Anal. Chem. 1998, 70, 1100-1107
HPLC Band Shape Analysis for Postcolumn Chemiluminescence Detection Obtained by Finite-Difference Simulation: The Chemical Band Narrowing Effect Ling Zhong and J. T. Maloy*
Department of Chemistry, Seton Hall University, South Orange, New Jersey 07079
Algorithms for the finite-difference digital simulation of partition chromatography with chemiluminescence (CL) detection have been developed for a proposed postcolumn CL reaction mechanism for acridinium esters reacting with peroxide and base. These algorithms use classical plate theory to establish the theoretical chromatographic band shape; subsequently, statistical moment analysis is employed to evaluate the retention time and the variance for the “spectrophotometric” peak obtained prior to postcolumn reaction with peroxide and base and for the CL peak shape detected downstream. The resulting model can be used to compare the two band shapes and to optimize postcolumn CL detection conditions such as the concentration of peroxide and base and the length of tubing connecting reaction tee and detector. The simulation assesses the effect of each photochemical reaction involved in the CL mechanism on detection level and chromatographic efficiency. As such, this work provides fundamental insight into the efficiency-enhancing phenomenon known as the “chemical band narrowing effect”. For one of the cases considered herein, a competitive dark reaction resulting in acridinium pseudobase formation is shown to contribute to this effect. The theoretical model predicts chromatographic behavior similar to the experimental chromatograms of 4-(2-succinimidyloxycarbonylethyl)phenyl-10-methylacridinium-9-carboxylate fluorosulfonate reported herein. Finite-difference simulation has been used to model partition chromatography in the absence of axial or longitudinal diffusion of the solute.1 The model, based on the Craig countercurrent distribution, assumes that a fixed fraction of solute is contained within the mobile phase at each theoretical plate on the column. A detector is placed at N0th theoretical plate to measure the fractional concentration of the solute at that plate as a function of time. Moment analysis of the temporal peak is employed to determine the retention time, the variance of the peak, and the chromatographic efficiency in terms of the theoretical plate (1) Kevra, S. A.; Bergman, D. L.; Maloy, J. T. J. Chem. Educ. 1994, 71, 10238.
1100 Analytical Chemistry, Vol. 70, No. 6, March 15, 1998
number. These simulations have confirmed the observation2,3 that, for partition chromatography, even in the presence of axial diffusion,4,5 the conventional estimate of the chromatographic efficiency (N) grossly overestimates the efficiency for a highly mobile solute; they also demonstrate that a more reliable estimate of the actual plate count is given by
N′ ) N(1 - X)
(1)
where X is the fraction of solute in the mobile phase. A summary of the symbols used in this work appears in Appendix 1. Chemiluminescence (CL) is a potentially useful method of detection in liquid chromatography. The emission of light resulting from relaxation of a chemically formed excited-state molecule provides an attractive means of measuring certain classes of analytes with high sensitivity. Recent examples of CL detection include the application of chemiluminescent acridinium-9-carboxylic acid derivatives6-10 labels in immunoassay and the use of CL detection in immunoaffinity chromatography,11 high-performance liquid chromatography,12-15 and capillary electrophoresis.16 In comparison with more traditional spectrochemical detection methods, postcolumn generation of CL has been reported to exhibit greater chromatographic efficiency, a wider linear dynamic (2) Fritz, J. S.; Schenk, G. H. Quantitative Analytical Chemistry, 5th ed.; Allyn and Bacon: Newton, MA, 1987. (3) Fritz, J. S.; Scott, D. M. J. Chromatogr. 1983, 271, 193-212. (4) Bergman, D. L. Ph.D. Dissertation, Seton Hall University, 1995. (5) Maloy, J. T. Digital Simulation of Electrochemical Problems In Laboratory Techniques In Electroanalytical Chemistry, 2nd Ed.; Kissinger, P. T.; Heineman, W. R., Eds.; Marcel Dekker: New York, 1996; Chapter 20. (6) Zomer, G.; van den Berg, R. H.; Jansen, E. H. J. M. Anal. Chim. Acta 1988, 205, 267-71. (7) Weeks, I.; Sturgess, M.; Jones, M. K.; Woodhead, J. S. Clin. Endocrinol. 