Moment analysis for evaluation of flow-injection manifolds

Analytrca Chrmrca Acta, 229 (1990) 35-46 Elsevter Sctence Pubhshers B.V., Amsterdam

35 - Printed

m The Netherlands

Moment analysis for evaluation of flow-injection manifolds STEPHEN ICI Pharmaceuticals

Group, ICI Amerrcas Inc, JOHN

Department

H BROOKS

of Chemrstry,

G DORSEY

*

Wdmmgton,

DE 19897 (US A )

a

Unrversrty of Florrda, Garnesvrlle, FL 32611 (US A ) (Received

27th Apnl1989)

SUMMARY

The apphcabrhty of the exponentrally modtfted Gaussian (EMG) peak-shape model to a vanety of flow-mJectron mamfolds is explored. Using previously denved equations and manual calculatrons, the second moment (vanance) 1s employed as the fundamental descnptor of flow-mJectron response curves. The apphcabrhty of the EMG model 1s venfmd over a wide range of flow rates (0.2-l 7 ml mu-‘) for coiled, kmtted and Serpentine II manifolds, single-bead stnng reactors (SBSR) and a coded reactor with a single confluence pomt The Serpentine II reactor exhtbrts decreased disperston at higher flow-rates. The determmatton of the vanance of flow-mJectron response curves reveals that for the exammed SBSR and Serpentine II mamfolds, reagent consumption is decreased as the flow-rate 1s increased from intermediate (1.0 ml mu-‘) to hrgh flow rates (1 7 ml mu-‘). Determinatron of peak vanance ts shown to yreld umque mformatron m the time domam winch assists m the opttmum design and evaluatron of performance in flow mamfolds

Detection of a chemical product in a flow-injection system is dependent on interactions among the sample zone, the carrier stream and the manifold itself. The magnitude of the resulting analytical signal is influenced by two competing kinetic processes. The dispersion coefficient, D, being the most universal flow-injection descriptor, is a convenient way to monitor this competition between increased product formation and increased sample dilution as the time spent within the manifold increases. Owing to its response height-based nature, D IS not designed to extract all the available information from a response curve. In order to ensure optimum performance of the microreactor and to understand more fully how changes in

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address: Department of Chemistry, Umversrty Cmcmnatr, OH 45221-0172, U.S.A.

C@O3-2670/90/$03

50

0 1990 Elsevter

Science Publishers

of

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system parameters effect the resulting response curves, it is desirable to monitor a descriptor which quantifies the relationship between timebased phenomena and manifold performance. The stimulus-response technique is commonly used to investigate the effect of the size and geometry of a flow reactor on the dispersion process in chemical reaction engineering [l]. The technique is based on measurement of the concentration at the output of a reaction vessel (response) following the introduction of sample into the system as a step input or instantaneous pulse (stimulus). Ruzicka and Hansen [2] have shown that the step and pulse methods of introducing a stimulus are equally applicable for the investigation of dispersion in flow-injection systems. Provided that the intercalated sample reaches a steady-state response (step input) or that its width is negligible compared with the distance traveled (pulse input),

36

S H BROOKS

the axial dispersion and the mean residence time of the response curve will be identical when obtained by either the step or the pulse method. The residence time distribution (RTD) curve resulting from sample introduction in flow-injection systems can be described by analysis of its statistical moments. Statistical moments can be used to momtor changes in geometry and encountered forces as a sample plug moves through a flowmg system. The zeroth moment (M,) of a response curve (plotting observed concentration against time) arising from the introduction of a stimulus into a flowing system is equivalent to the peak area [2]: M, = (sample

zone width)

x

C:o,

at the time of inJection (t = 0). The first statistical moment (M,) IS equivalent to the centroid (center of mass) of the peak M, = jtC

dt/ jC

dt

and its location defines the time interval between the time of injection and the mean residence time of the peak. The second statistical moment (M2) of the RTD curve: M2=(

jt’Cdt,jCdt)

-M;

defines the vanance of the RTD and can be determined in units of volume, allowing a direct comparison of the extent of dilution occurring in FIA manifolds. The second moment is proportional to peak width and mcreases with increasing dispersion m a flow manifold. Ramsing et al. [3] were first to propose the use of variance as a measure of peak width and to investigate its relationship to dispersion m flow-injection systems. Certainly much work has focused on the prediction of a response to a defined stimulus in a flow-injection manifold [2]. Far less evident in the literature have been attempts to acquire a greater understanding of forces responsible for the response by an analysis of the response curve. In most flow-inJection systems, the sample zone does not encounter a sufficient number of mixing elements to achieve a purely Gaussian profile. Several workers [4-71 have described the residence

