1410
Anal. Chem. 1986, 58, 1410-1414
Harris et al. (11, 12) have done this by assuming a specific peak shape and finding by iteration the set of peak shape parameters (two for each compound) that minimizes the residual of the least-squares fit to the data. It is important to realize that more can be done with more prior information and more computational effort. However, the biggest obstacle to the usefulness of these methods is not their limitations in handling complicated, highly overlapping peaks, but the problem of doing the required computations on the data produced by a chromatographic detector with a minimum of time and effort.
LITERATURE CITED (1) (2) (3) (4) (5) (6) (7) (8)
(9) (10) (11)
ACKNOWLEDGMENT I thank Barry Willis, Edward Reus, Leslie Hodges, and Edward Darland for providing the experimental data on which the program was developed and tested and John Michnowicz for guidance and encouragement.
(12)
Lawton, W. H.; Sylvestre, E. A. Technometrics 1971, 13, 617-633. Sharaf, M. A.; Kowalski, 8. R. Anal. Chem. 1982, 5 4 , 1291-1296. Osten, D. W.; Kowalski, B. R. Anal. Chem. 1984, 56, 991-995. Chen, J.-H.; Hwang, L.-P. Anal. Chlm. Acta 1981, 133, 271-281. Vandeglnste, 8.; Essers, R.; Bosman, T.; Reijnen, J.; Kateman, G. Anal. Chem. 1985, 5 7 , 971-965. Borgen, 0. S.;Kowalski, B. R. Anal. Chlm. Acta 1985, 174, 1-26. Gemperline, P. J. J. Chem. Inf. Comput. Scl. 1984, 2 4 , 206-212. Vandeglnste, B.; Derks, W.; Kateman, G. Anal. Chim. Acta 1985, 173, 253-264. Stoer, J.; Bulirsch, R. Introduction to Numerical Analysis ; SpringerVerlag: New York, 1980. Davis, J. M.; Glddlngs, J. C. Anal. Chem. 1983, 5 5 , 418-424. Knorr, F. J.; Thorshelm, H. R.; Harris, J. M. Anal. Chem. 1981. 53, 821-825. Frans, S. D.; McConnell, M. L.; Harris, J. M. Anal. Chem. 1985, 5 7 , 1552-1559.
RECEIVED for review November 13, 1985. Accepted January 21, 1986.
Integral Method for Evaluating Component Contribution to Total Solution Absorbance from Chromatographic Data David T. Rossi,* Frank Pacholec, and Linda M. Dawkins
Monsanto Industrial Chemicals Company, 800 N . Lindbergh Blvd., St. Louis, Missouri 63167
A method for the converslon of lsocratic HPLC ultravioletvisible absorbance data into static (solution) absorbance data has been developed and evaluated. The method is used to Indicate If all chromophores of a mutticomponent mixture elute from the chromatographic column and to estimate what percentage of solution absorbance at a given wavelength is attributable to a particular peak. The procedure Involves summation of absorbance vs. time chromatographicdata and subsequent normaiizatlon by constants that account for the sample Injection volume, the flow rate, and the tlme interval between data polnts. For single-component solutions linear regresslons of data obtained from this Integration process vs. static absorbance data yield straight lines wlth unity slopes and zero intercepts. The standard devlatlon associated with the integrated absorbance Is f8 mAU compared wlth f3 mAU for static absorbance.
A problem often presented to the analytical chemist involves the characterization of mixtures of solutes containing chromophores (1-3). High-pressure liquid chromatography (HPLC) is one of the most frequently employed techniques for separating such mixtures because it is readily implemented, has a great deal of resolving power, and in one form or another, is almost universally applicable (4). In such characterizations, it would be useful to determine if all the components that contribute to the static absorbance spectrum of the mixture contribute to the chromatogram in the same proportion. This is desirable because components that are stable in solution are not always stable under the conditions required for a HPLC separation and because components of interest often cannot be eluted from a particular column packing. With these limitations in mind, methodology for direct comparison of HPLC elution profiles with solution absorbance spectra has been developed. Previous work involved numerical integration and normalization of multiwavelength chromatographic data sets as a means for optimizing detection limits 0003-2700/86/0358-1410$0 1.50/0
of chromatographic components (5). Through a related numerical procedure, multiwavelength chromatographic data can now be integrated and normalized in order to yield absorbance data that are equivalent to those obtained by static absorbance measurements (Le., a spectrum of the solution). This data processing strategy has been applied to one-component solutions in order to evaluate accuracy and precision and to the characterization of a multicomponent reaction mixture.
