Anal. Chem. 1992, 64, 123-128
stability (for C02 generation) of solutions containing low oxalate levels. It should also be noted that although less desirable, use of preweighed solids which are diluted with appropriate liquids a t the point of use or other two-part systems represent an obvious way to address storage stability issues.
CONCLUSIONS Air-equilibrated, acidic aqueous solutions containing Fe3+ and oxalate may be used to generate highly reproducible levels of dissolved O2and C02 upon irradiation at h = 300-500 nm which are useful for calibration of blood gas measurements. Variation of the Fe3+/oxalateratio allows for generation of two levels of each gas with only two solutions. The solutions are easy to prepare and employ readily available and inexpensive materials. In addition, solutions containing high oxalate concentrations show excellent thermal stability. Since slow thermal decomposition of oxalate does occur, solutions containing low oxalate levels are less stable with respect to C 0 2 formation. This is simply due to the fact that C02 photoproduction is oxalate-limited in this case, whereas C02 photoproduction is Fe3+-limitedin solutions with high oxalate levels. Further study is required to determine if higher pH’s and/or removal of O2 during storage will result in better stability for the low-oxalate solutions. Finally, we believe that this general approach should allow realization of new calibration systems for other analytes.
ACKNOWLEDGMENT We thank M. S. Wrighton (MIT) for valuable assistance in the completion of this work. We also thank C. Calzi and A. Manzoni (Instrumentation Laboratory SPA, Milan, Italy) for some helpful comments.
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Registry No. 02, 7782-44-7;C02, 124-38-9;ferrioxalate, 15321-61-6.
REFERENCES Ptuden, E. L.; SiggaarbAnderson, 0.; Tietz, N. W. In Textbook of Cllnlical Chemistry; Tletz. N. W.. Ed.; Saunders: Phlladelphla, 1966; p 1191. Wlnckers, E. K. A.; Teunissen, A. J.; Van Den Camp, R. A. M.:Maas, A. H. J.; Veefklnd, A. H. J . Clln. Chem. Clin. Blochem. 1978, 76, 175. Cole, P. V. I n Re~pk8tOryMonnOrng In Intensive Cere; Spence, A. A.. Ed.; Churchill Livlngstone: Edinburgh, 1982; p 32. Calabrese, G. S.; OConnell, K. M. I n Elechochemistry I I . Topics in Current Chemistry; Steckhan, E., Ed.; Springer-Verlag: Berlin, 1986: Vol. 143, p 48. Parker, C. A. Roc. R . Soc. London 1953, 220A, 104. Hatchard, C. G.; Parker, C. A. Roc. R . Soc. London 1958. 235A, 518. Bowman, W. D.; Demas. J. N. J . Phys. Chem. 1976, 60, 2434. Slgaard-Andersen, 0.;Durst, R. A.; Maas, A. H. J. Clln. Chem. Acta 1980, 108. 501. Taylor, H. A. I n Analytical Photochemlical An8IySis; Fkgerald. J. M., Ed.; Marcel Dekker: New York, 1971; pp 91-115. Bunce, N. J. In CRC Handbook of Rwtochemistry; Scaiano, J. C., Ed.; CRC Press: Boca Raton, Florlda. 1989; Vol. 7. p 241. Vincze, L.; Papp, S. J . phofochem. 1987, 36. 289. Parker, C. A. Tmns. F8r8d&y Soc. 1954, 50, 1213. Winckers, E. K. A.; Teunissen, A. J.; Van den Camp, R. A. M.;Maas, A. H. J.; Veefklnd, A. H. J . Clin. Chem. Clln. Blochem. 1978. 16, 175. CRC Handbook of Chemistry and Physics, 65th ed.;Weast, R. C., Ed.; CRC Press: Boca Raton, FL, 1984, p F157. Balzani, V.; Carassitl, V. I n photochemistry of Coordlnatbn Compounds; Academic Press: New York, 1 9 7 0 pp 160-161. Szyper, M.;Zuman, P. Anal. Chim. Acta 1978, 8 5 , 357. Hltchman, M. L. Masswement of LWoIved Oky-n; Wiley: New York, 1978; p 28. Copestake. T. 6.; Url. N. Proc. R . Soc. London 1955, 228A, 252. Brauer, H A ; Schmidt. R. photochem. Photobbi. 1983. 37, 587. Wrlghton, M.;W k . S. Mol. Photochem. 1972, 3 , 387.
