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Anal. Chem. 1991, 63,2042-2047
dependence of the mobility of DNA was found to be different in the absence and in the presence of ethidium bromide, especially for the lower molecular weight fragments.
ACKNOWLEDGMENT We acknowledge Prof. Barry L. Karger for his stimulating discussions. We further thank Drs. Anita Costa, Richard Palmieri, and Herb Schwartz for reyiewing the manuscript before submission. The help of Phyllis Browning in the preparation of the manuscript is also highly appreciated. Regiatry No. Ethidium bromide, 1239-45-8. LITERATURE CITED Jorgenson, J. W.; Lukacs, K. D. sckmce 1089, 222, 266-272. Hjerten, S.; mu, M. D. J . Wnwmtop. 1085, 347. 191-198. WaUkrgfOrd, R. A.; Ewbrg, A. 0. Anal. Clwm. 1087, 59, 1762-1766. -don, M. J.; Hueng, X.; Pentoney, S. L., Jr.; a r e , R. N. S c h c e 1088, 242, 224-228. Karger, 8. L. Netwe 1980, 339, 641. Cohen, A. S.; Najarlan, D. R.; Paulus, A.; Guttman, A.; Smith, J. A.; Karger, 8. L. Proc. Net/. A a d . S d . U.S.A. 1988. 85, 9660-9663. Guthen, A.; Cohen, A. S.; Hew, D. N.; Karger, B. L. Anal. C b m . 1900, 62, 147-141. Hew,D. N.; Cohen, A. S.; Karger, B. L. J . chrometogr. 1900. 516, 33-46. Lux, J. A.; Yln, H. F.; Shombwg, 0. J . H@h Resdut. Chromtogr. 1000, 73, 436-437. Smith, L. M. ~ e t u e1001, 349,812-813. K a w , B. L.; Cohen, A. S.: " a n , A. J . Chromatogr. 1089, 492, 585-614. Horeisi, V.; Tlcha, M. J . clwomefcgr. 1081, 216, 43-62. Wejsi, V.; Tlcha, M. J . Chromtogr. 1080, 376, 49-67.
(14) Nekamura, K.; Kuwahara, A.; Takeo, K. J . Chfomatw. 1080, 796, 85-99. (15) " a n , A.; Paulus. A.; Cohen, A. S.;Grinberg, N.; Karger, B. L. J . ChromatogV. 1088, 448. 41-53. (16) Vacek. A.; Bourque, D. P.;Hewlett. N. 0. Am/. Blochem. 1082, 724. 414-420. (17) Flint, D. H.; Harrington, R. E. Blochemkrby 1072, 1 1 , 4858-4864. (16) Dlngman. C. W.; Fisher, M. P.; Kakefuda, T. 6kchemishy 1972, 7 1 , 1242- 1250. (19) Nathekarntkooi,S.; Oefner, P.;Chin, A. M.; Bonn, 0. Budapest Chromatography Conference, Budapest, Hungary, Aug 14-17, 1990 L-2. (20) Maniatis, T.; Fritsch, E. F.; Sambrook, J. In Molecukr Cloning: A lebwatw Manuel; Cold Spring Harbor Laboratory: Cold Spring Harbor, NY, 1982. (21) LePecq, J. B.; Paleotti, C. J . Md. Hol. 1967, 27, 87-106. (22) Nelson, R. J.; Paulus, A.; Cohen, A. S.; Guttman, A.; Karger. B. L. J . chrometogr. 1080, 480, 111-127. (23) . . Gurrmen. A. Beckman Instttute Inc. Research and DevebDment Laboratory, 1990. (24) Kasper, T. J.; Melera, M.; Gozel, P.;bownlee, R. G. J . Chromtugf. 1088, 458, 303-312. (25) Waye, J. S.; Fourney, R. M. Appl. Theor. Ehxtrophoressls 1000, 1 , 193-196. (26) Ukk%;,-K.; Schwerh. H. E.; Sunzeri, F. J.; Busch, M. P.; Brownlee, R. G. Thlrd Internationel Meeting on HI!& Performance Capillary Electrophoresis, Sen Diego, CA, Feb 3-6, 1991; PT-5. (27) Swthern, E. M. Anal. Blochem. 1070. 100, 319-323. (28). Stellwagen, N. C. B(0chemlStry 1989, 22, 8186-6193. (29) Lumpkh, 0. J.; Dejardln, P.; Zimm, B. H. B i o ~ n w s1985, 24, 1573- 1593. (30) Cantor, C. R.; Smkh, C. L.; Mathew, M. K. Annu. Rev. Siophys. Biophys. Chem. 1088, 17, 267-304. (31) Lennan, S. L.; Frisch, H. L. ekporvmers 1982, 21, 995-997. (32) Freifelder, D. J . Mol. W .1071, 60, 401-403.
