Anal. Chem. 1996, 68, 3871-3878
Theory and Practice of Rapid Flow-Through Analysis Based on Optode Detection and Its Application to pH Measurement as a Model Case Hideaki Hisamoto, Michiko Tsubuku, Takuya Enomoto, Kazuhiko Watanabe, Haruma Kawaguchi, Yasuhiro Koike, and Koji Suzuki*
Department of Applied Chemistry, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223, Japan
Rapid flow-through analysis (RFA) based on optode (optical chemical sensor) detection is proposed, and its performance is discussed using the RFA system equipped with a pH-sensitive optode as a model case. To demonstrate and understand the usefulness of the RFA system, long-lifetime pH-sensitive optodes were prepared using a hydrophilic poly(hydroxyethyl methacrylate) (polyHEMA) membrane covalently immobilized with a dye containing an amino group such as Congo Red or Nile Blue. The response equation for the optode with the RFA system was proposed, and satisfactory estimation for rapid pH analysis was obtained. The proposed RFA can stand as an advanced method for conventional flow injection analysis. Flow analysis, represented by the example of flow-injection analysis (FIA), is one of the most useful analytical methodologies in view of its practical applicability.1,2 FIA has been established by the development of small sample/reagent mixing and detection techniques and has been widely used for the determination of many chemical species. The major advantages of the flow system are (i) multiple analyses can be easily performed with great accuracy, (ii) short time analysis can be performed and the time can be controlled by varying the sample injection volume, and (iii) an easy, simple experimental setup and analytical operations are required. Unfortunately, FIA has one disadvantage in that the sample/reagent mixing step of the flow system essentially requires disposable analytical reagents such as chelating agents, chromophores, and buffers,3,4 this is a critical weak point of the FIA system in terms of economic and disposal problems. On the other hand, the detection step of FIA is basically simple and has no relation to this disadvantage. In general, an absorbance or fluorescence measurement is most commonly used for the determination of an analyte with FIA. As long as an optical sensing method such as absorbance or fluorescence is the basic principle of the analytical method, one of the simplest ways to measure the analyte is to use an optical chemical sensor (optode). The optode can be adapted to a flow analytical system that requires no disposable reagents except a pH-adjusting buffer reagent or salt. Thus, using an optode in the flow analytical system provides an ideal analytical methodology which can solve the one disadvantage of FIA. (1) Ruzicka, J.; Hansen, E. H.; Mosbach, H. Anal. Chim. Acta 1977, 92, 235. (2) Ruzicka, J.; Hansen, E. H. Flow Injection Analysis, 2nd ed.; John Wiley and Sons: New York, 1988. (3) Motomizu, S.; Kobayashi, M. Anal. Sci. 1994, 10, 187. (4) Kimura, K.; Iketani, S.; Sakamoto, H.; Shono, T. Analyst 1990, 115, 1251. S0003-2700(95)01149-8 CCC: $12.00
© 1996 American Chemical Society
In this paper, we propose the rapid flow-through analysis (RFA) method based on optode detection, as represented in Figure 1, that can be considered as an advanced FIA system. Using the RFA, the analyte concentration can be easily determined by simply introducing the sample solution to the RFA system, which requires no other chemical reagents. The combination of FIA with an optode has already been reported by us and others.5-15 Most of these papers, however, deal only with sensor response characteristics; no discussion is provided about the importance of the flow system. Though its application technique is important for the practical use of optodes, unfortunately, the theoretical and experimental response performances of optodes in a flow system have not been clearly discussed in the past. For this purpose, investigation of the theoretical response performance of RFA and a comparative experimental study are necessary and important. In general, the response of the optodes based on a color change or a fluorescent reagent is governed by sample diffusion in the membrane phase, i.e., a mass transport process of the