THEORY The mass, m,, of component i flowing through the chromatographic detector cell during a period between two observations can be given by the average concentration of that component between observations, ci,times the volume of the mobile phase passing through the cell between the observations (6),AV m, = CiAV (1) The volume of mobile phase that will pass through the cell between observations is given by AV = FAt (2) where F is the flow rate and At is the time interval between observations (6). Combining eq 1and 2 and summing between observation times a and b, the total mass of component i in the sample is
m=
b
b
t=a
t=a
Em, = x C i F A t
(3)
The concentration of the component in the sample, C,, is the total mass of i injected divided by the injected sample volume, V , (7),
CiFAt
c,
=
t=a
-
v,
(4)
By use of Beer’s law, the average concentration of component i between observations is given by Ci= Ai/lti (5) 0 1966 American Chemical Soclety
ANALYTICAL CHEMISTRY, VOL. 58, NO. 7, JUNE 1986
1411
Table I. Regression Results of Integrated Absorbance vs. Static Absorbance (AB)for Test Compounds
a
compd
wavelength, nm
slope
intercept
SEE"
rb
binaphthyl phenanthrene anthracene
229.5 251.5 251.5
1.003 f 0.032 0.965 f 0.029 0.967 f 0.016
-8.2 f 22.8 -44.5 f 27.1 -20.7 f 11.7
24.80 30.93 13.95
0.9985 0.9987 0.9995
Standard error of the estimate. Correlation coefficient.
where Ai is the average absorbance between observations, ti is the absorptivity for component i at a particular wavelength and in a particular solvent, and I is the cell path length. In a similar manner C, = A,/lg (6) where A, is the static absorbance of the pure component in solution a t the same wavelength and for the same solvent conditions. By substituting eq 5 and 6 into eq 4, the static absorbance of a chromatographic peak at each wavelength is given by b
AiFAt A, =
t=a
v,
(7)
Unfortunately, Ai cannot be precisely evaluated because it represents the average absorbance between two observations. A working equation for the integration procedure is, then, given by b
CAiOFAt A, =
t=a
VB where Aio is the observed absorbance a t time t(9. The application of eq 8 requires the adherence of the chemical system to Beer's law. Considerations should be given to the linear working range of the spectrophotometer and to the effects of solute interaction in the sample. The accuracy of this equation can be verified by linear regressions of measured static absorbance vs. summed chromatographic absorbance. The slope of this plot should equal the normalization factor, FAtl V,, and the intercept should be zero. As an alternate indication of the lack of systematic error, linear regressions of measured static absorbance vs. summed and normalized chromatographic absorbance for the same solutions and wavelengths should yield a straight line with a unity slope and a zero intercept. EXPERIMENTAL SECTION Apparatus. The chromatograph used in this work was a Spectra-PhysicsModel 8100 (San Jose, CA) liquid chromatograph, equipped with a manual injector (Spectra-Physics A0346-010). The volume of the sample injection system was accurately determined by filling it with a standard hydrochloric acid solution, injecting into a stream of reagent grade water, collecting the effluent, and titrating with a standardized NaOH solution. The volume of the sample loop was determined to be 9.705 & 0.006 NL. The detector used to collect chromatographic and spectra data was a diode array detector (1040A, Hewlett-Packard, Palo Alto, CA), equipped with a 5-Mbyte Winchester disk drive (9133, Hewlett-Packard), a plotter (7470A, Hewlett-Packard), and a desktop computer (85B, Hewlett-Packard). Data collection and data plotting routines were supplied with the detector. Data processing routines were developed by the authors and are described below. The HPLC column used was 4.6 mm x 10 cm, with a C18 stationary phase on 3-pm spherical particles (Microsorb, Rainin, Woburn, MA). Reagents. The anthracene and phenanthrene used were fluorescence grade (Kodak, Rochester, NY). Other test com-