RECEIVED for review April 5,1991. Accepted June 19,1991.
Optimization in Sample Stacking for High-Performance Capillary Electrophoresis Dean S. Bur& and Ring-Ling Chien* Varian Research Center, 3075 Hansen Way, Pa10 Alto, California 94304-1025
A simple modd for the opthrlzaUon of peak variance in sample stacking with a gravlty4nJect.dsample has been devdoped. I n sample stacklng, a long plug of low-concentration buffer containing a sample for separation lo introduced into a column filled with a buffer of the same wmpodtion but of a higher concentration. The sample lono then migrate very r a m underthe ed"d applied elecbicfleld Intlwcwnple plug untH they reach the concentration boundary. Once they cross the boundary, the ions slow down and stack Into a narrow band. Theoretlcally, the peak width in sample stacking b proportknd to the ratb, 7, ol buffer concentration In the odglnai cwnple SdUHon to that In the column. However, this difference in the concentratlons indde the capillary column a h generates an .kctrooemotk pressure orlglnatlng at the concentration boundary. The laminar flow resuiting from the electroosmotic pressure causes extra peak broadening. Sample stacking and laminar broadening work against each other to yield an optlmai point rdatlng to the sample buffer concentration, the separation buffer concentratlon, and the sample plug length. The predlcations of the model are in agreement with experimental results.
INTRODUCTION One area of concern in high-performance capillary electrophoresis (HPCE) since its inception has been the short 0003-2700/9 1/0363-2042.$02.50/0
optical path associated with on-column detection ( I ) . Conventional W detectors have detection limits between 1X lob and 1 X lo4 M analyte for a 75-pm4.d. column. An increase in sensitivity usually is obtained through improvement of the detector. However, it is possible to obtain enhanced detection limits by performing on-column concentration. Several techniques have been reported to perform on-column concentration to enhance the detectability in HPCE (2-8). For example, Everaerts and other groups used isotachophoresis to achieve a high sample concentration within a pre-CE column (2,3,6).However, a careful choice of leading, terminating, and background electrolytes was required to perform this isotachophoretic preconcentration step. A simpler concentration technique called sample stacking has been well-known in electrophoresis (7-10). An increase of a factor of 10 in detectability using sample stacking in HPCE was reported by Lauer's group (5). In our application of sample stacking, the compositions of the buffer in the sample plug and in the column are the same. A long plug of sample, dissolved in a lower concentration buffer, is introduced hydrostatically into the capillary containing the same buffer but with a higher concentration. Then the separation voltage is applied across the column. Because the buffer in the sample plug has a low concentration of ions, the resistivity in the sample plug region will be higher than the resistivity of the rest of the column. Consequently, a high electric field is set up in this region. As a result, the ions will migrate rapidly under this high field toward the steady-state 0 1991 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 63, NO. 18, SEPTEMBER 15, 1991
boundary between the lower concentration plug and the support buffer. Once the ions pass the concentration boundary between the sample plug and the rest of the column, they immediately experience a lower electric field and slow down, thus causing a narrow zone of analyte to be formed in the support buffer region. This phenomenon is in accordance with Kohlrausch’s regulating function (11). The thin zone of ions then moves through the support buffer and separates into individual zones according to conventional free zone electrophoresis. The stacking mechanism occurs for both positively and negatively charged species. The positive species stack up in front of the sample plug, and the negative species stack up in back of the sample plug. The neutral compounds are left in the sample plug and co-elute. Theoretically,the amount of stacking is simply proportional to the ratio of resistivities (or the inverse of conductivities) between the buffer in the sample plug and the buffer in the rest of the column. If the two different buffer regions have similar compositions, this ratio of resistivities is simply the inverse of the ratio of concentrations. Thus, a larger difference in the concentrations will yield a narrower peak; in other words, more stacking will occur. An extrapolation could be made that a rather long sample plug prepared in water or a very low concentration buffer should stack all of the analyte into a very thin zone in the high-concentration support buffer. However, a laminar flow is generated due to this mismatch between the local electroosmotic velocity in each individual region and the bulk velocity of the fluid inside the column. The laminar flow will broaden the sharp zone generated by the stacking process (12). A large difference in concentrations results in a large laminar flow. These two effects, stacking and broadening, work against each other. Therefore, the best matrix for the preparation of the analyte is somewhere between the case of pure water and the normal concentration of buffer used for separation in HPCE. In this report, we will describe in detail the mathematical model for the optimization of peak variance in sample stacking. Experimental results will also be presented.