RECEIVED for review June 26,1991.Accepted October 9,1991.
Problems of Quantitative Injection in Capillary Zone Electrophoresis Eric V. Dose and Georges Guiochon* Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996-1501, and Analytical Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 -6120
CZE effective Injection volumes are modifled by two effects discussed In thls article: diffuslon and Inadvertent hydrodynamic flow. Diffusion causes net flow Into or out of the capillary whenever there exists a concentration gradient at the capillary Inlet, and it Is most Important for small molecules, for short Injection zones, and for slow Injection sequences. Inadvertent hydrodynamic flow, most llkely caused by a difference In levels of the #qulds In the two reservoirs, Is most Important for llquld level differences of a few mllllmeters or more, for short lnlectlon zones, and for caplllarles of short length and large inskle diameter. Computer slmulatlons of the first few mlllbneters of caplllary length show how concentration profiles can develop rapidly.
INTRODUCTION Capillary zone electrophoresis (CZE) has over the past decade been improved in sensitivity, reliability, speed, and range of application. However, the method’s quantitative precision and accuracy have not been addressed as thoroughly.
Two injection hazards, diffusion and inadvertent hydrodynamic flow, to quantitative CZE analysis are discussed below. Since the amount of each analyte injected is altered if either effect is significant under practical experimental conditions, both effects should be carefully controlled. In a normal CZE experiment, a capillary is filled with a background electrolyte solution, and the capillary ends are first immersed in separate reservoirs containing this solution. At one capillary end the background electrolyte reservoir is replaced by the sample reservoir just before sample injection. Injection begins either when the sample solution is introduced to the capillary interior by hydrodynamic siphoning (hydrodynamic injection; effected by gravity, pressure, or vacuum) or when sample ions are drawn into the capillary interior by an applied potential (electrokinetic injection). Hydrodynamic injedion does not discriminate between the ions, and the same effective sample volume of each ion is injected. In electrokinetic injection the applied potential not only draws ions into the capillary but also induces a bulk electroosmotic flow of that fluid through the capillary and the velocity of this bulk flow must be added to each ion’s electromigration velocity (1, 2). While both velocity components are proportional to the
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applied potential (more precisely to the local electric field), the ion mobilities and thus the net injection velocities differ among the ions. This means that electrokinetic injection discriminates among the ions, as described in previous work (3-13). A method for correcting for run-to-run variations in the relative injection contributions of the electromotive and mechanical velocity components has been described ( 1 4 ) . Many CZE concepts have rough analogues in high-pressure liquid chromatography (HPLC), including detection methods, compromise in sensitivity and resolution in injection amounts, and nonlinear effects. However, CZE injection differs from HPLC injection in two ways which are very important to CZE quantitation. First, if a voltage drop is applied to the capillary length during injection, a greater effective volume of faster ions than slower ions will be injected ( 3 , I I ) . This means that when voltage is applied during injection (electrokinetic injection), there exists no single injection volume, whereas there always exists a single injection volume in HPLC analysis (as in CZE with hydrodynamic injection). Second, except when the capillary end is being moved from one solution to another, CZE injection zone boundaries are defined only by interfaces between miscible solutions, while HPLC injection zone boundaries are sharply defined by the valve and loop. Thus, both boundaries of a CZE injection zone are subject t o dispersion even in the absence of any applied mechanical or electromotive forces. This quantitation problem arises because each of the two boundaries resides at the entrance of the capillary a t some time during the injection sequence, at a minimum when the capillary is first immersed in the sample solution and when the capillary is returned to the running electrolyte. Whenever the analyte concentrations in the injection zone differ from those in the electrolyte solution with which it is in contact, net diffusive transport occurs a t the zone boundary, altering the number of ions in the capillary. This is quite possibly the basis of the CZE "ubiquitous injection" effect examined experimentally by other workers (15). This difference may be insignificant for longer CZE injection zones, but for the shorter injections needed for high resolution, dispersion due to diffusion occurring during the injection sequence may dominate CZE analytical error. If the liquid levels in the two reservoirs are at different