AND J G DORSEY

time distribution curve exiting a flow mjection manifold to be exponentially modified Gaussian (EMG) in character. The EMG function is obtained by the convolution of a purely Gaussian distribution and an exponential decay parameter, yielding an asymmetric peak. Owing to the need for digital data acquisition and subsequent computer processing, statistical moments have received only limited application for the analysts of the RTD curve m FIA [8]. Several workers [9-111, however, have derived expressions which allow for both the determination of the Gaussian or EMG character of response curves and the manual calculation of statistical moments of these peaks. Jeansonne and Foley [12] have recently demonstrated that the electronic analogy to the method used m this work yields superior accuracy to traditional summation methods for the determination of moments and related parameters. A previous paper [7] introduced the use of moment analysis for the separation and quantification of the physical and chemical contributions to dispersion in a flow-inJection system. The aim of this work was to examine further the germaneness of the EMG model as a descriptor of flow-mjection peaks. Having verified its relevance to a variety of flow-inJection systems, moment analysis was used to analyze purely physical contributions to zone dispersion. Additionally, it is shown that interpretation of results obtained by moment analysis serves as a useful tool for the design and optimum operation of flow-injection systems.

THEORY

Foley [ll] recently developed empirical equations for the manual calculation of peak area for symmetric (Gaussian) and skewed peaks. These equations can be used to examine the fit of real peaks to the Gaussian or EMG model. Foley and Dorsey [9] were the first to derive expressions which allow for the manual calculation of statistical moments of Gaussian and exponentially modified Gaussian peaks. Anderson and Walters [lo] modified these equations to extend the range of usefulness to greater asymmetry (b/a) values. Table 1 summarizes the equations, applicable asym-

FLOW-INJECTION

TABLE Equations

MANIFOLDS

31

1 used for peak evaluation

a

Equation Evaluatron of EMGfrt and calculatron of the zeroth moment (1) A,, ],, = 0.586h,W0 10( b/a)-’

13’

(2) A o 2s = 0 753b,% 15 (3) A 050= 1 07h,Wo,o(b/a)0235 (4) A,,, = 1 64h,Wo,,(b/a)07’7 Calculatron of the second moment (5) M, = (W, 1)2,‘[1 764(b/a)2 - 11 15(b/a) + 281 (6) M, = (W, 1)2/{7 35 + 22 6 exp[ - 0.708(b/a)]}

Asymmetry range (b/a)

RE b (%)

Rsd

100<(b/a)ol<360 100 Q (b/a),, d 3 60 100<(b/a)oI<3.60 lOOg(b/a),,d3.60

*OS0 -1 0, +0.6 -12, +10 -11, +06

1.44 1.41 1.49 2.01

11 11 11 11

, d 2.76

-15, +05 -07,+1.0

2.2 -

9 10

1 00 < (b/a), 2.77d(b/a)o,<56

A A IS the peak area, h, 1s the height of the peak, W IS the width of the peak at the designated asymmetry factor measured at the mdlcated peak height b Largest relative error of the equations over the designated asymmetry range ‘ The % r s d. of the gven equation

metry values and reported error limits provided m the aforementioned treatises which are used for peak analysis in this paper. The mean area values obtained using Eqns. l-4 [ll] were initially compared with the electronically integrated areas. Equations l-4 were then used to confirm the Gaussian or EMG character of the RTD profiles leavmg the various manifolds. No peaks observed were of purely Gaussian character. Consistency of the calculated peak area at 10, 25, 50 and 75% of the measured peak height is the test criterion used to verify that the examined peak is EMG in character. If the spread in peak-area values determined by Eqns. l-4 was less than 1548, the peaks were considered to fit the EMG model. Having determined the agreement of the flow-injection peaks with the EMG model, Eqns. 5 and 6 were used to calculate the second moment of the peaks.