analyte in the bulk optode sensing phase is needed in most of the optodes reported to date. In addition, in the case of a flow system in combination with an optode, the sample analyte diffusion process in the flow-through system must be considered in relation to the detection of the analyte. Thus, in a discussion of the response performance of RFA based on optode detection, not only the optode response parameters or functions but also the flow analysis parameters must be considered. Here we report the first simple example of RFA with theoretical as well as experimental discussions, in which a pH indicator-based optode was utilized as the model case. pH-sensitive optodes have been actively investigated for their potential in practical use such as clinical analysis, environmental analysis, and process control. They could be used not only for simple pH sensing but also for (5) Watanabe, K.; Nakagawa, E.; Yamada, H.; Hisamoto, H.; Suzuki, K. Anal. Chem. 1993, 65, 2704. (6) Hisamoto, H.; Watanabe, K.; Oka, H.; Nakagawa, E.; Spichiger, U. E.; Suzuki, K. Anal. Sci. 1994, 10, 615. (7) Hisamoto, H.; Watanabe, K.; Nakagawa, E.; Siswanta, D.; Shichi, Y.; Suzuki, K. Anal. Chim. Acta 1994, 299, 179. (8) Hisamoto, H.; Nakagawa, E.; Nagatsuka, K.; Abe, Y.; Sato, S.; Siswanta, D.; Suzuki, K. Anal. Chem. 1995, 67, 1315. (9) Wolfbeis, O. S. J. Mol. Struct. 1993, 292, 133. (10) Yerian, T. D.; Christian, G. D.; Ruzicka, J. Analyst 1986, 111, 865. (11) Yerian, T. D.; Christian, G. D.; Ruzicka, J. Anal. Chim. Acta 1988, 204, 7. (12) Weigl, B. H. Proc. SPIE-Int. Soc. Apt. Eng. 1991, 1587, 288. (13) Dremel, B. A. A.; Schmid, R. D.; Wolfbeis, O. S. Anal. Chim. Acta 1991, 248, 351. (14) Busch, M.; Gutberlet, F.; Hobel, W.; Polster, J.; Schmidt, H. L.; Schwenk, M. Sens. Actuators 1993, B11, 407. (15) Hobel, W.; Papperger, A.; Polster, J. Biosens. Bioelectron. 1992, 7, 549.
Analytical Chemistry, Vol. 68, No. 21, November 1, 1996 3871
Figure 1. Schematic representation of the experimental setup of the RFA system based on optode detection and the schematic cross section of the optode detection cell. PTFE, poly(tetrafluoroethylene); PET, polyethylene; poly-HEMA, poly(hydroxyethyl methacrylate).
the sensing of acidic and alkaline gas species such as CO2 and NH3.16-19 Enzyme-based biosensing optodes could also be prepared based on pH-sensitive optodes in which they measure pH change by monitoring protons generated or consumed by the enzyme reaction.10,11,13-16,20 These pH optodes mostly utilize pH indicator dyes, in which several kinds of dye immobilizations in the bulk optode sensing phase were reported with unique techniques such as trapping in dialysis tubing,21 adsorbing in polymer beads,22 covalently immobilizing onto porous glass or a cellulose membrane,23,24 and ionically immobilizing onto an anionexchange resin or sulfonated polystyrene surface.25,26 Among them, the covalent bonding immobilization of pH indicator dyes is the most effective in terms of a long optode lifetime, but this immobilization technique has not been fully established although it has been continuously investigated. In the present study, we prepared a pH-sensitive optode suitable for an RFA system based on a hydrophilic polymer membrane which covalently immobilized pH indicator dyes. We chose polymerized hydroxyethyl methacrylate (poly-HEMA) as (16) Kar, S.; Arnold, M. A. Anal. Chem. 1992, 64, 2438. (17) Mills, A.; Chang, Q.; McMurray, N. Anal. Chem. 1992, 64, 1383. (18) Parker, J. W.; Laksin, O.; Yu, C.; Lau, M. L.; Klima, S.; Fisher, R.; Scott, I.; Atwater, B. W. Anal. Chem. 1993, 65, 2329. (19) Weigl, B. H.; Holobar, A.; Rodriguez, N. V.; Wolfbeis, O. S. Anal. Chim. Acta 1993, 282, 335. (20) Trettnak, W.; Leiner, M. J. P.; Wolfbeis, O. S. Biosensors 1988, 4, 15. (21) Peterson, J. I.; Goldstein, S. R.; Fitzgerald, R. V.; Buckhold, D. K. Anal. Chem. 1980, 52, 864. (22) Guthrie, A. J.; Narayanaswamy, R.; Russel, D. A. Analyst 1988, 113, 457. (23) Offenbacher, H.; Wolfbeis, O. S.; Furlinger, E. Sens. Actuators 1986, 9, 73. (24) Mohr, G. J.; Wolfbeis, O. S. Anal. Chim. Acta 1994, 292, 41. (25) Moreno, M. C.; Jimenez, M.; Conde, C. P.; Camara, C. Anal. Chim. Acta 1990, 230, 35. (26) Igarashi, S.; Kuwae, K.; Yotsuyanagi, T. Anal. Sci. 1994, 10, 821.
