Anal. Chem. 2001, 73, 1316-1323
New Capability of Electroinjection Analysis: Investigation of Chemical Reaction Kinetics Victor P. Andreev,* Elena D. Makarova, and Naum S. Pliss
Institute for Analytical Instrumentation, Russian Academy of Sciences, 26 Rigsky pr., St. Petersburg 198103, Russia
Electroinjection analysis has been demonstrated to provide reaction kinetics information. Reactants are injected continuously from opposite ends of the capillary for the duration of the experiment, and reaction product formation occurs at the boundary where the zones merge. The width of the product signal measured by the detector depends on the ratio of the fluxes of reactants. The boundary moves toward the detector where the products are measured. A sharp peak at the edge of the main flat product signal peak was observed and most probably corresponds to the metastable intermediate product of reaction, a unique capability of this technique. A theoretical explanation and an experimental verification of the possibile use of electroinjection analysis for the study of reaction kinetics is given. A new combination of flow injection analysis (FIA) and capillary electrophoresis (CE) was proposed in 1993,1 called electroinjection analysis (EIA). According to this technique, sample and reagent are electrokinetically injected from opposite ends of the capillary. They meet in the capillary, pass through one another, and react. The product peak is then detected photometrically near the middle of the capillary. EIA takes advantage of the fact that analyte and reagent are often oppositely charged. But it is even possible, by this method, to mix reactants with the same charge when their electrophoretic mobilities are different. The only limitation is that the reactant that is injected in the direction opposite to the electroosmotic flow must have electrophoretic mobility of the opposite sign and higher than the electroosmotic mobility of the buffer. In refs 2 and 3, EIA was compared with FIA. It was shown that the main advantage of EIA over FIA is mixing of analyte and reagent zones without dispersion, which leads to considerably higher sensitivity. In the same papers, EIA was compared with electrophoretically mediated microanalysis (EMMA).4,5 It was shown that these techniques are complementary, and some advantages of EIA over EMMA were indicated. * To whom correspondence should be addressed. E-mail: vandreev@ online.ru. Fax: 7 812 251 70 38. (1) Andreev, V. P. Method of chemical analysis. Russian Federation Patent Appl. 2075070, July 19, 1993. (2) Andreev, V. P.; Kamenev, A. G.; Popov, N. S. Talanta 1996, 43, 909-914. (3) Andreev, V. P.; Ilyina, N. B.; Lebedeva, E. V.; Kamenev, A. G.; Popov, N. S. J. Chromatogr. A 1997, 772, 115-127. (4) Bao, J.; Regnier, F. E. J. Chromatogr. 1992, 608, 217. (5) Harmon, B. J.; Patterson, D. H.; Regnier, F. E. Anal. Chem. 1993, 65, 2655.
1316 Analytical Chemistry, Vol. 73, No. 6, March 15, 2001
An additional advantage of EIA over FIA, called kinematic focusing, was predicted theoretically3 and then verified experimentally.6,7 Kinematic focusing occurs in EIA when the concentration of reagent is much higher than the concentration of analyte and when the electrophoretic mobility of the product of the chemical reaction is close or equal to the electrophoretic mobility of the reagent. In this case, all analyte reacts at the front of the reagent zone, and all the portions of the product produced with time accumulate at the front of the reagent zone. The result is a sharp and high product peak that is measured. A mathematical model developed in ref 3 verified that, for the case in which product and reagent have practically equal electrophoretic velocities, the amplitude of the product peak was proportional to the length of the sample zone, ls, assuming that the reagent concentration is much greater than that of the analyte. The following question naturally arises: “What happens when the sample zone is very long and the ratio of reactant concentrations is finite?” A series of experiments studying the dependence of product peak amplitude on the sample zone length ls and the ratio of reactant concentrations were carried out, showing that at some limiting value of ls the peak amplitude stopped growing. A further increase of the sample zone length led only to an increase of the width of the flat product peak. The width of the product peak depends on the ratio of reactants concentrations and can be used as an analytical signal (measure of analyte concentration). Detailed information on these results will be published separately. The objective of this paper is to report on an important observation made during these experiments: that EIA could be efficiently used not only as an analytical technique but also for chemical reaction kinetics studies. Experiments with continuously flowing zones of reactants were performed; i.e., reactants were continuously injected from each end of capillary for the duration of the experiment. It was noted that the product signal observed by the detector returned to the baseline, even though the two solutions continued to flow (we expected the signal to remain constant until the end of the experiment). The width of the product signal depends on the ratio of the concentrations of the reactants. In addition, a sharp, short peak was observed at the rear edge of the main product signal. The amplitude and the width of the short peak also depend on the concentration ratio. Most probably this sharp peak corresponds to the metastable intermediate product. (6) Andreev, V. P.; Ilyina, N. B. Nauchnoe Priborostroenie 1997, 7, 100-103 (in Russian). (7) Andreev, V. P.; Ilyina, N. B; Holman, D. A; Scampavia, L. D.; Christian G. D. Talanta 1999, 48, 485-490. 10.1021/ac0003551 CCC: $20.00
© 2001 American Chemical Society Published on Web 02/17/2001
CA0(VA + VX) ) CB0(VB - VX)
Figure 1. Illustration of the principle of EIA with continuously flowing zones of reactants.
