Anal. Chem. 19a.4, 56,85-88
is the standard signal level in many SPC experiments. We have also verified that the parameters calculated from the PP method yield statistically valid fits. Using the least squares K , r , and a, we regenerated D ( t ) using eq 1 and compared the resultant curve with the original data using a x2 test (12). The reduced x2’s typically ranged from 0.9 to 1.1 which is acceptable for 200 data points (12). All data fits are unweighted, and in view of the excellent results, we recommend the use of unweighted fits for the range of parameters and fits indicated. Unweighted fits are easier to do, and the much more complex weighted data treatment appears unwarranted. This conclusion is the same as that reported by Greer et al. ( 4 ) for deconvolution of single exponential decays using the phase-plane method and also is consistent with the results of the PP method derived for base line correction of exponential decays (13). There is a potential problem with the treatment presented here when used with SPC data. These instruments actually measure the integral of the number of photons collected over the preceding time window rather than the instantaneous intensity. If too low a density of points is used, then the PP method, which is an integral method, gives systematic errors in the phase-plane plots and the evaluated parameters. However, for virtually all SPC data, the density of the data points is high enough so that the error should be negligible. Jezequel et al. (8)pointed out this error source and described a simple way to circumvent it should the errors ever become significant. When the PP method is used with analog data, this error source is not present. We conclude that for a reasonable range of decay parameters and fitting regions, the modified PP equation is accurate and precise. The method can be easily programmed and is
a5
computationally very fast. These features give the PP!method distinct advantages over much slower nonlinear leasbsquares methods, especially in view of the increasing use of microcomputers in data acquisition systems.
ACKNOWLEDGMENT We thank J. C. Andre for providing preprints of his manuscript and J. Y. Jezequel for helpful comments. LITERATURE CITED (1) Blrks, J. B. “Photophysics of Aromatic Molecules”; Why-Interscience, New York, 1970. (2) Demas, J. N. “Excited State Lifetime Measurements”; Academic Press: New York, 1983. (3) Demas, J. N.; Adamson, A. W. J. Phys. Chem. 1971, 75, 2483. (4) Greer, J. M.; Reed, F. W.; Demas, J. N. Anal. Chem. 1961, 53, 710. (5) Isenberg, I.; Dyson, R. D. Blophys. J. 1969, 9 , 1337. (6) Bernalte, A.; Lepage, J. Rev. Scl. Instrum. 1969, 4 0 , 71. (7) Huen, T. Rev. Sci. Instrum. 1969, 4 0 , 106. (8) Jezequel, J. Y.; Bouchy, M.; Andre, J. C. Anal. Chem. 1962, 5 4 , 2199. (9) Love, J. C.; Demas, J. N. Rev. Scl. Instrum. in press. (10) Reed, F. W.; Demas, J. N. “Time Resolved Fluorescence Spectroscopy in Biochemistry and Biology”. Cundall, R. B., Dale, R. E., Eds.; Plenum Press: New York, 1983; p 285. (11) Knuth, P. E. “Semlnumerical Algorithms. The Art of Computer Programming”; Addison-Wesley: Readlng, MA, 1969; Voi. 1. (12) Bevington, P. R. “Data Reduction and Error Analysis for the Physical Sciences”; McGraw-Hill: New York, 1969. (13) Bacon, J. R.; Demas, J. N. Anal. Chem. 1983, 55, 653.
RECEIVED for review July 29,1983. Accepted October 3,1983. We gratefully acknowledge the donors of the Petroleum Research Fund, administered by the American Chemical Society, the Air Force Office of Scientific Research (Chemistry) (Grant AFOSR 78-3590), the Department of Energy for SERI Grant DE-FG02-CS84063, and the National Science Foundation (CHE 82-06279).
Optimization of Anion Separation by Nonsuppressed Ion Chromatography Dennis R. Jenke and Gordon K. Pagenkopf*
Department of Chemistry, Montana State University, Bozeman, Montana 5971 7
The effect of eluent pH and eluent species concentration on the nonsuppressed ion chromatographic separatlon of anions has been studied. The retentlon times of CI-, Br-, NO,-, SO:-, and SO , :were determined over a large range of eluent composltlons and the data were utilized to construct window diagrams. These window dlagrams were used to optimize eluent composition for the separation of two or more anaiytes. I n virtually every case resolytlon is ilmlted by the separation of the NO,-/Br- pair.
