Anal. Chem. IQW, 60, 2737-2744
minations are presented in Tables IV and V. Of the 54 urine samples studied only 25 samples met the criteria for TMSe and Se02- determination, and after complete anion exchange chromatographic separation of TMSe and Se032-in these urine samples, we found that 28% of the samples had nondetedable TMSe and 48% had nondetectable Se032-. As can be seen in Tables IV and V, the selenium concentration of serum is greater than that of urine per unit volume. After determination of TMSe and Se032- in all qualified urine samples, only seven urine samples (28%) met the requirement for determination of selenoamino acids. While we did not attempt to ascertain clinical correlation among urine samples, correlations will be reported in future studies. By use of the method of Currie (26) the detection limit for determination of total selenoamino acids is 40 ng of Se/mL and for determination of total selenium, TMSe and Se032-is 10 ng of Se/mL.
ACKNOWLEDGMENT The authors thank K. P. McConnell and Margaret Tempero for supplying the urine samples and G. T. Hansen for carrying out some of the experimental work. LITERATURE CITED (1) McConnell. K. P.; Broghamer, W. L., Jr.; Blotcky, A. J.; Hart, 0. J. J . Nutr. 1975, 705, 1026-1031. (2) Broghamer, W. L., Jr.; McConnell, K. P.; Blotcky, A. J. Cancer 1978, 3 7 , 1384-1388. (3) Broghamer, W. L., Jr.; McConnell, K. P.; Blotcky, A. J. Cancer 1978, 4 7 , 1462-1466. (4) Shamberger, R. J.; Rukovena, E.;Longfeld, S. A.; Tyko, S.; Deodhar, C. E.; Wlllls, C. E. J. Natl. Cancer Inst. ( U S ) 1973, 50, 863-670. (5) Wlllett, W. C.; Polk, B. F.; Morris, J. S.; Stampfer, M. J.; Pressel. S.; Rosner, B.; Taylor. J. 0.; SchneMer, K.; Hames, C. 0.Lancet 1982, 2 , 130- 134.
2737
(6) Levander, 0. A. Fed. Roc. Fed. Am. Soc.Exp. Bbl. 1985, 4 4 , 2579-2583. (7) Buel, D. N. Semin. Oncol. 1983, 70. 311-321. (6) Iyengar. G. V.; Kollmer. W. E.; Bower, H. J. M. The Elemental Conpslfion of Human Tlssues and Bo@ Fluids ; Verleg Chemle: New York, 1978. (9) Cornelis, R.; Speecke, A.; Hoste, J. Anal. Chim. Acta 1975, 78. 317-322. (10) Versleck, J.; Cornells. R. Anal. Chim. Acta 1980, 776, 217-254. (11) Ishizak, M. Talanfa 1978. 25. 167-169. (12) Versieck, J. CRC Crlf. Rev. Clin. Lab. Sci. 1985, 22. 97-184. (13) Oyamada, N.; Ishlzaki. M. Jpn. J. Ind. Health 1983, 25, 319. (14) Nahapetian, A. T.; Young, V. R.; Janghorbani, M. Anal. Biochem. 1984, 740, 56-59. (15) Palmer, L. S.; Fischer. D. D.; Haalverson, A. W.; Olson, 0. E. Biochim. BiophyS. Acta 1980, 777, 336-342. (16) Blotcky, A. J.; Hensen, G. T.; melanio-Buencamino. L. R.; Rack, E. P. Anal. Chem. 1985, 57, 1938-1941. (17) Blotcky, A. J.; Hansen. G. T.; Bofkar, N.; Ebrahlm, A.; Rack, E. P. Anal. Chem. 1987, 5 9 . 2063-2066. (18) Byard, J. L. (Arch. Biochem. Blgphys. 1989. 730, 556-560. (19) Nahapetian, A. T.; Janghorbani, M.; Young, V. R. J. Nutr. 1883, 773. 401-411. (20) BUrk. R. F. J . NU?. 1988, 776, 1584-1586. (21) Sunde, R. A.; Hoekstra, W. G. Biochem. Bbphys. Res. Commun. 1980, 9 3 , 1181-1186. (22) Blotcky, A. J.; Arsenault, L. J.; Rack, E. P. Anal. Chem. 1973, 4 5 , 1056-1 060. (23) Roth, M. Anal. Chem. 1971, 4 3 , 880-882. (24) Kessler, G.; Pileggi, V. J. Clln. Chem. (Winston-Salem, N . C . ) 1988, 74, 811-619. (25) Goyal, S. S.; Rains, D. W.; Hauffaker, R. C. Anal. Chem. 1988, 60, 175-179. (26) Currle, L. A. Anal. Chem. 1988, 4 0 , 586-589.
RECEIVED for review May 31,1988. Accepted September 13, 1988. This research was supported by the US.Department of Energy, Division of Chemical Sciences, Fundamental Interaction Branch, under Contract DE-FG02-84ER13231.A003 and a University of Nebraska Research Council NIH Biomedical Research Support Grant No. RR-07055.
Dispersion Coefficient and Moment Analysis of Flow Injection Analysis Peaks Stephen H. Brooks,I Daniel V. Leff, Maria A. Hernandez Torres, and John G. Dorsey* Department of Chemistry, University of Florida, Gainesville, Florida 3261 1
The dlsperslon coefflclent ( D )Is the most popular peak descrlptor In flow Injectlon analysis (FIA). Yet thls concept of dlsperslon ylekls no dlred information descrlblng peak shape and no Information In the t h e domain. Using an exponentlaUy modlfled Gausslan peak shape model and previously derlved equatlons, we examine the second moment (variance) of single-Hne flow Injection peaks and use thls as a fundamental descriptor of the FIA response curves. Unllke the dlsperslon coefflclent, the second moment Is shown to obey a h e a r relatlonshlp wlth respect to flow rate and to yleld valuable lnformatlon In the presence of a chemlcal reactlon. Reportlng descriptors of an F I A response curve as a variance offers several advantages over the classlcal dlsperslon coeffIclent: peak wldth (In unlts of time or volume) Is lmmedlately obtalnable from the variance, yleldlng a more direct measure of sample throughput; varlous FIA manifolds can be readily compared from thelr varlance values, and the lndlvldual contrlbutlons to the total peak variance (Includlng the contribution of the chemlcal reaction to the total varlance) can be easlly obtalned through the addltlvlty of variances. 'Present address: IC1 Pharmaceuticals Group, Wilmington, DE 19897.