A theoretical explanation, experimental results, and computer simulation of the process are given below in order to prove this hypothesis. THEORY Consider a capillary of length L filled with background electrolyte, that we will call buffer. Consider the analyte and reagent, or two reactants A and B, with concentrations CA0 and CB0 electrokinetically injected from opposite ends of the capillary and forced to move in opposite directions by electric field E. The described situation is presented in Figure 1. Reactants A and B move in the electric field with velocities VA and VB that are the respective sums of their electrophoretic velocities and the electroosmotic velocity of the buffer. Reactants meet at the point with coordinate X0, where reaction takes place and the product AB is produced which moves with a velocity VAB. Note that here and elsewhere in this paper, all the velocities are considered to be positive, irrespective of direction of flow, and the fact that the reactants and/or products can move in opposite directions is taken into consideration by using appropriate signs in the corresponding equations. Injections of reactants A and B are not necessarily simultaneous but can be separated by any reasonable time interval, so that any arbitrary position of X0 can be established. A photometric detector is placed at the point with coordinate D. Concentrations of reactants are assumed to be much lower than the buffer concentration, and the reactants are diluted in the same buffer that fills the capillary, so that the electric field strength is constant along the capillary. The concentration of the buffer is assumed to be low enough that the thermal gradient across the capillary may be ignored, and this enables one to consider the problem as one-dimensional. The chemical reaction is considered to be fast, so that the product of any of the above-mentioned velocities (VA, VB, VAB) and the characteristic time of the chemical reaction is much smaller than the distance between points D and X0. One may then consider that interaction between reactants and formation of the product takes place on some flat boundary perpendicular to the axis of the capillary. This boundary, denoted by X, is motionless and occurs at X0 as the two solutions continue to flow only in the case where the fluxes of reactants are equal:
CA0VA ) CB0VB
(1)
(The product AB, which is continuously formed at the boundary, however, migrates toward the detector, and this results in the stepped continuous flat signal, observed in the case of equal fluxes. Here and elsewhere, the case depicted in Figure 1 is considered, i.e., X0 > D, and VAB is directed toward X ) 0.) For any other value of the ratio of the fluxes of the reactants, the boundary moves with a velocity VX determined by the following equation that is actually the condition of the equality of fluxes of reactants at the moving boundary:
(2)
The boundary is moving toward that end of the capillary in which the smaller flux of reactant is injected. There are two possible alternatives for unequal fluxes. If CA0VA > CB0VB, then the boundary X moves toward L, and the product step signal observed by the detector remains constant throughout the experiment as in the above-mentioned case of equal fluxes. But if CA0VA < CB0VB, then the boundary X moves toward 0 ,and the product signal observed by the detector is of finite duration and returns to the baseline. The velocity of the boundary is equal to
VX ) (CB0VB - CA0VA)/(CA0 + CB0)
(3)
and is larger the smaller the concentration of reactant A. The highest possible value of VX is equal to the second reactant’s velocity VB and is reached in the case where CA0VA , CB0VB. The moment, T0, when the first portion of the product molecules formed at the point X0 reaches the detector is determined by
T0 ) (X0 - D)/VAB
(4)
The moment, Tf, when the boundary reaches the detector is determined by