heights, siphoning also occurs, and quantitation becomes even more comp 1ex. We present computer simulation data which illustrate the nature of quantitative errors due to diffusion during CZE injection. We resorted to simulation because we feel it would be very difficult in physical experiments to rule out quantitation errors due to accidental hydrodynamic flow (caused by unequal sample and buffer elevations), surging of solution in the capillary due to changing the electrolyte reservoirs or to moving the capillary among reservoirs, electric potential rise times, and the like. Diffusion differs from these other possible sources of quantitative error in that it is a well-understood phenomenon, because one knows that it will in fact occur in open-tubular capillaries and because one can compute quantitatively the extent of diffusion's effects. Thus, we are able to focus solely on the magnitudes of error caused by diffusion, which we could not do with confidence in physical experiments. We also show how inadvertent hydrodynamic flow, a simple enough phenomenon, interacts with the effects of diffusion during an injection sequence. Diffusional problems with CZE quantitation are worst for short injections, electrokinetic "concentrating" injections, or long delays during the injection sequence. We present strategies for minimizing these effects in quantitative CZE. Diffusion effects during CZE injection are probably most important for singly-charged ions and less important for multiply-charged ions, including most proteins. Diffusive
effects on quantitation may be suppressed by using long or gel-filled capillaries. Quantitation errors due to inadvertent hydrodynamic flow may be suppressed by assuring that the reservoir liquid levels are equal; by using long, narrow, or gel-filled capillaries; or by using viscous background electrolyte solutions.
METHODS Computer simulations of electrokinetic injections were performed using the model and software previously described by the authors (16). The user defines the electrophoretic system to be simulated by specifying the ion properties, capillary dimensions, and initial capillary conditions (initial potential drop or current and the ion concentrations throughout the capillary length). The injection sequence is defined simply by user instructions to alter the applied voltage or current, the hydrodynamic or electroosmotic flow, or sample-reservoir analyte concentrations, each executed at a user-supplied time. This approach is designed to mimic as closely as possible the parameters that an operator or instrument controls in physical experiments, and the concentration profiles develop naturally from the interaction of applied forces and flows, diffusion, and concentration gradients. There is no manipulation of conditions inside the capillary except those propagated from the user-defmed quantities, just as occurs in physical experiments. The method yields analyte concentrations throughout the capillary length at any desired times (profiles) or the history of concentrations at a given point in the capillary (electrophoregrams). Mobility and electric charge are specified for each ion; the diffusion coefficient D,for each ion i is computed (17) from the signed mobility m, using the relation D,= R T m , / 3 Z , (1) where R is the ideal gas constant, T is the absolute temperature (25 "C throughout this work), Fsc is the Faraday constant, and Z, is the charge on ion i. We enforced electroneutrality in all simulations (16). The examples for which the figures are taken assume injection of three small univalent anions of mobility 5,6, and 7 X lo-* cm2 V-' s-'. Only the anion of mobility 5 X lo-* cm2V-' s-' w as used to generate the figures; results from the other anions are very similar. The capillary is of diameter 50 pm and length 9 cm. The background electrolyte contains ions with mobilities typical of small inorganic ions (18);the cation mobility is 5 X lo-* cmz V-' s-l, and that of the anion is 6 X cm2V-' s-'. These electrolyte ion concentrations were 0.006 M in the background electrolyte solutions and in the samples, except that they were 0.01 M in the background electrolyte for the concentrating injections. Concentration of each analyte ion in the sample reservoir was 0.002 M. The amount injected M , of each ion i was taken to be equal to the number of moles inside the whole capillary following the injection sequence and 10 subsequent seconds of migration, computed as
M I = ar2LLC,,,dz where r is the capillary radius, L is the capillary length, and C,, is the concentration of ion i at position z. Results reported in the figures were only computed after at least an additional 10 s of migration at 100 V cm-' applied field, with background electrolyte in both reservoirs, in order to isolate the zone from the capillary ends. When possible we verified that all analyte ion concentrations and their derivatives were zero at the capillary inlet before integrating. During the injection process itself there generally exist concentration gradients at the capillary inlet, so integrations performed during the injection period do not meet this criterion.