pounds were reagent grade or better (Kodak). All reagents were used without further purification, but each was checked chromatographically for purity. The phosphonate ester mixture was an actual sample from a laboratory scale synthesis that was run in-house. Reagent grade water was produced by passing deionized water through a Milli-Q water purification system (Waters, Millford, MA). Acetonitrile, for use in mobile-phase preparation, was liquid chromatography grade (Burdick and Jackson, Muskegan, MI). All mobile phase was filtered through 0.22-pm membrane filters (ALPHA-200, Gelman, Ann Arbor, MI). Procedure. A series of six solutions of each compound in the mobile phase was prepared. The concentration range of each series typically extended from 0.8 pg mL-l to 8 pg mL-'. The mobilephase composition ranged from 70 to 80% acetonitrile in water. The exact composition was selected to yield convenient retention times. Each solution was injected onto the column, and a data set of absorbance as a function of wavelength and time was collected with the diode array detector. Spectra were collected at 600-ms intervals in order to ensure sampling errors of less than 0.5% (8). In order to minimize instrumental variations, static absorbance spectra were collected by filling the detector flow cell with each solution using a 10-mL glass syringe (lOlOW, Hamilton, Reno, NV) equipped with a high-pressure stainless-steel fitting. Software. Two programs, UNPACK and SUMI, performed data processing. These programs were written in BASIC and executed on the desktop computer after data collection. UNPACK reads a data file from disk, converta it from ASCII to decimal, and displays it graphically in the form of sequential spectra. This program is useful for visually evaluating the quality of a data file and for helping the user to rapidly select the limits for numerical integration. SUM^ performs numerical integration on sequential spectral files in accordance with eq 8. The user fixes the limits of integration by specifying the starting and ending spectra. The program then sums all spectra between these limits, multiplies the sum by the time interval between spectra and the flow rate, and divides by the volume of sample injected. The resulting data set represents the static absorbance spectrum of those components that have eluted between the limits of integration.
RESULTS AND DISCUSSION All uncertainties are reported as standard deviations (iSD). Single-Component Solutions. In order to evaluate the accuracy of the model described by eq 8, sequential absorbance spectra were collected over time for binaphthyl, phenanthrene, and anthracene. Representative data sets for these test compounds are displayed in Figures 1 , 2 , and 3, respectively. Static spectra were also obtained for each of these solutions. This was done by filling the flow cell with a solution and acquiring several spectra. Ten spectra were averaged for each solution. Table I displays the regression results of static absorbance VS. integrated absorbance (from eq 8) for a series of solutions of each of the test compounds, a t a wavelength near the absorbance maximum. The regression results in each case display a slope that is nearly equal to unity and an intercept that is statistically indistinguishable from zero. The linearity for each regression is also very good, with correlation coefficients ( r ) better than 0.998 in each case. Any systematic errors that may be present in the data are obscured by random errors in the measurements. Sources of errors are discussed below.
1412
ANALYTICAL CHEMISTRY, VOL. 58, NO. 7, JUNE 1986 Absorbance [mAUl 115.0
1
Wave 1ength tnml
-1
.2
.3
.4
.6
.5
.7
Timo Iminl
Flgure 1. Absorbance vs. wavelength and time for the chromatographic monitoring of 29.1 ng of anthracene. The time axis has been offset by -3.5 min. Abeorbonco ImAUI
.2
.4
.E
.e
1.2 Tlmo tmlnl
1.0
1.4
Figure 2. Absorbance vs. wavelength and time for the chromatographic monitoring of 47.7 ng of 1,l'-binaphthyl. The time axis has been offset by -3.7 mln.
Table 11. Regression Results of Static Absorbance (A,) vs. Summed Absorbance (XA ") for Test Compounds compd
wavelength, nm
slope
intercept
SEE"
rb
binaphthyl phenanthrene anthracene
229.5 251.5 251.5
1.222 f 0.O3Sc 1.386 i 0.022d 1.512 i 0.045e
11.2 i 22.2 48.1 i 26.8 22.1 k 11.7
24.36 31.96 14.39
0.9985 0.9987 0.9995
Standard error of the estimate. Correlation coefficient. F A t / V = 1.230 i 0.014.