Tf ) (X0 - D)/VX
(5)
If the velocity of the product is larger than the velocity of the boundary, then T0 corresponds to the beginning of the product signal and Tf to the end of the product signal observed by the detector. After the time Tf, the molecules of the product are still produced but are not observed by the detector, because from this time the boundary and the molecules of product are moving from the point with coordinate X ) D to the point X ) 0. The important conclusion following from this reasoning is that the rear edge of the product signal corresponds to the molecules of the product observed exactly at the moment when the boundary of reactants is passing by the detector (time Tf). This means that they are observed by the detector at the time at which they are produced. If the chemical reaction is multistaged, and the intermediate product has an extinction coefficient greater for the given wavelength than that of the final product, then a sharp peak corresponding to the intermediate must exist at the rear edge of the signal observed by the detector. This peak must be of the shorter duration the smaller the half-life of the intermediate, and it must be greater the higher its concentration and/or extinction coefficient. If the extinction coefficient is equal to that of AB, then no intermediate product peak will be observed. A different wavelength of observation may provide an increased extinction coefficient. If the extinction coefficient of the intermediate is less than that of AB, but greater than zero, then a short step decrease should be observed. Both T0 and Tf can be easily measured during the experiments, and their values can be compared with theoretical predictions. It Analytical Chemistry, Vol. 73, No. 6, March 15, 2001
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is important, though, to take into consideration that both of them depend on the value of electroosmotic velocity (because velocities of reactants are the sums of their electrophoretic velocities and the velocity of the electroosmotic flow). It is well known that electroosmotic velocity is rather sensitive to any factors that can influence the conditions at the capillary wall, such as the concentrations of reactants. That is why, in the case of a broad range of concentrations, it is better to analyze a characteristic independent of the electroosmotic velocity. In our case, VAB and VX have the same direction, so (VX - VAB) does not depend on the electroosmotic flow velocity. According to eqs 3-5,
(X0 - D)/Tf - (X0 - D)/T0 ) VX - VAB ) (VB - VAB) - (VB + VA)
CA0 CA0 + CB0
(6)
The left-hand side of eq 6 consists of easily experimentally measurable parameters, and the right-hand side represents the linear dependence on the initial concentration ratio, so eq 6 is convenient for comparison of experimental results and theoretical predictions. Of course, this simple model itself can predict only the width of the main product signal and cannot describe the shape of the peak of the intermediate. To predict the shape of the product signal observed by the detector in the case of a multistaged chemical reaction, a more sophisticated computer simulation model was used, similar to the one developed for simulation of EIA and EMMA with comparable concentrations of reactants.8 All the above-mentioned assumptions were used in this model, thus leading to a one-dimensional and linear problem, but the reaction rate was considered to be finite. So, according to the computer simulation model, the reaction takes place not at the flat boundary, but within some zone having a finite thickness that is smaller the greater the reaction rate. The reaction is considered to be multistaged, with the metastable intermediate product AB* produced at the first stage, that is converted into the final product AB at the second stage of reaction. Evolution of concentrations for such a multistaged reaction is described by a set of four diffusion-convection-reaction equations (both final product and intermediate are considered to move in the same direction as reactant B, thus modeling the case that was studied experimentally):
