connect the electrode with the potentiostat. The electrode is mounted in the holder for rotating electrodes, constructed according to Coenegracht (11). This holder is placed with the tapered end in the conical part of the working electrode compartment of the flow cell. The height of the RDE is variable (g).
Three pulleys with different diameters have been constructed at the top of the RDE holder in order to rotate the R D E at different rotation speeds. The pulleys are driven via an elastic C 1979 American Chemical Society
