Anal. Chem. 1995,67, 1060-1066
Marker Techniques for High-Accuracy Juho H. Jumppanen and Marja-Lisa Riekkola* Laboratory of Analytical Chemistty, Department of Chemistty, University of Helsinki, P.O. Box 55 (A. 1. Virtasen aukio I), FIN-00014 University of Helsinki, Finland
Marker techniques have been developed for high-accuracy identification by capillary zone electrophoresis. The techniques employ two, three, or four markers of known electrophoretic mobilities which are used to determine the effectiveelectric field strength (E& and electroosmotic flow velocity (ueo) of a system. EeE was always a p proximated to stay constant within one run. With Merent numbers of markers, different assumptions were made about the time dependence of ueo within one run. With two markers, ueo was approximated to stay constant, whereas with three or four markers it was approximated to be linearly and nonlinearly accelerating, respectively. The information about EeE and ueo , together with the electrophoretic mobilities of the marker compounds, was used to determine the electrophoretic mobilities of unknown compounds. Extremely high repeatabilities (0.010.03%) were obtained for compounds with PKa values far from the pH of the electrolyte solution. Because electrode reactions alter the pH of the electrolyte solution, however, systematic drift in the mobility was found for one compound with a PKa value close to the pH of the electrolyte. In such situations, where analytes may have PKa values close to the pH of the electrolyte, fresh electrolyte should be supplied for every run. The reliability of the identification was increased up to 350-fold relative to the use of absolute migration times. The repeatability of analyte migration times in capillary zone electrophoresis (CZE) is poor when fused silica capillaries are used for the analysis. This is mainly due to nonrepeatable electroosmotic flow velocity (veo) caused by the unstable surface conditions of the capillary wall. The effect is particularly pronounced in new capillaries where ve, changes rapidly during the first few runs. Because veo changes constantly, it cannot be accurately determined at any specific time. On a macro time scale, the change is usually in the same direction. At high pH values (>9), there is usually a decrease as the capillary ages. Poor repeatability of the analyte migration times has prevented the use of CZE as a method for high-accuracy identiiication of molecules. The repeatability of CZE can be improved by making corrections for the changes in veo and effective electric field strength (,Fed.This can be done by introducing marker compounds with known electrophoretic mobilities. We earlier described the use of two markers for the determination of veoand ,Fen in a simple system of a few analytes.' The technique was later applied to a (1) Jumppanen, J. H.: Soderman, 0.:Siren, H.; Riekkola, M.-L.J. Microcolumn Sep. 1993,5,451.
1060 Analytical Chemistry, Vol. 67, No. 6, March 15, 1995
study of the effect of counterion systems on v,, and Eeff,l to the identification of stereoisomers of some ,b-blockers,3 and to the determination of self-diffusion coefficients of some diuretic^.^ In the present study, we used marker compounds to determine the electrophoretic mobilities of a group of model analytes. All but one were mono- and dicarboxylic acids containing aromatic substituents. Because these compounds are all fully dissociated under basic conditions, small changes in pH do not affect their mobility. To study the effect of electrode reactions on the electrolyte pH, we also included o-cresol among the analytes. Markers were used to determine the effective field strength (E& and the electroosmotic flow velocity (veo) during each electrophoretic run, and from these factors, the electrophoretic mobilities of the analytes were repeatedly calculated. The behavior of the electroosmotic flow and its effect on the repeatability of analysis were studied in nine consecutive runs in a fresh capillary with different approximations made of the time dependence of veo. Although the marker techniques introduced in this paper are straightforward, calculations involving three or four markers require a computer. Extremely high repeatabilities for the determination of the electrophoretic mobilities can be achieved by employing markers. Besides its power for identiiication purposes, the method is highly promising for the accurate and fast determination of self-diffusion constants of charged species. However, more work must be done before it can be fully exploited to yield accurate physical data on molecules. The reliability of the physical data depends entirely on the precision of mobility values of the marker compounds. The migration velocity of an ion in CZE is in fact a very complex phenomenon. THEORY
To explain the marker technique and some vital factors that were taken into consideration in developing it, we start from the basic equations: those which are familiar to everyone working with CZE. The analyte migration velocity vtot in CZE is utot
= veo + vep
(1)
where5m6 (2) Jumppanen, J. H.; Siren, H.; Riekkola, M.-L. /. High Resolut. Chromatogr. 1994,17,537. (3) Siren, H.; Jumppanen, J. H.; Manninen, IC; Riekkola, M.-L. Electrophoresis 1994,15, 779. (4) Jumppanen. J. H.; Haario, H.: Riekkola, M.-L.J. Microcolumn Sep. 1994,6, 595. (5) Hjerten, S. Chromatogr. Rev. 1967,9, 122. (6) Virtanen, R. Acta Polytech. Scand. 1974,123, 1.