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the optode membrane matrix for its high hydrophilicity. A hydrophilic membrane can be expected to have a large permeability for proton and ionic species. In this case, in order to introduce a large amount of pH indicator immobilizing sites in the poly-HEMA membrane, acrylic acid (AA), which has a carboxyl group, was copolymerized with hydroxyethyl methacrylate. As for the pH-sensing dyes, sensitive color-changeable dyes with an amino group, such as Congo Red and Nile Blue, were chosen and covalently immobilized onto the copolymerized hydroxyethyl methacrylate-acrylic acid membrane (poly-HEMAAA membrane). These membranes exhibited the high sensitivity and good durability that were necessary to evaluate the experimental results of the optode response characteristics with the RFA system in this investigation. Based on this prepared optode, the response performance of the flow analysis was discussed. Our experimental results revealed that the time response profiles of the optode in the RFA system can be well simulated by the proposed equation (eq 12) that was derived from the theoretical response based on Fick’s law in terms of sample diffusion and Lambert-Beer’s law in terms of absorbance measurement, in which two important variable parameters were introduced into the equation: an analyte diffusion coefficient [D(pH), pH-dependent pseudo-diffusion coefficient], which reveals the proton diffusion parameter for each prepared optode pH-sensing layer (membrane) as a function of sample pH, and a sample dispersion factor, ξ(t), which reveals the sample diffusion in the flow system including an optode flow-through cell as a function of time. Consequently, the RFA system with optode detection could rapidly determine the analyte using the calibration equation (eq 12). The theoretical and methodological understandings, and a demonstration of the usefulness of the performance
characteristics of the RFA system, are discussed on the basis of pH optode detection as the model case. EXPERIMENTAL SECTION Reagents. 2-Hydroxyethyl methacrylate and acrylic acid as the base optode membrane materials and benzoin methyl ether as the polymerization initiator were purchased from Tokyo Chemical Industry Co. (TCI, Tokyo, Japan). The pH indicator dyes, Nile Blue and Congo Red, were supplied from Merck AG (Darmstadt, Germany) and Wako Chemical Co. (Tokyo, Japan), respectively. 1-Ethyl-3-[3-(dimethylamino)propyl]carbodiimide hydrochloride (WSC) as the coupling agent was purchased from Dojindo Laboratories (Kumamoto, Japan). The flowing solution and the test pH sample solution were prepared using a buffer electrolyte or reagent in which their compositions were as follows: a 0.2 M HCl/KCl buffer (pH 0.6-3.5) and a universal buffer (∼0.0286 M citrate, phosphate, borate and 0.2 M NaOH, pH 4.0-12.0). All other chemicals used were of the highest grade for commercially available reagents. Preparation of the pH-Sensitive Optode Membranes. The pH indicator-immobilized poly-HEMA matrix membrane used as the pH-sensitive optode membrane was prepared according to the following procedures. 2-Hydroxyethyl methacrylate, acrylic acid, and benzoin methyl ether (90:3:2.5 weight ratio) were mixed and cast onto a dust-free poly(tetrafluoroethylene) (PTFE) plate. To obtain thin and flat membranes (normally ∼30-130 µm thickness), glass cover plates were placed onto the casting liquid, and UV light (using a Type XX-15S (15 W × 2) UV lamp, Funakoshi, Tokyo, Japan) was irradiated at a 10 cm distance from the casting membrane matrices for at least 3 h in a nitrogen atmosphere. The prepared polymer matrix membranes (poly-HEMA-AA membranes) were washed with water and methanol to fully remove any unreacted chemical species. These transparent membranes, possessing carboxyl groups, were then immersed into an aqueous solution containing WSC and pH indicator dye Nile Blue or Congo Red and stirred for 24 h at room temperature. In this case, the amounts of pH indicator dyes and WSC used were calculated on the basis of the membrane volume being 5 times the maximum amount of carboxyl groups (0.001 mol of carboxyl group/1 mg of poly-HEMA membrane). The obtained pH indicator dye-immobilized poly-HEMA membranes were washed with water and methanol using a supersonic cleaner until no dye leaching was obtained. Construction of the RFA System Equipped with the pHSensitive Optode. Figure 1 shows the cross section of the prepared pH optode and the schematic views of the experimental apparatus of the RFA system including the optode. The detection of light through the optode membrane (normally ∼30-130 µm thickness, 14 mm diameter) was done using