EXPERIMENTAL SECTION The experiments were performed on a research version CE instrument,similar to the one reported by Jorgenson and Lukaca (1). The high-voltage power supply (Glassman High Voltage, Whitehouse Station, NJ) delivered -30 kV in 5-kV increments. The column was a 1oOcm-long, 75-pm-i.d., 365wm-0.d. fused silica capillary (PolyMicro Technologies, Phoenix, AZ)with a detector window at 65 cm from the injection end. The detector window was formed by burning off a 1-mm section of the outer polyimide coating. The W absorbance detector was a Varian 2550 (Walnut Creek, CA) with a 1Wwm slit in a modified microcell holder. The wavelength of analysis was 265 nm. Stock solutions of 7.3 X lo4 M PTH-arginine and PTH-histidine were made up in HPLCgrade distilled water (Aldrich,Milwaukee, WI) and then diluted M. The buffer was 100 mM 2-(N-morpholino)to 3.6 X ethanesulfonic acid (MES) brought to a pH of 6.13 by adding 100 mM histidine (HIS) to the solution. The other buffer concentrations were made by serial dilution of the stock 100 mM MES/HIS buffer. All chemicals were purchased from Sigma (St. Louis, MO). The sample vial was positioned 15 cm above the floor of the buffer reservoir for gravity injection. The injection end of the capillary was inserted into the vial and held there from 10 s to 6 min. After injection, the end of the capillary was returned to the buffer reservoir and -30 kV was applied across the column. All runs were made in triplicate. RESULTS AND DISCUSSION Several investigators have studied, either theoretically or experimentally, peak-broadeningmechanisms in HPCE, which ultimately limit the HPCEs separation efficiency (13-15). In an ideal diffusion limited case, the detected sample peak has a Gaussian shape with a variance of 2Dt, where D is the
04
I 1
2043
I
I
I
I
I
2
3
4
5
6
Injection time (min.)
Figure 1. Plot of the peak’s full wldth at half-maximum of PTH-Arg vs injection time. The sample is prepared in the 100 mM MESIHIS buffer. Peak widths in the lower left-hand portion of the plot are detector limited, whereas peak widths in the rest of the plot are Injection limited. Run conditions are given in the text.
diffusion coefficient and t is the migration time. In reality, other factors such as sample plug length, thermal convection, electrokineticdispersion,wall interaction, detector width, etc., will add together to generate a broader peak. The totalvariance of a peak, 2,in HPCE is the combination of peak broadening from all factors and can be expressed as 0 2 = Ud2 + :a g0j” (1)
+
1
where ud2is the variance due to diffusion, u t is the variance due to the injection plug length, and is the sum of all the variances due to other sources. If the observed peak shape is Gaussian, the full width at half-maximum is then related to the variance: XFWHM = 2.35~. In our experiments, we use gravity injection because of its simplicity and because it does not have the bias associated with electroinjection. For a rectangular injection profile, the variance due to the injection is equal to x1/12,where x1 is the length of the injected sample plug (16). The sample plug lengths injected are calculated to be from 0.7 mm for the 10-s injection to 2.4 cm for the 6-min injection by using both the Poiseuille equation and by measuring the width at the base of the water peak. Figure 1shows a plot of the observed peak width as a function of injection time for a sample prepared in 100 mM MES/HIS buffer. Since the sample plug has the same buffer concentration as the rest of the column, there is no sample stacking. At short injection times, the peak width is mainly dominated by diffusion. For longer injection times, the peak width is dominated by the sample plug length. The peak width continues to increase in a linear fashion as the injection time increases. Sample Stacking and Peak Narrowing. In sample stacking, a long plug of sample prepared in a lower concentration buffer or water (region 1) is injected by gravity into a column filled with higher concentration buffer (region 2). After injection, the end of the column is switched back to the reservoir with the high-concentration buffer and a high voltage is applied to the column, causing electrophoresis to occur. The radius of the column is assumed to be uniform along the whole column; thus, the ratio of the electric field strength in the injected sample plug, El,and the rest of the column, Ez, is (2) W E 2 = PdP2 = Y where p1 and p2 are the respective resistivities of these two regions and y is the field enhancement factor. In general, the