0 1995 American Chemical Society 0003-2700/95/0367-1060$9.00/0
a sphere of oppositely charged ions with apparent radius r
1/12 = 8nNe2Z2/1000ekT
(8)
The electrophoretic mobility has been expressed as
(3) where
As the ionic strength of the solution increases, the ionic atmosphere draws closer to the ion it surrounds and interacts more strongly with it. As a result, the solvated radius of the ion decreases. The electrophoretic mobility can be expressed as Pep
Description of Eefi Although widely used, eq 3 is not an accurate description of v,,, because the migration of an ion is restricted by two effects, which Onsager described as an electrophoretic effect and a charge asymmetry effect in his classic studies regarding ionic conductivity in s~lution.~ We present the major equations governing these effects to give the reader closer insight, noting, however, that these equations are not themselves needed in applying the marker techniques. The electrophoretic effect is caused by the additional viscous force generated by ions moving in opposite direction, and it becomes more evident with increase in concentration of the background electrolyte. Onsager derived the following equation for the electrophoretic effect:
B = 8.20
x
lo5 A O / ( E Z ) ~ / ~
(5)
A charge asymmetry effect is generated when the symmetry of the ionic atmosphere around an ion is distorted under the influence of an electric field. Onsager's expression for this effect is
Onsager combined these results to form the well-known Onsager equation A = A" - (A
+ BAO)C'/~
(7)
Both the electrophoretic effect and the charge asymmetry effect are very familiar in the field of electroanalytical chemistry and apply directly to capillary electrophoresis. Vold and Voids called these effects retardation and relaxation, respectively. In the literature, the decrease of electrophoretic migration velocity when the ionic strength of the buffer is increased has been interpreted as the decrease of electrophoretic mobility of an i ~ n , ~or - ' it~ has been explained in terms of the 5 p0tentia1.l~ Both interpretations, however, are in contradiction with the Debye-Huckel concept of ionic atmosphere,15J6which is regarded (7) Onsager, L.; Fuoss, R M. J Phys. Chem. 1932,36, 2689. (8) Vold, R D.; Vold, M. J. Colloid and Interface Chemistiy, 1st ed.; AddisonWesley: Reading, PA, 1983; Chapter 6. (9) Atria, IC D.; Simpson, C. F. Chromatographia 1987,24, 527. (10) Atria, IC D.; Simpson, C. F. Anal. Proc. 1988,25, 85. (11) Bruin, G. J. M.; Chang, J.; Kuhlman, R.; Zegers, IC; Kraak, J.; Poppe, H.J Chromatogr. 1989,471, 429. (12) Nashabeh, W.; El Rassi, 2. J. Chromatogr. 1990,514, 57. (13) Issag, H.; Atamna, I.; Muschik, G.; Janini, G. Chromatographia 1991,32, 155. (14) Hjerten, S. J. Chromatogr. 1985,347, 191. (15) Debye, P.; Huckel, E. Phys. Z 1923,24, 185.