EXPERIMENTAL

Apparatus A Waters (Milford, MA) Model 6000A HPLC pump was used to propel the carrier streams. All connectmg tubing was made of Teflon (0.5 mm 1.d. X 1.5 mm o.d.) from Alltech Associates (Deerfield, IL). Connecting tees and flangless fittings were from Upchurch Scientific (Oak Harbor, WA).

height

‘(W)

fraction

Ref.

and

b/a

IS the

Teflon tubing was either from Alltech (1.5 mm id. x 3.1 mm o.d.) or Ramin Instrument (Woburn, MA) (0.8 mm 1.d. X 1.5 mm o.d.). Additional PTFE tubing was 0.6 mm i.d. x 1.5 mm o.d. Stainlesssteel tubing (8.5 cm X 4.0 mm i.d.) and 1.5-mm diameter stainless-steel ball bearings were from Spectra-Physics (San Jose, CA). Samples were mtraduced into the flow manifolds by means of a Rheodyne (Cotati, CA) Model 7126 sample injection valve in conJunction with a Varian (Walnut Creek, CA) Model 8055 Autosampler. Vanable injection volumes were obtained by using Rheodyne sample injection loops of various sizes. Benzaldehyde in the carrier stream was detected at 254 nm by a Kratos (Ramsey, NJ) Spectroflow 783 programmable absorbance detector operated with a 0.02-s rise time. Detector output signals were acquired by a VG Lab Systems (Manchester, U.K.) Vax Multichrom Data Acquisition System and were simultaneously monitored on a Houston Instrument (Austin, TX) Omniscribe Series D5000 recorder. Peak-height measurements were made electronically whereas peak-width measurements were made manually. All injections were made under ambient conditions (24 f 2’ C) without temperature control. Chemicals Analytical reagent grade from J.T. Baker (Phillipsburg,

benzaldehyde was NJ). All water used

38

S H BROOKS

AND

_IG

DORSEY

._________________________________~ Fig 1. SchematIc diagram of flow mamfolds exammed Table 2 for a descnptlon of the various mamfolds.

See

m the preparation of solutions and carrier streams was doubly deionized and passed through a Bamstead Nanopure II (Boston, MA) activated carbon system to remove organic impurities. All carrier streams utilized were purely aqueous and helium sparged prior to use. Manrfold construction

A schematic diagram of the various flow manifolds evaluated in this work is shown in Fig. 1. The physical specifications of the manifolds are given in Table 2. Manifolds A, C and D were constructed from the identical piece of tubing and, TABLE 2

SERPENTINE

II

Fig. 2 Stltchmg pattern for the Serpentine II manifold

therefore, have equivalent manifold volumes. Manifolds A2, A3 and B were deslgned to yield nominally equivalent void volumes to withm + 5% of manifold A. The construction and application of the Serpentine II manifold (manifold E) have been described elsewhere [ 131. Curtis and Shahwan [13] demonstrated that the Serpentine II manifold functioned efficiently as a post-column reactor for HPLC. An electronic breadboard (Vectorboard type 170H85WE; Newark Electromcs, Comwells Heights, PA) serves as the template for manifold construction. The stitching pattern ensures periodic flow reversal in two dimensions and is shown in Fig. 2.

Flow mamfolds evaluated Mamfold A Al A2 A3 B Bl C D E a b ’ d

Length x I d. (cm X mm)

Mamfold type

Dlsperslon coefficient

305 x0.5 305 X0.8 125 x0.8 35.5 x1.5 250 xl.5 8.50x40 305 x05 305 x0.5 307 x0.5

co11 a Cod Cod Cod SBSR b SBSR ’ Knitted Cod, confluence d Serpentme II

4.94 13.8 7.87 11.4 7.58 25.0 404 7.54 3.47

Codmg hameter of all coded mamfolds = 12.5 mm Packed wth Ottowa sand, dmmeter 1 mm Packed wth stamless-steel ball bearmgs, hameter 1.5 mm. Confluence pomt formed by stra&temng 10 cm of the cod for the mtroduction of a tee connector at a pomt 150 cm from mjectlon. A direct mput from the pump completed the tee and the total flow-rate was measured at the detector output.

RESULTS

AND DISCUSSION

Determmatron of dispersion coefficrents The dispersion coefficients (D) of the various

manifolds were determined at 1.0 ml mir-’ by the injection of a 0.005232 mg ml-’ aqueous solution of benzaldehyde. The resulting response curves are shown m Fig. 3 and the calculated D values in Table 2. The average value of the maximum response height resulting from a 20-~1 injection of this solution was compared with the steady-state response of the identical solution introduced directly into the detector flow cell. These values of the dispersion coefficients for the examined manifolds indicate that flow systems of medium (D = 3-10) and large (D > 10) dispersion are evaluated

FLOW-INJECTION

MANIFOLDS

0

3.0

15

0

1.5

3.0

Time (min)

Time (min)