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ANALYTICAL CHEMISTRY, VOL. 63, NO. 18, SEPTEMBER 15, 1991
resistivities, p, are inversely proportional to the buffer concentration, C, for buffers with the m e composition. muation 2 can then be simply written as
(3) where Cb2 and c b l are the buffer concentrations in these two regions, respectively. In the case of sample prepared in water or very low concentration buffer, the effects of sample ions and impurities on the total resistivity must be considered. Nevertheless, the field enhancementfactor, y, can easily reach several hundred if the sample is prepared in water. For a large y, the ions inside the injected sample plug will experience a very high electric field strength and move very rapidly toward the high-concentration region. Once they paw the concentration boundary, they will experience a lower electric field strength and slow down. Under steady-state conditions, the ion fluxes flowing through the concentration boundary have to be conserved (11);thus, where Cil, Ci2and uil, ui2 are the concentrations of sample ion species i and their electrophoretic velocities inside the injected sample plug and the rest of the column, respectively. Since the electrophoretic velocity of the ions is simply proportional to the electric field strength, eqs 2-4 yield ci2/cil
=
Cb2/Cbl
(5)
Equation 5 shows that the concentration of sample ions migrating into the high-concentration-bufferregion will be enhanced by the field enhancement factor, y. Because of m a conservation, the length of the sample zone in the high concentration buffer region must decrease by the same factor. Neglecting the diffusion effect, the effective plug length or the length of the sample zone after stacking is Xi2
= XI/Y
(6)
where zi2 is the plug length of sample ion species i in the high-concentration-buffer region after stacking and X I is the initial plug length of the injected sample. Equation 6 shows that the effective plug length is inversely proportional to the field enhancement factor. The larger the difference in the concentrations between the sample plug and the supporting buffer inside the column is, the n m w e r the peak will become. Now the variance due to injection, q2,discussed in the previous section becomes
Figure 2 shows the PTH-arginine signals of a sample prepared in various MES/HIS buffer concentrations and injected into a column fiied with 100 mM MES/HIS buffer. The effect of sample stacking on the peak variance is clearly observed. Laminar Flow and Peak Broadening. According to eq 6, the amount of stacking should be at least several hundred if the sample is originally prepared in water. As a result, the variance due to the injection should be negligible such that the total peak width reaches the diffusion-limited peak width. However, the result in Figure 2 indicates that a much smaller stacking effect than expected is found as the buffer concentration in the sample plug is reduced. The peak width for the case of sample in water is broadened to about the same as in the 12.5 mM MES/HIS buffer. This extra peak-broadening mechanism is the result of laminar flow generated during the stacking process. The origin of this laminar flow is discussed in detail by Chien and Helmer (12). Briefly, the nonuniform distribution of the electric field strength causes a difference in the local
0
10
20
30
40
Migration time (arb. unit)
50
Flgw2. &amofPrrCArgpeak shapesasafunctknof the buffer coI1cBntTBtkn in the sample plug. All sample plugs are 5mhr InJectkms wllh sample buffer concentratkns ranging from 100 mM to pve water.