a spectrophotometer (Hitachi U-2000, Tokyo, Japan) in the transmittance detection mode, monitoring in absorbance units. The optode cell assemblies were home-made, the detection volume of which was 30 µL. The pH-adjusted flowing solutions (carrier flow) were pumped by a pulse-free liquid delivery pump (Trirotar-2, JASCO, Tokyo, Japan) at the normal flow rate of 1.0 mL/min. The test pH sample was injected through an HPLC injector (Type 7025, Rheodyne Inc., Cotati, CA), in which the sample introduction volume was varied (100 µL-10 mL) by changing the injection loop equipped with the injector. Simulation of the Response Profiles of the Optode with the Flow System. The mathematical calculations and simulation
of the optode response as a function of time, pH, and the introduction sample volume were carried out on the basis of our proposed response according to eq 12 with commercially available software (Mathematica, version 2.2, Wolfram Research Inc., Champaign, IL) using an Apple Macintosh personal computer (Quadra 840AV, Apple Computer Inc., Cupertino, CA). RESULTS AND DISCUSSION Preparation and Characteristics of the pH-Sensitive Optode Membranes for the Flow System. Before discussing the response characteristics of the rapid flow-through analysis with optode detection, we prepared a suitable pH-sensitive optode membrane for the flow system. The major requirements for the ideal optode membrane are a fast response time, high response sensitivity and selectivity, long lifetime, and excellent reproducibility. Among these, long lifetime and excellent reproducibility are crucially important parameters in flow analysis, because the membrane used in flow analysis is always directly attached to the background flowing solution; subsequently, leaching of the sensory elements such as the dyes can occur. To obtain an optode membrane having excellent response reproducibility and durability, the covalent bonding immobilization of sensing components such as a pH indicator dye molecule into the sensor membrane is indispensable. Based on these considerations, we have attempted to prepare a hydrophilic polymer membrane having an immobilization site that is obtained by the copolymerization of hydroxyethyl methacrylate (HEMA) and acrylic acid (AA). In this case, acrylic acid plays an important role for covalent immobilization. Using this membrane, an indicator dye having an amino group can be covalently immobilized via amidation. The merit of this membrane preparation procedure is that many kinds of dyes having different immobilization sites can be immobilized by replacing the reactive group of the monomer. pH-sensitive poly-HEMA membranes prepared by amidation using Congo Red and Nile Blue responded to the test pH-varied solutions in a fully reversible manner. Covalent immobilizations of these two dyes were confirmed by their IR spectra, in which an absorption band at ∼1650 cm-1 due to the CdO stretching of the produced amide bond appeared after their immobilization onto the poly-HEMA-AA membrane. The pKa values of these two optode membranes were 7.5 and 2.3 for the Nile Blue- and Congo Red-based membranes, respectively, in which the absorbance maxima were ∼660 and 650 nm, respectively. These pH-sensitive poly-HEMA membranes reversibly responded to the test pH-varied solutions even after being stored in pure water for over 1 year. Theoretical Description of the General Response for the RFA System Based on a pH Optode. Figure 2 shows the pH response mechanism model for the investigated optode. In this sensing system, the pH indicator dye-immobilized poly-HEMA membrane was attached to the transparent polyester (PET) plate, and the other side of the sensing membrane faced the sample solution (see Figure 1). Thus, the uniform distribution of protons from one side at the sample solution/sensor membrane interface into the dye-immobilized bulk membrane phase was assumed. In the case when the sample solution flowed through the optode cell, proton diffusion through the poly-HEMA membrane proceeds from the interface into the bulk membrane phase along the direction of the membrane thickness (x-axis in Figure 2). In this case, since the protonation equilibrium between H+ and the immobilized indicator dye is very fast, the process of proton diffusion across the membrane mainly governs the total response Analytical Chemistry, Vol. 68, No. 21, November 1, 1996
3873
Figure 2. Detection model for protons using pH-sensitive optode. P, transparent polymer resin (see Figure 1); I, pH indicator dye; I0λ, incident light; Iλ, detection light (Aλ ) log I0λ/Iλ; Aλ, absorbance at λ nm); l, membrane thickness; x, direction along the bulk membrane thickness (x-axis).