IC1 Americas,
Inc.,
0003-2700/88/0360-2737$01.50/0
Flow injection analysis (FIA) is f i i y established as a rapid, precise, efficient, and extremely versatile analytical tool. Ruzicka and Hansen ( l ) ,however, recently reviewed the status quo in the field of FIA and concluded that "the theory of FLA, unfortunately, is still at a rather lamentable level compared with the sophisticated level of many of the practical developments. The concept of controlled dispersion, based on the dispersion coefficient, is a useful tool for the rational design of a flow system and for comparison and scaling of channels in FIA, yet it does not describe the response in a comprehensive fashion." There have been numerous attempts to derive a general expression to describe concentration as a function of time in a flow injection system. Historically, Taylor (2, 3) was the first to quantitatively treat the concept of axial dispersion occurring in straight, open tubes. Taylor's solutions of the diffusion-convection equation are most accurate for regions of flow where convection (high flow rates) or diffusion (low flow rates) is the dominant contribution to dispersion. Flow rates commolily employed in FIA result in conditions that are intermediate between these two limiting regions and are described by laminar flow. Dispersion in FIA is a consequence of both convective transport (axial direction) and diffusional transport (axial and radial directions) of sample molecules 0 1988 American Chemical Society
2738
ANALYTICAL CHEMISTRY, VOL. 60, NO. 24, DECEMBER 15. 1988
within the flow manifold. Ananthakrishnan and co-workers (4, 5 ) were the first to provide numerical methods for the solution of the diffusion-convection equation for intermediate values of the reduced mean residence times. Most FIA experiments do not lie within these theoretically treated regions (6) and, therefore, are not accurately described by either of these models. Painton and Mottola (7, 8) were the first to derive and test a numerical model that included values of reduced time (7)and Peclet numbers (Pel that are typically found in flow injection systems. The general aim of the theoretical work in the field has been to relate the characteristics of the signal profile to the experimental parameters of the FIA system. Common descriptors of an FIA response curve include the base-line-tobase-line time of the peak, travel time, mean residence time, theoretical plate height, peak area, and peak height. Experimental parameters that directly affect the response curve (and the descriptors of the response curve) and are commonly used to describe the manifold conditions include flow rate, sample volume, tube radius, coil radius, and reactor length. Additionally, the intrinsic characteristics of the carrier stream itself drastically affect the resulting response curve and must be considered in an accurate theoretical treatment for flow injection systems. It is obvious that any universally applicable theoretical treatment of FIA manifolds must include all iterations of the FIA manifold and resulting effects upon the response curve, requiring the consideration of a myriad of experimental variables. The dispersion coefficient, D, is the most common descriptor of dilution in an FIA system and is defined as the ratio of the concentration injected into the system to the concentration a t peak maximum. Experimentally, the value of D is determined by introducing an undiluted standard sample of known concentration directly into the flow-through detector to obtain a steady-state response height, Ho. The FIA manifold is then operated with the carrier stream of choice, and the standard is introduced into the continuously moving stream in the form of an injected sample. This ensures that the sample molecules will interact with the surrounding carrier stream, resulting in dilution of the sample and a subsequent peak height response, H,,, which is less than or equal to Ho. If the linear region of the calibration curve includes both Co and, C (the concentrations corresponding to Hoand H-), D = Ho/H,, and is equivalent to the dispersion of the flow injection manifold under investigation. The overall dispersion within an FIA system has been described as the sum of the dispersion coefficients originating from the injection, transport, and detection processes in the system (9). (1) Dtotal = Dinjection + Dtransport + Ddetection Many workers have examined the effect of manifold design and experimental parameters upon the response curve in an attempt to develop a more accurate measure of dispersion in a flow injection system. Coiling of the tubing has been shown to introduce additional mechanisms of transport (10-13) that obscure the significance of D. Additionally, as the FIA manifold becomes more complex in design, any available theory becomes increasingly inadequate in attempts to predict the behavior of the system. Vanderslice et al. (6)f i i t showed that the solute diffusion coefficient and tube radius directly affect dispersion. More recently, Hernandez Torres et al. (14) and Locascio-Brown et al. (15)have shown that viscosity plays a role in dispersion. Stults et al. (16) investigated the effect of temperature on dispersion in flow injection systems with and without a chemical reaction occurring. The major advantage of basing the dispersion measurement upon peak height is that the peak maximum is easily located on the response curve. The concept of dispersion coefficient, however, is of limited utility in conveying information about the FIA system since
it only accounts for dilution that affects peak height. Ruzicka et al. (17)and Vanderslice et al. (6)have derived expressions that allow the derivation of a relationship between the geometric and hydrodynamic characteristics of a flow manifold and the resultant FIA peak shape. In practice, however, these expressions cannot be directly used, due to the effect of the longitudinal dispersion number (18) and the accommodation factor (6) upon the FIA signal. The longitudinal dispersion number accounts for the non-Gaussian character of the observed response curves and is directly related to the variance of the response curve (19). The accomodation factor was introduced to compensate for the difference between the theoretical data and experimental values obtained for peak descriptors. Application of a computer program and a logarithmic multiple regression analysis enabled Valcarcel and Luque de Castro (9) to obtain empirically fit equations that allow for the determination of the relationship between the geometric and hydrodynamic characteristics of a defined manifold and the FIA signal. Unfortunately, these equations, derived for a given system, cannot be directly applied to any other FIA system due to different characteristics of the injector, connectors, and flow cell. Ruzicka and Hansen (20) recently published a mathematical model of Soeberg, based on equations of motion and continuity, which allows the computation of velocity and concentration profiles and the depiction of their microstructures by computer graphics. Kolev and Pungor have also recently described a mathematical model of single-line flow injection systems with no chemical reaction occurring (21). Much less visible in the literature have been attempts to examine FIA peak shapes and to use these descriptors to gain a better understanding of the dispersion process in the system. Tyson (22) derived equations for relating peak width to injected concentration for single-line and merging stream manifolds containing a mixing chamber tQ generate concentration gradients. Poppe (23) first reported that the total peak broadening in an FIA system was the sum of the individual contributions. Analogous to chromatographic systems (24, 25), the total variance of the system was described by the contributions from the injection process, flow-through reactors and connectors, the flow-through volume of the detector, and the time constants of the associated electronics. The total band broadening under conditions of no reaction contains contributions from these sources (12) and results in an equation that is completely analogous to eq 1: u2peak
