well established 70-eV electron impact fragmentation patterns of organic compounds or the performance of the quadrupole GC/MS system. The detection limits attained using conventional data acquisition were 1-50 ppm which makes the technique compatible with the concentrations of organic compounds found in domestic sewage and other waste effluent water samples. Greater sensitivity, to about 50 ppb, was attained with real time data acquisition from subsets of the ions used in conventional mass spectrometry.
This technique made the method applicable to the analysis of relatively clean surface or drinking water.
ACKNOWLEDGMENT We thank Tom Bellar of this Laboratory for the original suggestion to analyze tap water for chloroform.
RECEIVEDfor review May 8,1974. Accepted July 19,1974.
Sedimentation Field-Flow Fractionation J. Calvin Giddings, Frank J. F. Yang,’ and Marcus N. Myers Department of Chemistry, University of Utah, Salt Lake City, Utah 84 7 12
Sedimentation field-flow fractionation (SFFF), one member of the field-flow fractionation (FFF) class of techniques, is described and Its potential advantages and disadvantages for macromolecular and particle separatlons are discussed. Theoretical equations for retentlon and plate height are given along with an analysis of possible disturbances caused by relaxation effects, polydispersity, secondary flow, and sample size effects. The conclusions are tested experimentally using polystyrene latex particles having diameters from 907A to 4808A. Measured retention parameters are in excellent agreement with theory but a considerable discrepancy exists in piate height results. This is traced to a possible sample overloading effect. Particle fractionation is illustrated and the further potential of the method is discussed.
Sedimentation Field-Flow Fractionation (SFFF) is a name describing a group of separation methods constitut.ing a subclass of general field-flow fractionation (FFF) (1-6). In SFFF, sedimentation, induced by gravity or by a centrifuge, is employed to layer molecules or particles near one wall of a flow tube (see Figure 1). These layers are of different thicknesses for particles of different size and density. Solvent flow in the tube-perpendicular in direction to the sedimentation velocity vector-carries each constituent down the channel, but it carries fastest those particles forming the thickest layers and which therefore extend furtherest toward the tube center where flow velocity is greatest (Figure 1). One thus gets a differential migration according to layer thickness. As layer thickness is a crucial parameter in the migration rate of various components, we will deal with its characteristics in the theory section. In theory, SFFF has several advantages over conventional sedimentation techniques for analytical separations. First of all, SFFF, by its very nature, is an elution technique, with corresponding advantages in sample detection and collection ( I , 6). Second, it has been shown that for a Present address, Department of Chemistry, Oregon State Uni versity, Corvallis, Ore. 97331. (1)J. C.Giddings, Separ. Sci., 1, 123 (1966). (2)J. C.Giddings, J. Chern. Phys., 49, l(1968). (3) M. E. Hovingh, G. H. Thompson, and J. C. Giddings, Anal. Chern., 42, 195 (1 970). (4) E. Grushka, K. D. Caldwell, M. N. Myers, and J. C. Giddings, Separ. Purification Methods, 2, 129 (1973) ( 5 ) J. C. Giddings, J. Chern. fduc., 50, 667 (1973). (6)J. C.Giddingsand K. Dahlgren, Separ. Sci., 6, 345 (T971).
given field, SFFF can generate separability (as measured by the number of theoretical plates) per unit time or per unit length only two to three lower than the maximum values obtainable from the direct application of an equal field using normal centrifugal methods (6). This disadvantage is compensated in part by the fact that one can use, throughout the SFFF run, the more intense fields at the very outer edge of the rotating system. More importantly, one can extend the path length of the separation by coiling the SFFF tube any desired number of times around the outer perimeter of the rotation chamber ( I , 6). Because of this, the number of plates achievable is theoretically unlimited in SFFF, but has a definite ceiling in normal centrifugation. [Our comparison is valid for both kinetic and equilibrium forms of sedimentation, which have been shown t o produce roughly equal levels of overall resolution (7).] The third advantage of SFFF is that no special density gradients or other arrangements need be provided for convective stabilization. The small scale and cross-sectional geometry of the flow channel obviate this problem. (However one must take precautions to avoid secondary flow, as will be explained.) One obvious disadvantage of SFFF, compared to directfield sedimentation, is that it is inherently limited to small samples. Scale-up would be difficult and would involve other sacrifices, such as in separation speed. Another disadvantage, at this point in time, is that the special long-tube capability of SFFF requires the use of a low-volume seal to get samples out of the rotor system. As constructed in our laboratory, this seal was not able to handle rotation speeds greater than 4000 rpm, which provided about 1400g. Longer seal life was assured by not exceeding 500g. Higher speeds would extend the range of applicability to much smaller particles, and would improve both resolution and separation speed. For this reason, the present work is in no sense a description of an ultimate system. It must be regarded as a prototype system, used t o demonstrate retention, separation, the role of various parameters, and the applicability of theory. While SFFF was first envisioned as a special case of FFF ( I ) , it was developed independently as a method in particle separations by Berg, Purcell, and Stewart (8-10 1. These (7)J. C. Giddings, Separ. Sci., 8, 567 (1973). (8)H. C. Berg and E. M. Purcell, Proc. Nat. Acad. Sci. USA, 58, 862 (1967). (9)H. C. Berg, E. M. Purcell, and W. W. Stewart, Proc. Nat. Acad. Sci. USA, 5 8 , 1286 (1967). (10)H. C . Berg and E. M. Purcell, Proc. Nat. Acad. Sci. USA, 58, 1821 (1967).