electroosmotic velocities, which in turn generates an electroosmotic pressure across the concentration boundary. This pressure difference generates laminar flows in both the highand low-concentration regions with average laminar velocities that are exactly equal to the difference of the bulk electroosmotic velocity, ub, and the local electroosmotic velocities, ue1 and ue2 (84 ual = Vel - u b
(8b) = ub - ue2 where url and ua are the average laminar velocities in the lowand high-concentration regions, respectively. The bulk electroosmotic velocity is the average of the local electroosmotic velocities weighted by their respective lengths ua2
(12)
= X&el + (1- Xa)UeZ (9) where X , is the ratio q / L , L being the column length. By substituting eq 9 into eqs 8a and ab, the average laminar velocities ual and us2 can be expressed as (104 u,2 = Xu(Ve1 - Uez) (lob) ua1 = 41 - XJ(Ue1 - uez) In turn, the local electroosmotic velocities are simply proportional to their respective local electric field strengths ub
where uW1and ueo2are the electroosmotic velocities of the lowand high-concentration buffers under homogeneous conditions, i.e., under a uniform field E@ The local electric field strength will depend on the length of the sample injection by
Substituting eqs Ila, Ilb, 12a, and 12b into eq 10a and replacing p1/p2 by y, we obtain
ANALYTICAL CHEMISTRY, VOL. 63, NO. 18,
SEPTEMBER
2045
15, 1991
Table I. Relevant Parameters for Two Special Cases yx,
> 1
El Ea Vel ue2
ub
YUWl um2
-
(V~0)UWl
0
um2 YV.01
u-1
Val
Ud
-0
um1
-(1/xo)um1
which is the average laminar velocity in the high-concentration region. Substituting eqs l l a , l l b , 12a, and 12b into eq 10b yields the average laminar velocity in the low-concentration region, Le., the original injected sample plug 0
Equations 13 and 14 show the nonlinear relationships of the average laminar velocity in the high- and low-concentration regions,respectively, to the normalized injected sample length, x,, and the electric field ratio, y. Because the sample ions spend almost no time in the injected sample plug, the perturbation by the average laminar velocity in the low-concentration region on the sample stacking is assumed to be very small. Therefore, Figure 3a is a plot of the average laminar velocity in the high-concentrationbuffer region, u ~as, a function of the field enhancement fador, y, for various sample plug lengths. The plot shows there are two distinct cases for the average laminar velocity; one case is where y is very large, and the other is where y is small. When y is large, the average laminar velocity reaches a large steady-state value, which generates peak broadening. In the other case where y is small (Figure 3b), the plot of the average laminar velocity versus y is linear and the slope of the line is proportional to the length of the sample plug. Since the sample plug length has such a large influence on peak broadening, ita length will have to be kept reasonably short. Table I lista some relevant parameters for two special cases. For the case where the sample length, x,, is short and yx, > 1, the local electroosmotic velocity in the high-concentration region approaches zero. Both the bulk velocity of the buffer and the average laminar velocity in the high concentration region will be equal to the homogeneous electroosmotic velocity of the low-concentration buffer. The large mismatch between the velocities means the peak broadening is at its maximum and the sample plug is pushing the high-concentration-bufferregion through the column like a piston. The laminar flow in the high-concentration-bufferregion will broaden the sample peaks by adding an enhanced diffusivity term, D, = rO2u2/48D,where ro is the radius of the column and D is the normal diffusivity of the sample ions (7). The variance of the peak due to the laminar flow after a period of time t is equal to 2D,t or where DallDd and tl, t z are the enhanced diffusivities and times in the original injected sample plug and the rest of the column, respectively. Assuming the contribution from the injected sample plug is very small due to the relatively short resident time, eq 15 becomes (16)
50
100
150
250
200
300
Field enhancement factor, y
J ’
0.00
2
6
4
0
10
Field enhancement factor, y Figure 3. (a, top) Theoretical plot of the lamlnar velocity In the d u m vs the field enhancement factor for different sample plug lengths. Three sample plug lengths are 0.1 % , 1 %, and 10% of the total column length. (b, bottom) Enlarged view of the lower left-hand portion of a.
