Errors Caused by Flowrate Variation in High Performance Size Exclusion Chromatography (GPC) D. D. Bly, H. J. Stoklosa, J. J. Kirkland, and W. W. Yau Central Research and Development Department, E. 1. du Pont de Nemours and Company, Experimental Station, Wilmington, Del. 19898
In high performance liquid size exclusion chromatography (gel permeation chromatography, GPC), errors in M, and M, are produced by flowrate variation, especially in systems which are supposedly run at constant flowrate and monitored according to time rather than volume. High performance GPC provides much shorter analysis times than conventional GPC because of the use of chromatographic columns exhibiting a much larger number of theoretical plates per second. The current trend in high performance GPC is to operate on a basis of retention time rather than a retention volume. Because retention times (and volumes) are smaller in high performance systems, flowrate variation is more significant than In conventional GPC. Computer simulation has been used to study this effect and to determine the magnitude of the errors attributable to flowrate variation.
In conventional GPC, the analysis of polymers commonly takes 2-3 hours for completion. Recently, research scientists and instrument companies alike have sought to shorten this analysis time significantly. Several new types of column packing materials as well as certain commercially packed columns and systems have become available to perform rapid high performance GPC analyses. These systems have the potential for reducing a GPC polymer analysis to 15 minutes or less, since the number of theoretical plates generated per unit time are about an order of magnitude greater than those of conventional GPC (1-7). Unfortunately, however, this high performance adds a new dimension to the potential for errors in GPC analysis. One of these sources of error is flowrate or elution time variation. In conventional GPC, the elution volume is usually measured as a function of volume using a siphon technique ( 8 ) , and molecular weight is related to retention volume. On the other hand, modern high performance GPC systems frequently incorporate “constant volume” pumping, and molecular weight is related to time rather than retention volume. In high performance systems, the retention volumes associated with the measurements are relatively small, and errors associated with using a siphon can be significant. In addition, the limitation on the number of data points which can be obtained from commercial siphons during the course of an experiment have generally precluded their use. Experimental errors in GPC measurements can be minimized by using truly constant volume pumps or by accurate flow monitoring devices which will quantitate the time/volume relationship. At present, however, the constancy of pump output is not guaranteed, and there is a lack of appropriate flow monitoring devices for measuring or controlling the flowrate even in connection with “constant volume” pumps. Devices are needed which will measure or precisely control the flowrate, both on a short and long basis. With present pumping systems, flowrate variation can be significant not only during a given experiment but across the entire time base relating the calibration experiment to the analysis. Since precise flow control devices are not common, we 1810
have sought to determine expected magnitude of the errors caused by flowrate variation in the GPC analysis of polymers when using a “constant volume” pumping system. Previous studies of this type have involved only the effect of flowrate level (9-11) on separation mechanism and efficiency. No studies of the effect of small flowrate variations on MW precision have been reported for conventional or high performance GPC systems.
EXPERIMENTAL Tqestablish the effect of flowrate variation on calculated M n and M , values, a reference chromatogram and a reference flowrate are needed so that the distortion of the chromatogram by the flowrate variations can be determined. In this study, we used the experimental chromatogram of Dow B-8 polystyrene. The flowrate set in the experiment (2 ml/min) was assigned to this chromatogram as the reference flowrate. Variations of flowrate from the reference value were then imposed on the reference chromatogram by computer to generate the new, distorted chromatograms. In our GPC system, the chromatographic data were taken in units of time but the calibration and MW calculations are based on retention volume. Since it is necessary to relate time and volume, the retention volume at each point of the reference chromatogram was calculated by:
v, = ]=o i It,*FSET
=
5 (AV),
1=o
(1)
where I t , is the time increment between data points (2-second intervals), FSET is the set flowrate (2.00 ml/min.) and (AV), is the volume increment during the time period Atl. For the small flowrate variations in this paper, the retention volume is expected to remain constant. Accordingly, with increased flowrate, the chromatogram elutes sooner in time than the reference chromatogram and later with decreased flowrate. When the flowrate is varied by simulation a new retention time is obtained according to the equation:
where t,’ is the retention time for the ith point adjusted for flowrate variation, ( I V ) , is the constant volume increment defined above and F, is the new flowrate during the specified volume interval. These manipulations were necessary since peak retention was detected in time not volume units. From the corrected time, tL’, a new retention volume is calculated by:
V,’ = t,’* FSET
(3)
Equation 3 gives the new retention volume distribution which the computer used t o calculate average molecular weights or t o obtain the GPC calibration curve. The flowrate variation was executed in the computer program and, in all simulation experiments, the flowrate was updated every 12 seconds. Several calculations were performed updating the flowrate every second, but the results were not found to be significantly different. The experimental chromatogram was obtained on a high-speed GPC assembly composed of a Model R401 refractive index detector and a Model 6000 solvent delivery system (Waters Associates, Framingham, Mass.). The sample was injected using a high pressure Model CV-6-UHPa-C-20 valve with a 200-4 external volume loop (Valco Instruments Company, Houston, Texas). Four 30-cm X 0.76-cm i.d. columns of lo2, lo3, lo6, lo6 P\ p-Styragel (Waters Associates) were used in series. The GPC data were collected by the Du Pont Experimental Station Real Time System (12). The detector output signal (in millivolts) was sampled 30 times per second.