ANALYTICAL CHEMISTRY, VOL. 46, NO. 13, NOVEMBER 1974
1917
The steady-state distribution of solute in a segment of the channel is obtained by setting the net solute flux, J,, equal to zero. This and the substitution of Equation 2 for U yields the differential equation
SFFF SEPAHATITN
d n c - - m(1 - P/Ps)W2Y - l(3) dx fD where, in view of the discussion above, the right hand side is constant. Intergration provides an equation for the concentration profile over the column width (from x = 0 to x = w) PARABOLIC FLOW PROFI-E
''q
Figure 1. Principles of a SFFF column operating in a centrifuge Species of zone A have a larger etfective mass and are therefore pushed closer to the wall than those of zone B Because of this, zone A is retained more than zone Band separation occurs
authors used both gravitational and centrifugal fields in early work on the subject. They employed an ingenious centrifugal device that bypassed the need for complicated rotor seals (10).Flow occurred in a direction parallel to the axis of rotacion, thus precluding channels of extraordinary length. With this system, they demonstrated the retention of the bacteriophage, R17, of molecular weight 4 X lo6. Work with particles as small as 105 mol wt was regarded as possibie at IO5 g.
THEORY The flux density of dilute solute in the field direction (normal to flow) within an SFFF tube is (2) J - - D - dc uc
+
x -
dx
By convencion in FFF, coordinate x is the distance into the channel measured from the wall at which the solute accumulates. Quantity D is the diffusion coefficient, c is the concentration and U is the field induced drift velocity. For a sedimentation field induced by centrifugation, the latter is (11) L T = -F= -
f
d l - P/P,)02Y,
f
(2 )
in which F is the net force acting on the solute particle, f is its friction coefficient, m its mass and p s its density. In wnie instances it is necessary to replace p s by l/&where & is the partial specific volume of the solute. The centrifugal acceieration is 0 2 r g and the solvent density is p . The minus sign is applied because the sedimentation force is directed out from the center of rotation, whereas coordinate x measured the distance in from the outer channel wall. (The same sign can be shown to be applicable when inverted densities bring the solute to the inner wall.) Quality U is virtually constant in any given segment of a SFFF column. First of all, the channel width w is ordinarily small by comparison to the rotational radius ro. The SFFF columiis reported here, for instance, have a width of 0.635 mm, less than 1%of the radius, ro = 8 cm. Values of w significantly larger are not expected because column resolution deteriorates rapidly with increasing w. Another potential influence on U is the variability of p , p s and f across the column width; this variability is also reduced to negligible proportions because of the small magnitude of w The same argument shows that diffusion coefficient D is essentially constant across the tube width. ( 1 1 ) T Svedberg, "The Ultracentrifuge," T . Svedberg and K . 0 Pedersan Ed., Clarendon Press, Oxford, 1940.