Rg. 3. Resultmg response curves from the inJectIon of a 0.005232 mg ml-’ solution of benzaldehyde (a) (A) mamfold C, (B) mamfold A, (C) mamfold A2; (D) mamfold A3; (E) mamfold Al (b) (F) mamfold E; (G) mamfold B; (H) mamfold Bl Flow-rate, lOmlmn-’

in the present work [14]. It is beheved, however, that the present method of peak analysis will also be useful for the evaluation of low dispersion (D = l-3) systems, provided that the flow-rates are scaled accordingly. Figure 4 shows the relative dispersion coefficient (expressed as DOz ,,,, ,,,,n-l/Dflow ,,,) of manifolds A, B, C and E plotted vs. examined flowrates. Manifolds A, B and C, represent the coiled,

x

0.4’

Fig.

4.

Effect

of

(DO 2 ,,-,,rmn-l/&,wra,c) (0) E

x

x

x

Flow

Rate (ml

mamfold

type

on

of (x ) mamfolds

x

x

x

1.6

1.2

0.8

0.4

x

single-bead string reactor (SBSR) and knitted microreactors, respectively, which are the most frequently encountered geometries in flow-injection systems [2]. Manifold E is the Serpentine II channel geometry [13]. The observation of a relative decrease in dilution (dispersion) of the sample zone with increasing flow-rate (when compared with the simple coil of equivalent reactor volume) makes clear the practical advantages of the SBSR [15] and the knitted configuration [16] over the traditional coiled reactor. It is well established that deformation of channel geometry increases radial transport of the sample zone m an open tube. By increasing the intensity of radial mixing, the parabolic velocity profile in the axial direction is decreased. It is interesting that with the Serpentine II reactor, an actual increase in peak height is observed as the flow-rate increases. This contrasts with the commonly observed relationships in a flow system and one of the basic rules of FIA [2], which states that dispersion increases with increasing flow-rate. Simple analysis of relative (or absolute) values of D does not provide any information in the time domain, which would be helpful in explaining this apparent anomaly. This finding will be explored in further detail by the analysis of statistical moments of the resulting peaks.

min

-l)

relatwe

dlsperslon

A, (v) B, (0) C and

Verification of EMG character In order to apply Eqns. 5 and 6 to the moment analysis of flow-injection response curves, it is

S H BROOKS

40

necessary to verify that the peaks leaving the studied manifolds are, indeed, EMG in character. The response curves were initially acquired on the Vax Multichrom Data Acquisition System. The resulting response curves were then displayed on a monitor, and the time and response axes were expanded to permit accurate measurement of the a and b values. Equations l-4 were used to determine the average area at 10, 25, 50 and 75% of peak height at flow-rates of 0.2, 1.0 and 1.7 ml mm’, which represent the low, medium and high ranges examined. The assumption is made that by showmg adherence to the EMG model at the extremes of the flow-rates encountered for each manifold, the EMG character should hold at intermediate conditions. The injections were performed m duplicate at the three flow-rates and no attempt was made to determine if the injection was an obvious outlier from the mean in terms of peak height, area or shape. Table 3 presents the average area determined using Eqns. 1-4, the true area of the FIA peak as determined by electronic integration and the percentage deviation between the two. There is excellent agreement between the average calculated and electronically integrated area, lending additional credence to the accuracy and precision of Eqns. l-4 [ll] for the treatment of flow-injection response curves. In all cases the agreement of the average area determined using Eqns. l-4 is within 10% of the nominal value (determined by electronic integration), 83% of the analyzed peaks yield an area accurate to within f 5% and nearly 60% show agreement to within * 3% of the electronically determined area. A response curve is considered to be well modeled by the EMG function if the spread in area values calculated using Eqns. l-4 is less than 15%. The response curves from manifolds A, A2, C, D and E are determined to be EMG in character over a flow-rate range of at least 0.2-1.0 ml mu-‘. Manifold Al yielded EMG peaks over at least the range 0.4-2.0 ml mm’. Manifolds A, C and D produced EMG peaks over the entire flowrate range examined (0.2-1.7 ml mm-‘) while response curves from manifolds Al, A2 and E deviated from EMG character at higher flow-rates. Previous work [7] has shown the percentage devia-

TABLE

AND J G DORSEY

3

Comparison of average area (A,) determmed by Eqns. 1-4 and computer-mtegrated area (A) for the exammed mamfolds a Mamfold

A, (lo5 PV s)

A (lo5 PV s)