∂CA ∂CA ∂2CA + VA ) DA 2 - k1+CACB + k1-CAB* ∂t ∂x ∂x ∂CB ∂CB ∂2CB - VB ) DB 2 - k1+CACB + k1-CAB* ∂t ∂x ∂x
(7)
∂CAB* ∂CAB* ∂2CAB* + - VAB* ) DAB* ∂t ∂x ∂x2 k1+CACB - k1-CAB* - k2+CAB* + k2-CAB 2
∂CAB ∂CAB ∂ CAB + k2+CAB* - k2-CAB - VAB ) DAB ∂t ∂x ∂x2 with boundary conditions 1318
Analytical Chemistry, Vol. 73, No. 6, March 15, 2001
CA ) CA0, CB ) 0, CAB ) 0, CAB* ) 0
for x ) 0
CB ) CB0, CA ) 0, CAB ) 0, CAB* ) 0
for x ) L
and initial conditions (for t ) 0)
CA ) CA0 for x < X0;
CA ) 0 for x > X0
CB ) CB0 for x > X0;
CB ) 0 for x < X0
CAB ) 0,
CAB* ) 0
where DA, DB, DAB*, and DAB are sample, reagent, intermediate, and product diffusion coefficients, and k1+, k1-, k2+, and k2- are direct and reverse reaction rates of the first and the second stages of the reaction, respectively. An algorithm for computer simulation of the physicochemical processes that are described by the set of eq 7 was constructed. This algorithm is based on a combination of the method of weighted great particles, introduced by Bird9 and modified in ref 8 to imitate the motion of reactants and the change of their local concentrations in the process of reaction, and the method which can be called “cells scanning” and which has much in common with that used in ref 10. The details of this algorithm and the results of its testing were presented in refs 8 and 11. Another piece of theory that will be needed for the interpretation of experimental results concerns the values of the velocities of the reactants. The experimental situation is possible wherein not all of the reactants can be observed by the detector at the given wavelength, and so not all of the velocities can be directly measured. The mathematical model of EIA developed in ref 3 gives the possibility of calculating the unknown velocity of the reactant from the measured values of the product peak amplitude. For the case where CA0 , CB0 and the chemical reaction is fast (the product of the characteristic time of chemical reaction and velocity of any of the reactants is much smaller than the length of the zones of the reactants), it was shown that the amplitude of the peak of the product of the chemical reaction is equal to
CAB max ) CA0(VA + VB)/|VAB - VB|
(8)
The corresponding equation given in ref 3 for the general case is rewritten here, taking into consideration the above-mentioned directions of movement of the reactants and product for the special case studied in this paper. From eq 8 it is evident that VB can be calculated from the values of VA and VAB if the value of the focusing factor f ) CAB max/CA0 is known:
VB ) VAB - (VA + VAB)/(f + 1), if VB < VAB
(9)
VB ) VAB + (VA + VAB)/(f - 1), if VB > VAB
(10)
These equations will be used in the Experimental Section to (8) Andreev, V. P.; Pliss, N. S. J. Chromatogr. A 1999, 845, 227-236. (9) Bird, G. A. Molecular Gas Dynamics; Claredon Press: Oxford, 1976. (10) Patterson, D. H.; Harmon, B. J.; Regnier, F. E. J. Chromatogr. A 1996, 732, 119. (11) Andreev, V. P.; Pliss, N. S. Nauchnoe Priborostroenie 1997, 7, 13-27 (in Russian).
Table 1. Experimental Conditions set Ia Ib II III IV Va a
copper concn, M 10-4-5
10-4
1× × 1 × 10-4 5 × 10-6-2 × 10-4 1 × 10-6-2 × 10-4 1 × 10-6-2 × 10-4 1 × 10-5-2 × 10-4
EDTA concn, M 10-3
1× 2 × 10-4-1 × 10-3 5 × 10-4, 2 × 10-3 1 × 10-3, 2 × 10-3 1 × 10-3 1 × 10-3
U, kV
L, cm
D, cm
initial injection of copper
t, °C
current, µA
10 10 15 15 12 10
31.6 31.6 37.1 37.1 37.1 37.1
20.1 20.1 19.8 19.8 19.8 19.8
electroinjection electroinjection pressure pressure pressure pressure
26 26 16 16 16 16-18
23-27 23-27 27-30 28-30 21-22 17-18
The length of the copper zone is equal to the length of the capillary.