1984, 20, 489-95. (8) Weeks, I.; Beheshti, I.; McCapra, F.; Campbell, A. K.; Woodhead, J. S. Clin. Chem. 1983, 29/8, 1474-9. (9) Richardson, A. P.; Kim, J. B.; Barnard, G. J.; Collins, W. P.; McCapra, F. Clin. Chem. 1985, 31, 1664-8. (10) Weeks, I.; Morgan, B. P.; Campbell, A. K.; Woodhead, J. S. J. Immunol. Methods 1985, 80, 33-8. (11) Hage, D. S.; Kao, P. C. Anal. Chem. 1991, 63, 586-95. (12) Novak, T. J.; Grayeski, M. L. Microchem. J. 1994, 50, 151-60. (13) Toyoka, T.; Imai, K. J. Chromatogr. 1983, 282, 495-500. (14) Sigvardson, K.; Kennish, J. M.; Birks, J. W. Anal. Chem. 1984, 56, 1096102. (15) Mann, B.; Grayeski, M. L. Biomed. Chromatogr. 1991, 5, 47-52. (16) Ruberto, M. A.; Grayeski, M. L. Anal. Chem. 1992, 64, 2758-62. S0003-2700(97)00789-0 CCC: $15.00
© 1998 American Chemical Society Published on Web 02/12/1998
range, a lower limit of detection,8-11,16 and a higher sensitivity because of elimination of fluctuation and light scattering from light sources. Acridinium esters12,16 are typical of the compounds that exhibit these effects. In some cases, a decline in relative chromatographic band broadening, as compared to traditional UV or fluorescence detection, has been noted in CL detection. This phenomenon has been identified as the “chemical band narrowing effect”17-19 and has allowed CL detection to be proposed as a means to improve resolution. Evidence of this effect presented by de Jong19 showed that a CL compound exhibiting a shorter half-life also exhibited a narrower peak width when the size of the flow cell was increased. The chemiluminescence of acridinium compounds makes them particularly attractive for detection in HPLC. Acridinium CL has no catalytic requirement for the production of high quantum yields. The rate of photon emission depends on the reagent concentration and pH. Measurement of acridinium CL is more straightforward as the emission wavelength (∼470 nm)20 is easily accessible to detection using a high-efficiency photomultiplier tube (PMT). The solubility of acridinium esters in the aqueous phase makes the postcolumn detection suitable for a reversed-phase HPLC system. The succinimidyl group on the acridinium derivative, 4-(2-succinimidyloxycarbonylethyl) phenyl-10-methylacridinium9-carboxylate fluorosulfonate (AC-C2-NHS), can undergo rapid reactions with amino acids to form highly stable asymmetric urea compounds with CL characteristics. Thus, AC-C2-NHS exhibits potential as an analytical tag in chromatography applications. A general mechanism of light emission of N-methylacridinium carboxylate has been proposed by McCapra and Chang21 (Figure 1). An important property of acridinium esters is the OH- attack on the 9-position of the positively charged aromatic ring under basic conditions (k4). The corresponding product, the pseudobase, does not undergo a subsequent photon emission process; instead, it will be consumed slowly via a dark reaction.22 In this report, a finite-difference simulation model is developed to gain an understanding of the effect of this reaction mechanism upon the postcolumn CL signal in partition chromatography. This model predicts the photochemical sequence that occurs when a partition distribution of acridinium ester emerges from a column and is mixed with peroxide and base. The effect of the each photochemical reaction upon the CL detection level and the chromatographic efficiency may be computed. Thus, this model also allows the optimization of CL postcolumn detection conditions such as the concentration of peroxide and base, the size of the flow cell, and the length of tubing connecting the reaction tee and the detector to be used. The simulation also provides some fundamental insights to the phenomenon known as the chemical band narrowing effect. The elucidation of the mechanistic aspects of this effect comprises the remainder of this report. EXPERIMENTAL SECTION Reagents. Chemiluminescent tagging reagent, 4-(2-succin(17) Rule, G.; Seitz, W. R. Clin. Chem. 1979, 25, 1635-8. (18) Grayeski, M. L.; Weber, A. J. Anal. Lett. 1984, 17 (A13), 1539-52. (19) DeJong, G. J.; Lammers, N.; Sprint, F. J.; Brinkman, U. A. Th.; Frei, R. W. Chromatographia 1984, 18, 129-33. (20) McCapra, F. Acc. Chem. Res 1976, 9, 201-8 (21) McCapra, F.; Chang, Y. C. J. Chem. Soc., Chem. Commun. 1966, 522. (22) Zaklika, K. A. Ph.D. Thesis, University of Sussex, Sussex, U.K., 1976.