Error b (%)

A A A A A A Al Al Al Al Al Al A2 A2 A2 A2 A2 A2 B B B B B B Bl Bl Bl Bl Bl Bl C C C C C C D D D D D D E E E E E E

I 36 8.99 1.44 1 34 0 736 0 983 31.4 30.7 6.36 645 3 84 3.96 64.4 62 1 12 7 12 8 I 82 1.62 58.7 58.7 114 11.0 6.48 6.59 414 39.2 10.3 10.4 6 58 6.40 70 9 71.2 13 5 137 1.26 7.21 140 142 27 0 26.4 15.3 15 4 7 98 138 1.61 169 103 101

7 19 8 76 1.37 1 35 0 772 0 999 300 30.0 6 20 6 33 3 17 3.76 62.9 63.3 128 12 8 1.46 7.45 61.5 58.9 12 1 12 1 7.19 7.23 38 2 35.6 10.6 10 5 648 641 72.1 72.5 130 13 1 7.53 7.55 141 142 26 5 26.5 15.5 15.5 7 45 7.54 1.67 1 64 0.984 0.982

2.36 2.63 490 - 0.39 - 4.67 -159 4 96 195 2.58 1.94 1.89 5 15 244 -0.54 -022 0.40 4.75 2.32 -4.55 -038 -559 - 8.72 - 9.87 -891 8.52 100 -258 -123 1.54 - 0.20 - 1.57 -180 3 59 4.92 - 3.67 -450 -112 - 0.06 198 -029 -084 - 0.32 7 04 -209 - 3.50 2.89 4 92 3 29

a Duphcate mjectlons at 0 2, 1.0 and 17 ml rmn-‘, respectlvely, for each manifold. b Percentage error vs electromcally integrated area, - mdlcates A> A,

FLOW-INJECTION

MANIFOLDS

tion of the variant area from the mean to be most promment at high flow-rates. The observation that a variety of flow manifold geometries produce peaks which are EMG in character is a significant finding. It is possible, therefore, to use manual calculations to obtain significant information in the time domain through the analysis of statistical moments using Eqns. 5 and 6. This will allow for a greater optimization of manifold selection and performance in terms of peak height and sample throughput. The response curves produced by the singlebead strmg reactors examined (manifolds B and Bl) did not meet the proposed criterion and hence are not well modeled by the EMG function. Therefore, the variance of these response curves obtained by Eqns. 5 and 6 should only be used for qualitative comparisons as the absolute value of the second moment may not be accurate. Although these peaks are not strictly EMG in character, the average areas determined using Eqns. l-4 show reasonable agreement with the corresponding electronically integrated area. In the absence of electronic integration, these equations yield a practical mean for determining the approximate peak area of response curves from SBSRs [ll]. Manifold A3 produced asymmetry values at 10% peak height which were outside the b/a range defined by Anderson and Walters [lo] and thus were not classified as EMG. Manifold A3 (35.5 cm x 1.5 mm i.d.) did, however, produce peaks with reproducible values of the peak height (n = 6, 0.73% r.s.d.) and integrated area (0.90% r.s.d.). Additionally, in this large-bore flow manifold, the peak height increased with increasing flow-rate up to 7.0 ml mu- ‘. These findings are m agreement with those of McGowan and Pacey [17], which indicate the feasibility of large-bore flow systems for certain samples containing particulate matter. Precwon of the second moment Having established the EMG character of the response curves, it is possible to apply Eqns. 5 and 6 and to examme the precision of the second moment determination for the analysis of FIA peaks. Table 4 indicates the precision of the second moment (n = 11) and compares it with the

41 TABLE 4 Comparison of preclslon for second moment (M2), peak he&t (h p) and computer-mtegrated area (A) determmatlon a h, @A)

A (lo5 /JV s)

8 9 10 11

13 5 11.6 130 13 1 13 2 13 1 13.1 13 1 11.9 13.1 12.9

79.84 81 94 80 07 80 21 80.00 80 14 79 95 80 21 82 09 80 17 79 73

12 5 12 4 126 12 7 126 12 7 12 6 12 6 12.5 12 7 127

Average Sd R.s.d.