1918
where c g is the concentration at x = 0. 'I'his exponential layer of solute has a thickness characterized by the length parameter I, a quantity fully defined by the relationships of Equation 4. From Equation 4
When 1 (crn/secl
Figure 6. Plate height vs. mean flow velocity, ( v ) , for polystyrene beads of diameter 2339 A (top) and 3 1 17 are obtained theoretically
A (bottom). The solid lines
Retention is affected by variations in solvent density as well as by changes in spin velocity and particle size. Equations 7 and 8 show that X should be inversely proportional to the density difference, Ap, between sample and solvent. This conclusion was tested using various aqueous solutions of sucrose and n-propanol solutions. The experimental data and theoretical lines are compared in Figure 5 . The agreement is, again, most satisfactory. Plate Height. Plate height values a t different flow velocities were measured for two different sizes of polystyrene beads. Samples of 2339-A beads were rotated a t 1080 rpm ( G = 104g), producing a retention of R = 0.117 and X = 0.0203. Beads of 3117-A diameter were run a t 715 rpm (46g) and were retained a t the level R = 0.098 and X = 0.0168. Plate height curves for the two are shown in Figure 6. These tend to form a straight line cutting the H axis well above the origin. Also shown in Figure 6 are the respective theoretical plots for these two samples. These were obtained from Equation 14, with x calculated from exact nonequilibrium expressions by Y. H. Yoon of this laboratory. The error introduced by ignoring the longitudinal diffusion term is negligible over the present experimental range. The diffusion coefficients were obtained from Stoke’s law for friction coefficient, f , and Einstein’s diffusion equation, D = k T / f . The deviations between the experimental and the theoretical plate height curves are considerable. It is, therefore, necessary to look carefully a t various perturbations to see what role, if any, they play in this departure. 1922
Hcorr, cm
% of H contributed
0.0145 0.0103 0.0062
0.98 0.85 0.69
0.95 0.81 0.68
3.3 3.4
by end effects
2.4
Table 11. The Polydispersity Contribution to Plate Height, Hp,and to Plate Height per Unit of Column Length, H , / L , under Conditions of High Retention According to Equation 23, Hp = 9 L ( u , j / d ) 2 H
Particle dimensions, d*od(in A)
907 i 57 1087 + 27 1756 k 23 2339 k 26 3117 k 22 3570 i: 56 4808 18
*
05 r
0
Hobsd, cm
(v),
x
0
cm f sec
H ~L I
0.036 0.0056 0.0015 0.0011 0.0004 0.0022 0.0001
resent column, p ( p L = 4 5 . 7 cm (in cm)
1.6 0.25 0.070 0.051 0.020 0.101
0.006
Relaxation Effects. The precautions described above (stop-flow injection) should eliminate any significant relaxation effects stemming from the injection process. Any other disturbance in geometry or flow is potentially capable of causing similar disturbances. However, it is difficult to imagine how disturbances major enough to create the observed plate height discrepancies could occur. The general agreement of theory and experiment insofar as retention is concerned support this conclusion. Furthermore, relaxation effects could cause the greatest plate height distortion a t high flow velocities, a trend opposite to that observed. End Effects. End effects, including dead volume, frequently augment chromatographic plate height. Along with a detector and inlet and outlet tubing similar to those in chromatographic systems, the special rotor seal has its own set of unknown characteristics. The entire dead-volume train was evaluated by substituting a short column (1.8 cm) into the system, measuring the plate height, and isolating its contribution by the subtraction method of Giddings and Seager (16). Results for the 3117-A beads are shown in Table I. I t is apparent from this table that end effects constitute only a minor part of the observed plate height. Polydispersity. The contribution of sample heterogeneity to plate height can be estimated by the method outlined in the theory section. For the cases a t hand, retention is high and X is small, making Equation 23 applicable to good approximation. Quite generally in the high retention range, as shown by Equation 23, plate height is independent of retention, temperature, and all other parameters of the SFFF system except column length. We can therefore calculate, for sample beads with a given dispersion in size, a heterogeneity contribution per unit length, H,IL, that will be applicable to any SFFF system working a t high retention. In Table 11, we show these values for the polystyrene beads used in this study. We also show the contribution, H,, for our particular column. Particle size dispersion values are those reported by the manufacturer, Dow Chemical Co. Table I1 shows that the heterogeneity effect is negligible in the present study for all but the smallest beads. However, the effect would be quite generally noticeable in a high efficiency system in that a number of the H p contribu(16)J. C. Giddings and S. L. Seager, lnd. Eng. Chem., Fundam., 1, 277 (1962).