Figure 1. Proposed mechanism for acridinium chemiluminescence emission.
imidyl-oxycarbonylethyl) phenyl-10-methylacridinium-9-carboxylate fluorosulfonate, was purchased from Lakeland Biomedical (Eden Prairie, MN). HPLC-grade acetonitrile was supplied by EM Science (Gibbstown, NJ). Sodium dodecyl sulfate (SDS), sodium hydroxide, triethylamine (TEA), and nitric acid were purchased from Fisher (Pittsburgh, PA). Hydrogen peroxide (30%) was from Sigma (St. Louis, MO). Deionized water was HPLC filtered (>15 MΩ/cm resistivity) by Milli-Q (Bedford, MA). All reagents were analytical grade. Instrumentation. The HPLC with CL postcolumn detection system shown in Figure 2 consisted of a Perkin-Elmer ISS100 autosampler (Perkin-Elmer, Norwalk, CT) equipped with a 10-µL sample loop (Alltech, Deerfield, IL), a Waters pump (Milford, MA), and two Perkin-Elmer series 10 pumps (Perkin-Elmer) for the delivery of mobile phase and two postcolumn reagents, hydrogen peroxide and base. A Valco mixing tee (VICI, Houston, TX) was used to premix the peroxide and base. A second Valco mixing tee then served as the reaction tee for the mixed reagents and the chromatographic effluent. Chemiluminescence was detected with a Spectroflow 980 programmable fluorescence detector (Kratos, now ABI/Perkin-Elmer, Norwalk, CT) equipped with a 5-µL flow cell and operated with its excitation source turned off. An ABI/Perkin-Elmer 785A programmable absorbance detector was connected immediately after the HPLC column and before the CL reagent mixing tee with its wavelength set at 265 nm. The Analytical Chemistry, Vol. 70, No. 6, March 15, 1998
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Figure 2. Instrumentation for HPLC with postcolumn chemiluminescence detection.
chromatographic output was collected by an Access Chrom data acquisition system (PE Nelson, Cupertino, CA) via a PE-Nelson 941 analog-to-digital interface. Chromatographic Conditions. Separation was performed on an ODS Hypersil column, 5 µm, 150 × 4.6 mm, (Keystone Scientific, Inc., Bellefont, PA) using the mobile phase of 50% acetonitrile and 50% 15 mM SDS with 10 mM TEA aqueous solution. The apparent pH was adjusted to 3.0 with diluted nitric acid solution. The mobile-phase flow rate was set at 1 mL/min. CL Postcolumn Detection. Two pumps, each operated at 1 mL/min were used to deliver 10 mM hydrogen peroxide solution and 10 mM sodium hydroxide solution to a Valco mixing tee connected by a 5-cm segment of 0.01-in.-i.d. PEEK tubing to the second Valco mixing tee, where the chromatographic eluent mixed with the postcolumn reagents to produce chemiluminescence. A 5-cm segment of 0.007-in.-i.d. PEEK tubing connected the reaction tee to the 5-µL flow cell of the detector. The PMT was operated at 800 V. COMPUTER SIMULATIONS Algorithms for Partition and Diffusion Chromatography. The partition and transport algorithm for the chromatographic column was adapted from previous work in our group.1,4 In this computer model the column is divided into a defined number of theoretical plates (N0) and a solute having a fixed fraction (X) in the mobile phase is allowed to move down the column after attaining its partition equilibrium distribution between the stationary phase and the mobile phase on each plate. The fractional concentration of the solute at rth plate after nth transfer, f(n,r), is calculated using the following algorithm for convection-partition:
f(n,r) ) f(n-1,r) (1-X) + f(n-1,r-1)(X)
(2)
At the end of the column, i.e. at the N0th theoretical plate, the fractional concentration of the solute is recorded as a function of time, i.e., as f(n,N0), to obtain the “spectrophotometric” peak. Kevra et al.1 modeled the chromatographic distribution pattern using different values for N0 and X and thereby presented a clear illustration of the partition model. While the software4 employed in this work allows both convection and longitudinal diffusion effects to be modeled, the results reported in this initial study are based solely on the partition mechanism (i.e. convection in the absence of diffusion1). A summary of the relevant chromatographic parameters appears in Appendix 1. Algorithms for the Postcolumn CL Mechanism. Based on the CL mechanism shown in Figure 1, the following series of 1102 Analytical Chemistry, Vol. 70, No. 6, March 15, 1998
Figure 3. Block diagram for digital simulation.