ANALYTICAL CHEMISTRY, VOL. 47, NO. 1 1 , SEPTEMBER 1975
CONSTANT FLOW RATE
DECREASING FLOW
INCREASING FLOW RATE,
Figure 1. Random variation in flowrate about a fixed level from time zero to end of GPC curve
Figure CUNe
RnfE
3. Uniform change in flowrate from time zero to end of GPC
’
TO
FLOW RATE
2
A
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ L__SPECIFIED 2 FLOW RATE
Figure 4. Fixed flowrate deviation from specified value Figure 2. Uniform change in flowrate across the GPC curve
The test standard, Dow B-8 polystyrene (fin= 113,000, fi, = 278,000) (Dow Chemical Co., Midland, Mich.) was chosen because of its fairly broad molecular weight distribution, M,/M, = 2.47, common to many commercial polymers. With a sample of this type, differences in the effect of flowrate variation on M, and M, are readily measured by the procedure used in this study. Molecular weight calculations were first performed assuming the flowrate for the calibration runs to be accurate and constant, the same as the reference chromatogram, while that for the sample analysis run varied in the described manner (Figures 1-4). These
Table I. Random Variation in Flowrate about a Fixed Level from Time Zero to E n d of GPC Curve during Calibration Random i a r i a t i o n in ilor\-rate,
0 0.5 1.0 3.0 5.0 10.0
V n mean
2 0 for 10 runs
112,900 112,800 112,800 112,900 113,200 114.300
V,
mean
2 0 for 10 runs
0
278,100 278,500 278,400 278,600 279,200 280,900
0 700 1,400 4,300 7,lOC 13,800
1,100 2,200 7.000 11,300 21,900
assumptions then were reversed and the calculations were performed again (Tables 1-111). The possible range of errors from combined significant effects is also illustrated in Figures 5 and 6. The molecular weight calculations were performed using the algorithm of Pickett, Cantow, and Johnson (13,14). The “effective linear calibration curve” used in the calculation was obtained using the algorithm of A. E. Hamielec (15, 16). DISCUSSION AND CONCLUSIONS This study shows that, under some conditions, flowrate variation is very significant in the analysis of polymers by high performance liquid exclusion chromatography. Information obtained in this work can be used to predict the expected error in a measurement which results from flowrate variation. It can also be used to select the equipment necessary to perform analysis at a given level of precision with regard to flowrate variation. Figure 1 illustrates the effect of a random variation in flowrate about a fixed level from time zero (sample injection) until the end of the GPC curve. The information in this figure is interpreted as follows: If during the analysis a 5% random variation in flowrate occurs, the M,,for the test polymer could vary from the expected mean by 7,000 ( 2 0 significance) and M u could vary by 11,200 (2a). Note, however, that if sufficient runs are made, the mean M,,and M,,, values approach the expected value. The effect of a uniform change in flowrate occurring dur-
Table 11. Uniform Change in Flowrate across the GPC Curve during Calibration Total Flowrate increasing
percent change in
-
Relatibe
flowrate
M”
percent error
0.0 0.5 1.0 3.0 5.0 10.0
112,900 112,100 111,000 107,800 104,400 96,800
0.0 4.7 -1.7
4.5 -7.5 -14.3
Mi‘
278,100 277,900 276,600 273,700 270,100 262,800
Flowrate decreasing
-“ n
percent error
0.0 4.1 4.5 -1.6 -2.9 -5.5
112,900 113,600 114,500 118,300 121,800 131,100
Relative
-LL
percent error
0.0 0.6 1.4 4.8 7.9 16.1
Relative percent error
0.0 0.4
278,100 279,100 279,900 283,700 286,800 294,500
0.6 2.0 3.1 5.9