ANALYTICAL CHEMISTRY, VOL. 46, NO. 13, NOVEMBER 1974
.{ Figure 7. Plate height and retention vs. mg of injected polystyrene. Bead diameter = 3117 a: field strength = 45.89; flow rate = 6 ml/hr. Points a and b are the concentrations used for the retention and plate height studies, respectively
tjons are in the vicinity of 1 mm-rather large in terms of ultimate plate-height potential. Heterogeneity of the magnit,udg shown here could obviously he measured as an independent parameter in a high efficiency SFFF system. Concentration Effects. Nonlinear concentration effects, might also be responsible for extra peak spreading. To investigate this possibility, sample content was varied by utilizing a range of Concentrations of 3217-A beads in a 5 - ~ 1 injection. Figure 7 shows the resultant effect on both retention parameter X and plate height H. Clearly there is a major concentration effect whose onset in this particular experiment begins for samples conhining well under 0.1 mg of polystyrene. While the retection parameters reported earlier are not, much disturbed, the influence on plate height is very substantial and appears to explain the plate height discrepancies noted earlier. The foregoing conclusion is supported in a qualitative way by the trend in the discrepancies between theory and experiment shown in Figure 6. The discrepancies tend to disappear at high flow velocities. At high flow velocities, of course, the “theoretical” peak is relatively broad-wide enough to contain the sample without undue concentration and distortion. A quantitative view of this phenomenon can be gained by using Equation 31 t,o calculate cooL, the maximum concentration within the zone predicted by theory to exist at the column exit. This quantity is plotted against mean solvent flow velocity, ( v ) , in Figure 8. Along with it is shown a curve of the departures of plate height from their theoretical values. Certainly the trend in the two curves is similar, suggesting some connection. We note that the calculated cooL values are below the maximum possible concentration of about 630 mg/ml by a factor of about 500. (The value 630 mg/ml comes from the assumption that the beads are packed as closely as possible in a random structure, thereby filling about 60% of the local volume element with material of density 1050 mg/ml.) Thus, the physical crowding is not excessive, but forces between particles might be sufficient to disturb their normal equilibrium distribution. The following processes would be expected to occur if significant repulsion existed between the particles. Following injection, the particles sediment toward the wall but fail to reach the normal exponential distribution because of repulsion. The particles which cannot adequately sediment are held at abnormally high altitudes and are thus swept downstream rapidly, once flow commences, until adequate dilution occurs beneath for normal sedimentation. The high velocity contrasts with the low velocity of particles next to the wall, arid is responsible for widening the zone along the flow axis. This excessive spreading is accompanied by a slight displacement forward in the zone’s center of gravity, a slightly earlier elution, and thus a slightly higher value for measured R and X values. While this pro-
Figure 8. Maximum concentration in the exiting peak awl the fractional departure of plate height from theory plotted a s a function pf solvent flow velocity
Figure 9. Separation of polystyrene fractions at ( a ) 1140 rpm and (h) 1520 rpm
cess would occur with the greatest intensity near the column entrance, it would continue’to occur along the path of migration up to the point that dilution is able to restore the normal distribut,ion. The effects of the disturbance would, of course, increase with increase in sample size. These hypothetical processes would explain why the effect on plate height is much greater than that on retention, why the consequences are greatest a t low flow velocities, and why both effect,s are magnified by further increases in sample size. The results obtained here show that nonlinear disturbances can occur with very small samples (under 0.1 mg). I t is probable that the effect is most marked for highly retained peaks and high efficiency columns. However, more work is needed to clarify these factors. The availability of sensitive detectors for this work is obviously desirable. Particle Fractionation. The differential retention of particles of different size, as exemplified in Figure 2, makes particle fractionation feasible. This is illustrated in Figlire 9 which shows the elution pattern and separation of polystyrene beads of different diameters. This figure also demonstrates the ease of controlling retention and separation by variations in field strength. A change from 1140 rpm in Figure 9a to 1520 rpm in Figure 9b increases t h e sedimmtation field strength by a factor of 1.78 and thus insreasps considerably the retention volume of the peaks. This, in turn, increases the resolution volume of the peaks. This result confirms the potential utility of a programmed field SFFF system; such a system will be reported in a subsequent paper.