photochemical reactions can be written: k1
H2O2 + OH- 98 H2O + OOHk2
2OOH- 98 2OH- + O2 k3
OOH- + A+ 98 P k3p
P 98 R + hν k4
OH- + A+ 98 HO-A
(reaction 1) (reaction 2) (reaction 3) (reaction 3p) (reaction 4)
Reaction 1 is the generation of hydrogen peroxide anion, OOH-. Reaction 2 is the possible decomposition pathway of OOH-; it is believed to be a slow process in the system under consideration. Reaction 3, a step to produce the intermediate 1,2-dioxetane (compound P), is the essential step for photon generation. Reaction 3p comprises a series of reactions (Figure 1), starting at the loss of the leaving group R from compound P, the formation of dioxetanone (compound B), and the subsequent release of CO2 to produce excited-state N-methylacridone followed by photon generation. The reason for combining these reactions into one step is that the rate-determining step in this sequence is the loss of the leaving group R. Efficient CL reactions of acridinium esters require that the conjugated acid of the leaving group be acidic enough for R to be stable in water. The subsequent release of CO2 is instantaneous, and the relaxation of N-methylacridone from the excited state to the ground state is also very fast with high efficiency.20 Therefore, the rate of light emission depends only on the rate at which the leaving group is lost. Reaction 4, the formation of the so-called pseudobase, is a competing dark reaction without the emission of light. Figure 3 shows the simulation scheme for partition chromatography with postcolumn CL detection. After being subjected to convection and partition on the column, the acridinium derivative reaches the reaction tee, where it meets the premixed reagents, hydrogen peroxide and base. Subsequent CL reactions occur within the postcolumn flowing stream. The five chemical reactions are equilibrated in each of the theoretical plate volumes (corrected for dilution) on the postcolumn during each time frame, ∆t. The fractional concentration of each species, either reactant or product, in each volume element at the end of each iteration is computed on the basis of the rate laws involving that species. This photochemical reaction mechanism carries on within each volume element until that volume element reaches the CL detector at plate (N0 + m). Table 1 lists the species whose postcolumn distributions are predicted and the bulk concentration terms upon which
Table 1. Concentration Terms of Each Species in the CL Mechanism species
relevant bulk concn
fractional concn
acridinium (A+) OHH2O2 OOHHOO-A (P) HO-A hυ
CA COHCH2O2 CH2O2 CA CA CA
fA fOHfH2O2 fOOHfHOO-A fHO-A fhυa
a
Proportional to dI/dt (see Appendix 1).
the fractional concentration of each species is based; a sample calculation for one of the species in Table 1 appears below. The methodology employed in these calculations was developed for the investigation of electrochemical kinetics.5 The following example illustrates the computation of the postcolumn concentration of OOH- in any volume element, r, during any iteration, n (omitted in the symbolism for the sake of clarity). These calculations begin by writing the finite difference rate laws for reactions 1 - reactions 3:
d[OOH-]/dt ) ∆[OOH-]/∆t ) k1[H2O2] [OH-] k2[OOH-]2 - k3[OOH-] [A+] (3)
All concentrations are then expressed fractionally using one of the bulk concentrations appearing in Table 1.