Equation 16 is very similar to the well-known equation in chromatography for the peak broadening due to laminar flow. However, the mobile phase in conventional chromatography migrates down the column with the average laminar velocity. One can simply replace vat in eq 16 by the column length, L. Conversely, in HPCE, the sample migrates with a combination of the electrophoretic and the electroosmotic velocities. Therefore, the migration time and the average laminarvelocity are not directly related and eq 16 is used to calculate the variance due to the laminar flow. Optimization in Sample Stacking. Adding the variance due to laminar flow into eq 1, the total variance of a peak in HPCE is now 6 2 = Ud2 q2 + fJ,2 cuj” (17)
+
+
1
Substituting eqs 7,13, and 16 into eq 17 and neglecting the contributions from other sources, we obtain the total peak variance in terms of normalized length, x,, and field enhancement factor, y, as
or
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ANALYTICAL CHEMISTRY, VOL. 63, NO. 18, SEPTEMBER 15, 1991
where
80
a, 0 C
.-m
I\
,
4 min injection
60
> b = -ue02
Y
u,01
For the case yr, b, which is the case of most interest, eq 19 can be simplified as c2 =
2Dt(l
+ A ( ~ , / y+) B~ ( x , ~ ) ~ )
dr
40
20
(20)
Equations 19 and 20 show that while the variance due to injection will decrease as the buffer concentration in the sample plug decreases due to sample stacking, the variance due to laminar flow will increase as the difference in buffer concentration increases. These two effects, stacking and broading, work against each other so that the best concentration for sample carrier is somewhere in between the case of pure water and concentrated buffer. Figure 4 presents both the theoretical calculations (solid line) and the experimental data of the total peak variance as a function of the field enhancement factor, y, for several different sample plug lengths. When y is small, the peak variances scale with the length of the sample plug. As y becomes larger, the peak variances narrow due to the sample staking mechanism, generating a local minimum. For very large y, the peaks begin to widen as the laminar broadening mechanism manifests itself. To find the minimum of the peak broadening, the first derivative of eq 20 can be taken with respect to y to be equal to zero.
dU2 = 2Dt( - 2 A g
a
..
0 3
2
5
A
6
10
1
7 8 9 l
100
Field enhancement factor, y
Flgurr 4. Plot comparing the experimental data and the theoretical calculated total peak variance of PTH-Arg vs the field enhancement factor as a function of the injection time. The circles, squares, and triangles are for the 2-, 4, and 6-min injections, respectively. The theoretical calculations are the solid lines. y = 1 corresponds to the sample buffer concentration equal to the separation buffer concentration.
301\
min injection
25] +6
+ 2BxU2y
Y3
Solving for eq 21 yields the following relationship: I
y = (A/B)1/4
(22)
Substituting the measured diffusion width from our experiments, 2Dt = 8.4 X lCr3cm2,and the radius of our column, ro = 37.5 pm, into A and B, an optimum value of 8 for y is calculated, which is the same value obtain from experimental data. Figure 5 is an expanded plot around the optimum y. As the w p l e plug length is increased, the peak variance will also increase. Although a longer plug length will mean a larger signal, it is of practical interest to limit the contributions from sample stacking and laminar broadening to 10% of the diffusion-limited variance. With this criterion,Figure 5 indicated that the sample plug length can only be 1% of the total column length, which in the case of a 1-m-long, 75-pm-i.d. capillary column corresponds to a 2-min injection. Alternatively, the maximum sample plug allowed can be calculated by letting the peak variance in eq 19 be equal to 1.1(2Dt). Figure 6 shows the effects that different buffer concentrations of a long sample plug have on the separation. The lower electrophoregram, which has the sample in the same 100 mh4 buffer that f i the column, displays the characteristic flat top shape of the peaks for long sample plugs. The migration times for peaks l and 2, PTH-Arg and PTH-His, respectively, are normal for these separation conditions. The middle electrophoregram, which has the sample prepared in 12.5 mM buffer, shows the sample stacking and the
2
3
4
5
6
7 8 9 ’
to
2
3
4
5
Field enhancement factor, y
6
7 8 9 l
100
Figure 5. Expanded plot of the Calculated optimum field enhancement factor in Figwe 4. The dashed horizontal line is the location of the peak variance, which is 10% greater than the diffusion-limited case.
improvement of the detection of the analyte. The migration times are now shorter due to the increase in the bulk electroosmotic velocity. The shape of the sample plug indicates that the boundary between the high-concentration region and the sample plug doesn’t deteriorate during separation. The tall impurity peak around 13 min is due to contaminants in our water supply. The upper electrophoregram, which has the sample prepared in pure water, reveals the effects of the long water plug length. The migration times have all increased because the water plug is pushing the bulk fluid through the column. All of the peaks show signs of laminar broadening and a loss of resolution. The two small impurity peaks around the base of the PTH-Arg peak can no longer be seen because of peak broadening. In Table I, the special case of y x , >> 1 predicts that the electric field in the high-concentration region will approach zero with the injection of a long water plug. With no electric field in the high-concentration region of the column, there will be no electrophoretic movement of the molecules; thus, the peak separation will decrease. In Figure 6, middle and bottom
ANALYTICAL CHEMISTRY, VOL. 63,NO. 18, SEPTEMBER 15, 1991
g4j
6 minute injection with pure water
I I
3
3
-I
6 minute injection with 12.5 mM buffer
I
@
I
SP
J
'1
6
3
I
W
minute injection with 100 mM buffer
2047
purity at about 11 min in the middle electrophoregram becomes a single peak in the upper electrophoregram. Also the small impurity peak at 15 min is closer to the sample plug in the upper electrophoregram, indicating that the negative ion is not moving as fast against the bulk electroosmotic flow.