=
u2injection
+ u2transport
+u2detection
(2)
Assuming that the flow-through detector and the electronics of the detector are well designed, $dewion may be neglected, and the total variance is given by D'peak
=
u'injection
+ u'transport
(3)
Several workers (12,14,26)have described the distribution curve of a flow injection peak to be a modified Gaussian function. The exponentially modified Gaussian (EMG) function is obtained by the convolution of the Gaussian function and an exponential decay function, providing an asymmetric peak profile. The exponentially modified Gaussian function describes many peaks of analytical interest, and the EMG model itself has been reviewed (27). Ramsing et al. (19) were the first to propose the use of variance as a measure of peak width and to explore its relationship to dispersion in FIA. Reijn et al. (28) proposed that more fundamental information about the dispersion process in flow injection systems could be obtained by analyzing the statistical moments of the residence time distribution function. Statistical moments have not been commonly used to describe FIA peaks due to the need for digital data acquisition and
ANALYTICAL CHEMISTRY, VOL. 60, NO. 24, DECEMBER 15, 1988
subsequent computer processing. Foley and Dorsey (291, however, have derived expressions for the calculation of chromatographicfigures of merit of Gaussian and EMG peaks that allow for manual calculation of statistical moments. Only limited attention has been given to the effect of chemical reaction upon dispersion (7,8,30,31).While changes in peak shape from kinetic contributions are of an entirely different nature than the physical dispersion process, it is still useful to examine these contributions, as they occur simultaneously in the flowing stream. Painton and Mottola (32) were the first to assess the kinetic contribution to the overall dispersion in a flow injection system. The kinetic contribution to dispersion was determined by subtracting the dispersion coefficient due to purely physical factors from the dispersion coefficient obtained in the presence of a chemical reaction. In the presence of chemical reactions, the dispersion coefficient loses much of its significance, since it conveys little information related to peak width (an indication of the throughput of the system) and there is much difficulty in determining Ho (with a reaction occurring, Ho is no longer time independent). For a flow injection system that produces Gaussian or EMG peaks under conditions without chemical reaction, the principle of additivity of variances allows the addition of the effect of a chemical reaction to eq 3 and the totalvariance of the resulting EMG peak is given by g2psak = 0 2 injection . . + transport +a2chemicd reaction (4) This paper examines a new method for defining dispersion in FIA based upon the presence of EMG peaks and calculation of the resulting second central moment. Reporting dispersion in an FIA system as a variance offers several advantages over the classical dispersion coefficient: (a) peak width is immediately obtainablefrom the variance, (b) various FIA manifolds can be readily compared from their variance values, (c) the difference in peak widths may be obtained in either units of time or volume, yielding a more direct measure of sample throughput, and (d) the individual contributions to the total peak variance (including the contribution of the chemical reaction to the total variance) can be easily obtained through the additivity of variances.
THEORETICAL SECTION Foley (33) has recently developed empirical equations for the accurate calculation of peak area of Gaussian and exponentially modified Gaussian peaks. Based on measurements of peak height, width, and asymmetry, the equations are also useful in determining whether or not an exponential peak is Gaussian or EMG in nature. Equations 5-8 were used here
W t n
7i
P
TIME Figure 1. Measurement of peak width, W , and asymmetry factor, b l a , at 10, 25, 50, and 75% of peak height In an FIA response curve.
character. These equations can be used to examine unknown peaks for their fit to the Gaussian or EMG model. The goodness of fit is determined by the agreement of calculated areas at the four peak heights. For the present work, if the largest outlier from the mean area determined by using eq 5-8 was within 20% of the mean area calculated at the four heights, the peak was considered to be EMG in nature (three trials). Once the Gaussian or EMG character of the peak was verified, the following equation was used to calculate the second moment (variance) of the peak:
M2 = (Wo,1)2/[1.764(6/~)2- 11.15(b/~)+ 281 (9) where M2 is the second moment (29) and the additional variables are defined as in eq 5-8. For the asymmetry range of 1.00 I( b / a ) I2.76, eq 9 results in a relative error of -1.5%, +0.5%. For asymmetry values greater than 2.76, Anderson and Walters (34) have modified the equations of Foley and Dorsey (29) and extended the range of usable asymmetry values to b / a = 5.6 ( T / U = 6.8). With this modification, the second moments for the asymmetry range 2.77 5 ( 6 / a ) I5.6 were calculated by using
M2 = (W0,1)~/[7.35+ 22.6 exp(-0.708(b/a)]
to calculate the peak areas from measurements made at 10%, 25%, 50%)and 75%)respectively, of the total peak height, where A is the peak area, h, is the height of the peak, W is the width of the peak at the designated peak height fraction as indicated by the subscript, and b / a is the asymmetry factor measured at the same peak height fraction as the width (Figure 1). A Gaussian or EMG peak is indicated by agreement of calculated areas a t the four peak heights. The largest relative error of eq 5-8 from the true area of a Gaussian or EMG peak is given by Foley as -1.2%, +LO% over the interval 1.00 I(6la)o.l I3.60 (33). Equations 5-8 were used to verify that the peaks exiting the flow injection system were either Gaussian or EMG in
2739
(10)
The maximum relative error resulting from eq 10 is given as 4 7 % ,+LO% (34). The variance of an exponentially modified Gaussian peak is equivalent to the second moment (M2) and is described by 2
a EMGpeak
M2 = aG2 +
(11)
where aG2 is the variance resulting from purely Gaussian processes and T is the time constant of the exponential peak tailing function. The previously derived methods (29,34) can again be used to calculate the variance of the peak due to processes that are purely Gaussian in nature: "G
= Wo.1/[3.27(b/a) 4- 1.21
(12)
for 1.09 I( 6 / a ) I2.76 with a percent relative error limit of -1.O%, +0.5%, and
2740
ANALYTICAL CHEMISTRY, VOL. 60, NO. 24, DECEMBER 15, 1988 QG
+ 0.9691
= W0,1/[3.38(b/a)
(13)
for 2.77 5 ( b / a ) 5 5.6, with a percent relative error limit of -1.3%, +1.6%. Having calculated the second moment and the variance of the underlying Gaussian peak, one can quantitatively separate both the exponential time constant and the contribution resulting from Gaussian processes from the overall peak variance through eq 11. The use of this asymmetry-based method for peak analysis is appealing because of the simplicity of measurement of the necessary variables in order to find M2, UG and T. Once the exponentially modified Gaussian character of the peaks has been verified, it is necessary only to measure the values of a and b at 10% peak height to obtain M2, UG and 7. The accuracy of measurement obtained with this method can be maximized by adhering to the following suggested measurement conditions (29): (a) a chart speed yielding W,,l 1 4.3 cm, (b) a minimum distance of 10 cm for appearance of flow injection peak maximum, and (c) a minimum peak height such that h, 1 10 cm. The b / a ratio itself has the additional advantage of agreeing with the intuitive perception of peak asymmetry (35).