CH2O2∆fOOH-(r) ) k1∆t(CH2O2 fH2O2(r))(COH-fOH- (r)) k2∆t(CH2O2 fOOH- (r))2 - k3∆t(CH2O2fOOH-(r))(CAfA+(r)) (4)
COH- and CH2O2 are normalized to CA by defining COH- ) R1CA and CH2O2 ) R2CA so that
∆fOOH-(r) ) k1∆tCAR1fH2O2(r)fOH-(r) k2∆tCAR2 fOOH-(r)2 - k3 ∆t CAfOOH-(r)fA+(r) (5)
Substitution of t0/N0 for ∆t yields
∆fOOH-(r) ) fH2O2(r)fOH-(r)(k1CAt0)R1/N0 fOOH-(r)2(k2CAt0)R2/N0 - fOOH-(r)fA+(r)(k3CAt0)/N0 (6)
where kiCAt0 is the dimensionless rate parameter associated with ki. In this manner, each rate constant ki is incorporated into the algorithm using the dimensionless input parameter kiCAt0 to define fi(r) in time and space. The computation of the fractional concentration of each species proceeds in an analogous fashion. It should be noted that N0, R1, R2, and kiCAt0, where i ) 1, 2, 3, 3p, and 4, are user-defined dimensionless input parameters required for each simulation. After the fractional concentration of each species is computed within
each postcolumn volume element, convection is simulated by computing the fractional concentration of each species i in the next volume element as
fi(r+1) ) fi(r) + ∆fi(r)
(7)
A “detector” placed at the end of the tubing, in the (N0 + m)th volume element, measures the fractional concentration, f(n, N0 + m), proportional to the photon flux dI/dt during the nth transfer as a function of time recorded in units of theoretical transfers. The simulation carries on until the entire band passes the (N0 + m)th plate corresponding to the CL detector and an insignificant photon flux is detected. The CL output is then subjected to moment analysis using the statistical algorithms appearing in Appendix 2 in order to evaluate the band shape parameters U0, tr, and σ. RESULTS AND DISCUSSION Experimental Chromatography. Figure 4 shows the chromatograms of AC-C2-NHS. UV detection prior to CL postcolumn detection was used to estimate t0 for the column; however, the UV sensitivity was too low to permit statistically significant UV chromatograms to be recorded. CL detection shows a significant increase in sensitivity. Results of the moment analysis (U0, tr, σ) for each experimental CL chromatogram are listed in Table 2. These quantities were computed using the well-established statistical algorithms appearing in Appendix 2. (We have sometimes noted disparities between the results obtained using these algorithms and the results obtained using the “moment analysis” option in some commercial chromatographic software packages.) The logarithmic calibration curve for CL detection has a coefficient of determination of 0.9981 and a slope of 1.0045. It represents a linear dynamic range of 4 orders of magnitude. The experimental variance of the CL chromatograms goes through a minimum as the concentration of AC-C2-NHS increases, thereby yielding a regime of maximum apparent efficiency. In the absence of statistically significant UV chromatograms, we have interpreted this trend in plate count variation as evidence of the chemical band narrowing effect. Some of the finite-difference simulations reported below confirm this interpretation. Digital Simulation of HPLC with CL Postcolumn Detection. The results of the moment analysis of a set of the theoretical CL chromatograms obtained by finite-difference simulation appears in Table 3. As each simulation executes, the theoretical signal is obtained as a function of n, the iteration number, at r ) N0 and r ) N0 + m. These “signals” are then subjected to moment analysis to obtain U0 , tr , σ, and N for the chromatograms obtained at either “detector”. Recognition of the fact that N0 and N0 + m correspond to t0 for the respective detectors allows one to compute N′ for either distribution. These results are displayed for the “UV” detector placed at r ) N0 in the model (identical for all runs) and for the “CL” detector placed at r ) N0 + m. The theoretical chromatograms recorded at the latter position varied with changes in the dimensionless rate constant associated with the ratedetermining step for CL emission, k3pCAt0. In general, for this set of input parameters, the CL peaks get narrower as k3pCAt0 increases, thereby illustrating the chemical band narrowing effect. Analytical Chemistry, Vol. 70, No. 6, March 15, 1998
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Table 2. Summary of Moment Analysis Results of the Experimental Chromatogramsa concn (mM) 10-6
3.96 × 3.96 × 10-5 3.96 × 10-4 3.96 × 10-3
area Uo
tr (s)
X
variance, σ2 (s2)
N
N′
1 987 14 822 145 373 2 053 172
94.99 94.10 93.83 97.36
0.76 0.77 0.77 0.74
79.49 26.11 22.49 49.55
113.51 339.13 391.47 191.30
27.47 79.65 91.08 49.83
a t ) 72 s was determined as the average of three runs at the highest concentration using UV detection; X ) t /t ; N ) t 2/σ2; N′ ) t (t - t )/σ2 o o r r r r o (superior diagnostic for partition chromatography).
Table 3. Moment Analysis Results for a Typical Finite-Difference Simulationa method of detection partition detected at r ) N0 CL detected at r ) N0 + m
a
k3pCAt0
N
N′
σ2
NCL/NP′
NCL′/NP′
σCL2/σP2
1 5 10 20 30 50 90
414.51 796.50 865.54 968.55 1190.38 1345.82 1465.09 1521.77
100.24 161.97 175.81 196.45 240.92 272.07 295.97 307.33
41.97 28.49 26.20 23.40 19.01 16.81 15.44 14.86
7.95 8.63 9.66 11.88 13.43 14.62 15.18
1.62 1.75 1.96 2.40 2.71 2.95 3.07
0.68 0.62 0.56 0.45 0.40 0.37 0.35
Other input parameters: N0 ) 100, X ) 0.76, m ) 20, k1CAt0 ) 10, k2CAt0 ) 1, k3CAt0 ) 10, k4CAt0 ) 1000, and CH2O2/CA ) COH-/CA ) 0.1.