time of the optode. Thus, the proton diffusion can be determined by eq 1 using the well-known Fick’s law, where [H+] is the
∂2[H+] ∂[H+] )D ∂t ∂x2
(1)
concentration of the proton, D indicates the diffusion coefficient (cm2/s), t expresses the time (s), and x means the membrane thickness (cm) or the direction in relation to the membrane thickness (cm). To mathematically solve this equation, some initial and boundary conditions are required. The conditions can be expressed by eqs 2-4 for the proton concentrations as a function of time that were considered on the basis of the model shown in Figure 2, where l denotes membrane thickness, [H+]in and [H+]fn indicate
[H ](x,0) ) [H ]in
(2)
[H+](0,t) ) [H+]fn
(3)
+
+
∂[H ](l,t) )0 ∂x +
J(l,t) )
(4)
the initial background proton concentration and the sample proton concentration, respectively, and J is the flux of the proton in the membrane, but no flux was assumed in this case. Based on these conditions, the proton concentration at a certain time and a certain depth ([H+](x,t)) can be expressed by eq 5, where D(pH) ∞ 4 1 [H+](x,t) ) [H+]fn + ([H+]in - [H+]fn) × π n)1 2n - 1
[
(
exp -D(pH)
)]
π(2n - 1) 2l
∑
2
t cos
π(2n - 1) x (5) 2l
represents the analyte diffusion coefficient (pH-dependent pseudodiffusion coefficient) that reveals the proton diffusion property through the optode membranes. In a general case, the D value is constant; however, we found that this factor obtained by experimental response profiles varies with variation in the sample pH, because it depends on the components and structure of the respective optode membrane. The factor D(pH) is important to 3874
Analytical Chemistry, Vol. 68, No. 21, November 1, 1996
Figure 3. Typical response profiles of the optodes based on Nile Blue-immobilized poly-HEMA membrane (a) and Congo Red-immobilized poly-HEMA membrane (b).
fit the real response of the optode (the practical importance of this factor will be discussed later in this section). On the other hand, the protonation/deprotonation equilibrium of the immobilized indicator dye (I) is expressed by eq 6. Based
I + H+ T HI+
(6)
on the mass action law, the depronated indicator dye concentration [I] and the protonated indicator dye concentration [HI+] can be expressed by eqs 7 and 8 using Kind and [T], which represent the proton association constant of the immobilized indicator dye based on eq 6 and the total indicator dye concentration ([T] ) [I] + [HI+]) in the optode membrane phase, respectively. Furthermore,
[I] )
Kind[T] Kind + [H+]
[HI+] )
[H+][T] Kind + [H+]
(7)
(8)
the absorbance measurement using the pH-sensitive optode membrane can be expressed by eq 9 based on the integral form of Lambert-Beer’s law, where 1 and 2 are the molar absorption
Aλ(t) ) (1 - ξ(t))(1[Iin] + 2[HI+]in) +
∫ ( [I](x,t) + [HI
ξ(t)
l
1
0
](x,t)) dx (9)
+
2
coefficients of the deprotonated form and protonated form, respectively, of the immobilized indicator dye, Aλ(t) represents the measured absorbance at λ nm as a function of time, and ξ(t) is a sample dispersion factor which reveals the condition of the introduced sample dispersion in the flow system including the optode flow-through cell. In the case of the flow-through analytical system, the dispersion of the sample solution occurs in the flowthrough tube as well as in the detector cell during the measurement. Especially when a small amount of sample solution is introduced, this factor critically affects the response of the optode; also, this dispersion effect is generally different in a different system (this effect will be discussed later in relation to the important factor, ξ(t), based our experimental results). The combination of eqs 5, 7, and 8 leads to the following eqs 10 and 11:
(
4 [I] ) Kind[T]/ Kind + [H+]fn + ([H+]in - [H+]fn) × π ∞
(
[
1
∑2n - 1
exp -D(pH)
n)1
{ [
)]
π(2n - 1) 2l
2
t cos
)
π(2n - 1) x 2l (10)
∞ 4 1 × [HI+] ) [H+]fn + ([H+]in - [H+]fn) π n)12n - 1
(
exp -D(pH)
(
)]
π(2n - 1) 2l
∑
2
t cos
}
π(2n - 1) x [T]/ 2l
∞ 4 1 × Kind + [H+]fn + ([H+]in - [H+]fn) π n)12n - 1
(
[
exp -D(pH)
∑
)]