= zF/f = z F / 6 n y N a
(9)
where a is the Stokes radius. As the ionic strength of the electrolyte increases, the electrophoretic mobility of a solvated species is affected by the increased viscosity and decreased solvation: increase in viscosity tends to decrease the electrophoretic mobility, whereas decrease in solvation increases it. The electrophoretic and asymmetry effects have a far greater effect on the migration velocity; that does the change in electrophoretic mobility, however. The total effect induced is seen as a decrease in the electrophoretic migration velocity as the ionic strength of the background electrolyte increases. The full scope of solvation is too wide to be discussed here, but excellent descriptions on the phenomena are found in the literat~re.'~-'~ In our previous studies on E,. and veo,we found that for the 0.06 M CAPS buffer at pH 10.6 the Eef was approximately 20% lower than E.' The factors retarding the electrophoretic migration are difticult to determine quantitatively,8but their effect can be experimentally deduced by determining E,f, which we define as
E,,
IE,
l i d e , =E I-0
(10)
Smaller effects possibly related to E,., such as power loss, the presence of zones of higher or lower conductivity, and the potential drop on the electrodes, were approximated to be negligible in this study. Marker Techniques. In all three marker techniques, E,, was taken as constant during one run. In principle this is a valid approximation as the medium is considered to be homogeneous. The major cause of nonrepeatable migration times tmigr = Ldet/vtot
( 11)
is the electroosmotic flow. With each marker technique, a different approximation was made for the time dependence of Ueo. Preliminary studies showed that the migration times usually drifted into the same direction. Furthermore, when new capillaries were used, the change in the v,, seemed to decrease gradually as the capillary aged. With the two-marker technique (2m), v,, was approximated to stay constant within a run. (16) Debye, P.; Huckel, E. Phys. 2. 1923,24, 305. (17) Plambeck, J. A. Electroanalytical Chemistiy, 1st ed.; John Wiley & Sons Inc.: New York, 1982. (18) Burgess, J. Metal Ions in Solution, 1st ed.; Ellis Honvood Ltd.: Sussex, England, 1978. (19) King, E. J. Acid Base Equilibria-The International Encuclopedia ofphysical Chemistiy and Chemical Physics, 1st ed.; Pergamon Press: Oxford, England, 1965.
Analytical Chemistry, Vol. 67, No. 6, March 15, 1995
1061
veo = a
(12)
And the corresponding matrix presentation is 1 2
Zt' With the three-marker technique (3m) it was approximated to be linearly accelerating so that
veo = bt
+a
+ bt + a
svtot dt
4
~
2
4
Ldet
b
B = Ldet
X=a
(21)
After solving for X in eq 18, we calculate the electrophoretic mobilities of the analytes from Pep@) = (Ldet/tr
(14)
The distance of the analyte from the capillary inlet as a function of time can be calculated as s=
2
Pltl
(13)
With the four-marker technique (4m), veo was approximated to be nonlinearly accelerating and we used the expression
veo = ct2
A = $12
tl
(22)
Four-Marker Technique. The use of four markers enables the approximation of veo as nonlinearly accelerating (eq 14). The basic equation is
(15)
When s = bet, we can derive equations for electrophoretic mobilities. Note that the markers should always be selected so that their values are as far apart from each other as is reasonably possible. Two-Marker Technique (2m). In the two-marker technique, both veo (eq 12) and E,f are approximated constant. Earlier we employed the method to determine veoand E,&2and then applied it successfully to the identification of stereoisomers of some /%blockers3and to determination of self-diffusion coefficients for some diuretic^.^ We now present the technique in matrix form. Especially with more complex marker techniques, the matrix form provides ease of data processing. The basic equation for 2m contains two unknowns (a and E&, and hence two equations are needed to determine these variables. Thus, two marker molecules are needed. The basic equation for 2m is