As an alternate test for systematic error in the model, linear regressions of static absorbance vs. summed absorbance were
Fat/ V = 1.342 * 0.015.
eFAt/
V = 1.463 i 0.016.
performed for each compound. The results of these regressions are summarized in Table 11. In each case, the slope of the
ANALYTICAL CHEMISTRY, VOL. 58, NO. 7, JUNE 1986
1413
Absorbance lrnAUl 119.
01 ~
Wavelength Cnml
340
4.0
4.2
4. 4
4. 6 Tine h i n l
Figure 3. Absorbance vs. wavelength and time for the chromatographic monitoring of 63.1 ng of phenanthrene.
regression line is equal to the normalization factor for the integration. For each regression, the determined value for the normalization factor equals the known value (footnotes c-e in Table 11) to within the limits of experimental certainty. Uncertainties reported for the determined values are standard deviations in the slope derived from the regression process. Uncertainties reported for the known values are derived from the propagation of uncertainties in the known values for flow rate (f0.5%) and time interval between measurements (f0.69%)through eq 8. The precision of the injection volume is assumed to be very high relative to the precisions of the other parameters and is not included in the propagation of errors. In order to gauge the precision for the static absorbance measurements, five replicate absorbance spectra of a 3.5 Fg mL-l phenanthrene solution were collected. The relative standard deviation (RSD) in the absorbance at 252 nm was f0.21% (f3.2 mAU). Propagation of uncertainties through eq 8 suggests that the RSD of the integrated spectrum should be f0.83% (f12 mAU). This value is in good agreement with a precision of f0.55% (f8 mAU) determined from five replicate integrations of the spectral chromatograms collected for the phenanthrene solution. This integration procedure can be applied to absorbance values in the range from 10 to 2000 mAU with good results. At absorbance values greater than 2000 mAU (static) the linear range of the photometric detector is exceeded, and the data sets of integrated vs. static absorbance exhibit a negative deviation in the direction of the static absorbance axis. At absorbance values less than 10 mAU (integrated) base-line noise (fl mAU RMS) begins to interfere with the signal, and the integrated data points may exhibit random fluctuations. The technique is, then, applicable over 21/2orders of magnitude. When integrated absorbance data, obtained by using eq 8, are compared to static absorbance data for the same solute and concentration, the integrated absorbance is consistently found to be 87-95% that of the static absorbance. This loss of absorbance during the detection of a chromatographic peak can be attributed to two main causes. First, during each absorbance measurement, there is a loss due to an unde-
tectable mass that gives rise to an absorbance lower than the detection limit of the system. Though the level of this undetectable absorbance is generally very low (our data suggests 1-3 mAU), it could become significant when several absorbance measurements are added together as in the case of integrated absorbance. Second, there will be some undetectable mass lost in the tails of the chromatographic peak. The amount lost will depend on the peak shape and the limits of integration. It is possible that there exists an optimum rate at which to collect data so that the losses occurring during each scan and in the tails of the chromatographic peak are minimized. Future work will involve studying how various parameters (number of scans, solute concentration, peak shape, and retention time) contribute to the loss of absorbance observed in integrated absorbance values obtained using eq 8. Multiple-Component Solution. In certain applications of modern liquid chromatography to complex mixtures, direct comparison of chromatographic data to absorbance data is desirable in order to obtain accurate information about the chromophores present. Such a comparison can be key in ascertaining whether or not all of the chromophores that are present during the static absorbance measurement are also present under chromatographic conditions, and whether or not all of these chromophores have eluted from the column. The conventional method for testing to see if all of the chromophores have eluted is to flush the column with a mobile phase of high solvent strength for an extended period of time. This approach is time-consuming, and it is not always successful. The following example illustrates how a chromatographic data-absorbance data comparison may be made in order to obtain such information about a chromatographic separation. Figure 4 displays a three-dimensional chromatographic representation of absorbance vs. wavelength and time for the separation of a mixture of phosphonate esters by reversedphase HPLC. The emphasis of this separation is to characterize the mixture by observing the nupber of components present and by documenting the spectral properties of each component. Only the components that are depicted in Figure 4 were successfully eluted from the column. The purity of
ANALYTICAL CHEMISTRY, VOL. 58, NO. 7, JUNE 1986
1414
Absorbance LmAUI 202. 6q
I
.4
.B
1.2
1.6
2.0
2.4
2.8
Tima tminl
Flgure 4. Absorbance vs. wavelength and time for the chromatographic monitoring of 1.94 bg of a complex mixture of organophosphonate esters. The mobile phase is 40% acetonitrile in water.