Since its introduction in 1975, ion chromatography has rapidly evolved into a widely accepted method for the quantitative determination of anions in aqueous samples (I). Single column or nonsuppressed ion chromatographic techniques have been successful in a variety of applications (2). As is the case with all chromatographic techniques, the most effective utilization of the ion chromatographic process requires accurate characterization of the analyte retention times and identification of analytical variables that affect the relative 0003-2700/84/0358-0085$0 1.50/0
retention characteristics of the analytes. Of particular interest is the development of a predictive capability and optimization of ion chromatographic resolution, while minimizing analysis time. This can be complicated by the potential existence of multiple optima and the large range of eluent related variables that control chromatographic separation. The concept of “window diagrams” has been utilized to locate optimum conditions in gas chromatography ( 3 , 4 ) . This technique also has been applied to high-performance liquid chromatographic separations (5-8). This study utilizes the technique to optimize the separation of inorganic ions and to predict the behavior of selected analytes under various experimental conditions.
EXPERIMENTAL SECTION The chromatographic system employed consisted of a Perkin-Elmer Series 3B liquid chromatograph, a Vydac Model 3021 C4.6 anion separator column, a Vydac Model 6000CD conductivity detector, and a Sargent Welch XKR strip chart recorder. Injector sample loop volume was 0.10 mL and samples of 0.5 mL were injected with a Hamilton Co. Model 750 microliter syringe. Laboratory temperature was maintained at 22.5 f 2.0 OC and the 0 1983 American Chemlcal Society
86
ANALYTICAL CHEMISTRY, VOL. 56, NO. I , JANUARY 1984
Table I. Legend for Analyte Pairs in Window Diagrams diagram desiynation 1 2 3 4 5
analyte pair
diagram designation
so,2-,c1-
6
NO;
7 8 9 10
SO,’., SO,’.,
Br-
s20,2-, so,2s20,2-,
c1-
1.0
-
analyte pair S,O,’-, S,O,’-,
-
BrNO;
4
-
NO;, C1NO;,Br-
Br-, C1.6-
active chromatographic components were thermally isolated to minimize the effect of short-term temperature fluctuations (9). Thirty-two phthalate eluents with a pH range of 3.8 to 6.0 and a total concentration range of 1.0 to 6.0 X M were prepared from the potassium salt. KOH (0.1 M) was used for pH adjustment. Final pH measurement was made after degassing under suction. Stock analyte solutions (0.10 M) were prepared by dissolution of NaCl, NaNO,, Na2S04,Na2S203,and KBr in doubly distilled water. Standard solutions of the analytes, 0.2,2.0, and 10.0 X M, were prepared by diluting the stock solutions with the desired eluent. This minimized the solvent dip in the chromatogram. Retention times were measured at maximum peak height of the recorded chromatogram and each analysis was done in triplicate. The retention time data have 5een previously presented (IO). A flow rate of 2-3 mL/min for 1.5 h was used to allow the chromatographic system to equilibrate when the eluent was changed.
RESULTS AND DISCUSSION By convention, window diagrams express the relationship between retention characteristics of two analyte species and an operational variable of the chromatographic system. In this study, the relationship is the relative reduced retention ratio a which is defined as a=-
tA
- tV
tB
- tV
is the retention time of and@ species A, tB is the retention time of analyte B, and tv is the time equivalent of the void volume. Values of t~ and t B are readily obtained from the chromatograms while tv is estimated from the appearance time of the solvent dip. The operational variable is the eluent composition which, for a nonsuppressed chromatographic system, is regulated by the pH and the total phthalate concentration. Since pH and total eluent concentrations vary, three-dimensional diagrams may be generated; however, their interpretation is complicated by the large amount of data. As a consequence two-dimensional iso-pH and iso-total phthalate contours are presented. When a equals 1.0, the two analyte peaks overlap. In addition, a is always kept greater than 1by reversing the pairs, i.e., t A 2 tg. As a increases, the relative separation between the two pairs increases. Changes in a and the operational parameters are sizable and thus log-log diagrams are utilized. The identification numbers for the 10 ion pairs arising from the combinations of C1-, Br-, NO,, SO:- and SZO2- are listed in Table I. A plot of log a vs. log PTat pH 3.8 is shown in Figure 1 and the pH 6.0 data are shown in Figure 2. The values of log a are independent of the total eluent concentrations provided that the charges of the analytes are the same (pairs 4 , 8 , 9 , 1 0 ) . This is not the case when divalent and monovalent ions are compared. Divalent retention times decrease more rapidly than the monovalent retention times as the eluent concentration increases. The slopes of the divalent-monovalent lines are the same at any given pH but they do not change with pH. This change is due to species distribution change within the eluent. The bottom line of the window diagram identifies the pair with poorest resolution and the top line identifies the pair with
-
c
-6
W
.4-
0
8
4,lO
9 I
-3.0
I
I
-2.8
I
-2.6
I
I
-24
LOG ( PT 1
Figure 1.
Window diagram for variable eluent concentration pH 3.8.