calculate VB from the independent experiments. Equation 8 also enables one to rewrite eq 6 in another convenient form:
VX - VAB ) (VB - VAB) - f(VB - VAB)
CA0 CA0 + CB0
(11)
EXPERIMENTAL SECTION Apparatus. Experiments were performed with a laboratorymade electroinjection analyzer that was described previously2,3 and is very much like the usual capillary electrophoresis instrument, but with two samplers enabling one to inject reactants from both ends of the capillary electrokinetically simultaneously, or with any desired time interval between injections. Untreated fused silica capillaries (BGB Analytik AG) of 0.1 mm i.d. × 0.375 mm o.d. were used. Photometric detection on the capillary was utilized at a wavelength of 254 nm. Chemicals. The following chemicals were used: copper sulfate, pentahydrate (Sigma); ethylenediaminetetraacetic acid, disodium salt, volumetric (dry) standard (Ecros, Russia); sodium acetate, trihydrate (Reanal, Hungary); acetic acid, glacial (Ecros, Russia). All chemicals were used without further purification. The stock solutions of copper and EDTA, 0.1 M each, were prepared by dissolving the respective salts in distilled water. Diluted reagent solutions were prepared from individual stock solutions by serial dilutions with distilled water. Acetate buffer (0.2 M, pH 4.6) was prepared according to ref 12. For experiments, solutions of copper in acetate buffer, EDTA in acetate buffer, and copper-EDTA complex in acetate buffer were used. These solutions were all freshly prepared by diluting the appropriate volumes of each reagent solution and buffer in distilled water and making up to final volume to give the desired concentrations of individual reagents in 0.02 M buffer (background electrolyte). Concentrations used for experiments were in the following ranges: [copper] ) 1 × 10-6-5 × 10-4 M; [EDTA] ) 2 × 10-4-2 × 10-3 M. (Polyethylene sample vials with attached flip-top caps were used for the mixing of ingredients and the storage of prepared solutions.) Exact concentration values and other experimental conditions are listed in Table 1. Procedure. The experimental procedure included two stages. During the first stage, the whole length of the capillary was filled with reactant A (the solution of copper), so that the coordinate of the meeting point X0 was equal to L. One of the reasons to perform this stage of the procedure was to make the coordinate of the meeting point constant and independent of the experimental (12) Dawson, R. M. C.; Elliott, D. C.; Elliott, W. H.; Jones, K. M. Data for Biochemical Research, 3rd ed.; Claredon Press: Oxford, 1986.
conditions. Otherwise, the coordinate of the meeting point would depend significantly on the value of electroosmotic flow velocity, and so could be influenced by changes of the temperature and/ or concentrations of the reagents, making the analysis of the characteristics of the observed peaks less convenient than in the case of constant X0. For some sets of experiments, the capillary was filled with copper solution by electrokinetic injection, and for other sets the solution was injected by pressure (see Table 1). During the second, main stage of the experiment, the second end of the capillary (L) was placed into a reservoir with reactant B (EDTA solution), while the first end of the capillary (0) was already in the reservoir with reactant A (copper solution), and then the electric field was applied. Values of applied voltage, reagent concentrations, detector coordinate D, capillary length L, temperature, and electric current are presented in Table 1. Copper solution and the copper-EDTA complex absorb at 254 nm, so their velocities were determined both by independent experiments (where copper and copper-EDTA zones were injected into the capillary) and during the EIA experiments (for copper, during the first stage of the experimentselectrokinetic filling of the capillary). The velocity of EDTA was calculated according to eqs 9 and 10 from the independent experiments performed for low values of copper concentration ([copper] ) 1 × 10-6 M), thus satisfying the condition of eq 8 (CA0 , CB0). The value of the focusing coefficient f was determined with the help of a calibration curve, produced by injecting into the capillary the copper-EDTA complex prepared by mixing of reactants outside of the capillary: f ) CAB max/CA0 ) (HAB/CA0)(Ccal/Hcal), where HAB is the amplitude of the product peak determined during EIA experiments, and Ccal and Hcal are the concentration and peak amplitude determined by injection of the calibration solution of copper-EDTA complex. All experiments were performed at room temperature. Between determinations, the capillary was rinsed for 2 min with running buffer solution under pressure. RESULTS AND DISCUSSION The product peak shapes observed during two sets of experiments are presented in Figures 2 and 3. In the first set (Ia), the concentration of EDTA was kept constant (CB0 ) 1 × 10-3 M), and the concentration of copper varied from CA0 ) 1 × 10-4 M to CA0 ) 5 × 10-4 M, while in the second set (Ib) the concentration of copper was constant, CA0 ) 1 × 10-4 M, and the concentration of EDTA varied from CB0 ) 1 × 10-3 M to CB0 ) 2 × 10-4 M. As was predicted in the Theory section, the signals observed by the detector are flat with very thin and sharp peaks at the rear edge. In all the experiments, the flux of copper was smaller than the flux of EDTA, so the product signal durations are finite and are Analytical Chemistry, Vol. 73, No. 6, March 15, 2001
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Figure 2. Illustration of the effect of copper concentration (CA0) on the width and shape of product peaks (set Ia). (Absorbance in this and other figures is given in arbitrary units. Absolute values will depend on experimental conditions.) CB0 ) 1 × 10-3 M; CA0 ) (a) 1 × 10-4, (b) 2 × 10-4, and (c) 4 × 10-4 M.