π(2n - 1) 2l
2
t cos
)
π(2n - 1) x (11) 2l
Finally, combining eqs 9, 10, and 11 leads to the basic response equation of the pH optode using the flow-through system as a function of time (t) and sample pH:
(
Aλ(t,pH) ) (1 - ξ(t))
∫
ξ(t)
(
l
0
)
1Kind[T] + 2[H+]in[T]
{ [
Kind + [H+]in
l+
4 110-pKind + 2 10-pHfn + (10-pHin - 10-pHfn) × π ∞
1
∑
n)12n
-1
})
π(2n - 1) x cos 2l 4
{
2l
)] 2
t × D ) l2/t
(13)
[T] dx/ 10-pKind + 10-pHin +
(10-pHin - 10-pHfn)
π
[
(
π(2n - 1)
exp -D(pH)
profile in the flow-through system. We used personal computer software (see Experimental Section) to simulate the response profile of the pH optode, in which the necessary parameters were inserted into eq 12 by the software. Application of the RFA System to the pH Sensing. Figures 3 shows the typical experimental response profiles of the pH optodes based on the poly-HEMA membranes immobilized with Nile Blue (a) and Congo Red (b), respectively. The profiles of these pH response curves were obviously different. The membrane based on Nile Blue showed a slower color change response to protons in a high proton concentration range under pH 7 compared with that in a low proton concentration range over pH 7. On the other hand, the membrane based on Congo Red showed a faster color change response to protons in a high proton concentration range under pH 2 compared with that in the pH range over pH 2. These differences in the response are mainly caused by the following two factors: (i) the different amounts of carboxyl group residue in the sensing membrane affect the rate of the proton diffusion and (ii) the hydrophobicity/hydrophilicity of the dye molecule (which depends on the chemical structure of the immobilized dye) promotes or resists the proton diffusion in the pH-sensing membrane. Consequently, the time response profile of the pH optode based on a dye-immobilized membrane was different for each different dye used. Regarding these complicated mechanisms concerning the experimental facts, introduction of the variable diffusion factor with the analyte concentration, D(pH), into the theoretical response equation is a conventional way to express the response. A good theoretical description of a pH optode was recently introduced by Kostov et al.27 They simulated the pH response behavior of an optical absorption-based pH optode. They showed one experimental result in which the pH response was compared with the theoretical equation. However, their mathematical simulation expressed an ideal proton diffusion process and did not take into account the real response phenomena, which include a more complicated proton diffusion process, as pointed out in the discussion above based on the optode response curves shown in Figure 3. For considering the real and general response profile of the pH optode, other factors have to be added to the simple theoretical response equation, which is basically derived from the basic Fick’s law of diffusion and Lambert-Beer’s law. As already discussed, introduction of the variable diffusion factor, D(pH), into the theoretical equation was attempted in order to describe the real experimental response with mathematical simulation. The experimentally obtained diffusion coefficients as a function of pH are plotted in Figure 4, in which the values were calculated with eq 13, which was derived from Fick’s law of diffusion, where l and t represent the membrane thickness (cm)
(
exp -D(pH)
∞
1
∑2n - 1 ×
n)1
)]
π(2n - 1) 2l
2
t cos
}
π(2n - 1) x 2l
(12)
Equation 12 can mathematically estimate the optode response
and the required time (s) for 100% response, respectively. As shown in Figure 4, an obviously different relation of the diffusion coefficient as a function of pH was observed between the two membranes based on Nile Blue and Congo Red. From these facts, it is expected that the introduction of the analyte concentrationdependent diffusion coefficient, D(pH), rather than the diffusion constant, D, to the theoretical equation could better fit the real (27) Kostov, Y.; Tzonkov, S.; Yotova, L. Analyst 1993, 118, 987.
