375
Anal. Chem. 1988, 6 0 , 375-377
Mo, 1439-98-1; Ni, 7440-02-0; Se, 1182-49-2; Ag, 1440-22-4; Sr, 7440-24-6; T1,1440-28-0; V, 1440-62-2;Zn, 1440-66-6;Brz, 112695-6; 12,1553-56-2;Ce, 7440-45-1;Ar, 1440-31-1;H20, 7132-18-5. LITERATURE CITED Hieftje, G. M. Spectrochim. Acta, Part 6 1983, 386,1465. Galan, L. de; Plas, P. S. C. van der Inductlvely Coupled Plasmas h Ana/ytlcal Atomic Spectrometry; Montaser, A., Gollghtty, D. W., Eds.; VCH Publishers: New York, 1967; Chapter 14. Ripson, P. A. M.; Jansen, L. B. M.:Galan, L. de Anal. Chem. 1984, 56, 2329. Kawaguchl, H.; Tanaka, T.; Miura, S.: Xu, J.; Mizuike, A. Spectrochim. Acta, Part 6 1983, 396, 1319. PlasmaQuad; VG Isotopes, Ltd.: Winsford, Cheshire, England. Gray, A. L.;Date, A. R. Analyst (London) 1983, 108, 1033. Plas, P. S. C. van der: Galan, L. de Spectrochim. Acta, Part 6 1984, 398, 1161. Olhrares, J. A.; Houk, R. S. Anal. Chem. 1985. 5 7 , 2674. Douglas, D. J.; French, J. B. Spectrochim. Acta, Part 6 1986, 4 1 6 , 197. Gray, A. L. Spectrochlm. Acta, Part 6 1986, 416, 151. Gray, A. L. J. Anal. At. Spectrom. 1986, 1 , 247.
(12) Fulford, J. E.; Douglas, D. J. Appl. Spectrosc. 1986, 40, 971.
J. S. Gordon
VG Isotopes Ion Path, Road Three Winsford, Cheshire CW7 3BX, England P. S. C. van der Plas Leo de Galan* Laboratorium voor Algemene en Analytische Scheikunde de Vries van Heystplantsoen 2 2628 RZ Delft, The Netherlands
RECEIVED for review January 29,1987. Accepted October 1, 1987. This investigation is supported by the Netherlands Technology Foundation (STW), future technical science branch of the Netherlands Organization for the Advancement of Pure Research (ZWO).
Bias in Quantitative Capillary Zone Electrophoresis Caused by Electrokinetic Sample Injection Sir: The use of capillary zone electrophoresis (CZE) has grown dramatically since the papers of Mikkers, Everaerts, and Verheggen ( I ) and Jorgenson and Lukacs (2) first appeared. There are two principal methods for introducing sample into the capillary tube: (1) electrokinetic injection, sometimes referred to as electromigration, and (2) hydrostatic injection, also sometimes called suction, pressure, or gravity injection. The electrokinetic injection method arose from the finding (3) that electroosmosis acts as a pump. It has been tacitly assumed by many that this method delivers a representative sample into the capillary. In fact, under some conditions, it does not. This problem has been mentioned (2, 4 , 5 ) , but, to our knowledge, no one has presented any definitive data illustrating this phenomenon. We found that there are two biases involved. One is brought about by the different mobilities of the species in the sample solution. This effect causes a distortion in the ratio of peak areas for species having different mobilties. The other effect is related to the electrical resistance of the medium in which the species are dissolved. This alters both the electrophoretic and electroosmotic flow rates for different solutions and thus changes the absolute amount injected. Once the origin of this bias is understood, it is possible to correct for it approximately; alternatively, it can be avoided entirely by using hydrostatic injection, provided that the inside diameter of the capillary is not so small that it distorts seriously the injection front. BIAS WITHIN A SINGLE SAMPLE CAUSED BY ELECTROKINETIC INJECTION As previously discussed (6),the amount Q(i) of species i introduced into the capillary by electrokinetic injection is given by Q(i)= l(i)AC(i) (1) where l(i) is the length of the sample zone, A is the crosssectional area of the capillary, and C(i) is the concentration of the species i in the sample solution. The length &) is determined by the electrokineticinjection time t, and the total ion velocity u&), which is equal to the total ion mobility b ( i ) times the electric field strength E
Z(i)
= u,,(i)t = pLtot(i)Et
(2)
0003-2700/88/0360-0375$01.50/0