- btJ2 - a)/Ee,
&et
= ct,3/3
+ bt:/2
+ a + E&Pep(x)tx
(23)
and the matrices are
A=
C
Ldet
1 3 34
B=
1 3 35
Ldet
b a
Ldet
Ee,
Ldet
X=
1 3
3t4
after solving for X in eq 18, the electrophoretic mobilities of the analytes can be calculated from Pep(x) = (Ldet/tx
- Ct,2/3 - btx/2 - @)/Ee,
(25)
EXPERIMENTAL SECTION
Correspondingly, the matrices are Ldet
A= t2
P2t2
Ldet
and vea and Eefcan be determined by a matrix operation
X = AB-'
(18)
The electrophoretic mobilities of analytes can then be calculated from
Three-Marker Technique (3rd. In this method, v,, is a p proximated linearly accelerating (eq 131, to be able to account for changes in v,, during one run. The basic equation for 3m is
1062 Analytical Chemisfry, Vol. 67,No. 6, March 15, 1995
Chemicals. 3-(Cyclohexylamino)-l-propanesulfonic acid (CAPS), ethacrynic acid, and probenecid were purchased from Sigma @orset, UK). HPLC grade methanol, KOH, benzoic acid, phthalic acid, phenylacetic acid, and L2-phenylenediacetic acid were from Merck @armstad, Germany). @Cresolwas from Fluka (Buchs, Switzerland), triphenylacetic acid from Aldrich (Steinheim, Germany), and mes~2,3-diphenylsuccinicacid from TCI Uapan), and xanthene-$carboxylic acid and (-)-mandelic acid were from EGA-Chemie (Steinheim, Germany). Diphenylacetic acid was synthesized in the Organic Chemistry Department at the University of Helsinki. All chemicals were used as received. Distilled water was further purified with a Water-I system from Gelman Sciences (Ann Arbor, MI) before filtering through 0.45 pm membrane filters (Millipore, Molsheim, France). The pH meter was calibrated with Radiometer standard buffer solutions (Copenhagen, Denmark). Apparatus. CZE was performed in a 77.0 cm long fused silica capillary (70.0 cm to the detector) with 50 pm i.d. and 360 pm 0.d. (Polymicro Technologies, Phoenix, AZ) . The CE apparatus was a Beckman 2050 P/ACE capillary electrophoresis system with a W/visible detector and a liquid cooling system for the capillary (Beckman Instruments, Fullerton, CA). The data were analyzed with HP 3396A integrator (Hewlett Packard, Avondale, PA). The
absolute viscosity of the electrolyte solution was determined with an S.I.Ltype viscometer and a pycnometer. All calculations were carried out with "in-house" designed programs operating in MATLAB (Mathworks Inc.). Methods. CZE. The electrolyte solution was a 0.08 M CAPS solution with K+ as counterion. The pH was adjusted to 10.6. The sample solution contained 10 ppm of each analyte, 10 ppm of each of the markers, and 10 mM KOH with 10%(v/v) methanol. Other operational parameters were as follows: 20 kV; 19.3 p& 7 s hydrostatic injection (0.500 psi); 220 nm; liquid cooling at 25 "C. Viscosity Determination of the Electrolyte Solution. All experiments were made at 25 "C.The solution was immersed in a water bath for 20 min before determination. The apparatus was first calibrated with water. The kinematic viscosity of the electrolyte solution at 25 "C was 0.939 89 f 0.000 64 cSt (n = 6). The density of the buffer was 1.005 98 g ~ m (n- =~ 3). Vacuum correction was employed after the weighing. An absolute viscosity of 0.9455 CP was used for further calculations.
Table I. Marker Compounds, Their Use in Marker Techniques, and Their Mobility Values marker
used in marker techniquese
triphenylacetic acid diphenylacetic acid benzoic acid o-phthalic acid
4m 2m, 3m, 4m 3m, 4m 2m, 3m, 4m
a Conditions: 0.08 M CAPS, pH 10.6, 25 "C. Determined by the two-marker technique from runs 41,42, and 43. Calculated from the conductivity value in HzO at 25 oC.20 Calculated i?om the conductivity value in HzO at 25 CZ1 e 2m, 3m, and 4m correspond to the two-, three, and four-marker techniques, respectively.