12 9 0 623 4 81%

80 40 0.82 101%

12 6 0 095 0 82%

Tnal

M,

(lo3 ~1’)

a Injected sample 000532 mg ml-‘, flow-rate 1.0 ml nun-‘, 138 cm x0 6 mm 1.d. cod, 12.5 mm collmg radius.

most commonly used descriptors of response curves, peak height and peak area. As expected, the precision of the second moment determination is less than those obtained by either peak-height or peak-area measurement. The second moment is a direct measure of peak width and, as such, is more sensitive to pump fluctuations, which result in slight alterations in flow-rates. Additionally, the day to day reproducibility is highly dependent on accurate flow-rate reproducibility or accurate monitoring of the delivered flow. Dependence of second moment on sample concentratlon The large range of dispersion coefficient values from Table 2 indicates that a wide concentration range of benzaldehyde solutions were leaving the manifolds. A study was undertaken to ensure that variations in the sample concentration (response peak height) did not affect the calculation of the second moment, allowing for a direct comparison of moment values from manifold to manifold. The sample concentration was varied in four increments over a 50-fold range. The 20-~1 injection volumes of benzaldehyde solutions into manifold E resulted in peak heights which varied from 5 to 310 milliabsorbance at 1.0 ml mm’, bracketing all peak heights encountered in this work. The

42

S H BROOKS

r.s.d. of the 12 trials was 1.89%, verifying that the second moment did not vary with concentration in the Serpentine II manifold. These findings are in agreement with previous work with straight and coiled manifolds [7], which indicated that the second moment calculation was independent of the initial concentration in the examined systems.

Dependence of second moment on sample volume Manifold A2 and an aqueous solution of benzaldehyde were used to investigate the effect of changmg the sample volume on the calculated value of the second moment. Variation of the sample volume from 5 to 20 ~1 resulted m a constant value of the second moment, as shown in Table 5. The practical implication of this fact is that the injection sample volume (and sensitivity) in a flow-injection system can be increased up to a certain point without affecting the throughput of the system as measured by the width of the peak. In fact, a lo-fold increase in sample volume from 5 to 50 ~1 results in only a 6% increase in the second moment. This is a strong indication of the extent to which one can gain sensitivity without a great sacrifice in throughput in a flow-injection system.

Additrvtty of variance Poppe and co-workers [18,19] reported that the total variance which occurs in a flow-injection system due to purely physical forces is equivalent to the sum of the individual variances from the

TABLE 5 Effect of sample volume on the second moment a Sample volume (PI) 5

10 20 50

Second moment b (104 jL12)

Sample volume (PI)

Second moment b (104 /.l12)

1.89 1.93 189 2.01

100 200 500

2 12 2.49 5 53

a InJected sample 0.00532 mg ml-‘, 1.0 ml mu-’ b Average value of n >, 4

mamfold A2, flow-rate

AND

JG

DORSEY

injection and transport processes (neglecting variance contributed from a well designed detector): 2 ‘peak

=

2 %,ectmn

+

dansport

(7)

An attempt was made to verify this equation experimentally for the studied system. A benzaldehyde solution was injected into a coiled 250 cm x 0.6 mm i.d. tube (coiling radius 12.5 mm). The average second moment of the resulting peak was measured, a 50-cm length of tubing was removed and the process was repeated until a final length of approximately 50 cm was reached. Following the entire process, four connection joints were inserted and the second moment for the Jointed 250-cm coil was determined. A plot of the second moment (variance) vs. the length of the tubing resulted in a linear relationship ( y = 92.01x + 2647; r2 = 0.9959) for the coiled manifold. The 250-cm coil with four coupling unions resulted in an average peak variance which was 76% of the variance of the non-segmented tube. The observed decrease in variance indicates that each union coupling functions as a localized mixing element, uniformly redistributing the sample bolus over the entrance to following tube [20]. Comparuon of mamfolds by moment analysis Figure 5 is an absolute comparison of the second statistical moments determined using Eqn. 5 for the coiled, knitted and Serpentine II geometry manifolds. As previously mentioned, the response curves leaving mamfold E are known to deviate from the EMG model at a flow-rate between 1.0 and 1.7 ml rnin-‘. The variance values for manifold E at higher flow-rates are, therefore, only included for qualitative comparison purposes. The emergence of decreasing peak widths (variance) in manifold E at flow-rates greater than 1.0 ml mm-l is consistent with the observation (Fig. 4) of increasing peak height at higher flow-rates for the Serpentine II reactor. The traditional coiled reactor (manifold A) exhibits a much greater rate of increase in variance as the flow-rate of the system increases from 0.2 to 1.2 ml min-‘. This increase in the second moment is manifested by a broader peak for tubing of the same length and inside diameter. Manifold C, while displaying unusually large scatter in the plot of variance vs. flow-rate,