static absorbance at 550 nm. This type of quantitative characterization could prove to be useful for evaluating the degree to which colored components contribute to the total color of a multicomponent mixture.
'-4 i -in.o 2;
,
.o
,
I
,
I
,
I
,
,
l
,
310.0
,
,
,
I
/
,
,
,
,
,
,
I
(
,
,
I
S
,
1 ,
,
,
I
,,"I
510. 0
410 0 Wsvmlsrngsh
Cnml
Absorbance vs. wavelength for a 200 pg mL-' solution of and for organophosphonate esters in 40% acetonitrile/water (-), chromatographic data (Figure 4) integrated accordlng to eq 8 (.-.). Flgure 5.
these peaks may be ascertained by any of several previously described procedures (5). A prolonged column flush (15 min) with 100% acetonitrile failed to elute any other components. Figure 5 displays absorbance vs. wavelength for the total solution before it is injected onto the column 1-( and for the integrated spectrum (. * .) produced by application of eq 8 to the data set shown in Figure 4. It is obvious from Figure 5 that one or more component(s) in the mixture has not eluted from the column. This component(s) has a large absorbance band centered at 550 nm. Smaller discrepancies seen at 310 nm and 360 nm could be attributed to this same component or to another component in the mixture which also does not elute. The slight positive deviation seen at 240 nm is, possibly, a systematic error arising from the difficulty in precisely measuring absorbance over a steeply sloping spectral region. From the data shown in Figures 4 and 5, it is possible to evaluate the percentage of total absorbance at a given wavelength that can be attributed to a particular component. For example, at 550 nm, the integrated absorbance for the 2.5-min component shown in Figure 4 is 201.6 mAU. The total static absorbance of the solution, as shown in Figure 5, is 607.4 mAU. The 2.5-min peak, then, contributed 33.19% of the total
CONCLUSION The method that has been described here for direct comparison of HPLC elution profiles with solution absorbance spectra appears to be reasonably accurate and to yield a reliable representation for the total static absorbance spectrum as produced by individual components. This method has been shown to be a useful indicator of whether or not all chromophores in a mixture have eluted from the chromatographic column. The method also has applications in determining what percentage of solution color at a given wavelength is attributable to a particular component or components in a multisolute mixture. ACKNOWLEDGMENT We are grateful to Alan E. McDowell for early discussions concerning this method. We also wish to thank Paul D. Jager for helpful discussions concerning various aspects of this work and Larry Holden for a discussion of linear regression parameters. LITERATURE CITED (1) Anderson, D. G.; Vandeberg, J. T. Anal. Chem. 1985, 5 7 , 15R-29R. (2) . . Garbarlno, J. R.; Steinbrelmer, T. R.; Taylor, H. E. Anal. Chem. 1985, 57. 46R-88R. (3) Yeransian, J. A,; Sloman, K. G.; Faltz, A. K. Anal. Chem. 1985, 5 7 ,
27SR-315R. (4) Snyder, L. R.; Klrkiand, J. J. Introduction to MWern Liquid Chromatography, 2nd ed.; Wiley: New York, 1979. (5) Rossl, D. T.; Desliets, D. J.; Pardue, H. L. Anal. Chlm. Acta 1984, 161, 191-199. (6) McDowell, A. E., personal communication. (7) McDowell, A. E.; Pardue, H. L. Anal. Chem. 1977, 4 9 , 1171-1176. (8) Rossi, D. T.; Pacholec, F., manuscript in preparation.
RECEIVED for review October 21, 1985. Accepted February 6, 1986.