EXPERIMENTAL SECTION Apparatus. An Isco (Lincoln, NE) Tris Model peristaltic pump with Silastic peristaltic tubing propelled the carrier streams. Sample volumes of 20 pL were introduced by a Valco Instrument Co. (Houston, TX) C6W injector. All connecting tubing was Teflon (l/lKin. 0.d. 0.5-mm i.d.) from the Anspec Co. (Ann Arbor, MI). The flow manifold was a 100-cm tubing, with its shape being straight or coiled with a coiling diameter of approximately 14 mm. The total volume of the flow manifold (including injector and preflow cell detector tubing) was determined by measuring the time from sample injection to initial base-line disturbance at 10 flow rates (three trials each) between 0.058 and 0.26 mL/min. The injection of an aqueous 0.10 M NaI solution yielded a manifold volume of 299 f 2 pL. Ionic solutes in the carrier stream were detected by an LDC/Milton Roy (Riviera Beach, FL) conductoMonitor I11 conductivity detector, and the resulting output signals were recorded on a Houston Instrument (Austin, TX) Fisher Randall Series 5OOO recorder. All injections were performed at room temperature (25 A 1 "C) without temperature control. The flow manifold for the base hydrolysis of acetylsalicyclic acid has been previously described (36) and employed a 200-cm length of 1/16-in. 0.d. 0.5-mm4.d. Teflon tubing, coiled with a diameter of approximately 14 mm, and an injected sample volume of 20 pL. All reactions were again carried out at room temperature. The same 200-cm coiled reaction manifold was the reaction volume, and a 10-pL sample volume was employed for the pyridoxal determination. This reaction was carried out with temperature control at 45 0.2 OC as described elsewhere (14). All least-squares calculations were performed by the Interactive Microware, Inc., (State College, PA) Curve Fitter program run on an Apple I1 Plus microcomputer. Chemicals. Sodium iodide, reagent grade (Class 1C) butyl alcohol, and reagent grade sodium hydroxide, as well as ACS certified solutions of potassium cyanide, phosphate buffer (0.6 M), and concentrated hydrochloric acid, were obtained from Fisher Scientific Co. (Fairlawn, NJ). Acetylsalicylic acid was obtained from Sigma Chemical (St. Louis, MO), and prior to use it was recrystallized from chloroform. Purum grade cetyltrimethylammonium bromide (Fluka Chemical, Hauppauge, NY), 2iodo-2-methylbutane (tert-amyl iodide) (ICN Biomedicals, Inc., K + K Labs, Plainview, NY), absolute ethyl alcohol (Florida Distillers Co., Lake Alfred, FL), and standard solutions of pyridoxal, Sigma grade (Sigma)were used in this study. All water used in the preparation of solutions and carrier streams was deionized. Reactions. The reaction chosen for this work was the hydrolysis of 2-iodo-2-methylbutane in aqueous ethanol (80% by volume ethanol in water): CSH11I + 2Hz0 ---* CSHI1OH + H30' + 1-
*
The conductivity of the sample zone is monitored in the FIA
0.4 0.6 0.8 1.0 1.2 Flow Rate (mUmin) Flgure 2. Dispersion coefflclent versus flow rate for a 20-pL sample of 0.10 M NaI injected into a lOOcm straight tubing manifold. 0.0
0.0
0.2
0.2
0.4
0.6
0.8
1.0
1.2
Flow Rate (mUmin) Flgure 3. Peak area (as determined by eq 5-8) versus flow rate for a 20-pL sample of 0.10 M NaI injected into a 100-cm straight tubing manifold.
system and increases as the reaction proceeds, due to the formation of the hydronium and iodide ions. The reaction is first order in CSHllIand the rate of the reaction is independent of the pH of the solution (37). The reactionsfor the determination of pyridoxal and the base hydrolysis of acetylsalicylic acid have been previously described (14, 36).