The total mobility pLtot(i)is the sum of the electrophoretic mobility p(i) and the electroosmotic mobility hoam ~t.ot(i)=
~ (+4poam
(3)
Here we assume that ptot(i)is independent of distance along the capillary. This approximation is expected to hold, in general, to high accuracy when the species i is present in low concentration. Combining eq 1-3 we have the relation
Q(i) = b(i)+ ~ o s m l C ( i ) A E t
(4)
For a sample solution containing the species 1and 2, the ratio of the amounts electrokinetically injected is given by
When b = 1, then Q(1)/Q(2) is directly proportional to C(l)/C(2) and electrokinetic injection is free from bias. Note that Q(l)/Q(2) approaches C(l)/C(2) only when poam greatly exceeds both ~ ( 1and ) ~ ( 2 ) Otherwise, . electrokinetic injection introduces a sampling bias which must be taken into account for accurate quantitation. In order to make this correction, it is useful to introduce the concept of a retention time R(i) for the species i to reach the detector located a distance d from the injection end of the capillary
-
d
[ ~ (+ i )~ o a m I E
(7)
Reference to eq 6 shows that for a two-species system the bias factor is given by
b = R(2)/R(1)
(8)
Thus, by measuring the ratio of the retention times, we can 0 1986 American Chemical Society
376
9
ANALYTICAL CHEMISTRY, VOL. 60, NO. 4, FEBRUARY 15, 1988
Table I. Comparison of Peak Area Ratios and Retention Time Ratios Obtained from Electrokinetic Injection and from Hydrostatic Injection peak area
ratio ratio hydrostaratio of inverse electrokinettic column 2 to retention ic injection injection column 3 time ratio peak area
ion pair
rl
Rbt/Kt (b)
Electrokinetic Injection
Time (SI Portions of electropherograms showing the peaks for Rb', Li , and Arg: (a) hydrostatic injection and (b) electrokinetic injection.
a
FI ure 1.
calculate the bias factor and relate the apparent ratio of the injection amounts to the ratio of the concentrations in the sample solution. To confirm this analysis, we carried out the following experiment. A sample solution was prepared that has equal concentrations (5 X M) of Rb+, K+, tetramethylammonium (TMA), Li+, diethylamine (DEA), and 1 X M arginine (Arg) (listed in decreasing order of mobilities). These ions were dissolved in a 20 mM morpholinoethanesulfonic acid (MES)buffer adjusted with histidine to pH 6.0. The concentrations of sample ions were chosen to be sufficiently low that distortion in the capillary zone electrophoresis separation process is negligible. The sample was injected into a capillary by using two methods: electrokinetc injection (1 s at 10 kV) and hydrostatic injection (the capillary inlet elevated 10 cm higher than the capillary outlet for 10 s). We assume that hydrostatic injection is free from bias; actually, there is some bias caused by variation in viscosity, but for dilute solutions this bias is negligible. The ions were quantitated by using an on-column conductivity detector described elsewhere (7). Figure 1 shows portions of the resulting electropherograms (Rb+,Li+, and Arg only). A t first glance the peaks appear similar, but closer inspection reveals that the peak areas of the ions with slower mobilities are smaller for electrokinetic injection than for hydrostatic injection. This conclusion is brought out more clearly in Table I, which lists ratios of the peak areas of different ions, the Rb+ serving as a common reference. In preparing this table, we made repeated mns and we assumed that hydrostatic injection is free from bias so that the different peak areas represent only the different response functions of the conductivity detector. Thus column 3 of Table I shows that electrokinetic injection introduces a sampling bias as much as %%, depending on which ions are compared. However, this bias can be approximately corrected by taking into account the different retention times in order to calculate the bias factor. This is shown in the last column of Table I. Comparison of columns 3 and 4 in Table I shows good agreement. It should be noted that a reproducibility study of 20 consecutive runs using hydrostatic injection showed a precision of peak area and retention times of 2.78% and 1.85% coefficient of variation, respectively. To establish the use of retention times as an approximate correction for electrokinetic injection bias, we made a leastsquares fit of the ratios of the ion peak areas, corrected for conductivity detector response, to the inverse ratio of retention times for the same ion pair, using the data given in Table I. We find good correlation ( r = 0.999). The intercept varies