Figure 4. Illustration of the effect of copper concentration (CA0) on the width and the shape of product peaks for set III, including the cases of low copper concentration. CB0 ) 1 × 10-3 M; CA0 ) (a) 2.5 × 10-5, (b) 5 × 10-5, (c) 7.5 × 10-5, (d) 1 × 10-4, and (e) 2 × 10-4 M.
Figure 3. Illustration of the effect of EDTA concentration (CB0) on the width, amplitude, and shape of product peaks (set Ib). CA0 ) 1 × 10-4 M; CB0 ) (a) 7 × 10-4, (b) 6 × 10-4, (c) 5 × 10-4, and (d) 3 × 10-4 M. Double scale factor with respect to Figure 2.
shorter the larger the ratio CB0/CA0. As can be seen from Figure 3, the amplitude of the product signal depends significantly on the value of the EDTA concentration. A linear relationship between the amplitude of the signal and CB0 was obtained with a correlation coefficient r ) 0.9994. The regression equation was HAB(mm) ) 1.345 × 105CB0. This kind of dependence is quite understandable, because the maximum concentration of product that can be produced due to kinematic focusing is equal to the concentration of the reagent (CB0), and the experimental conditions of the studied sets correspond to efficient kinematic focusing. Figure 4 corresponds to set III, including the cases of significantly lower concentrations of reactant A, leading to shorter product signals according to theoretical predictions. As can be seen, the product signal shape significantly changes with the concentration of copper. When repeated measurements are made for a constant set of concentrations, not only are the signal width and the signal amplitudes reproducible, but the fine structure of the tops of the signals are reproduced also, thus providing evidence that reaction kinetics may be investigated by analysis of the signal shapes. For example, kinetics information can be obtained from the slopes of the signals, but preferably computer 1320 Analytical Chemistry, Vol. 73, No. 6, March 15, 2001
Figure 5. Comparison of the theoretical and experimental values of velocity VX of the boundary between reactants zones. O - set Ia, b - set Ib.
simulation may be done, and a signal similar to experimentally observed signals may be generated by varying the kinetic parameters. Figure 5 presents a comparison of theoretical and experimental values of VX for the sets Ia and Ib. Experimental values of VX were calculated as VX exp ) L/Tf exp, where Tf exp is the experimental value of time corresponding to the end of the product peak, while theoretical values of VX were calculated according to eq 3. As can be seen, the theoretical and experimental values are very close for all the experiments, thus proving that product peak width is really determined by the mechanism (movement of the boundary between reagent zones) described in the Theory section.
Table 2. Data of the Least-Squares Lines of the Plot of (VX - VAB) versus CA0/(CA0 + CB0) in Comparison with CAB max/CA0 from Independent Experiments set
R (cm/s)
β
∆R
∆β
β/R ) f
CAB max/CA0 (n ) 3)
II IV
-0.0045 -0.0032
-0.30 -0.22
0.001 0.001
0.01 0.01
67 68
70 66
When the experimental values of (VX - VAB) determined from the sets II, III, and IV (Table 1), including the “low-concentration” cases of Figure 4, are plotted against CA0/(CA0 + CB0), the results for the sets of experiments with different values of CB0 and CA0, but the same values of CA0/(CA0 + CB0), practically coincide. The dependence of (VX - VAB) on CA0/(CA0 + CB0) is linear for a wide range of reactant concentrations, as predicted by eq 6. The values of the intercept R, slope β, and their confidence intervals ∆R, ∆β for experimental sets II and IV are presented in Table 2. As can be seen from the values of intercept and eq 6, the difference between VB and VAB is very small, in conformity with the fact that very efficient kinematic focusing takes place. From the values of the intercepts and slopes, one can easily determine the values of the kinematic focusing factor f (see eq 11). They are also presented in Table 2. In the same table, the values of CAB max/CA0 determined during the same experimental sets for the case of very low