FLOW-INJECTION

43

MANIFOLDS

x

14 I

x x

x

x

x x

x

x

>: 0

4) l t 0.4

1.2

0.8 Flow

Rate

(ml

1.6

min -I)

Fig. 5. Comparison of vanance (~1’) vs. flow-rate (ml mm-‘) for mamfolds ( X) A, (0) C and (0) E.

shows only a slight increase in variance over the range of the flow-rates examined. This finding is supported by the dispersion-based results in Fig. 4, which showed only a slight increase in the dispersion coefficient over the examined flow-rate range. The steady decrease in the curve for manifold E after reaching a relative maximum indicates that at higher flow-rates the variance of the peak actually decreases with increasing flow-rate. This is consistent with Fig. 4. With regard to the coiled manifold A, Fig. 4 shows that the rate of decrease in peak height is also reduced above 1.1 ml mm-‘. This corresponds to the decrease in peak variance observed at higher flow-rates in Fig. 5. The observed decrease in peak variance in manifold E occurs at lower flow-rates compared with manifold A. This observation can be attributed to the increased radial mixing occurring in the Serpentine II manifold. An increased radial distribution of sample molecules in the manifold results in increased integrity of the sample bolus. This is manifested by a 30% larger peak width at half-height (0.4 ml mm-‘) for manifold A than for manifold E. This difference increases to 70% at

1.0 ml mm’. It is clearly evident that the unique and highly ordered geometry of the Serpentine II manifold is effective in redistributing molecules of the sample zone in the radial direction, resulting in a substantial reduction in band broadening of the sample zone. Moment analysis was employed to determine the effect of changes in manifold tubing interior diameter on the variance of FIA response curves. Figure 6 reveals that the effect of increasing tubing inside diameter while maintaining a constant manifold volume is to shift the variance plot to greater values of the second moment. The agreement in the overall trends of the variance plot justifies the inclusion of flow-rates greater than 1.0 ml min-’ for manifold A2 and implies that the forces responsible for the trends observed are essentially independent of the inside diameter of the tubing. Therefore, it is postulated that the volume and geometric configuration are the factors responsible for the decrease in variance observed at the higher flow-rates. Figure 7 shows the resulting variance curve from an increase in inside diameter without changing the length or geometry of the reactor. In this instance, the linear range of the

x

x

x

5 0.4

0.8

1.2

1.6

FLOW Rate (ml min -l) Fig. 6. Effect of changing tubing Inside duuneter (constant volume) on the plot of variance (~1’) vs. flow-rate (ml ruin-‘) for manifolds (X) A and (A) A2.

S H BROOKS

44

variance plot extends to much greater flow-rates. It appears, therefore, that the difference in manifold volume is responsible for the different trends observed in the two variance plots. Figure 8 indicates the effect of introducing a post-injection confluence point (at 150 cm) on the variance plot. The flow-rate before the mixing point is roughly half that beyond the confluence pomt, winch should result in decreased dispersion in the first 150 cm of the manifold (as in Fig. 4). Excluding the introduction of the tee connector (and associated straightening of a lo-cm length of the tubing), the geometric configuration of the manifold remained unchanged and the overall shape of the variance curve was fundamentally unaltered. It is also interestmg that the absolute variance values of manifold D are very snnilar to those of manifold A2, which indicates that the introduction of a confluence point approximately doubled the variance of this system. The practical implication of this finding is that in an attempt to

A

AND J G DORSEY

AAA

aAA

A N r( q

ms

A A

AA

A

a

x

x

x

xx

x

Flow

Rate

(ml

x x

min -l)

Rg. 8 Effect of mtroductlon of a confluence pomt (constant length and volume) on the plot of vanance (~1’) vs. flow-rate (ml mu-‘) for mamfolds (X) A and (A) D.

obtain maximum sensitivity, the number of confluence points should be kept to a mmimum. Moment analysis for design and operation of mamfolds Analysis of statistical moments provides valuable information for the rational design and operation of flow-injection systems. Figure 5 provides a convenient method for evaluating manifolds from a purely diffusional perspective and determining the optimum flow-rate for operation. A knowledge of the variance of the flow-injection response curve allows for the determination of the throughput of the system through Eqn. 8 [2]: S max =

Flow

Rate

(ml

min -l)

Rg. 7. Effect of changmg tubmg mslde diameter (constant length) on the plot of vanance (~1~) vs. flow-rate (ml nun-‘) for mamfolds ( x ) A and (m) Al.