Figure 4. Experimental chromatograms of AC-C2-NHS. UV and CL detection was in series.
It is noteworthy that the computed value of N′ for the UV detector placed at r ) N0 falls within 0.2% of the actual plate count for this column; thus, N′ for the UV detector (designated below as NP′) provides a more reliable figure of merit for subsequent comparisons of chromatographic efficiency. Using this NP′ as the basis of comparison it may be seen that the actual change in apparent efficiency due to the chemical band narrowing effect ranges from 1.62 to 3.07 times the reliable partition plate count for the column, rather than ranging from 7.95 to 15.18 times the plate count as shown by NCL/NP′. For the broadest CL peak shown, i.e., for k3pCAt0 ) 1, having a peak width ∼82% of the UV peak, the NCL′/NP′ ratio falls within 35% of (N0 + m)/N0. (a) Influence of k3p and k4 on Chemical Band Narrowing. The effect of variations in k3pCAt0 and k4CAt0 on relative column efficiency NCL′/NP′ and the area under the peak (U0) are shown in three dimensions in Figure 5. Figure 5a shows the effect of the variation of these two parameters on the relative column efficiency. The higher the NCL′/NP′ ratio, the more efficient the column appears to act with CL detection. The bottom surface of the graph, where NCL′/NP′ ) 1.0, represents those values of the two parameters where the CL peak shape is identical to the partition peak. In the CL mechanism, k3pCAt0 is the dominating factor of CL emission. A higher k3pCAt0 value indicates a shorter 1104 Analytical Chemistry, Vol. 70, No. 6, March 15, 1998
half-life for the CL compound and a faster light emission process. At all values of k3pCAt0, however, reaction 4 dominates the appearance of the CL peak and is seen to be the cause of chemical band narrowing indicated by NCL′/NP′ ratios greater than 1.0. Note that if k4CAt0 is very small, the compound fails to exhibit chemical band narrowing and produces a CL signal that appears to have the partition peak shape. This peak narrowing effect generally increases as k4CAt0 increases, but at some point near to where k4CAt0 ) 2500, i.e. at a specific concentration if k4 and t0 are constants, the NCL′/NP′ ratio goes through a maximum. This simulated trend in peak narrowing agrees, in general, with the experimental results shown in Table 2. Figure 5b displays the effect of variations in k3pCAt0 and k4CAt0 on the CL peak area. Under the defined postcolumn conditions, light signal increases as k3pCAt0 increases. After a maximum is reached, any further increase in k3pCAt0 results a decrease in the CL signal as measured by U0. This behavior can be rationalized by noting that the detection window is located a fixed distance (m volume elements) from the reaction tee. All other input parameters remaining constant, the magnitude of the signal observed at the detection window depends upon the relationship between k3pCAt0 and the detector position. If k3pCAt0 is too small for the given detector position, unreacted acridinium compound will emit downstream from the detector. If k3pCAt0 is too large for a given detector position, the acridinium compound will emit prior to reaching the detector as it is being converted to non-CL product. Therefore, there exists an optimum value for k3pCAt0 that will produce a maximum CL signal at a given detector position. This maximum is exhibited in Figure 5b. This observation indicates that CL detection offers the opportunity to distinguish among chemiluminescent compounds exhibiting different rate characteristics using a spatially resolvable detector, e.g., a photodiode array. The construction of numerous calibration curves at constant values of k3pCAt0 and k4CAt0 reveals that variations in k1, k2, and k3
Figure 5. Combined effects of k3pCAt0 and k4pCAt0 on CL response. (a) Column efficiency, N′ and (b) peak area, U0. Input parameters: X ) 0.76, N0 ) 100, m ) 20, k1CAt0 ) 10, k2CAt0 ) 1, k3CAt0 ) 10, COH-/CA ) CH2O2/CA ) 0.1.