Table 2. Average Values and Standard Deviations for Absolute Migration Times and for Electrophoretic Mobilities Determined by 2m, 3m, and 4ma (n = 9) analyte 0-cresol
RESULTS AND DISCUSSION
Our aim in this study was to apply merent marker techniques in CZE to enhance the repeatability of CZE for identification purposes. We selected eight compounds for analysis and included four marker compounds. For markers to be employed, their electrophoretic mobilities must be known. We used conductivity values of diphenylacetate ionz0and o-phthalate ionz1to calculate the mobilities of these compounds in the electrolyte solution (viscosity 0.9455 cP). The marker techniques presented in this paper are capable of yielding accuracies better than 0.1%easily. Because the accurate physicochemical data needed for our studies were not available, we determined the electrophoretic mobilities for the other two marker compounds, triphenyl acetic acid and benzoic acid, in the stabilized CZE system (constant veo from run to run). The electrophoretic run was performed 43 times and the data from the last three runs were used to determine the mobilities of the other two marker compounds (triphenylacetic acid and benzoic acid) by using the two-marker technique. During these last three runs the decrease of veo was less than 0.1% per run. The mobility values used for the marker compounds are given in Table 1. We would point out that because the conductivity values of the marker compounds are reported at zero ionic strength, the values deduced for other analytes cannot be considered completely accurate. We display the results for mobilities to 5 digits solely to indicate the effectiveness of the marker techniques for identification purposes, and to allow comparison of the use of different numbers of markers. The reader is reminded on the fact, that, although the techniques presented in this paper provide exceptional accuracy of the determination of the electrophoretic mobilities, the mobility values determined by this technique are only as reliable, as are the values for the marker compounds. Repeatability of the Different Marker Techniques. The first nine runs were evaluated for the repeatability of migration times and for the electrophoretic mobilities determined by using different marker techniques. The new capillary was pretreated (20) Landolt Bornstein Zahlenverte und Funktionen aus Physik, Chemie, Astronomie, Geophysik und Technik; Berlin, 1960, Vol. 11, Part 7, p 264. (21) CRC Handbook of Chemistry and Physics, 71st ed.; CRC Press: Boca Raton, FL, 1990; pp 5-99.
-2.0560b -2.4694' -3.4286b -5.1047d
tabs,
mm
9.76 11.97% probenecid 10.58 &2.33% ethacrynic acid 10.61 f2.34% xanthene-%carboxylicacid 11.30 f2.48% mandelic acid 12.54 12.72% benzoic acid 12.75 12.77% meso-2,3-diphenylsuccinicacid 15.27 13.21% 1,2-phenylenediaceticacid 19.05 13.80% a
pep,10-8 mzV-l ssl
2m
3m
4m
-1.7323 11.09% -2.1826 10.072% -2.2138 &0.067% -2.5533 10.016% -3.0667 10.081% -3.1438 10.084% -3.9064 f0.088% -4.6700 &0.050%
-1.7283 &0.93% -2.1811 10.025% -2.2125 f0.025% -2.5537 10.024% -3.0693 &0.021% -3.1466 10.036% -3.9108 10.014% -4.6731 f0.015%
-1.7258 +0.89% -2.1804 10.017% -2.2119 10.017% -2.5538 &0.026% -3.0697 f0.018% -3.1470 & 0.034% -3.9096 10.022% -4.6704 10.030%
See footnote e in Table 1.
by rinsing with 0.1 M KOH, HzO, and then the electrolyte for 5 min with each solution. Because the electroosmotic flow varies mostly in fresh capillaries,the first runs were the most interesting and challenging for the evaluation of the marker techniques. The two-marker technique makes use of o-phthalicacid and diphenylacetic acid, the three-marker technique also of benzoic acid and the four-marker technique of yet a further compound, triphenylacetic acid (see Table 1). The results of the calculationsare given in Table 2. In terms of repeatability, all the marker techniques gave results superior to the absolute migration times. The repeatability achieved with three and four markers is good enough to be used for high-accuracy screening and for identification purposes. Figure LA shows the absolute migration times of all the compounds, including the markers, in the nine first runs, and Figure 1B shows the excellent results obtained for the eight analytes, when electrophoretic mobilities are calculated by the four-marker method. In Figure 1C we see how the mobility of o-cresol systematically decreases from run to run, while the mobilities of ethacrynic acid and probenecid remain constant. The pKa value of o-cresol (10.2) is close to the pH of the electrolyte (10.6). Although the electrolyte solution is adequately buffered, it is obvious that, while a high voltage is maintained, electrode reactions occurring in the electrolyte vials effect small changes in the pH of the electrolyte solution, reducing the repeatability of the results for o-cresol. Although the effect is so small that it can Analytical Chemistry, Vol. 67, No. 6, March 75,7995
1063
A 1
241
I -2
-
1
-
3
1
P
a
.4-
, I
2
3
4
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5
6
7
8
9
OF EXPERIMENT
I
-1.6-
-1.9-
-
in
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f .2,1?