Table 111. Uniform Change i n Flowrate from Time Zero to E n d of GPC Curve during Calibration Tot31 percent c’lange ~n floi\rate
0.0 0.5 1.0 3.0 5.0 10.0
-
41,
112,900 111,000 103,100 86,000 71,800 45,100
Flowrare increasing Relative percent error
0.0 -1.7 -8.7 -23.8 -36.4 40.1
*‘w
278,100 274,000 258,600 222,700 192,100 131,200
Flowrate decreasing Relative percent error
0.0 -1.5
-7.0 -19.9 -30.9 -52.8
C‘”
112,900 117,800 123,100 146,800 174,700 266,800
Relati\ e percent error
0.0 4.3 9.0 30.0 54.7 136.3
-
M,
278,100 288,400 299,000 345,500 398,800 565,800
Relatibe percent error
0.0 3.7 7.5 24.2 43.4 103.5 ~
ANALYTICAL CHEMISTRY, VOL. 47, NO. 11, SEPTEMBER 1975
1811
3001
rr
75L
W
50
Ea
4
I
I
I
a
w
200
I
-1
25
+z W
g W
o
a
-25
k!
3-
I
250L
0 U
1
lE
I
-50-
w
-751 I "V
0.0 0.5 1 .o 1.5 2.0 2.5 3.0 PERCENT FLOWRATE VARIATION IN TERMS OF DRIFT
Figure 5.
Range
of
possible M,,. values with flowrate drifting
from
time zero Top: Combination of positive sample flowrate error with negative calibration flowrate error. Bottom: Combination of negative sample flowrate error with positive calibration flowrate error
ing the time of sample emergence, that is, during the time the entire polymer sample elutes from the columns and detector, is shown in Figure 2. Flowrate variation of this kind could arise when the viscosity of the sample is high and the viscosity of the total liquid system decreases as the sample emerges from the column. Another origin of this kind of flowrate variation comes from the technique of staggered injections, in which a new sample is injected a t the head of the column while a previous sample is emerging a t the outlet. The data in Figure 2 show that a 5% change in flowrate of this type causes 8% error in M,, and 3% error in Mu. However, a 5% change in flowrate of this type is unusual with high performance systems. At a more realistic 1% change, there is only about 1-2% change in the computed molecular weights. A long-term constant drift in flowrate causes much more serious errors, as indicated in Figure 3. This type of flowrate variation may occur if pump check-valves become dirty or clogged during use and also from temperature drift in the column oven. If the flowrate changes by 5% between time zero (sample injection) and the completion of the run, then there is a 37 or 54% change in &?, and a 31 or 43% change in M a depending on whether the flowrate is increasing or decreasing across the course of the experiment. Even a t only a 1% drift in flowrate for this sample M , changes by about 10,000 and Mu,by about 20,000. On a percentage basis, a t the 1%flowrate drift level, these errors amount to 7-10% error in M a which is certainly important for some applications. Note that since the running of the sample took about 17 minutes in this example, the drift rate is only O.O6%/min. or 3.5%/hr. The most significant effect of flowrate variation is exhibited by poor flowrate repeatability, as illustrated in Figure 4. Flowrate repeatability or resettability is defined as follows. It is the ability of the pump to deliver exactly a specified volume per unit time on a day-to-day basis under the same set of operating conditions. T o obtain the information for this example, a flowrate of 2.00 ml/min. was specified. The calibration was then made establishing a relationship between retention time and molecular weight (15-18). The sample was analyzed in the same manner, except that it was assumed that the flowrate had changed between the calibration and the sample runs by some fixed value. In this case, there was no additional randomization or drift in the flowrate. 1812
- 100'
0.0
Figure 6.