.6-
tA
c
K
W
0
.4-
J
.2
-
t I
-3.0
9
I
1
I
1
-2.8
-2.6
-2.4
LOG ( P T )
Flgure 2. Window diagram for variable eluent concentration pH 6.0.
best resolution. As a consequence, the bottom of the diagram limits optimization in terms of resolution whereas the top limits in terms of analysis time. The ratio of elution time for the last eluted anion and the first eluted anion will be largest and, thus will limit the analysis time. In Figure 1 the only optimization available is analysis time which decreases as total phthalate concentration increases. Resolution is limited by the N03--Br- pair, number 9. As eluent pH increases, the divalent retention times are significantly reduced and the bottom of the diagram is determined by the separation of the S0,2’-NO< pair at the highest eluent concentration; see Figure 2 (line 2). At pH 6.0 the optimum conditions occur at log PT = -2.43, the intersection of lines 2 and 9. For PT concen-
ANALYTICAL CHEMISTRY, VOL. 56,
NO. 1, JANUARY
87
1984
I 4
5
A
J
3
2
I
I
I
4
5
I /
,
-.6
6 1
I
I
I
2
I
3
-.4 -.2
0
I
.4
I
.6
I
.8
,
1.0
I
1.2
4
1.4
1 1.6
9
,
1.8
LOG( AHp/A$-)
5
4
.2
Flgure 5. Window diagram for total phthalate concentration of 5 X lom3M, pH varies from 6.0 to 3.8.
Table 11. Comparison of Predicted and Observed Retention Times retention time, min eluent
c ,
I
I
I
2
3.5 x
1
I
I
3
4
5
M KfiP
pH 5.85
species c1Br-a NO;
s0,zS,032'
RETENTION
TIME
1.0x 10-3M KHP
Cmln
Flgure 3. Calculated retention times for different total eluent conM, for B, PT = 3.7 X centrations, pH 6.0. For A, P, = 3 X M, and for C, P, = 5 X
M. Typical peak widths at the base are 0.4 min. The elution order is Ci-, Br-, NO3-, SO4'-, and S2O3'-.
l.oi
PH
..-
-.6
-.4-2
1.0 x 10-3 M KHP ~JH 4.20 1.0 x 10-3 M KHP pH 5.20
,
I
5
pH 4.00
4
Cl-a NO; Br-
so,2Cl-a
NO ; s0,z-
Cl-a NO ;
so,2-
predicted observed 1.78 2.16 2.45 2.83 3.70 2.65 3.74 3.34 13.56 3.63 6.50 18.40 2.00 2.72 5.30
1.74 2.16 2.45 2.84 3.73 2.65 3.58 3.23 14.00 3.63 6.55 18.40 2.00 2.63 5.15
Analyte used as reference peak.
0
.2
.4
LOG ( A
.6
.8
1.0
1.2
1.4
1.6
1.8
/A
HPF"' Flgure 4. Window diagram for total phthalate concentration of 3 X
M, pH varies from 6.0 to 3.8.
trations greater than this value, the analysis time is reduced but resolution is sacrificed. At log PT less than -2.43 resolution does not change whereas analysis time increases. The absolute retention times cannot be obtained from Figures 1 and 2; however, with knowledge of the retention time of one analyte and tv, the retention times of the other analytes may be calculated by using eq 1. A graphical presentation of the change in retention time at the PT values cited above is shown in Figure 3. By reduction of PTfrom 3.7 X M to 3.0 X M the analysis time increases from 4.1 min to 4.8 min with no change in resolution. When PT increases to 5.0 X M sulfate and nitrate peaks become indistinguishable but analysis time is reduced to 3.2 min.
Figures 4 and 5 demonstrate the change in the window diagrams as the pH varies. The conclusions are similar to those previously presented with analysis time being regulated by Sz032--C1- separation (line 5). At low pH, resolution is limited by the N03--Br- pair (line 9) whereas at high pH, the S04z--N0< pair (line 2) determines the resolution. Once again the intersection of lines 2 and 9 represents optimum chromatographic conditions, and as PT increases the pH at which this interaction occurs decreases. The slopes of the lines in Figures 4 and 5 are not parallel because of the relative elution capability of HP- and P2-. As their distribution changes, so does the net elution efficiency and thus nonparallel lines. Since the a values are relative, they should be applicable to any column with the same packing material. While the absolute magnitude of the retention times will be a function of column size and flow rate, the relative ratio is only a function of selectivity. The agreement between data obtained for two Vydan columns appears to be quite good. Linear least squares provides a slope of 0.935. The absolute retention times differed by approximately 20%. In addition to their ability to facilitate the optimization of the chromatographic process, window diagrams provide a means of predicting the retention profile of any suite of analyte species in response to eluent compositional changes over which such diagrams are defined. The linear nature of the window diagrams for nonsuppressed ion chromatography allows for
Anal. Chem. 1904, 56,88-9 1
a0
accurate exptrapolation and interpolation of the a values. With tv and the retention time of one analyte, tA, the retention time of the other analytes can be predicted from eq 1. This has been done for a series of snow melt samples. The results are summarized in Table 11. In all cases the agreement is within &3% RSD which is equivalent to the experimental precision.