RESULTS AND DISCUSSION The dispersion coefficient of the system was determined with an aqueous NaI solution. The value of the time-dependent conductance signal height (Ho) corresponding to undiluted 0.10 M NaI was determined to be 585 pS. To determine the response height equivalent equal to the maximum concentration of the injected sample (H&, 20 pL of 0.10 M NaI was injected into a straight 100-cm tubing with an aqueous carrier stream. The straightness of the tubing was ensured by strapping it to a 98-cm length of angle iron. The variation of D (three trials) with flow rate was examined over the range of 0.058-1.03 mL/min. Figure 2 shows that the resulting plot of dispersion coefficient vs flow rate is fit by a logarithmic equation of the form Y = 7.99X0.397with a correlation coefficient of 0.999. Another common descriptor of flow injection response curves is the area of the peak. From eq 5-8, the average area of the response curves (three trials) was determined for the 100-cm straight tubing manifold over the flow rate range of 0.058-1.03 mL/min. Figure 3 shows the relationship between peak area and flow rate is again most accurately described by a logarithmic equation, Y = 107.6X-0.349with a correlation coefficient of 0.999. This decrease in peak area with increasing flow rate is characteristic of a concentration-sensitive detector
ANALYTICAL CHEMISTRY, VOL. 60, NO. 24, DECEMBER 15, 1988
Table I. Effect of Flow Rate upon Dispersion Coefficient (D), Area, Percent Deviation of Calculated Areas (% Dev), and Standard Deviation of the second moment (M2), Underlying Gaussian Peak (ua) in a Flow Injection System" flow rate,
mL/min
D
0.0576 0.122 0.126 0.139 0.154 0.172 0.187 0.254 0.257 0.259 0.387 0.391 0.521 0.605 0.659 0.787 1.03
2.58 3.45 3.58 3.60 3.76 3.93 4.11 4.84 4.63 4.64 5.44 5.54 6.10 6.59 6.71 7.17 8.22
area, mL pS dev, % 287 222 222 213 211 204 197 162 177 174 152 148 135 128 128 118 102
5.6 11.9 14.3 9.7 11.6 10.1 9.4 7.1 10.2 11.4 9.3 10.6 13.1 15.6 17.0 16.7 20.9
M2, wL2
UG, pL
746 1371 1557 1640 1860 2112 2184 3053 3105 2782 4443 4395 5554 6776 7658 8657 10385
21.3 29.5 28.3 32.2 30.1 32.3 34.2 39.7 39.0 35.4 41.9 41.6 41.6 42.5 40.6 42.7 41.9
f
cm
W0.1, cm
M,,pL2
uG, pL
1 2 3 4 5 6 7 8 9 10
1.09, 1.03, 1.06, 1.02, 1.10,
2.31 2.46 2.35 2.44 2.24 2.28 2.40 2.28 2.36 2.44
3.40 3.49 3.41 3.46 3.34 3.38 3.45 3.40 3.44 3.46
9977 11303 10 323 11120 9386 9721 10 765 9724 10411 11120
43.1 39.9 41.6 39.5 43.8 43.6 41.0 44.6 42.5 39.5
10 385 676 6.5%
41.9 1.9 4.5%
6000
4000
2ooo
w
.
,
trial
a , b,
cm
1 2 3 4 5
1.13, 1.10, 1.10, 1.10, 1.09,
0.01 2.26 2.30 2.30 2.29 2.37
-
I
-
I
'
I
-
1 2 3 4
I
0.8 1.0 1.2 Flow Rate (mUmin) Figure 4. Second moment (as determined by eq 9) versus flow rate for a 2&pL sample of 0.10 M NaI injected into a lOOcm straight tublng
0.4
1.05, 1.12, 1.08, 1.02,
WO.~, cm
0.6
manifold. (38). Although peak area relays more direct information of peak size than the dispersion coefficient, it yields no information concerning the shape of the peak and no information in the time domain. For the detection system employed in this work, an additional drawback of area as an FIA peak descriptor was that as the sensitivity setting of the conductance detector was varied, the absolute area values were not consistent, severely limiting the linear range of the descriptor. The agreement of the calculated areas at lo%, 25%, 50%, and 75% of total peak height can be used to verify the exponential character of the peaks under investigation. Table I shows that as the flow rate of the system is increased, the percent deviation in the calculated area increases. For the 51 determinations of peak area for the 1Wcm straight tubing, 73 5% of the peaks were found to fit the EMG model to within 15%. A large majority of the peaks that did not fit the model to within 15% were at the higher flow rates. At flow rates of less than 0.6 mL/min, 90% of the peaks fit the model within 15% and 92% fit the model to within 20%. This apparent aberration can be explained by considering two factors: (1) the relatively short manifold length (100 cm) ensures that at high flow rates, less time will be available for diffusional averaging within the sample plug and, most importantly, (2) the straight character of the manifold minimizes mkiig within
1.08, 1.10, 1.09, 1.08,
0.004 2.32 2.29 2.31 2.32
average std dev RSD
M,,pL2
UG, pL
M NaI Solutiona 3.39 3.40 3.40 3.39 3.46
average std dev RSD
1 /
0 : . I 0.0 0.2
1.10,
Table 111. Effect of Changing Concentration on the Determination of the Second Moment
8000
U
U J
a , b,
t
N -
5
trial
"Injected sample 0.10 M NaI solution, 20-pL sample volume, 100-cm straight manifold, 1.03 mL/min, 100-pS full scale sensitivity setting.
"Injected sample 0.10 M NaI solution, 20-pL sample volume, All results indicate the average value of three trials.
2c
Table 11. Reproducibility of the Second Moment Determination"
average std dev RSD
100-cm straight manifold.