Analytical Chemistry, Vol. 68, No. 21, November 1, 1996
3875
Figure 4. Diffusion coefficient as a function of pH: Nile Blueimmobilized poly-HEMA membrane (a) and Congo Red-immobilized poly-HEMA membrane (b). Formulas for the curves: (a) D(pH) ) (3.39 × 10-10) × 100.27pH; (b) D(pH) ) (9.86 × 10-6) × 10-0.59pH.
experimental response. Based on this consideration, D(pH) was used in eq 12, in which D(pH) ) (3.39 × 10-10) × 100.27pH (for the Nile Blue-based membrane) or D(pH) ) (9.86 × 10-6) × 10-0.59pH
(for the Congo Red-based membrane). Other parameters for simulating the response profiles of the pH optode with eq 12 were all experimental values, in which pKa was estimated on the basis of the response curves shown in Figure 3. Figures 5 shows the simulated response profiles of the optode based on Nile Blue and Congo Red, where the curves are drawn using eq 12. In this case, the time-response curves in Figure 5A were obtained with a constant D value instead of D(pH), while the curves in Figure 5B were obtained using the variable parameter, D(pH). Comparing these curves in Figure 5 with the real response curves in Figure 3, the curves using D(pH) (the curves in Figure 5B,D) are obviously a better fit to the real experimental responses. Consequently, eq 12 using D(pH) was confirmed to fit the real responses of the pH optode. In the case of the RFA system, the response time can be controlled by varying the sample introduction or injection volume; a faster time for one determination run is obtained by introducing a smaller volume of sample, though the response sensitivity is sacrificed (reduced). In this case, the sample dispersion factor, ξ(t), which is calculated on the basis of the dispersion behavior of the sample solution in the flow-through system, including the optode detection cell, plays an important role in the expression of the real experimental response based on eq 12. In the present investigation, ξ(t) was estimated using the following procedures: different volumes of the sample solution (100 µL, 200 µL, 500 µL, 900 µL, and 10 mL of 0.5 mM aqueous Congo Red solutions) flowed through the RFA system including the optode cell without the optode pH-sensing membrane (see Figure 1), and the sample dispersion profiles were monitored by the resulting absorbancetime curves. In this case, pure water was used as the background flowing solution. The typical results are shown in Figure 6A. A nearly 100% response was obtained when more than 500 µL of sample was introduced into the flow system. Similar experiments were carried out with three different concentrations of aqueous
Figure 5. Simulated response profiles of the pH optode. Parameters for the optodes based on Nile Blue-immobilized poly-HEMA membrane in (A) and (B): l ) 37.5 × 10-4 (cm); pKind ) 7.5; 1 ) 4.8 × 103; 2 ) 1.3 × 104; [T] ) 5 × 10-3 (mol/dm3); [H]in ) 10-11 (mol/L); D ) 3.6 × 10-8 for the curves in (A); D(pH) ) (3.39 × 10-10) × 100.27pH for the curves in (B). Parameters for the optodes based on Congo Red-immobilized poly-HEMA membrane in (C) and (D): l ) 130 × 10-4 (cm); pKind ) 2.3; 1 ) 1.01 × 104; 2 ) 6.84 × 103; [T] ) 5.01 × 10-3 (mol/dm3); [H]in ) 10-6 (mol/L); D ) 4.334 × 10-7 for the curves in (C); D(pH) ) (9.86 × 10-6) × 10-0.59pH for the curves in (D). 3876 Analytical Chemistry, Vol. 68, No. 21, November 1, 1996
Figure 7. Simulated response curves of the pH optode when different instrumental factors were used as the mathematical simulations (A) and the real response curves of pH sensing optodes based on Nile Blue-immobilized poly-HEMA membrane (B). The simulation curves expressed as solid lines and dashed lines in (A) were obtained based on eq 12, in which the ξ(t) values were used in the calculation based on the curves in Figure 6B, in which they were obtained based on the condition of ξ(t) ) f(t) and based on the formalism of ξ(t) ) ∫0td(f(t)) dt/t, respectively. Experimental conditions for obtaining the response curves in (B): flow rate, 1.0 mL/min; carrier solution pH, 11.0. Figure 6. Sample diffusion profiles in the optode cell in which the injection volume was varied (A), and the mathematical fitting curve for the sample diffusion parameter, f(t) (B). Experimental conditions for obtaining the response curves in (A): flow rate, 1.0 mL/min, flowing solution, 0.5 mM Congo Red. The formalism for the f(t) curve in (B) was obtained using computer software (see Experimental Section) based on the results of the curves in (A) (0-12 s,