I
0.5
I
I
1
1.0
1.5 2.0 2.5 PERCENT FLOWRATE ERROR
1 3.0
Range of possible Mwvalues for resettability errors
Top: Combination of positive sample flowrate error with negative calibration flowrate error. Bottom: Combination of negative sample flowrate error with positive calibration flowrate error
The data in Figure 4 show that for a 1%change in the flowrate between the time of calibration and the time of chromatographing this polymer sample, there is corresponding change of 25,000 and 21,000 in M , for increased and decreased flowrate, respectively. These changes correspond to relative percent errors of 22.4% for the increased flowrate and -18.6% for the decreased flowrate. Similar We suggest that such errors are inchanges occur for Mu,. tolerable for many uses. These results aptly demonstrate that a flowrate repeatability significantly better than 1%(e.g., 2.00 ml/min. f 0.02 ml/min.) is desired for precise analysis by high performance GPC. Tables 1-111 show the effect of similar studies in which the flowrate during sample analysis is held constant and a variation in flowrate is imposed during calibration. These data lead to conclusions similar to those presented above. In addition, in real life experiments, many combinations of these effects may occur. Figures 5 and 6 are included to illustrate the range of errors in Mw which occurs when drift or resettability errors, respectively, are combined in the samplelcalibration relationships. It should be emphasized again that this study indicates the level of error which can be expected only from flowrate variation in high-performance, time-based liquid exclusion chromatography. Errors also can accrue from other sources (e.g., sample overloading, poor injection technique). The investigator ultimately must decide what level of analytical precision can be tolerated, depending on the objectives of the study. The results obtained in this study can be used to predict the specifications needed for pumping systems in high performance GPC. Of prime importance is the repeatability of solvent delivery on a longer-term basis. The example in this study suggests that flowrate repeatability must be better than about 0.3% for errors of about 6% in M,, and Mu. Long term drift of flowrate (increase or decrease) is also serious, and GPC measurements with M n and M u errors of 6% are caused by flowrate variations of somewhat less than 1%.The short-term stability (random fluctuations) of the pumping system appears to be less critical in GPC work, and random short-term flowrate variations of 1-4% apparently can be tolerated for all but the most critical applications. This conclusion assumes that the flowrate stability has no effect on detector response or separation mecha-
ANALYTICAL CHEMISTRY, VOL. 47, NO. 11, SEPTEMBER 1975
nism, as these factors were not studied in the simulation experiments. From knowledge of the principles and specifications of the various pumping systems, one can conclude that many of the currently available units have performance deficiencies for use in high performance GPC for the calculations of molecular weights as described here. (The reader is reminded that qualitative information is usually obtained without serious bias and does not fall under the described restrictions.) Most modern solvent delivery systems are limited to pumping stabilities of 0.5-1.0% or greater. Design and fabrication of sophisticated pumps which will directly deliver solvents with variations of 0.3% or less is difficult and expensive. Therefore, a more practical approach might be to operate a less expensive pump in conjunction with a very precise flow-measuring device with feedback control to the pump to ensure the desired short- and longterm flowrate precision. Another option is to interact flowrate measurements with data acquisition software to correct for flowrate aberration. During the preparation of this manuscript, a paper was published by Patel (19) describing the use of "oligomeric" internal standards to compensate for flowrate variation. The technique appears promising. In addition to the errors in molecular weight measurements caused by flowrate variation in high performance GPC, additional errors due to factors associated with the very efficient columns (>lO,OOO theoretical plateslmeter) also can be significant. Studies are now under way in this laboratory to determine the effect of column and extra-col-
umn peak variances (band broadening effects) on molecular weight measurements by high performance GPC.