l2O0O
2741
9558 9892 9892 10075 10500
45.1 43.6 43.6 42.0 42.9
9983 344 3.4%
43.4 1.1 2.6%
M NaI Solutionb 3.40 3.39 3.40 3.40
10062 10075 9977 10062
42.6 42.0 43.1 42.6
10044 45.1 0.45%
42.6 0.4 1.0%
"Injected sample 0.01 M NaI solution, 20-pL sample volume, 100-cm straight manifold, 1.03 mL/min, 10-pS full scale sensitivity setting. bInjected sample 0.004 M NaI solution, 20-pL sample volume, 100-cm straight manifold, 1.03 mL/min, 10-pS full scale sensitivity setting. the tube in the radial direction, which again results in less averaging of the concentration within the sample plug. It was observed that by coiling the 100-cm tubing (coiling radius 14 mm), a flow rate of 1.04 mL/min resulted in asymmetric peaks that fit the EMG model to within 10% (an average of 7.80% for three trials). Having verified the EMG character of the peaks, one may apply eq 9 and 10 to examine the dependence of the second moment upon flow rate for this system. Figure 4 shows that there is a linear relationship ( Y = (1.04 X 104)X + 290; r = 0.999) between M2 and the flow rate for 20 pL of 0.10 M NaI injected into the 100-cm straight tubing. We next examined the reproducibility of the second moment and the standard deviation of the underlying Gaussian peak as EMG peak descriptors in a flow injection system. Table I1 shows that for a 20-pL sample of 0.10 M NaI and a flow rate of 1.03 mL/min, the average second moment is 10385 f 676 pL2 (RSD = 6.5%). The standard deviation of the parent Gaussian is 41.9 f 1.9 p L (RSD = 4.5%) for the same 10 trials. Table I11 shows that the effect of changing concentration and detector sensitivities (compared to Table 11) on M2 and uG is negligible for the examined system. The contribution of purely Gaussian processes (diffusion related)
2742
ANALYTICAL CHEMISTRY, VOL. 60, NO. 24, DECEMBER 15, 1988 70
,
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3000
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Flow Rate (mumin) Figure 5. Gaussian contribution as a percentage of the total peak variance (as determined by eq 12)versus flow rate for a 2GpL sample of 0.10 M NaI injected into a 100-cm straight tubing manifold. 12000 10000
1
1
I
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0,200
0.400
0.600
0.800
Flow Rate (mUmin) Figure 6. Second moment versus flow rate for the tert-amyl iodide hydrolysis (straight manifold). The symbols Indicate whether (A) prereacted tert-amyl iodide solution (see text for explanation) is introduced Into the system or (B) a reaction is occurring in the lOO-cm straight tubing manifokl. The sample volume is 20 pL and the carrier stream is 80:20 ethanokwater (v/v). is minimized as the flow rate is increased in the straight manifold. It is expected, therefore, that as the flow rate is increased, the percent contribution of Gaussian processes to total peak variance would be decreased. The use of eq 11 allows us to quantitatively examine the percent contribution of purely Gaussian processes to total peak variance as shown in Figure 5. Hydrolysis of tert-Amyl Iodide. The results of the moment analysis for the response curves monitoring the products of the tert-amyl iodide reaction are shown in Figure 6. The carrier stream was 80% by volume ethanol in water, and the configuration of the 100-cm manifold was straight. In order to monitor the dispersion of the sample plug without reaction occurring, 300 pL of the tert-amyl iodide was reacted in 50 mL of the carrier for 24 h, ensuring completion of the reaction. This prereacted solution (containing the reaction products) was intercalated into the carrier stream at various flow rates to provide a direct measure of the dispersion occurring in the sample plug as a result of purely physical processes. Figure 7 again shows the dependence of the second moment upon flow rate, with and without chemical reaction, in the same experimental system with a coiled manifold (coiling radius, 14 mm). Examination of the data contained in Figures 6 and 7 yields much information about the dispersion occurring in the sample plug. It is observed that at slow flow rates, for both the straight and coiled manifolds, the peak variance for injected samples with chemical reaction occurring exceeds the second
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e
-
-
0 *
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1000 0.000
I
I
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0,200
0.400
0.600
0.800
Flow Rate (mUmin)
Figure 7. Second moment versus flow rate for the tert-amyl iodide hydrolysis (coiled manifold). The symbols indicate whether (A) prereacted tert-amyl iodide solution (seetext for explanation) Is introduced into the system or (B) a reaction is occurring in the 100-cm coiled tubing manifold. The sample volume is 20 pL and the carrier stream is 80:20 ethanokwater (v/v).
moment of the sample without chemical reaction. As more time is allowed for the reaction to proceed, the production of product becomes the paramount factor determining the width of the peak, overwhelming longitudinal dispersion due to physical dispersion processes. By use of eq 4, it is then possible to examine the contribution of the chemical reaction to total peak variance. In both straight and coiled manifolds it is observed that as the flow rate of the system is decreased, the contribution of the chemical reaction becomes increasingly important to the total peak variance. Painton and Mottola (32) analogously observed that the dispersion due to chemical reaction increased with decreasing flow rate in a straight manifold. With increased flow rate, however, the effect of the chemical reaction becomes less important in determining the total peak variance. Figure 7 indicates that for coiled tubing and flow rates above 0.4 mL/min, the variance of the reaction-present response curves is identical with that of the nonreacting tracer curves. The analogous observation was made by Reijn et al. (28)who found that at high flow rates the variance of an FIA curve was virtually independent of reaction rate for a single bead string reactor manifold. It can be concluded that for typical FIA flow rates, the effect of chemical reaction upon total system dispersion is negligible for this reaction. It is expected that as the rate of reaction is increased, the chemical reaction contribution to total peak variance will persist until greater flow rates. In Figures 6 and 7 it is apparent that at a flow rate of 0.20-0.30 mL/min, a region of transition occurs where the chemical contribution to dispersion is no longer the dominant factor determining total peak variance. This region of flow corresponds to the flow rates at which the prevailing mechanism of transport within the sample plug changes from purely diffusional (at low flow rates) to convective diffusional (9). Valcarcel and Luque de Castro (9) have shown that for single-line manifolds, the transition from diffusion-controlled to convective diffusional dispersion occurs at an L to q ( L = length of manifold; q = flow rate) ratio between approximately 200 and 550 (this corresponds to a flow rate of 0.18-0.50 mL/min for the present system) for a sample of 0.10 M NaI with a diffusion coefficient of 1.52 X lo4 cm2/s (39). An 8020 mixture of ethanol and water has a viscosity approximately twice that of pure water, decreasing the diffusion coefficient of the NaI solution by one-half its value in water. For our system, the L / q ratio of 550 (0.18 mL/min) is predicted to be the cutoff for pure diffusion-controlled behavior. The transition from diffusional to convective diffusional transport
ANALYTICAL CHEMISTRY, VOL. 60, NO. 24, DECEMBER 15, 1988
,
12000
10000
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I
1
I
8000 6000
4000 2000 0 ELUTION TIME
-
Flgure 8. Response curve shapes as a function of elution time and flow rate in a straight tubing flow manifold with the direction of indicating the direction of increase in parameter. Shown is the development of the hump, which moves from the tail (high flow rates) to the main peak (low flow rates) (adapted from ref 41).