concentrations of copper (1 × 10-6 M) are presented. As was shown in the Theory section (see eq 8), CAB max/CA0 is equal to the kinematic focusing factor f if CA0 , CB0. The rather close values of f determined by two independent procedures again provide evidence of the validity of the theoretical explanation of the observed effect. A set of experiments was performed in order to make sure that the sharp peak at the edge of the main signal is not an artifact connected with the experimental design but really reflects the kinetics of the multistaged reaction. Results of these experiments are presented in Figure 6. For the cases presented in Figures 6a-c, the capillary was filled with copper solution by pressure, and then one end of the capillary was placed into the pure buffer solution and another into the EDTA solution. The electric field was then applied. Thus, the situation was achieved where the zone of reactant A had a finite length equal to L, while the zone of reactant B exceeded this due to continuous injection. The concentration of copper was varied in these experiments from 2.5 × 10-5 to 2 × 10-4 M, and so the velocity of the boundary VX changed with concentration according to eq 3, thus leading to an increase of the signal width. Figure 6d presents the case where the copper concentration was the same as in Figure 6c, but both of the reactants were injected continuously. It is important to note that the sharp peak exists in case 6d and does not exist in case 6c. Figure 6e presents two stages of experiment. During the first stage (e1), the capillary was electrokinetically filled with copper solution of rather high concentration (2 × 10-4 M). The moment when the copper front passed by the detector can be seen as a step in the detector output. The first stage was finished when the capillary was filled with copper solution. One end of the capillary was then placed into the pure buffer solution and another end into the EDTA solution, so the copper zone length was again finite and equal to L. During the second stage (e2), chemical reaction took place, and the product was produced. As can be clearly seen
Figure 6. Illustration of the effect of copper concentration and the length of copper zone on the product peak shape. Absorbance in arbitrary units. CA0 ) (a) 2.5 × 10-5, (b) 7.5 × 10-5, and (c-f) 2 × 10-4 M; CB0 ) (a-e) 1 × 10-3 and (f) 0 M. (a-d) Injection of copper under pressure; (e,f) electrokinetic injection of copper. (a-c), (e,f) Copper zone length ls is equal to the length of capillary L; (d) continuously injected zone of copper.
from e1 and e2, the concentration of copper in this case was high enough to contribute significantly to the absorbance. The signal presented in e2 is due to absorbance of light by both copper and copper-EDTA ions. The amplitude of the “step down” in the product signal (e2) is equal to the amplitude of the “step up” in (e1). Furthermore, the moment when this “step down” occurs is the same as in the case of Figure 6f. Case 6f is similar to case 6e, but during the second stage both ends of the capillary were placed into the pure buffer solution. The easiest way to understand the depicted effects is to start with Figure 6f. It takes 225 s for the copper ions to travel from the point X ) 0 to the point X ) D; after this moment copper ions are present only between points D and L. The “step down” in Figure 6e occurs for the same reason: there are no more copper ions passing by the detector after 225 s. The output after this moment is only due to the copper-EDTA ions that have been produced by the ions of copper and EDTA that met each other between points D and L. It is quite understandable now why there is no sharp peak at the rear edge of the signal in this case: by the time the front of the reagent passes by the detector, there Analytical Chemistry, Vol. 73, No. 6, March 15, 2001
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Figure 7. Comparison of computer-simulated (A) and experimentally observed (B) peaks. CB0 ) 1 × 10-3 M; CA0 ) (1) 2 × 10-4, (2) 3 × 10-4, and (3) 5 × 10-4 M.