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OF EXPERIMENT
Flgure 1. (A) Absolute migration times of all analytes (a) and marker compounds (m) from nine first runs in a fresh capillary. Migration order: ocresol (a), triphenylacetic acid (m), probenecid (a), ethacrynic acid (a), diphenylacetic acid (m), xanthene-9-carboxylic acid (a), mandelic acid (a), phenylaceticacid (a), benzoic acid (m), mese2,3diphenylsuccinic acid (a), 1 ,Bphenylenediacetic acid (a) and 0phthalic acid (m). (B) Electrophoretic mobilities of the analytes in the first nine runs, determined by the four-marker technique. Order of increasing mobility: 0-cresol, probenecid, ethacrynic acid, xanthene9-carboxylic acid, mandelic acid, phenylacetic acid, mese2,3diphenylsuccinic acid, and 1,2-phenylenediaceticacid. (C) Electrophoretic mobilities (from top) of ecresol, probenecid, and ethacrynic acid in the first nine runs, determined by 4m.
1064 Analytical Chemistry, Vol. 67, No. 6, March 15, 1995
only be detected by using a powerful calculation method such as we describe, it is nevertheless an important effect. We therefore recommend that a fresh electrolyte solution be used for each experimentif any of the analytes are likely to have pKavalue close to the pH of the electrolyte solution. Table 2 includes the rather surprising result that, for 2,3-mesodiphenylsuccinic acid and 1,2-phenylenediacetic acid, the threemarker technique works better than the four-marker technique. This is due to the overdetermination of veo, when it is a p proximated to be nonlinearly accelerating. Figure 2 depicts u,, as a function of time during the nine first runs, where ue, was determined by 2m, 3m, and 4m. As can be seen in Figure 2C, in some runs the approximation of nonlinearly accelerating u,, with four markers yielded an approximation of increasing ueo at the end of the run. Even though the technique worked well, this approximation is clearly false and shows how a false model for the electroosmotic flow can reduce the repeatabilities even where a large number of marker compounds are used. This result was particularly evident when more complex functions were used for approximating the time dependence of v,,. Excellent results can be obtained with 3m and 4m because all information about the markers is utilized in determining the electrophoreticmobility of the unknown compound, and compensations are made for changes in Ue, during a run. However, if large extrapolations are required, the use of 2m and 3m may be preferable because more complex techniques (4m) could suffer from overdetermination, as was seen for the compounds migrating close to the o-phthalate. Extrapolations can, of course, be avoided by using marker compounds that cover the range of analytes that are screened for. Reliability of the Identification. To express the reliability of the identification, we introduce a new concept which we call the coefficient for identification, Qid. &id
= ( ~ 2- x,)/(a,
+ 02)
(26)
&id yields information on the reliability of identification between two compounds. Equation 26 is a direct application from the resolution equation in chromatography. Thus, if the value of Qid exceeds 2, the identification between two compounds is considered reliable. X I and xz are the responses of interest, and q and uzare their standard deviations. In our case, the responses were either absolute migration times or the electrophoretic mobilities of the compounds calculated by 2m, 3m, or 4m. The results are displayed in Table 3. The Qid values for the mobilities are far greater than those obtained for peak absolute migration times. The poorer value for ocresol and ethacrynic acid than for the other pairs is simply due to the large 5 for o-cresol caused by the changes in pH. The result is clear. According to these data, no member of this group can be reliably identified if peak absolute migration times are used for the identification. However all the compounds can easily be identified with the use of markers, even just two. The &id value obtained for the pair ethacrynic acid and probenecid by 4m (Qid = 21) is 350 times greater than it is with absolute migration times (&id = 0.06). Furthermore, as this pair was not adequately resolved and the difference between the migration times of the peaks was only about 3.5 s in 10 min, we can conclude that with 4m some compounds can easily be identified if their absolute migration times differ in one run by only 0.5 s.