RESULTS AND DISCUSSION One may compute an "ideal" number of moles M I of anal@ i introduced into a capillary by electromotive or bulk flow transport as
M, = rr2u,tin,Cl
(3)
where u, is the net ion velocity during injection, tlnj is the
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Time (sec)
0 0
0.02
0.06
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0.08
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Displacement from Column End (cm) Figure 1. Amount of sample in the capillary at 2 (leftmost curve), 4, 6,8, 10, 12, 14, 16, 18, and 20 s (rightmost curve) after Immersion of the capillary end into the anatyte solution. Conditions: capillary inside cm2 dnmeter, 50 pm; analyte, monovalent anion of mobility 5 X V-’ s-’; ion concentration, 2000 pM. Inset: points correspond to the profiles at the lower left, this figure; curves correspond to amounts in the capillary with underlying hydrodynamic flows of -0.001 cm s-’ (out of capillary end, upper curve) and +0.001 cm s-l (into capillary end, lower curve). injection time, and C, is the concentration of analyte i. Equation 3 fails to account for sample ions introduced to or removed from the capillary due to diffusion. For example, any significant delay between the end of the injection pulse and the start of the electrophoretic separation (running electrolyte present at the capillary end) allows sample ions or molecules to enter the capillary or migrate back out of it, depending on the sign of the sample concentration gradient at the capillary end. In all cases the rate of analyte introduction due to diffusion is given by Fick’s law
-aMj-
200
z--o+
600
400
Delay Time (sec) Flgure 2. Amount of analyte in the capillary after immersion of the capillary end into the analyte solution. The points are the amounts in the capillary calculated from simulation resuits. The curve is the best fit of the timasquare-rootfunction to the data. Other conditions are as in Figure 1. 2000
%
v
s
.-
. I -
E
. I -
20
C
!
Time (sec)
0
VHo= +0.001 cmisec
dCo,i
- -.nr2Di lim-
(4) az This effect must be considered because (1)the change in M i caused by diffusion will differ among sample species, causing uncertainty in quantitative accuracy even if internal standards are used; (2) as CZE injection zones are shortened to increase separation efficiency, delay times and the resulting diffusional errors will become more important; and (3) as we show below, net diffusional introduction of sample occurs most rapidly immediately after sample presentation. This last observation implies that it will be very difficult to solve these problems solely by minimizing delay times, that is, by relying on making rapid, automated reservoir changes. We caution the reader that though eq 4 makes it appear that the amount introduced by diffusion is proportional to the diffusion constant, this is not so. Greater diffusion coefficients generate faster decreases in the gradient a t the capillary end, and the overall effect is that the amount introduced is closer to the square root of the diffusion coefficient. Net analyte diffusion into the capillary begins immediately when one end of a capillary previously filled with background electrolyte is placed in the sample solution. Initial rates of analyte migration into the capillary can be extremely high, though the rates slow considerably after a few seconds. For example, for the small analyte ion in Figure 1, the amount introduced by diffusion in the first 2 s after presentation of the sample is about 10% of the amount contained in a 1-mm injection zone. Because the amount introduced by diffusion in this manner increases roughly as the square root of the delay time (Figure 2), decreasing the relative error due to diffusive influx from 10% to 1%would require that the delay time after presentation of the sample and before the start of injection at
0
0 0
0.02
0.04
1 0.08
0.06
0.1
Displacement from Column End (cm) Figure 3. Profile of the analyte concentration at 2 (leftmost curve), 4, 6, 8, 10, 12, 14, 16, 18, and 20 s (rightmost curve) after immersion of the capillary end into the analyte solution. Conditions: underlying hydrodynamic flow rate, +0.001 cm s-l s (into capillary end). Inset: points correspond to the profiles at lower left, this flgure; curves correspond to amounts in the capillary with underlying hydrodynamic flows of 0 (upper curve) and -0.001 cm s-’ (out of capillary end, lower curve). Other condffions are in Figure 1. be decreased from 2 s to 20 ms. Even for analyte ions with diffusion constants of 10% of that in Figure 2, the reservoirs would have to be changed and the injection begun within 200 ms. It is not clear how such rapid changes could be achieved. We expect these problems to be much less important for large molecules with their much lower diffusion coefficients. The amount of sample introduced during such delays is modified by significant hydrodynamic flow or siphoning into the capillary due to,for example, unequal heights of reservoir liquid surfaces. If a hydrodynamic flow rate of only 10 pm/s or 19.6 pL/s (which would require only 6.3 mm difference in reservoir liquid levels for an aqueous background electrolyte in a capillary of 50 cm length and 50 p m inside diameter) is introduced in the case in Figure 1, the analytes enter the capillary more rapidly (Figure 3), and the amount injected in this manner continues to increase, approaching a linear asymptote. This asymptote is linear because while the diffusive influx contribution decreases as the front moves farther from the inlet, the hydrodynamic flow contribution remains constant until the leading edge of the injection profile reaches the opposite end of the capillary.