would then be expected to occur somewhere in the flow rate region of 0.18-0.50 mL/min, in agreement with experimental observations. As the flow rate of the system is increased and the prevailing mechanism of transport becomes convective diffusional, the linear relationship between M 2and the flow rate is again observed. Double hump peaks were observed at relatively high flow rates ( > O H mL/min) in the straight tube manifold when no chemical reaction was occurring. When, however, the same flow rates and carrier stream were employed with a reaction occurring in the straight manifold, no double hump peaks were observed. This would indicate that the chemical reaction itself increases radial mixing within the sample plug in the straight manifold and should result in a decrease in M 2as shown in Figure 6. Double hump peaks were not observed for any examined flow rates in a coiled tube manifold. The shapes of the double hump peaks are in agreement with those observed by Atwood and Golay (40,411. They show that for short open tubes, the hyperbolic tail of each peak is truncated by a combination of radial diffusion and velocity shear. These forces combine to sweep the molecules in the trailing portion of the sample a t the tubing walls in the form of a hump of concentrationthat eventuallycatches up with the average flow in the system. As the flow rate of the system is increased, there is not sufficient time for the hump of concentration to convolute with the main peak. As shown in Figure 8, the sharp front of the peak is eventually destroyed by diffusion as the flow rate is decreased. Increased radial mixing and stronger concentration gradients as a result of chemical reaction eliminate the double hump in our straight tube manifold. The diffusion-related nature of the double hump phenomena was verified by the observation that introduction of the prereacted sample into a purely aqueous carrier stream (lower viscosity, higher diffusion coefficient) did not result in double hump peaks a t the examined flow rates. Tijssen (IO) has developed a comprehensive theory describing laminar dispersion in coiled tubes, and it is wellknown that secondary flow increases radial mixing in such systems. Painton and Mottola (32)showed that radial mixing in coiled reactors generates secondary flow that is perpendicular to the centrifugal forces present in the flow channel. This flow is in opposition to dilution of the solute by longitudinal dispersion and in the present system is manifested by the decreased absolute values of the second moment in coiled tubing when compared to straight tubing. Effects of Coiling and Carrier Stream Viscosity upon Total Peak Variance. The straight or coiled nature of the FIA manifold and the viscosity of the carrier stream were important factors determining the variance of the response
0.0
0.4
0.2
0.6
0.8
1.0
1.2
Flow Rate (mUmin) Flgure 9. Second moment versus flow rate for a 20-pL sample of 0.10 M NaI injected into an aqueous carrier stream through a 100-cm manifold. The symbols indicate whether the manifold is (A) straight or (B) coiled.
N -
I
4
I
I I
4
0.0
0.2
0.4
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Flow Rate (mumin) Figure 10. Second moment versus flow rate for a 20-pL sample of 0.10 M NaI injected into a high-viscosity 80:20 ethano6water (v/v) carrier stream through a 100-cm manifold. The symbols indicate whether the manifold is (A) straight or (6)coiled. curves for this system. Figures 9 and 10 allow for the determination of the effect of manifold coiling upon the variance of the FIA response curves in this system. Figure 9 compares the variance determined for the injection of 20 pL of 0.1 M NaI solution into both a straight and coiled manifold with an aqueous carrier stream. The resultant equations of the two lines are Y = 10370%+ 290 for the straight manifold and Y = 2606%+ 691 for the coiled system. One should not attempt to place any physical significance upon the values of the yintercepts obtained for these plots due to the scarcity of data points for low flow rates. The ratio of the slopes of the two lines is 3.84 and accounts for the presence of coiling in otherwise equivalent manifolds. Figure 10 makes the analogous comparison for the same injected sample into a more viscous (80:20 ethano1:water) carrier stream. The equations of the two lines are Y = 26970%- 1534 for the high-viscosity,straight manifold and Y = 7025% 1536 for the high-viscositycoiled system. The ratio of the slopes of these two lines is 3.98, which is in agreement with the slope ratio for the aqueous system, showing that the difference in slopes of the variance vs flow rate plots is a direct result of the coiling of the tubing. Therefore, a 4-fold decrease in the second moment and an accompanyingincrease in the throughput can be achieved by coiling the tubing in this system. The effect of changes in carrier stream viscosity upon the second moment has previously been shown for the flow injection determination of pyridoxal (14).The rate constants of the reaction were reported as 0.0490 and 0.0971 min-' in
+
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ANALYTICAL CHEMISTRY, VOL. 60, NO. 24, DECEMBER 15, 1988
static aqueous and 0.05 M CTAB systems. For the flow determination, the temperature of the 200-cm coiled manifold was maintained at 45 OC. The resulting variance calculations based on peak measurement at 10% peak height indicated an increase in the second moment from 9300 to 11000 pL2 as the carrier stream was changed from an aqueous to a 0.05 M CTAB micellar system. The previously reported base hydrolysis of acetylsalicylic acid (36)employed the identical flow manifold as the pyridoxal determination. The rate constants of the acetylsalicylic hydrolysis were reported as 0.109 and 0.153 min-' in static aqueous and microemulsion (microemulsioncomposition (wt %): 98.8 H20:0.6 CTAB:0.6 butanol) solutions at 25 "C. Analysis of the response curves from the flow determination indicates that the second moment increased from 10 000 to 36600 pL2 as the carrier was varied from an aqueous to a microemulsion stream. Both of these reactions were performed in an identical flow manifold, showing that temperature, flow rate, and rate of the reaction strongly influence the shape of the resulting response curve. In an analogous fashion, a comparison of the slope ratio for the viscous carrier, straight manifold, to the aqueous carrier, straight manifold, and the slope ratio for the viscous and aqueous carriers in the coiled system allows for a determination of the effect of viscosity differences on the second moment. These slope ratios are again consistent, 2.60 and 2.70, respectively, and account for the differences in the second moments in the system as a result of viscosity changes. The use of an 80:20 ethano1:water carrier stream increases the variance of the system approximately 21/2 times. Therefore, the maximum throughput of the system will be obtained by using a carrier stream of lowest possible viscosity. These conclusions are also available by analyzing the relative dispersion coefficient values of the various configurations; however, moment analysis yields direct information in the time domain. This work has shown that moment analysis is a valid method for examining response curves from flow injection systems. Much information concerning the behavior of the sample plug within the manifold can be obtained, and a direct comparison of the throughput of various systems can be made. By analyzing the width of the EMG peaks exiting the manifold, the experimenter does not need to attempt to account for all variations in manifold design and carrier stream constitution to gain valuable descriptors of the response curves. The investigation of peak shapes arising from multiline manifolds and packed bed reactors is under way. The observation that decreased viscosity decreases variance of injected samples may provide an interesting variation on the classical flow injection theme. The use of a supercritical fluid as the carrier stream would exploit the relatively high solute diffusion coefficients of supercritical fluids (lo4 to cm2/s compared to cm2/s for liquids), increasing sample throughput and lowering limits of detection in flow injection analysis.