Rb+/TMA Rbt/Li+ Rbt/DEA Rbt/Arg
1.00 2.08 1.17 6.91 4.34
0.94 1.33 0.69 3.93 1.92
1.06 1.57 1.70 1.76 2.26
1.04 1.57 1.73 1.81 2.31
from zero only by experimental error. This relationship appears to hold true for other ions, such as Ca2+,M2+, and Ba2+. It also holds under different operating conditions for electrokinetic separations, such as different capillary diameters, different electrolytes, and different electric field strengths. For using the retention time ratio to correct the bias in electrokinetic injection, it is necessary that the electroosmotic flow rate of the sample solution be nearly the same as the electrolyte and that the electroosmoticflow rate during sample injection be nearly the same as the electroosmotic flow rate during the CZE run. The first condition can be met if the sample ion concentration is low compared to the electrolyte concentration. The second condition can be met if the applied voltage during electrokinetic injection is nearly the same as during the CZE run. Please note that posmis linear with current but not with applied voltage (4),so that special care must be taken if retention time ratios are to be used to correct sampling bias.
BIAS BETWEEN DIFFERENT SAMPLES CAUSED BY ELECTROKINETIC INJECTION So far we have treated the total velocity of species i, ubt(i), as independent of sample concentration and sample ionic strength. However, when two different sample solutions are compared, this assumption no longer holds and eq 4 must be modified to read
Q(i;S) = [u,,(i;S)]C(i;S)At
(9)
where S denotes the sample solution. It follows that
Therefore, when electrokinetic injection is used, the absolute amount of the same species will vary for different solutions because of the variation in u&) from sample solution to sample solution. To illustrate this bias, we prepared a series of sample solutions with different MES/His buffer concentrations but with the same concentration of Li+ and K+ and compared the results of electrokinetic injection to hydrostatic injection. Figure 2 illustrates the behavior we observed. Here we plot the peak areas of Li+ and K+ as a function of the sample solution resistance (which is inversely proportional to the electrolyte concentration). We observe that hydrostatic injection gives nearly the same ion peak areas for all conditions studied, whereas electrokinetic injection introduces a linear bias (7 = 0.994 for K+ and r = 0.993for Li+) in which more ions are injected for solutions having higher resistance. The reason for this behavior is that the electrophoretic velocity of species i and the electroosmotic flow rate of the solution both increase approximately linearly with decreasing electrolyte concentration and hence the velocity, ut&), varies
Anal. Chem. 1988, 60, 377-380 80
Electrokinetic Injection
LITERATURE CITED
Hydrostatic Injection
(1) Mikkers, F. E. P.; Everaerts, F. M.; Verheggen, Th. P. E. M. J. Chromatogr. 1979, 769, 11-20. (2) Jorgenson, J. W.; Lukacs, K. D. Anal. Chem. 1981, 53, 1298-1302. (3) Pretorius, V.; Hopkins, 6. J.; Schieke, J. D. J. Chromatogr. 1974, 99, 23-30. (4) Tsuda, T.; Nornura. K.; Nakagawa, G. J. Chromatogr. 1983, 264, 385-392. (5) Tsuda, T.; Mizuno, T.; Akiyama, J. Anal. Chem. 1987, 59, 799-800. (6) Lukacs, K. D.; Jorgenson, J. W. HRC CC,J . H/gh Resolot. ChromatWr. 1985, 8, 407-411. (7) Hiang, X.; Pang, T.-K. J.; Gordon, M. J.; Zare, R. N. Anal. Chem. 1987, 59, 2747-2749.