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1.5 I
V ni,
m
.
cmlsec +0.001
I
m
m
I
0 I
20
D m
, ,V = -0.001 cm/sec
. . - I
m m m . m . - - g
"7.-
-0.001
Asymptote '
0 0
0.04 0.06 0.08 Displacement from Column End (cm)
0.02
0.1
We find that diffusional sample entry can be significant even in the presence of a small opposing hydrodynamic flow (Figure 4). Just as when such flow is absent, a small amount of sample diffuses into the capillary by diffusion in the first few seconds after sample presentation. However, when opposing flow is present, the net inward migration of sample ions is initially rapid but slows considerably, and the concentration profile approaches a limit. We can solve for the shape of this limiting profile by combining a differential representation of the concentration rate of change due to hydrodynamic transport toward the capillary end az and a similar representation of the effects of diffusion at
ac, a2c. - = D .1 at
a22
to yield a stationary state (Figure 5 ) 221. = co,ie-uz/D2
c
0
10
20
30
Time (sec)
Figure 4. Profile of the analyte concentration at 2 (leftmost curve), 4, 6, 8, 10, 12, 14, 16, 18, and 20 s (rghtmost curve) after immersion of the capillary end into the analyte solution. Conditions: underlying hydrodynamic flow rate, -0.001 cm s-' (out of capillary end). Inset: points correspond to the profiles at the lower left, this figure; curves correspond to amounts in the capillary with underlying hydrodynamic flows of 0.001 cm s-' (into capillary end, upper curve) and 0 (lower curve). Other conditions are as in Figure 1.
ac, - -u aC1 _
0 4
(5)
Flgure 5. Amount of analyte ion in the capillary after immersion of the capillary end into the analyte solution. Underlying hydrodynamic flow rates are as shown. The asymptote shown is the limit of the amount injected, calculated as in eq 8, for a hydrodynamic flow of -0.001 cm s-'. Note the rapid entry of the analyte in the first 2 s. Other conditions are as in Figure 1.
1
(7)
that is, that the profile tends toward the exponential decay form as a limit. The limiting amount injected is the product of the capillary cross section and the profile integral from eq 2, that is areai = Co,iDi/u (8) This limit is represented by the horizontal asymptote in Figure 5, inset. To summarize, immediately after initial presentation of a sample solution to an electrolyte-filled capillary, there is rapid diffusion of sample ions to the capillary. The rate of entry slows, and in the absence of hydrodynamic flow the amount in the capillary is proportional to the square root of the time passed. When hydrodynamic flow into the capillary end occurs, still more sample enters the capillary, and the rate of entry approaches a constant until the sample reaches the opposite end of the capillary. When there is hydrodynamic flow out of the capillary and into the sample reservoir, entry begins very rapidly, but the amount injected and indeed the entire injection zone shape each approach a limit. Regardless of the direction or magnitude of the underlying hydrodynamic flow, the initial rate of the diffusional component of sample entry is very high so that a strategy of limiting analyte entry solely by limiting the time during which diffusion can take
--6 4.5 z
2000
0 0
(6)
Osec
0.1 0.2 0.3 Displacement from Column End (cm)
0.4
Figure 8. Profile of the analyte concentration inside the capillary at 0, 60, 120, 180, 240, and 300 s after hydrodynamic injection at 0.01 cm s-' for 10 s. Sample solution is still present at the Capillary end. Inset: integrated amount in the capillary at the indicated times after the end of injection. Other conditions are as in Figure 1. Profile and integated amounts are similar for electrokinetic injections of equal zone lengths.