LITERATURE CITED
Laub, R. J.; Purnell, J. H. J. Chromafogr. 1975, 112, 71.
(4) Laub, R. J.; Purnell, J. H. Anal. Chem. 1976, 4 8 , 1720. (5) Dernming, S. N.; Turoff, M. L. Anal. Chem. 1978, 5 0 , 546. (6) Price, W. P., Jr.; Demrnlng, S. N. Anal. Chlm. Acta 1979, 108, 227. (7) Price, W. P., Jr.; Edens, R.; Hendrlx, D. L.; Dernming, S. N. Anal. Blochem. 1979, 93, 233. (8) Sachok, B.; Strawahan, J. J.; Demming, S.N. Anal. Chem. 1981, 53,
70. (9) Jenke, D. R.; Pagenkopf, G. K. Anal. Chem. 1982, 5 4 , 2603. Jenke, D. R. Ph.D. Thesis, Montana State University, 1983. (10)
RECEIVED for review Mav 31.1983. AcceDted October 11.1983. project A-138 MONT.
Models for Prediction of Retention in Nonsuppressed Ion Chromatography Dennis R. Jenke and Gordon K. Pagenkopf*
Department of Chemistry, Montana State University, Bozeman, Montana 5971 7
The retention behavior of Br-, NO,-, CI-, SO:-, and S2O;- in nonsuppressed Ion chromatography Is studied as a functlon of changlng eluent composltlon. Three models, multlple specles.eluent, single species eluent, and single Interaction sles, are utlllzed to predlct chromatographic Fhavlor. While all three are based on a thermodynamic equllibrlum conslderatlon of the Ion exchange process, they dlffer in their characterlzatlon of the analyte/eluent competltlon or the ion/resin Interaction. Desplte thls dlff erence in approach, all three models effectlveiy characterlre the behavior of the analytes under elution condltlons which are of practlcai importance. The relative utlllty of each model Is discussed.
Ion chromatography has rapidly evolved into an accepted method for the determination of solute species in liquid samples (I, 2), and correspondingly characterization and modeling of the separation process are critical for method optimization and subsequent development. The current models are based upon an equilibrium distribution of analyte and eluent between the mobile phase and the resin ion exchange sites ( 3 , 4 ) . These models differ through the definition of the number of active components in the mobile phase that participate in the chromatographic separation. The single active species model (3) for nonsuppressed anion chromatography utilizes the phthalate dianion as the active eluent. A multiple active species model (5) has been used to predict the chromatography of arsenate and orthophosphate. Three models, multiple species eluent, single species eluent, and single interaction sites have been utilized to predict. the chromatographic behavior of chloride, bromide, nitrate, sulfate, and thiasulfate. These models are an extension of the ion-exchange theory developed by Mayer and Tompkins (6) with appropriate modifications. Multiple Species Eluent. The equations used to model the multiple eluent treatment are similar to those previously developed for suppresed ion chromatography (4). There are four basic considerations. (1)The reduced retention volume of the analyte, U, is equal to the volumetric distribution coefficient (6). In this case 0003-2700/84/0356-0088$0 1.50/0
UA = DA
(1) where UA is equal to the observed retention volume minus the void volume, DA is the ratio of analyte in the resin and solution phases associated with a given theoretical plate. (2) All of the "available" exchange sites are occupied by eluent anions and therefore the effective column capacity is given by
Q, = Cm[Ex"-I
(2)
X
where m is the ionic charge. (3) Electroneutrality is maintained during the elution process by exchange of charged species. (4)For anions interacting with a strong base anion exchanger, the following equilibrium is established at the resin sites. The equilibrium constant for this reaction is defined as the selectivity coefficient, KA-E.
(A"-)
+ n/rn(E-Rn)
= n/m(E"-)
+ (A-Rn)
(3) (4)
Experimental observations were made with phthalate eluents. For the multiple eluent treatment, HP-and P2- are assumed to be active eluents and eq 2 becomes
&e = AHP-R~
2AP-Rn
(5)
Use of eq 4 to describe eluent/eluent and analyte/eluent exchange and substitution into eq 5 provides
The volumetric distribution coefficient for analyte A is expressed as
DA = KA-~(D~)"/" and for a monovalent eluent-divalent analyte
0 1983 American Chemlcal Society
(7)