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-0
4
8
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12
Xiaohua H u n g Manuel J. Gordon Richard N. Zare*
16
Resistance ( k i l l
Flgure 2. Plot of K+ and Li+ peak areas as a function of sample solution resistance for both electrokinetic and hydrostatic Injection. Electrokinetic injection causes a bias linear in sample solution resistance (which is inversely proportional to electrolyte concentration).
almost linearly with sample solution resistance. This bias needs to be recognized when comparing the results from different sample solutions if it is desired to place all data on a common footing.
Department of Chemistry Stanford University Stanford, California 94305
RECEIVED for review August 10, 1987. Accepted November 2,1987. Support for this work by Beckman Instruments, Inc.,
is gratefully acknowledged.
TECHNICAL NOTES Temperature Control and Local Heating Effects in Laser- Illuminated Samples Cooled by Closed-Cycle Helium Refrigerators J. W.Hofstraat,*’ A. J. Schenkeveld, C. Gooijer, a n d N. H. Velthorst Department of General and Analytical Chemistry, Free University, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands Here we report on the applicability of a closed-cycle helium refrigerator for cooling of samples in laser-excited Shpol’skii and fluorescence line-narrowing (FLN) spectroscopy. In both techniques low-temperature solid samples are employed to obtain spectra that show vibrational resolution, and hence have similar selectivity as an infrared spectrum, but with the inherent sensitivity of fluorescence spectroscopy (1-3). The closed-cycle helium refrigerator contains gaseous helium as refrigerant; the gas is cyclically pumped through a closed system so that no helium is consumed (4),as in the generally applied helium-bath cryostats. However, in the latter instrument cooling is more direct as the sample is in contact with the refrigerant; the closed-cycle apparatus applies conductance cooling. In studying the applicability of a closed-cycle cooling system in low-temperature spectroscopy it is appropriate to discern several aspects. Firstly, it has been shown that in Shpol’skii spectroscopy fast freezing of samples is required to obtain narrow-line spectra of compounds that do not fit well into the n-alkane matrix (5). A study in our laboratory has shown that such fast freezing can also be realized in a closed-cycle system provided that a suitable construction of the sample holder is employed to ensure good thermal contacts (5). ‘Present address: Ministr of Traffic and Public Works, Department of Public Works, Ti& Water Division, Nijverheidsstraat 2, 2288 BB Rijswijk, The Netherlands.
Secondly,particularly in FLN sufficiently low temperatures, i.e. below 30-50 K depending on the mode of excitation and the nature of the system studied, are required in order to get useful spectra. Namely, as the temperature increases an intensity shift occurs from the narrow lines to broad spectral features (“phonon wings”) that arise from the coupling of the electronic transitions of the guest molecule with vibrational transitions of the host lattice (1). In addition, temperature rise results in a broadening and shift of the narrow lines (I). Recent experiments in our laboratory have shown that temperatures down to 10 K, readily attainable with closed-cycle refrigerators, suffice for application of low-temperature high-resolution fluorescence techniques (6). From the above it is evident that effective temperature control and stability are crucial for the reproducible application of low-temperature high-resolution fluorescence techniques. Especially when highly intense laser excitation is employed, one has to be alert for (local) heating of the conductively cooled sample. In this paper, first the effects of inadequate cooling will be discussed as related to the FLN spectrum of tetracene in a polyethylene film. Secondly, optimal conditions for experiments with closed-cycle systems will be sketched. Under such optimal conditions the performance of the system with respect to temperature control, stability, and homogeneity across the sample will be investigated. As an internal temperature probe the phenalenyl radical is used, a compound with temperature-dependent spectral
0003-2700/88/0360-0377$01.50/00 1988 American Chemical Society