effect does not appear very promising. There may exist some injection sequence which manipulates the timing of sample presentation, hydrodynamic flow, and voltage such that one minimizes the effects of diffusion on effective volume injected, but to date we have discovered no such sequence. The most complex behavior in this study was found for cases in which delays are introduced immediately after sample injection, that is, just before the background electrolyte solution is reintroduced. For hydrodynamic injection and nonconcentrating electrokinetic injections (that is, where the concentrations in the injection zone are the same as in the sample, Figure 61, there is little quantitative error introduced even after considerable delay. This is so because the zone must broaden substantially a t the leading edge before any concentration gradient can develop at the capillary inlet. Without gradients at the capillary ends, no net diffusion occurs into or out of the capillary (eq 7 ) , regardless of the shape of the concentration profile inside the capillary. Thus, quantitative accuracy does not seem to be affected much by delays after hydrodynamic or nonconcentrating electrokinetic injection as long as the capillary end remains in contact with the sample solution.
ANALYTICAL
--5
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-f .-6
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e
L
..........*.. ....’*
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CHEMISTRY, VOL. 64,NO. 2, JANUARY 15, 1992 127
.-
I
e *
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Displacement from Column End (cm) Flgure 7. Profile of the anaiyte concentration inside the capillary at 0, 20, 40,60,80, 100, 200,300,400,500,and 600 s after a concentrating electrokinetic injection at 100 V cm-’ for 2 s. Sample solution is still present at the capillary end. Inset: integrated amount in the capillary at the indicated times after the end of injection. Background electrolyte ion concentrations are 0.01 M; other conditions are as in Figure 1. By contrast, when the sample solution conductivity is lower than that of the background electrolyte solution, the sample zone is compressed during electrokinetic injection (Figure 7 ) . If the capillary end is then left in the sample solution, the injected zone broadens, which causes sample ions to migrate forward at the leading edge as well as out of the capillary at the capillary inlet. At first the concentration gradient at the capillary inlet causes rapid loss of sample ions from the capillary (see inset, Figure 7 ) ,but as the zone broadens further, the inlet gradient decreases in magnitude and then reverses in sign, and sample ions begin to diffuse back in, increasing the amount injected. There exists a minimum in the plot of amount injected vs time. In the example of Figure 7 , the minimum occurs at about 180 s of delay; for shorter injections or greater concentrating effect (lower sample conductivity), the reversal would occur sooner. Delays introduced just after the capillary end is placed back in the background electrolyte solution and just before the driving potential is applied to start the separation result in very rapid loss of sample ions. This loss is due to the very steep concentration gradient which develops immediately upon immersion of the capillary end in the background electrolyte solution. The concentration profile resulting from hydrodynamic and nonconcentrating electrokinetic injection (Figure 8) decays very rapidly near the capillary inlet, and the amount of sample in the capillary (see inset, Figure 8) decreases several percent in just the first few seconds. The effect is even more rapid in the case of concentrating electrokinetic injection (Figure 9) because the concentration gradient at the capillary inlet is already partially developed by the concentrating effect of the conductivity differences. Such quantitation errors due to diffusion during CZE injection may well become more important in the future because injection volumes are likely to become shorter. Many investigators are now working to achieve better removal of heat from the capillary, greater detector sensitivity and signalto-noise ratios, and improved inertness of the capillaries’ internal wall. These efforts are aimed at accelerating the separation process by obtaining higher separation efficiency and/or using shorter capillaries. However, success in these approaches will call for shorter optimum zone lengths, and quantitative problems due to diffusion during injection will become relatively more important. Other approaches to minimize quantitation errors due to diffusion should be considered. Using longer capillaries will allow one to inject longer sample zones, decreasing diffusion
0
0.1
0.2
0.3
0.4
Displacement from Column End (cm) Flgure 8. Profile of the analyte concentration inside the capillary at 0, 20, 40,60,120, 180, 240,and 300 s after hydrodynamic injection at 0.01 cm s-’ for 10 s and immersion of the capillary end into the background electrolyte solution. Inset: integrated amount in the capillary at the indicated times after the end of injection. Other conditions are as in Figure 1. Profile and integrated amounts are similar for electrokinetic injections of equal zone lengths.