are no more copper ions to meet it and to produce the intermediate product, and all copper ions are consumed already. In case 6d, the concentrations are the same as in case 6e, but copper is introduced continuously, so copper ions are present at the front of the reagent continuously, including the moment when it passes by the detector, so there are some intermediate product molecules that are observed exactly at the time when they are formed, resulting in the sharp intermediate product peak. The situation depicted by Figures 6a-c is understandable also. The higher the copper concentration, the slower the boundary moves (according to eq 3). So, for cases 6a and 6b, the velocity of the boundary is high enough and the copper ions are not completely consumed by the time the boundary passes by the detector, and the sharp peak exists. In case 6c, the boundary moves more slowly, and copper ions are consumed by the time the boundary passes by the detector. Thus again, the fact is proven that the sharp peak exists only in the case where there are some molecules of the intermediate that are formed exactly at the time when the boundary passes by the detector. Computer simulation according to the model described by eq 7 was performed. Product signals computer simulated for the experimental conditions of set Ia are presented in Figure 7, together with the corresponding experimentally observed peaks. The values of reactants and product velocities used in the simulations were taken from the corresponding experiments. The reaction rate of the first stage of the reaction was considered to be k1+ ) 4 × 105 M-1 s-1, and the reaction rate for the second stage k2+ ) 10 s-1. Both stages were considered to be irreversible, 1322 Analytical Chemistry, Vol. 73, No. 6, March 15, 2001
k1- ) k2- ) 0, and the ratio of extinction coefficients for the intermediate and product of the reaction was considered to be equal to 2.5. A calibration curve of experimentally observed signal amplitudes versus copper-EDTA complex concentration was used to convert the computer-simulated results to millimeters. Note that while computer-simulated signals correspond to absorbance due to the presence of product AB and intermediate AB* only, the experimentally observed signals include the absorbance due to reactant A (copper) also. That is the reason the experimentally observed signals are augmented by the preceding plateau. Taking into consideration this difference, one can see that computersimulated signals have shapes very similar to the experimental ones. Sharp peaks at the rear edges of the signals are present in both experimental and computer-simulated product cases. Amplitudes and widths of the signal, and their dependence on the values of reactant concentrations, are in good agreement for theoretical and experimental results. The shapes of computersimulated signals appeared to be practically insensitive to any reasonable values of diffusion coefficients of reactants and to the value of electrophoretic velocity of the intermediate (two cases with velocity of the intermediate equal to the velocity of the product and half the velocity of the product were compared). The shapes are very sensitive to the ratio of concentrations of reactants and to the value of the reaction rate k2+. It is important to note that, for the experimental conditions of set Ia, the value of k2+ ) 10 s-1 led to a quite satisfactory correspondence between experimental and theoretical peaks, but for set II this value of k2+ led to values of amplitude of the peak of the intermediate much lower than those of the experimentaly observed ones. Satisfactory correspondence between simulated and experimental peak shapes for set II was produced in the case of k2+ ) 1 s-1. The impossibility of finding a value of k2+ suitable for computer simulation of both experimental sets most probably reflects the fact that the mechanism of the examined chemical reaction is more complicated than was supposed in eqs 7. One of the possible explanations for the observed discrepancy is that both copper and EDTA can exist as different species. For example, copper can form complexes with acetate in the buffer. Reaction rates k1+, k2+ could be significantly different for free copper ions and copper-acetate complexes. The distribution of copper between different species could depend on the copper concentration. Thus, one may speak about an apparent reaction rate constant depending on the concentrations of reactants and reflecting the fact that they are present as different species. Another possibility is to develop a more complicated mathematical model described by the set of diffusion-convection-reaction equations for each of the species. It is planned to develop such a model soon. CONCLUSION A new capability of electroinjection analysis, using continuously flowing zones of reactants, was predicted theoreticaly and verified experimentally for the investigation of chemical reaction mechanisms and kinetics. The most important fact is that the technique enables one to detect the molecules of the intermediate and/or product of the chemical reaction exactly at the moment when the ions of reactants meet each other. The present study employed the copper-EDTA reaction as a model, but the technique should be generally applicable to any chemical reaction whose intermediate could be detected. It may be possible, for example, to detect
an intermediate, indicated as a sharp peak in the absence of product detection. It is planned to further develop the technique described in the present paper by exploiting different experimental procedures for different chemical reactions and by using more sophisticated spectrophotometric detectors. It is important to note that the suggested technique can be achieved in microscale total analysis systems and can be combined with the methods of flow reaction kinetic studies described in ref 13, the main advantage of the present technique being the possibility to detect the intermediate molecules and thus to study the mechanism of (13) Fletcher, P. D. I.; Haswell, S. J.; Paunov, V. N. Analyst 1999, 124, 12731282.
multistage reactions. ACKNOWLEDGMENT This study was, in part, financially supported by the Russian Foundation for Basic Research under Award 98-03-32626, and by NATO Grants SfP 974373 and SA(CRG.CRG.974521). The authors are very grateful to Prof. Gary D. Christian for interesting and productive discussions. Received for review March 27, 2000. Revised manuscript received September 10, 2000. Accepted November 28, 2000. AC0003551
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