LITERATURE CITED (1) D. D. Bly, "Recent Advances in Size Exclusion Chromatography," FACSS, First National Meeting, Atlantic City, N.J.. November 20, 1974, Paper No. 72. (2) J. J. Kirkland, J. Chromatogr. Sci.. I O , 593-599 (1972). (3) R. J. Limpert, R. L. Cotter, and W. A. Dark, Amer. Lab., 6 (5). 63 (1974). (4) K. Unger, R. Kern, M. C. Ninow, and K.-F. Krebs, J. Chromatogr.. 99, 435-443 (1974). (5) M. J. Telepchak, J. Chromatogr., 83, 125-134 (1973). (6) W. W. MacLean, J. Chromatogr., 99,425-433 (1974). (7) "Chromatography Notes," IV (2), Waters Associates, Milford, Mass.. June 1974. (8)W. W. Yau, H. L. Suchan, and C. P. Malone, J. folym. Sci., fart A-2, 6, 1349-1355 (1968). (9) A. R. Cooper and J. F. Johnson, Eur. folym. J., 0, 1381-1391 (1973). (10) A. C. Ouano and J. A. Barker, Separ. Sci., 6, 673-699 (1973). (11) H. A. Swenson, H. M. Kaustinen. and K. E. Almin, folym. Led.. 9, 261268 (1971) or (J. Polym. Sci., Parts). (12) J. S.Fok and E. A. Abrahamson, Chromatographia, 7,423-431 (1974). (13) H. E. Pickett. M. J. R. Cantow., and J. F. Johnson.,~J. ADO/. Polvm. Sci... , I O , 917-924(1966). H. E. Pickett, M. J. R. Cantow, and J. F. Johnson, J. folym. Sci., Pari C, 21, 67-81 (1968). S.T. Balke. A. E. Hamielec, 9. P. LeClair, and S. L. Pearce, lnd. fng. Chem., Prod. Res. Develop., 8,54-7 (1969). T. D. Swartz. D. D. Bly, and A. S. Edwards, J. Appl. folym. Sci., 16, 3353-3360 (1972). D. D. Bly, "Progress in Liquid Exclusion Chromatography," "Du Pont Innovation", 5 (2), 16-20, Winter 1974. D. D. Bly, "Gel Permeation Chromatography in Polymer Chemistry" in "Physical Methods in Macromolecular Chemistry", Vol. 2, Benjamin Carroll, Ed., Marcel Dekker, New York, 1972, Chap. 1, pp 16-25. G. N. Patel, J. Appl. folym. Sci., 18,3537-3542 (1974). ~~~~
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RECEIVEDfor review April 30, 1975. Accepted June 11, 1975.
Extractions with Metal-Dithiocarbamates as Reagents Armin Wyttenbach and Sixto Bajo Swiss Federal Institute for Reactor Research, 5303 Wurenlingen, Switzerland
The metal-dithlocarbamates Ho(DDC)~, Ag(DDC), Ni( DDC)2, Cu( DDC)2, Sb( DDC)3, Te( DDC)4, Se( DDC)3, II~(DDC)~,As( DDC)3, Cd( DDC)2, Zn( DDC)2, Co( DDC)3, Fe(DDC)3, and TI(DDC) have been tested as reagents for the extraction of 12 different metals from 0.1N H2SO4 and from solutions of pH 5 into CHC13. These reagents show excellent selectivity for the extraction of metals with higher conditional extraction constants. In the majority of all cases, extraction is complete within 2 minutes; Se(DDC)4, Co( DDC)3, and Fe( DDC)3, however, react only slowly and in some cases incompletely or not at all. The successive extraction of a sample with several different reagents yields a series of organic fractions that contain dlfferent metals. As an example, the application of these reagents to a neutron activated biological sample is given, where the resulting organic fractions can be directly submitted to y-spectrometry without any further chemical treatment.
The diethyldithiocarbamate anion (C2Hs)zNCSz- (in the following denoted by DDC) forms complexes extractable into organic solvents with many metals. If the reagent is added in excess as water soluble NaDDC to an aqueous phase containing several metals, and if the complexes formed are subsequently extracted, selectivity may be achieved by the choice of pH andlor the addition of mask-
ing agents. Because of the fast decomposition of DDC in this time acid solutions ( I ) , the pH should not lie below 4; problem can be considerably eased by applying the reagent in a form that is soluble in the organic phase, Le., as Zn(DDC)2, in which case decomposition in contact with acid solutions even of [HI = 1 is slow enough to allow extraction times up to 1 hour before DDC decomposition is substantial. Alternatively, selectivity can be achieved by the application of the substoichiometric principle ( 2 ) , which uses quantities of reagent sufficient to extract only part of the metal to be separated. Beside the necessity to remove any metal with a higher conditional extraction constant beforehand, application of substoichiometry is greatly complicated in the case of DDC by the formation of mixed C1-DDC complexes ( 3 , 4 )with many metals. As another possibility, we propose the application of different metal-DDC complexes as reagents to achieve selectivity. This paper gives the principle of the method, screens the behavior of 14 metal-DDC complexes in the extraction of 14 ions from the aqueous phase, and gives some representative applications. It should be noted that this mode of operation is somewhat similar to the method proposed by Elek et al. (5-7) for substoichiometric multielement separation with dithizone. However, in using solutions of metalDDC complexes as reagents, the need to employ exactly measured amounts of metals and chelating agent to fulfill
ANALYTICAL CHEMISTRY, VOL. 47, NO. 11, SEPTEMBER 1975
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