T = 7
Time (sec)
0
0.1
0.2
h 0.3 (
4
Displacement from Column End (cm) Flgure 9. Profile of the analyte concentration Inside the capillary at 0, 20, 40,60,120, 180, 240,and 300 s after a concentrating electrokinetic injection at 100 V cm-’ for 2 s and immersion of the capillary end into the background electrolyte solution. Inset: integrated amount in the capillary at the indicated times after the end of injection. Background electrolyte ion concentrations are 0.01 M; other conditions are as in Figure 1. effects, but this approach is of very limited utility because the potential drop across the capillary at constant analysis time increases as the square of the capillary length. One may minimize diffusion problems by applying CZE to the separation of multiply charged sample ions due to these ions’ increased charge-to-diffusion constant ratios. This approach is also extremely limited not only because it constitutes tailoring the analytes to the technique but also because the analyst needs conditions like pH to be available for maintenance of analyte stability, analyte mobility, and separation selectivity. It is true, though, that the diffusion problem is less important for proteins and larger peptides than for small molecules. In this regard, large molecules have an inherent advantage in hydrodynamic injection since the diffusion constants are small while the rate of injection, which depends on the bulk flow rate is unaffected by analyte ion size. For example, a large molecule or small peptide with a typical diffusion coefficient of cm2s-l would require about 7 times as long to diffuse into the capillary to a given degree as would cm2 s-l. A a small ion with a diffusion coefficient of 5 X very large protein with a diffusion coefficient of 5 x lo-‘ cm2 s-l will require 30 times as long to diffuse into the capillary to the same extent as a small ion would. Thus, the quanti-
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tation problems that occur on a time scale of tens or hundreds of milliseconds for small molecules will require several seconds for large proteins. Multiply charged molecules have a similar advantage in electrokinetic injection. Thus quantitation of large proteins by CZE will apparently not be interfered with by delays typical of modern autosamplers so long as no other significant delays are introduced. Errors due to inadvertent hydrodynamic flow will not be protected against in the same manner, however, since this effect is a bulk-flow effect. The most promising solution to the problem of diffusion during the injection sequence is the use of gel-fiied capillaries. The convoluted nature of diffusion pathways through the liquid phase of the gel tends to suppress the effects of diffusion more than it does those of electrokinetic migration. Thus, one can load the sample onto the capillary, and delays during the injection sequence should be less important than in simple open-tubular capillaries. The accuracy advantage gained from the use of gels will depend upon the exact nature of the gel a t the capillary entrance, which may be more difficult to control than it is in the rest of the capillary. More specifically, the gel must terminate flush with the end of the capillary. However, there are potentially great gains in accuracy for short-injection zones or short capillaries. It is also important that accidental hydrodynamic flow effects be eliminated for short injection zone lengths. One computes the hydrodynamic flow velocity as uHD =
pgr2Ah/8qL
(9)
where p is the background electrolyte density, g is the gravitational acceleration, r is the capillary radius, Ah is the difference in height between the two reservoir liquid levels, is the background electrolyte viscosity, and L is the capillary length. Decreasing the injection time and the delays between the injection steps will mitigate these effects as well as those of diffusion mentioned above. One can also increase the capillary length, decrease the capillary inside diameter, and ensure that liquid levels in the two reservoirs are at the same height. Increasing the capillary length will lengthen the time of analysis, but decreasing the capillary inside diameter has much to recommend it, especially in that it also affords increased heat dissipation. One could also conceivably increase
the viscosity of the background electrolyte solution, but any such change will probably change the chemistry of the system as well, adding an unnecessary complication. Splicing a small-diameter injection capillary to a wider-bore separation and detection capillary may provide some protection in the same way that axial diffusion in narrow-bore HPLC transfer tubing is made relatively unimportant. We expect that gelfilled capillaries will minimize CZE quantitation errors due to diffusion, and we are quite confident that it will entirely eliminate the inadvertent hydrodynamic flow problem since in this case the capillary's total flow resistance, not the properties a t the ends, is what is most important.
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RECEIVED for review July 8, 1991. Accepted October 2, 1991. This work is supported in part by Grant DE-FG05-86ER13487 from the U.S. Department of Energy, Office of Energy Research, by Grant CHE-8901382 from the US. National Science Foundation, and by the cooperative agreement between the University of Tennessee and Oak Ridge National Laboratory.