do not cause significant changes in the CL band shape. However, the area under the CL peak increases proportionally with CA, the built-in concentration factor in the dimensionless rate constant. These observations are in general agreement with the calibration curve shown numerically in Table 2. (b) Assurance of Simulation Validity. In carrying out any finite-difference simulation, one must exercise some care to ensure the validity of the reported results. At a minimum, this requires the demonstration of the material balance of all species in time and in space. This material balance is illustrated in Figure 6, which shows the postcolumn spatial distribution of each acridinium-related species (A+, HOOA, HOA, R) and the spatially distributed CL signal at three different times (n ) 152, 180, 209). The set of input parameters used to obtain the mass balance snapshots shown in Figure 6a is similar to those used in Figure 5 with the exception that k1CAt0 ) 1000 and k3CAt0 ) 50. These relatively fast dimensionless rate constants for reaction 1 and reaction 3 accelerate the generation of HOO- (not shown) and all light-generating intermediates. This allows all four acridinium species to appear within the figure. Under these conditions, A+ and HOOA are seen to decrease as the total acridinium band moves down the postcolumn while R and HOA, the pseudobase,
Figure 6. Snapshot of concentration profiles of all acridinium related species (A, HOOA, R, HOA, total acridinium) and normalized CL signal within the postcolumn at three different times. Input parameters: (a) X ) 0.76, N0 ) 100, k1CAt0 ) 1000, k2CAt0 ) 1, k3CAt0 ) 50, k3pCAt0 ) 10, k4CAt0 ) 1000, and COH-/CA ) CH2O2/CA ) 0.1; (b) same as Figure 5 with k3pCAt0 ) 30 and k4CAt0 ) 2500.
increase. At each of the three times shown, mass balance is achieved: the distributed sum of the concentrations of all acridinium species is spatially identical with the original partition peak for the acridinium ester. Figure 6a also compares the spatial distribution of the sum of all acridinium species with the spatial CL band shape. In this comparison, the CL signal has been normalized to the area of the partition band shape, i.e. the constant peak area of the total acridinium. Each of the CL band shapes shown in Figure 6a is virtually identical to the partition band shape; thus, under these kinetic conditions, no chemical band narrowing would be observed. This behavior may be contrasted with the mass balance and the CL peak shapes shown in Figure 6b. These mass balance snapshots were obtained using the kinetic parameters of Figure 5. Mass balance is still achieved at each time; however, because k4CAt0 is quite large, much of the acridinium is converted to the pseudobase so that very little HOOA and R appear in this distribution. Because the pseudobase formation results from a bimolecular reaction of acridinium ester with OH-, most of the acridinium compound is lost from the tails of the original distribution. This produces the much more narrow distribution of acridinium ester shown in Figure 6b with its corresponding CL peak shape. Drawn to the same area as the partition distribution of total acridinium, the CL peak is much higher than Analytical Chemistry, Vol. 70, No. 6, March 15, 1998
1105
Figure 7. Comparison of the resolution of two theoretical peak pairs using UV and CL detection. Input parameters: N0 ) 100, m ) 46. k1CAt0 ) 10, k2CAt0 ) 1, k3CAt0 ) 10, k3pCAt0 ) 90, k4CAt0 ) 1000, and COH-/CA ) CH2O2/CA ) 0.1.
the partition peak; this clearly indicates that the chemical band narrowing effect would be observed as these distributions pass by a downstream detection window. It is also informative to note that the CL peaks heights in Figure 6b increase at longer times, thereby indicating that chemical band narrowing becomes more extensive as pseudobase formation proceeds. (c) Resolution Improvement with CL Detection. The simulated chromatograms for an arbitrarily chosen pair of solutes under partition chromatography with UV detection and with CL detection are shown in Figure 7. As a result of the rapidly decaying signal produced by the proposed CL mechanism, the column appears to be more efficient with CL detection. The resolution of either pair of adjacent peaks can be calculated using
resolution ) (tr2 - tr1)/(1/2W2 + 1/2W1) =
acting in conjunction with a competitive dark reaction that results in acridinium pseudobase formation have been identified as the probable cause of the phenomenon known as the chemical band narrowing effect. The postcolumn reaction of base with peroxide (reaction 1) and the subsequent reaction of peroxide ion with acridinium (reaction 3) both exhibit significant positive effects on CL response; however, the degree is limited by the rate of pseudobase formation. The decomposition of OOH- to base and oxygen (reaction 2) is likely to be a slow process that does not contribute significantly to the CL response. Variations in the magnitude of the dimensionless representation of k3p predicts that different acridinium esters will exhibit different CL results; the model thereby offers the opportunity to study CL kinetics using chromatographic band shape analysis. This computer model also provides a useful tool for optimizing the chromatographic results through theoretical variations in postcolumn reagent concentrations and flow rates and variations in the length of the postcolumn and the size of the flow cell. A more detailed discussion of these kinetic effects and their role in system optimization will be the topic of a future communication. This work illustrates the utility of finite-difference simulations in the interpretation of chromatographic peak shapes obtained from only one mode of postcolumn detection. It is our belief that these simulations may be applicable to the elucidation of other postcolumn “focusing” techniques in addition to aiding in the investigation of other chromatographic mechanisms and the optimization of other column conditions. ACKNOWLEDGMENT This paper was presented, in part, at the 1996 Eastern Analytical Symposium & Exposition, Somerset, NJ, (Paper 363). The authors gratefully acknowledge helpful discussions with Professor Mary Lynn Grayeski during the early stages of this work. The use of research facilities and equipment of Merck Research Laboratories to perform some of the experimental part of this work is also gratefully acknowledged.