POTENTIAL OF SFFF It was mentioned earlier that the present system is a prototype system with characteristics far removed from those
ANALYTICAL CHEMISTRY, VOL. 46. NO. 13, NOVEMBER 1974
* 1923
expected in an optimal system. Most importantly, the rotational velocity and the field strength must be increased to gain any significant advances. The degree to which performance might be enhanced is shown below. Under conditions of high retention, Equation 13 can be substituted into Equation 14 to yield the potential plate height
H = 24h'~~(~)/D
(33)
With the aid of Equation 10 this expression becomes
H = 4h2w2v/D (34) where the zone velocity in the column, R ( u ) has been written simply as u. If now Equation 8 is used to eliminate X2, we have 144 ( k T ) 2 v H = (35) i72d6G2 (4p)2D If diffusion coefficient D is replaced by the Stokes-Einstein value, D = kT/3agd, where 7 is the coefficient of viscosity, we get 432 kTyv H = T dsGz(Ap)z If H is written as Cv,then the nonequilibrium coefficient C not only reflects the level of H achievable, but, more importantly, C can be shown to equal the minimum time in which a theoretical plate can be generated. We have
c = -432 T
kTy d5G2(4~)~
(37)
This equation shows that the efficacy of SFFF can be improved by manipulating a number of variables, including viscosity, temperature, and density. The method will, in theory, work much better with large particles than small, as reflected in the fifth power dependence on particle diameter d. However there are practical limits to this gain which will become apparent as d approaches either layer thickness 1 or surface-roughness dimensions in magnitude. Equation 37 shows that C for a given particle is inversely proportional to the square of the sedimentation field strength, G. The dependence on rotational velocity is therefore inverse fourth power. In the present study the maximum G was about 500g. If ultracentrifuges, with field strengths up to 300 times greater than this, were adapted to SFFF, C values could in theory be reduced by (300)2 = 90,000. While such gains would not be totally applicable to particles in the size range used here because of the previously mentioned restrictions on size, the above factor would be applicable to much smaller particles and to macromolecules, thus making their separation convenient also. Particle size analysis is significant in many fields of environmental control and industrial operation. The present method is promising in such analyses by virtue of its predictable dependence on simple mass and density parameters and its potential for further improvements in fractionating power.
RECEIVEDfor review March 21, 1974. Accepted July 12, 1974. This investigation was supported by Public Health Service Research Grant GM 10861-17 from the National Institutes of Health.
Programmed Sedimentation Field-Flow Fractionation Frank J. F. Yang,' Marcus N. Myers, and J. Calvin Giddings Deparfment of Chemistry, University of Utah, Salt Lake City, Utah 84 7 72
This paper describes the development of two programming systems for sedimentation field-flow fractionation (SFFF): programmed field strength SFFF and programmed solvent density SFFF. The necessity for developing programming systems in SFFF is discussed, and both general and specific theories of programming are developed. A centrifugal SFFF system was adapted to programming by the controlled variation of rotation speed and solvent density. Polystyrene latex beads with diameters from 1756 to 3117A were fractionated by this device. Agreement between theoretical and experimental retention times was within about 5%, showing that the essential features of the technique are well characterized.
Sedimentation field-flow fractionation (SFFF) is a method designed for the separation of particles and large macromolecules. The essential features of the method, and a review of related work, appear in the preceding publication (1). Present address, Department of Chemistry, Oregon State University, Corvallis, Ore. 97331. (1) J. C. Giddings, F. J. F. Yang, and M. N. Myers, Anal. Chem., 46, 1917 (1974).
1924
ANALYTICAL CHEMISTRY, VOL. 46, NO.
All field-flow fractionation (FFF) methods, including SFFF, generate or are expected to generate elution patterns for macromolecules resembling the patterns generated by gas and liquid chromatography for smaller molecular species (2-4). When attempts are made to fractionate wideranging mixtures by chromatography, problems are encountered due to the incomplete resolution of early peaks and the excessive retention time and peak width of late peaks. The same difficulty can be expected to occur with most forms of FFF as a result of the analogous elution patterns. This problem in the field of chromatography has been referred to as the "general elution problem" ( 5 ) ;its scope appears, from the present analysis, to encompass certain nonchromatographic techniques as well. The solution to this problem is quite effectively realized in various programming techniques. Programmed temperature gas chromatography (6) and gradient elution liquid (2) G. H. Thompson, M. N. Myers, and J. C. Giddings, Anal. Chem., 41,
1219 (1969). (3) E. Grushka, K. D. Caldwell. M. N. Myers, and J. C. Giddings. Separ. Purificafion Mefh., 2, 127 (1973). (4) M. N. Myers, K. D. Caldwell, and J. C. Giddings, Separ. Sci., 9, 47 (1974). (5) L. R. Snyder, "Principles of Adsorption Chromatography,'' Dekker, New York. N.Y., 1968. (6) W. E. Harris and H. W. Habgood, "Programmed Temperature Gas Chromatography," Wiley, New York. N.Y., 1966.
13, NOVEMBER 1974