1.6
1.58
1.52
.
A
Qid
hd
analyte pair
@id (tabs)
2m
3m
4m
o-cresol probenecid probenecid ethacrynic acid ethacrynic acid xantheneScarboxylic acid xanthene9carboxylic acid mandelic acid mandelic acid phenylacetic acid phenylacetic acid meso8,3-diphenylsuccinic acid meso-2,3-diphenylsuccinic acid 1,2phenylenediacetic acid
0.90 0.06 0.65
11.0 5.09 88.5
13.7 14.3 147
14.5 21.0 163
0.99
88.4
206
209
I ! I
I 1.5
200
400
Boa
600
'000
1200
TIME (s)
B 1.62
Table 3. Values of Coefficient for Identification (&) Obtained for Successive Peak Pairs Where identification Was Based on Absolute Migration Times and on Electrophoretic Mobilities Determined by 2m, 3m, and 4ma
x10=
0.15
7.52
21.9
23.6
1.50
62.8
226
199
1.55
66.0
302
171
See footnote e in Table 1.
for determination of the electrophoretic mobility of any unknown compound. Furthermore, marker techniques should be of great assistance in studies where small changes in mobility are induced by effects such as minor changes in electrolyte pH or changes in the conformation or pKa of the analytes. The mathematics involved are straightforward,and the calculations can be executed rapidly by MATLAB or other suitable software. To apply the full power of the techniques, more research is needed on chemical physics related to the transport of molecules in CZE. The analyte velocity is a highly complex phenomenon, and it cannot be explained solely in terms of the electrophoretic mobility of an analyte and the electric field strength. If all physical factors can be identifled and taken into consideration, CZE can become one of the most accurate and simplest methods for determination of the s e l f - d ~ s i o constants n of ionized compounds.
15A155ssSs
>$ 1 5 2
:
15
200
400
600
800
1000
1200
TIME (s)
1.6
k
ACKNOWLEDGMENT
The authors thank Markku Sundberg for fruitful discussions on ionic solvation. GLOSSARY
Symbols are listed in the order of appearance
0
200
400
600
600
1000
I 1200
TIME (s) Figure 2. Electroosmotic flow velocity during the nine first runs as a function of time (veo(f)),determined by (A) 2 m , (B) 3 m , and (C) 4 m . CONCLUSIONS
Marker techniques allow highly reliable for molecular identifications in CZE. Good estimationsfor effective field strength (Eed and the electroosmotic flow velocity as a function of time (veo(t)) can be obtained, and these estimations together with the primary information on the marker compounds can be very effectively used
total velocity of the analyte electroosmotic flow velocity electrophoretic velocity dielectric constant of the solution electric field strength zeta potential absolute viscosity electrophoretic mobility voltage total capillary length parameter for electrophoretic effect conductance absolute temperature parameter for asymmetry effect kinematic viscosity of the medium molar conductivity concentration apparent radius Avogadro constant Analytical Chemisfty, Vol. 67, No. 6,March 15, 7995
1065
e
I k 2
F
f a
Eefi tmim Ldet
t
U
b C S tx
electronic charge ionic strength Boltrmann constant ionic charge Faraday constant frictional coefficient Stokes radii effective electric field strength migration time of an analyte capillary length to the detector time constant for v,, coefficient for linear acceleration of Veo coefficient for nonlinear acceleration of distance migration time of compound x
matrix of parameters to be determined data matrix data matrix coefficient for identification response ( t i , or yep)of compound 2 response (tmi, or yep)of compound 1 standard deviation of response 1 standard deviation of response 2 Received for review June 16, 1994. Accepted December
19,1994.B Veo
1066 Analytical Chemistry, Vol. 67,No. 6, March 15, 1995
AC9406118 @
Abstract published in Adoance ACS Abstracts, February 1, 1995.