(tr2 - tr1)/(2σ2 + 2σ1) (8) APPENDIX 1. SYMBOLS USED IN THIS WORK Chromatography Parameters where W1 and W2 are the peak widths of the earlier and later eluting peaks, respectively, and tri and σi are the corresponding retention times and standard deviations. Because the variance of each CL peak is reduced by the chemical band narrowing effect, the CL peak pair resolution is 1.39, while that of the UV peak pair is 0.67. Thus, in this example, the band-narrowing effect would allow the peaks that are unresolved with UV detection to be resolved with CL detection.
CONCLUSION The finite-difference simulation model for HPLC with CL postcolumn detection provides a quantitative description of the experimentally observed peak shapes obtained using this method and a useful rationalization of the unusual column efficiencies that may also be observed when this mode of detection is employed. In particular, a series of rapid postcolumn photochemical reactions 1106 Analytical Chemistry, Vol. 70, No. 6, March 15, 1998
N0
defined number of theoretical plates on column
L
length of the column
∆x
length of the finite difference volume element on column, )HETP ) L/N0
∆t
finite difference element of time, )t0/N0
t0
retention time for an unretained peak
tr
retention time
σ2
variance of the chromatographic peak
N
conventional estimate of column efficiency, )tr2/σ2
N′
corrected estimate of column efficiency for partition chromatography, )tr(tr - t0)/σ2
X
fraction of solute in the mobile phase
f(n,r)
fractional concentration of solute on rth plate after nth transfer
U0
area under the chromatographic peak
vm
mobile phase velocity
vc
combined flow rate of mobile phase, base and peroxide
Finite-Difference Simulation Parameters
Rj
ratio of the bulk concentration of reagents j (j ) 1 for OH- and j ) 2 for H2O2) prior to postcolumn mixing to the bulk acridinium concentration at the point of injection
m
number of adjusted plate volumes on postcolumn
∆VUV
plate volume of each column volume element
∆VCL
volume of the postcolumn finite-difference volume element
ki
rate constant of reaction i (i ) 1-4, 3p)
CA
bulk concentration of acridinium analyte
[i]
molar concentration of species i (i ) acridinium, H2O2, OOH-, OH-, HOO-A)
f(n,r)
fractional acridinium concentration contained within the rth column plate after the nth transfer
fi(r)
fractional concentration of species i (i ) acridinium, H2O2, OOH-, OH-, HOO-A) contained within the rth postcolumn plate after the nth transfer
dI/dt
CL photon flux, )fhυ(n, N0 + m)CA(∆VCL)ΦCL/∆t
Received for review July 22, 1997. Accepted December 9, 1997.
ΦCL
overall quantum efficiency of CL process
AC9707895
APPENDIX 2. STATISTICAL DEFINITIONS FOR MOMENT ANALYSIS1 Zeroth, First, and Second Moments about the Origin ∞
µ0′ ) zeroth moment ) 0∫ f(t) dt ) area under the peak (U0) ∞ µ1′ ) first moment ) 0∫ tf(t) dt/µ0′ ∞ µ2′ ) second moment ) 0∫ t2f(t) dt/µ0′ First and Second Moments about the Mean µ1 ) first moment ) µ1′ ) retention time (tr) µ2 ) second moment ) µ2′ - (µ1′)2 ) variance (σ2)
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