60Q/b

(8)

is the maximum throughput (samples where S,, h-l), Q is the flow-rate (ml mm-‘), k is a factor depending on acceptable carryover and is equal to 4 and a, is the volume standard deviation of the peak (the square root of the second moment). Figure 9 shows the relationship between S,, and flow-rate for the examined manifolds. As expected, the throughput increases with increasing flow-rate. If the linear nature of the plots of

FLOW-INJECTION

45

MANIFOLDS

0 0 rl

‘0 l 0

no

0'

0.8

0.4 Flow

Rata

1.2 (ml

x

1.6

min-l)

Fig. 9. Companson of sample throughput (samples h-l), determmed using Eqn. 8, vs. flow-rate (ml min-‘) for mamfolds ( x ) A, (v) B, (0) C and (0) E.

throughput vs. flow-rate holds for systems where chemical reaction is occurring, moment analysis may provide an a priori method for the prediction of throughput over a wide range of flow-rates in flow-injection systems. It is well understood that the throughput of a flow-injection system increases with increasing flow-rate. This increase in flow-rate, however, typically results in an increase in reagent consumption and a decrease in analytical signal due to increased dispersion. It was noted earlier that most of the variance plots in this work exhibited either a plateau or a reduction in variance values at high flow-rates. Since the second moment is a direct measure of peak width, there is a possibility that reagent consumption may actually decrease at higher flow-rates in certain manifolds. This statement is based on the assumption that the injection interval is optimized, leaving no dead space between the appearance of adjacent peaks. In this work, the volume width of the peak was directly measured at 3% of the total peak height, assuming that at that time another peak may begin to appear. Table 6 summarizes this study and reveals some interesting results. The coiled and knitted

manifolds show an increase in reagent necessary to elute 97% of the peak from the manifold as the flow-rate is increased. The SBSR and Serpentine II manifolds studied actually show a decrease in reagent consumption as the flow-rate is increased from intermediate (1.0 ml mm-‘) to higher (1.7 ml mm-‘) values. This means that for a well designed spacing of injections, use of these manifolds (assuming sensitivity is not a limiting factor) allows for increased sample throughput and an accompanying decrease in reagent consumption. These ideas are certainly departures from classical flow-injection theory, and without the use of a peak descriptor which monitors response curves in the time domain (moment analysis), this information would not have been obtained. Recent work by Korenaga and Stewart [21] and Vanderslice et al. [5] has explored the effect of a reduction in tubing length and diameter in addition to an increase in flow-rate in increasing sensitivity in flow-injection systems. The present work has shown that sensitivity (owing to purely physical processes) over the examined flow-rates in the Serpentine II flow manifold is increased by increasing the flow-rate as shown in Fig. 4. This and previous work [13] have shown the Serpentine II to be a promising microreactor design for flowinjection systems. The compactness of design, ease and reproducibility of construction and minimal band broadening of the reactor make it attractive for many flow-injection applications. This work has further explored the utility and applicability of statistical moment analysis of flow-injection peaks. Manual moment analysis has

TABLE 6 Dependence of volume (~1) needed to elute peak on flow-rate (Q) for vanous mamfolds a Mamfold

A B C E

Q (ml min-‘) 0.2

1.0 b

1.7

412 985 423 376

595 1155 410 430

629 1122 510 382

* Average value (n = 2) of elutlon volume determined at 3% of total peak he&t b Flow-rate for manifold B = 1.1 ml mm-l.

46

shown that the EMG model can be employed to describe flow-injection response curves from a variety of manifolds. Additronally, the application of the EMG model to several of flow manifold geometries has been experimentally verified. Ruzicka and Hansen [2] have recently stated that the first and second moments “do not yield useful information on their own”. The analysis of statistical moments has been shown not only to provide information which is complementary to D measurements but also that the second moment yields information which is unobtainable from simple height-based measurement of flow-injection response curves. This unique information provided by statistical moment analysis should serve as an impetus for examining both peak height (D) and peak width (M,) based phenomena when determining the design and optimum operation of flow manifolds. J.G.D. is grateful for support of this work by NSF CHE-8704403.

REFERENCES 1 0. Levenspiel, ChemtcaI Reaction Engmeenng, 2nd edn , Wdey-Interscience, New York, 1972. 2 J. Ruzxka and E.H. Hansen, Flow InJection Analysis, 2nd edn , Wiley-Interscience, New York, 1988.

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