CONCLUSION We have developed a simple model for the optimization of peak variance in sample stacking with a gravity-injected sample. Experiments confirm that the optimal condition for sample stacking is to prepare the sample in a buffer concentration that is about 10 times less than that used for electrophoretic separation and a sample plug length up to 10 times the diffusion-limitedpeak width. Less concentrated buffer in the sample plug than the optimal conditions will generate laminar flow, thus causing peak broadening. Longer plug lengths than the optimal conditions lead to a dramatic decrease in reaolution due to laminar broadening end a reduction of the electric field in the high-concentration-buffer region. Based on a desired peak width, the sample plug length, the sample plug concentration, and the concentration of the buffer used for separation all combine to achieve over 1 order of magnitude improvement in detectability for gravity injection.
1
LITERATURE CITED ii
b
2
1
1 -
n U 6
8
io
12
14
16
18
Migration time (min.) Flgurr 6. Comparison of electrophoregramsof three different buffer concentrations in the sample plug. Peak 1 is PTH-Arg, peak 2 is PTH-His, peak SP is the sample plug, and peaks I are impurities. The upper eb3mptw-m is a 6-min injection ofsample prepared in pure water, the middle electrophoregram is the same injection time but the sample is prepared in 12.5 mM buffer, and the lower electrophoregrem is the same In]ectkn but the sample is prepared in 100 mM buffer that is the same concentration as the high-concentration-buffer region.
regions, the loss in resolution can be seen in the small difference in migration times between peaks 1and 2, PTH-Arg and PTH-His, respectively, comparing the 12.5 mM sample plug with the water sample plug. The split peak of an im-
(1) Jorgenson, J. W.; Lukacs, K. D. Anal. Chem. 1981, 53, 1298. (2) Foret, F.; Sustacek, V.; Bocek, P. J . kMwocokmn Sep. 1990, 2 , 229. (3) Dolnlk, V.; Cobb, K. A.; Novotny, M. J . sep. 1990, 2 , 127. (4) Hjerlen, S.; Jerstedt, S.; Tiselius, A. Anal. Bbct". 1985. 1 1 , 219. (5) Morlng. S. E.; Colbwn, J. C.; Qrossman, P. D.; Law, H. H. L C - m 1990, 8, 34. (6) Everaerts, F. M.; Vemeggen, Th. P. E. M.; Mikkers, F. E. P. J . Chromew.1979, 169, 21-38. (7) Mikkers. F. E. P.; Everaerts, F. M.; Veheggm. Th. P. E. M. J . ChroM t ~ g r 1979, . 769, 11-20. (8) Colbum, J. C.; Black, B.; Chen, S. M.; Demorest, D.; ~ o r o w i c rJ.; . Wilson. K. Appl. Bbsyst. Res. New 1990, 1-14. (9) Omstein. L. Ann. N.Y. Aced. Sol. 1964. 121, 321-349. (10) Davis, B. J. Ann. N.Y. Aced. Sol. 1964, 121, 404-427. (11) Kohlrausch, F. Ann. Phys. Chem. 1879, 62, 209-239. (12) Chen, R . I . ; Helm,J. C. Anal. Chem. 1991, 63, 1354-1361. (13) Wings, J. J . C h t - . 1989, 480, 21. (14) Roberts, G. 0.; Rhodes, P. H.; Snyder, R. S. J . C h @ , w . 1989, 480, 35. (15) Huang, X.; Coleman, W. F.; &re. R. N. J . chrometogr. 1989, 480, 95. (16) Sternberg, J. C. A&. Chrometugr. 1988. 2 , 206-270.
RECEIVED for review April 16,1991. Accepted June 7,1991.