ACKNOWLEDGMENT We are grateful to Joe P. Foley and Laurie Locascio-Brown for encouragement and many helpful comments. LITERATURE CITED (1) (2) (3) (4)
Ruzicka, J.; Hansen, E. H. Anal. Chim. Acta 1988. 779, 1. Taylor, G. Proc. R . SOC.London, A 1953, 219, 186. Taylor, G. Proc. R . SOC.London, A 1954, 225, 473. Ananthakrishnan. V.; Gill, W. N.; Barduhn, A. J. AIChE J . 1985, 1 1 , 1063. (5) Gill, W. N.;Ananthakrishnan, V. AIChEJ. 1987, 13, 801. (6) Vandersllce, J. T.; Stewart, K. K.; Rosenfeld, A. G.; Higgs, D. J. Talenta 1981, 2 8 , 11. (7) Painton, C. C.; Mottola. H. A. Anal. Chlm. Acta 1983, 154, 1. (8) Painton, C. C.; Mottola, H. A. Anal. Chlm. Acta 1984, 758, 67. (9) Valcarcel, M.; Luque de Castro, M. D. Flow-lnjectfon Analysls:Rinciples and Applkatlons; Ellis Horwood: Chichester. U.K., 1987. (10) Tijssen, R. And. Chlm. Acta 1980. 714, 71. (11) Reijn, J. M.; Van der Linden, W. E.; Poppe, H. Anal. Chim. Acta 1981, 123, 229. (12) Reiin. J. M.; Van der Linden, W. E.; Poppe, H. Anal. Chim. Acta 1981, 126, 1. (13) LeClerc, D. F.; Bloxham, P. A.; Toren, E. C. Anal. Chim. Acta 1988, 184, 173. (14) Hernandez Torres, M. A,; Khaledi, M. G.; Dorsey, J. G. Anal. Chim. Acta 1987, 207, 67. (15) Locascio-Brown, L.; Plant, A. L.; Durst, R. A. Anal. Chem. 1988, 60, 792. (16) Stub, C. L. M.: Wade, A. P.; Crouch, S. R. Anal. Chim. Acta 1987, 192, 301. (17) Ruzicka, J.; Hansen, E. H.; Zagatto, E. A. Anal. Chim. Acta 1977, 88, 1. (18) Levenspiel, 0.; Smlth, W. H. Chem. Eng. Sci. 1957, 6 , 227. (19) Ramsing, A. V.; Ruzicka, J.; Hansen, E. H. Anal. Chim. Acta 1981, 129, 1.
(20) Ruzicka, J.; Hansen, E. H. Flow Injection Analysis, 2nd ed.; Wiley: New York, 1988. (21) Kolev, S. D.; Pungor, E. Anal. Chem. 1988, 60, 1700. (22) Tyson, J. F. Anal. Chim. Acta 1988, 779, 131. (23) Poppe, H. Anal. Chim. Acta 1980, 114, 59. (24) Huber, J. F. K. J. Chromafcgr. Scl. 1989, 7 , 172. (25) . . Kirkland, J. J.; Yau. W. W.; Stoklosa, H. J.; Dllks, C. H., Jr.; J. Chromatogr. Sc!. 1977, 75, 303. (26) Vanderslice, J. T.; Rosenfeld, A. G.; Beecher, G. R. Anal. Chim. Acta 1988, 179, 119. (27) Foley, J. P.; Dorsey, J. G. J. Chromatogr. Sci. 1984, 22. 40. (28) Reijn, J. M.; Poppe, H.; Van der Linden, W. E. Anal. Chem. 1984, 5 6 , 943. (29) Foley, J. P.; Dorsey, J. G. Anal. Chem. 1983, 55, 730. (30) Betterldge, D.; Cheng, W. C.; Dagless, E. L.; David, P.; Goad, T. B.; Deans, D. R.; Newton, D. A.; Pierce, T. B. Analyst (London) 1983, 108, 17. (31) Hungerford, J. M.; Christian, G. D. Anal. Chim. Acta 1987, 200, 1. (32) Painton, C. C.; Mottola, H. A. Anal. Chem. 1981, 5 3 , 1713. (33) Foley, J. P. Anal. Chem. 1987, 5 9 , 1964. (34) Anderson, D. J.; Walters, R. R. J . Chromatogr. Scl. 1984, 22, 353. (35) BMllngmeyer, 8. A.; Warren, F. V. Anal. Chem. 1984, 56, 1583A. (36) Brooks, S. H.; Wllllams. R. N.; Dorsey, J. G. Anal. Lett. 1988, 2 1 , 583. (37) Matthews, G. P. Experimental Physical Chemistry; Clarendon: Oxford, England, 1985; p 314. (38) Dolan, J. W. LC-GC 1988, 6, 222. (39) CRC Handbook of Chemistw and Wysics; CRC Press: Boca Raton, FL, 1980; p F-62. (40) Atwood, J. G.; Golay, M. J. E. J . Chromafcgr. 1979, 786, 353. (41) Atwood, J. G.; Golay, M. J. E. J . Chromatogr. 1981, 218, 97.
RECEIVED for review June 30,1988. Accepted September 7, 1988. The authors are grateful to Pfizer, Inc., Central Research, and NSF CHE-8704403 for partial support of this work.
